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NASA TT F-622 



WAYS TO SPACEFLIGHT 
By Hermann Oberth 



Translation of "Wege zur Raumschiffahrt," 
R. Oldenbourg Verlag, Munich- Berlin, 1929 



NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 

For sale by the Clearinghouse for Federal Scientific and Technical Information 
Springfield, Virginia 22151 - CFSTI price $10.00 



ACKNOWLEDGEMENT 

The National Aeronautics and Space Administration 
gratefully actaiowledges the permission granted 
hy Dr. Hermann Oherth and the R. Oldenboiirg Verlag 
to translate and publish an English version of 
the "book Wege zur Raumschif fahrt . 



Translated for the National Science Foundation and the 
National Aeronautics and Space Administration, Washington, 
D.C. by the Agence Tunisienne de Public-Relations, Tunis, 

Tunisia, 1970 



111 



Gratdfnllj Dedicated to 

Thea r. Harbou 
and 
Fritz Lang 



Forevord 



In a relatively abort timey it already became necessary to prepare 
a third edition of 117 book, "The Rocket to Interplanetary Space". 
I tried to mcJce this edition someirfaat more easily comprehensible. 
Hence I explained things vhich, in the first tvo editions, I simply 
presupposed as known. — I also omitted hair-splitting and confusing 
details where they did not appear requisite for the proof of the 
whole. For the same reason I arranged the material in a somewhat dif- 
ferent sequence. Vhereas, formerly, I first derived a rocket theory 
and only then discussed certain pcurticulars of construction in greater 
detail almost only to illustrate the theory, here I would like to 
first give the reader a clear picture of the whole matter. — Finally, 
I marked everything with a marginal line that is intended only for 
specialists and wrote the rest so as also to be understandable by it- 
self. I chose this somewhat popular wersion l) in order to bring vsy 
book closer to tiie understanding of a wider circle of readers. \Then 
I wrote the first edition I did not believe that the material would 
find interest in such wide circles. 2) I also feel induced to prepare 
this easily-Hinderstood version by the circumstance that, as I will 
yet show, even the trade publications have largely mi simder stood my 
book. 

Originally, I had the intention of writing a two-volume work. 
The first volume was supposed to develop the theoretical bases of 
space-flight and the technics of rockets for liquid fuels; the necoud 
voltme was to contain the history of the rocket, the areas of applica- 
tion of rockets hitherto, the experiments and research of other 
authors publicized so far, the results of my own experimental worTc, 
a survey of the most important novels about space-flight and relai-ed 



Vll 



technical futnristic novels, a patent display, the reception of the 
idee of space-flight by various professions, aiifl the like. — Upor 
the advice of the publishing house I then decided to \rrite a one- 
volume work that represents a self-contained whole. I achieved that 
by taking over from the second volume irfiat iras needed for rounding 
off and, for the rest, restricting myself to the theoretical aspects 
of the science of space-flight. Hence, in its style, the book is a 
self-contained vhole. — Nevertheless, I also intend to publish the 
second book some time, and at places ubich did not appear important 
enough to be included here in viev of the topic of this book 1 have, 
for the sake of completeness, already referred to the second book 
which'! have designated as Volume II for short. By the iray, all the 
respective matters have already been published somewhere by the 
cited authors th«nselves and do not concern the basic probl^ns of 
space-flight. 

For the rest, how often I quote from the work of others is no 
indication of the value or non-value of that work. It just so happen- 
ed that one work contained more, the other fewer passages by which 
I could illustrate the theory developed here. Thus, for example, I 
consider the book by ROBERT ESNAULT-PELTERIE, "L' exploration par 
fus4e8 de la tr^s haute atmosphere et la possibility des voyages 
interplan^tairea", to be one of the most important books on the tech- 
nics of space-flight, although I had no opportunity to discuss it in 
the volume in hand. Just as little is one justified in concluding 
that I was unable to refute a number of objections, because I reserved 
answering several less serious objections for Volume II, where I will 
discuss them in connection with the works in which they occur. For 
example : It is very uncertain whetiier a parachute in a space-ship 
will open — (actually, before the space-ship enters the atmosphere, 
lack of counter-pressure prevails and the passengers can move the 



Vlll 



parachute into the position they irill require later) or t A space- 
ship represents just as a great a danger to it3 surroundings as a 
powder magazine in ufaich one handles open fire (ve actually have no 
explosives here at all but simply inflammable liquids that are being 
taken cdong in separate containers; but even if they did mix, that 
-would still not be dangerous. A mixture of gasoline and liquid air, 
for example, does not bum at all in open air); or again t The rear- 
mtrd thrust cannot vork in air-free space because here the ont-f loving 
gases become infinitely thin and, as a result, lose their mass, and 
the like. 

I had to extend this edition somewhat. Meanvbile, notable liter- 
ature on the theory of rocketry appeared irfaich I did not want to 
leave unconsidered. I also included something on the prospects of 
space-flight, on the present state of 117 vork, and on the ob.jections 
to wj plans. Uoreover, I also vish to mention that none of the basic 
presuppositions of this book : the reanrard thrust principle, the 
level of the exhaust velocity, the fact that my rocket can take on 
cosmic velocities, the possibility of treating liquified gases in 
the vay indicated, aad the like, have not already been oonfinied as 
correct by some scholar. Since the book has been essentially remodel- 
led, the publishing house advised me to give it another name. I gladly 
followed this advice and called the new edition "^t^ays to Space- 
Flight". 

Finally, in this place I would like to thank all those readers 
who have assisted me in my work by word and deed. I will return to 
this in Volume II. This time again I owe high thanks to the Oldenbourg 
Publishing House. Only the extensive obliginriiess of ray publisher 
has made it possible for me to publish this edition. I thank Alexander 
n. Scherschevsky, Berlin, for reading the p'-oofs. llr. Scherschevsky 
has kindly pointed out a number of obscure passages to me and en- 
riched the book by several additions. 

Medins, September, 1928 

Prof, H. Oberth 



IX 



Excerpt from the Foreyard to the Second Edition 

I considered it necessary to draw the attention of vide circles 
to Eoy vork, for onlj in this Tagr could I hope to get the means and 
the opportunity for further work* In the third section of my writing 
I make fantastic claims 'which, although they cannot be scientifically 
refuted today, are othenrise seldom found in scientific works. I 
Tould ask tlie reader to remember that unusual circumstances are in 
question in the mentioned third section. 

I ask to be permitted, in this place, to point out the didactic 
value of the rocketry problon. I consider the questions posed here as 
suited to have a stimulating effect in other directions also, and 
not only on the accomplished engineer, astronomer, physiologist, and 
psychologist, but, above all, on the citudying person. As a irhole, 
the subject is built on simple principles irfaich ire actually meet 
daily but for exactly that reason do not take note of. Through the 
peculiar connection of these things, entirely netr and, for the young 
academician, interesting results c(»ne about. The "taumadzein" of 
Aristotle comes to mind. If a teacher, for example, poses certain 
problons resulting from his irork, he can direct the attention of his 
auditors to these in themselves elementary things and induce them 
to clarify their scientific knowledge on various topics. 

In conclusion, it is a pleasant duty to express my thanks to 
the n. Oldenbourg Publishing House for being so obliging, to a 
measure far exceeding;' nhat an author can expect from his publisher. 

Medias, May, 1925 

Hermann Oberth 



X 



Table of Contents 

Part I. 
Prelimina ry Remarks 

Chapter Paf-® 

1. Introduction ..... 1 

2. The Pveanrard Thrust Principle 3 

3. General Description 5 

4. Improv«nents and Conpletioi'S 19 

Part II. 
Technical ^e- tio na of Phy sicg 

5. The Speed of Out-floif 34 

6. The Ide?il Propulsion "'^3 

7. The Maaa Ratio 64 

8. The Most Advantar;eous Velocitv 78 

9. Counter-Pressure ^^^ 

i) Explanation 116 

2) Calculation of Counter-Pressure 120 

3) Phenomena of Counter-Pressure 123 

4) lion's Peaction to Increased Counter-Pressure 126 

a) Physical Effect of Hich Covmter-Pre.gsure . 126 

b) Psychological Effects of Abnormal Condi- 
tions of Counter-Pressure ...... 130 

5) Lack of Counter-Prefisure 138 



XI 



Chapter Paf;e 

6) The Effect, on Man, of IJinor or aitirelj LacTfing 
Counter-Pressure ....... 1^0 

a) Physical Effect 140 

b) Psychic Effect 1 U 

7) Critical Remarks 147 

10. Range, Orercorairrr Gravitation 151 

11. Further Ascent Calculations 163 

l) Vertical Ascent of a manned rocket 164 

a) Effect of air repistance witli free-flying meteoro- 
logical and lon,'7-di9tance rockets ...... 175 

3) Details concerning the oblique flight of jet- 
propelled aircraft nithin the atmosphere .... 187 

4) The oblique, straight-line ai*cttit of aodel E . . 190 

12. Corsiderations of ihergy 193 

l) Impulse uid \Vork 1^4 

a) The Synergy Problem 217 

3) The Synergy Curve 230 

13. Questions of Control 253 

l) Stability of the Arroir 253 

8) Stability of the Rocket 256 

3) Active Steering 260 

4) Gas Fins 266 

5) Other Steering Possibilities 268 

6) Control of the Velocity 270 

7) The Rocket Projectile 276 

8) Orientation of the Ether Ship in Space .... 281 

9) Automatic Observance of the Most Advantageous 

Velocity . . . ^ 281 

14. The Landing 884 



XU 



Chapter Page 

Part III. 

flueationa of Conatr uction 

15. The Uodel B Alcohol Rocket 315 

1) Prelimlnarj Remarks ......... 317 

2) The Alcohol Rocket 331 

16. The Uodel B Hydrogen Rocket 332 

1) General 332 

2) Description 334 

3) Precision Instruments 336 

17. Discussion of the Operatioi. and Perforning Capacity 

of Rockets vith Liquid Fuels 336 

1) The Auxiliary Rocket of Model B 337 

2) The Ascent of Model C 338 

3) Size and Air Resistance . 339 

4) Comparison of the Alcohol Rocket emd the Hydro- 
gen 'locket . 341 

5) Inside Pressure in the Oven and Combustion . . 345 

6) Form of the Atomizer 346 

7) Importance of the Pumps 346 

r) Division of the Nozzle 347 

9) Launching Manned Rocket 348 

10) Rocket Space-Ships . 349 

11) Filling the Hydrogen Rocket 349 

12) Starting Uodel B 350 

13) Height of Ascent 350 

14) Evaluation of the Fuels 351 

15) Simplifications in Model B 358 

16) The Advantages of Liquid Riels 360 

17) Division of the Rocket 360 



xiii 



Chapter I'age 

Part IV. 
Possibilities of Use 

18. Possibilities of Using the Rocket Nozzle for 

Liquid Fuels on Earth 362 

l) The Verticall7-Ascen<ling Rocket 363 

a) The Meteorol ogical Rocket 363 

b) The Reconnaissance Rocket 368 

a) The Long-Disteuice Rocket 368 

a) The Geographical Rocket 368 

b) The Mail Rocket 368 

c) The Rocket Projectile 370 

3) The Rocket Airplane . 371 

19. The E Model 406 

20. Stations in Interplanetary Space 477 

£1. Trips to Strange Celestial Bodies 507 

l) The Moon 508 

S) The Asteroids 518 

3) Mars 529 

4) Venus 547 

5) The Reriaining Bodies of Our Solar System .... 556 

S2. The Electric Space-Ship 557 



XIV 



Part I. 

Preliminary Remarks. 
Chapter I. 

X. With the present state of scientific knowledge and the science 
of technology^ it is possible to build machines thiat can rise 
higher than the limit of tlie atmosphere. 

2. If perfected further, these machines can attain speeds by virtue 
of vhich - if left to themselves in ether space - they do not 
have to fall back to the earth's surface again and are eYen able 
to leave the sphere of attraction of the earth. 

3. Such machines can be built so that human beings (apparently with- 
out danger to health) can go up irith them. 

4. Under today's econcxaic conditions, it vill pay to build such 
machines. 

In the present book, I vould like to prove these four statements. 

First, I will report mainly on nqr principle of the rocket with 
liquid fuels with regard to the physical aspects (Fart II ) and the 
construction (Part III). In Fart IV, I will discuss the application pos- 
sibilities of my rockets, the more immediate ones in Chapter 18; the 
following chapters will deal with the rocket as space-ship and furnish 
proof of the four claims set up at the beginning. Then, a second, more 
popular book (Vol. Il) will report on the history of space flight, on 
the works in the technical area of rockets to date, and on the present 
state of questions regarding space fl;ight. 

In the first chapters, I will theoretically examine the method of 
operation and performance of these machines. 

In so doing, I am following the principle of first describing models 
that are easily understood and figured out. With tliese as a basis, I will 



- a - 



gradually come to deal vith a machine that is suitable for construction 
but whose operation is not so easily understood, I considered this 
procedure necessary since most of the readers could be unfamiliar vith 
the material. Naturally, it is not my intention to actualize all the 
construction suggestions enumerated here or to build all the models 
described. Especially the description of my B model is merely for 
dononstration purposes. I will build only model C and possibly model A, 
if that is requested of me. The space-ships I hope to build later 
irill perhaps res^nble model E but vill likely not be exactly like it; 
they Till perhaps be iride and flat and be equipped irith lifting surfaces 
(cf. p. 393), although the machine paxts irill essentially be the same. 
I consider it premature, hoireTer, already to sketch a space-ship in 
every detail. I irould like to wait and see what the experience will be 
with uiunanned rockets and with rocket aircraft. Naturally, in the two 
decades during which I have occupied myself with the matter I have 
reflected much on how a space-ship should look if the preliminary trials 
turned out one way and how if they turned out differently; I ccmsider 
it fruitless and tedious to write about it already. Hence I shall limit 
myself to showing only the essentials. 

I must also keep some things to niyself, especially what appear to 
be fortunate technical solutions, because I am here not dealing with 
guarded intellectual property. 

It was n^ purpose to be brief. I was often able to simplify the 
mathematical derivations and formulas considerably by using approximate 
values for certain quantities, which were easily treated mathematically. 
I applied this method espocially if it served to clarify a matter 
when discussing the foru^ulas. {Bj the way, beside that I have often 
also stated the resulting figure or at least shown how it can be 



- 3 - 



determined from the approximate value b7 indirect calcnlation; some- 
times I have also simply estimated the error). Technical problems, 
▼hose solution no one doubts, I have only touched on briefly. 

\fhere the numerical values of the quantities of the equation are 
still uncertain, I always calculated under unfavorable assumptions. 
By proving that my rockets perform as required under these unfavorable 
conditions I have proved that they irill surely measure up in reality. 

Chapter 8 
The Rearvard Thrust Principle 



I irill here designate as a rocket any apparatus that is driven 
forward by the rearward thrust of discharged gases. The rearward 
thrust principle is best explained as follows t 

Every action is opposed by an equal reaction. It can also be 
expressed in this tray : Every mechanical force at once acts at two 
different places on iriiich it seeks to produce the opposing but equal 
effect t no body sets itself in motion, a force oust act on it, to 
which it opposes a reaction as great as the force itself. If I hit 
a stone, I employ a force and the stone in return presses iqy hand 
with the same force. If, at the same time, I stand in a boat, I am 
set in motion together with the boat by this opposing pressure. If 
I place an elastic spring between two balls, they are forced apart 
by the same force on each. If I leap from a boat, the boat is thrust 
backward. It is impossible to push a car forward if one stands in it, 
even if one exerts a force considerably greater than would be required 
to move the car, for the legs press it back with the same force with 
which the arms push it forward, so that the total effect equal zero. 



- 4 - 



!•'■ 



/iff 



rig. 1 

The gas which is formed in the rocket (cf. Fig. l) escapes irith 
a considerable speed since just as much gas as id formed mast also 
flov out. But it does not attain this speed "hy itself", that is 
without a force acting upon it. If no force acted on the gas molecules, 
thej -would just remain in the chamber. It is a though elastic springs 
were iuterpo;5ed betveeu c^as and char'?:cr •r'dcli ^ieelc tc soiruru, ■*.•-; •i:ili'.i. at. 
gas and chamber from each other; in so doing, the rocket is naturally 
also propelled forward. 

On this occasion, I would also like to comment on one of the most 
frequent objections that has been raised against 117 idea (among ottiers, 
even by such outstanding scholars as for example, Prof. Dr. RIQ\i in 
"Umschau"). He states i Rearward thrust cannot act in a vacuum because 
there is no air on which the out-flowing gases can support thonselves. 

But no outside air is required here. The rearward thrust "supports" 
itself on the outflowing gas. The force which expels the gas at the 
bottom is supported toward the inside bj the gas still in the chamber 
and is transmitted from gas molecule to gas molecule up to the rocket 
wall with the natural result that (even in a vacuiua) the rocket is 
pressed upward with the same force with wliich the gas streams downwe^d. 
The American physicist, GODDAJU) (cf. Vol. II; I here refer, in part, 
to material that follows later, but it is not necessary to look it up 
to understand the text), has by meaningful experiments directly 
measured the rearward thrust in a vacuum and found that it is actually 
as great as was expected according to this theory. (Cf. GODDARD t A 
method of reaching extreme altitudes, Smithsonian Institution, Washington). 



- 5 - 



From this folloiris a remarkable advantage to the rocket space-shlpt 
the rocket can be steered ether space. If, for example, gas is discharged 
toward the front, the speed is retarded; if gas is discharged backward, 
the space-ship speeds up; vhen the gases stream out to one side, the 
direction of travel bends tovard the other side. 

This steering possibility is not great. It already takes very much 
fuel for the rocket to reach cosmic speed, and every additional steering 
is connected irith a loss of fuel, so that the rocket soon reaches the 
limit of performance. In this respect, the rocket space-ship is less 
like an earth-bound vehicle than a projectile which when once shot off 
must observe its trajectory. Fortunately, -Uiis steering possibility 
is sufficient for the purposes of space flight. Thereby, l) unavoidable 
mistakes in respect of magnitude and direction of motion made at 
launching can later be corrected. In this respect, the rocket space- 
ship is like a bullet which can still hit the target even though it 
was not aimed correctly, fi) The rocket can be put into paths which a 
projectile catapulted from the earth cannot describe, e.g. an orbit 
around the earth or the moon, among others. 

Chapter 3 

General Description 

The usual fireworks rocket (cf. Fig. 2) consists of a solid shell 
loaded with any kind of explosive (the charge B) that does not bum 
too fast. ^Vhen it bums, the gases stream out at the bottom, so that 
the rearward thrust sets the whole in motion. At F there is a rapidly 
burning powder, the detonator composition, at I the artificial composi- 
tion; these are all rockets or other objects which the rocket must 
carry up with it. Stave W serves as rudder; when it is missing the 
rocket describes any irregular zigzag curve without flying upward a 
longer period of time. 



- 6 - 



Fig. 2 

In 1117 rockets, gun-povder is not employed but a combination of 
oxygen and any kind of liquid fuel. 

In the simplest model , the oxygen vaporizes and the vapor is 
brought to a temperature higher than the ignition temperature of the 
fuel, about to 700-900® C, by any kind of gas flame that bums in the 
oxygen. Into this hot gas, still high in oxygen content, the fuel is 
sprayed by means of special spray diffusers (l call them "pores", in 
contrast to the rocket jets)^ The fuel bums up completely emd thus 
furnishes the discharging gas by vhose rearvard thrust the -whole 
apparatus is driven forward. 



In the more complicated models, I, first, in a similar vay, inject 
liquid oxygen into a flame containing much excess vapor of the fuel| 
it bums up as did -Uie fuel in the hot oxygen (vhether the fuel bums 
up in the oxygen gas or the oxygen in the vapor of the fuel is basic- 
ally the same thing). Into this hot gas vith oxygen content, I eigain 
inject liquid fuel. In still larger machines, fuel and oxygen can in 
this iray be injected alternately a number of times in succession. 



- 7 - 




Fig. 3 



In its simplest form, the apparatus vould look someirfaat as follows 
(cf. Fig. 3). The irhole is made of sheet metal; at S there is oi^gen 
that has been liquified by loir t«nperature. B is any inflanmable liquid 
such as gasoline, alcohol, liquid natural gas, liquid ethylene, liquid 
l^drogen or the like. Noir the oi^gea in S is somehow Taporized. It 
would already Taporize if kept in containers that conduct beat well, 
but that would be too slow a process for our purposes) it must be 
promoted artificially by injecting fuel into the liquid oxjgeo. and 
somehow igniting it by means of a red-hot platinum grid and additional 
use of diatranite or Ottmann artificial pumice. As is well known, 
combustion is very vigorous in liquid oxygen. The combustion gases 
then rise in the liquid oiygen cuid gasify it on the way. The transfer 
of heat from these small gas bubbles to the surrounding liquid is 
suff ici ently good. The gaseous oxygen then enters pipe A, where fuel 
vapor from pipes m is also added. A guard plate v prevents larger 
drops of oxygen from being swept along and at G the fbel vapors bum 
up, heating the gaseous oxygen to 700-900*. At Z (in the atomizer) 
the fuel is then sprayed into this hot gas of high oajgen content 
through fine jets (pores) in the wall. Fig. 4 shows this part of the 
wall from the outside somewhat enlarged and in cross-section at b, d. 



- 8 - 



0©® 



Fig. 4 

Under circumstaaces, screir-tTpe guide bolts must be built into these 
poresi but this qpiestion can only be decided after comprehensive 
preliminary tests (see Vol. II). 




Fig. 5 

Fig. 5 shoirs the atomizer in cross-section at^. The fuel is ignited 
where it comes into contact irith the 800^ hot oxygen. The nidth of the 
pipe at Z and the difference in pressure betveen B and Z as irell as 
the size of ihe pores must be calculated so that the quantities of 
liquid coming from B Just bum up before reaching the middle of pipe Z. 
What is achieved thereby is that the combustion gas streaming from the 
rocket has fairly well the same composition everyerhere. On the irall 
of the atomizer the drops of liquid are relatively far apart. None of 
it is burnt up yet. Here, however, combustion is stronger 1) because 
the same drops are thicker, 2) because they still have a high relative 
speed compared to the surrounding o:^gen. By contrast, in the middle, 
the drops are small and have almost the speed of the surrounding oxygen, 
but here they are closer together so that the two circumstances even 



- 9 - 



each other out. The onlj exception is a narrow layer of gas on the edge. 
That is as it should be, so that it remains relatirely cool. Ifhile 
(because of c(»npression) temperatures of 4000* are reached in the mid- 
dle, no danger exists for tlie vails. Experiments in this regard have 
shown that normally there is no turbulence on the wall of LAVAL jets. 
Thus the gas which sweeps along the edge remains on the edge. Ferhc^s 
it is necessary for the gas on the edge to be somewhat cooler, but the 
gas in the centre should be just as hot as possible. That can be 
achieved by directing the combustion more toward the centre. Later we 
will get to know better means of protecting the wall from the heat. 
This protecting wall of gas can be thin. It remains in the chamber less 
than 2 seconds, so that it escapes before the heat has penetrated it. 
I would like to call this principle the "principle of dynamic heat 
protection". I call it "dynamicj' because the rocket (while working) is 
guarded against heat. The oven is situated below the atomizer. Here 
combustion is the strongest. Next follows a narrowing down, the neck F . 
This appears necessary to effect a certain daraaing up in the oven. 
Thereby I achieve the following t 

1) the fuels remain in the oven longer | 

2) higher pressure (i.e. greater oxygen density); 

3) higher temperature; 

all in all more thorough combustion. 

The Jet is connected to F . It is built according to the LAVAL type 
of jets and widens up to aperture F. under an angle of 7-8*. I will 
give a detailed description later ' » 



' The passages marked with a marginal line ————— are intended for 
the reader who wishes to study the material more thoroughly and 

possesses the necessary technical knowledge. Other readers can skip 
th^ii without loss. 



- io - 



In Mi^, 1928, Lt. Col. REIIiER disputed the assumption that a rocket 
can bum in a Tacuum at all. He thought the fire Jet vould be inter- 
rupted, i.e. the gas -would stream out so fast that the flame irould not 
have time to ignite the ne-r fuel that folloirs. This is not possible 
Tith my rocket once it bums. Due to inertia, the gas stream cannot 
iomediately escape through jet F, considerable pressure vill always 
be needed in chtunber to force out the total gas that has developed 
(5-20 atmospheres). 

Hence, only the following question remains 1 If the rocket stops 
burning in the vacuum (say, because ve have turned off the fuel supply) 
and all the gas escapes from chambers Z and 0, will we be able to 
light the rocket again in case that is necessary? 

This can be directly accomplished with the gas flame in pipe G. We 
only need to let this flame bum in a closed tank into which -we conduct 
a suitable quantity of gas and allo-w a correspondingly smaller quantity 
of gas to escape (naturally, this is only one possible solution, there 
are still others). We thus hawe a gas of high oxygen content in this 
tanlc. But what happens to the excess gas which escapes into the vacuum 
space Z? 

One often reads that the temperature of a mass of gas must drop 
to absolute zero if the gas mass is allowed to expand freely. This is 
only conditionally correct, for temperature is here purely a matter of 
definiti<m . It all depends whether we hold the thermometer still or 
move it with the Jet of gas. As is well known, the temperature of an 
oiclosed quantity of gas is based on the fact that the single gas 
molecules whirr about. If a thermometer is held into it, the gas mole- 
cules 8-trike its molecules and jar them, and -this vibration causes 
the -thermometer to get warm. The heat of a gas is therefore based on 
the irregul ar motion of its molecules. If all the molecules flew in the 



- 11 - 



scone direction at the scuue speed, ire voald not speak of heat but of 
Telocity. 

When these gas molecules suddenly have the opportunity of unlimited 
expansion I every gas molecule continues to fly in a straight line 
at the speed that it Just had. The fastest moving molecules irill fly 
ahead and the sloirest-moving ones vill naturally fall behind. If, in 
addition, the space over which the gas mass has spread is relatively 
large, the effect is almost as if all the gas molecules came from one 
point and all the molecules flying side by side had ihe same speed. 
Therefore, ire can so carry along a thermometer that it receives no 
impact and Indicates a very lov temperature. If, <m the other hand, 
■we kept the thermometer still, the gas molecules irould naturally 
strike it at their original speed and, as a result, it would register 
the original temperature. (For example, the builder of gas turbines 
knows to his chagrin that, in spite of the adiabatio expansion of the 
gases in the turbine Jet, the turbine plates heat up as though tiiey 
were in the combustion chamber itself). Now, at Z the streams of 
liquid do not share in the motion of the oxygen stream, which has 
the effect as though this oxyg«i still had its original temperature 
of 800* C. In spite of the strong rarefaction of the air, vigorous 
oxidation takes place, for the number of oxygen molecules has not 
decreased. Hence we have vigorous develo{MDent of gas, the pressure 
in rises and after a few seconds, at the latest, the normal state 
is reached. 

If, to prove his point, REIl^IER states that, with a quantity of 
powder in a vacuua, it is impossible to start combustion l^ a single 
ignition, I counter with the statement that we are here not dealing 
with a single ignition. Rather, the situation is as though we 



12 - 



continuously pressed hot metal against the poirder until it is burnt up, 
or, even better, as though ve hetd piled the povder on a meteor irhich 
already bums up in thinnest upper layers of the atmosphere (cf. also 
Chapter 14). 

Someone else objected and said that the o:i7gen stream rushing by 
at almost 100 m/sec must normally bloir out the flame even Then the 
fuel has actually caught fire. - This would happen only if its temper- 
ature were beloir the ignition point) if, hovever, it is above the 
ignition point, it can only bum the matter, and that the more, the 
stronger it blows. What takes place here is that the oxygen vaporizes 
the outer layer of the drop and carries it airay, while the drop, due 
to its inertia, stays behind and is constantly in touch with new oxygen. 
The vapor that is carried along is set on fire by the oxygen, at which, 
because of the short distances, the gas currents caused by the drop 
are sufficient to effect a mixture. We will later see the significance 
of the fact that we here have no turbulence worth mentioning. 

Atomizer and oven are further enclosed in a pipe t in which the 
fuel rises, so that atomizer and oven are constantly surrounded by 
liquid. - Namely, in fuel tank B, vapor develops which forces the fuel 
(the same process as in a pop bottle) into pipe t, open at the bottom, 
which conducts it to the atomizer and the burners h. The vapor forming 
around the hot oven is conducted to burner G by pipe t. 

How to create the vapor for the space above the fuel in B need not 
worry us at present. A cartridge could be inserted in B which bums 
for so and so long, (in so doing, the ratio of fuel to oxygen would 
regulate itself automatically. The greater the pressure in B, the more 
fuel spurts from the atomizer but the stronger will the flames at b 
bum also, so that a corresponding greater eunount of oxy^^eu vapor izoa.) 



- 13 - 




Fig. 6 

Another possible solution -would be to conduct part of the vapor 
(cf. Fig. 6), instead of to G, through pipe x to the fuel tank. 





Fig, 7 

Again, another solution (cf. Fig. 7) Tould be to let pipe t begin 
higher up so that part of the fuel vapor vould not go to B but to t. 
L, L are spaces filled with air, for with this construction fuel at L 
would only be dead weight. 



- 14 - 



If the rocket is sufficiently long and the fuel is very light compared 
to o^^gen, irhich irould for example be the case if liquid hydrogen is 
used as fuel (spec, weight of liquid hydrogen, 0.06), a pipe i, sufficiently 
insulated against conducting heat, could simply be led from the oxygen 
tank to k (of. Fig. 8), irhere the oxygen is alloired to bum up (naturally, 
oaygen bums in hydrogen just as irell as hydrogen in oxygen) and the 
heat produced would then in part vaporize the hydrogen and have the desired 
effect. - If the differences in pressure are not adequate to bring this 
about, a pump m oust be installed. It has been objected that a pump would 
not work in liquid oxygen and it would be impossible to seal it here. 




Fig. 8 

The answer is i l) Lubrication could be done with petroleum ether or 
liquid coal gas (as G. CLAUDE atteinps to do with his air liquifying 
apparatus; cf. KOLBS : Liquid Air). Z) Not even that is necessary. This 
pump does not have to work by far with the precision required, for 
example, of a pump in an air liquifying apparatus. It does not matter 
if even a third of the liquid comes through again and friction heats 



- 15 - 



the Trhole by a feir degrees. - If one fixes cocks to the burners h and 
the pipes 1, the coutbustion process can be regulated in flight. 

The Tails of sheeting should be as thin as possible in order to 
include little dead material. Since the propulsion apparatus (that is 
pipe A, the atomizer, the oven, and the jet) is under less pressure 
than the surrounding liquid, it and to a lesser degree also pipe t are 
in danger of collapsing under the outside pressure. That can be prevented 
(as indicated in Fig. 35, p. 7l) by attaching braces of sheeting irhich, 
on the inside, are soldered to the propulsion apparatus and, on the 
outside, are bolted or otherwise connected to the rocket vail (jacket 
surface). Then, the cross-section of the propulsion apparatus does 
not appear round but polygonal or star-shaped. At pipe A, pipe t, and 
the jet, pressure is no problem. The atomizer can be reinforced by 
connecting it to pipe t vith a number of metal braces, as can be seen 
in Fig. 36. These braces must be perforated, l) in order to save 
material; &) to alloir the liquid to pass through. The openings utust be 
serrated to prevent the liquid from flooding. 

By the use of these braces of sheeting ire achieve tiro things t 
l) the only demand on the material is traction; everything can be thinner 
and lighter. 2) These braces act like radiators. Thereby the danger 
from the Leidenfrost state is reduced. (The more so, since the walls 
of the oven are thin.) If, in addition, the propulsion apparatus is 
surrounded by liquid hydrogen or oxygen, the heat conductivity of the 
metal increases because of the low temperature. For example, it is 
impossible with our strongest heat sources to melt a thin lead container 
with liquid hydrogen in it because the metal immediately passes on all 
the heat to the hydrogen (cf. also p. 40 and Fig. 24). 

The outer walls can likewise be thin without the air resistance or 



- 16- 



the torque produced by the fins causing the apparatus to collapse. The 
stress on them is likewise only traction. Since the inside pressure is 
at least 5 atmospheres but the outside pressure of air resistance iS| 
at the most, supposed to equal the weight of the rocket divided by its 
bottom surface, the inside pressure keeps the vhole thing rigid as a 
nonrigid air-ship or a pumped-up car tire is solid thanks to inside 
pressure. 






Fig, 9 Fig. 10 

According to KOLBE j "Liquid Air," Leipzig, 1920. 

Concerning the question of material, I vould only like to say that 
high requireaeats are mainly placed on the tensile strength of the 
material. Requiraaents of flexibility are less stringent, for the whole 
consists of thin tin plates irbich bend far even if made of relatively 
brittle material. This is of value especially for apparatus which work 
with liquid hydrogen and liquid oxygen since most materials become 
very hard but also very brittle when in contact with these cold liquids. 



- 17 - 



Figs. 9 - il shov experiments on the tensile strength and brittleness of 
metals at loir temperatures. The small glass tube in Fig. 9 is filled 
vith liquid nitrogen and surrounds a thin lead vire. That makes the irire 
so firm that it carries the 2 kg veight. ^Yhen the nitrogen evaporates 
and the lead vire irarms up, it breaks (fig. lO). Fig. 11 shows a coctnon 




Fig. 11 

oil can made of iron sheeting vhich vas filled vith liquid osygen. It 
became so brittle that it could be smashed irith a hanmer. (According to 
KOLBE » "Liquid Air.") 

In spite of that, I do not irish to dispense with flexibilitj of the 
material, at least not when building the first model. So I would make 
the parts that come into contact with the oxygen of copper, to which 
I could add some zinc, iron, nickel, or manganese to achieve greater 
tensile strength. At a temperature of - 182*, copper has a tensile 
strength of 30 kg/mm2. By a wire of 1 mm2 cross-section, 3.3 dm3 of 
the substance can be suspended t a fact we want to take note of. By 
adding zinc, this figure could be raised considerably. The machine 
parts which come into contact with the liquid hydrogen I would make 
of lead, to which ■one copper could be added (up to 40 Jt). At - 253*, 
pure lead has a unit stress of 3 - 4 dm3/mDi2 and a flexibility some- 
where between that of copper or iron at the usual temperature. If copper 
is added, its tensile strength (indeed also its hardness) increases 
so far as to become like steel. 



- 18 - 



As material for machine parts only coining into contact with gasoline, 
alcohol, etc., I irould suggest iron irith ,8 - .4 ^ carbon ctrntent . 

The ideal material for the atomizer pipe vould be silver since it 
does not oxydize, does not melt easily, and remains flexible at lov 
temperatures. It should be mentioned here that, vith a hydrogen rocket, 
no oxydation takes place during flight in spite of the proximity of 
the oven because of the low temperature of the wall; yet the material 
could easily deteriorate in the time between launchings, whereas a 
rocket with a silver atomizer ring could be sent aloft many hundreds 
of times if handled properly. It would not be too expensive. It should 
be remoabered that the whole of model A is only 2-3 -j long. According- 
ly, the atomizer section is 10-30 cm long and 10-15 cm wide, and the 
sheeting is scarcely 1 mm thick. With large alcohol rockets, the atomizer 
may be made of copper, possibly with addition of s<»ne tin. The soldered 
joints between flexible and brittle material may not be situated at the 
edges of the two tanks but must be over the hotter materials. Up to 
joint a, the soft material on the hotter tank must be built thicker 
corresponding to its decreasing tensile strength (cf. Fig. 12). 



««??« 



\r««> 



oxv^^e 



=c^« 






Fig. 12 



^ As a matter of fact, it is through the amiabilily of Mr. A.B. 
SCHERSCUQVSKY that I know of a material, one square millimeter of which 
can safely be weighted with 9-12 dm3 at the usual temperature as well as 



- 19 - 



at the temperature of llqpiid oiygen, and irhich, besides, is not inferior 
to copper in flexibility at lov temperatures. %at that means vill be 
understood irhen reading the folloving chapters. - I have no inclination 
to publicize the material. Whoever wants to built liquid-fuel rockets 
vould do well anyray to contact the people who have d<me the preliminary 
work under great personal sacrifice. 



With larger rockets, some sort of insulation, asbestos or wool, would 
have to be attached at b, so that the heat is not transmitted too 
suddenly. I would like to mention here that no rocket with liquid fuel 
is shot from a cannon; these rockets are only light and then they rise 
by their own power. 

Chapter 4 

Improvements and Completions 

Disadvantages (especially with hydrogen rockets) arising from uneven 
heating of the metal parts can be largely offset if care is taken to 
have all more expanded metal parts in contact with the liquid or vaporized 
hydrogen. With the model shown in Fig. 13, the hydrogen is kept in a 
ring-shaped container which floats freely within the hydrogen tank. 
Here "free" means held only by the metal braces g. By suitable choice 
of material for the hydrogen rocket, it is possible to make the braces 
contract by the same amount at the temperature of the osygen as the 
Jacket surface at - 353*. 

Between this ring and the shell there is a free space c filled only 
with fuel vapor. Here the vapor rises and flows into the propulsion 
apparatus at A. By the expression "propulsion apparatus" I designate 
the pipes t, pipe A, the atomizer, the oven, and the jet. 

The walls of the oxygen ring must be as thin as possible (namely, 
the pressure in the oaygen chetmber is exactly as great as in the hydrogen 
chamber). In addition, they must be of porous material (say asbestos); 



- 20 - 



the burners h must extend along the irall higher them with model A. The 
aim is to make the vaporized hydrogen penetrate the asbestos, and 
the combustion between hydrogen and oocygen on the inner edge is to 
continue along the whole wall. Thus the oxygen on the edge is heated 
by the rising fuel vapor and does not solidify, otherwise it would 
only represent dead weight. 




Fig. 13 



The advantages of -this arrangement, except for the atomizer pipe, 
which must be made of flexible material anyway, and the cross-braces q, 
which are here subjected to little stress emd can taper off as wires 
toward the shell, all remaining metal parts have a uniform heat. Thus 
tensions are eliminated which can easily arise with xmevenly heated 
material or the cooling-off of soldered joints. It is hoped that the 



- 21 - 



model can also be built out of brittle material (aay, out of iron or 
aluminum). Nothing can happen to it during flight since there is little 
vibration. The landing is planned to be in irater. After landing, there 
is no danger to the model. If it still contains liquid hjdrogen, it 
irill be quickly coated urith a layer of ice which protects it against 
pounding by the vaves, etc.; if it contains no more hydrogen, the thin 
sheeting will presumably soon be flexible again. Critical will be 
only the moment when the apparatus, although weighing scarcely 10 kg 
when empty, touches ihe surface of the water while suspended from the 
parachute. ^Vhether it will stand the first impact, only the trial will 
show. 

Filling an iron Ig^drogen rocket would naturally be involved. It 
would first have to be carefully cooled down to - 253* by means of 
vaporized oxygen. Then the liquid hydrogen could be put in. With this 
inside and partial starting of the burners h, the liquid oiygen could 
be filled in. Fastening the propulsion apparatus and its braces to 
the shell would not be simple. Copper could nowhere be soldered to iron. 
The gap between the jet wall and the shell at F^ (cf. Figs. 3, 6, 13) 
could only be sealed with solidifying coal gas shortly before filling. 

The advantage of iron construction would be tremendously improved 
tensile strength. At ihe temperature of boiling hydrogen, soft iron 
has a tensile strength of 150 - 250 kg/mm^« Since the specific weight 
is about 8, its specific tensile strength is around 25 dm^nm^. 
What that means we will see later. I would only like to say in advance 
that, built of lead, the same model rises about 30 bm, whereas manu- 
factured out of iron it rises 1500 km under otherwise equal conditions. 
The question is only whether landing is possible. Only in a single 
case would the matter be certainly possible, namely if a long-distance 
projectile were built according to this principle which is to make one 
flight an4 reach its target (cf. p, 276 ff on this). 



. 22 - 



With the model of Fig. 13, a further improveaent consists of the 
fact that the oxygen is, in part, also sprayed into the atomizer pipe 
(at Zg) as a liquid. Advantages : l) the boiling in the oxygen chamber 
need not be as violent, vfaich reduces the danger of sleeping along 
drops of liquid. 2) The combustion gases flowing through the liquid 
oi^gen change to snov, part of vhich is carried to the propulsion 
apparatus through the boiling gas and part of vhich is only dead veight. 
\?itb the arrangement of the model in Fig. 13, the quantity of dead- 
veight snov is reduced to about if 10, 

A further considerable improvement vould be that only the propulsion 
apparatus and its imnediate surroundings are put under pressure, irhere- 
as the fuel tanks are under as little excess pressure as possible. 

Even vith the fuel tanks ve cannot get along nithout inside pressure 
altogether, for the vhole machine is only made of thin sheeting and 
▼ould collapse under the pressure of the front air if the inside pressure 
did not keep it taut like a nonrigid balloon. 

Nevertheless, it trould be a very considerable saving in weight if, 
as a burning liquid, ire did not use a liquid irhich vaporizes and bums 
as easily as liquid hydrogen but gasoline or kerosene, vhich must be 
sprayed in under an excess pressure of at least 40 atmospheres if 
they are to bum up properly. (Because of its lov spec, ireight and 
loT viscosity, it seems to me with hydrogen an excess pressure of 1-4 
atmospheres is sufficient* Unfortunately, I have not yet been able to 
experiment with liquid hydrogen.) On the other hand, with ihe liquid 
tanks (depending on the form of the tank) a pressure of l/3 - 4 atmo- 
spheres is sufficient to keep them rigid. This can be achieved by the 
use of tlie pump chambers invented by me (cf. Fig. 14). 

The apparatus (l call it model S) is in the main similar to the 
model of Fig. 13. The only difference is the pump chambers pi, pg, P3 P4. 



- 23 - 



These are thick-iralled, ring-shaped boilers. Fig. 16 shoirs one (pg) by 
itself. If it is filled with liquid, the liquid is vaporized according 
to one of the methods we learned to know on page 12 (in this connection 
also cf. pp. 326, 327 }. 




Fig. 14 



The vapor forces the liquid belov it through pipes o^ into pipe t. 
From there on, everything else is as with the models described earlier. 
After the liquid has left pg, a valve closes against o^ (not sho'vm in 
Fig. 14). The rims Og and o^ in Fig. 15 are connected to pj. Here the 



- 24 - 



liqiuid noir flovs from p^ to t^. At the same time, a valve opens and 
allows the gaa to escape to the open through the exhaust K. (Someirhat 
schematized in Figs. 14 and 15.) Thereupon, the pressure prevailing 
in the fuel tank again forces liquid into the circular boiler through 
valve oj* 

I cannot avoid shoving Just irfaat kind of arguinents opponents of nry^ 
ideas Sometimes advance. For example, Dr. \fEEER (Leipzig Observatorj) 
writes among other things : ''Imagine the action of pumps vhich are 
supposed to have the capacity to force such quantities of liquid fuel 
into tiie oven (when a very large rocket, 3000 kg in the first second"). 
Y/ell, it is the hundredth part of the weight of the rocket. Whoever is 
not acquainted with oy book will naturally think of piston or vane-type 
pumps and the like when reading this article, which do not have the 
capacity. Actually, these "pumps" are nothing Eore than fuel tanks with 
somewhat thicker walls. I believe it is not difficult to imagine vapor 
pressure from a boiler of 10 m content forcing 3 m^ through a screen 
or sufficiently large opening in one second. 




Fig. 15 

Furthermore, the pressure of 20-30 atmospheres in the oven of larger 
rockets makes ll^ER wonder when he thinks of our steamships whose 
boilers have a pressure of only 16 atiuospheres. The answer is that 
the pressure could easily be lowered to 10 atmospheres if a pressure 
of 30 atmospheres should cause suspicions. Now, the parts of the boiler 



- 25 - 



that are to stand 20 atmospheres are not as large as marine boilerS| 
at the most as large as locomotive boilers. And the smaller the boiler, 
the greater the pressure it can endure. - Besides, another thing 
should be noted. The main difficulty vith the steajn boiler is the fact 
that the heat must be transmitted from the oven, which is not under 
pressure, to the water, which is under pressure. If, with high inside 
pressure, the walls are made too thin, they brealc; if they are made 
too thick, not enough heat passes through. Besides, the fire affects 
the walls more strongly, so that the machine cannot be used for long. 
For this reason, large steam boilers are not subjected to pressure 
above 15-16 atmospheres. - If, on the other hand, the gas enclosed in 
a machine does not need to be heated from outside, the pressure can 
naturally be raised much higher. The pistons of diesel raotors and gas 
motors, for example, stand a pressure of 30-50 atmospheres, cannon 
barrels are subjected to several 100 atmospheres during firing, and 
NATTERSR'S air liquifying apparatus built in 1854 stood a pressure of 
28C0 atmospheres, - With n^ rockets, the conditions are similar to 
those with the last-named machines, since the oven is under the same 
pressure as the surrounding liquid. 




Fig. 16 



- 26 - 



In model D, the pressure in the fuel tanks is still almost as 
great as in the oven. It can be lowered still farther if the pipe 
is closed on top (model A). Fig. 16 shoirs the upper part of this 
machine. The sketch is sch«natized; actually, for reasons of 
equilibrium, all pipes are at least in pairs. I usually drew only one 
in order not to canfuse the picture. 

The pipes d serve to press the fuel against the tip, since the 
latter would heat too strongly at higher speeds. Space c is under 
greater pressure than the fuel tanks. The vaporized liquid passes 
to the propulsion apparatus through a pipe (in order to utilize the 
compression heat that has developed in front of the tip for 
propulsion). The remaining liquid flovs back into the tank again. 

I have been told that the rocket must bum up like a meteor 
vhen cutting tJirough the upper layers of the atmosphere. I would 
like to answer t What is crucial in the ascent is not only the 
temperature of the air in front of the tip but also its beat 
content, for only where there is high heat content can great 
transfer of heat take place. But the air is dense only at the 
bottom where the rocket flies relatively slowly, so that the 
air in front of the rocket heats up little. Above, where we are 
faced with high speeds and therefore high temperatures, the air 
is so thin due to the low barometric pressure that it contains 
but little heat due its low mass even at the highest temperatures. 
The heat is easily absorbed by the liquid which sprays out at d. 
In this connection, also compare Chapter 14. 

I would also like to mention here that, with models B, C, D and 
£, the fins mast also be cooled by liquid. 

In the fuel space are pipes k], which lead to safety valves and 
the open air at K (cf. Fig. 14), 



- 87 - 




Fig. 17 



- 28 - 



I provided theae safety Talves for all casesi although th^ are 
not absolutely necessary. The supply lines to the pumps can be 
fitted with cocks vhich close hy means of pressure gauges if the 
pressure in the tank rises too high. 

I will not further describle hov to go a^out preventing the 
snov that floats on top of the oaygen from plugging the pores of 
G and hov to remoTe the snov lying at the bottom of the hydrogen 
tank. Those are problems that any ccmstructor of average ability 
can solve. 

If veil-built and potrered nith liquid nitrogeni model A can 
almost attain cosmic speed. 

Model C (cf . Fig. 17) t The basic ideas are the same as irith 
model A. The designations in Fig. 17 likewise have ^e same meaning 
as before. Attached to thiS| hoirever, is not only a propulsion 
apparatus but a vhole rim in the centre of ^ich the propel lant 
containers hang down like a tail. The rest of the rocket I will 
call the head. Naturally, all available space in the bead is also 
filled vith fuel. Here, the pump chambers do not have the form of 
rings but the form of spheres or ellipsoids. The pressure in the 
tail is only as high as is necessary to keep its form and force 
the fuels to the head through pipes x and y. At start of the flight, 
even the pump chambers are filled, since all available space 
must be utilized for carrying along fuel. As vith model A, the 
pumps vork alternately, so that one is alvays filling the high 
pressure tank vfaile the other is being filled from the lov pressure 
tank . 




Fig. 18 



- 89 - 



Model B (in this connection, compare model B, Plates I and II, 
and model E, Plate IV) t 

Here, the pump chambers are situated above the apparatus and 
the fuel tanks above the pumps. 

This can only be accomplished vith large apparatus. Here it is 
advisable to divide the atomizer and, -with very large machines, 
the nozzle also. Fig. 18 shows a nozzle divided into seven parts 
seen from below. Thus, with large machines, a number of atomizer 
pipes empty into a common oven, from which a number of nozzles lead 
out again. (Cf. Plate IV) 



Ifevertheless, the nozzles and the atomizer pipes may not be 
too small nor too short, otherwise the friction in the propulsion 
apparatus is too great euid the fuel does not stay in the apparatus 
long enough for complete combustion. This type of construction is 
only suitable for apparatus of considerable absolute length, and 
they must not only be long but thick as well, for the force of the 
rearward thrust P must be regarded as acting on the area somewhat 
above the combustion chamber. The components of the inside tension 
of the tanTcy balance each other, so that these tamks can be regarded 
als a closed system. Now, the pressures p.dF act on this system 
(Fig. 19). We can find their point of attack by imagining a horizontal 
plane drawn through the combustion chamber and drawing lines upward 
parallel to the axis. The place where they first strike metal is 




Fig. 19 



- 30 - 



the point from where the metal transmits the stress to the shell 
surface. We can thus consider the pressures Pg.dF as acting in the 
same plane as the atomizer and on the side of it. There is also 
upward pressure against the wall of the nozzle between F^, and F^, 
but it is obviously less than the downward pressure against the 
bulge W. 




Fig. 80 

Now, the air resistance, that is the resistance against accelera- 
tion - (R + G) in the centre of gravity, acts on the tip emd force 
P at the bottom. In addition, the air resistance has the undesirable 
side-effect of tending to immediately set the rocket horizontally 
with the slightest motion sideways and causing continuous oscillation. 
This can only be remedied by affixing suitable tail fins w. These 
serve to steady the back end while the air resistance bends the 
front end, so that the occurring forces constantly have the tmdency 




Fig. 21 



- 31 - 



to buckle the rocket as Pig. SI shows. To prevent this in a long, thin 
rocket, either the excess pressure Tould have to be very high, irhich 
would cause nmch dead weight, or the rocket would have to be braced 
with pieces of metal which, in our case, would make the dead weight 
much too great. To keep the dead weight at a minimma, nothing is left 
but to make the diameter, that is the mass of the rocket, appropriately 
large so that the inside pressure is reduced. 

Compared to the previous models, models B and C are quite coaplicated 
machines. Keeping the various valves, pumps, cocks, and the ignition 
operating would be best accomplished by electrical means. 

A further very considerable improvcuient consists of carrying the 
fuel in a number of tanks and promptly casting off the eiupty tanks 
in order to reduce the dead weight. I will discuss the theory of 
these apparatus in detail later and show why we must strive to reduce 
the dead weight. With model C that is relatively easy to achieve. 
The tail must consist of a number of tanks (tape^vurm rocket, Pig, 23), 
at which the lowest ones are emptied first and cast off (Fig. 23). 
With model B, that can be achieved by placing a number of rockets 
above or inside one (mother, cf. Plates I and IV, at which it is 
always the lowest one which supplies the power and is cast off as soon 
as its fuel is used up. Here the hydrogen rockets (l designate them 
II, R, in abbreviation) are shown in red and the alcohol rockets (A.H. ) 
in black. 

Both model B and nodel C can be built so that they are able to 
fly to beyond the earth's field of gravitation. Actually, I would only 
build meteorological rockets siiiilar to model C and long-distr: ce 
rockets sivailar to model A (cf. p. 2 and p. 366 ff) rockets .diich 
reiaain in the sphere of attraction of the earth. 



- 32 - 



y 



Pig. 23 




Fig. 22 



- 33 - 



^yhat I did not mention in this chapter are arrangements to guard 
against sudden pressure increases resulting from^uiieven c<»abustion. 
Ncuaely, if for any reason tlie pressure in the oven rises, it causes 
more rapid combustion and development of more gas, so that pressure 
and combustion force each other up. Large "balanced pressure" jets 
of gas turbines sometimes aait a tremendous hoirl vhich can cause 
such strong vibration as to make the oven explode or at least 

become useless in a short time. So far, attempts have been made 
to combat this condition Trith large surge tanks; but that way is 
out of the question for us, as ire shall see. Attempts vere also 
made to bring in cooling vater or irater vapor to offset explosive 
shocks, but that has not been very successful to date, since all 
such arrangements react too slovly. For my part, I believe I have 
solved the problem. At 20 atmospheres of pressure, vxy gas jet has 
not howled, and the solution is surprisingly simple. Since the 
matter is not yet patented, 1 must be silent about it for tlie present. 

Other details of construction again I can only discuss later, 
since they can only be understood in connection with the rocket 
theory. 



- 34 - 



Part II. 

Technical Questions of PhyalCB 

Chapter 5 
The Speed of Out-Flov 



Formula quantities of Chapter 5 t 



G 

^d 

C 
P 

Cv 
P 

Pd 

Po 
F 

Fd 



F 



H 
N 

2 
s 

T 

Td 
To 



speed of out-flow 

speed of out-flov at end of nozzle. In the succeeding chapters, 
I vrite this simply as c. 

specific heat of the gas at constant pressure 

specific heat of the gas at constant voluae 

absolute pressure of the outf loving gases at the place examined, 
likewise in kg/m* 

pressure at end of nozzle 

absolute pressure in the oven in kg/in 

cross— section of the nozzle at the place examined 

largest cross-section of nozzle (end of nozzle) 

smallest cross-section of nozzle (neck of nozzle) 

weight of hydrogen 

weight of nitrogen 

q[uantity of heat 

weight of o:iygen 

absolute temperature 

temperature at end of nozzle 

temperature of oven 



- 35 - 



V t Tolume of 1 kg of gas in m 
Vq j Tolvune of 1 kg of gas in m® in the ot&i 
^ x pressure of outside atmosphere 

Of this chapter, the la;)aiian could note only the following : 

Gases flow best from funnel-shaped nozzles (cf. in this connection, 
Figs. 3, 6, 7) since vith then the highest speeds of out-flow can be 
achieved. That will surprise the layman, for it is observed that 
water, for example, strecuas fastest from the mouthpiece of a spray 
that is tapered toward the front. One can likewise blow with the 
aouth more strongly through pipes tapered toward the front thcoi 
through a funnel with the small end to the mouth. 

The deviating behavior of the rocket gases is explained by the 
fact that they are highly compressed in the oven and can therefore 
expand strongly, while the air in our lungs is compressed but 
little and so can only expand little. Water, finally, is as good 
as completely incoaprcssible. 

Namely, a liquid, incapable of exponding, in a container open 
at the top that flows through a hole in the bottom, flows (apart 
from friction) at the same speed that a body would acquire when 
falling from the level of the surface of the liquid to the level 
of the hole . If this liquid is under pressure in an otiierwise 
entirely closed container, the speed of outflow is obviously found 

TJ — ;— 

This speed is already reached with relatively snail openings, as 
is found by direct and rearward thrust measureaents. One can, however, 
be deceived if one only measures the quantity of liquid that flowed 
out and divides it by the cross-section of the opening and the tiise. 
The water does not attain its speed mocientarily but is still accelerated 
while flowing out. Hence, the stream of water before the hole is 
thinner than the hole itself (according to experience, about 3/3). 



- 36 - 



by asking t Hoy high above the opening irould the surface of the liquid 
in a container open on top have to be for the ground pressure to be 
as great as the inside excess pressure (pressure height of the liquid) 
is here. The speed of out-flov will be as great as the falling speed 
of a body from this height. Since, in order to exercise a certain 
ground pressure, a liquid must naturally stand the higher, the lighter 
it is, therefore the aaae excess pressure of a lighter liquid iaparts 
a higher speed of out-flow. 

So far for incompressible liquids. With elastic gases something 
else can be observed i '?lien they pass through a hole in the vail, 
they naturally floir out approximately just as fast as if they irere 
incompressible. VHiile flowing out, hovever, the pressure to vfalch 
they are subjected decreases and gases at lower pressure are speci- 
fically lighter. With the use of funnel-shaped nozzels we have the 
possibility of letting the gas get still lighter specifically irtiile 
it flows out, which naturally increases its speed of out-flow some- 
what. If, during out-flow, we conduct the gas through a funnel-shaped 
nozzle, the cross-section and the speed of the gas stream increase 
simultaneously. Thereby (depending on what one wants to call it), 
we either cause the out-flowing gas stream to be specifically 
lighter at the end of the period of acceleration or we cause the 
same accelerating pressure drop to act on a larger surface. Hence, 
the accelerating force acting on the gas streaia is greater. (The 
two clauses mean approximately the same thing.) 

Theoreticully, em infinite increase in speed could be achieved 
l) if the gas could expand to zero pressure, 2) if the gas remained 
gaseous at any expansion, 3) if there were no friction between it 
and the side of the nozzle. Naturally, requirement 1 cannot be ful- 
filled at the bottom of our atmosphere, although it could almost be 



- 37 - 



realized in planetarj space. On point S vq have to say tliat gases 
cool off urith expansion and, therefore, in a vacuum, the out-flowing 
gas vould finally condense to fine drops of mist, if the funnel 
is made sufficiently long and vide. 

This is self-evident if considered from the standpoint of energy, 
for the gas attains its speed of out-flov at the expense of its 
oim pressure and heat energy, and this can naturally not be infinite. 
The friction on the side of the nozzle even makes it appear advisable 
not to let the gas expand until it becomes a liquid (or solid). 
Namely, with highly rarefied gases, the friction is relatively great 
(as is evident, for example, with GAEDH'S molecular air pump), and 
this friction would finally even lower the speed of outflow. 

Within certain limits, the exhaust speed only depends on the 
form of the nozzle, the nature of the fuel, and the temperature in 
the oven; hardly, however, on the pressure of the outside air and 
the pressure in the oven. 

At first sight, this is likewise astonishing. The independence 
of the atmospheric pressure results from the form of the nozzle, 
which conditions a very definite nozzle-end pressure, proportional 
to the oven pressure, on which (as long as it is greater than one 
atmosphere) the outside air pressure has no influence. The inde- 
pendence of the inside pressure sounds still more incredible. Water, 
for example, spurts the faster from the mouth piece of a spray 
the higher the pressure in the hose; likewise, a stream of air 
blown by us moves the faster, the stronger we blow. In order to 
understand the devious behavior of the rocket gases, we must again 
visualize their compressibility. Namely, with the rocket oven, the 
density of the gas is ceteris paribus proportioBal to the pressure, 
so that tlie gas opposes the greater pressure with an inertia resistance 



•. 38 - 



just as much greater. (Note i Taken precisely, this naturally only ap- 
plies to equal temperatures. On the other hand, irith the saijie fuel 
composition, raising the inside pressure can increase the speed of ou-^ 
flow. Here the inside t^nperature grovs vrith the pressure under vhich 
the gases form. It is the sarae thing as at first letting the process 
go on under loir pressure and later heating the gas by compression. 
That gases beat up yrhea compressed is a phenomenon that could be familiar 
to most bicycle and car drivers from pumping tires. 

The absolute force of the rearward thrust naturally groirs with the 
oven pressure. I vill report on the principles for using fuels on 
p. 341 ff and p. 351 ff. Here, I irill only vrite concerning the speed 
of out- flow. 

At the bottom of our atmosphere (that is, with a nozzle-end pressure 
of one atmosphere) and irith an inside pressure of 20 atmospheres, of 
the fuel compositions knoim to me, a composition of 1 part (by weight) 
of hydrogen and 2 parts of oxygen produces the highest exhaust speed, 
namely 4000 m/sec. 

Now, this will again surprise a chemist. Namely, with this mixture, 
a large part of ihe hydrogen ronains unbumed and acts as ballast, for 
2 kg of oxygen can only absorb l/4 kg of I^drogen. Thus, a mixture of 
one part by weight of hydrogen and 8 parts by weight of oxygen contains 
the highest therm och^nical energy per kg, if we can achieve complete 
combustion. (The so-called stoichiometric proportion) 

The fact that, with an outside pressure of one atmosphere, the 
first-mentioned mixture proves to be better is due to dissociation. As 
is well knoim, the higher tlie temperature, the faster the molecules 
whirl about, and at very high temperatures they strike each other so 
violently that the cohesive forces between the single atoms are no 
longer sufficient to hold the molecules together. A partial disintegration 



- 39 - 



of the molecules occurs, tlie so-called dissociation (an expression which 
irould be literally translated somevhat as "desocialization")* For 
excunple, above 2500**, vater vapor HgO breaks down into H + OH; above 
4000*, it further disintegrates into monoatomic hydrogen and oxygen. 

Vifith this dissociation, a large part of the developing heat is again 
destroyed, since the tearing apart of the atoms is naturally connected 
-with a loss of energy. This heat is again set free only when we cool 
the gas 80 far that the atoms cling together again. Dissociated gas 
is relatively heavy and cold (indeed, it cools little with expansion). 
But if it is still dissociated at the outlet, it only flows out slowly. 

There is less dissociation, however, if one gas is taken in surplus 
(e.g. hydrogen). 

When flowing out of a funnel-shaped nozzle, the gas cools off and 
the dissociation recedes again. Unfortunately, exactly water vapor 
would have to expand and cool very strongly if it were no longer to be 
dissociated at the nozzle outlet. Therewith, the inside pressure would 
have to be one-hundred ticies greater than the pressure at the outlet, 
which can naturally not be achieved with an outside pressure of one 
atfiiosphere; we cannot work with an oven pressure of 200 atmospheres. 
On the other hand, with a rocket operating above the earth's atuosphere, 
we can assume any low outlet pressure and nothing prevents us from 
using the stoichiometrically correct ratio of Hg : 0. ICspecially one 
other circumstance stands us in good stead here : 

The cross-section of the outlet must be very large in relation to 
the weight of the rocket. ^7ithin the atuosphere, the rocket is heavy 
and thin, but by the time it has reached planetary space it has lost 
a large part of its fuel, ao that now the weight is small enough in 
relation to the largest cross-section. Beside the advantage of a higher 



- 40 - 



exhaust speed (theoretically up to 5000 m/sec, in practice presiimably 
4500 m/sec), the stoichiometric composition also has the advantage of 
a higher specific weight; more fuel can be taken along in the same tank 
(the specific weight of liquid hydrogen is .06; but 1 liter of liquid 
oxygen weighs 1.13 kg). ^Vhat folloura from this is we will only operate 
the rocket on hydrogen above the relevant parts of the atmosphere, while 
for the start of the flight we will look for other fUels. 




Fig. 24 

The second-best composition that I know consists of 9 parts of 
ethyl alcohol and 20 parts of oxygen. With this mixture at 20 atmospheres, 
the gases would theoretically flow out at 2700 m/sec. In practice, 
one should reach 2000 m/sec. They consist of carbon dioxide and water 
and some nascent oxygen. 

After what was said on pp. 8 , 15, the high oven temperatures need 
not worry us. For example, it is impossible to melt a thin lead dish 
containing liquid hydrogen over an electric arc. 

Another instructive experiment is the following t A seuicircular 
copper pipe approaches a flame at A, as is shown in Fig. 24. If water 



- 41 - 



flova through it in the direction of the arroir, it is imposaible to 
bum the pipe with the flame of an oxyhydrogen blovpipe earring 
excess hydrogen. The misgivings of Dr. \7EBIll of the Leipzig Cbservatory 
concerning the high degrees of heat in the oven are thus unfounded. 

In spite of that, in order to obtain lover oven temperatures for 
model B described on p. 315 ff, I provided weaker compositions. For 
the alcohol rocket, instead of rectified alcohol, I provided 13.4 ^ 
dilute edcohol vhich only gives an ov^i temperature of about 1400* C 
and an exhaust speed of roughly 1700 m/sec« The last figure I only 
represented by 1400 m/sec in the equations (in order to meet possible 
objections regarding imperfect combustion, friction in the nozzle, etc.), 

An additional feature of models B and E is the insulation of the 
vail by the vapor of the coolant in t (cf. Plate II), so that burning 
of the oven vail is completely excluded. With the other aodels, ve 
at least sav that combustion is less vigorous near the vail. Thus 
thorough precautions have been taken against burning of the vails. 

With models B and E, this dynamic cooling can finally be made 
very effective by letting gas of the same composition as the forming 
gas flov donn along the vails of the oven. According to KIRCimOF, 
this almost completely absorbs the radiation coming from the inside 
of the ovoi. 

For the hydrogen rocket, I provided a composition of 1 part by 
veight of hydrogen and 1.43 parts by veight of o:^gen, vhich likevise 
produces a temperature of about 1400° C. The exhaust speed vould 
be roughly 3700 m/sec, idiich I set at 3400 m/sec in the calculation 
for the reason stated above. If then I can shov that, even under 
these conditions, certainly assumed to be too unfavorable, apparatus 
can still be built vhich advance into planetary space, I hope I have 



- 42 - 



proved that sending a rocket into planetary apace is actually no chimera. 

I chose these unfavorable fuel mixtures mainly on account of some 
critics. I myself knoir that the rocket oven can endure a considerably 
higher temperature, but perhaps critics who only read the book super- 
ficially do not knoir that and I would like to avoid giving the appearance 
of impracticability as far as possible. For that matter, after describ- 
ing model £, I irill state what, in my opinion, an apparatus built 
like it but propelled with good fuels is capable of. 

The following is only intended for specialists who would like to 
check my figures. 

The out-flow speed of gases from such large nozzles (F^ = 705 cm ) 
has not yet been measured directly. On the basis of the performance 
which examinations to date show, the following can be assumed (in 
agreement with the theoretical reflections ) t 

The more nearly perfect the form .of the nozzle, the greater the density 
of the gases, and the wider the nozzle, the more will the disturbing 
influences (friction and the like) be minimized and the speed of out- 
flow more and more approaches the figure already calculated on the 
basis of thermodynamic considerations in the foregoing century. 

ZEUNER (Turbines, p. 261 ff) gives a clear derivation of the 
out-flow theory. The relationships with raj rocket approach his formulas 
by so far that I can use them as the basis of my discussion. According 
r to Z3UNSR (Turbines, 155), for every place of the jet J. 



-)/2-9,81.^,:.7„.[l-(£-j 
as long as p ^/^ . 



(1) 



- 43 - 



Vg is the volume In m^ of 1 kg of exhaust gases irith the conditions 
in the oven. If the temperature in the combustion chamber is not to 
exceed a certain maximum value, pg. V^ simplj depends on the composi- 
tion of the gases. With reference to po and p, it can be remarked i 
According to ZEUNER, vhen p^^ » the connection betveen nozzle cross- 
section Fp and the pressure p for every place is given bj the formula t 






/x-1 f_2_^''-' 
/ XJ- l'\K+l/ 



K-tl 



/ /nN** /n\»* 



(£r^(£ 



(«) 



From that ire read off i 



Pd ^d 

The ratio — — is (actually only approximated) constant, when ■ 

m 

and X (that is, the composition of the gas) is constant. Nov, according 

to (l), irith a certain gas at a certain temperature, c. depends only 



on 



Pd „ Pd 



. If — — is constant, the exhaust speed also becomes (almost) 



P P 

*^o "^o 



constant and independent of the inside pressure. 

The named formulas are approximate formulas. They ignore the 
friction; yet, even for an ideal gas, they irould at best be correct 
if the outlet pressure equalled atmospheric pressure, i.e. if p^ ^A • 

Proof : According to the lair of reanrard thrust this exactly 
applies I 

Noir, according to (2), irith p and T (T is the absolute tempera- 
ture in the combustion chamber) constant, p. and irith that also specific 
volumetj v. of the exhaust gases at the outlet vould be constant; 



- 44 - 



according to (l), the exhaust speed c, the mass ' ejected in one 



''d-^d 



^d 



second, and its momentum > c.. ■■■■ ■ ■ «- -would also be constant. IHirther- 

more, according to (l) and (2), y\ p.dF vould also be constant and 

the reanrard thrust irould be b7^>F greater in a vacuum than in a 
space irith an ataospheric pressure of ^ . 

Thus, opposite to an equal momentum of the exhaust gas vould be 
an unequal impulse dealt to the rocket, irhich cannot be reconciled 
▼ith NE\'/TON'S third principle (the clause concerning preservation of 
the centre of gravity). 

Actually, the situation is as follows t l) As i^ decreases, partial 
freeing of the gas stream from the nozzle wall occurs; therewith, 
apparently p and, as a result, also \y p.dF become smaller. 

2) At the same time, starting from F in "Uie nozzle, the gas must 

undergo greater acceleration (c grows). 3) Finally, more gas also 
flows through F . 

With tlie alcohol rocket of model B, which I will describe later, 
starting with the launching, c theoretically grows by 6 - 7 ^. 
According to w^ estimation, the lowest value that c can have is 
between 1530 and 1700 m/sec. (This uncertainty is greater than the 
whole amount by which c can vary. It is so great because I have until 
now only been able to compute the atomizer theoretically and have 
not been in a position to examine its operation experimentally. 

F^ 
If p (and with it p ) becomes so small that from ^e ratio 



t according to (2), PjC^ would follow, c decreases rapidly and, 



F 

m 



- 45 - 



in the sequel, we vant to figure ■with the highest value of c attainable 
vrith certainty . If I call p -j^' ^ the excess pressure, the folloir- 
ing is supposed to resul t : 







1 








2 




" 


/ 


«- 1 




2 


\x-l 

tJ 

«+ 




£ 


~ 


7< + \ 
2 


+ 






1 1 




— 


fr 





Othenrise, according to (l), it is desirable that 



be as small 



as possible. For technical reasons, <i (and vith it p ) soon reaches 

an upper limit and, vith a fluctuating p., ire vould have to build 

our rocket taking into account the largest value of p,. That -rould, 

in the first place, generally lower c, and a further drawback vould 
be that p fluctuates and is therefore in general lower than it 
might be with a stationary nozzle. 



' I would like to mention here that Prof. Dr. PUOLL of Hanover has 
suggested to me to build the rocket nozzle as a diffuser, that is to 
widen it out and possibly equip it with side canals for the ingestion 
of air (so-called Venturi tubes). That is supposed to reduce the 
exhaust speed, but the exhaust gases drag along a greater quantity 
of air on which they support themselves, so that the repercussion of 
the driven air mass is added to the rearward thrust effect of the 
rocket gases. 



I hav9, until today, not 
of important scholars doubt 
in this way for theoretical 
set up in the introduction, 
my calculations on the most 
thinkable, that is the one 
are executable under the mo 



tested the matter experimentally. A number 
whether the rearward thrust can be increased 
reasons. Therefore, following my principle 
until further notice, I here also base 
unfavorable value of the rearward thrust 
for a vacuum, in order to prove that i^y ideas 
st unfavorable conditions thinkable. 



The rocket theory derived here would not be overthromi by the diffuser 
Jets, but, instead of the actual out-flow speed, we would have to set 
an "effective" out-flow speed in place of c, based on the fact that, 
with the same loss of mass, the same rearward thrust must be produced 
not taking the air into account. 



- 46 - 



The folloving arrangenent might be suitable for making p inde- 
pendent of the rearward thrust P. One could (cf. Fig. 2S) at F make 
the nozzle cylindrical or slightly converging for a longer distance 
and) from the combustion chamber, project a regulating pin e (as 
in the FELTON water turbines) into the nozzle as needed. Uodels A - D 
do not need the regulating pin for bere the required rearward thrust 
for the alcohol rocket is well-nigh c<mstant. The hydrogen rocket 
cannot attain the velocity v at all, for technical reasons (which, 
as we shall see, p. 332, does not matter much). Here, the rearward 
thrust is completely constant. Hence, p and c can actually be set 
as constant. 




Fig. 25 

With the alcohol rocket, the size of outlet F, is determined by 
the fact that at the place where "ifB is the smallest, with pressure, 
and the absolute temperature i 

x-1 






-) 



the exhaust gas must fill the space c.F. in one second. 

The quantity of heat produced by oxidation equals the quantity 
of heat wfaich the coolant and the combustion products must absorb, 
for the heat which the oven gives off to its environment can be 



- 47 - 



r ignored, irith models B and D because of the size of the oven and the 
speed of the flov, -with the other models because there all the heat 
radiated to the fuel is again utilized in combustion. With the alcohol 
rocket, oalj that heat is lost irhicb the alcohol gives off through 
the shell surface, but that is offset hj an equally large quantity 
of heat vhicb the oxygen absorbs through the shell surface. The 
hydrogen rockets give off no heat at all to the environment, but 
only absorb heat from it. The thermochemical tables usually give 
the beat of combustion for the case in vhicb combustion takes place 
at a pressure of 1 atmosphere and all matter involved is brought to 
+ 15* C. We must therefore calculate as folloirs : 

The quantity of heat produced by the oxidation equals the quantity 
of heat required to bring the fuel aad the oxygen to 15* C plus the 
quantity of heat required to bring the combustion products to the 
tfflaperature reduced to 1 atmosphere by means of the POISSON formula. 

We calculate the reduced temperature separately for the diatomic 
and tri atomic gases i 

at vhich, in the first case, x is set equal to 1*406 and, in the 
second case, equal to 1.30; T. and T are rated as absolute. From 
this, T. must be calculated. In the foregoing relation, the ratio 
between fuel and oxygen is given by the chemical connections. For 
example, 46 g of ethyl alcohol absorb 96 g of oxygen, or 8 g of 
oxygen absorb 1 g of nitrog^i. Thus, after having calculated T., 
we could determine the relation between fuel and coolant by the use 
of this formula. 




- 48 - 



In order to vaporize H k^ of liquid hydrogen at - 253* C and bring 
it to the reduced absolute temperature T., 

H. 3.400 (T + 12) cal. 

must be applied to it (if T. lies high above the boiling point). 
This figure is obtained as follovs j 

We shall let !„ be the temper fiture at i*ich the ppecific heat of the 
gas c becomes constant at a pressure of 1 atraosphere. Not the quantity 
of the heat is determined that is required to bring 1 kg from the boiling 
point to Tg, We iirill call this Q-. From T- to Tj, 1 kg absorbs the heat : 

therefore, in all 

With hydrogen, c = 3.400 cal/kg and ~ T- = 12". Therefore, 1 kg 

P P 

of hydrogen absorbs : 3'100 (T^ + 12) cal. H kj absorb H-tinie?? as much heat. 

To vaporije S kg of liquid oxygen at - 183* C and bring it to T,* abs. 
requires 

S« 0.218' (T. + 144) cal. 

If liquid air is used instead of oxygen, the r.itr^pei irhich it con- 
*pivF n-cts PS a cool-',n+. Up +o T,. N friP' of lirvid ?iitro,o;eu at - 195, 7* C 
and atmospheric pres'^ire re"'i^re i 

N« 0.244 (Tj + 121) cal. 

It irould lead ns too ^ar to 30 into further details of calculation. 
Whoever Irishes to check my figures otin best find the lacki.ig data in 
the physico-chemical tables of LANDOLT and BOWSTEIK, 

If the conposition of the gas and T. is knoifn, p 'V is easily 

1 00 

calculated. 



- 49 - 



Before applying the formulas (l) and (2), x must once more be 
calculated for the exhaust gas as ^ vbole. V/itb the alcohol rocket, 
water vapor and hydrogen flow out. Here x decreases with increasing 
water vapor content. The following are its values for different 
ratios of oxygen to hydrogen (by weight) : 



! j ! I ! 
Wght. of hydrogen ! I ! ! ! 


! ! ! ! ! 

X - 1.400 I 1.398 I 1.396 I 1.394 I 1.393 I 1.391 
! I I ! I 


! ! I ! ! 
yS^il..2?.,2S6?'^ . 1 -1 ! 1 5 116 I 1.7 ! 1.8 I 1.9 


Wght. of hydrogen I I I I I 


II!!! 
X - 1.389! 1.388 1 1.386! 1.385! 1.384! 1.383 
II!!! 



For 3 parts of hydrogen and 16 parts of ojygen, x = 1.33, although, 
with ray rockets, the strong dissociation will likely change this 
figure. By how much, only experience can show. 



I do not wish to conceal the fact that Prof. Dr. KABL WOLF of 
the Vienna Technical University has written in an article that it is 
impossible to reach out-flow speeds above 2000 m/sec. He bases his 
statffiaents on theoretical considerations. He reasoned somewhat as 
follows J Ifydrogen burning in oxygen produces water vapor. Water 
vapor cannot be hotter than 3000** (on account of dissociation). 
Therewith, the average speed at which the molecules whirl about is 
somewhat over 2000 m/sec. This speed is the maximum we can expect 



- 50 - 



at all. ~ WOLF has forgotten only one thing, that we here have a 
large quemtity of surplus hydrogen. Hence, what we have here is not 
dissociated water vapor but a 4000->5000*- hot mixture of undissociated 
gases, the largest , art of idiich is light hydrogen. If one make the 
same calculation for this, one obtains an upper limit of approximately 
4 1/2 km/sec, a figure which could be reduced by 300-400 m/sec because 
of loss through friction and other imperfections of the machine. 
Actually, I was able to achieve 3800-4000 m/sec with a machine far 
from perfect. 

The relation between rearward thrust and loss in substance was at 
least as great as it should have been at 4000 m/sec (to be sure, 
there was a certain trick involved which I cannot divulge here). That 
is a higher figure than on what I based the calculations in this 
book and, as I already said, there is hope, with a good experimental 
method that is more expensive, of reaching over 4000 m/sec. 

I wish to remark also that GODDARD, by using nitrocellulose 
powder, has reached 2400 m/sec and, with the alcohol rocket, the 
rising gas is still lighter. Moreover, it must be considered that a 
LAVAL nozzle is not as efficient when it opeirates intermittently, 
as in GODDARD'S experiment, as my rocket nozzle in which the gas 
flows out uniformly. This fact is rather unpleasantly noticeable, 
for example, with the HOLZWARTH turbine. 

Admittedly, n^ experimental apparatus was a gas burner, not an 
atomizer; but here I only wish to prove that it is possible to send 
a rocket into planetary space. If it should not be possible with 
atomization in the liquid state, I would somehow try it with gasifica- 
tion. (To be sure, not by heating from the outside, but by heating 
by means of rising gas bubbles.) For that matter, the atomization 
and c(Hnbustion experiments I have conducted to date likewise Justify 
quite good expectations. 



- 51 - 



DOPF (Journal of the Ihiion of German Ekigineers, 1899, p. 752, 
and EYEBLIANN-SCHULZ, Gas Turbines, 2nd edition, 1920. M. Krayn Publ. 
Hse., Berlin W), shortly before the petroleum enters the mixing 
and combustion chamber, transformed every single charge of petroleum, 
delivered by a pump, into highly over-heated vapor — under as 
perfect a vacuum as possible — , -which vr&a then divided into single, 
fine, ray-shaped streams by means of screen-type openings. 

Readers have suggested that I also use this principle in qy 
rocket. I believe DOPP'S atomizer would be too heavy for our purposes. 
It should not be forgotten that the propellant vhich, -vrith unmanned 
rockets, escapes during the entire period of propulsion and, irith 
manned rockets, at least during the first second amoimts to 1.2 fe 
of the total veight of the rocket. Such large quantities of gas 
vould require too vide pipes, vhich again would unfavorably influence 
the specific ireight and tliereby the air resistance as irell as the 
mass ratio. Cf. p. 76 and p. 93 . In addition, with the high velocity 
which tlie stream of gas must necessarily take on in the nevertheless 
small oven, a sweeping out of the flame (cf. p. 11) is actually 
to be feared with gas mixtures. Therefore, I will rather try my 
luck with atomization of the fuels in a liquid state, especially 
since, instead of the viscous hydrocarbons, we are dealing with 
easily movable and more rapidly inflammable liquids and, instead 
of the atmospheric uir, I am using highly-concentrated hot oxygen. 
My first experiments in this direction were certainly encouraging, 
although there is not much to report about them. 

Beside that, all sorts of things have been suggested to me by 
readers. For example, to simply use atomizers in which the liquid is 
drawn in and diffused by a stream of gas; the necessary experience 
can be derived from construction of the gasoline motor. Many readers 



- 5a - 



have doubts concerning the rapidity with vhich the gas leaves the 
oven; the gas hardly remains in the oven for l/50 of a second* 

Ify ansver to this is that the drops of fluid themselves remain 
in the oven considerably longer due to their inertia, the more so 
the larger they are. Besides, the speed of the gas stream increases 
steadily from Z to Fg^ due to the strong development of gas, so 
that the drop is not struck by the full speed of the gas stream 
at the very beginning and accordingly remains in the oven longer. 
Larger drops vill perhaps ataj in the oven l/20 of a second. One 
should consider vhat that means if an inflanmable body of the size 
of a drop of mist is, for l/SO of a second, exposed to a stream of 
o:cygen of SO atmospheres density and 800* hot irith a relative speed 
of many metres per second. In addition, I consider it a very fortunate 
circumstance that the period of combustion and the relative velocity 
are the greater, the larger the drop. — This advantage vould be 
lost if I used an atomizer in vhich the liquid flies along with the 
gas stream, ind if I blev the mist produced by such an atomizer 
into a hot stream of oxygen from the side, the combustion process 
would be disturbed because of the low radial velocity and the cold 
gas that is being carried along. (In spite of that, I need naturally 
not emphasize that I am very thankful for every suggestion from 
readers. We are dealing with an entirely new area of technology, 
and everything must naturally be carefully reflected on. In so 
doing, it is only too easy to forget some important aspect.) 



- 53 - 



Chapter 6 
The Ideal Propulsion 

Formula quantities : 



c t speed of out-flov 

e : base of natural logarithms 

m I mass of rocket 



m i initial mass of rocket 
o 



m. : final mass 

s : distance 

t : time 

V : velocity 

T : ideal propulsion 

P : force of the backirard thrust 

S t distance 

V i velocity 

^ : finitely small part 

1^ I mass of an arrangement to increase the velocity 

Of this chapter, the layman could note only this much t In higher 
mathematics, there is a number designated as e. It equals 2.71828... 
By burning, the rocket receives propulsion (increase in velocity), 

V , and naturally becomes lighter at the same time. If this propulsion 

V is to be as great as tlie exhaust speed of the rocket gases 

(I designate it as c), the mass at launching together vith the fuels 



- 54 - 



must be e times as great aa after the burning . V/e designate the 
initial mass as m and the final mass as m , and vrite : 

m > m. .e. 
o 1 

If the propulsion is to become tirice as great as the exhaust 
speed (ire vrite s v = 2.c), the final mass must decrease bj the 

a 

e-th part once more, and the initial mass must be e.e « e' times 
as great as the final mass. If we irant t b 3c, then 

3 

m > m. • e 
o 1 

(as is Tell knoim, e'' = e .e). 

4 
For V = 4c, m - m. .e • etc. 
X ' o 1 ' 

If the propulsion is to be 2.5 times as great as the exhaust 
speed, then 

2.5 
m = in, • e • 

o 1 ' 

2 3 

irhich is greater than e and less than e ; the exact figure is found 

by the use of higher mathematics. In the table given beloir, the top 

line of figures indicates the required final speed. The eidiaust 

speeds are given on the left. The numbers in the table indicate bj 

how many times, with the exhaust speed given left of the number, 

the initial mass of the rocket must be greater than its final mass 

if the rocket is to receive the propulsion indicated at the top 

of the column t 



' In the succeeding calculations, I always relate the exhaust speed 
c to the rocket. I just do not understand how BAETZ, for example, 
could think that by c I had meant the absolute speed of the propel- 
ling gases after they are ejected. 



Table for Basic Equation (e) 



"o 
mi 



>< 



c. = 500 


1000 \ 2000 3000 4000 1 5000 C000| 7000 { 8000 


c= 1000 


1,64 


2,72 7,39 


20,0 


54,5 


148 405 i 1089 


2987 


2000 


1,29 


1,64 


2,72 


4,48 


7,39 


12,2 


20,0 


33,0 


54,5 


3000 


1,18 


1,39 


1,94 


2,72 


3,78 


5,29 


7,39 


10,25 


14,35 


4000 


1,13 


1,29 


1,64 


2,11 


2,72 


3,49 i 4,48 


5,76 1 7,39 


5000 


1,10 


1,22 


1,49 


1,82 


2,22 


2,72 


3,32 


4,06 


4,95 



9000 


10000 


11000 


12000 


13000 


14000 


15000 m/sek 


8060 


22070 


60000 


163100 


444000 


1200000 


3290000 


89,6 


148,7 


243,5 


402 


662 


1091 


1805 


20,0 


27,95 


39,0 


54,6 


76,1 


106,3 


148,7 


9,50 


12,20 


15,75 


20,0 


25,8 


33,2 


42,7 


6,06 


7,39 


9,02 


11,0 


13,47 


16,42 


20,0 



Ol 



- 56 - 



Taken preciselj, these figures only apply to a vacuum and 
gravitation-free space. In reality, air and gravitation hamper the 
rise and, -with utilization of the same fuel, the final speed is loirer 
than it should be according to the table. I therefore call this 
figure the "ideal propulsion". HOEFFT, FUCHS, and ULINSKT designate 
it as "virtual speed"; recently, HOEFFT likeirise calls it "ideal 
speed" or "ideal propulsion". NOORDUNG calls it "ideal speed". 
For exaople, with model C, the final speed is only 1/2 - 3/4 times 
as great as the ideal propulsion, depending on the size of the 
machine. With model E, it becomes 0.95 times as great. It yrill be 
the task of the following chapters to show how air resistance and 
gravitation must be represented in the calculation and how their 
unfavorable influence can possibly be avoided. 

We learn from the above table that a rocket attains higher final 
speeds by means of which, like a thrown stone, it can naturally fly 
higher and farther the greater the ratio of initial to final uass 
(that is, the lighter the eapty weight of the rocket is in relation 
to the fuels carried along) and the greater the exhaust speed c. 
What appears especially important to me is the discovery that rocket- 
type aircraft can reach speeds greater than the exiiaust speeds of 

•"o 
the propellants if the ratio — — is only sufficiently large. 

The following is only in ten ted for the specialist : 

I refer back to p. 3 . There wo saw that a force P acting 
between two freely-moving masses m and (i, m moves both, and the motion 
is in opposite directions. 

If force P acts for a period of time, let us say forX seconds, 
it imparts velocity Av to mass m and velocity c to mass A m. We now 
learn that these velocities are inversely proportional to the masses, 



- 57 - 



therefore : 

\m\:\dm\ = \c\:\A^>\ 



or 



]m-Jc\ = \c-Jm\. 



(3) 



This theorem is called the "Law of the Preservation of the 
Centre of Gravity". If, at a certain aoaent of motion, the masses 
vere halted and fastened to a weightless rod (cf. Fig. 26) we would 
obtain a form resembling a dumb-bell whose centre of gravity S 
would lie between m and^ m. If D and d were tlie distances of the 




H f- 




+# 



am 



Fig. 26 



two masses from the centre of gravity, according to the rules of 
mechanics 



\dm-d\ = \m-D\ 



(a) 



During a certain period of time t, m must traverse distance 
S =^ V. t and^ ra disttmce s = c.t. Ifultiplying equation (3) through 
by t, we obtain 



• dti-tl = I 4m-e-tl 



or 



i.S\ = I Jm-s\. 



(b) 



Comparing (a) and (b), we learn that d and D can serve as values 
of s and S, and vice versa; i.e. during any time t, the initial 
point of the masses remains the common centre of gravity. If m and 
Am are placed at the centre of a balance beam and a force is allowed 
to act between them, the beam remains horizontal as long as m and 
Am both run on top of it, for the common centre of gravity does not 
move from its place at the fulcrum of the balance beam. 



- 68 - 



If, by giving c and A t opposite signa, one wishes to indicate 
that the tvo masses run to opposite sides, equation (3) is vrittm i 

m.Av " - c.^m or m.A^ + c.Am ■■ 0. (4) 

Here, I irould as the specialist to take special note of a 
circumstance, since there is danger that a misunderstanding may arise. 

In the usual textbooks on mechanics, the "Law of the Freseryation 
of the Centre of Gravity" is written in other symbols. There, one 
mass is designated as m^ and the other m^, the absolute velocity of 
the whole syston before acting of the force (that is, before the 
impact) as v,; the velocity of m. after the impact as v., and the 
velocity of m„ after the impact as Vg, and one writes i 

fflj^.Vj^ + Dg'^a ■ ("i + "a^'^^a* ^**^ 

Now, a number of readers of the first edition of my book understood 
me as having said t 

mj,.Vj^ + mg.Vg - 0, 

and thereupon declared all my calculations fundamentally incorrect, 
("(fhich they would have been had I based them on this pronise.) 
But the two masses designated as m and m^ in formula (4a) I have 
actually designated as m andAm. On the other hand, c and A v are not 
the velocities v. and v. thonselves but only the differences between 
them and the common initial velocity. Therefore we cnist set 

A V - Vj - Vg 



and 

and what I have writtmi as formula (4) with wy symbols would look as 
follows when written with the usual ones ( 



- 59 - 



This is actual I7 a transforciation of (4), of vhich one is easily 
convinced if one opens up the brackets in (4b) and (4a). 

The advantage of my script lies in the fact that thereby I become 
independent of absolute velocity tuad can at every moment regard the 
rocket as stationary and eveiything else as in motion. 

If ^ m is infinitely small beside m, someirhat as a gas molecule 
beside the vhole rocket, then /^ v irill likewise be very small beside 
the exhaust speed c. As is veil knovn, such small quantities vhich, 
because of their great number, can never tliel ess not be ignored are 
designated by a preceding small Latin d, and so the equation can 
be mritten 

c.dm + m.dv - 0. (5) 

The ideal case irould be where the rocket advances in a straight 
line in a vacuum and gravitation-free space, in vhich case ire could 
add up all dv, that is integrate over dv. Over dm ire con integrate 
anyiray since m is a scalar quantity. We vould then get t 

c-(ln/no — Inwi) = v„ 

Ideal propulsion is an important quantity in rocket theory, for 

it is a measure of certain requirements demanded of the rocket as 

veil as of the performance of the rocket and the value of teclmical 

improveuents. Here is an example 1 

m 
At high speeds. In — -— is approximately inversely proportional 



- 60 - 



to exhaust speed c. Since In is also large, usually much more is 

°1 m 

gained if Te can enlarge c than if we enlarge — — , 

Now, when does a device, which increases the mass of the empty 
rocket and c, increase the rising force and when does it not 
increase it ? 



We will let U be the mass of the loaded rocket, IL the mass of 

the empty one,yU the mass of the device which is to increase the 
speed of the out-flow, C the higher exhaust speed, c the lower exhaust 
speed. The ideal propulsion in the case of C I designate as V , in 

the case of c as t . 

Now, if V^ v^, then V> t. 



C [In (wo + f) - 1" i>'i -■- ^)- = ''' ■ 



If V:: v^j,, theu : 

c-(ln ni(, — In j/ij) < «-[ln (m, + fi> — In (nii -1- /<)]; 

log (/n, + f'l - log ("'i + f ) ^ f 
log mo — log Hi C ' 

V/ith a small mass ratio and equal exhaust speeds, ▼ is approxi- 
mately proportional to the fuel carried along. Namely, according 
to (6), it is 

m, c 2 i- 



y 

That is approximately — 2L, when v « c. As a rule, therefore, more 

is gained here by a specif icly hea-vy loading, even though the 
exhaust speed is somewhat reduced thereby. 

HOE.IAIsTN ("The Reachibility of the Celestial Bodies", Oldenbourg, 
1925), instead of giving the ideal propulsion, prefers to state the 



- 61 - 



mass ratio required to reach it ■with c = 2000 m/sec. It seens to me, 
the advantage of my representation lies l) in the fact that the ideal 
propulsions are being added, irhereas the mass ratios must be multiplied ' 
and 2) in the fact that the requirement set for c is not yet included 
in the description and we con therefore (as in Chapter 12), conven- 
iently compare single performances -with one another. 

LORIJKZ of Danzig has objected that the equation 

c.dm + m.dv = 

is naturally correct but that it is inadequate for integration 
because it contains the two variables m and v. Here I could simply 
answer that one already learns in the 3rd to 5th seiaester of 
university that the equations between two variables and their 
differentials are sufficient for integration. Here, dm is actually 
the differential of m, and dv the differential of v. That the two 
variables are functionally connected is seen when formula (5) is 
divided through by m. 

J dm 
dv = - c— — . 
X m 

If we designate the speed increases in succession as dv , dvg, 
dv„, dv., etc., the losses in mass causing them as dm^, dm^y ^o* 
dm., etc., and finally the mass belonging to dv. as m , the mass 
belonging to dv- as m^, etc., then obviously 

dm. 




If, however, the single dv are added together, the result is 

) dv = V , which naturally is i 

>r- dm f* dm m 
j C.-5 y--5- " c.ln ~ , 



Cf. p. 97. 



- 62 - 



dm 

for _ c is nothing other than dv. From that, (6) follows directly. 

m 

As is well known, the effective force of the rearward thrust 
also follows from the principal impulse. We vill let P be the force, 

____ the mass flowing out in the unit of time (dt must be so short 
dt 

that we can regard th mass of the rocket and the stream of gas as 
constant), and c the exhaust speed. Then 

dm 
/P.dt/ = /c.dm/ or P - - c— — . (7) 

dt 

Therefore 

P dv 
= b^ . (8) 

m dt 

I will call b the ideal acceleration, the acceleration which 
the rearward thrust imparts to the rocket in a vacuum and gravitation- 
free apace. If a force Q opposes the ideal acceleration straight on 
and the situation is still that in which all single imulses occur in 
the same direction, then the decelerating effect of force 2 will 
be inversely proportional to the mass of the rocket, I will designate 

this deceleration as -~-^- j therefore 

dt 

'' " ''x " m ' 

b = b 5S_ . b.dt - b .dt - dqs 

^ dt 

Here, b.dt is the actual increase in velocity during the element of 

of time dt. From now on I will designate it as dv. 

The increase in velocity in a vacuum and gravitation - free space 
would be b .dt; henceforth it will be called dv , Therefore 

dv = dv^ - dq. (9) 



- 63 - 



Addition of the single velocity increases dv will obviously give 
us the actual velocity v, provided all dv are in the same direction. 
By integration, ve then obtain 

V = V^ - q , 

Here q is obviously the sum of all single decelerations, or the 
asiount by irhich v remains behind v . As is veil known, if velocity 
increase dv makes an angle g. with the direction of v, then only 
component dv. cos £, serves to change the velocity, the part dv. sin S- 
only has a direction-changing effect. If we are interested only in 




the velocity and not the direction of motion, we obtain the velocity 
from the formula : 



= 5 cos£..dv. (10) 



A special case which we will use in calculating the "synergy 
curve" is that in which dv acts in the direction of S and q makes 

an angle (<£.) with this direction. If I determine that eC is to 

equal when dq and dv act in the some direction, then : 

(11) 



dv = dv + cosdC.dq, 

X 



V = V + Tcosj^.dq 



- 64 - 



Chapter 7 

The Mass Ratio 
(If necessary, the layman can skip this chapter) 

Formula quantities of Chapter 7 

d : thickness of irall (in cm) 

1 t length of a cylindrical disc or pipe 

p s inside pressure in atmospheres 

r : radius 

V t capacity of a container 

/ 2 

z : tensile strength in kg/ cm 

F : sectional area or plane of projection 
S : specific veight of the building material 

V : ratio of veight of contents to veight of empty container 

Z : specific tensile strength Z - — , 

5 
'Tr i 3) 14, 15 etc. 

<f J specific treight of the filling 

I ask the engineer to excuse me if I here express thyself in some 
detail; I vould also like the non-engineer to understand this material. 
It is incredible hov helpless even physicists are vhen confronted 
irith my calculations of the mass ratio. 




Fig. 28 



- 65 - 



Let us assune that ve have cut a disc 8 cm in diameter and 1 cm 
thick (Fig. 28} through in the middle. Then each of the two cylinder 
halTes is 2 cm -vide, 1 cm high, and 1 cm thick. The common surface 
of contact is a rectangle 2 cm long, 1 cm 'wide, and 2 cm in area. 
If, betireen the two pieces, ve place a rubber balloon vhicb exactly 
fits the contact surface and piuap irater under a pressure of 10 atoo • 
spheres into it, the vater -rill seek to force the two pieces apart 
with a force of 2 cm^.lO kg/cm - 20 kg. We shall try to prevent 
it by holding the pieces together by metal strips at A and B (Fig. 
29). Then the strips must together hold 20 kg, and 10 kg fall to 
each. If the inside pressure were not 10 but p a-tmospheres, p kg 
would fall to each strip. Ve shall ignore ihe length of the strips 
but assume that they are as wide as the disc was thick (here, 1 cm). 





Fig. 29 Fig. 30 

If the radius of the disc were not 1 cm but r cm, the contact 
surface would be r-times as great and each strip would have to hold 
r.p kg. If this disc were not 1 cm but 1 cm thick, the contact 
surface would be 1-times as great, and the stress on each of the 
two strips would be l.r.p kg. 

Strips A and B would have to hold the same amount if the two 
cylinder halves were not solid but hollowed out like a trough (Fig. 
30), at least as long as they were thick enough not to bend under 



the influence of the Inside pressure. But hov thick would they have 
to be for the purpose? Well, no thicker than to prevent them from 
breaking. They -would by force take on the form of a cylinder under 
the influence of the inside pressure; that can be observed on every 
inflated rubber tube. Therefore, they need only be as strong as 
bands A and B, and the whole would thus be a pipe of uniform thickness. 

If the water in a pipe 2.r cm wide has a pressure of p atmospheres, 
the wall at right angles to the direction of the pipe is under so 
much stress as to require a force of l.r.p kg to hold it together 
along an 1 -cm-long cut made at A or B. 

In this case, the sectional area would have the form of a 
rectangle whose length would equal the length of the cut and wiiose 
height would equal the thickness of the pipe; therefore F = Id 
(d measured in cm) . 

If z is the weight in kg which a wire of 1 cm^ thickness made 

of the material of the pipe can just carry without breaking, then 

2 
a wire of F cm thickness would carry F.z kg. In order to burst 

the pipe, the force acting frraa inside would have to be greater 

than F.z = l.d.z kg. Therefore, the pipe would endure the excess 

inside pressure as long as 

Irp i Izd. 

The symbol ^ means "at most equal", ^ means "at least equal". 

Dividing both sides of this equation by l.z, we get 

r.p 
d> . 

— z 

Hence, the pipe will hold together as long as the wall is stronger 



- 67 - 



than is indicated by the right side of the equation. The strength 
of the vail is independent of its length. 

Now, what is the relation of the weight of a cylindrical pipe 
to the weight of the water it contains? (The word "weight" is here 
always to be understood in its customary not its astrononic sense.) 

p 
in l-cm-long and 2.r-cm-wide pipe can hold t » r-.TT.l g of water, 

g 
The shell surface of the pipe would be 2.rTt.l cm and, if S is the 

specific weight of a cubic centimetre of the raw uaterial, the shell 

weighs S.r.'^T.d.S g, at least as long d is only small beside r. 

The proportion of water content to pipe weight is as 

V = r^.-TT.l I 2 rV.l.d.S ; 
or if we substitute the value of d from (l2) 

v4 r^.tf.l : z.r.lV.l.S.~L. » -i. . -L., _5„ (13) 

^ a P s 

g 

The Tolume is measured in cm , the wall weight in kg, the pressure 
in kg/cm^, and the tensile strength likewise in kg/ cm . Wien converting 
to other systems of measurement, an additional factor x must often 
be taken into consideration. 



Here, z indicates how many kg can just be suspended from a wire 
1 cm in cross-section, S is also the niimber of kg which one cubic 

decimetre of the pipe wall weighs, and is therefore the number 

S 
of cubic decimetres irliich can be suspended from a square centimetre. 

17e call it the specific tensile strength and designate it as Z. 

Therefore 

V i _i_.-2. . 



- 68 - 



The relationshipe are very similar if, instead of the pipe open 
at both ends, ire have a closed cjlinder, as long as the latter is 
only so long that ve can ignore the conditions at the tvo basal 
surfaces in coaparison to those at the shell surface. 

Here, there is an additional tensile stress directed longitudinal- 
ly since the inside pressure seeks to force out the tiro basal surfaces 
and since this stress continues throughout the vhole cylinder jacket 
from one basal surface to the other. This stress is half as great 
as the stress at right angles to the axis. If the basal surface 
equals r^.TTom^, it is pushed out with a force of r^.'TVp kg. This 
force is evenly distributed along the -whole jacket. Therefore, 1 cm 
of the jacket must carry 

r^'.'tr.p : 2.r.'tt= »r,p kg (14) 

whereas, as we saw, the cross-stress amounts to 

r.p.l J 1 ■ r.p kg 

As is well known, in metal sheeting, two tensile stresses acting 
at right angles to each other influence each other but little, 
and if the sheeting is strong enough to stand the stress of the 
stronger force it can also absorb the stress of the wealcer force. 
In other words, the sheeting need only be so thick as to send the 
stress at right cuigles to the cylinder axis, which is as strong as 
is indicated by formula (iS). Formula (l3) applies likewise. It is 
interesting to note that the length and the diameter of the cylinder 
cancel out. The ratio of content to wall weight (with sufficient 
length) only depends on the material and the inside pressure, being 
directly proportional to the specific tensile stress and inversely 
proportional to the inside pressure. 



- 69 - 



Similar considerations can be undertaken for spherical containers. 
If ve piunp water into a rubber balloon between tiro solid hemispheres 

(cf. Figs. S9, 30), they are likewise forced apart just as the 

2 

cylindrical surfaces earlier, by a force namely of r .TT.p kg. 

If a hollow sphere is to be split along its longest circumference, 
a force of 2.r.Tl'.d kg is required. The sphere will hold together 
as long as 

r^.p<2rtT'd.z 

or 

r.p 

d > . 

* 2z 

The sphere will hold -*-.r'*\t'g of water and the hollow sphere 

3 
itself weighs 4,r' ."TT.d.S g. Accordingly 

4 4 r.p 

V =. .r^VTs 4r2'^.d.S < .r^V: 4r^tr. .3. 

3 "3 2z 

Therefore 

S 1 

V < —.-2 

- 3 S P 



or 



Z 

V <66.7. . 



So, with the sphere also, this ratio is independent of the size 
of the container and is only directly proportional to the specific 
tensile strength and in Tersely proportional to the inside pressure. 
It is better than with tlie cylinder because here the wall need be 
only half a.:: thicjc. 

This will surprise those who have never heard of curvature or 
normal pressure. At first sight (cf. Figs. 29 and 31), a spherical 



- 70 - 



zone A B appears to have the saiue properties as the jacket of a 
cylindrical disc. In order to force out a piece of the spherical 
vail, shall ve say, at B, not only oust the resistance of zone A B 
be overcome, as with a cylinder, but also that of zone C D. 
The two stresses are perpendicular one above the other; therefore, 
the sheeting at £ need be only as strong as a single one of these 
stresses would require. These stresses act as tiro ropcn slung 
about a bundle at right angles to one another (cf. i.'ig. 32). The 
cylindrical surface, by contrast, acts only as a single rope (cf. 
Fig. 33), The strain on it is naturally twice as great as that on 
one of two ropes. 






Fig. 31 



Fig. 32 



Fig. 33 



If, on the other hand, we were dealing with a saddle surface, 
it would be as though one rope were pulling up and the other down. 
Therefore, the carrying rope would have to be stronger than if the 
other were completely nissing (Fig. 34). If, finally, ve have 
surfaces which are arched toward the side of pressure, these are 
held entirely only by the stiffness of the zuaterial and can therefore 
not be nade of thin sheeting. Saddle surfaces and recesses should 
be avoided, if possible. A very special advantage of model C is the 

fact tiiat its pump chambers F^ 4(cf. Fig. 17) con be built almost 

spherical. 



- 71 - 




Fig. 34 



'7ith a cylinder closed by 2 heaispheres, the content ratio 
(provided, naturally, that the -wall is as thin as possible) is easily 
calculated and -will, in general, be between that of the cylinder 
and that of the sphere. Calculating the content ratio for conical 
containers or containers of the form of an oval rotating body is less 
easily, although it likeivise lies between the figures for the 
cylinder and the sphere; the limiting case of the oval is represented, 
on the one hand, by the cylinder and, on the other, by the sphere. 
A cone can be thought of as composed of zones of ovals. (For teclinical 
reasons, it vill admittedly not be possible to raalce the -wall (Fig. 
35) as thin as possible everyvhere vlth any type of material. 
Fortunately, however, it is relatively easy exactly with copper and 
lead.) 




r-, Xirv-i ; <V«. ^\ ^v 




Fig. 35 



Pig. 3G 



- 72 - 



Containers of the fona ahovn in Figs. 35 and 36 and schematized 
in Fig. 37 and 38 as well as related forma still occur in my rockets. 
Here, troughs a and b, Joined to each other would result in complete 
cylinders. For these, we have already calculated V. If they are to 
be shallower as in Figs. 35, 36, and 39, they must naturally be 
put under greater tension and necessarily be made thicker and heavier. 
Each of the metal braces c must stand the tension exerted by the 
inside pressure p on a rectangle which is as long as the troughs 
and as wide as the distance between trough axes. In Fig. 38 that 
would be 2.r, and the whole force would be 2.r.L.p. If z is the 
tensile strength of the material per cm^ and s its specific weight, 
then a cross-brace of length c weighs t 

S.r.L.p.S.c 





Fig. 37 



Fig. 38 



Of the liquid not contained in the troughs, each cross-brace 
must bear a parallelepipedon-shaped volume which a S.r.l.c. Here the 
relationship between volume and weight of material is 

2.r.L.c Z 

V < — « . (15) 

" 2.r.L.p.c.S/z p 



- 73 - 



That is less than irith a sphere, but ve are here not dealing vith 
a closed form. If we wanted to close off the tank -ire would have to 
attach ivlres or plates d at right angles to these braces (as indicated 
in Fig. 40) or we would have to put the walls under so great a 
tension (cf. Fig. 39), as I have done, that the whole thing is held 
together thereby. In the first case, the ratio of content to mass 
would be half as great as with a cylinder. In the second case, the 
radius of curvature of the trough axes grows; hence its walls become 
thicker and the wall weight becomes just as great as with a cylinder. 
The exact calculation is done with the use of normal pressure and 
the consideration that, at best, the curvature axes of the troughs 
lie in the central plane. I cannot go into greater detail here. 
The layman can well-nigh grasp the situation if he visualizes the 
following : the cross-wall d of Fig. 40 has been cut into 2 leaves 
and such a leaf has been welded on top of each of the side-walls a 
and b for reinforcement. 





Fig. 39 



Fig. 40 



Finally, in Fig. 37, the ratio is just as great as with a simple 
cylinder for the following reason. 



The outer wall lies on a larger circle and therefore has a greater 
surface. It must endure greater pressure and must be made correspondingly 
stronger. The layman will understand that if he imagines that the 
cross-wall d in Fig. 40 has been removed and placed around the outer 
wall of pipe t as reinforcement. 



- 74 - 



With the toroid (e.g. irith the circular pump chamber of models 
A and B^ cf. Fig. 15), the ratio is also just as great as vith a 
cylinder. The layman vill understand that if he imagines the cross- 
baces c in Fig. 37 to have be«i cut through and one half laid over 
the upper vail of pipe t for reinforcement and the other over the 
lover wall . 

What should especially be avoided is putting a shearing or bending 
strain on the material. (By contrast, compare VALIER'S rocket oven, 
Volume 8.) With n^ forms of construction, the stress on the material 
is vell-nigh only that of traction (except irith model B, vhich, as 
I already vrote, I actually do not want to build). 

'(Vhat will surprise the layman most in these calculations is the 
fact that, in the ratio of content to wall weight, all absolute 
measurements (length, breadth, height, wall thickness, etc.) cancel 
out. Beside the specific tensile strength Z and the inside excess 
pressure p, this ratio V only depends on the form of the container. 
It can be expressed by the formula 

Z 

"p" 



^-^'-r- (16) 



at trhich k is a definite form factor. The most favorable form is 
the sphere, followed by the oval and conic forms, and then the 
cylinder, toroid, and mattress forms. If possible, other forms should 
be avoided if as much liquid as possible under a given pressure is 
to be put into a light tank. All this applies only if the wall is 
nowhere thicker than necessary, which is especially hard to achieve 
with a toroid. 

In teclmology, the material may never be strained to the breaking 
point. For example, with iron bridges, the material is taxed at the 
most to 1/5 of what it is just expected to be able to carry. Even 
with aircraft and wire conductors, l/3 of the actual limit of 



- 76 - 



resistance is seldom exceeded. The thinner the piece, the closer one 
can approach the limit of resistance; for example, the barrel of 
hunting rifles is sometimes strained to half of its tensile strength, 
similarly heating pipes and telephone vires. 

In my uniaanned rockets, I iroald strain the material up to half 
of its tensile strength, irith the manned rockets up to l/3, V^ith 
model B, I have strained it up to l/3, in order not to estimate too 
favorably. Tliat -will be sufficient, for l) in the main, we are only 
dealing with thin metal sheeting and 2) the rocket is only -working 
for a few minutes. Therefore, with cylindrical pipes and cylindrical 
forms of construction 

Z Z 

V = up to . (17) 

6p 4p 

V/ith spherical containers it would be 

Z.2 Z 

V = up to (18) 

9.p 3.p 

This shows how important it is to have Z as large as possible 
and p as small as possible. As stated, this ratio is observed for 
all tanks of ray rockets, no matter how large their absolute size 
may be; I hope I will no longer be reproached for not having calculated 
the ratio for all tanks. The fact is : if I have calculated it for 
one container, I can directly substitute the respective figure in 
the calculations for all similar containers. 

Here, I would also like to/say something regarding the ratio 

between the weight of the contents and the wall. If the specific 

weight of the contents is , then 

Z 
V^=k.---.5. (19) 



- 76 - 



Naturally, — — becomes larger, the larger V^ j therefore it is 
good to use specifically hea'vy propellants. 

A few words about gas-filled tanks t In general, they should be 

avoided in a rocket, for their content is specifically light. Other 

p 
circumstances being equal, irith a gas -^ > R, at irhich R is a 

constant figure. Therefore 

R Z p Z 

<S ■ — - and Vj. « k.— . — ■ k, — . 

P ^ P R a 

Taken precisely, this fommla naturally only applies if there 
is no atmospheric pressure outside, for, under normal conditions, 
the pressure of the atiaosphere helps to hold the gas together. 
If either the inside pressure is very high or the outside pressure 
above the earth's atmosphere equals 0, it can actually be ignored 
and then V is entirely independent of the inside pressure p; then 
it only depends on the temperature and the choaical composition of 
the gas.- I frequently receive letters advising me to talie gaseous 
hydrogen instead of liquid hydrogen; I should compress it thoroughly, 
then it vould become specifically heavier and the veHl relatively 
lighter because it vould no longer have to cover so large a volume. 
In reality, the situation is rather -worse with high pressure, for 
then the compressing force of atmospheric pressure is not as 
effective. It is therefore best to liquify the fuels (if necessary, 
by means of low temperature) and, at launching, make it a point 
to leave little space unfilled irith liquid. 

The finimess of my machine is mainly based on the excess inside 
pressure, similar to the firmness of a thigh tly-fil led balloon. 
I based its calculation on the formulas theoretically set up for 
rigid filling and checked my calculations experiaen tally by encasing 
thin-walled rubber balloons in canvas sacs of a certain form and 



- 77 - 



testing the trliole on the apparatus shown in Fig. 41. A was a l-cm-vide 
glasstube vhich also served as a pressure gauge. B is a funnel and 
C a rule suspended vertically by cord D to indicate the water level. 




Fig. 41 

E is a perforated cork stopper. F is the sac. The rim of E is sealed 
with tallow or vaseline, F is inverted and filled with water. Then 
E is stuck into F and bound tight. The whole is turned over, pressing 
together B so as to fill A with water. Then water is poured through 
B to give the whole the necessary tension. H is a glass pipe with 
a squeeze tube through which water can be drained from F or air 
blown in. G is a piece of dried clay which fits the point of F. 
A board I is glued on top of that, on which additional weights K can 
be laid. 



It is clear that the firmness of the apparatus and with it the 
inside pressure p must be the greater, the higher the air resistance. 
This is mainly the case in the lower air strata, as I will show 
later. If, however, it is possible to lift an apparatus (say, inside 
an air-tight protective jacket) high enough before it is made to 
operate, the inside pressure in the apparatus itself can naturally 
be lower and the ratio between mass and content can be larger. 



- 78 - 



Chapter 8 

The Most Advantafyeous Velocity 

(This Chapter is intended only for the specialist, with the exception 
of a few passages.) 

Poriaula Quantities of Chapter 8 

b : actual acceleration 

b^ : ideal acceleration 

c i speed of out-flow 

e : base of the natural logarithms 

g : acceleration due to gravity with altitude s 

go t acceleration due to gravity at earth's surface- 
fa : altitude above earth's surface 
m : respective mass of rocket 

mg : initial mass of rocket 

m^ I final mass of rocket 

q : loss in propulsion 

r : loss in acceleration 

Tq i radius of earth 
s-s I distance covered 

V I actual velocity 
t : time 

Vg I laost advantageous velocity 
v J ideal propulsion 

V : most advantageous velocity for s and ds 



- 79 - 



Vq t most advoatageous velocity at start of flight 

Tj^ I most advantageous velocity at end of flight 

F t largest cross-section of rocket 

G : force (in kg) by -which the weight opposes acceleration 

h' I constant -i- =. (-i- - -?- ) 
H H '' 

H : altitude at trhich the barometric pressure decreases to 
the e-th part 

L i total air resistance (in kg) 

MjTK^: masses of tiro-stage rockets 

P t total force of rearward thrust P ■» 2 + R 

J2 t propulsion-obstructing force Q = P - R 

R : the part of the rearward thrust serving to accelerate the 
rocket R >= P - 2 

S « H .coseco^tdistance the rocket must traverse in order to 
rise U kilometres 

^ : angle at which the rocket rises 

Q t air density 

^ Q > air density at place of ascent 

O I resistance coefficient 

yU t mass of top part of a series of rockets 

Vtt had 

m.dVjj. + c,dm = /cf. (4)/. 

IVe are considering a rocket that is ascending within the atmosphere. 
Here air resistance and the force of gravity oppose upward accelera- 
tion. Therefore dv S dv, let us say 



- 80 - 



/dvj/ - /dv/ + /dq/ 
6md 

hi = /v^/ - /q/ /cf. (8)/. 

If the force that opposes the ascent is designated as Q^ then 
obviously 

and if ire not that Q acts in a backirard direction, it must be given 
a negative sign, 

/dq/ . -8-,dt. (20) 

For every rocket there is a definite velocity (l will designate 
it as v) at irhich q becones a ninimum. Namely, if the rocket flies 
too slowly, it must overcome the force of gravity for too long. 

For example, if w© let the rocket bum fast enough to just 
keep it suspended, then it would eject gases downward for a few 
minutes and, after its fuels were used up, would fall to the ground 
at the some place. Thus it would have effected nothing. The faster 
it flies, however, the more advantageous the utilization of fuel 
becomes from this view-point. The fuel utilization of a rocket 
depends only on how long and how fast it has burnt, whereas the 
work perforued on the rocket by the rearward thrust obviously depends 
on the distance the rocket traverses during the burning, for work 
equals force tines distance. It folliws from this that the satie 
quantity of fuel will obviously perfona the greater work on the 
rocket, the faster it fliea even while burning. I will give further 
details in Chapter 12. 

il^'ain, if we fly too fast, the air soon opposes the rocket as an 



- 81 - 



impenetrable wall. The air resistance increases as the square of the 
velocity, while the operation efficiency of the fuels only increases 
as the first power of the velocity. V/ith regard to the air resistance 
it would be best to fly slowlyj with regard to the force of gravity 
it would be best to fly fast. A comproiaiae between the two requireaents 
is possible; there is a velocity at which the suu of the retardations 
q becomes a minimum, which is the uibst advantageous velocity v. 
V/e can find it by the following method t 

We imagine a rocket traversing a layer of air of strength dh in 
a straight line at any velocity v at on altitude h above the earth's 
surface. In so doing, the moment of the rocket is to increase by a 
prescribed amount /m.dv/. Naturally, it suffers a loss in substance dm. 

As soon as the rocket has passed through, we fetch it back in 
thought, replace the fuel dm and again let it traverse the layer of 
air dh at a somewhat varied speed v +^v. In so doing, the fuel 
utilization will obviously be somewhat diffirent, if the angle of 
ascento^, dh, and /m.dv/ are to remain constant. In thought, we now 
vary v still more and look for the velocity at which dm becomes a 
minimum. 

From (8) and (20) follows t 

Q 

- dv^ + dv + — — ,dt = 
3c m 

or 

- mdvj + m.dv + 2 dt = 0, 
and since according to (4) 

— mdv^ « c.dm, 

we get 

cdm + mdv + fi dt - 0. (2l) 



- 82 - 



Not 

dh 

dt (22) 

v. sino^ 

Bjad from (2l) and (22) follows t 

a dh 

cdm + mdv + -~-,— — ■> 0. (23) 

V sincA 

c is uov constant. According to our conditions, dh, sine^C., and 
/m.dv/ must likewise not vary. Therefore 



^ W dh ^ r Q 
c. + . I . 0. (24) 



^dmj dh a r a 1 

+ . . 0. 

dv sinoC ^v *- V -J 



Obviously, dm becomes a ininicium if 

^ dm 

^ V " ' 

In this case, the fol loving oust also apply t 

A. [±1.0. (25) 

^V L V J 

Now, fi consists of two forces, the amount L, by which the harmful 
air resistance seeks to stop the rocket and the amount G, by which 
the weight opposes acceleration. If g is the acceleration due to 
gravity which, for the sake of convenience, we will regard as constcmt 
within the atmosphere (one can calculate more exactly, but that is 
not necessary under present conditions; cf. pp. 101-107), then the 
weight of the rocket is m.g. If the rocket rises at an angle «^ , the 
weight, like a load on an inclined pleme, breaks up into the two 
components, m.g.sin^Cin the direction of ascent and m.g.coso^ at 
right angles to it. 

f\irther calculation will depend on what we assume concerning o^ . 



- 83 - 



As ve shall see in Chapter 11, certainty of reaching the mark 
is greatest trith automatic control if the rocket observes a straight 
line course, that is if o^^ remains constant. In this case, the component 
m.g.coc^must be compensated for by making the axis of the rocket 
point upvards more steeply than irould correspond to the direction 
of flight; ve irill call the angle between rocket axis and flight 
direction^. — Setting the rocket on a slant in this iray causes a 
loss in propulsion, for nov the rearward thrust will no longer act 
in the direction of flight with the impulse c.dm but only with 
c.dm.cosot Since, however, cos(( is very nearly 1 and the uncertainty 
in determining c is greater than 1 <- cos^ , we can ignore this 
loss, the more so since there is a gain sin^ .c.dm/dt opposite to it. 
For the rest, setting the axis on a slant will bring about an aerodynamic 
lift which is supposed to just cancel out the component m.g.coscA.- 
sin^ .c.dm/dt with flight in a straight line^connected with this is 
a drag k.m.g.coso<^. Just now, the Aerodynamic Institute in GSttingen 
is conducting systematic exi^eriments concerning the ratio k between 
drag and uplift with supersonic speeds. IJr. SCIIEHSCHirVSEY will soon 
begin another type of experiment in Berlin. On the basis of observa- 
tions on projectiles, however, we can already say that k will be 
approximately 1/3 to l/6. Therefore 

G *= m.g (sinc7(>. + k cos<A). (26) 

The harmful air resistance is given by the formula t 

L . Fy^v^ . (27) 

Therein F is the largest cross-section of the rocket, V is the 
ballistic resistance coefficient. 

The form of the rocket, especially the tip, resembles that of 
the German S-projectile, for which y (according to CILiNTZ and BECKER) 



- 84 - 



^ has the following curve t 



— I— 

ISO 



Fig. 42 

The absolute magnitude of "V does not interest us as yet. Up to 
300 m/sec, v* is approximately constant; as the speed of sound is 
reached it rises rapidly to a maximum of 425 m/sec (ca 2.6 times the 
figure for subsonic speeds) and then asymptotically approaches a 
figure about 1 l/2 times as great as the figure for subsonic speeds. 
- ROTHE, K'UTFP, and O.v. EBKRHAKDT, among others, obtain similar 
curves for artillery missiles, SIACCI as average for various projectiles. 
Other authors arrive at this curve on the basis of theoretic 
considerations. 

Now, why doesV first increase and then decrease? 

The increase between 300 and 400 m/sec is simply explained. If 
the projectile moves slower than sound, the compression of air in 
front of the tip can be equalized t 

1) by the air flowing off on the side; 

2) by an equalization taking place toward the front by virtue of 
the elasticity of the air. 

If V is greater than the speed of sound, only a flowing off on 
the side is possible, at which compression of air in front of the 
projectile naturally increases. The effect of air compression, the 
pressure, is proportional to the square of the velocity with subsonic 
speeds, on the one hand, as well as with supersonic speeds, on the 
other. 



- 85 - 



Behind the projectile, a rarefied air space is created. Its 
effects (the undertow) at first also increases as the square of the 
velocity, but at the speed of sound ' it reaches a limit, for the 
air behind the projectile cannot be rarified farther than to an 
absolute vacuum nor can it strike together behind the projectile 
faster than Tvith the speed of sound. Therefore, at high velocities, 
the undertow as a constant retreats more cmd more behind the pressure, 
as a result of which the expression 

pressure + undertow 

asymptotically approaches the value 

pressure 

F.^ .v2 

With the burning rocket, there is no undertow at all, since the 
space behind the rocket is filled by the exhaust gases. y takes a 
course similar to that indicated by the curve in Fig, 43, 




ifoo eoo 800 

Fig. 43 



At first it is constant, rises between 300 and 400 m/sec, and 
above this velocity becomes almost constant again. Below 300 m/sec 
and above 460 m/sec it con be replaced by a constant figure, and 
in the interval it con be interpolated by the central section of a 



' More exactly, somewhat above it, about at 400 m/sec. Namely, the 
air beside the projectile is to a certain extent propelled forward, 
with reference to which v appears smaller. That is why there is a 
steady and distinguishable, not a sudden transition. 



- 86 - 



parabola of the third degree. Nov, vith good rockets, y^ > 500 m/sec 
mast be true (cf. p. 112). Henceforth ve can consider Y* as & constant 
figure. 

^ is the air density 

Since 

Q L G 

taking (26) and (87) into account, this follovs from it i 

V '*^ • 9 (29) 

According to our conditions, must not vary (ire are dealing 
vith a cooiparison of various values of v on the spot. Hence, in this 
consideration, the air density dependent on altitude oust remain 
constant). Therefore 

.al.[f]"^'''^"^^"^"'^*"°'*^' (30) 

an expression vbich obviously equals if 



In this case 



G . L - -— 
2 



" FvB 



(32) 



Lately, it has often been suggested (VALIER, GAIL, and others) 
that a rocket vould rise higher if it vere provided vith lifting 
surfaces and made to ascend under a small angle o^ . In so doing, 
becomes small and hence L could also be small. That can be 
eountered by saying i 



- 87 - 



According to (20), the loss in propulsion is 



|d?l = 



dt = 



Q dh 

m psina 



now, the most advantageous velocity for every angle ^ is v. Tfith 
other velocities the rocket only fares worse. Therefore, if, 
according to (32), Q is replaced by 2 G and v from (3l) is sub- 
stituted ve have : 



I dqmln I 



2 m g (sin x + kco3 a) _ __ ^' 

m n/ wg(sma"+Tco5a )^.^^ 



f 



Fyp 



or 



dh 



jFy fg Vsin g 4- fe cos g 



sing 



This expression obviously indicates how great are the losses 
in velocity dq during penetration of the layer dh, and it shows that, 
with the most advantageous velocity, it is smallest when Ji, = 90*, 
for then 



Vsin g + A cos « . 
zrrz = 1. 



sin a 



whereas othertfise 

Vsin a. + k cos « Vsina 



sina 



> ' . " = Vcoseca > 1 . 
sin* 



(it casts an odd light on the capabilities of VALISH, who is the 
intellectual originator of this idea, that he still has not grasped 
this even today, although I already derived it for him in this 
way two years ago.) 



A rocket cuts off somewhat better if it starts to ascend steeply 



- 88 - 



and is gradually drawn more into the horizontal direction by the 
force of gravity, but, considered only from the standpoint of penetra- 
tion of the atmosphere, this ascent is not as advantageous as the 
vertical one. In the section on the "synergy curve", I will discuss 
this in detail. Namely, then the term at G, k.m.g.coscA, drops, 
which is conditioned only by flight in a straight line, and 



Q =Fyfi(>'i^+ wgsina 



and 



--f 



'mg sin a. (31a) 

Fyfi ■ 



A mathematical analysis of this formula shows that here also 
Q ■ a.G, but it is smaller than with straight-line flight because 
here G is smaller. Besides, it is an advantage not to be under- 
estimated that exactly at the beginning, in the air of greatest 
density, the rocket ascends much more steeply than it is supposed 
to fly after the burning has stopped. Considered from the standpoint 
of range, this type of ascent would be by far preferable and it is 
presumed that it will generally find application with large machines. 
As was said, for small apparatus it requires too complicated means 
of control. 

Note s V is the most advantageous velocity at location s when 
it is simply a matter of cutting off well at this location; but v 
need not necessarily be the most advantageous velocity when the 
ascent as a whole is being considered. 

V/e shall let v^ be the value of v at the start of ascent at 
altitude s. The rocket is to obtain this propulsion through a foreign 
force. V must be so great and the loss in substance so small that 
the outside air pressure^ and, with it, L decrease faster than 
the weight of the rocket; then v will increase, let us say, until 



- 89 - 



the rocket reaches velocity v. at altitude s. If the fuels just reach 
to s^ and Vj^, it can be shovn by indirect calculation that the 
rocket vill rise the highest, let us aay to BQf if at s^ it flies at 
y^ m/sec. If it reaches t^ earlier, the greater air resistance beloir s^ 
retards it to the extent that it no longer has velocity v^ at Sj and 
as a result cannot reach Sa, If it does not attain velocity v^ at s,, 
it must overcome its oim -reight for so long that it liketrise does 
not get to s„. 

If Vq , s, , and v, are given, the most advanteigeous velocity v 
between v^^ and v^ is defined by the fact that (cf. p. 80) 

J P-dt{v,) =j'R-dt +J Q-dt =^/m-dv. + jQ-dt 

Uo to to Co u^ 

must become a minimum. In so doing, R ■= F - fi is to designate the 
force trhich supplies acceleration to the rocket, that is the portion 
by vhich F is greater than Q. 

^ov, i Q«dt is a minimum with velocity v since then all i2><lt 
become minimum /cf. (23) and (25)/; on the other hand, m.dv is a 
minimum vben the acceleration is zero to begin trith and only makes 
up for the default after a good part of the fuels have been used up 
in overcoming gravity and air resistance. The effect of this is that, 
in the lower part of the way, v stays behind v, then keeps the 
difference constant, and at s^ suddenly reaches v again. "^ " '^g ^''^ 
be found by indirect calculation as a function of s. For example, 
in the case v^ = 500 m/sec and atmospheric conditions, the maximum 
difference is 200 m/sec (for v^ = 8000 m/sec). It becomes the smaller, 
the larger c becomes. If v increases, it decreases relatively and 
increases absolutely (for example, in the above example, for 
VI = 10,000 m/sec, it would be 850 m/sec). 

Now, the discepancies in my calculation are considerably greater 



- 90 - 



(mainlj ;>ecause I have not taken c accurately enough, and could not 
have done so at all in that way). A further deviation from v is 
conditioned by the technical conditions. That is likewise greater 
than V - V , although it does not interest us in the purely 
theoretic part. 

Therefore, I base uy derivations on the case in vbich the velocity 
everywhere equals v, for then the foroulas becoKC ecpecially simple. 

17ith straight-line ascent, frc»-i (21) yrc get 

In m •= ln(^y) + ln/9 - In [g{um + Jfcco« a)] +. 21n i^. 



(33) 



The air density p (after the atmospheric conditions such as 
teciperature, -weether, and the like are given) is simply c function 
of tLe rltituc'e s (s c J r.dt). 

Fox" the u;iper uir strcta we do not know p exactly, nor do ve 
need to know it exactly, as I will show later. For the lover cAr 
a-li'cta, /? ecu be calculated quite accurately from barometric altitude 
fornulas given in textbooks on. meteorology. We find, hon-ever, that 
■we would get unsolvable integral equations if T.e used these foruulns 
directly. Hence, we uuet resort to indirect calculation. We set 

. &««W«e'^- (34) 

Therewith, e is the base of the natural logarithms and H a 
distance which, at first apprc:;iination, we can set as constant e-nd 
equal to 7.5 km, S = H cos ec</\. Therefore 



- 91 - 



ln|8..1n^o-A 



ana 



or Tby differentiation of (SsA 



7? 



Furthermore, from (.""jS) foil ova i 

Not, according to (32) and according to (A6) 

^ = 2g(8ur(>i + icosa) . . 

m (Ml 

and from (36), (23), and (35a) it follows thai 



' /ifc , 2rf^ , ij ■ 2-g(giira + ftco3a) dk ^ 



or if ire note that 

dh s v.ainol^.dt 

and that Htsin<<<> S is nothing else but the distanco thai SM«i 
be covered for the atmospheric presaure to drop to tho avili pari 
of its original amount, and if, finally, ve eall iha aBWMi kgr vlllall 
the rocket is retarded in one second by air raaiaiaaea ar hgr gravltgf 

(they are equal) the follotring t 

g (sin^+ k cos «k ) > r, 
then this formula can be vritten i 

A + i 
dt__ c V 

5 c 



- 98 - 



From thtity by integration^ ve can find the connection between 
the most advantageous velocity and the time t : 



.-(^7)'4^4-7'"s- (3S) 



Note i When calculating irith the slide rule, one is advised 
to construct : 




then 



V : — -ii 17 c 



,_^, = 2,3026. 

If in (38) we set 

Vq.c - 2.r,S , 
and if 

^T^^o ' 
then t becomes infinite. For v = v^ , t becomes indeterminate. That 
neons the folio-wins s The air density decreases to the extent that 
the rocfeet advances upward. But the weight of the rocket likewise 
decreases as a result of loss in mass. Three cases are possible s 

1) lyhen Vq.c = 2.r.S, the weight decreases just as fast as the 

air density. Now, v^ is given by the ratio of the ballistic coefficient 
to the air density Tcf. fomula (12) | . But here this ratio remains 
constant and therefore the figure for the most advantageous velocity 
also resnaias constant. 

2) V/hen v^.c ^ 2.r.S, t can be positive only if v ^ v^. 

In the first case, the rocket cannot advance beyond the earth's 
atmosphere because fory$ = the rjass of the rocket would also equal 0. 



-ga- 



in the second casCi it can do so still less because then the velocity 
even decreases with the tiue. (For this i-eason, Yi\LISIt'S rocket 
aircraft, for example, will not fly to Aaerica at em altitude of 
50 Ion, as he hopes, but will not even rise 5 loot and, after their 
fTiels are exhausted, will have to land 20-30 kju froa the point of 
ascent.) Only 

3) ^Vhen v^.c ^ S.r.S, can v - v^ and t be positive at the same time. 
In this case, the amount for the most advantageous velocity grows with 
the time. The reason why the rockets built until now fared so badly 
lies in the fact that this circumstance was unknown among experts and 
that, in all these machines, v. c was much too small. A machine that 
is to advance beyond the relevant part of the earth's ataosphere (ca 
50 km) must be at least 5 m long. Besides, with these apparatus, 
too little attention was paid to the form. There was too much air 
resistance. 

I have included these theoretic considerations mainly in order 
to disperse the bias that these failures have caused among experts. 
Furthermore, I wanted to give the examining expert a few mathematical 
clues so that he night more easily evaluate what I have to say in 
the sequel. Since we now have formula (38), calculating the remaining 
formula quantities presents no more difficulties. 



The ideal propulsion of an automatically-guided rocket flying 
in a straight line at the most advantageous velocity amounts to i 

Vj - V - Vq + 2tr. (39) 

According to (6), the ratio between the full and the empty 
rocket is 

"1 



- 94 - 



from vhich foil ova t 



T_ = c.ln--- 
X mi 



(39b) 



From formulas (38) to (39b), one also finds the mass that is 
used up vith this form of ascent. 



Noir, according to Chapter 7, cannot increase indefinitely. 



m 



Hence, irith a kerosene or alcohol rocket, v^ will at the most equal 
4 km/sec, irith a hydrogen rocket at the most 7 km/sec. V/e can resolve 
the problem in the following way i 

After a rocket has burnt, it flies 4-7 km per second faster than 
it flew before the burning. On p. ^^S®"" rocket, instead of the pay- 
load, I now place one that is teu tiues smaller. When the fuels of 



m, 
<»1 



















































^ 











1 








^ 


^ 






--■- 








^ 


-^ 



















^ 


^ 











d 


^ 


^ 























.,.. 


'-—' 


— - 


— - 


- — 










— 
















^ 


1 


; 




; 




i 






i 


■ 






i 


Mm. 



Fig, 44a. 

the larger rocket are used up, the whole could have a velocity of 
4 km/sec. If I now drop this rocket and let the upper one continue 
working, its own velocity is obviously added to the velocity to which 
it was brought by the lower rocket. Thus, by placing rockets one 
on top of the other, we can achieve high final velocities without, 



- 95 - 



in a single rocket, having to carry fuels 16 or even 1000 times its 
empty veight. In this case ve can speak of an ideal mass ratio, 



►v 




fTtff 



30 



« 



10 



Fig, 44b. 
one equal to the mass ratio that a singl e apparatus -would have to 



,' — 


























,.-- 


'- 


**%, 


c 
















— 


_.—■'' 










« — 












r-^ 


''' 


— 
















y 


v"^ 


^ 




_^ 


— 


- — 










♦ — 

/ 


^ 


r 

y ^ 


7^ 




















>^ 




















































2 ^ — 
























































A-. 


't 








■ 




■ 




i 


• 






J 


^ At 


m 



Fig. 44c. 

have in order to attain the same ideal velocity as this series of 
rockets. We find it in the folloiring manner. 



- 96 - 



From (6) and from (39) ire obtain i 



ln5 = f[5-^„ + 2r(?-/.)]. 



(40) 



If I noir set a number of rockets one on top of the other (cf. 
Fig. 45) so that it is altrays the bottom one that is irorkiug and ia 
ejected as soon as its fuels are exhausted, then the speed limits 
add up . If UfTf^, fX are the masses of the single rockets, then the 
speed limits resulting in succession are 



In 



Af „ + gfR„ + /lo + 



In ?k±£'oJ 



In 



fo + ■ 



Mi + i)h + f'<,-i----' 3)^1 + /'<, + ■•■' """/'i + - 

and the total increase in velocity is obtained hy substituting 

Ml 4- 9Jio + /'o ■ ■ • ^i + i"» + ■ • ■ /'» + ■■■ 



for 



m. 



in 



(40). 



in) 



U 




Fig. 45 



LORIS^Z, for example, should have thought that over! 



- 97 - 



Neuneljj according to (40), 



^1 c c 



Bj adding these equations, ve obtain i 

'"m. + SIR, + /*„ + ■■ -"^ "aj[, + /r„ + --- /<. + •■• 
= \ ■ [(^1 - ^o) + (i^ - ?x) -f (p, - ''.); + ^ [ih - «o) + («, - «i) + («, - «i)i 



or 



If a single rocket Trere to have the same performance, according 
to (40i the foil owing -would have to be true of it t 



nil c *• 

""o 
A comparison of (42) and (43) shows that -"— is as large as the 

product of all the single mass ratios. In this connection, also 
compare p. 61. 

From (41), this follows J 



(43) 



("i - "o) = ' 



ln^;-2r.(, -.„)], 



i.e. the propulsion v - v becomes the greater, the greater c or 



"•o 



, or the smaller (t^ - t©) becomes. 

Now, c is limited and the mass ratio in a rocket can likewise 
not exceed Vq. (cf. p. 76), The product of the mass ratios, however, 



- 98 - 





+ 
+ 

re 


• • « 

• • • 




+ 
+ 


• • • 

^1 


-^0 


> 


"»0 



•Ml b«eMM •« larg* «• iLs deaired and vith it {vi - t^) also. 

F«r ikf «••• in vhieb r i» not observed, the advantage of partiticm 
is ttl«9 vbviMls iff it ia r«o«abered that less dead material is toted 

Vi 

•iMig tlwi V«gr* Ns|arall7f here too, can become as large as desired. 

Th«s« e«a«idM'«tions «ppl7 ^^ ^^^ ideal propulsion v^ and therefore to 
Mgr «jp« vff Micciit. 

It Misi b« r«i«ab«r«d| hovever, that 

nA thai thia aspraaaion already grows with reference to 

c 

•ttmr tba oatuiar af tha axponantial curve. If the most advantageous 

valaaitgr ia aat fvan abaarved^ tbe loss in substance is naturally still 

(raatar and «• aoan eooe to quite impossible figures. There is a liait, 

fia«ll7f ffar wt* tfith pftrtitim, it would be advisable to make each 

raakat lurgvr tha* 9dl tlioaa above it together, otherwise the auxiliary 
mppvnkima siada uatmtauj hy the partition would weigh too much. For 
•saHpl«f vitll iMdala B and £, each rocket oust, among other things, 
iMVf • aaparaia propalling apparatus. 

fbm ajaaiiag of tha aupty fuel tanks with model C works in a very 
•inilar vagr* Far U^ va anst bara substitute the mass of the whole 

hiaa ia tha fillad atata. il^ is the machine with the first fuel tank 
aB^tiaictl^ tha apporataa without the first fuel tank filled;^^ is the 
iMakia* with tha aaeond fUal tank «nptied, etc. As I already said, model 
C ia far variaiia raoaona tha ideal meteorological rocket, but this 

Mm* ia aat aiiitabla for conveying persons. There is, namely, only 
prai^lliag ifiparataay as a result the rearward thrust is always of 
tha »$o» na^itaiai and tha acceleration naturally becomes greater and 
graatar m tha pnaa daora^saa* If persons are to be carried along, the 
•aa^lamtian mat bt aora uniform. 



- 99 - 



Nor is this model suitable as a long-distance rocket, since it 
can only ascend vertically. 

According to (37), the acceleration is ; 

dv V (vc - 2rS) 

b = = . (44) 

dt S (v + 2c) 

The ideal acceleration b^ , that is the acceleration the rocket 
would undergo while burning the soae quantity of fuel in vacuom and 
gravitation-free space, is t 

c v-3 + 4rS 

b = b + 2r = . (45) 

^ S v + 2c 

The force of the rearward thrust P we find to be : 

P = m.bjj = mb + 2rm. (46) 

In the calculation, the mass itself often does not interest us 

very much, for v does actually not depend on the mass itself but on 

P 
the form emd the ballistic coefficient; hence the size of — is 

"o 
more useful for the general discussion. 

P m 
-~-.(b+2r). (46a) 

P 

The quantity -— actually indicates the acceleration which the 

rearward thrust required for observing the most advantageous velocity 
would impart to the initial mass of the rocket. - Here, the right ^ 
side is independent of the absolute nass; like — — , it only depends 

on V. Hence, the values calculated by means of this formula in the 
same way apply to every meteorological and long-distance rocket. - 



- 100 



They are a measure of the rise and fall of the reanrard thrust, for 

P P 

1 2 

•IT- * -^ - Pi I Pg . 

no »»o 

This formula finally teaches us that the fluctuation of the inside 
pressure in the oven resulting from the rise and fall of the reanrard 
thrust only depends on v and c and not on the absolute size of the 
rocket. 



It is fortunate that Irith rockets propelled -with gasoline or 
kerosene the acceleration increases approximately to the same extent 
as the mass decreases. In flight at the most advantageous velocity, 
P is Trell-nigh constant during the -whole burning period, especially 
if the rocket is not artificially brought to on initial value of 
the most advantageous velocity but is made to start under its o-vn 
poirer. 

In so doing, the velocity at first is somewhat lower than the most 
favorable velocity, while the rearward thrust must be somewhat greater. 
The latter retains almost the same value during the whole burning 
period, so that the nozzles can be made to operate at top capacity. 

The distance covered is likewise easily determined. It is 

Si — 5o = J v-dt. 

That can be integrated if, while taking (2l) into account, we express 
dt by V and dv. Then we obtain : 



Jo = 



- . ^ ^f. rS\, v,-c-2rS 



The altitude h reached is : 

h = (si " So)*sin(A. (48) 



- 101 - 



These are the aost important formulas for the oblique, straight- 
line ascent. We obtain the corresponding formulas for rertical ascent 
from fornmlas (38) to (48) if ve seto*.- 90" in them. Then 

sin oC<= 1; cosc^= 0; r = g; S <= Hi 

For example, formula (38) vould then be vritten i 



c , /A, vc- 2gH c, V 

J = - + - In = 7i--fi In--- • 

\g c) VaC-lgH g (-0 



(38a) 



In the following portion of this chapter we vant to consider 
vertical ascent. We could learn to knoir the theoretic principles 
applicable to straight-line rocket ascent just as well with an7 
other angle of ascent, but I shall show its effect in practice on 
a vertically-ascending model and am therefore already basing the 
derivation of the theory on a 90" angle of ascent in order to avoid 
confusing the succeeding explemations, 

We did some simplifying in our formulas and it will, first of all, 
be well to estiuate the limit of error. 

The most obvious error was the fact that I set H as constant in 
formula (34). The actual air density could differ by two or three 
times this amount. 

First of all, I wish to examine the effect of this error with 
high final velocities by means of a somewhat schematized example. 
Let us aim for : 

VI - 11,000 m/sec. 

In so doing, s. - s^ becomes large and, according to (34),^ ^ 
becomes especially erroneous. 

I now set H/^^ h' = 6300 m. That is much too low a figure, and 



- 102 - 



\f P Q was correct, then ^i, certainly becomes fundamentally incorrect. 
At the mcsnent t^, in vhich our observation begins, the rocket is 
already supposed to have attained the most advantageous velocity v 
and the joint effect of the variables is supposed to make v^ = 500 m/sec, 
Then, according to (48) : 



Si — s^ = H 



2gH 



Vi — Vo 



+ (2 + 2gf)ln:^-^ 



Va — 



/ 2 I 

'^e further substitute : g » 9.70 m/sec , c = 3000 m/sec, 



2i£ . ■'-^^^ . m-U - 40.740,„/s«, 






Va — 



In" = 2^026 -log" = 3^7233 , 

^ S 

(2 +^)-ln rV " 2/>1358- 3^7233 = £1,37882 , 



t-o- ^ 



9t- Pq ^ 1^00 ^ 



3000 



3^000, 



Biel used : 



^^ = 3-5000 + 6^7822 = 9^7822 , 
Sy - s, = H" = 6300-9^7822 = 63239^ »». 



log^ = [(?, - 5o)- 0,4343 + 2g-(«i - «o)' 0,4343] - , 



(namely, if (4l) is multiplied by the modulus of the comnon logarithms) 



- _2£^ 
('> - 'o)Q^343 =f Iog--^,-..-H _ '^.log 



IgJi 



g - 2gII f, c '-" 2gH 



- 103 - 



(from the note on (38) this follows) t 



2g// 



- = 30^8sek, 



log 2^'? '^ ^'^'"^ "'■ ^^^^^^ ~ ^^'^^^ °" OJt>3530, 



'"- 



(i, - g- 0,4343 = 309^28 0,03530 + V -137^772 = IQi^lS + 2^93 

= 13^11 sec, 

2 g • " = 13^1 1 • 1 9,4 = 267,93 m/sek , 

(V, - (io)- 0*4343 = 10^500-0^343 = 4560^5 , 

log ^ (4560,1 5 + 267,93) : 30OO = 4828^/3000 = 1 JB09 36 , 

^ = 40,678. 
nil 

At altitude sj, "■ s^ ■< 62,833 m, according to our statement t 

E!>= e " = eW?882 ^ jo''^' = 19330. 

a 

But, as -was stated, P ^ — — — , since H^ 6300 m. For example, if 

19S30 

s equalled 5000 m and s equalled 67,233 m, ^ ^ vould in reality be 

4-6 times as great. i.t, however, I had regulated the velocity of 
the rocket so as, by all means, to observe v (let us say, \ij fk 
mechanism that reduces the exhaust when L > G, and vice versa), 
then vi would have been attained only at a higher altitude end some^ 
what later. The apparatus would have had to combat air resistance 
and gravity longer and would have used more fuel. 

I will assume that, at an altitude of 67,833 m, ^ is not 4-6 
times but 60 times as great as I calculated earlier, which would 
make t 



ihen 



- 104 - 



^^-^ = 2,5I25.1og. (I) 

^^^ 4.2907. log c (II) 



end by division ^^ii i 
(I) 



' ^==3,5863 sec. 
^^ = IV -3.5863 = 6^574 m/set, 



- 2gH 

c, — 

c 



Jog: 2e^ ^ *°^ 10930,426 - log 430,426 = 4.D3864 - 2^3390 

== 1,40473 , 
log(-^) = 1,40473 + 2»C9897 - 4,04139 = 0^06231 , 

ih - «o) -0.4343 = 309,28-0,06231 + 3.5863-1,40473 = 24.309 , 
2g-" = 471.59, 



mo 



log^ = (4560,15 + 471.59): 3000 = 1,67724 (fur H = 10^5^8 m ,) 



^ = 47,560 , 



No-w, (even if -re t^e. into account id-at is stated in p. 365), during 
the ivhole period of propulsion, certeinly 6300 m < PI < 10,759 ei, 



thus certainly 40.678 < — ~< 47-56C. 



If I mite s 

E 

ID 



1 



this figure can in no cat;e deviate from the truth by more than 7,5 %, 
if everything else is cori .^ct. 



- ic-r - 



in ~ (for H = 10759) ^^^^^^^ 



1.0404. 



In -~ (for H . 6300) ^'^^^^^ 



Now, according to (40), In — - is approximatelj proportional to -r— 

The same uncertainty would also have resulted if c were indefinite 
to 2.02 /(. But c is indefinite to jh 7-8 ^ and, besides siostlj fluc- 
tuates by more than 4 % (cf. p. 44). So, today, this estimate for yS* 
is entirely adequate. At high velocities, y^ - v^ is likewise propor- 
tional to — . Hence, according to what has been said so far, our 

" - "o 

most important problem, namely calculating v from — , can, at high 

velocities, be solved to + 7-8 fo with certainty, for the rest of 
the formula quantities influence the relationship between m and v 
only a little. 



The resistance coefficient v can be found fairly exactly from 
measurements of speeds of projectiles up to v = 1000 m/sec. That it 
is constajit from there on is actually only an hypothesis, v.'hich, 
however, is as good as proved by theory as well by the measurement 
of the resistance of bodies moving in water. But even if y for high 
velocities should deviate from this value by two or three tiues its 
amount, that would not change its capacity in performance. Above, we 
allowed the air resistance to fluctuate 60-fold without causing the 
result to be noticeably innaccurate. 

Ti^hen we gave g a constant average value, the error we comnitted 
was still smaller. 

The deeper reason why the result changes so little if we wrongly 
estimate /^ , V » and g for the upper air strata lies in the fact 



- 106 " 



that dt is of the order of magnitude of — — (cf, 37). As v increases, 

dv becoiaes increasingly prominent in comparison to dt. In the dif- 
ferential equation irhich detenaines performance, the increase 

2.dt g 

. 2. .dt 

m.c c 

loses the more in importance, the greater v becomes. But all three 
quantities, /3 ^y , and g, are contained in j2 and, in (3l), occur only 
in this member. 



At low velocities, we would accordingly get much larger errors if 
ire here estimated ^ just as wrongly. But here one circumstance (at 
least with my apparatus) is very important. Since t^ already equals 
50 m/sec, with small v^ - Yo> ^i " 'Bq ^^bo becomes small. Over this 
short distance, H and g also deviate much less from the average value 
and can much better be replaced by constants, by which the result 
(if c were exactly known!) would become still more accurate. 

From all this we can derive the principle for use of the formulas 
that those values must be substituted for H, g, and^ , even if v is 
to become large (further for^ , etc.), which they have in the lower 
air strata. In short t at the beginning, Q must be accurate. 

Our most important task is to calculate the performance, i.e. we 

want to calculate y^ and ~ from iUq and mj. Now, at high velocities, 

^1 

1 

▼, - Vq is approximately proportional to — . Since, todc^r, c remains 

*■ 6 

indefinite to ± 7-8 ^, so the same margin also remains for ▼! - Vq j 

to which must be added a 1-2 % uncertainty connected with^ . On the 
whole, we can today state v^ as l/lO certain. What is mainly in need 
of improvement is our knowledge of the respective formula quantities, 
in particular the exhaust speed. 



- 107 - 



Assuming that the formula quantities have been aecuratelj determined 
b7 experiment, then we could achieve considerable accuracy bj indirect 
calculation with formulas (36) to (48). Bj the use of dm (40) and 
ds (47), ve could make a correction, in case c to a small extent 
depended on L and v. 



To begin irith, we trould somehov have to express ~~— as a function 



of V, 



be 



dm 



Then ve vould have to calculate -— . It is approximately : 

ds 



dm 



— _ ^'^^ 2m-g 



dt, 



ds = v-dt = 



c c 

H ~v + 2c j- 

,-2.g.- 



According to (40) 



According to (47) 



dm m V* -f ig -H 

ds ~ H' 'v(v + 2e) 



Instead of (25), ve obtain t 



dvl 



_ ac OT t>^ + 4gvg _ 

dv'Ji' v-(v-\-2c) ~ 



0. 



(49) 



From that ire could determine v, and irith this value of v 
;alculate t, m, s, and P. Nevertheless, I n^self irould calculate 
^he most advantageous velocity for aty machines by another method, 
or the above procedure is recommended only if i 



( 11 1< ..: 

» ^V ' TO 



1 

7000 



Then (easy especially in the case vhere c is independent of P) 
ie could more accurately express^ and g as functions of s and there- 



- 108 - 



irith more accurately determine the remaining quantities. The formulas 
of the second approximation -would certainly already approach the 
truth to irithin a few thousandths. In the third approximation, it 
would be advisable to divide the increase of v into small sections 
and figure out each section with the formulas of the second approxima- 
tion. In so doing, we could substitute exact average values for c, 
g, s, etc., and afterwards, under circumstances, undertake some 
numerical approximations for the respective section. At the same time, 
we would also have to make the corrections which take into account 
the fact that v "di v . In this place, I would also like to remark 
that I myself have calculated the performance of my machines according 
to other methods. But these methods do not lead to such plain formulas. 

Now we also want to derive a similar formula for ^ . It is 
Taking into account (47) or (40), that results in 



^ = 


= ^0- 


e ' 


/ 
\ 


v — 


2g// 1 
c / 


•(-"c^) 


V 


zJ'.o 
c 


+ 2 


1 


+ g 


^-0 


2gII 
c 




2g/i 
c 



(50) 



(51) 

__ — : :." J- ■) . 1 1 -i- ff " - 1 • In =-.. . 

Svuaaary j 

As we just saw, with the propulsion formulas, the more exact 
approximations can be calculated from the values of the first approxima- 
tion with the help of minor corrections. Since the corrections are 



- 109 - 



so small that they no longer change the essentials of the matter, we 

can use these foriaulas together with the out-flow and projectile fomulaa 

in our discussion of the performance and operation of rockets. From 
them we read off J 

1) If a certain rocket is to pass through a certain thin layer of 
air and, in so doing, receive a certain impulse, there is a certain 
velocity (v) at which there is a minimum loss in fuel. But v is not 
yet simply the most advantageous velocity; rather, that (v..) is a 
small amount less than v, which, however, is of no further interest 
to us here. 

2) From foriuula (49) we read off that v is very strongly influenced 
if the out-flow speed c depends on the rearward thrust P. The formulas 
(25 ff) only apply if c is constant. 

3) We can write formula (3l) : 



m.g 1 

( :^).-_. 



V 



Now, all apparatus are similar, especially their tips, and so y is the 

ra.g 

same for all. m.g is the weight of the rocket, therefore is the 

F 
ballistic coefficient, and we can say i 

The most advantageous velocity for s and ds is solely influenced by 
the ratio of ballistic coefficient to air density (at which weight, cross- 
section, ballistic coefficient, and air density themselves con have any 
value). 

From (38a) _ 2g// 

^^ c 

(since g and II can be considered as constaiit) it follows that {t^ - tg) 

depends on c, Vq, and v^; if c and v© are given, solely on v^. if c 

- . "o 

and vo are given, -^~- likewise depends only on v^. The sane holds 



- 110 - 



for b; — -; (sj - s^); -g~, etc. (^cf. (ll), (4G), (1G), (SDJ. If ue 

coEapute a table coutaining v aa argu ;ciit and 'jhe enuneratod qui'ji titles 
as functions, then this table aolfis for all rocLets vrith v^ aad c 
re^-ardless of how v^ and c cone about, i.e. re^^ardleas of how l^^r^e 
weight, cross-aectiou, or air density are iudividually, or -what are 

the te iperature and composition of tie eiaia'ast cjas, or uoir lar-c • 

Po 
;8o> etc., are individually. 

That is not all : the differGuiial for.iulas still do not contain v^, 
Sq, etc. Instead of basing the inte;jration on v, we could have based 

it on any other value of v., let ua say v^j tlien vro would have obtained 

"a' 

the fomulas for v, - v , a, - a , In , etc. lut according" to the 

b a' b a' »a, ' ^ 

b h 5 ^ 

rules of integration 5 ds = 5 ds - $ dx, that is, the table holds for 

^ ^ c 

all rockets and any fuel, if only velocity v and errhaust s'^ieed c a:;iount 
to I 



If the initial velocity is v aiid the finrl velocity v, , then the 

a 

tine (t, -t) = (t^-t)-(t -t). The loss in fuel follovrs frou 
^ b a' ^ b o' ^ a o 

^^ m u 

In - — = l»i --— == In ---, The altitude a^^ - s_^ = (s,^ - s^) - (s_^ - s^), 





in, m, m_ ' b a b o a o 



etc. b (OO) is not affected by this coJ culi\i.^on, for the acceleration 
I is alrerdy the derivative of t!ie velocity with rar.;?ect to ti'ie. 

For the .=5aT:e of clarity, I have included a table which ;_;ive.o these 
quantities for c = 140C n/ssc, II = TQuO ri. 



- Ill - 



500 

600 

700 

800 

900 

1000 

1200 

1400 

1500 

1700 

2000 

2200 

2400 

2600 

3000 

3400 

3800 

4000 

m/sck 



i — to 

0,0 
7,3 
11,9 
16,1 
21,5 
21,5 
25,2 
27,7 
29,0 
31,2 
33,6 
35,0 
35,9 
36,5 
38,2 
39,3 
40,3 
40,7 



11,7 

17,0 

23,3 

30,1 

37,8 

40,0 

64,1 

84,3 

95,0 

117,1 

153,7 

179,5 

206,0 

234,0 

291,5 

351,0 

414,0 

447,0 

m/sefc- 



log— ■ 
m 

0,0000 

0,0754 

0,134 

0,191 

0,240 

0,286 

0,371 

0,448 

0,486 

0,560 

0,625 

0,735 

0,808 

0,872 

1,006 

1,138 

1,267 

1,330 



mo 
m 

1,000 

1,190 

1,362 

1,552 

1,738 

1,931 

2,349 

2,803 

3,062 

3,631 

4,217 

5,434 

6,427 

7,446 

10,139 

13,74 

18,49 

21,38 



m„ 

31,4 
30,9 
31,4 
31,4 
33,0 
34,1 
35,6 
37,0 
37,2 
37,8 
.41,2 
36,7 
35,1 
34,1 
29,9 
26,9 
23,4 
21,8 

m/set 



For example, if vrith a rocket c = 1400 m/sec, v^^ = 800 m/aec, and 



m. 



•vb = 3000 m/sec, and ve wish to know how large log — — is, we must 

in(500) m(500) 

look up log ~ 



— » and log — — .— and subtract the first from the 
m(800) m(3000) 

°a 
second, log -- — «» 0,815, hence = 6,5, The propulsion would require 

38.2 - 16.1 '» 22.1 sec, etc. 



As already mentioned, this must be true : 



V c > 2rS " SgH, 



We found (p, 93) that Vq must be as large as possible. \Vhen we 
assumed the resistance coefficient (V) to be constant with flight at 
velocity v, we especially arrived at the requirement that 

vc> 2r S 



- 112 - 



or I 

vc >• % H. 

Here it is not superfluous to point outl^according to p. 89) that 
V :jtvg. At such lov velocities, the difference is quite considerable 
Olid, theoretically, the rocket can actually just get to beyond the 
earth's atraosphere if v^.c = 2.g.n, although only with the use of 
fajitastic amounts of fuel. A few 40-60 ra/sec below this figure, 
traversing the atmosphere is entirely inpossible for rockets. 

To be precise, for 330 to 460 m/sec, v is not defined. Since, however, 
we are not exactly aiaing for accuracy here, we can base our calculations 
on the case in which the rocket flies at a velocity at which the air 
resistance becomes equal to the force of gravity. 



m.g 



m.g = v' . Y • P«I^ ; V <- 



Here also, the square of the velocity becomes proportional to the 
ratio ifi. Accordingly, v' and v are directly proportional to the 

F 
root of the ratio between ballistic coefficient and air density. At 

the sa.ie tine, this velocity increases still siore slowly than v above 
460 m/sec, for, because of the considerable retardation (b = b + 2.g} 
3 g is const.mt, b is relatively suall here), the mass and with it 
the ballistic coefficient decrease rapidly, while the air density only 
decreases slowly because of the slow uovenent upward. Now, if the 
initial ratio between ballistic coefficient. and air density is small 
enough, we arrive at the linit where the velocity at which the slightest 
retardation occurs no longer increases but decreases because the bal- 
listic coefficient decreases riore rapidly than the air density. 

That a high ballistic coefficient is advantageous for a rocket con 
be understood without higher niathesjatics. Let us imagine a rocket with 
a cross-section of 1. The air resistance is i leg and so is its weight. 
Hence, if its 



- 113 - 



upward acceleration is 30 m/sec , the total rearrrard thrust must be 5 kg, 
the fifth part of irhich la nullified by air resistance. If, however, 
the veight of the rocket equalled 2 kg and all the other data regained 
as in the first exataple, the total reanrard thrust -would be 9 kg and 
the air resistance irould only nullify l/9 of the total propulsion. 
Noir, if ire teike into account that v also increases, the calculation 
becomes still more favorable. Although the air resistance increases 
to 2 kg, the iriiole propulsion lasts for a correspondingly shorter time, 
so that, irith traversing of the saae layer of air at the sane accelera- 
tion, losses through air resistance and gravity vould drop from 40 ^ 
to 28 %, And if it is remembered that Vith greater v the acceleration 
also grows, the losses due to air resistance and gravity are still 
s::ialler. If the ideal propulsion is the same in both cases, the final 
velocity is considerably greater in the second case. 

Naturally, the condition is that the ideal propulsion is the same 
in both cases. "High ballistic coefficient" in this context does not 
mean that the ballistic coefficient can be achieved by multiplying 
the metal parts, as vritli a missile. In this case, the value of v irould 
increase but only because the rocket would now have to fly faster in 
order to save at least what can be saved while combatting tlie greater 
force of gravity. In addition to the lower mass ratio — —- ', there 

would now also be the necessity of flying faster and overcoming greater 
air resistance. 

In order to express tliis more clearly, HOEFFT has coined the 
expressions, "dynamic" and "dead" ballistic coefficient. I am e^ainst 
coining new exprftsaioas if I believe I can say what I wish to say 
by use of the existing ones. I thought I had already expressed this 
clearly enough in the first two editions of this book when I wrote 
that the ballistic coefficient must be as high as possible and the 
empty weight, on the other hand, as low as possible, and when I filled 



- 114 - 



a third of the book vith construction suggestions to shov hoir that 
can be achieved. 

In spite of that, two authors (l do not irant to mention names) 
have managed to assert that I wanted to increase the ballistic coefficient 
by increasing the dead weight. Apparently, with the one, a certain will 
not to understand was involved in this ', with the other I cu,i only 
assujae that he has not read ay book properly, if I am not to assume 
that he has understood almost half of it. 

Now it is slnply a natter of uaking v^ as large as possible in 

relation to 2.g. , or, what amounts to the same thing, making the 

product Vq c in absolute terms as large as possible. Means to achieve 
it are a long and thin type of construction, usiu^; apecifically hea'vy 
liquids, reducing the air density, for example, by carrying the rocket 
aloft by aircraft before the ascent, or, finally, increasing the 
exhaust speed, 'ii'hat is preferable in one case or the other can only 
be determined by detailed calculation; for example, with aodel B, for 
the lower rocket the moments that speak for the choice of specifically 
heavier fuel predominate, for the upper rocket ihe moments favoring a 
high exhaust speed predominate (cf. p. 341 ff). The same applies to the 
filling of the fuel tanks of model C. 

Although, precisely speaking, no rocket can fly at the most 
advantageous velocity, these derivations are still of value. They 
show us what to strive for and what we ccm at best hope for. Besides, 
they tell us this s If we do not move too far from the conditions 
presupposed here, we can easily estimate the deviations and apply them 
to the calculations in the form of corrections. These formulas give 
( us a framework for a more comprehensive theory of rocketry. 



' He would very much like to deal me a blow, and since he does not 
have the means to do so in factual matters, he at least attempts it 
by stylistic means. 



- 115 - 



The Trell-kno-im writer VALIEIl has reproached nie for involving too 
much calculation in the problem, I ansirer bj sajing i 

A theory can never be vorked through too accurately. ^That I have 
read out of the formulas for the most advantageous velocity (for 
example, that time, mass ratio, force, acceleration, altitude, air 
density, etc., are functions of the most advantageous velocity alone 
and do not also depend on the absolute size, etc.) is extremely 
important, and that can only be read out of these formulas. It vould 
be another natter if I wanted to figure out a specific model in 
every detail; then it would be entirely at my convenience how far to 
simplify these formulas and round off the figures employed. That I 
have done so I already said on p. 2. In my opinion, every approximate 
calculation must be based on accurately computed theory; only then 
is one permitted to simplify and only then can one give account of the 
implications of the simplifications. Indeed, later one mus t simplify, 
for there is no sense in substituting figures accurate to a hundredth 
part for values that need only be accurate to one-tenth. 

To the accusation of "over-calculation" I would like to respond 
with another thing. I have computed these foraiulas once and checked 
them several times. Now I have them and, by using them, can satisfactorily 
solve any problem of construction in the course of a few hours. On the 
other hand, if one carefully reads the first edition of GODDiUlD'S book, 
"A Method of Reaching Extreme Altitudes," one cannot avoid the impression 
that he has worked weeks or months on some of his tables, studying and 
changing them until he approximately found the best solution. Yet, 
he is still far from sure whether he really has tlie best solution. 
I believe one exactly calculates less if one has good formulas. 
- In fact, VALIIIR has often avoided much calculation by letting me do his 
. calculations uid derivations when he was stuck. 



- 116 - 



Chapter 9 
Counter-Pressure 
Formula quantities of Chapter 9 

a : counter-pressure 

t : time 

g : acceleration due to gravity on the earth's surface 

h : distance from the ground 

m i mass of rocket 

r : radius of earth 

s : stopping distance 

V : velocity 

z : centrifugal force 

T : period of revolution of a carrousel, etc. 

s radius of curvature of trajectory 

1, Explanation 

Let us observe a aau who is standing still. The force of gravity 
acts on all the atoms of his body and seeks to pull them doim. If the 
atoms vere able to follow the pull of gravitation, each one would fall 
with Ml acceleration of 9.81 m/sec", that is, at tlie end of the first 
second, it would moT'e dowiwards at the rate of 9,81 m/scc, at the 
end of tlie second Sri,). 81 m/sec, at the end of the n-th i;t0.81 m/sec. 
Now, the soft parts are held firu by the bony framework, vrhich in turn 
is supported by the feet, and the feet (as we saw on p. ff) are 



- 117 - 



being pushed upirard by the earth -with the same force with wiiich the 
body presses down. V7e say : The body cannot fall for it is supported. 

The fact that the single atoms would all like to fall but are 
prevented froa doing so by a force which only acts on the body from 
the outside, results in certain tensile and conipressive strains within 
the body. Tor example, we cannot hold the arm horizontally without 
nniscle strain; the intestines are pressed dowi, etc. T.'e designate this 
state by saying t The man is subjected to a counter-pressure of 
9.81 m/sec^ against the earth's surface. 

If gravitation were lower, for ezanple, only 3,72 m/sec , as on 
Mars, all these strains would naturally be correspondingly snaller. 
Our man could stand on his big toe like a ballet dancer; according 
to LASS\71TZ, the side branches of trees could be three tines as long 
without breaking off; according to GAUSS, the aninals could grow three 
tiues as large without getting too pluup, and so on. If, on the otlior 

band, the acceleration due to gravity were 271 m/aec*, as on the sun, 

271 
all these tensile and compressive strains would be --— - = 28 times 

9.81 
greater than on the earth. A person would instantly fall to the {ground 
and splutter apart as though he were made of soft dough. 

If the force of gravity were completely lacking, these tensile and 
compressive strains would cease : the feet wquld no longer press against 
the ground, nan would float in the air like an angel, he could stretch 
out the arms horizontally without tiring, up and down would lose their 
meaning, etc. 

Thus, counter-pressure arises when all the atoms of a body tend to 
carry out the same accelerated motion, but a force, acting on a part of 
the body only, prevents the motion from taking place. - According to 



- IIG - 



thin (-efiuition, the niui t.'ouIcI also be aubject to counter-pi'ossi'.ro irueu 
he hnaj^, sits, lies, oi- stcuicls on his hectl. These various posiiioua 
affect tlie poraou nnite differcutly; ivhen he haii;js on a bar he bccones 
tii'ed, T.'heu he stands oa his head he boco'ies ^itlt-y, vheu he lies he 
rests, etc, Dut these fliffereiit effects are based only on cliff erejiccs 
in Su;:nortj in all these cases, fis long os the person does not tiove, 
the counter-pressure ft'-ounts to P.Gl n/sec '. 

Counter-pressure can also arise in ai:;other vay t If the brakes arc 
put on when a rra^on is noviu^- at full sneed, all its occupants and 
every part of the body proportional to its i.iass are pressed forv'ard. 
If the Tva^ou starts suddenly, they are forced backirard. 

If our nan irere to float in a lift in gravitation-free space and 
the lift irere set into accelerated .:;otion in the direction from feet 
to head, he irould be pressed to the floor. Objects let ^o in this lift 
T,'ould apparently fall to the floor -vrith xniifori-ily accelerated notion 
Olid the saiae tenaile and coripressive strains iiroald arise in the person's 
body as.thouii^h he fouiad hinself on an attracting heavenly body, ^7ith 
an acceleration of O.Gl m/soc*, for esanple, his state irould be no 
different from that on earth, (Counter-pressure through inertia,) 

If a Tva^^on describes a sharp curve, the occupants are hurled side- 
Trays by the centrifugal force. Since the centrifugal force is only a 
nanixestntion of inertia, it can likewise cause counter-pressure. 

Definition : A body (or systeri of bodies) is subject to counter- 
pressure, that is, part of the body is affected by an outside force 
(the support) rrhich influences the state of motion of the centre of 
gravity (for exa:nple, preventing the body froa falling, forcing it 
out of its track, accelerating or decelerating it), so that tensile 
and coEjpressive strains arise between the single nolecules which 
vould not exist if this force did not act, that is, if the body were 
not subject to the counter-pressure. 



- 119 - 



Here we are only thinking of bodies which appear large in compariaon 
to the effective radius of the molecular forces but infinitely small 
in coaparison to the nore important celestial bodies. (Although, on the 
one hand, the phenomena of adhesion, capillarity, etc. as well as of 
ebb and flow and the like, on the other, could also be treated as an 
aspect of counter pressure.) 

The expression "support" must here be understood in a very wide 
sense. Any force that holds the body nay be considered as support as 
long as it does not seek to impart the saiue acceleration to every 
particle of the aass. Accordingly, a book lying on the labl e is sup- 
ported just as well as a han^i'Q'C lawpj the liquid in a tunbler ia 
supported, so is a floating body; bits of paper clinging to an electri- 
fied rod of sealing wax or iietal shavings hanging froiu a na^^uet arc 
also supported. The electric or raagnetic attracting forces would not 
give each molecule the same acceleration (as does the force of gravity) . 

Cn the other hemd, according to our definition, the cyclist in the 
interrupted loop (Fi^. 46) is not supported. 




Fig. 46 

It is true, the perfori:ier cannot drop in the direction of the 
earth's attraction; that is prevented by the centrifugal force. But 
the centrifu[;;a] force has the same accelerating effect on each particle. 
Gravity and centrifugal force are certainly in balance in every aton 
and the body Doves (apart from air resistance) as every atom would 
move if it were freely novable. The motion of the body does not result 
in cuiy tensile and compressive stresses between the single atons : 



- 120 - 



the body is not at all subject to £uiy counter-pressure. If, however, 
it vere "supported", a counter-pressure against the support vould have 
to exist which uay only arise from tensile and conpressive stresses 
between the single nolecules. 

The counter-pressure has the dimensions of acceleration (in the 
technical measuring system m/sec ) and is, like it, a vector quantity. 
Its physical effect depends only on its absolute magnitude, on the 
nature of the body affected, and on the type of support, not on the 
force of gravity or inertia producing it. 

S, Calculation of Counter-Pressure 

Counter-pressure through inertia : In this case, the counter-pressure 
is equal to the acceleration or the deceleration. To that, the force of 
gravity must be added vectorially idien t-H© occasion arises. For example, 
if velocity v is uniformly produced or decelerated over distance s, 
we find the counter-pressure a from the foriaulas for uniformly accelerated 
notion (t i period of acceleration ) i 

8 2 

1 ^3 ^ V V V /^„\ 
V = a.t 5 a = -a.t j t = ; s = j a = -. (52; 

2 * aa 2s 

If the velocity changes unevenly, this calculation naturally ^ives 
us only the average value for the counter-pressure during a certain 
period of tiue, while the top figure would be greater. But laost bodies 
(arjoug others also the huutai body, cf. p. 128) are so constituted aa 
to be able to endure a counter-pressure constantly if they con endure 
it at all, and so the observation of an uneven chaiii^e in velocity only 
gives us the lower liuit of the resistance to counter-pressure, not 
the resistance to counter-pressure itself. Here is an exoiaple : 

If a person jumps into the water fron a 5-rj-high diving board, he 



- 121 - 



meets the imter at a speed of \fe.g.h = 10 la/sec. Nov, he sinks about 
2 m into the water, so that the averai^e deceleration would be 

— — = 25 ra/sec"". To this, gravity of roughly 10 m/sec would have 



p 



to be added, so that the average counter-pressure endured is 35 m/sec' , 
Sut this is only the lower liuit of the person's resistance to counter- 
pressure in the direction from head to feet, 'ulien he struck the water 
at full speed, Iiis resistance was obviously greater than when he was 
already subaerji;ed to the cheat and now, practically only under the 

influence of gravity, slowly sank altogether. This observation only 

2 
shows that man endures uore thoii 35 m/sec ; how much nore he endures, 

that it does not teach ua. 

This figure can be deterriined uore accurately by aeasuring the 
velocity with which a diver dives into the water on a suitable film 
shot (still better on a slow-motion shot). If one charts the diver's 
advance frota one picture to the next and also loiows the tine interval 
between the single shots, one can easily calculate his velocity and 
the deceleration he experienced in the water. One obtains the counter- 
pressure by adding the gravity to the deceleration. In this way, 
I obtained figures 1.4 - 2 times as large as the average values- 
I cited here. Unfortunately, nry aeasurements in this respect wore not 
accurate, I simply had to take a few sport films that I Imd just 
received and on which I estiuated the distance traversed only on the 
body length of the swiiuEier. It would be a rewarding task to repeat 
the measurement on nore accurately-prepared slow-motion shots. 

Since counter-pressure has the dii.sensions of acceleration, its 
magnitude naturally depends not only on the absolute velocity which 
is being decelerated but also on the period of velocity change or, 
what is connected with it, on the braking distance. 



lis ~ 



Tor czanple, Ir. "T^U-II is rjist,?':eu Trtieu ho wite;] that the por-necourl 
chnii'j,^. in velocity vhich one suflcrs when leaning ^vov. a train noviu3 
at ISC liEi/hr ia 3C rr./sec'-. The e:^^>res.g trcin ■-.ove.'; at n speed of 33 ri/.'5eC| 
L'ut as soon .-s tlie liody of the pei"i;on touches the (VJ'oiii.cl the cpood is 
tilncst instantly decel ertvterl to 4 - 5 n/sec. At this speed, the y.erson 
keeps on runniu^j bedcle the train for a feiv raetres . During the first 
tenth of a seconc!, the v.er3oii's change in velocity is thus consirlerahly 
greater; if it vnvp. to net for a vhol e second, it -..•oulc! cause a decelera- 
tion of at loust ^oC n/sec", rrliich no \:'?T:^ni\ en r^.t^vre. The per-secnud 
velocity change ivould not errcood 3C m/sec ^only if a stop occurred 
during o. sufficiently lon^ period or, Trhnt onounts to the sar.e thin^', 
over a sufficiently lone distance; i.e. if './e junped on n 3C to 40-ei- 
high pile of feathers or very loose straw. For that ratter, an vicaderaic 
teacher shov.ld not confuse velocity and acceleration. Dr. U'vIN has nade 
the snne error in his well-Icuoira article on tlie cosrsos, in •which he 
writes that a swirwer striking the surface of the water at 40 ni/sec is 
subject to a counter-^: res. 'sure of 4C n/sec^, 

JuL"3S "v^TUs'I3, in his wcll-kiioivn novel, "Journey Around the L'oon", 
also conrnits several gross sins with respect to the calculation of 
counter-pressure. I here p.ention, ononj others, the idea that the 
occupeuits would survive the impact of shooting; off the projectile if 
they lie on a cushion of water S l//l n thicli. Actually this cushion 

v2 
would have to be at least 1000 loi hi(;;h : a = -— ; the formula is 

ine:iorGble. 

On impact, a solid body is subject to verj' high counter-pressure 
for a short tine. For ezanple, if an ivory billiard ball falls on a 
li'.arble floor from a hei-j,ht of (iC cm, it aeets the floor at a velocity 
of roughly 2 la/sec. This velocity is decelerated during the irapact, 
at which the stopping distance is certainly not nore thou 1 mm for any 
point of the ball. The avera£;e counter-pressure (a) during the impact 



- 133 - 



Tve find to be : 

a, = c: 2000 n/sec . 

0.G03 

The highest value ia still higher. 

The couuter-pressure due to ceutrifugftl force naturally equals the 
centripetal acceleration, that is, iu case v is the velocity and g the 
rcidius of curvature, then 

a = -|- (53) 

increases vectorially by the amount of gravity. For exoiiiple, when PSGoUD 
rode in a horizontal spiral with a radius of curvature of 30 in at a 
speed of 40 m/sec, the centrifugal acceleration equalled 53.3 ni/sec 
and he was in all subject to a counter-pressure of 

53.3' + lO" = 54.8 m/sec . 

(This follows from Pythagoras* Theorem.) 

3. Phenomena of Counter-Pressure 

The state of coxmter-preesure is characterized by the fact that 
every part of the system seel.sto displace itself in the vertical direc- 
tion as lauch as possible; the force of this tendency e<iuul3 the product 
of its nass times t!ie counter-pressure. 

Example s The plumb bob exactly shows the direction of the counter- 
pressure. The strength with which it draws on the line is directly 
proportional to the counter-pressure. Thus the counter-pressure can be 
aeasured by the pull which a certain weight exerts on an elastic spring. 

As long as the rocket burns, it is subject to a counter-pressure 
from the tip toward the nozzle outlet; when the fire is shut off and 



- 124 - 



the rocket flies on like a closed projectile, all counter-pressure is 
lacking. Then, not even the strongeat gravitatioual field can attract 
a pluup bob because the point of suspension follows the pull just as the 
weight itself. So the pluuimet cannot be used to deteriaine whether the 
rocket is rising vertically since, when the rocket does not bum, the 
plunmet has no consistent direction and, when it bums, the plutamet 
always points toward the nozzle outlet. The direction of travel is best 
regulated by the use of gyrocoapasses (K 13). On the other hand, the 
counter-pressure produced can be used for measuring acceleration, say 
by the use of a spring balance or the adjoining apparatus : 




Fig. 47 



Glass tube Gj, which nust not be too wide, is stuck air-tight into 
glass tube Go, where it does not quite reach the bottom. The two air 

colui-ins h^ and Lq are separated from each other by mercury :2j tl^e thin 
section of Gj^ is of metal. If the counter-pressure increases, L| becomes 

larger and Lg snaller, causing wire dj^ to eiaerge farther out of the 

iji lercury, by which the current passing through d^ dg is weakened, visa 

j valve for punping air into La or drawing off air, in case the apparatus 
does not indicate correctly. The doiaping coefficient of the oscillation 
uust be 2.1, or else the period of oscillation luust be very long. The 
influence of the gravj^tational coaponents can be taken into account by 
inserting controllable resistances into the current passing through d^ d^. 



-■ 195 - 



Liquids tend toward the pliuab line as uuch as possible. If they are 
hindered froa doing so by bein- kept in a container, tliey seek to burst 
open the container (side pressure). Side-pressure is also proportional 
to counter-pressure, which should be noted, for exaraple, when calculating 
the wall strength of my rocket. Liquids in tall, thin containers also 
tend to buckle thew (cf. Fig. 48). 

If the container is hermetically sealed, that coii be prevented, 
ai^ong other thincs, by rigid filling, thus making the inside pressure 
greater than the outside pressure. 

Bodies of different densities suspended in water are precipitated 
due to molecular forces the faster, ceteris paribus, the greater the 
counter-pressure. For excuaple, milk is skinmed by gravitational pressure 
in 24 hours; in the milk separator, the sane process is completed is 
5-6 minutes. In the sozie way, with models A and D, ice crystals forming 
in the liquid hydrogen quickly precipitate in the groove botweou the 
shell axKl the nozzle and are not easily swept into pipe t. In boiling 
liquids, the gas bubbles rise the faster, the greater the counter-pressure, 
but the particles of liquid swept along again fall back into the liquid 
so much faster and are not even sprayed upward as high, since the vapor 
resistcuice against liquid particles swept along increases as the squire 
of the velocity. This is important in evaluating tlie operation of 
rockets with liquid fuels. 




Fig. 4S 



- i.^e - 



4. .fan's Reaction to Increased Covmter-Pressure 

a) Physical Effect of lli-h Coxmter-Pressure 

'..'ith all too high counter-iireasuro, i'U[5ture.'3 or contusions of the 
inner orgQdis, disruptions of certain nerve tracks in the brain, arid 
similar inner injuries siust occur. If, therefore, lire viah to place a 
man in a vehicle that is bein^; accelerated rapidly and for a prolonged 
period, vrc must seek to deter...ine ho-w iiuch we can just esiiect froni 
hira in this respect. I shall do so by means of several examples : 

V/hen juupin^ onto a water surface froia a height of S n in a straight 
position, the counter-pressure rises to over iC a/sec". The counter- 
pressvire connected with the junp has never yet harried a he.-.lthy person. 
ICevertheless, with head-diving from this height, rushing of blood to 
the head, fainting, and apoplexy are observed, although here the stopping 
distance is greater (stretching the anas forward, turning over baclCT/ards). 
3o nan endures ;.iore counter-pressure in the direction fron head to feet 
thaii in the opposite direction. - .'Ian endures the greatest counter- 
pressure in the transverse or sagittal direction, that is aa nuch as 
to say "in the lying position," Because, with equal counter-pressure, 
the tensile and ccnpressive stresses are thus the sr.ialleot, nature could 
give him the greatest r^.^latmi e to coun tor-pressure in this direction. 
Now, nature could just as well have saved material and left the connec- 
tive tissue weaker in this direction. Very likely, this did not happen 
for reasons of expediency. Vie often slip sideways and fall, and we 
could not liv'e if we come away with inner injuries every tizue, such as 
are caused by too high coumter-pressure. Because the stopping distance 
is usually short, the counter-pressure in such cases is high. - Je are 
fatiiliar with the backward head dive into the water. One turns the 
back toward the water and lets oneself drop backiirard, while the feet 



- 127 - 



at first atay in contact with the diving-board. That results in a 
rotary motion that must go just so far that one meets the water with 
the head vertically rtoimward. If the feet are tal:en from the diving- 
board too soon, one falls on his back (Fig. 4C). If the diving-board 
was 2 m above the water, the sicin has stood a counter-pressure of up 
to 200 m/sec" (because of the hardness of the water surface). (As a 
result, it becomes red as a crayfish.) 






<==SS3 



Fig. 49 

The rest of the body suffers a couiitcr-iiressure of GO m/sec , the 
head and legs up to 70 ra/sec". If one is careful and extends the ams 
so far backward that there is no ii.ipact with the water surface in the 
lusiibar region, the countex'-preosure for the kidneys also does not 
exceed 80 la/sec ' and one is not inconvenienced e^rcO'it for a red back. - 
At one tit'.e, while diving into the water from a G-ci-high staaid, 
I slipped and fell on uy side. I could not find the slightest d;ii;iage 
fro.' counter-pressure. 

Accordingly, the hunoji body appears to endure without hani a 
counter-pressure of up to GO ti/sec" in the direction from head to feet 
and one of CO - 90 m/aec"" at right angles to that direction. The 
question is whether it can also endure tJiis counter-pressure persist- 
ently, i.e. at least for SCO - 600 seconds. One could argue as follows f 
If I tie a cord to a dynaaometer and bring the indicator of the dynario- 
raeter to 100 g by a short, slsarp pull on the cord, then I can say 
that the cord endures a constant pull of 100 g, certainly it constantly 



- 138 - 



endures uore than CO g. But if, instead of a wool or cotton cord, I 
take a thread wound out of pitch, the fact that it stands a pull of 
iCO g at the ..loiuent does not aay by far that it endures even 10 g 
persistently. In fact, by the smallest constant weight, say by its 
own wei£;i»t, it becomes steadily longer and thinner and finally breaks. 




i'lg. 



!. "The Dasin Gondola" denioustratop t''^ resistance 



of the connective tissue of the hiu.ian thigh-ball. 
Froia lOimi, "Man." 



- There are also interaediate levels. For extuaple, a strong paper tube 
filled with pitch is a structure which does not breaL with the slightest 
constant pull and endures a very strong pull by jerica, if it is later 
only given tiue to regain its foriu. Hut if the pull acts constantly, 
the resistance decreases considerably. One could say that our body is 
sich a syster.i of rijjid and plastic substances and that various organs 
(liver, kidneys, s[ileGn) have the recistfuace of pitch at SO" C. This 
argument, however, is not sound. The liquid substance of our body has 



- 129 - 



nowhere the viscosity of pitch at ^5'. (At best the glue contained in 
the bones and liga-'enta, hut exactly these structures best endure 
continued pull ca\d pressure for other reasons (cf. Pi^. 50) ), 

The noEientary resistance of the aentioned tube of pitch is solely 
based on the viscosity of the pitch. The fluid and pulpy ingredients 
of our body, on the other hand, ivill not oppose a choui^e in fonJ with 
more resistance than say that of the intestinal pulp. 3o at least i9/S0 
of the resistance of our body depends on substances that behave like the 
ivool cord above. 

The folio-wing case was observed during- the war : A pilot went 
aromid 4 tines in a spiral at the uost 140 m in dioiaeter at a speed of 
approximately 216 Ism per hour = 60 ra/secj he was thus exposed to a 
counter-pressure of 51.5 ra/sec*" for over 29 seconds without suffering 
harm. This case naturally greatly favors my assumption that man will 
endure this counter-pressure for even 200-^100 seconds (without completely 
confirming it). 



W^ — - 




Fig. 50a 

The figures of 60 or 80 to 90 m/sec given here are only good 
average values as are borne by persona who have never been especially 
accustomed to enduring high counter-pressure. Now, the counter-pressure 
depends only on the resistance of the connective tissue in our body 
and, as is well-Imoim, that can be strengthened by practice, whereas 



- 130 - 



it clei^eneratea with iion-use. For exaiirle, I Ioiot,- of a case vliere a 
firenon jumped from a height of t>,5 m, struck the safety net in a lying 
position, and boxiIs. into it 1 m ivlthout suffering any ham from the 
jiuap. The counter-pressure which he had to endure during the iiipact 
certainly exceeded 240 m/sec . 

The Hawaii islanders are supposed to leap into the sea in on upright 
position from on 80-m-high cliff. Theoretically, they raust strike the 
surface of the water ot 40 m/sec. Even if the circurastance is taken 
into account that tlie acceleration due to gravity is actually somewhat 
less than 10 m/sec^, and the air resistance is considered, a good 
CS m/sec still remain as their falling velocity, ^id since, in the first 
moment, the counter-pressure here increases as the sr^uare of the 
velocity, we are dealing with a counter-pressure of over 300 ra/sec-. 
(More than the gravitation of the sun! ) In "./oche", I saw the photo- 
graph of an iUnericon who jumps into the water head first from a height 
of 40 m. Here the counter-pressure is "only" 150-5500 m/sec^, but it 
acts from the feet to the head; it would certainly kill on unpracticed 
person. 

These cases are exceptions; nevertheless, the cited exasjples show 
that I estimated very carefully when I based ay rocket calculations on 
a human resistance to counter-pressure of 40 ra/sec . Other observations 
on the effect of high counter-pressure were collected by GflllM, ^.TINliLliKl, 
and l)r, GILL3RT. In this connection, also compare "Die Rackete", journal 
of the Society for Space Flight, Bresleu. (Especially the July, 1922 
issue contains valuable observations.) 

b) Psychological Effects of Abnonagl Conditions of Counter-Pressure 

Our sense organ for counter-pressure is the vestibule of the inner 
ear, Floating in the perilymph and held in the center of the space by 



*131 - 



sensitive, elastic fibers is a calcareous uecibroQe vhich, trlieuever 
counter-pressure prevails, nust be supported by several fibers, thereby 
indicating- the aa^-nitude and direction (to the head) of the couuter- 
pressvire. This organ is supplenented by the three seui -circular canals 
of the inner ear which indicate the i.;ove...eut of the head in space, 
and by the general body sensation; e?;pecially by the liiuscle, joint, 
touch, and pressure sensations as iirell by the eye and the judgment 
as to location, positibu, and motion. The relationship betveeii these 
components, i.e. the connectici. oT the various types of inpreasious 
are only to the smallest extent based on conscious reflection, 
individual learning or practice | they are to the greatest extent by 
far based ou inherited instincts, whence the rai-idity, dependability, 
and self-evidence of this organ as lonf^ as the aovciiouts are of a 
Eiagnitude which can still be produced by our oivn muscular force} whence 
also its striliins failure with uovenents of another nayiituda. Following 
are two oxoriples of the above > 



^r^^ 



FiE. 51 

Let us imagine a carrousel (cf. Fx^j. 5l). The diameter of the roof 
is u in aiid the seats are suspended by S o, I5ven if it turns fast, 
naking one revolution in 6.5 sec, the sense of equilibriuui of the 
riders is not in the least disturbed (if they do not becone dizzy; 
about that later). For T = 6,5 sec, the seats are pushed outward 1.15 m, 
making the radius of curvature 5.15 n. The velocity is 5, . ra/sec and 

the central acceleration 6 m/aec '. The resulting counter-pressure is 

/ ^ 
11 la/sec and is inclined toward the vertical by 26,3*. In spite of 

this considerable inclination of the plunb line, in which our body and 

the seats participate, we can hold a stick parallel to the earth's 



- IS!? - 



surface witii eyes shut; at least, the averages of various positions of 
the stick shoiT no systematic error. If a pilot (Fi^* 52) flies on a 
curve with a radius of curvature of 520 m at 100 laii per hour, the 
coimter-pressure has the saiie coiaponeuts, that is it has the savie 
direction and majjnitude. But the pilot no longer has the feeling that 
the earth is fin.;; he has the impression that his plumb line is inclined 




Fi£. 53 

toward the vertical by about 10"*, and the earth has lifted by 16" and 
revolves about the axis of his path A (Fig. 53). He does not feel 
dizzj' CvS long as he does not reflect about his position. The pilot 
about ifhoE I spoke on p. 1S9 had sofnewhat the impression of Fig. 54. 
He did not feel dizzy either but felt hiwself to be "reriarkably thin 
aiul heavy". His velocity did not "actually seen very great" to hiin, 
a si^^n that to him time appeared to pass uore slowly than normally. 



Fig. 53 

In a siriilar way, although to a lesser extent, one thinks that the 
telegraph poles are staiHlin;^: on a slant when one looks frcan the window of 
an exi^ress train that is talcing a curve. 

Because of the close connection between various conpoaents, the 



133 - 



psychic effects of tlie scuae counter-presaure differ under different 
circumstfuices. Counter-pressure resulting from circular notion is the 
least unpleasant. V/ith horizontal acceleration it already has a more 
unpleasant effect; with slight upward acceleration it is still more 



■'x=> 



Fi£,% 54 

unpleasant (lift, boiv of a ship in heavy sea). Stronjjer upward accelera- 
tion, on the other hai\d, in no way has the 3a;ie unpleasant effect. If 
a lift descending at 1 m/sec is brought to a halt over SO ca, the 
resultin^^ counter-pressure a = 2.5 + g m/sec lasting for 2/5 second 
is decidedly aore unpleasant than if a = 25 + g m/sec (soiy, when 
junping into the water) for 2/5 of a second. (V/e have on analogy in 
ticklisliness. Lighter touch tickles more than stronger touch . 

' This phenomenon only occurs with straight-line acceleration. That 
has been sufficiently proved by several hvuidred observations. The deeper 
reasons probably lie in the fact that, for slight changes in velocity, 
our psychological judgnent is still adequate; with abrupt changes in 
velocity, however, that judgment fails, so that we just do not grasp 
these changes in velocity. 

For example, the fact that OPEL and VOLiaiAHOT were so affected when 
riding the rocket-car was not the result of starting too rapidly, but, 
one could almost say, of starting too slowly. Here the acceleration 
amounted to 8-10 m/sec", which since the acceleration was perpendicular 
to the force of gravity, resulted in just that infamous covuiter-pressure 
of 13-14 m/sec^ which makes it so unpleaseuit in a lift and in heavy seas, 
and which should be absolutely avoided with rocket vehicles. If the 
rocket-car had started at 30 m/sec^, the occupants would presumably have 
been affected just as little as say 'TITTliUHN in Breslau was affected in 
his tests. 



- 134 - 



Furtheraorc, the effects seen to differ greatly if Tve are already aware 
of being in motion or are at least prepared for the occurrouce of 
counter-prcG.sure. It also contributes much to the paychic effect whether 
we feel we are in control of the acceleration or, still better, whether 
we con suggest to ourselves that we desire the respective motion. The 
voluntary dive into the water (especially if we simply jviinp in an erect 
position and slightly bend the knees to give us the subconscious 
inpression as though we wanted to jump doira on something), I believe 
this dive has a quite different psycliic effect than an involuntary fall. 

In fact, only such counter-pressures sean to differ in effect in 
which the producing kinematic quantities are similar to those that, 
xinder favorable circuiiataiices, we can still produce by nere niuscle 
power or artificial supplementary neans. On tlie otlier hand, strong, 
persistent, o,nd uuifonn counter-pressure, independently of how produced, 
seeas to have the same psychic effect; the sense of the earth's position 
is lost and the vertical is transferred to the pluiab line (almost 
achieved in Fig. 54). Over-all view is lost of the raoveraent actually 
carried out. Curves are being underestimated. Time seens to pass more 
slowly (cf. p. 143). The pleasant or unpleastuit side-effects mentioiied 
fade away the more, the stronger and more persistent the counter-pressure. 

The sensations of dizziness are basically quite variable. Only one 
thinj,' is counon to all types : distrust in our topic organ, that is 
distrust in our ability to orient ourselves in space and in our motive 
apparatus, and the desire to hold on to souething or to lie as low as 
possible. \'Ie beccsne dizzy irhen, for any reason, our topic sense apparatus 
does not work nor:ially, that is 

1) V7hen the periljTnph is in action instead of at rest (for exanple, 
when we turn suddenly, swing, etc.) or when we have a disorder of the 
inner ear as a result of disease (ueniere's disease) and have not yet 

'jOoouo Dccuptonod to the new coiidition (as deaf oiid dunb persons have 



- 135 - 



become accustoued to the laclr of the organ of equilibrivin). 

S) IVhen the extreuely conplicated counectiou between the topic 
impressious is disturbed because the respective braiu areas do not func- 
tion properly (for example, because of blood pressure, lack of blood, 
fever, or poisoning say with alcohol or nicotine). Finally, because 
certain hallucinations hinder the nonaal associative processes (height- 
dizziness, stagef right, agoraphobia, and the like). 

3) Dizziness occurs irhen the single components of our topic sensiti- 
vity contradict each other, so that it appears inadequate. Fortunately, 
dizziness, iu this co..^<^, sets in almost only with intense reflection 

on our position. For example, on curves, aviators only become dizzy 
vhen they think about the motion of the earth. 

4) .Then Tre allow thoughts of distrust in our topic organ or our 
capabilities to suggest themselves to us. V/hen we aay to ourselves 
that we are not equal to the task before us. ( Hence the old mle i 
^Then working on a roof, mountain climbing, or flying, do not reflect!) 
- If our topic organ works norually, no sense of dizziness will arise 
even with the wildest topic illusion (cf. FJg. 54). 

Uniform counter-pressure itself produces no dizziness. 

The deeper causes of sea-sickness have actually not been explained 
until today. Certainly it is not a light "brain shock", (that is, a 
mechanical injury due to abnonml counter-pressure) as can be read in sone 
laedical books, for l) we saw that the brain endures quite different 
shocks thva\ those caused by a heavy sea; l) adults becone sea-sick acre 
readily than children, (e.g. TAio would like to be rockrd in a cradle 
for hours ?) It has been shown that actual brain shock occurs with less 
counter-pressure with children thou with groim-ups. 3) Sea-sickness 
stops very quickly as soon as one stands on solid ground. Brain shock 



136 - 



that had just as raainous symptoms can last for days, weeks, and even 
uonths. 4) Sea-siclcuess can be produced by suggestion in hypnosis and 
soiaetiues even healed for a tiae, brain shock cannot. 

3ea-siclaiess appears to be a matter of stimulation of the para- 
sympathetic nervous system. It is interesting to note that apparently 
no means exist by wliich to malce adults dizzy for longer than l/S hour 
ifithout sea-siclmess ensuing. No matter whether dizziness is caused 
by revolution, swinging, excess or lack of blood, brain shock (hence 
the error neutioned), nicotine, or anything else, if only the dizzy 
sensations persist long enough, sea-siclmess will result. Conversely, 
however, sea-siclmess con apparently arise without being preceded by 
sensations of dizziness. (Afterward, once present, nausea and vomiting 
are naturally always connected with dizziness because the noriaal course 
of topic associations is disturbed in the process.) With tay rocket, the 
abuon.ial counter— pressure certainly produces no sense of dizziness. 
V.'hether the observer, even then, does not become sea-sick, is another 
question. I, personally, would like to deny it. I believe sea-sickness 
is produced aore by the up and doim change. V/ith uniforia counter- 
pressure, no matter how abnorual, if, for exazaple, during the whole 
voyage the ship only had to go over a single giant wave, no sea-sickness 
would occur. 

The followiig apparatus laight serve for experimental research 
concemiug our resistance to long-persisting and strong counter-pressure, 
and for getting accustomed to it. About Axle A (cf. Fig. 55) revolves 
a long metal arm D, B*, which is supported by wheels C running on rails 
D. At the end of B', wagon F hangs fr<xa hinge E' . F does not touch the 
groxmd and, being furnished with wheels bottom front and sled runners 
behind, stops quickly in case B' breaks, /tii equalizing weight F' hangs 
in 3 at the end of B'. The whole apparatus ia made to run as smoothly 



- 137 - 




B B 




Fig. 55 



as possible; at c, elastic springs that are not too stiff (still better i 
chambers L filled with air) are to absorb the vibration. The period of 
oscillation of this resilient device is supposed to be at least one 
second. The person e^erimented irith is placed in F, freci vhere the 
speed of the iragon is being regulated. Naturally, the revolution speed 
ia accurately recorded. Since F runs in ditch G and the earth is piled 
in an embanlonent all around, the experiment is further not dangerous. 
Because of the slow starting, the large radius of curvature (the radius 
of curvature must not be under 60 m), and the jolt-free motion, the 
experimental person thinks the counter— pressure is almost vertical, and 
so we have a means by which to observe the physiological as well as 
psychic effect of high counter-pressure . 



' Numerous ezperinents have already been made on man's resistance to 
counter-pressure on apparatus with small radii of curvature. They are 
valuable in that they show us that man actually endures a counter-pressure 
of 4 g and more. According to all that has been saia here, however, they 
are uusuited for studying the psychologic effect of a counter-pressure 
with which the direction of motion changes less rapidly or not at all. 
V/e surely do not wish to over-estimate the psychologic aspect of the 
matter, but neither should we under-estimate it. - Hence, at the con- 
vention of tlie W. G.L. in Danzig on J\ine 4, 1928, I suggested building 
this apparatus. It would be far from representing consuming capital. 
If it stood in the Vienna amusement park or a similar place, there would 
always be people willing to pay a few pence for riding around on it. 



- 138 - 



KOOIiDUNG suggests a centrifur^-e on which the exj>erimeiital wagon at 
first hangs aliiost vertically from a tover and is only lifted to alnost 
vertically froa a tower and is only lifted to aliaost the height of the 
tower during rotation. On this occasion, I will divulge the fact that 
my first sketch was very similar to his. Nevertheless, I moved away 
from this plan again because, for one thing, this apparatus would be 
much too costly. Besides, ivith the slijjhtest displaceuent of the centre 
of gravity, this tower would swing (e.g., because of the wind, radio 
towers swing up to 1 la). Hence, the experiments would be dangerous. 

iVgainst my plan, railway engineers raised the objection that the 
wheels at C would hardly stand the outside speed and that, above all, 
at such speeds the use of guide rails is out of the question. - I counter 
by saying that, in the first place, the rails do not serve as guides here. 
Even if the wheels bounced up fron the rails, they could only fall back 
on the rails again, for the strong base at A permits as good as no 
oscillations and arm B also can only swing a few centimetres longitu- 
dinally. So it would not be necessary to furnish the wheels with rims 
to engage the rails. For this reason the rails are not subject to any 
side force in spite of the curve. Since we are not dealing with railway 
wheels, the principles of LAVAL'S turbine wheel could be applied when 
constructing these wheels, so that their outside speed need not worry us, 

5. Lack of Counter-Pressure 

Cn the ground, we observe the lack of counter-pressure only when 
nothing but the inertia of a body balances its weight, i.e. when the 
body can freely follow the pull of gravity. This is the case of unsup- 
ported (thrown or falling) bodies. And even there, counter-pressure is 
actually completely lacking only when the body is not in notion, a»d 
that con only be the case for a noment (a noving body is supported by 
air resistance). 



- 139 - 



In the universe, the lack of counter-pressure is naturallj more 
frequent. Either no counter-pressure producing forces act on the system 
(as on the irfaole universe), or (as SEELKSER assuiaes, for ezample) the 
attracting forces of the single systems of fixed stars do not reach 
each other, or they still attract each other, but the different attract- 
ing forces acting on the system from the outside cancel each other out 
(that could, for ezan^le, be the case vlth the fixed stars inside the 
Milky Way). Finally, the body may be able to freely follow every gravita- 
tional pull (stars on the edge of the Uilky Way, placets., etc.). 

The lack of eoimter-pressure is characterized by the fact that no 
outside forces tend to displace the parts of the system vith respect 
to each other. Hence movable parts arrange th^selves in the directicm 
of the forces inherent in the system. For example, if I jump into the 
vater from a sufficient height holding a flask irith mercury in it, 
the mercury forms a sphere in the middle of the flask and clings to 
the glass at only one place (cf. Fig. 56). (To compensate for the air 
resistance, I first hold the flask above oy head and then move it 
doim vith increasing acceleration! often it must also be tilted side- 
vays.) A vetting liquid, on the other hand (e.g. vater), seeks to rise 
on the sides and force the air to the middle of the flask (Fig. 57). 



Fig. 56 



Fig. 57 



(This experiment succeeds only if the iralls of . the flask are moist . 
Othenrise the vater does not have time to rise.) If there are pebbles 
at the bottom of the water flask, they are drawn away from the bottom 
into the water, etc. 



- 140 - 



This is importaut for re-starting a space-ship, for example. Vfhea 
the fire is shut off, the liquids ascend along the iralls and force the 
vapor to the centre. Therefore, the pipes used for drawing off liquids 
nust not protrude to the centre. If, however, pipes are provided for 
drawing off vapor (in model E, I was able to avoid it), they must run 
from top to centre and have a closable opening both on top (for start 
of flight) and in the centre (for re-starting). 

If we con ignore the forces originating in the system, all freely 
moving parts of a system remain in the same position or observe the 
sane unifona motion with respect to each other. If, while cialcing the 
above-iaentioned jump, I hold a stone in cry hand, I can let it go and 
it will reaain in the some position in relation to ray body. If I touch 
it, it continues to move uniformly, as seen from ay position. In so 
doing, because of the air resistance, its ballistic coefficient laust 
equal that of my body; so it must be quite large. 

6, The Effectt on Man, of Minor or Ihtirely Lacking Counter-Pressure 

a) Physical Effect 

Reducing the counter-pressure for a few hours or days can do us no 
physical harm. All the conditions necessary for life ere possible in 
the upright as well as in the lying position, and it is irrelevant 
whether we lie on the bacL, side, or stomach. This fact alone shows 
that we are not de!)endent on counter-pressure frou a certain direction 
as are plants, for exoi^ple, which have a very queer way of growing 
with abnor.ial conditions of counter-pressure (Dr. R. STOiPSL, Hamburg, 
has proved this by raeans of meaningful ejrperii'.euts). 

It would be a different matter if counter-pressvire were lacT:ing 
for days or even woeI:s; in this case, our niuscles aiid ligat:ients would 
de^ienerate through c-i^use and, when returning to earth, vfe would suffer 



- 141 - 



serious injury from the counter-pressure (as, for example, Natulka in 
G;JL'S novel, "The Shot into the Universe"). 

If a space-ship is to travel for weeks, it vill be good to arrange 
the observer' s cockpit so that it is connected to the rest of the 
space-ship by only a cable and rotates about it so rapidly that a 
counter-pressure si;::ilar to that of the force of gravity prevails in 
the observer's cockpit due to the centrifugal force. (c.'7, GAIL gives 
a vivid description of such a rotatin.'^; observer's cc<^Tipit in his novel, 
"The Stone froa the L'oon". For psychological reason?, however, I would 
have nade the connecting cable considerably lon(2;er.) 

h) Psychic Effect 

Although reducing the counter-pressure has no physical effect worth 
rentioning, it does have considerable psychic effects. Althou^ih, today, 
nan caii be v.'i thdrawa frorj counLer-prestiure for fractions of a second 
only (ntuviely, vrlieu ho jvirips fro.i an ol f?va let' poiiit), we Cfiii, hy "liuiniz- 
iu,'3 the f eel iui^ of couuter-proasure (by influencing the or;^an of 
Oi_uil ibriuj-i appropriately), pi'odncc the pnychol ojiccvl efrects of the 
I ucTc of couuter-proiiGui'e, for they are not ceterr.iued hj the actual 
state Tjut oiJ;- 'iy tlie ■le.'^sa^erj fron our se;i.se or^^aus. I'sychol o^;y teaches 
that cni.intcifeiting '■;.„' event hy ; !is;leac1in^_, the sense organs has the 
pnyclioloi^ic effect of the evevit itsolf. 

If the seiisatioiis thus created are coripared with thor^o o..e has ■s.'heu 
ji.;'pia^ or falliu;^ Tro--. ai' elevated point, or ■ obtains ,i picture of 
■tlift [■■zycl.j.r effect of t'lp Inck of co'Uitoi'-p'-ecsure, which is certainly 
correct at first; so.je uncertaiiity re.iains at the later stages, since 
they cannot be verified by the juinp. 

Certainly, the connection between our conscioutquess and the or?;an 
of equil ilsriuii (which is riy desi^ination for the calcareous r.ie ibrane 



- 142 - 



in tlie vestibule of the ear, as already nentioned) is interrupted during; 
sleop. Ctaenvise it would -.lot be po^ssible to dreoji of ezpeviaacaa other 
thtui thoae ^e liave when iii a lyin^- position, lu so doiu^;, the reivTOiiinr; 
fmictioiis ;:iUi:t norually fall a,slec'p Tirst aud the jaa;jlici of the sensory 
nerves ot'.ly later. Othenrire one has the faniliar drenzi of fallin;; fron 
sone^rhere shortly before falliu^- asleep. This impression can also be 
prociuced by hypnosis or uuto-su^'j^'edtion (l cannot ^o into further detail 
hero). If the or^'an of ec;uil ibriuii is put into aufficieutly deep sleep, 
the first frij^ht no lon^'er has an arousin;; effect and one can later 
observe the psychic effects of the lack of counter-pressure. There are 
alkaloids that aiiestlietize the or^jau of equil ibriui;i, e.^. scopola'"'.ine 
upwards of C.LCH (!) ^| unfortunately, it is already dpji^orous in such 
a dose. In feet, scopolanine alone is not sufficient to produce a 
comiterfeit of the lad: of counter-pressure, the general ::u3cle and 
joint sensation rr^ust also be suppressed (say by ..cans of alcohol), and 
the skin no-.isc lihev.-ir.e (by ^ettin^ into the water or by applying; ..nosth- 
etizin^ substances (cocaine) to the skin at the supported places). 
- The ill-reputed witch's ointcient of the "'iddle ^es also had the 
effect, aiou^ other thinj;s, of deadening the feeliur of counter-pressure,— 
Certain compounds of bronine likewise affect the organ of equilibrium 
in this sense, but they disturb the psychic side-effects of the lack 
of counter-pressure. - The organ of equil ibriun can also be irritated 
by electrification; we think we are falling; toward the cathode. 

In the first fifth of a second, the lack of counter-pressure produces 
fright. The fri-ht is the less, l) the uore often we have already exper- 
ienced the lack of counter-pressure? P.) the better we are prepared for 
it occurring. If the sensation of counter-pressure is not extinguished 
suddenly as in a junip or in hypnosis, but gradually as in the application 
of poisons, no frif|;ht at all is felt. 



- 143 - 



The fright is followed Ly a peculiar draivin^ sensation iu i!ie area 
of olie esophagus, 7.'Iiicli ivraduclly subsides a^ain after about l/*? niuute. 
In the first socoiid, the braiu and the sense ori2;ans also be^in to func- 
tion very intensively, the recepti'vdty to sense and touch inpreasions 
increases, the brain associates incredibly fast, thou^^hts and decisions 
ar* dispassionately and lOj^'ically directed to concrete things. The first 
two uiuutes sco;:'. li!;e four hours, yet one lias a feeling for how -;uch 
tine has actually pas.sed. Goin^j hmd in hand with it is a peculiar 
insensibility to pain and listlest-ness wliich continues 1)eyond the state 
of laclcing counter-pressure, if the latter does not last too long. 
This nay be the reason why jusipinj in the water is felt as an amusement 
and not a torture. In itself, neither the punish-ieut on the soles of 
the feet that one ;;ets when r.ieetin^- the v;ater feet first nor the rush 
of blood to the head when the head cones first is a pleasure. A concep- 
tion of up and dowi is preserved but, with eyes closed, it can hardly 
agree with reality. In ny opinion, this observation furnishes the 
objective indication that the sensation of covuiter-presaure is actually 
extinguished . The beart works faster than usual. It uay be possible 
to e^^laiu all these syaptoms teleolo£;ically. In nature, counter-pressure 
is lacking wi en we fall off somewhere, and then it is a natter of not 
being lacLadaisical , of observing clearly and sharply, and using every 
possibility to save ourselves. 



Novels on space flight often describe in vivid colors the intense 
inner experience that persons nust have when they no longer see the 
earth as the foundation of all that exists but only as a star a=iong 
stars. Here is on ezanple : 

"Lindner suddenly uttered a loud cry and pointed downward with 
outstretched am. West and east, south and north, beside and behind 
the earth, they saw space, they sav: the stars glimner. As they saw 
the mighty sphere float freely in space (the earth can never be seen 
as a sphere, at best as a disc in the sicy; no ciore could one see the 
stars behind the earth, for the huuan eye cannot estimate such distances. 
11. C.}, the sphere on which tliey had stood and, in all physical and 
natheraatic-geographic education, had always been a firm, iumovable, 
straight foundation in the subconcious, they suffered an inner shock 



- 144 - 



Later, these phenomena grow weaker. The heart, obviously fatigued, 
works more slowly them usual ', the brain also works aore slowly, and 



comparable to the blow of a cannon-ball which, in the turaoil of battle, 
rips off a soldier's ana and makes hiu the more conscious of the fact 
that he is missing something and can and umst live without tliis part 
of his body which he had considered as an inseparable part of his person.' 
(From LUDV/IG jiJJTON'S "Bridges Across Interplanetary Space", Johann Georg 
Ilolzwarth, publisher.) 

Dr. KAHL DEBUS even asks whether man will be able to survive the 
emotional shock at all (LEX* "The Possibility of Interplanetary Flight", 
Hachmeister and Thai, Leipzig). 

To clarify the question, I would like to renark : "Up" and "down" 
are concepts or categories, that is modes of contemplation which we 
associate with stimuli from our sense organs. One cem also say that "up" 
and "down" are elenents of representation which, because of the way 
our brain works, must be absolutely included in every sensation and 
concept of ours. (Both designations say bivsicLy the same thing.) 

The space traveller will naturally also have the sensation of Hip" 
and "down" simply because he cannot have a single experience in which 
these eleuents of representation would not be included. For that matter, 
a high-flying airuan no longer views the earth as the foundation of 
all that exists but as a basin covering the lower four- tenths of the 
large empty sphere at the centre of which he finds hinaelf. I'ho exper- 
ience of the space traveller will differ from that of the high-flying 
airiaan only in that, with him, the lower part of this sphere is not 
pointed over with a terrestrial map but with a stellar map. 

This change in the heart through abnonaal conditions of coimter- 
pressure is a purely psychological process. Physiologically, the work 
the heart must perform, even with tlie hi^_;he3t acb^isnable countor-^iro^.sure, 
iacreases at the uost by l/lO. 

If, as sketched in Fig, 57a, we make the water in a circular pipe 
circulate by neons of puup P, the work of the puup will be nearly inde- 
pendent of counter-pressure. It is true, lifting the lir^uid in the one 
arm is more difficult, but for that, Lae downward pressure in the other 
arn is greater, 30 that the ti/o exTects Ciincel each other out. 




Fig. 57a 



- 145 - 



At nost, the circumstance trould have to be considered that, in the 
lover part of the pipe, actual liquid is under greater pressure and hence 
the friction against the v,'all is jjrei.ter. 

Ill 01:1' snalleat j1 oorl vcsaels, the so-culled capillaries, the fric- 
tion is greater when the blood-pressure is higher. In so doing, however, 
the increase in friction is not proportional to the increase in pressure 
(the pressure of the outside air of 1 atm laust be added to the blood- 
pressure), for the capillary imll is elastic and expands somewhat when 
the blood-pressure increases. As is well-Imown, however, liquid flows 
•jiore easily through wide pipes than through narrow ones. 

Let us figure the outside-air j^jressure to equal the pressure of a 
coluran of water 10 m high and the nonaal blood-pressure in the capillaries 

(the pressure in the larger veins does not interest us here) on the 
average to equal that of a colunm of water 60 cm high. Now, if a nan 
experiences the counter-pressure in a lying position, the increase in 
blood-pressure in the lowest-lying capillaries equals the pressure of 
a column of water under nomal conditions whose height equals the 
diameter of the nan tiiues the counter-pressure in units of gravitation. 
Naturally, on the average, the increase in pressure is only half as great. 
The work of the heart is still not 1 l/2 tinea as great as the work it 
normally has to perform in lying position. But it can manage 4-8 times 
this work. 

Therefore, one could at the uost consider the heart as stopping for 
psychological reasons, But every iiiedical doctor will confirm that nothing 
can ever follow from psychological reasons alone that causes death. 
At any rate, ay investigations give adequate proof that very high counter- 
pressure produces no psychological effects whatever, ^fhen YALISl writes 
that, with high counter-pressure, the heart would not be capable of 
fulfilling its task, he is expressing complete nonsense. '/ITTKUflN'S 
experiments in Breslau (cf. "ilakete", Vol. 1928-29, p. lOO) have shown 
that high counter-pressure in no way alters the functioning of the heart. 



the sensitivity to pin-pricks, pressure, and pinching increases, but 
does not become as great as usual. Only the peculiar freedom from list- 
lesness appears to continue imdiminished as long as there is no sensation 
of counter-pressure. No sea-siclcness was ever observed, even afterwards. 
In fact, sleepiness set in soon; drear^s were iiostly pleasant. 

Vifith repetition of a certain experi-ient, all these phenomena decrease. 
For exoiiple, every flyer will confirm that the draiiring feeling in his 



- 146 - 



chest caid stomach region was much stronger during his first rapid 
descents than during the later ones. In fact, the question is hoT iaany 
of the observed symptoms can really be attributed to the lack of counter- 
pressure. They are of the type that coiimouly arise irith excitetuent over 
an unusual situation. It is possible that the lack of counter-pressurei 
once it is no lonj^er an unusual state, irould have no psychic effects. 
If a deaf— aute, whose organ of equilibrium is disturbed, closes his eyes 
vfaen in the water, he no longer knows where is up or doim and at first 
becomes frightened. If he often repeats the experiment (preferably 
holding an air tube in his mouth), every trace of anxiety finally vanishes. 

The last observation supports the assumption that uan can live with- 
out the sensation of counter-pressure just as well as with it. But if 
that were not the case, it would not prevent man from ascending in a 
rocket. For, l) as we saw, we have means by which to delude our sensation 
of counter-pressure, so 'Uiat we would sense abnormal conditions of 
counter-pressure as normal ; S) by conditioning as in the case of deaf- 
mutes, the effect of abnormal conditions of counter-pressure could 
likely be ronoved; 3) finally, there would always be the possibility of 
connecting the observer's cockpit and rocket by only a cable and letting 
them rotate about each other. 

Note : Our knowledge of the physiologic effect of abnormal conditions 
of counter-pressure is today still quite fragmentary. Hence I would be 
honestly thankful for any information in this area. It was here actually 
my desire only to show that preparatory work is possible in this area. 



I was already acquainted with this effect of scopolamine in 1916 and 
suggested it as a remedy for sea-sickness. Today, it is actually being 
used together with atropine (in order to ronove certain unpleasant 
side-effects of scopolamine) in the Vasano tablets. In nry opinion, 
their effect is based not, as the inventor. Prof. Dr. STARKINSTEIN, 
Prague, believes, on a primary calming of the sympathetic nervous 
systemi rather, this is only a result of the fact that the feeling of 
counter-pressure is being partially suppressed. 



- 147 - 



7. Critical Reaarks . 

In conclusion, I would like to point out a few errors that are verj 
frequently being made in literature on space flight. 

1. One often finds the viewpoint represented that counter-pressure 
stopti 09I7 when the space-ship is found in gravitation-free space. 
For example, JULES VHIDNE lets his travellers to the moon float inside 
the projectile only as long as it passes through the gravitation- free 
zone between earth and moon. As I already said, that is wrong. If we 
(Fig. 58) hold an object into a fraae of laths b and let both drop 
at once^ the figure remains in the centre of the frame without "falling" 
to the bottom, for the frame naturally drops just as fast as the 
figure. 




Fig. 58 

The rocket is exposed to counter-pressure only as long as it bums; 
with free flight, however, even the strongest field of gravity can no 
longer pull the observer to the ground (cf. p. 184). On the other hand, 
writers who dreau about space-ships made of weight-less materials (as 
DOIUNIK, LASSiVITZ, or LUD'TIG ANTON) can naturally let their heros feel 
counter-pressure during flight, for here the body follows the pull of 
gravity, but the space-ship on which he sttuids does not. 



JUT^ES VERNE is just as wrong when he writes that tlie projectile 
always turns the heavy bottom surface toward the attracting heavenly 



- 148 - 



body. In air-free space, the acceleration due to gravity of the tip 
in naturally just as great as that of the bottom, and so the position 
of the projectile is entirely arbitrary. By sliding their bands along 
the Tails (Fig. 59), the occupants could give the projectile any 
desired position in space; th^ could also set their rocket into 
operation at any time . 




-fJ^r-M-i^f^ 



Fig. 69 

According to HOKLiUJN, "The Reachibility of the 
Heavenly Bodies". (Oldenbourg, Munich, 1925) 

8. Jbiother sin against the problem of counter-pressure even has 
the honor, auong other things, of having been copmitted by ii doctor of 
engineering. Concerned is the folloiring i 

A body at an altitude of about 500 km above the earth's surface 
(just high eiiough so that the atiuosphere is no longer felt), vhich 
uoves at a velocity of 7.8 bm/sec in a horizontal direction, cannot 
fall to earth because the centrifugal force just balances the force 
of gravity. Proof i 

2 8 

V ^ / . 

Z = — 1 .m, G - m.g . (54) 

r + h (r + h)2 

The first foruula folloTS frco (53) and the second frwn NE^VTON'S 
lair of gravity. Substituting the above figures, we obtain 

Z - 0. 



' I am including this illustration as an extuaple of HOIIIANN'S peculiar 
talent of achieving his purpose by simple means. For an engineer, that 



- 149 - 



Ib certainly a capability tliat ctumct be valued too highly. 

Since there is de facto treightleBSneasj this crawling about along 
the Tails is quite useless. ItOETTT has criticized HOIILANN on this 
account, among other things; it seems to ae, very unjustly. Since 
IIOl^TFT often referred to ae in these explanations, I irish to explain 
herexrith that I consider IIOIELANN'S vork as basic in soae points and 
that I have learned much from it. It irould be veil for IIOEFFT to 
produce soaething approaching HOIILVNN'S achieyeinents in value before 
railing at HOUWUNN'S. 



This body noturally ireighs nothing; it is not subject to any 
counter-pressure. Nov, many people imagine this body only needs to be 
given a fillip upward and it would fly away frora the earth, since it 
"weighs nothing". That that is incorrect can be shown in two ways. 
First of all, this idea uilitates against the law of the preservation 
of energy. V^e con iiaagine a high tower being attached to any heavenly 
body. Then we let a body fly up in a spiral in the suggested manner 
and at the very top it is to arrive at the tip of the tower. There 
wc recover it iond use its kinetic energy in the perforaance of work. 
Then we siviply let it fall inside the tower and likewise use the force 
with which it arrives at the botton for work purposes. If the tower 
is infinitely high, the body arrives at the bottom with the parabolic 
velocity, by which it acquires twice the energy required to later 
give it the cijcular velocity again. Here also, half of its kinetic 
enev'jy coulcl he used for vork purposes, and we would have the finest 
perpetual motion uachiue. 

VHieu I itt-ote this to a young student of physics, he answered that 
we still had found tlie law of the preservation of euerg;)- to be true 
only under terrestrial conditions and from that it could not be con— 
eluded that it riust also apply in general. 

The philosopher has nothing with which to counter that, but the 
physicist can show that, this tine also, the law of the preservation 



- 150 - 



of energy is not in jeopardy : llaraely, if the body is to ascend in a 
spiral, that is like pushing it up on an inclined plane (cf. Figs. 79 
and 63). Nott, hoveTer, the force of gravity of the earth has a braking 
effect (it does not bralce only as long as it acts at right angles to 
the direction of motion; in this case it only has a deflecting effect). 
As soon as the direction of motion makes an angle irith the force of 
gravity, it has a braking effect and the body can make the ascent only 
at the cost of its energy of motion. 

3. ZIOLKO^ySIQ (in this connection, also conpare the second volume 
and LADKIANN'S article in the Journal for aeronautics) is thinking of 
placing the occupants of his rocket space-ship in a liquid that has 
approximately the specific ireight of the human body in order to protect 

them against the effect of counter-pressure. Thus he hopes to be able to 

/ 2 
increase the acceleration to 100 m/sec and uore. But that can be count- 
ered by saying that the part of the htiman body most sensitive to counter- 
pressure is the brain, and the brain cannot be helped in this iray. 
Dr. GAHSAUX placed dogs on rotating discs and found that the main damage 
caused by strong, persistent counter-pressure consisted of the brain 
pressing against the irall of the cranium. Rupturing of blood vessels in 
the rest of the body occurred less often. These causes resulted in 
death even before other injuries set in. 

4. VALIEU suggests letting the counter-pressure stop gradually so 
the occupants can get used to the neir state; he likeiriae vants io let 
it begin sloirly. First of all, this means an mormoua waste of fuel, 
as ire shall see in Chapter IS. Secondly, it is quite unnecessary for 
physiological reasons, for ire daily experience the most abrupt changes 
in counter-pressure vithout harm (e.g. irhen Jumping, driving, etc.). 
For example, if ire drive on a bumpy road, the counter-treasure may 
change 10 times from the value of up to S-3 g in the course of a 
second. As far as the psychological side of the question is concerned, 



- 151 - 



•with regard to p.ld3| it seems to me like carefully and gently taking 

a young pi^; by the stonach so as not to tickle it too strongly by touching 

it suddenly. 

5, The layrjon largely visualizes a counter-pressure of n units of 
gravitation as being siuilar to a load lying on top of the experiaental 
person that veighs n tix.ies as much as the person himself. But that is 
not correct. In reality, it is a natter of the loirest-lying body parts 
being pressed together with this force while the body parts lying on 
top carry a considerably smaller load. On the average, the state of n 
uiiits of gravitation can sooner be compared to that of a man irhen a 
■weight only l/S n tiues his body weight lies on top of him. That is why 
\ eop] e who are iinder a counter-pressure of 30—40 n/sec con still 
get up and nove, whereas that would be iapossible to most if they 
had to bear 3-4 tiues their body weight. 

Chapter 10 

Ilant!;e. Overcoming Gravitation 

It is well to say sonething on the topic in this general section. 
Later I will speak about a nunber of imaediate prossibilities of utiliz- 
ing my rocket nozzle, e.g. for propelling air-craft, etc. 

Of these explanations, the layuan night only take note of the following! 

There are two possibilities of elevating a body : l) lifting it up, 
2) throwing it up. 

It can be lifted only as Long as there is something on which to 
support the lifting force, let us say the ground, or a fulcrum for a 
lever, or a roller, or surrounding air (e.g. with aircraft); a burning 
rocket is supported by the ejected gas particles. IXirthemore, we can 



- 158 - 



regard bodies as being lifted that are kept aloft hj electric or magnetic 
repulsive forceS| etc. 





Fig. 60 



Fig. 61 



But all these means irould fail if ve wanted to lift a body avay 
fr(Hii the sphere of attraction of the earth. There are no supports for 
levers or block and tackle in interplanetary space; there likewise is 
no air, and a rocket cannot bum forever, at the uost 8-10 minutes. 
No more could ve, vith all the means on earth, produce electric or 
magnetic repulsive forces capable of lifting a body out of the field 
of attraction of the earth. 

On the other hand, it is theoretically possible to throir a body so 
high "that it no longer falls back". Astronomy teaches that a body can 
no longer fall back to earth if it is hurled avay at a speed of 11.2 
km/sec. At a someirhat slotrer speed one can throv it as high as one 
pleases, but aftenrards it again falls to earth. 

Hence, iu order to recover a rocket, it is not absolutely necessary 
to tie a string to it, as a irell-knoim astonomer somevhat ironically 
suggested to me in 1919. 



NoTT, this velocity of 11.8 km/sec is approsimately 6 tiiues as great 
as the highest uissile velocity achieved so far, and it is not at all 
likely that a connon-ball could ever be given such a velocity. But 



- 153 - 



today we Imow three devices Trhich could theoretically be perfected so 
far as to uake possible achieving this velocity, nanely the electro- 
magnetic gun, the electric vind-wheel (cf. Chapter 22), acd the rocket. 

The electrouggnetic gun : If a magnet m (cf. Pig. 68) irith poles n 
and s is slipped into a magnetizable pipe M and it is possible to 
continuously aalie the pipe south-polar at S in front of the north pole 
of the magnet and north-polar at N in front of the south pole of the 
laagnet, the magnet is hurled out (in Pig. 68, D indicates the winding). 

(0 )'l KET^ S^3() )llSiIl) * 

Fig. 62 

Theoretically, the capacity of this gun is unli'.uited, except that such 
gi 1 .'i Tci-Ti S'l ui become uuncuiageably large and expensive. For curiosity's 
sake, I once calculated the diuensions of such a gun that irould have 
the capacity to hurl a nan into outer space. It would have to (under the 
uost favorable assunptions) consist of a tunnel over 10,000 Lm in length. 
The tunnel could lie horizontally (the only way possible), but it would 
have to be punped out to a vacuum and sealed in front by a breakable 
cover aiid by bulkheads. The hurled space-ships would have to weigh at 
leaat ?0,OCO,OCCi kg, otherwise they would have little hope of getting 
through the earth's atriosphere intact. For this reason, it would be 
possible to shoot the projectile from a corapletely horizontal tunnel, 
uot one that is bent upward at tlie end, as PIil.jU3T declared it to be 
necessary, (in this connection, cf. LEY : "The Possibility of Travelling 
in Interplanetary Space", p. 303 ff.) For the rest, however, I endorse 
everything that PI-iJUST has said about the electroi^agnetic g-uii. The 
source of the electricity and the storage cell would naturally also 
have to be of appropriate foruat. 



- 154 - 



The electric vind-whcel iroultl not roc^uire any leaa gi^;;aitic ;:-.ean3 , 



Ou the other haud, today it a^jpeart, inconparably si spier to reach 
iuterplanetary apace by i-ieaias of rockets. 

Ilan.:e . V/ith hi£,h iuitial velocities, rockets can naturally not 
only fly Iiich but far as veil (long-distance rockets). Astronony teaches 
that, if Iftuncbed correctly, a long-distance rocket can reach any point 
on earth. 

Index of the aost inportant fonuula quantities i 

A : energy 

a : minor axis of the trajectory ellipse 

e^ I angle of the trajectory curve vith the horizontal 

«*>i: angle of the trajectory curve with the horizontal at the place 
where the rocket stops burning 

e t linear eccentricity of the trajectory 

g : nuaerical eccentricity of the trajectory 

F I area covered by the radius vector 

g I acceleration due to gravity 

gg: acceleration due to gravity at the earth's surface 

gji acceleration due to gravity at the point vhere the rocket 
stops burning 

p I paraneter of the trajectory ellipse 

r t distance of the rocket fron eeiitre of the earth (radius vector) 



' Besides, vith respect to the financial -technical aspects, these 
▼ould be "indivisible units". Cf. Chapter 18. 



- 155 - 



r^ : radius of earth 

r, I r wheu burning stops 

rj, ; r at the place T;here the trajectory is horizoutal 

r J hi^ihest point of the trajectory flotm 

r . : lowest theoretical point of the trajectory ellipse 

t ! tiiae 

V : velocity with restject to the centre of the earth 

Vj : V when burning stops 



Sl^l 



±. 



9 



5> 



: iiiijile of direction 



As soon as the lou^-distoiice rocket stops bumiugj it continues 
to fly like a shot projectile, './ith the use of gasoline and with constant 
rearward thrust, it only stops burning above the relevant part of the 
atiosp'iere; with the use of kerosene, it leaves the atmosphere at least 
within a few seconds after burning has stopped. It finally covers the 
greate-it part of its flight in air-free space. 

The flight trajectory fron the point where it leaves the atmosphere 
to the point where It re-enters it again can be calculated with astron- 
OBic accuracy, but the usual ballistic formulas are not suitable for 
the purpose, for the final velocity is of a aagnitude at which the fact 
must be taken into account that the attraction of the earth decreases 
with th)9 altitude reached and also is not parallel to itself (as is 
assumed for simplicity's sake with the ballistic calculations). 
Furtheraore, there is no air resistance, so that the trajectory does 
not represent a ballistic curve but a pure couic section. 



- 156 - 



Astronocy teaches that, with starting velocities of up to 11,180 
laa/sec, the trajectory curve is an ellipse -with the centre of the 
earth at one if its foci. 

According to IC5PLJ3Il'S second lav, the radivs vector r draim from 
the centre of the earth to the rocket covers equal areas during erxual 
periods. If v is the initial velocity (with respect to the center of 
the earth), o( the angle between the flight trajectory and the horizontal 
when leavin«- tlir> earth's atiTiosphere, t the tine, and F the area covered 
by the radius vector, the following is Icxiown to be true : 

dF = --- V co3«k dt . (55) 

2 

Since, with dt constant, this figure is likewise suj^jposed to renain 
constant, and for different points of the trajectory 

V r^ cos c^ 

~v„~ ^ "rj"cosoJL ' K^'^&f 

In this connection, also conpare Figs. 31, 67, and 100. Concerning 
the work A that is required to lift a body within the gravitational 
field of the earth, one can say : If m is the aass of the body, g the 
acceleration due to gravity, and the body is to be lifted a distance 
dr, then (independently of the direction of the trajectory - cf. Pig. SO) 



Naturally, here 



dA = lagdr . (oO) 



dr = dh . 



Furthermore 



.. *dr .dr 



- 157 - 



If the body has ncde the ascent at the cost of its velocity, i.e. 
at the cost of its kinetic energy, then 

A = -i-..n (y^' - v^) (58) 

2 1 - 

oud from (58) and (56a), thl» 'ollows : 

- 8-2/1 1 ^ /_q\ 

Vi - vg - 2gjrj (-- - --) . (59) 

',/e con find the hichest (r ) and the lowest (r . ) theoretical 

point of the flight trajectory if ive reue.iber that here the flight 
trajectory is horizontal and we lust therefore set coaoL^ = 1. From 
(55a), (57), and (59), we then obtain J 

^ f^ ^^ ^/\ <» 2,1 Ix 

^ (1 - ---- cos cC^) = ^ C^r^ (~ - --), 

from which we find 



gi ^ ± Hgx ^1)' - (2 g.> i - tp i'\ cos' «. (60) 

agiTi-i-', 



''i — ^l' Oo I- _«' 



If we choose the plus sii^ii of the 3f|uare-root, ^;c■ gtft r , with 
the :iinus si^^n wo ^et r 



nin 



If we set 



v^ = "^ 2s^r^ , 



then r_ = o» . A body hurled array fror.! the earth at this velocity 
uiax 

does not fall back; it describes a parabola wJiose second vertex lies 

at infinity. If the velocity is still greater, the earth is naturally 



- 15G - 



atill leas able to pull the body bnck. Hero the valuoa for r have 

aax 

negative signs, iirhich neons that this point of the trajectory is not 

traversed at all, for, in our inquiry, t^e racliua vector ::u3t always 

be positive. 

For the sake of siui^l ification, we now introfiuco a new quantity z, 

i^T^. (a) 

From (go), we tlien obtain : 



»■, = ri ^— 2_i 



(b) 



The najor axis of the ellipse eritials the sum of r and r . . The 
ninor axis a is t 



The linear eccentricity e equals 



-^ 9.-1' vc; 



(d) 



and the numerical eccentricity ; 

, i ^ Vr^r(2"-^)icc03' «i . (e) 

* a ' 

Aa analytic geouetry teaches 1 

1 — e cos 9» ' 

as long as we designate the para^ieter of the ellipse as p and 



- 159 - 



substitute the augle of rlirectiou ^ = 180» for r . and 9=0 for r . 
Therefore 

/•in« = j-™; rmin = j-;^— , (s) 

Froa these two e;^vmtioii3, trJciu^j into account (e) oiid (b), ve find i 

p = >, I cos* «i .. ^' ' 

To deter-jjue the ahootin^ distance on the earth's ,w.rfnce, ire -lust 
deter line the an^le ^ „ -?i enclosed by the rn,dii vector dro.im from 
the centre of the earth to the rocT-.et. The shootiiig distance S is given 
by the for? ail a 

S = 2t,<Pi, (i) 

since 

This applies if we e::pressQ» in arc neasure; if we r^eaaure (h in 
de(;;rees, we laiow that 






KoTT, according to (f) J 



(lO 



V = arcco3[^(l-^)j 
and from (k) as well as fron (e), (h), and (i), it follows that 



(1) 

5 = 2ro arc C6s - ,. J^^^J^gg-' . 



- 160 - 



Here, the shooting distance depends on cos<^ as veil as on x. It 
becomes greatest when (p iB a laaximum. One -way of deteruining this 
inaxiuuin is by making 



d(lo g cos If] * 
3(cos'a] ~" 



(m) 



Notr, according to (k), (e), and (h) j 



log cos 9? = log (1 - X cos' a) - -= log [i ~{2-x)x cos^ a] , 



3 [log cosy] _ — 
d [cos* a] ~ I - ^cos^a "^ 2 ■ r ^T- x) a; cos="a 



-+7.T 



I {2-x)x 



(n) 



and this expression becomes zero irhen 



cos' a = 



2- x' 



(o) 



To illustrate, I here include a curve iu '^^^. CH, irbich sboirs the 
connection betireeo coso^^and x. 



.*' 


V" 








1 — 










•1^ 

X 


— ' 





— - 


— 


"^ 


"< 


N 


V 




« 




-- 







4 






\ 




» 


1 i } ¥ S i T t 


*^v 








Fi 


g. 


6; 


J 









By arc aeasure, 



S =2roai'CC03-2rrx ' 



(p) 



- 181 - 



and if ve note that 



3 2 

cos a " I - ain /k , then 



X 



5 = 2roarc6in#2zli (q) 

and by angle meauureLient 

n fan , ■ X / \ 

5 = -^^arc*ir,^- — , (r) 

This expression becones inaginary whon x> 1, for, irith horizontal 
launchlu^;, the rocket thon circles the earth and returns to the starting 
point (as long as x^ 3 is not true, in which case the rocket leaves 
the earth altogether) and there is no souse in looking for the most 
advantageous lauuchinQ an^le. 

Flir;ht period of lonr;-<li stance rockets . 

V/ith long-distance rockets, the appro.:i:.!ate flij^ht period can be 
quickly calculated if the distance on the earth's surface is divided 
by the horizontal coraponeut of the speed of flight at the nonent when 
burning stops ', 

The es;act flight period can be found according to iL'ilPL^Ill'S second 



' The calculation is sonewhat acre accurate if one divide s 9* ^7 *li® 
avorafie value of the anrular velocity iiud develops ^1 - x according to 
t'iO binomial theorem, sxippreasing the higher powers of x. For exapple t 

or in greater detail n«>«« (» — »)• 



&• 



2>ice*«i(>~s)* 



- IBS - 



dP 
laTT. The constant area — — , vliich the radius vector covers in (me 

dt 

second is Imotm. From it follovs 



i.. " 



and 



(s) 



: (^^COteii 



Koir 



(u) 



In this connection, also compare Fig. 67. 

V/e can integrate tills expression, if ire use another variable 

a 

Then (noting that dF - t. dP) ^ /df = 2 • J (Ji^) J 

(v) 



Pf 



j?5»|irRrgitt^+7fb'^"«[yB^'']| 



' As is Trell-Imown, 




- 1J3 - 



Chapter 11 
Further .iscent Calculatioaa 

Formula quantities for pp. 

a I counter-presaure 

b : acceleration 

c : e::hauat velocity 

e : base of natural lo^^aritluas 

g : acceleration clue to jvravity at the iiltitudd examined 

g J acceleration due to [gravity at earth's surface 

h : elevation above earth's centre 

In : natural lo^aritlim 

m s nass in general 

m i initial mass 



m : final mass 

m^ : loss in mass caused by air resistance 

r J radius of earth 

s : elevation of rocket above the ground 

t I time 

V I velocity with reference to the place of ascent 

V s advantageous velocity according to (26) 
V I parabolic velocity 

F I largest cross-section of rocket 
G i weight of rocket 

i 

Q ; altitude at which the air resistance decreases to --*• 

e 

As an index, II refers to the highest absolute air resistance. 



- 184 - 



L : air resistance 

U : fiaal nass, if we could disregard air resistance 

P : required rearward thrust 

jj : L + G 

P> ; air density 

Y ! ballistic resistimce coefficient 

5 : angle between the direction of acceleration and the horizontal 

M ! that which has reference to greatest deceleration through 
air resisteiice 

1, The vertical ascent of a manned rocLet is characterized by the 
fact that, taking the occupant into account, the counter-pressure iiust 
not exceed a certain limit. The ballistic coefficient is t^uite high, 
for generally concerned are large machines with high ballistic coef- 
ficients. Therefore, according to (-31), the value of v is also veiT^ 
high, so that usually it is not achieved at all because of the rei^uireds 
lAinor acceleration. Froa (Sl), by transforiiation and into<;ration, 
follows : 

m 



c.ln — - ■ V + 
m 



J-~ ^*- (<^^) 



Now, we want to use as -luch fuel as possible for increasing the 
velocity v and as little as possible in worliing against air resistance 
and gravitation. V^ith vertical ascent 



l2-^' = l|-^'+I^-'' = I^-''"-f"' 



dt . 



'Vith vertical ascent, we have no influence on^ g.dt. The accelera- 
tion due to gravity g is given and w& cannot shorten the fli^jht period t 
as we please because of the occupants. On the other heuid, 



- 165 - 



\— — dt is the smaller, the smaller -^- becomeS| i.e. the higher 

ballistic coefficient. Hence, here also, we are striving for a high 
ballistic coefficient, although v is not being reached. 

Similar considerations apply to the oblique ascent (cf. p. 190 ff). 
The Batter can be explained by saying : the greater the ballistic 
coefficient, the snaller is the relative effect of air resistance. 

Naturally, such large machines can also be sent aloft froa sea-level 
(cf. p. 348 ), for if only — is large, even with greater air pressure, 
equals^ and so v is sufficiently large. 

Thus, model E rises vith the highest adaissable counter-pressure. 
Here, a is constant during the burning. 

If b forms an angle 6 with the horizontal, then 

b + g, sino = a. 
(cf. Fig. 65). 

./ith vertical ascent (cf. Fig. 64), sin 6 - 1, and ire get t 

b = a - g. (62) 

V'ithin the atiiosphere, the actual acceleration is as good as 
constant, while the ideal acceleration 

\' ^*-Z- (33) 

is variable, for it is not confjiderations coucerniug the iTiachiiie and 
the required reurivard thrust that are setting a limit to acceleration 
but only considerations concerning the huiian organism. If L increases. 



we siuply increase P, ao that the counter-pressure re laius constant. 

Penetration of the Attiosphere ; Uecause of the low acceleration, 
inodel S oust cover a c;reat distance before attaining full velocity. 
In 30 floin^-, within the ati-.osphere, we can consider g as very nearly 
constant. In vertical ascent, b is also constant, and we have : 

V = b.t dv = b.dt a = ~- b t^ (6-l) 

8 

cdia + ndv + 2 dt = ("21) 

cdn + mbdt + Q dt + L dt = (35) 

G = ng. 
. I\irthermore, froEi (27) follows t 

L = Fy^v^ 
and this, taking into account (34) and (64), results in s 

Substituting this in (G5), we obtain ; 

_ *'■ 
c-dm + mb-dt i m-g-dt+F-po-b'-yi^-e "-"•dl=^ (37) 

That is a differential equation between n and t. Fron it follows j 



TO =■£ 






•■.[c-J'':f=....../ 



We find the constant of integration C when we substitute t = 0. Then 



- 157 - 



ire set C = ra . Therefore, 

^ ' 



m — c 



• '«»- J ,. -y '■■<'■ •«']• (60) 



A change in the factors conditioning the air resistance obviously 
only chan(ie3 the expression under the integral sign. Therefore, the 
latter re^^resents the loss in r.ass through air resistance, that is, 
naturally in its effect on the final Mass of the lifted and accelerated 
rocket. If n, is the loss in .-la^s due to air resistance, then it follows 
froti (88) that t 

. (70) 

li-i-S.t 

The ouantity e also occurs in the e:iq)ression. That is 

understandable if ve ponder the f-ict thnt air reaistiUice hn,a a relat- 
ively -reater bralcing effect on tux e.:pty rocket thaa on a full one and 
that the entire for;ula is oriented according to the lav of irapulse. 

For.-Jula (70) does not contain n^. That is as it should be. The loss 
in substance through air resistoiice does influence the naas of the rock- 
et, but it is dei-endent only on size, shape, and velocity, not on 
initial nass or specific weight. 

If we wish to exanine the effect of air resistance on the loss in 
iiiasa, it is best to divide (OS) by the e'juaLion 

^ + e .. 

i.i 3 m . e 
o 

vhicU we obtain from (38) when we disregard the air resistance and, 
for exanple, set^, or y ef;ual to 0. Then -./e get : 

3 . ^:l«_i!.f,.t^.e""'-dt. (71) 

j\f c-mo J 



- 168 - 




From that ire realize directly that m ctai only resain positive, i.e. 
the rocket can penetrate the atciosphere only if the second nember on 
the right side is smaller than 1. 1'hat is, the fol loving must be true t 



(78) 



We must, therefore, choose c and ra as large as possible, and F as 
small as possible; ire hardly have a choice irith respect to ^ . Large 
rockets must be sent aloft from a water surface, which, in most cases 
can only be the ocean. 

As the formula shows, reducing acceleration b has a favorable 
effect on the air resistance, at least at first. ^That that expresses 
is only the fact that the air resistance is the lower, the slower the 
rocket flies. Later, the initially favorable influence is naturally 
eliminated again by the widening of the integration linits, for the 
slower the rocket flies, the more invonvenient it becomes with time 
that it does not leave the ataosphere as soon. Wholly regardless of 
that fact, however, below the most advantageous velocity, we shall 
always make acceleration b as large as at all possible, while taking 
into account the human organism. Beside the loss of mass through air 
resistance, there is that through gravitation and, with the vertical 
ascent of model E, it exceeds the air resistance. 

At the beginning, the air resistance is small because of the low 
velocity} later it increases, then decreases again, and finally stops 
ctmpletely, for toward the end the air density decreases faster than 
the velocity increases. We can find the maximum air resistance (Ljj) by 

differentiating L from (66), or still better In L, with respect to t. 
If L is a maximum, naturally In L must also be one, and we obtain : 



_ 8 

L = In (F. ^.P^.b*) + a.ln t - ^^ 



- 169 - 



As we shall see ijiiediately, the :ja::invua value of L (ire will call 
it Ly) is reached irith V constant, and therefore s 



d f, -1 2 b.t 



from which follows : 



hi - \ b ' 



(73) 



"h " "^'^II ' V^-'^'I^ > (T4) 

"11 = -~.to.t^;i = U . (T5) 



Theae figures iiitereat us in so far as, at this altitude, the 
uanned rocket is ;;o!jt in dojiger of beinc crushed by the air reaiattjice. 
The inside pressure of itn tculis Liust therefore be so great that they 
atcind.the nir re;3istance. If they here endure the air resiataiice, they 
Trill eiidnre it throughout. 

■^iiice it is deoiraLle to place the tanks of the hydroj;eu rocket 
under low treasure taid lalce the:i so thin that they could not bear up 
under this outaide air rosisti^nce, the hyclro;jen rocket (cf. p. 76) 
ivust be enclosed in a Iierr.eticnlly sealin^j, strong-walled jacket which 
unfolds only when the fuels of the alcohol rocket are exhausted and 
the air re.3i.itance has Leco.ie less, 

7or H = 70C0 n and b = 30 a/sec", t.j becomes equal to .'22.0 sec and 

V|j «= uGl ra/sec. Jere, the force of the air resisttmce aiiounts to 

(substitutixig for V ) 

34 I 

L^ = 3000 k^'/m" = 0.G09 kg/cm^ . 



- 170 - 



The deceleration flue to air reisistcviice, in ot'ior worila tTje loss in 
propulsion cauaed hj air roaist^uce, can be found by dividing- the force 
of the ftir reui stance by the r.aaa of the rocket or, what aiov.nts to 
the aar.ie thiu^;, by dividin^i the share of the air resistcuice falling to 
the aruare centiaetre by the ballistic coefficient, and :".ul tiplyiug 
the fiuotient by the conversion factor 9,81. At this altitude, the bal- 
listic coefficient of model 3 still oraounts to 0,935 lti;;/cm". Therefore, 
the deceleration ia 

J; £i2SL.9.Gl - 7.1 m/sec^. 

^ 0. oas 

In the following seconds, it beco. s-.a atill larger, for here the 
denoninator of the fraction ~~ is steadily decreasing whereas the 

nunerator L, being close to its naximun, is naturally alriost constant. 
The uaxivauia relative deceleration ia about 



a/ a H , b +^g 



(76) 



(in construction, the fact must be noted that, at this time, ---=g)» 

The direct calculation of this quantity is so difficult and conplicated 
that I do not think it profitable to go into it here. One can convince 
oneself of the correctness of formula (76) in each specific case if 
one constructs a table or diagram for the relative deceleration of a 
tianned space-ship in vertical ascent. 

The calculation of 



r:Pp±.jy.t^.i^ "^''>.4t (77) 



mainly depends on what function of v, therefore of b.t, we substitute 
for S . I consider it premature, however, to ract ones brains over it 



- 171 - 



alreadj. In the first place, a few yeurs will likely pass before model E 
is sent aloft imdj secondly, the exact value of V irill really be laiown 
only after an ascent. As ?.0T11^ has shoim, the curve for v ^^ ^'^^ ^^'^ 
sa::ie for all projectiles, and it is to be expected that model IS trith 
its size oud its lar(^e fins irill shov a soaevhat different resistance 
coefficient than artillery missiles similar in fona. If one laioirs the 
exact course of the resistance curve, one vill have to substitute for 
it a function of v siuilar in shape, vhich is sufficiently close to V . 
The interpolation especially for v » COO m/sec raust be exactly right, 
since here the relative deceleration due to air resistance becones 
greatest (cf. (78)). In addition, the aim should be to malce integration 
in a closed expression possible by substituting this function, (if one 
does not prefer inte^jration by iieaiis of a (jraph, vhich is especially 
convenient here.) 

I, for rjy part, have used both <^raphic and calculation methods. 
In so doius, I dispensed vith closed expressions and siaply set V from 
- 3C0 m/sec eonsteiut, liLeTrise above 460 m/sec. Then I introduced a 
new varialile 



X » t. 



by which the integral (77) is brought to the form 
A ■Jx*-e-'^dx + B-Jxe-'^-di + Cje—'dx 

This expression can be represented in the form 

(Dx + E)e-" + F + Gj e-''dx 
The capital letters A to G indicate constant uunbers. 




- 17a - 



The integral ) e .dz cannot be represented in a closed expression, 
but it can be developed in a rapidly converging exponential series end, 
for X ^ 1, reduced to the still more rapidly convergent integrals 

\ ?__. .dx and [ S.»i~.dx. Namely, if one sets t 
) ~^ / x* 

a further result is t 






For -y between 300 and 400 ra/sec, I use a parabola of the third order of 

S3 
the form H + I.x + K.x -f L.x , at which the integration is very sinilar. 

In this way, I found the loss in propulsion due to air resistance 

to be 

t-«i 
L 



t "O 



-•i-.dt *->^ 800 m/sec, (78) 



Therefore, with the vertical ascent of model E, the ideal propulsicm v 

must be greater by 300 m/sec than If the air were infinitely thin or 
the space-ship infinitely hea-vy. 

In formula (88) we quietly assuaed b and g to be constant, but, 
taken accurately, only the sum b + g - a is constant. By ccmtrast 

e - So (rr^) • t^^) 

In calculating the ascent within the earth's atmosphere, such accuracy 



- 173 - 



is unnecessary (especially in this book). We need calcutate irith 
fornula (68) only up to an altitude of 150 laa; from there on ire can 
ignore air reaistonce end so use considerably sinplified fonaulas. 
At an altitude of 150 Ikn above the cJ'ound, the acceleration due to 
gravity is : 

g = 0.95. go . 

Since, up to this altitude, gravitation causes a loss in propulsion 
of 100 la/sec, we aalce an error of less than 0.05*100 « 5 m/sec if Tre 
S " So* ^^ ^® "^® * suitable neon value of g, the error becomes 
infinitely small. For example, for g^^ = O.OS.gg, it is less than 1 m/sec. 

It Tfould be another matter, however, if with the vertic^-.l ascent 
of a space-ship we assumed g to be constant up to the moment at which 
the space-ship has reached say the parabolic velocity. Here the error 
would be of the order of magnitude of 1 Ism/s, In this case, the change 
in acceleration due to gravity would absolutely have to be token into 
account. 

The problen can be solved by calculation, but the results would 
only have theoretical value, for, as we shall see in the next chapter, 
a manned space-ship does not ascend best vertically, but the energy 
loss in starting is least if it flies level above the atmosphere while 
burning. Since, with vertical ascent, the formulas which take into 
account the changes in g are quite complicated, I would here like to 
restrict nyself to simply showing the limits between which the loss 
of propulsion through gravity lies. 

'7e are presuming that our task is to give the space-ship parabolic 
velocity and make the simplifying assumption that g is constant. Then 
we can also assuae the acceleration to be constant (b = a — g). 



- 174 - 



If Vp desi^ates the parabolic velocity and r the earth's radius, 
and if 3 is the distance over which the rocket must bum for it to 
reach parabolic velocity, then, according to (57), (60), and (5C) i 



v-^ 



5} 

r + s 



Furthermore, according to the laws of acceleration (with b constant) 

'Y^.b.a . 



Vp = 



By equating the two values of v^, we obtain 

(CO) 




A. '7e now make the certainly too unfavorable assunption that during 
the whole burning period g = go = 10 m/sec. Then, according to (GO), 
we could have obtained s 

s » 1970 Lm; Vp = 9S5U n/sec; 
in this case, the ideal propulsion would have been i 



v^ = Vp + 



j gg.dt + \ — -,dt - 14080 ra/sec. 



B, Now, when the parabolic velocity waa reached, the acceleration 
due to gravity was only 5,75 m/sec". Presupposing a counter-pressure 
of 35 m/sec , in the last second the acceleration b would have equalled 
S9.35 m/sec^. If we had based our calculations on this acceleration 
figure, the result would have been too favorable. We would have 
obtained : 

V = 10,040 m/sec 



- 173 - 



(and if, with respect to the loss in velocity through i;;ravitation, ire 
had also used this too low value of g as a basis) 

"^s " % + J ^~ ^* +) 0«535 (^o*<^* = 12^0 m/sec. 
o / 

ThGi-efore, with a coiuiter-pressure of 3o m/sec'i 

l'?,3C0 m/sec <:^ v^^ < 14,0G0 ci/sec. 

The idonl propulsion does not lie say in the aiddle between these 
two limits but considerably closer to the upper one (about 13,700 m/sec), 
for during ascent the space-ship is considerably longer under the 
influence of the stronger field of gravitation. 

'.7ith a counter-pressure of 40 m/sec, we would have obtained i 

ia,7a0 n/sec <, v^ <, 13,630 m/sec, 

'?itli a counter-pressure (already hypothetical) of 70 m/sec^, we 
would have obtained t 

13,300 m/sec <C, ▼x ^ 13,500 m/sec. 

Mere we can ignore the difference between the velocity with refer- 
ence to the earth's centre and the velocity with reference to the 
earth's surface. 

3) affect of Air Ilesiatance with Free-Flying Heteorolorcical and 
Loug-Diatonce Ilockets . 

Here, v is to designate the air speed; all the other formula 
quantities are to designate the same as on pp, 163-164 

a) 3ffect with vertical ascent < 



- 176 - 



As e::plainec1 on p. 154, •.irith uniaemued rockets, propulsion stops 
Tfhile they are still within the earth's atrjosphere. Let Vj be the air 
speed at the noaent ivhen propulsion stops, Lj the air resistance, and 
^1 the air pressure at this place. After tp, - t^ seconds, vo is the 
velocity, Lg the eiir resistance, y^p the air pressure. Then : 

Consideriug that v changes very little as long as there is still 
air resistance worth uentioning* we con also write 

II, f^ V, ; i>i ^-^ i^i K 



The deceleration due to air renir.tnuce is ; 



t.' 






Total deceleration : 



J: 






ii 



If Vj was the uost advantageous velocity at the place s^, then 

L U 

(cf. p. 76 ff) -r- = G fui<3 the total deceloi'atiou is equal to --.-.3, 
"1 V 

If t'le velocity had been less thari Vj^ by (Vjj), the total deceleration 
due to air reiiistanca would be correGpoudinfjly snialler, na^iely s 






(G3) 



V 

that is, oaly ti"iGS as f^reat. 



- 177 - 



For vj = 1000 m/sec and the x'euaining respective quantities, we 
obtain, for ezaxaple i 

L 




73 m/ 



sec 



(exactly 69 m/sec. The difference is so snail, in part, because various 
errors that we nade compensate for each other). 

For vi = 10,000 la/sec; — - = 3 m/sec"* (here s, and hence the 

hydrogen content of the air, therefore II is greater), the total decel- 
eration anounts to 2,3 m/sec; an infinitely small cunount. 

X (' ^ 

to) '7ith oblique ascent, we nust divide \ — -.dt by the sin of the 

angle of inclination oat the nbnent when propulsion ceases. I aai 
choosing the oiagle of inclination at the be^'innin^ of free flight for 
the same reason why I carae to the conclusion on p. 107that 3 aust be 
correct, to begin with. 

For re-entry of rocliet projectiles into the earth's att^-osphere, 
the air resistance could be calculated as for artillery missiles. 
Here I aust refer the reader to textboofcs on ballistics. 



A few words light also be said concerning the landing of long- 
dist?Jice rocliets provided with a parachute , 



They enter the atuosphere with a velocity of 2 - 7 loi/sec at on 
angle o^ , assigned to this velocity according to foiTiula (o) of the 

preceding chapter. Then the parachute opeus, the velocity is retarded. 



These calculations apply only to long-distance rockets. They are 
not applicable, however, to space-rjhips that enter the atmosphere 
horizontally with a greater than circular velocity. 



- 173 - 



aiid the apparatus fiimlly laiicla at a luiifora velocity ve. 

Not :auch can be said about the last stage of the flight. The 
velocity ia deter.;ined Iry the fp.ct t'lat the air refjistance is equal 
to the weight. According to ("^7), it is 



7y^ 



cij G . (a) 



The foriula quantities have the sa. le .leaning here as in Chapter 8. 

At a higher altitude, v is greater because the air ressistance is 
sraaller, it is 



^eo 




(b) 



The braking distance, on the other hand, we oust er:aviine siore 
closely. We con si:;:plify our calculation considerably if, according 
to a iiethod given by PI?.,J/?3T for similar cases, we ignore the accelera- 
tion due to gravity in the first appror-ination. '7e are allowed to do 
so. At first, the rocket behaves alnost like a body left to itself in 
space and, beside velocities of kilonetres per second, the changes 
in velocity due to the force of gravity play no significant role during 
this short period. Later, the countor-pressuro heconss so considercble 
again that we are justly entitled to ignore gravitation beside it, the 
':ore so since, even now, the counter-pressure is still deter-iined only 
by the uir resistance. This iiethod of calculation would be theoretically 
iuad- '.is sable only toward the end of the braking distance, but that 
part of the flight does not interest us in the following investigations. 
V'e CTU further simplify our calculation by regarding this short distance 
as straight. 



Therefore, we e:ipress t'.ie deceleration as follows s 

dv 

^ = --dt' 



dv L 1 /} ^ o 

,_ = = FyP^ ~- v'^ (c) 



- 179 - 



In 80 doing, ^ ^ is the air density at the earth's surface, cmd the 
rest of the formula quantities indicate the same as in Chapter 8. 
FVirthermore. 

-^ - e "^ (cf. (34)). (d) 

n 

■ ia the distance of the straight flight line from the rocket to the 
ground, S is the distance the rocket nnist traverse for the air 

r 

resistance to increase to e times its value. fHirtherauKre. 

ds = - v«dt . (e) 

From (c), hy multiplication irith — — and taking (d) end (e) into 

V 

accoxmt, ve obtain : 



. FTfl£* e SUs 5 



dv 1 «_,A . S 




V n»i 

From that, by integration and taking (d) into accotint, this follows t 



(f) 



Here, v. is the velocity above the atmosphere, v is the velocity 
at the trajectory point examined;^ j -rould be the air pressure above 

the atmpspheire, but this number naturally equals zero. Ife finally 

obtain i 

Fy^ 

V = Vj .e. ~ 1 (g) 

Taking (c) and (e) into account, the deceleration is t 

b . - -IZ 2^ . (h) 

dt df 



- 180 - 



We find v.dv from (g) : 






m 



while, according- to (d) : 



d/3 



Therefore 



' m. (x) 

r'roa that, b is easily calculated. Fi^;. 71a shows tlie curve of h. 

Once the connections between distance covered, velocity, and 

acceleration are laaofm, calculatin^i the other fonula c^unntities 

l) 
naturally presents no nore difficulties '. Unfortunately, I cannot go 

into this any further for reasons of space and nust leave the reader 

to investi^^ate further theoretical connections hinself if it interests 

bin. As it is, the book is already considerably iiore corprehensive 

than I orii^iually intended, 

I only Tvont to state the iiarri'iuiu values of deceleration in order 
to investigate how strong the parachute ropes iiust be and to what 
counter-pressure the freight is eaqjosed, although only for a few seconds. 

We can find the air density at which the counter-presnure roaches 
its maxi.juin if we differentiate b with respect to^ in (i) : 



' Calculating the ti.ie leiids to the ex^ireasion \ dx, for which 

no clo'ied deaigantion hna boon intro'^'uced xiutil today (as say for nin, 
log, etc.). 



- 181 - 



r 



■»" asp 



If this value for S is substituted in (i), the result is the 
naximun value of deceleration : 

b = . (1) 



Interestingly or logically enough, F, V > o^<i ^'i cancel out. Since 

the graph of the air reaistance is on e:iponential curve, the saae brak- 
ing process will simply set in sonevhat later when, in the second case, 
the braking force of the parachute has increased nuny times over (then 
p' quite logically shows itself dependent on the brading force), 

but the course of the braking process will be the sa.je in both cases, 
Cf. Fig. 71b. It is evident that the size of the parachute does not 
affect the degree of counter-pressure due to braking. It should also 
be mentioned here that we have assumed the parachute to be a simple 



— -I- IS 



one, with which — I- ia thought to be constant. On the other hand, the 

curve for b would look quite different if we had equipped the parachute 
with regulating flaps that open when the difference between the pres- 
sure inside and outside becor.es too grep,t (cf. Fig. 71 c). 

According to Chapter 8, S = H.coseco<v, when o'^represents the 
angle between the trajectory ojid the horizontal. For exarjple, with a 
neteorological rocket rining vertically, oC would equal 90* and 

^1 

b = , (m) 

na:: 2 eH 

a figure which, for e:ia.iple, for vj = 100 ra/sec, would a-jount to 35.8 
a/sec" or ^.S units of gravitation. 



- 182 - 



Long-disttuice rockets ascend beat at the cvn^le derived from fonnula 
(o) of the preceding chapter. Natural I7, they enter the atsiosphere 
again at this an;jle. Froa the mentioned fomula (o) of the preceding 
chapter, this follows : 



coseccAw . 
opt 




and according to formula (a) of Chapter 10 

X " . 

61 ri 




b„„ - -i-i-.\ (n) 



Then we find that 



^^'^ 2 ell 

For exeuaple, for a shooting distance of 1000 Im, vj = 3160 m/sec and 

b would equal 18 g; for a shooting distance of 2000 km, b would 
max 1 61 b > QQjj 

be not quite twice as great, hence about 38 g. 

Now, on the whole, what is the greatest counter-pressure that can 
occur in the worst case with a regular long-distance shot, and what 
are the corresponding values for the distance shot and the final 
velocity ? 

We can answer this question precisely by differentiating b with 

, .1) d(lnb) 

respect to x in formula (n) .For — «= 0, we thto obtain 

dx 

X •> 0.T4923... 



' It is self-evident that all the calculations of extremes indicated 
here are acre convenient if one does not differentiate the figures 
theuselves but their logarithas. If a function reaches its extreae, 
its logaritliia also reaches its extreme at the sane place. 



- 103 - 



Accordiu2 to foraula (a) of Chapter 10, the corresponding final velocity 
would be VI B 6830 m/sec; the corresponding distance shot would be 
G130 loa. The deceleration would reach 53 l/3 g, 

A rocket weighing 50 leg would esert a force of 50'o3 l/S = 3675 kg 

on the parachute ropes, and 30 kg of nail would exert a pressure of 

1605 kg on the carrier. If the hottorj surface of a nail-box ia 0,1 m^, 

1 cm would take a pressure of 1 1/2 kg. Thus, the bottora letters 

o 
would have to endure about a tenth of the pressure per cm' which they 

endure when we grasp theu firuly with thumb and index finger. Naturally, 

the pressure on the letters lying on top would be still less. I cannot 

quite understand how sone authors .maintain that the letters would not 

stand the counter-pressure. It is likely one could also transport 

quite different objects than letters with such rockets. They would 

only not have to be packed at the bottom. Uesides, these conditions of 

counter-pressure only apply to the laost \mfavorable shooting distance 

of G150 km; with shorter distances they becoae Dore favorable because 

the velocity to be decelerated is not as great. The same holds for 

larger ones because the rocket enters the atmosphere on a more level 

plane aiid the stopping distance becomes greater. For exai-iple, with 

a shot of 1000 km, they would be only a third as great. And that is 

not even taking into account that the naxiuum counter-pressure can be 

reduced to less than l/4 of the figure calculated here by the use of 

parachute flaps already nentioned. 

Just a few words concerning the parachute flaps. The reader will 
excuse me for not yet stating anything on their construction for 
reasons -lentioued in the introduction. They operate approxir.-ately as 
follows t 

The parachute siuply adiits no greater air resistance them, let 
us say, b.'^.n^. As soon as, according to (i), the air resistance would 
be greater, the air simply opens elastic flaps on the parachute and 
partially escapes through then, thus suitably reducing its braking force. 



- 184 - 



The retardation remains constantly b2 until, due to the steady decrease 
in velocity, 



-Ltf.-a 



mj 



V <b2 again. 



This may occur trhen the velocity has dropped to V3. 

As long as the braking flaps are in operation, because of the 
constant deceleration, the velocity is 

V =» vg - bgt. (o) 

The distance covered since the flaps began to operate is : 

1 , . 

<y . vj;t - --- bt , (p) 

and the corresponding air density we obtain is 

av»bt-b2t8 
-^.e^ -e 2bS . (q) 

B> g can be found from (i) by means of a graph or by use of the 
Regula falsi, since all the raaaining fon-iula quantities are given. 
Kno-wing ^„, ▼« con be calculated; it is 

bg mj 

i - -.7^- • <^> 

Nov we shall do Viig To) lu^T'utj mental experiaeut t 

We imagine a rocket vith a siiiple parachute (l irill call it the 
virtual rocket, since no better irord occurs to ue). The tiro rockets 
have the sane laass and the parachute of the real rocket, vith flaps 
closed, is to have the soEie braking force as that of the virtual rocket. 
Finally, this virtual rocket is to be taken up beside the real rocket 



- 185 - 






at the SQue velocity by laeaus of acme assuued force. Obviously, vitb 
the virtual rocket, the air resistance will equal t 



.^ - x'-y^vS 



L^ - F 



After a feir conversions (taking (q) into account), ve obtain 

; ' 

vj iij+tr. K-t'C r|_ _»;_ . 

or, taking (r) into account : 

T A. -JL. 

mi 6, ^ ' 

The point irhere the regulating flaps close again is indicated by the 
fact that here L. becones equal to the actual air resistance iTi^.b„. 

X 1 •'3 

Therefore, here 

-^- . .. 

This point is best found by ^ji'aphic neons. Ife set 

^i 

and 

V' m J. 

Then ire plot the curve 

z==e^iSi>;*-e'^^-y (t) 

and find the place at which z ■ 1. 



- ICG - 



Noiv the fjviestion still interests ua, '.vhen, with a specific velocity 
and a gpecific, still Remissible maxii-mia deceleration bj,, are the 
re^julatiuij flapa put to the t^J'^'^test ur,e ? 

That will obviously be the case •.vhen L. reaches a iiaxinium in 
covipariaon to the hi^^hest perussible air resistance. 

^ron (t), this follows i 

v| y 

In z = * 2 In v„ + In y , 

abgS ^ abs 



d(lnz) X 1 



This expression obviously becones equal to zero when 

y B v^ = 3b S. 

After the velocity has fallen short of the value v-, the flaps 
will close and the parachute vrill again function like a sinple 
parachute. Accordin^-ly, we will base further calculations on forr.iula 
(f) again, except that aow we will use v- and f' „ as initial values 
for velocity and air pressure. We obtain i 



in-lL-s-!-I{/i-y93) . 



Note I In general, I follow the principle of publishing ne formula 
with which I have not worked for at least a year without discoverinc 
contradictions. With the forriulas of Chapters 10 and H, narked by 
letters, I have departed from this principle. They come from work 
which I began about 4 months ago and conpleted 2 months ago. I am 
publishing then already because, by using them, I can better support 



- 187 - 



my idea of the mail rocket '. ^ong the formulas of this book that are 
marked bj number* in parentheses, on lAe other hand, there is not a 
single one vith iriiich I have not irorked at least for S years, and 
hence, I believe I can vouch for their correctness. 

Formula quantities for pp. 187 — 190. 
drag 



uplift 



T I most adTantageous velocity 

R = p - a 

tf I angle betveen the direction of ascent of the horizontal 
All other formula quantities hare the same meaning as on pp. 169 - 164. 

3. Some details concerning the oblique flight of jet-propelled 
aircraft vithin the atmosphere . 

Here I irill call such aircraft ** Jet-propel led aircraft" or "jet- 
propelled flyers", -which are provided with carrying surface like aero- 
planes but are being propelled forward by rocket jets instead of by 
propellers. JLs in Chapter 8, ve again set 

P - R + a. (84) 

P is the total rearward thrust, Q is the force required to carry and 

In the meantime, another 9 months have passed, during which I repeat- 
edly had the opportunity of applying and testing the formulas. The 
calculation itself is correct. The formulas, however, ignore the circum- 
stance that the flight trajectory bmds downward somewhat during braking. 
That causes somewhat faster re-entry into iiie atmosphere and an Increase 
in the maximum counter-pressure due to braking. But the difference is 
very small. At the very most, for example, the deceleration amounts to 
54 g instead of 53 l/S g. The greatest relative difference occurs with 
the 1000-km shot, where the maximum counter-pressure is not quite 19 g 
(instead of somewhat over 18). Therefore, the above formulas can be 
confid«atly accepted. 



- 188 - 



hold the iiachine and overcoue the air resistance. It is the surplus 
that serves to accelerate the rocket. 

■'/e find Q from (^6) and (27) s 

3 = F. V.y^.v + in.g. (sin t> + k cosS). (GS) 

Vie already derived the for::iulas for the ascent with the uost 
advantageous velocity in Chapter 8 and saw that the rocket works best 
when it ascends vertically. Nevertheless, as I will show in the next 
chapter, other circuiastances can have the effect that fuel is saved 
with oblique ascent. 

In the ascent of aanned rocket aircraft, which cannot fly at the 
uost advantageous velocity because of the counter-pressure, the loss 
in itself due to air resistance and gravitation within the atmosphere 
is also least with vertical ascent. Ilaf.iely, for 6 ^ 90* : 

^^* ni^.(sin 6 + k.cos^) + L 
(J. . -.--._ 

dh v.sm <5 

Dig L ^ mg L 

B -— (l + k.cotg o) + — — cosec^^x,— + — — • 

V V — v V 

'.'/ith/:^ 90", the suiiiuaads of the latter expression nust be rmltiplied 
by the nuiifcers [^vetxter than 1 if one wishes to obtain the su'^mnds 
of the forriier expres-uou. Sven then, tlie friction of the air a^jp/inst 
the carrying surfaces has not been taken into account, ifliich falls 
away with aachiues that have no cari'ying surfaces. Therefore, an 
oblir;ue ascent rrith carrying surfaces can never facilitate advuncins 
to intornlauetary spj,ce. (As, for exivaple, VAJ.I'illl and GmIL a33U::e, 
evidently ruialed by the fact that, considered by itself, 2 is uctuully 
siaaller with obliijue ascent.) A rocket aircraft with cari-ying surface 
will also do vrell to aacend vertically at first. 



- 189 - 



It is true, in descent, such surfaces can very considerably extend 
the range of rocket aircraft and long-distance rockets. For example, 
if a long-distance rocket without carrying surfaces starts at on angle 
of 45* with a velocity of 3 km/sec, it will fly 400 km according to 
Chapter 10. If, on the other hand, it flies horizontally and the descent 
occurs with carrying surfaces from an altitude of 50 km, it reaches a 
distance of 1350 km, (in Chapter 18, I will state how I obtained this 
figure.) 

It is actually anazing how little the theory of rocketry has 
progessed. The primary rea,3on appears to ne to be 

because it is so difficult. The theory of rocketi*y is one of the raost 
difficult chapters in the vhole theory of nechanics. In a certain 
respect, the notion of the rocket contrasts with every other type of 
ciove.jent. 



In the first place, with all other propulsion nachiues (as with 
the lissiles of catapulting cannon), the uiass on which the propulsion 
iuechauisin can be supported is unlinited. For exoiiple, when a loco.iotive 
sets a train in i.totion, its wheels seek to push the iriiole earth bacl:- 
T.-ard and find their support on it. In coupariaon to the I'.ass of the 
vehicle, propellers likewise throw back enorvious cuid, above all, 
uiilinited lar^e fjuantities of air a,ud imter. 3y contrast, with a rocket, 
the mass tavoim backward can never be {^,s jreat as the initial wei^jht 

of the vehicle . 

/ 



"< 



^b 



?i;". 64 



' Y.iT;Il.i, and Ci.VIT,, for ex 



jiple, have Tor^otteii tliia fact. Tlioy r,iijply 
applied the principles of t^ie airorart to the rocTret f.ircruft. 



- 190 - 



Secondly, the supporting; mass of all other vehicles is in relative 
motion during travel. With the rocket, the fuels are being carried 
along and, therefore, always have the same notion as the rocket itself '. 

The rocketry theorist must always be aware of the entirely different 
conditions under which the rocket works and cannot adopt any models 
that have proved theuselves in the calculation of other propulsion 
devices without first testing theu. It took me, for exauple, over 
10 yesrs to work out the theory of rocketry. Not every one is suited 
for such a method of work, which is one reason wliy, until 15 years 
ago, no theory of rocketrj* existed. 

The second reason is that, because of the insignificant possibilities 
for use of the rockets built so far, the whole field was not regarded 
as very fruitful and, hence, there was not very much concern about 
doing research in it (even today, most specialists in ballistics do 
not consider it necessary to read what has been inritten on the theory 
and application of the rocket), 

4. The Oblique, Straip-:ht-Line Ascent of Model E 

Fonnula quantities for pp. 190 - 193 

s : distance of trajectory covered 
y : altitude above the ground 
j^: angle of trajectory with the horizontal 
A : angle of rocket axis with the horizontal 



' Iftiat follows from this is, for exMjple, the peculiar fact that the 
concept of energy, by the use of which we con evaluate the performance 
of aircraft so well, can only be applied with utmost caution to the 
rocket, for depending on the state of notion of the rocket, with equal 
action, the saiBe rocket uotor ceui effect nothing up to millions of 
horsepower. Details in Chapter IS. 



- 191 - 



The reiiiaiuin^ formula quantities are explained on p. 187 

^e are visualizing (cf. Figs. 79, 27, 65, and 79a} a space-ship 
ascending in a straight line at on angle ok to the horizontal. In so 
doing, the rocket axis is to be someirhat steeper so as to compensate 
for the force of gravity by the rearward thxnist and the aerodynamic 
uplift; othenrise, the direction of flight irould gradually incline 
toirard the horizontal (Pig. 65). In air-free space, the axis irould 
have to make quite a large angle irith the direction 6f flight. In the 
atmosphere, the angle between the axis and the direction of flight 
brings about an aerodynamic uplift, so here the inclination could \)e 
considerably less. The angle between the axis and the horizontal is 
to be ^ . On this trajectory, the rocket is to ascend vith a counter- 
pressure of a m/sec^. Ve can then find the actual acceleration d 
according to the acceleration parallelogram of Pig. 65. 




Fig. 65 
We shall use foroula (6l). Here 

Q > L + g.sin^.m. 

From that, analogous to (61) to (65) and (85) ff, this folloirs t 

dv^ dm 

P ■ — — .m " - c. — - - bm + g.siUiS.m + L. (96) 

dt dt 



- 192 - 



Now 

b + g.si.jxp" a, 

L - Fa^^.v^ . 

If 7 indicates the altitude above the ^roimd and s the disteiuce 
covered, then 

y = s-sinoC, 



From all that, this folloirs i 



dm a Ffiob' , 'IT'^'^ „ 



m = e 



, bt' 



rrin 



:mj,,.,.-^-,, 



(97) 



(98) 



Because the structure is the some, application and discussion of 
this forraula is like that of the fonmlas (€8) ff throughout. So I need 
not go into that any further. 

It is interesting to note that, vith oblique ascent, as long as it 
occurs in a straight line, the air resistance is absolutely greatest 
at an altitude of H Ton, -whereas the relative deceleration reaches its 
naxiaun 3-5 km higher up. 

If the space-ship ascends on a bent curve, lire must build the 
fol loving equation from (96) < 



dm ^ a F 8ay „ 



0. 



(99) 



- 193 - 



lutegratiug that, we obtain : 

•[»*o p-jyi>^-e -dt 



ni = e 



(100) 



Naturally, in evaluating the integral, v, t, and y vould have to 
be esqireased by a given arguiieut. 

Chapter 12 

Considerations of TSnerfCT 

Formula Quantities for pp. 193 to 217 

A : total thermo-cheaical energy of the fuels 

B J designation of energy (with wrong starts) 

K : designation of energy with right starts 

E ; kinetic energy of erapty rocket 

I exhaust velocity 

e : base of natural logarithms 
nij B. : aaas of rocket 



V 


• 


vel 


oci 


ty 




X 


: 


ide 


al 


propul 


si on 


X 


* 
• 


V 


or 


^x 

c 





Out of this chapter, I can pick only single, loosely-connected 
pieces. Only a detailed treat:aent would show the deeper connections. 
Perhaps, in a nore detailed work, I will report on the three-body 
problem and on an alternate approximate calculation apparently first 



- 194 - 



used hj me. Vfliether, with cy everlasting shortage of funds and the 
resulting impossibility of spending much time in scientific studies, 
I will ever be able to coaplete this comprehensive work or even £;et 
it printed is another question. 

Relative to the three-body problems^ for example, I shall here 
sc^ this much > We are in a position similar to that with higher than 
4th degree equations; as has been proved, they can in general not be 
solved with the supplementary means of our mathenatics. But that does 
not prevent us from figuring out every numerically given problem as 
long as a solution exists at all. With three-body problena, part of 
the figures can even be replaced by letters. Besides, I have 

plans of apparatus with which three-body problems can be solved in 
the shortest of time by the graphic method. 

In this chapter, I am staying in the area of classical mechanics 
and am completely avoiding EINSTEIN'S theory of relativity. Wiat I 
have substantiated here, however, is easily converted to EINSTEIN'S 
system, 

1. Impulse and Work 

If one applies the energy concept to problems of rocketery, one 
experiences the most peculiar surprises. Not that the principle of the 
conservation of energy no longer applies in interplanetary space; 
naturally, it is valid as heretofore, but, since we know of no absolute 
rest in the cosmos, it is here impossible to simply speak of motion 
and, with that, of the energy of motion. One must always state with 
reference to which fixed point the body has the energy of motion 
mentioned. 

For example, a block of ice lying at rest at the north pole of 



- 195 - 



the earth has no Ifinetic energy -with reference to the centre of the 

earth. '7ith reference to the centre of the sun, on the other hand, it 

, 1 2 

has a velocity of 19.1 Ian/sec and a kinetic energy of .m.S9700 mkg. 

2 

No nore can ire speak siuply of potential energy. Ifith our block of 
ice, we even get three different values for it. Naaely, l) the value 
with reference to the north pole of the earth; i) the value trith refer- 
ence to the centre of the sun, when one thinks of the body being carried 
away fro;u the earth and brought to the suin; 3) finally, the value of 
its potential energy with reference to the centre of the sun, when one 
thinks of the whole earth together with the block of ice as being 
brought to the sun. In this case, the work necessary to talce the body 
away from the earth would not be required. In calculating the energy 
and estiuating the kinetic energy in the reitiainiug parts of the earth, 
it is aifj^nificant whether the notion of the body is being considered 
with reapect to the earth's surface or with respect to the earth's 
center. 

In space, the principle of the preservation of the centre of gravity 
(naturally, in the framework of classical nechanics) is absolutely 
valid, i.e. not taking into account the actual state of motion of the 
system, Otherwise we would find considerable deviations from this 
principle on the earth, which could not be explained any other way. 
According to COU.iVOISISt'S research, which can be regarded as established 
today, the whole system of the Ililky TTay is raoving toward a point 
lying barely 25* above the plane of the ecliptic with a velocity of 
roughly 300 km/sec. Since, however, the earth itself revolves about 
the sun at 39,7 km/sec, its absolute velocity in spring differs from 
that in fall by 3*39.7*eos 85* = 45 lan/aec, i.e. almost l/lO of the 
absolute velocity, and, in any case, we would notice discrepancies in 
the law of impulse resulting therefr(Ha» In this connection, also coopare 
p. 56 ff. 



- 196 - 



The principle of the coiiservatiou of euer^^ in interplanetary space 
also appears ostabliahed; the principle of the preservation of the ceutre 
of gravity con be derived frora it. 

For ©sample, if a aysten of t»o masses n and dm has no notion, and 
a force acts betveen the two which inparts velocity dv to aass m and 
velocity c to nans dm (here one should iniagine the differentials as 
small but finit'e ai:d easurable quantities), then the worlc perfomed 
by this force is : 

A, = -i-.n.dv^ + -i-.dni.c3 . (lOl) 

a 8 

If, on the other hand, the sa::e systen is related to an origin of 
coordinates which, relative to the systeu, advances in a straight line 
aiid uniforily with velocity v, then, after the iaterveniug force has 
acted, uass m has the velocity v + dv, and mass dn has the velocity 
V + c (ncanely, if we nake c relative, i.e. assi^ii a negative number 
to the letter c). Then, the work perfomed by the force is 

1 11 1 

A^ = n (v + dv)^ mv^ + Cm (v + c)^ dnv^. (lG2) 

a 3 2 3 

Opening the braclcets and rei;roupin£, we obtain : 

1 1 

1 1 

=■- -frmd(''+n<^mc*-rv(mdv + cdm). 

2 2 (1C3) 

TProDX the principle of the conservation of energy and that of the 
relativity of motion, it now follows that it is irrelevant to the 
absolute quantity of work performed by the force how ;;-reat velocity v 



- 197 - 



of the reference system is. In other words, 

A^ must equal Ag . 
From that, it follows that 

Ag - Aj = . 
That is (according to (lOl) and (l03)) 

V. (la.dv + cdm) = or ci.dv + c.do = . (104) 

Relative to the ayateu ivhere v = 0, nass m ^-eta on energy increase 
---indv 5 relative to the r.ioving systei, on the other hand, it gets an 
energy increase 

.i3.(v + dv)^ .ra.v" = m.dv + .n.dv^ . (105) 

3 s a 

That is considerably lore. Nevertheless, the total energy in inter- 
planetary s!>ace is not ^reuter, for, Tath reference to this systeu, 
work to the aiaoont of cdm is simply withdra'tm from nasa dm. 

Naturally, this ^jreater traiisfor.iation of energy was not perforued 
by the nechanism which caused the two uasses to be impelled apart. 
4s heretofore, its performance was 

— radv^ + — - dmc^ lakg . 

a a 

This extra work was exclusively perfoi-jed (sit veuia verbo) by the 
theoretic mechanics resulting from the choice of the reference systoa. 
In thousht, we sinply withdrew a conaiderable aciount of kinetic 
energy (c.dn) frota the recedin^i nass aiid ^ave it to the advv-uicing uasa 
in the form of a.dv. That is the so»rcalled principle of relative work. 



- 1S8 - 



If I staiid in a boat cv^cl weijh IDG lig together vdtli the boat, ara 
is ivell-Ioio^ra, the s/sten : nan + boat maLea "^O teclmical unita of nnss. 
Now, if I have a stone ivei^hing 19,6 kg (that makes 2 teclmical units 
of nass) on the boat and throT it ava^ with a velocity of 1 ci/sec, the 
boat is propelled in the opposite direction at C.l n/sec, 

'.7ith reference to the earth's surface, I h<xve ^lerfor ;ed the vovh 

-3— a.'i' + -i-. 50. 0.1'^ =1.1 nikc . 

V/ith respect to the sun, the place where that happened is to have a 
velocity of "G loa/sec, and the stone is to be throim in the saine 
direction in which the respective region raoved. So, with reference 
to this systeii, I have done work on the stone a;!Ountiug to 

2.(39001^ - 290002) = 58001.0 mitg . 

2 

In 30 doing, I withdrew energy fron the boat amounting to 

.20 ( 29000^ - 18099.92) = 57999.9 nil:g. 

This shows that nan can be considered as a good, light, efficient, 
and cheap uotor - if one does not loiow all about the principle of 
relative work. In reality, the energy troaiafomation by the nan's 
^uacles was only 58001.1 - 57999.9 =1,1 mkg. 

As ia apparent, we have so far dealt with latters of pure definition. 
That changes, however, as soon as we are dealing with a body raoving 
between different reference systeas. Let us denonatrate it by means 
of a nental experiment. 

Aa asteroid ia to circle the earth at a distance of 900 radii of 
the earth's orbit. Then, according to the rules of astronony, its 
velocity equals 1 km/sec, and its period of revolution is 27000 years. 
Let us suppose there is a long-living astronaut on the asteroid. He 



- 199 - 



Irishes to fly to a fi:ed star 10 (that ia one quadrillion) laa airay 
(that is about the cUstaiice of the rej^oilus ia the Lion). The fixed 
star is not supposed to nove relative to the tlui and ia to lie in the 
trajectory plane of the asteroid. Tlie asteroid is to stand e::actly 
at point A' (cf, Pi^. 6G) Ijetiveeu the sun and the fixed star (A indicates 
the direction to the fixed star), nad the available fuels of the 
rocket are to correspond to an ideal ;->ro;iul3ion of G lii/sec. Here, the 
parabolic velocity Tvith reference to the sun is p «= 1.4 laa/soc. Later 
in the chapter, I will show that ive can conpletely ignore this quantity 
in the follovin^j calculation; the parabolic velocity with reference to 
the asteroid is likewise to be irrelevant. Now the question is : How 
can our astronaut /-et to the distimt firced star fastest ? 



Pis. 36 

Sone lay;ien vdll naj : He T\ust stax-t rifjUt now. l) In no doinj^;, 
he loses no ti.ie waiting-. 2) This is the best tii'.e to leave nnyimy, 
for the asteroid is nearest to the fixed star. Then he will arive in 

-—-"-s- m 3,555,000 years (in this connection, cotapare the answer ^iven 
G'3'10 

by the astronomic observatory in JuL'lS Tl'^j'il'S novel, "]From the Jilarth 
to the Iloon", Point 4), 

Others again will say : No, he v.iust wait another 30C00 years; then 
the planet has conpleted 3/4 of its revolution and its notion ai.is 
exactly at the fi:;Gd star. If the roc7:et starts then (that ia on line 
C'C), the asteroid's velocity of 1 kti/sec is added to its oim velocity. 



- 300 - 



It covers the distance in •'-- «= 4, 7 JO, 000 years cjid nalces up for 

7.4'io'^ 

tlie nOCCO years of .wnitin£. - '.Tlio is ri-ht? 

No one. It ia best for the rocket to start a few centuries after 
this period with a velocity o;:actly opposite to t'le velocity of the 
asteroid and not quite as ^reat. In so doiiif;, it uses a propelling 
force of 1 Ian/see and describes an elon^^ated ellipse around the sun 
that is to briu2 it to the edge of the .golar corona. In the perihelion 
(that is the trajectory point ucarefjt the sun) it should have a 
velocity of SCO Ion/sec. IJow, the astronaut adds the rev.aiuiag 3 Ian/sec 
to this velocity and travels toward the fixed star with the hyper- 
bolic velocity of 505 loa/sec on trajectory D'D, The velocity of JOO 
Ion/sec corresponds to the kinetic energy used up in order to brin^ 

the rocLet back up to the trajectory of the asteroid a^ain. That 

1 2 

would reruire energy azvounting to •n.5C0 . The additional kinetic 

a 

energy which the rocket has at 505 laj/scc is expressed in the fact 
that it does not stop when it reachoa the range of the asteroid but 
flies on vith a velocity whose kinetic energy is equal to the differexico 
between the ener^^y present at 505 kia/sec end at SCO loa/sec. If this 
velocity is a:, then 

.ns.z' = -—•a. 3^5'' - — .n.SCO". 

3 2 S 

From that follows 

X " 70.9 laa/sec. 

'Tith this velocity, our astronaut gets to the unknoim fi::ed star in 
470,000 years, which is l/l2 or l/lO of the tine stated above. 

It ia lost reiiarkable that, at 70. S kia/sec, the kinetic energy of 
the rocket con be ;jroater than the total che-:ical finerjjy of the fuels 
carried alon^. For excuaple, if it was filled with hydro^^en and o:iy;jen, 



- .201 - 



which result in an exhaust velocity of ca 4000 laa/aec, and ve let the 
naaa of the empty rocket equal m, then the mass of the full rocket 
(accordius to formula (6)) equalled e^'^ = 4.48 n, and the mass of the 
fuels carried along ivas 3.48 m. The nechauical equivalent of the heat 
of coabustion was 30.5 - 35,9 nillion irikg/k^. 'Flien returning from the 
sun, on the other hand, the kinetic eneryy of the I'ocket, when it was 
as far away fron the sun as the aateroid, ouounted to 

-3— »• 70, 900'' = ---IC^'ia nkg, 
which is 70-100 tines uore than the chemical oneri^y of the fuels! 

The first tine I nade this calculation, I believed nothing else in 
the first ninute but that here the law of the conservation of energy 
was broken, or at least that one could gain work at the cost of energy 
stiiiulating the field of gravity sonewhat siiiilar to the work perfoined 
by on electronagiiet which is counterbalanced by weakening of the 
stinulatiug current, I3ut neither is the case. The fuels have performed 
the whole work alone. Beside their energy of covibustion, they contained 
potential energy, since they were so high above the sun to begin with, 

xiy the drop, that was converted to kinetic energy, which now was 
considerably dininished hy the erdiaust velocity of i Ln/sec. The gases 
trailing behind the rocket are still flying away from the sun, but 
they no longer cone to the height of the asteroid; and because we 
brought then nearer to the .'3un, energy was released which is now 
evident in t'.ie nore ra|,jid notion of the rocket. 

In the case of the burning rocket, we cire also dealing with two 
different reference systens. Tlie exhaust gas attains velocity c with 
reference to the rocket, but the rocket gets its propulsion with 
respect to the earth. With that wo novo from the aro;i of Lieutal 
experiiients to the cphere of the tan(_,ible. 



- nca - 




Fi:j. 37 

In ■worka on the tlioorj- of roclcetry, one frec^uently fiads the 
followiuc error : 

If the exlianat velocity of the fuels is c n/sec, thou the I:iuetic 
euer^ of a r.iass particle dn is ; 

d A= -•— •c'^.dn . 
8 

(That ia correct, but only with roference to the rocket, not with 
reference to the earth.) If ejecting this ruass particle raises the 
velocity of the rocket to the value v + dv, then the kinetic energy 
(if we disregard dv) increases hy 

d 2= n»v«dv . 

That is also correct but this tine only with reference to the earth. 

But now dA and d3 are equated. (One raay still reckon with the 
principle of the conservation of euerj^y! ) In this way one obtains 

-— •c''«dn o m«v«dv 



or 



d a 
m 



2vdv 

""TT 



- 303 - 



3/ integration -we j^et 






°1 

IJaturally, thnt soon results in terrible fi^'jures. For ox;ir,iple, for 
V = 4 c, one /^eta 

-~— = e^"* - C, COO, ceo . 

Oiie can coiipre'iend why these acliolurs cane to the conclusion that 
recchiu^ iuter^^lanetary apace by rocket ia not feasible. 

The folloTTinjj error io very ai.ilar : If a imss unit of fuel has 
the therao-chenical ener^^y B, by barninj; up the ..ass da, the Liuetic 
enerjy of the re aisiin^' rocliet nass ra (uoiinally) coanot be increased 
by nore than t1n«B. Uain;^ the f omul a 

ia« V'dv C ^'to , 

a fantastic fij;ure is liLewiae arrived at, noiaely 

V ' 

As Tve already saw, for the in^)en. in3 apart of the nasses u and dn, 

the principle of the constancy of the erihaust velocity and the principle 

of the preservation of the centre of £;ravity, which furnishes foriula 

(3), are valid independent of the state of notion of the rocket. 

Or, as I wrote to V-ILI"^ in 1G25, who, anonc other thinijs, had also 

!:3ade this error : 'Tith reference to itself, the rocket is alwoys at 

rest. 

Last year, I corresponded, a.ion^- others, with Privy Coiincillor 
H, LOIl^iiZ, Dauzijj, concemiuc this topic, and it took three letters to 



- 204 - 



conviuce Iiiu that this assumption contradicts the principle of the 
preservation of the centre of gravity . 



If one -wishes to use the energy principle as a basis, one nust 
consider the fact that the fuels of a fast-flying- rocket do not only 
have thermo-chenical eneri^y but also considerable kinetic energy, 
ivhich is considerably reduced as they are throTm back, For exoiaple, 

if — .c*»dv is the portion of chemical energy 2 ■which can be 

2 
converted into notion, then, in flowing out, the fuels not only lose 

energy in amount of 





1.2 
2 


but also the nnount 




dm 


fv^ - (v - 



For exoEiple, if a rocket flying at 12 km/sec ejects a technical nasa 
unit of propellants with a relative velocity of 4 kn/sec, then the 
latter lose not only 



.1.4000^ = 8.10 nkg 

2 



but beside that also 



•l.ri'^,000^ - (I'JjOOO - 4000)® J = iO.lO^ dlig. 

Altogether they release 48* 10" irskg. 

That is 6 times as nuch as the bare therno-cheraical energy. Naturally, 
this energy nust go somewhere OJid is sinply expressed in the fact that 



^^ I neution this only tiS an example of how difficult the inquiry here 
is exactly for physicists who have worked with the concept of energy 
a lot. 



- S05 - 



the oneri;^ increase of the rocket ia 6 times greater 

than should he esqiGcted accorclinc to the calculations cited above, 
I need not e::plain to matheuaticicviis and physicists irhat it means if 
ire con multiply a lo^aritlimic increment by 3. 

i\nother offence against the ener^ principle is fotind especially 
iu the first ivri tings of VALIS?.. In his early irri tings, he as suited 
that the energy of the fuels is divided in a Christian spirit between 
e:chc»-u3t energy and energy increase of the rocket, so that the exhaust 
jaoes get e::actly as nuch energy as the advancing rocket; or, that 
the total energy benefits the advancing rocket. 

In this connection, I vould also like to mention that, anong other 
things, it lyas suggested to me to culculate as folloirs i 

If a reflector i.iacle of sodium i>late weighing 100 kg per hectare 

enters a cloud of cosnic dust, also containing only 1,2 g of mass in 

a cubic kilonetre, with a relative velocity of 7 km/sec perpendicular 

to the reflector surface, then the reflector would be slowed doira at 

/ P' 
6,1 ri/dec . l;anely, in one second, the reflector traverses a space of 

COT o 1.2 

lau', the ij.ittcr filliu^i this space uunbers 0,C7« — teclmical 

v.iass iinits, oxid tlieir energy of action is 

1 1.3 _ 

___.C.07.-~-.700v>2 . 910 nkg. 

Jut the energy of notion of the reflector (according to this method) 
nust also change by the sasne number of mkg; with the reflect)^', 
1 ovr'cr, 'h5s energy of motion would correspond to a velocity of 
6,4 la/sec. 

Actually, here also, only the irapul se would be the same on both 



- -906 - 



sides. If X is the acceleration of the reflector, then it would be 

given hj the formula 

1,3 100 

0.07.-- .7000 = X.. 



9810 9.81 

Prom thatf ve get x = 0.59 nna/sec^. 

The deceleration of an electric space-ship, that treighs at least 
10,000 kg per hectare, trould be all of 10,000 tinea smaller. 

(in this chapter, I in.ll disregard all the other errors lying in 
this train of thought, 'l) Certainly, there is not 1.2 g of dust per 
km^ in interplanetary space. 8) Those dust particles siaply pierce a 
sodium plate 0.005 mm in thickness and, in so doing, lose at the 

1 ^ 

most -— of their velocity; the impact they are able to impart to 
100 J 

the reflector is also only — — as great, and so forth.) 

100 

For our purposes, the concept of energy is on the tfhole too general 
and hence ueaninglesa. Ifhen calculating the propulsion of a rocket 
flying through space, \re have an equation containing 5 different 
energy quantities, each of which can be calculated only by the use 
of other formulas. We shall let the energy of aotion of the rocket 
before ejection of .a' e&rtain quantity of gas be Ej^ and after the 
ejection Egj the chetiical energy of this quantity of gas is Eg, the 
kinetic energy of the escaping gases with reference to the earth 
(not irith reference to the rocket) E4, and the heat the exhaust gas 
still retains, E_. Then, the principle of the conservation of energy 
tells us only that 

Sj + Eg « E3 + E^ + Eg . 

As to how large these single energy quantities are, we learn 
nothing from the principle of the conservation of energy. 



507 - 



Foi' threo-body problena, this law is also too general, for it 
only states : The sum of the tinetic enerjp' of the three bodies with 
reference to any unifornly uoving systea of coordinates is constantly 
so and so jreat. Sut it does not state how nuch falls to one body or 

the other. 

The principle of the conservation of energy cem be applied only 
to the ^J^Q-vitating of a very small body in the field of gravity, of a 
very large one, if the body is only exposed to the pull of gravity 
(no pressure or impact), if it can freely follo-w this pull of gravity, 
and if the influence of all other stars aay be disregarded. 

For example, if we regard the systen rocket + earth as at rest 
before start of the rocket and assume that the earth has the mass M 
and, ifith start of the rocket, receives thb velocity V by the pressure 
of the powder ^ases, and that the rocket has the mass it and receives 
the velocity v upon starting, then obviously 

U.V = m.y . (103) 

Afterwards, the kinetic energy A of the earth is i 

A = .M«V^ . (104) 

a 

That of the rocket is 

a = --—m v^ , (105) 

Aia-Viv=miM. (l06) 

r That is obtained if, while talcing (l03) into account, (l04) is 
divided by (l05).J Since m4^ll, A can actually be ignored beside a. 
The sotae holds when we consider free flight of the rocket in the 



- ao8 - 



field of Ci'ravity of the earth. Here, instead of the pressure of the 
£,asos, ire sinply substitute the pull of gravity. If the rocket were of 
the order of nayiiitude of the earth, that could naturally no longer be 

done, ^very antrono. ler will, for excvnple, coxifim that the vioon coupletes 

^ 
a revolution around the earth in -rrr- of the tinie that a rocket would 

requii'e whose centre of ^'ravity is the scane distance from the centre 

of the earth as the centre of the r.;oon. 



V/lien we want to deter :ine the flight of a rocket space-ship between 
two planets , the principle of t'le conservation of energy is also 
inadequate. For exanple, between earth and Mars, the space-ship would 
describe a 1C5PPL!]!I1 ellipse only if the influence of the earth's 
i^ravitation could be disregarded. At the beginning, it runs ahead of 
the earth, for when it starts off it haa a greater on^-ular velocity 
with reference to the sun than the earth has (cf. Fig. 67). Later, 
however, its angular velocity sinks below t'aat of tlie earth, so that 
the earth [iasses it by once more. The re.^ult is a velocity component 
of ca 300 a/scc whose energ^y value benefits the iuotiou of the earth 
about the sun. This trajectory disturbance would naturally be wholly 
sufficient to nake the rocket miss 'lars, if it were not taken into 
account. 

I have often been asked concerning the heat tone, that is the 
thenml effect of my rocket nozzle. Naturally, that is a question 
which can only be answered conditionally, '7ith £jOod nozzles and the 
ri;:;ht combination of fuels, the kinetic energy of the exhaust ^as 

— -.din.c will nake 50 - 70 p of the therno-che:iical ener^jy of the 
1 

fuels. ■JC'D'J.CJ) achieved 07 j5 in his experiment a, TJiis is attributable 

to the fact that hero all trans ittin.'^, braking, cooling, etc. uachiue 

parts fall away. 



- 309 - 



As a response to this ansirer, I usually get the partly scornful, 
partly irell-tneaut advice to mount the rocket nozzle on a car since 
it is a splendid propellint^ motor (aaong other thin<3S| this iras also 
VALIEH'S advice at the beginning. Later, the rocket airplane crystal- 
lized from our correspondence). 

Usually, Ely tmswer to that is that I would first have to be (jiven 
a car that can run 1000-4000 n/aec. It is not enough to develop this 
kinetic energy, it oust benefit the vehicle and not siaply be borne 
away by the exhaust gases. If the vehicle stops, the energy utilization 
is infinitely bad, for all the energy is now used only for blowing out 
the propelling gases more violently. The greater the velocity of the 
vehicle becoaes, the smaller the velocity renaining to the propelling 
gases after they are bloim out. ^Tlien v - c, energy utilization is 
best, for then the propelling gases cone to a stop behind the vehicle 
and, in so doing, transfer 50-70 $ of the thermo-chenical energy 
contained in the fuels and all the kinetic energy of the fuels to the 
vehicle. If the vehicle travels faster than the gases flow out, the 
erhaust gases apparently perform still more work per vmit of mass. 
In this case, however, it must be reaeabered that they were enabled 
to do so only because the fuels were earlier brought to this high 
velocity. That naturally required energy. This energy is not returned 
to us in full measure, for the ezhaust gases behind the vehicle still 
retain a velocity forward} that aeaus that part of the energy of the 
propellents is converted into kinetic energjf of the exhaust gases. 
Therefore, with high velocities, the efficiency becones worse again. 

Of the therno-chenical energy B of the fuels, per unit of mass, 
the part Kj^ « — .c* can be converted into kinetic energy (here Ki is 

a 

naturally talcen with reference to the rocket). The kinetic energy with 



- .^10 - 



reference to t'le oartli contained iu the faela before the Tjurain;; 

1 n 
Qjaouiits to Kg = .v' per unit of na.T.s. Therefore, xritli reference 

to tlie etirtli, the totnl enor^- contfviuetl in a unit of uass of the 
propellant c.nounta to : 

As can 'oe seen, that (^oes not tal:e into account the ther:ial euer^ 
that cannot 'oe converted into notion; it does not interest ua here. 

The energy ivhich the unit of taaas of fnel atill retains after the 
out-floiT aviounts to (naturally here alcio without the heat which the 
n;ase3 still carry) 

Accorrtin;jly, the rocket benefits from the enor^ 

Kj. = Kg - Kj = -J-, v^ + c'^ - (lv\ - lc|)^ =|v.c|*). 

2S 



KilPPISL'IAYISR, for erztuuple, ahould have considered this when he wrote 
his hi£5hly-recogni,.;ed article (but crawling with errors) on the inpos- 
sibilitj of space fli;:;ht, in which, otion^ other thing's, he sinply 
transferred the decree of efficiency of OP!^*S rocliet car to the space- 
ship, which travels TOO titaes faster. 

NCCIiDUNG here aalces a very peculiar misiako. flg <i^Jf*^3 hinaelf the 
question, how long the kinetic ener'^ of a rocket increases and whether 
later, in spite of the increasing velocity, it does not decrease again 
because the nass becones smaller. In so doing, he envisages the whole 
kinetic energy of forward-speeding rocket including its fuels and does 
not exonine the share falling to the eapty rocket, as I have done above. 
Naturally, one is permitted to exeunine that, although, for the present, 
the qiiestion is only of acadeaic interest; actually, the total kinetic 
energy does not even interest us with the rocket projectile. 

To clarify the (question, HOOIlIiUlIG ia quite right when he reflects 



- 211 - 



that the ejected fuels still have the kinetic energy 

1 dm / \2 

(I an here mriting the formula with cay STinbols). Then he simply equates 
the work the unit of mass does on the rocket to 

1 dm S 
-2- -3t- "" ' 

so that he naturally arrives at completely Trrong values. 

Especially the conclusion : a rocket airplane should strive to fly 
•with a velocity v = c, is wrong. Cf. also "Autoteclinik" (Automobile 
Technics), Volume 18, 

It is uost remarkable that, a few pages farther down, he finds 
formula (l09a) (and that, as he means to emphasize, independently of 
ZI OUCCTOiaf or me). Then, in the sequel, he works with both formulas 
without being aware that they contradict each other. 



I have here inquired only after the absolute quantity of this 
energy; we find its sign if we note that an energy increase can take 
place only when v and c are opposite to each other. If v and c work 
in the saae direction, that Is when the exhaust gas flows out toward 
the front, the rocket is being retarded; in so doing, it loses energy. 
So we must set 

Kg = v6 . (107) 

Fig. 68 shows the nature of this function in the solid curve. For 
constant c, it is a straight line; K in itself becomeis large at raadom 
if only the velocity is correspondingly large. The broken line in Fig, 68 
represents the thenao-chenical energy of a unit of mass of fuels which 
can be converted into motion. Thvs, it is seen how much more 1 kg of 
fuels can do with considerable velocity. 



If, on the other hand, we inquire into the part y of the total 
kinetic and themio-chemical energy of the fuels which benefits the 
rocket at a specified moment, we must divide K_ by K-. Then we obtain t 

O u 

y - - -2®^'-25 or, if we set X- = i, y = ^Sx» , (ioq) 

V* + C 3~ + 1 



^ la X f>* ^ 




ri2. 6S 




h->-# 



Pis. G9 

-Tif^-, 39 ijivea the nature of thia curve. Tliua ^'rQ ccui soe tliat tlie fuel 
utilization is relatively (not ^ibsolutely) the 'oeat for v = + c. 



The;3e foi*nulas and ciirveg only iufUcats what nutuitity of the fuel 
oner;_j^ is beneficial in nro;5ellinj the rocl^et at a s;.ecifiod :o;ient. 
- "he following;;; i^uestion is more inportant : If the roc'ret haa burnt 
30 and 30 lon;j, how much of the total convertible enei\jy of the fv.els 
spent acaiii becoraea appviront in the total Tcinotic er.er^ of the final 
lass of the rocliet and how nuch have the e::hau3t ^n^es carried avay? 



- 213 - 



For the time being, no definite ansirer can be given to this question. 
Let us consider a rocket flying in air-free and gravitation-free space 
and choose our coordinate system so that, vith reference to the same, 
the rocket just stood still before the burning. Noir, if A is the total 
energy contained in the fuels irhich can be converted to motion of the 
exhanst gases (irtiich, therefore, does not serve (mly to heat the ex- 
haust gas), £ the kinetic energy which the rocket has after the pro- 
pulsion V (here v is the ideal propultion), then 



A = l.(m^ - mj) c« - i-.m^ (« ^ " V «'• ( 



According to (6)) 



From that fol loirs 



A 



(7)" 

1 (- ) ~l ■ 



i 

2 •'"'*' 



(109) 



V 

"c" 



We shall designate r— as y and ~ as x; then we directly read from 
the equation 



r 
e^- 1 



(I09a) 



that as z increases (when we regard c as constant; hence, as v 
increases), y must tend toirard the limitinfj value 0, for,'^in so doing, 
the denominator increases faster than the numerator. That, for x 
(or v) = 0, y also becomes equals to 0, we ceui prove by our equation 
if we apply the method of variable fonus to it. 




Fig. 70 



- -^li - 



"i^. 70 shows the nature of the curve for for..uln (iCCa). ''e cou 
cTotorninc the oirti))un erxe.ctly, a:J&nj other things, hy difioreutiation. 
It is 

dy (g"" - l)«9.;-x'»e" 

dx (e^ - l)^ 

Then, for s ., the nunerator liuat be 0. I'Vora that (hy flroppiu.-;; the 
' opt 

Cienoninator, ifliich ia everyivhere fiuite, and diviiiia;j the iiuiierator by 
a X . e*) this folloira i 

>L + e-^^ . 1. 

2 

Proa that, x .can be easily calculated accordiu:^ to the re^ula falsi. 
' opt '' 

It is foujid to be 1,50-3.... If v = 1.39S*c, thea, at the conclusion 

of propulsion, the ratio of Tciuetic onovjy to fuel euarjy is the .-ost 

ad-/anta-eo\i3. Then, a^ = i. S-i«n. and the lorss in fuel -(irould eciual 

El ~ u^ " 3,2'i'n., In no doin~, 
o 1 1 ' 

.(a - n^J.c = 1.S5G c 'n^ 

of the theiMo-chenical ener^ iraa converted into kinetic ener^jy. Cn the 
other hand, the rocket Tiually has the kinetic energy 

E » •!!! .v^ = l.-^TO a..c^ . 

2 1 1 

Therefore, = 64.7 %, With reference to the aturtiu^ point, a 

rocket cannot perform better -with constant out-flo'w velocity, even if 
the propulsion apparatus ia ICO fJ efficient. Not/', if one fii^ures that 
the kinetic enerj^y of the exhaust gases at the uoat nal^es 70 fo of the 
cheuical energy of the fuels, then one finds that, trith constant eshauat 
velocity, under even the raost favorable conditions, the rocket can only 



- 215 - 



convert half of the fuel energy into energy of motion of the final nass. 

E 
The ratio -— turns out better if c is variable and increases 

siciultaneously with vj it turns out best if c = v constantly, so that 
the fuels just cone to a stop behind the rocket. Then, the total kinetic 
energy produced benefits the rocket, and the only energy lost is that 
used in heating the eshaust gases and that used in lifting the fi:els 
to their present altitude. V7ith vertical ascout, even in this nost 
favorable case, a tall gas pillar would fom behing the rocket, the 
erection of which naturally requires work as does the erection of any 
high pillar. T?e shall soon see that that is not a little, relatively 
spealiing. It is true, the state in which v = c is only possible fron 
a certain mininun velocity on and stops when velocities are to be 
achieved that are higher than the highest ;^ossi"jle e:din,ust velocity. 
For the type of flight just nentioned, the fo/loving foiTiulas are valid : 

c = V} a>dv + v»dn = C, 

m»v = ao'^^^o • (llO) 

□ere the nass is inversely proportional only to the velocity itself. 
Nevertheless, it is still greater than if the erchanst velocity had 
constantly had the highest value attainable. In the case whero t'.io 
flight velicity deviates little fron the exhaust velocity, the energy 

loss is relatively snail, for it only increases as the differcixce of 

c 
the squares. For esoaple, if v = -5-, the exhaust gases carry away 

1 c^ 

only dm* of the produced energy, whereas the energy of the 

2 4 

rocket itself increases by the anouut of 

p-v«dt = v*(p«dt) = -y»(c.diu) = -.=— dm.c 
That is four tines the kinetic energy of the esliaust gases and, by 



- 216 - 



f 



compariaoni exactly as much can be converted into kinetic energy of 
the exhaust gases from the thermo-chemical energy. 

Note I The circumstance that the rocket operates most economically 
'When its flight velocity is close to the out-flov velocity is an at- 
tributing factor to the fact that alcohol rockets are more suitable for 
lov^er velocities, that is for the loirer layers of the atmosphere, and 
hydrogffia rockets are more suitable for higher velocities. As upper 
rockets in the operatioui they are still cheaper (although, today, 
liquid hydrogen is 5 times as expensive as alcohol), because the fuels 
are better utilized. Farther up, the efficiency of the hydrogen rocket 
bec<Mnes worse again. Perhaps, later, one could attempt to impart a 
greater velocity to the out-f loving material by using electrical forces. 
Yet, as a basis, hydrogen and alcohol rockets irill presumably hold 
their ovn for a long time, for, up to 7000 m/sec, they utilize the 
provided thermo-chemical energy better than other thermal engines. 

Actually, I am here speaking purely academically. Today, the entire 
invention is about at the stage irfaere the railway stood around 1805, 
the motor car around 1850, and the aeroplane about 1900. One irill be 
happy if the thing will Vork at all, and not ask about the thermal 
efficiency. I mentioned this here only because VALIER has dealt with 
these questions in the book, "Advance into Interplanetary Space", 
and because his explications relative to them have occasioned numerous 
misconceptions. 

Slogans such as i "Space flight is a question of energy", "Space 
flight is a motor problem", and others, coined I^ ViLIEIl, lead to 
similar misconceptions. Naturally, I also know that the most important 
aspect is the achieving of high e^aust velocities, which, in other 
words, is the creation of a good propulsion apparatus and the discovery 
of propellants containing sufficient energy. But, in the first place, 
the esdiaust velocity does not depend only on the propulsion apparatus 



- 217 - 



emd the energy content of the fuel; many other things are involved. For 
exeunple, of all the fuel compositions knoim today, the one irith the 
greatest energy content in relation to its volume, namely 8 parts 
oxygen and 7 parts silicon, produces no e:diaust velocity at all, and 
the substance containing the nost energy in relation to its weight 
that /ve knoir of today, nanely nonoatonic nitrogen, cannot be considered 
as rocket propellant for other reasons. In this connection, also 
compare Chapter 17, Point 14. We see, furthermore, that one cannot 
simply speeik of absolute work performed on the rocket by the propulsion 
apparatus and that the theory of rocketry is built up only on the 
theory of iapact and not on the lav of energy. Therefore, the novice 
in these things "will do well first to consider the things as though 
the principle of the conservation of irork has not yet, been discovered 
for him. 

2. The Synergy Problem 

Formula quantities for pp. 217 - 229 

a : counter-pressure 

b I acceleration 

c : out-floTf velocity 

g : acceleration due to gravity 

gg : acceleration due to gravity on the earth's surface 

m : mass of earth 

p ; parabolic velocity 

r : distance from centre of the earth 
rg ! radius of earth 

t : time 

V : velocity 



- 218 - 



V I ideal propulsion 
A s TTork perfomed on rocket 

5 s energy 

P I rearward thrust 

c*k J angle between flight direction and rocket axis 

6 \ angle between the horizontal and the fli^iht direction 
^ : angle of direction 

All other formula quantities relate only to the sections in which 
they have been explained. 

In Greek, "syn" neons "together" and "ergon" neeuia action or work. 
"Synergy" has the meaning of correct working together. I have chosen 
this word to e:xpress the ccmplex of all the research related to the 
problem of how, with the out-flow velocity being give^, it c;ai be 
achieved that the rocket receives as nnch of the kinetic energy produced 
in the propulsion apparatus as possible and the enhaust gases as little 
as possible. (Hence, research concerning the proj^ulsion apparatus itaelf 
and the conditions for high out-flow velocities does not belong to the 
topic.) 

If the direction of the rearward thrust makes the angle o(. with the 
flight direction of the rocket, then the component of the rearward 
thrugt in the direction of flight anounts to : 

P'cosok. 

As is well known, this cojaponent only serves to increase the energy 
of the body in motion, whereas the component perpendicular to it 
(P«sin<A) changes only the direction of aotion. 



- SlCa- 



Ditrin^ the aeguent of time dt, the rocket covers the distance vdt| 
and the work performed on the rocket, wiiich ei^uals the increase in 
virtual energy (l call it virtual because Tre are here disresardinjj air 
resistance), amounts to : 

d A = P.cosd<.«v.dt. (ill) 

On the other hand, the loss in 3ub.Ttance dn, according to (t), is 

P.dt 



do = 



If -we divide dA by dui, •we obtain the ratio between the energy increase 
produced and the aass expended. It is 

-— = coao*i.'V«c . (lis) 

d m 

1) In this foniula, the factor c neons nothing nore than that, 

with ejection of the sasiie quantity of propellant, the rocket experiences 
a greater increase in energy if the propel 1 ants flow out rapidly . 

2) 3y contrast, factor v is interesting. It tells us i Other things 
being equal, the increase in energy is the greater, the faster the 
rocket flies. That results in a requircaent which I would like to express 
as follows : \7e must atrive for high velocity of the burning rocket. 



' Here the inquiry is adiaittedly only into the absolute increase in 
energy of the rocket and not into the utilization of the energy inherent 
in the fuel. 

As is well laiown, the energy of the fuel quantity dm which is con- 
vertible into kinetic energy is 

d S = --.dm.c , 

and from that and from (llS) we find 

dA V 

—J- a 2 COSCA* — • 

dE c 

We will not need to discuss the consequences of this fact before 
p.55T, foraula (235) ff; for the time being we only wish to achieve high 
performance without taking economy into account. 



- 219 - 



I will show vhat that meaas by a few exanples. 

a) TThether I lift a body out of the earth's sphere of attraction 
in the course of years or, in the course of ainutes iapart a velocity 
to it that hurls it out of earth's sphere of attraction is quite 
Irrelevant from the standpoint of the conservation of energy. In one 
case as in the other, I must inpart 6,370,000 mlcg per lig to it. - On 
the other hand, if a rocket ascends with constant velocity or ninor 
acceleration and uses rearward thrust only to conpensate for the force 
of gravity, it needs inconparably riore fuel than if it is nade to 
attain a velocity rai^idly, under whoso influence (sinilar to a shot 
bullet) it then continues to fly without giving off more fuel. In the 
latter case, in order to reach the sane height of ascent, it rmst have 
a much higher velocity when the propulsion stops, since it is still 
nearer to the earth. IJaturally^ it already had a higher velocity during; 
a good part of the period of propulsion, and, during" this tiae, the 
ejected fuels contributed acre to the energy increase than in the case 
of slow forward notion neutioiied earlier. 

In this place, I would also like to point out that, beside fomula 
(112) derived fron the differentials, en integral fomula ovists which 
enables us to apply the energy principle to rocket propulsion t^roblens. 
Concerned are energy calculations related only to the increase in 
energy of the final nass. 

If m. is the part of the rocket that is te regain after propulsion, 

and b the ideal acceleration of the rocket, then n b is the share of 

the total force of the rearward thrust falling to zija^s n. ; the rest 

falls to acceleration of the fuels which are ejected later. In the 
course of the segment of tine dt, the final nass receives the enei^gy 
increase n.«v*b«dt, so that, at the conclusion of propulsion, the 



- 220 - 



rocket carries irith it the kinetic energy mj*jb'V»dt. This formula Is 

Unconditional Ij valid; from this ire also notice that -we must knoir b or 

m 
at least tiie ratio -~^ and the actual reanrord thrust. On the other 

"l 
hand, as stated, absolutely nothing can be done with energy calculations 

alone in connection with the burning rocket. 

Of course, different considerations con also verify the correct- 
ness of the necessity of throwing the rocket instead of lifting it. 
The greater the acceleration, the quicker one gets out of the earth's 
sphere of gravitation and the shorter the time during which one has 
to work against the acceleration due to gravity. 

b) Furthemore, what results from the requirement of rapid flight 
during the burning is the requirement to have low-lying trajectory 
curves during the propulsion; in so doing, the point at which propul- 
sion stops is lower, and hence, other things being equal, the required 
ground speed is greater. The advantage of slanting trajectories is 
also grasped without the formula (ll2) if the fact is considered that, 
with vertical ascent, the force of gravity works against acceleration 
in a straight line, whereas, with oblique ascent, it only cancels out 
the amount g sin<^. Cf. Fig. 63. (Naturally, this requirement con- 
tradicts the necessity of passing through the aixnosphere vertically, 
so we must still discuss this question.) 

c) From the requirement of rapid flight during the burning follows 
also the requirement to utilize the rotation of the earth or the 
requirement of inclining the trajectory toward the east. For example, 
if the rocket ascends from the equator, it already has a velocity of 
460 m/sec because of the rotation of the earth. Other things being 
equal, it achieves more if the rearward thrust works in this direction. 



- aai ~. 



d) Resulting from the requireueut of higher velocity during burning 
ia also a requirement which I would like to designate as "ccEibinatioQ 
of impacts". Here ia an example : In his book, "The P^eachibility of the 
Heavenly Bodies" (Oldenbourg, !>Iunich, 1925), HOHLUHN describes a trip 
to liars as fol loirs ' i 

The space-ship is to ascend in the direction of the sun at noon with 
almost parabolic velocity up to an altitude of 800,000 km. This ascent 
would take about 15 days. In so doing, the space-ship would in effect 
get out of the earth's sphere of gravitation. Although liars is farther 
from the sun than the earth, H0HMANN advocates ascending in the direc- 
tion of the sun so that the space navigator has the earth before him 
in full light and can find positions Qore conveiniently and accurately. 
(Here I cannot agree with HOH&lANIf. In i^y opinion, the fiuding of posi- 
tions, could be carried out just as easily and surely if the earth is 
seen as a sickle. Then they should not only be possible because of the 
brightness of the ether but perhaps be still more dependable because of 
the lack of Irradiation. If the rocket flies completely in the earth's 
shade, the earth is seen either as a dark disc before the zodiacal 
light or as a disc illuminated by the moon and sonewhat lighter than 



' In this book, I must repeatedly criticize HOIEIiilJN'S explanations. In 
order to avoid nisunderstandings, however, I declare at the very outset 
that I regard his book as a very valuable contribution to the teclinics 
of rocketry and to cosmonautics. I only consider it my duty to do my 
part 30 that the theoretical principles of space flight are clarified 
as well as possible. It is an entirely new field, in which it is self- 
evident that we have nothing perfect and in which, therefore, everything 
must constantly be tested and improved. I myself, likewise, am grateful 
to anyone who draws my attention to any mistake in lay work. In no way, 
do I have the ambition to renain the winner in every debate and later 
to break nsj neck with the first nanned rocket. I would rather take a 
slap here and there and later fly in a correctly-constructed space-ship. 

In the meantime, HOIEIAI^N has in another place (Ley, The Possibility 
of Interplanetary Travel, Hachceister and Thai, 1928; likewise pointed 
out the advantages of combining impacts. 



- 2-^2 - 



the background. The position findings could also be eaoily executed if 
the space-ship has already advanced so far that the atmosphere becoiaea vis- 
ibly ■« a light border.) - If then, accordins to IIOiriAiJlI, the space- 
ship a[ prosinately stops at an altitude of 800,000 Itm with reference 
to the earth, Tfith reference to the sun it still has the sane lateral 
motion as the earth, namely 29.7 laa/aec. ^ith this velocity, the space- 
ship trould circle the sun once in a year and, in so doing, continue to 
keep the sa:'je distance froia the snn as the earth. The GOO, 000 Im Mentioned 
can be ignored here. To take it to the distance of I'ars fron the sun 
it .'equires a new inpulse. That, according to HOir'JUui'S resecrch, is the 
sua! lest if it occurs eziactly in the direction of notion and is so 
great that, because of the increase in velocity, the space-ship describes 
an ellipse (similar to an independent comet. Hence IlOIf LAIjN also speaks 
of "coaet flight") ^rhose perihelion touches the earth's orbit and vrhose 
aphelion touches liars* orbit (cf. Fig. 67). This propulsion nust ariouut 
to 3 Lri/sec. Ilaturally, the trip rmst be undertaLen at a tine when liars 
has a position so the space-ship actually !;its it, and not only reaches 
the nathenatical position of I'ars' orbit while the planet itself is sone- 
where else. 

Purtherrjore, the space-ship nust eject propellants for v^ = 320 u'/sec 
in order to conpensate for the trajectory rtir.turbance nentioned on 
p. 208, Now, HOiriAJW calculates as follows : The first inpulse occurs 
with T,^ = la to 14 Im/sec, after 15 days a second i-.-.petus with 

v^ = 3C00 m/sec is given, and, in the course of tho flight, a few 

smaller inpulses together naking v = 320 n/sec are given. Altogether 

that would require taking along fuels for Vj, = 15,3,'30 to 17,3^^0 a/scc. 

I in no way deny the fact that this clear and si^'^plo state";eiat, 
combined with the elegniit and easily-understood calculations, anTces the 
book valuable (especially to the rjnateur), but a slcillful space 



. 283 - 



traTeller vill not give gas three tiraes in succession at relativelj 
lev velocity, but he vill seek to reach his goal vith a single propul- 
sion so that the propulsion occurs at a higher Telocity. Namelj, if p 
is the parabolic velocity at the altitude vhere the propulsion stops 
and the rocket flies vith the hyperbolic velocity v., outside the 
earth's field of gravity, it still retains the velocity t 

As is ▼ell knoim, the relationship betveen the kinetic energy E required 
to overcome the earth's field of gravity and the parabolic velocity is 



1 _ a 
-p - a 



B« - "5 n P f 



and after overcoming ihe force of gravity, the rocket still possesses 
the kinetic energy E., for vhich this is naturally valid t 

FroB that, (113) follows. 

The advantage of this type of flight is expressed by the fact that 



^ At the same time, ve here recognize an important basic lav of space- 
ship travel t 

With the freely flying rocket, the velocity values of the energy 
effects add up in accordance vith Fythagora's Theorem. Namely, if the 
initial velocity of the rocket is v^, its initial energy is 

E^ - I m vj . (114) 

If a second energy effect + Eg is added, vfaich vould impart a 
velocity Vg to a body at rest, then obviously 

+ Eg - + jf m Vj } (115) 



- 334 - 



If a third and fourth are added 

+ E4 - + -J. n vj , (117) 

and the Iiiuetic residunl oiier^jy of the rocliet is obviously 

3r = Sji^alEg + E^ , (118) 

Ita residual velocity v^, idLll be ^iven by the fact that 

Er = Y n v,^ 5 (119) 

then, fron (ill) to (ll9), thin followa : 



VS 8 2 ^ / \ 

^1 ± "^3 ± "^3 ± "^4 • (120) 

But this applies only to ener^ effects thtvt are independent of the 
notion of the body influenced, for e:i:ariple to lift work required to 
taT;e the body from one field of (gravity to the other, etc. 



We can deal with the trajectory disturbiuice velocity in a siailar 
way. If we designate it aa x, then we will have to ain in a sonewhat 
different direction and enploy v ao that 

vj^v| + X* + p^ . (121) 

(The atatenent for x is not entirely correct, for we are here dealing 
with a three-body problea which can be built up on the principle of 
the conservation of ener^^y conditionally only. The trajectory disturb- 
ance also depends on the velocity of the rocket. Actually, v^^ nust be 
^jreater by 100 n/sec than if there were no trajectox-y distui'bancej at 
least not by 3f50 m/acc, as IIOIC-AIJIJ aasuued.) 



- 235 - 




Fig, 71. Nature of covmter-pressure ivitli re-en trj- into the earth's 
atmosphere of unnanned rackets provided "with a parachute. Tlie ordinatea 
indicate counter-pressure and the abscissae a aonotouous function of 
tine not described in detail in this book. 

Fig. 71a shows the nature of the counter-pressure vith a rocket with 
a very strong parachute (solid like) and with a very weakly-braking parar- 
chute (broken line). The process is the very sasje in both cases, in the 
one it only sets in later. 

Fig, 71b shows the nature of the counter-pressure, in the sone coordinates, 
with a simple parachute (dotted line) and with a flap parachute (solid 
line), whose air resistance, with open flaps, is reduced to 44 JS. Tie 
highest counter-pressure occurring here is only 57/5 of the counter- 
pressure with a simple parachute. 

The advantage of conbining the impulses becones clear if we consider 
that, according to this set-up, 



^1 =/V^2 + 



p + 100 



Hence, v^^ ■ 12 km/sec makes 18,470 m/sec and v^ ■ 14 Lm/sec makes 
14,470 a/sec, which is 3850 m/sec less than what IIOI£L\IW declared as 
necessary, 

e) The astonishing nental experiment on p. 200 ^ also belongs to 

Perhaps, this case will be realized if a visit to a noon of Jupiter 
should aaterialize. In so doing, the space-ship will pass close "to Jupiter 
and the propulsion will occur in two impulses, one of which will only 
overcome the field of gravity of the satellite, whereas the actual pro- 
pulsion will occur near to Jupiter. 



the topic, "Buruinr; with Ilicii Velocity-". P.enuire.ients a), b), and e), 
as a special ^Toup, ecu he chnrncterized hy the sttiteuent : "'.Tliile it 
burns, the rocket nuat retain as low doim an possible". Thua a ^-reater 
part of the eiierjj is trausf or -ed into kiuctic energy* the rocket burns 
while riyic^ with a higher relocitj. 

0. In forniila (112), the factor cos Ot also appears. Froa it we read 

off that — 7~- is a na;cinua when cos Ot is a i::a"inun, that is whenOC = \ 
If the rocket ascended vertically irith respect to the centre of the 
earth, it rfould describe a strai;^-ht line. If, on the other hand, it 
moves on a slant, at oiiy point considered, its trajectory forms an 
an^;;leO with the horizontal and, if the iiipulse acts in the direction 
of fli(^ht, what is added to the acceleration caused by the reanirard 
thrust is the conpouent of the force of gravity 

2«cos O 

which acts perpendicular to the direction of flijjht. It causes a curva- 
ture of the trajectory. 

The curves which are described in that way I have called rocket 
lines because a rocket provided with short, wide fins (not with steering 
lu;js), if left to itself in oblic;ue ascent, likewise describes a rocket 
line. Fi^. 72 shows a number of rocket lines. The acceleration is 
assumed as being constant and sonewhat snaller than with model E, I chose 
such low acceleration because, in this way, the nature of the curves is 
expressed nore distinctly. As can be seen, part of th^a lead back to 
earth a^ain. Another one, however, no longer strikes the earth. Since 
no force sets in to deflect to the right or to the left, »11 such 
curves always lie in a plane passing through the centre of the earth. 



^ For this reason, it was the intention, in building rockets with a 
nunber of noazles, to avoid placing the nozzles at an an^le to each 
other. 



- 227 - 




FiC 72 

In air-free space, observing the rocket line is difficult. '7ith 
automatic steering, it requires quite a conplicated steering uecliauism, 
ot'aerwiae the aatrouaut has to do the steering. Hence, flying on a 
roclcet line cannot be considered for unnanued aeteorological and long- 
diattmce rockets but only large manned machines from 10 Ixi upward. 
Here, the counter-pressure can be considered constant; I will designate 
it by a and use it in the equation as an acceleration. To begin i/ith, 
we wont to disregard air resistance. Let & be the angle with the 
horizontal again, r the distance from the centre of the earth and (p the 
angle between the point of ascent, the centre of the earth, and the 
position considered, g the acceleration due to gravity at the position 
considered, g^ the acceleration due to gravity at the earth's surface, 
and r^ the radius of the earth. Then the upward acceleriition is : 




( ma) 



- aaa - 



For the horizontal acceleration, the following is valid 

dr dC? i"Q) q 

2 — + r —-a' a a«co3 • 

dy? dt d t« 

The vertical conpouent of the velocity v onounts to s 

« v> siu O • 

dt 

The horizontal conpouent 

r — *■- = v«cos O . 
dt 

From that, thi.i follovrs : 



(123) 



"-nwitj. 



(124) 



(125) 



(126) 



dfl \dtJ 



dr 




dip 



go 



ar 



dt 



^drdfp ^ 



(137) 



So here vc have tiro dilTeroutial erjuations i;i three variables r, 
^f t. Inte;ji'atiou is nossihle after a 2e'\T obvious trauafor-iationa in 
the fuiTn of infinite ;:erie,'3 with use of the rietliod of indeterminate 
coexficionts. The finictional coniioctioas botireen r and t, fl) and t, 
s (s >= distauco covered in flight) and t, v and t are in general 
traiisceiif'ent. 'vliether they can be i'epre.oeuted a.o cloned eiqireaaious 
betv-'oon fiUictioii;3, "or ivhich nntheMntica is already ufiin^ short synbols, 
I CQulf' not yet deter; duo. 



These fuuctious are also inpoi-trsiit for the p.pprorrinatin^ t'uree- 
oody cr-lculation . So, in tlie nlrea'.^>j r'eutioaed ivork oa tarec-bocly 
ccilcul?/tiou, I will write iiore ■-',')out it. 




Fir;, 73. 'JiatancG of the rocl:ot line fron the en,rth'3 surface 
renreoeuted in s'^uare coorfliu,'iten. Abacirjsae in de^-reea of the 
earth's circu:iference, ordinates each in lOoO Ixi rvhove the 
centre of the earth. 



Ilaturnlly, the curves run siviilar to those in T^i^. 78, escopt that, 
ivheu they are plotted on a square systen of coorcliuates as in "ig. 73, 
the distance up to the point of inflexion is nhorter. 



- *5ao - 



^* The nyiierry Curve 
J'or::-.ula c^uantities for pp. 830 — 252, 



a ; counter-pr ensure 
h I acceleration 



f » 

a 



£ ; acceleration <lue to rjravi ty 

Cm ' average value for ^ in t'le fourth section 

h J altitr.de of space-ship above the ^roi'iid (in the fourth section) 

h' : vortical conponent of the velocity (in the fourth section) 

k : e:q5lanation on n, 240 

p = g - z 

r t distance from centre of earth 

a : lenr;th of trajectory 

t : time 

V ; velocity 

v^, Vn, v„, V J velocities at the end of the first, second, third, 
and fourth sections 

Vq : averaije value of the velocity on the bent curve 

Vj t ideal propulsion 

Vj to v^4 : ideal propulsion in the first to fourth sections 

^xk ' ^^^^ ^^ propulsion conditioned by the difference between 
OC andy^ 

v_ t circular velocity 

V ; horizontal conponent of the velocity 

:: : horizontal coordinate of the point of the trajectory 



- 231 - 



x' : horizontal component of the velocity 

dx' " 
— - : horizontal conponent of the acceleration 

dt 

7 : vertical coordinate of the point of the trajectory 

y' : vertical conponent of the velocity 

dy» 
: vertical conponent of the acceleration 

dt 

z : centrifugal acceleration 

A : aerodyuanic drift 

B = tgcCo + aecOCj, 

C J integration constant of (l4S) and (l52) 

OC : angle of inclination of trajectory 

/O : an^le of inclination of axis of space-ship 

/lOC « direction difference conpensated for by the aerodynajic drift 

£, t angle betTreen azis of space-ship and direction of flight 

Pl t initial value of £ 

^ ; period of flight with Liore thou circular velocity 

Having established the requireaeut of burning with high velocity, 
it is reasonable to investigate how the space-ship worI:s if it travels 
horizontally (at least above the earth's atiiosphere). 

In so cloir,';, \re would have to point the nozzle downward at a 
definite angle £(cf. Fig. 87) so that the vehicle would be just carried 
by the U'jT.-ard conponent of the propulsion (i.e. so that the space-ship 
would retain its horizontal direction of flight in opposition to the 
effect of gravitation; then the horizontal conponent of the propulsion 
b serves acceleration). 



- 238 - 



I 0D here intentionally writing only about space-ahips| on utunaimed 
meteorological rocket flies nost econonically under all circunstauces 
if it rises aloft vertically vith the nost advantageous velocity y, 
and it can attain any velocity aluost nonentarily, as soon as the air 
resistemce peruits it. Inclining the trajectory and reaainin^ in the 
atmosphere longer would here be absurd. An unmanned lone— distance 
rocket also attains its highest velocity while still within the earth's 
atrjospherej research into the most favorable an^le of ascent is super- 
fluous here also. - It is different in the case of the space-ship 
which, with vertical ascent, only attains its highest velocity at an 
altitude of 17C0-2CCC Ion. Here, the energy required %o erect a 2000-Iaa- 
high c;as pillar can obviously be saved by slanting the trajectory. 
The rii^ht curve should rise above the earth's ataosphere as little as 
possible so that a hi^h velocity is attained quickly. 

*'.'ith flight above the ataosphere, we want to uake QC = 0> /S " € • 
TTe find : 

(US) 

£= arc sin — ^ arc sin — ■ , (130) 

a - ' a 

b - a-coa^ ^L a«co3 fi , (l3l) 

b^Va^-/, (132) 

V3. = a t , (133) 

= J b«dt^ia-cos ^ J .t = Vjj^'cos ^1 . (13^^*) 



2 = , 

r 



- 233 - 



For example, if we apply a = 35 m/sec ; r = r^ + 140 km (r^ radius 
of earth), then g o 9.5 m/sec', £^ ~ 15.5", and ve find t 

v^ Vjj^T.sec 15. 5* B 1.035 v. 

So here, almost the entire ideal propulsion benefits the velocity of 
the space-ship. In addition, if the trajectory is inclined tovard the 
east, ire are also assisted by the earth's rotation, vhich amounts to 
roughly 300 m/sec in our latitude and as much as 460 m/sec in the 
tropics; whereas, with vertical ascent, it contributes almost nothing 
to increasing the final velocity. In space flight, naturally only the 
velocity with reference to the centre of -Uie earth is determining, and 
this gain in propulsion through the earth's rotation -would, up to the 
circular velocity, even over-componsate for the losses due to setting 
the nozzle on a slant| so that for this part of the flight ▼iV'^^x* 

On the other hand, the requireuent to pass through l^e atmosphere 
quickly contradicts the requirement of horizontal departure. I\irther- 
more, bending of the flight curve, as we have it here (cf. farther down), 
means a loss of energy and, finally, the parabolic velocity is greater 
closer to the ground than farther up. Hence, we will be able to give 
conclusive judgement on the best form of ascent only when we shall 
know how to manage this horizontal departure and how great are the 
losses in propulsion when converting the initial steeply upward directed 
motion into a horizontal one. 

So, the space-ship will at first ascend in a straight line and 
steeply; large space-ships with a high ballistic coefficient somewhat 
mere level than smaller ones. A.t an altitude of a few kilometres, with 
large ones perhaps at 3 to 4 km, with small ones at 80 to 30 km, we 
will then set the nozzle of the vehicle parallel to the direction of 
motion. Now, the force of gravity will effect a bending downward of 
the trajectory and, if we constantly keep the nozzle in the prevailing 



234 - 



direction of motion, the motion vill finally be in a horizontal direc- 
tion. This is to happen at an altitude of 120-140 km and vith a 
velocity of 2-6 km/sec. With steep ascent, smaller space-ships would 
not get into the horizontal as quickly. We can solve the problem by 
making the rocket axis more level than the inclination of the direction 
of travel. That brings about (cf. Fig. 74) an aeorodynamic drift A 
which bends the flight direction toward the horizontal faster (since 
the true flight direction is shallower than the apparent because of 
the rotation of the earth, this inclination itself need not even be 
connected with loss of work. On the whole, however, that space-ship 
naturally flies more economically which is so large that it need not 
first ascend steeply and then change its trajectory through air pressure). 
- Then horizontal flight follows until circular velocity is reached. 
With circular velocity (v =-Vs^)> gravitation is just cancelled out by 
the centrifugal force. From there on, the centrifugal acceleration 
outbalances the centripetal? the space-ship will gradually lift off 
from the horizontal under the influence of the centrifugal force. 

The curve which the space-ship describes in this type of ascent 
I shall call "synergy curve". It naturally falls into four sections » 
l) straight-line, oblique ascent, 2) deflection of the oblique flight 
direction into the horizontal, 3) horizontal flight until circular 
velocity is reached, 4) from there until ground speed is reached, 
flight on a rocket line. 

Calculations i 

1) For the first part of the synergy curve, formula (98) is valid. 

2) With the second part, we shall begin with the case in which the 
bending of the flight curve is caused only by the effect of the force 
of gravity, since that makes the calculations simpler. Taken precisely, 
here the flight curve is a rocket line to which the formulas (l27) 



- 235 - 



Tould be applicable. Since, hoireyer, it is a matter of a relatively 
short distaQce, we can disregard the curvature of the earth's surface, 
set g constant, and, because of the centrifugal force, ignore the 
temporarily still small horizontal component of the velocity. (We ceua 
estimate and correct the error later.) We thus make the irork considerably 
easier. For this part of the synergy curve, we are introducing the 
fol louring designations : 

X : horizontal coordinate of the trajectory point 
y ! vertical coordinate of the trajectory point 
t : time 



dx 
X* •• -— : horizontal component of the velocity 

dt 

dy' 
y* = — — — vertical component of the velocity 
dt 

oC angle of inclination of trajectory curve 

dx' 
— — - i horizontal component of the acceleration 

dt 

dy' 
— — vertical component of the acceleration 
dt 



To begin with i 



dy* 
— i — B a sin CC - g, (l35) 



dt 



dx' 

-T7-- - a cos cC J (136) 

dt 



dividing (l35) by (136), we obtain : 



dy' g 

„ tg qC sec OC. (137) 

dx' a 



- i36 - 



g 
We ahttll introduce a new letter for , let as say 

a 



e (138) 



f = -=- . 



EHirthermore, since nozzle and flight curve have the same direction, 



tg a - --— = ~ ; sec oC= V^ ' I ""7 ) * <i®^) 

dx x« y ^ x«/ 

Substituting (139) and (138) in (l37) gives us t 



j!iL.ji..vrr7S'. (140) 

dx« x« V \.x'/ 

That is a homogenous differential equation between the variables j* and 
x' . The solution is < 

at iriiich 

C - Xo'^ (tgOCo + secoCo) (142) 

is an integration constant. 

Taking (139) into account, this caa also be written i 

x'^ (tgoC+ sec C5C) - C. (143) 

This equation gives us the connection between the horizontal component 
of the velocity and the inclination of the trajectory. From it, we 
can also easily find the connection between y* or v and OC . It is t 

X* " v cos OC or V - x' secCjC , (144) 

y' - x' tg OC. (145) 



- 237 - 



Since 



. , „ ainOC+ 1 

tg oC + sec OC » ~ and since 

cos CC 



sin QC- yi - cos^OC. , 
Vl - cos*a + 1 c 

With reference to cos OC , this is a mixed quadratic equation. We can 
exclude the value cos OC = 0. What remains is t 

2 2 

C03 « = —p -Tf = ' 

^ + V ^-'-'+^-*-^' (146) 

Furthemore, from (143), this follows t 



tgOC+Vl + tg^OC = Cx'f , 
that is : 

tgCX = -^ (C i'-^ - C-l.x'f). (147) 

Frwii (146) and (147), this folloTS t 

y« - —- x» (C x«-f - C-i x'^). (148) 

rrom (136) and (l46) follows 

rfx' 1 

'^' = ^c^ = 2^(^^"'+^"-")'^^' (149) 

Taking (l38) into account, that is 

y - y. = Jy'-d' = ^ J^' (<^^'-" - c-'x'«o-d:t' 

"^L-^T^^'-^-^'"-"^ -a^(^"*"-^H- (151) 



- S38 - 



As soon as the flight is horizontal, tgOC becomes " 0. Then, according 
to (147), it fol loirs that 

x^f = C . (152) 

If ire subsitute that in (l5l), ire obtain the equation nhich Indicates 
at vfaat altitude the trajectory becomes horizontal. ~- If, in it, ire, 
according to (l52) and (l42), replace C and x\ by x^ and QCq* and 
finally set cosqCq for x^, = Vq and, for the sake of brevity, irrite 
B fox tgQfjj + aecQCo* ^® obtain the equation i 



t\ 



■o-2' 



/" 2ia'~f-){iJ~-y,) 



(153) 



■ 2gB' + (a - g) B-^' - {a + g) B'- 



vhich indicates hoT great velocity v,, must be irith a certain flight 
angle (cjCq^ ^^» ^^1 ~ ^o^ ^ higher up, the trajectory is to become 
horizontal merely under the influence of the force of gravity. 

I am here giving a table for Ji ~ 7o " ^^^ ^ ^'^^^ a » 35 m/sec- 

ao^-- 60° 50° 40° 30° 20" lO^* 

Co =- 170 300 GOO 1140' 2340 5700 rn/sek " 

Nov, vith a counter-pressure of 35 m/sec^ and an angle of ascent 

Q^ Q = 60', the velocity Vq = 170 m/sec is already attained at the 

2 

V 

height of Jq = 485 m, since yo « sinGC « at irhich b must be 

2b 
estimated according to p. 191 ff; irith Vq = 600 m/sec and q£^ •• 40", 

Jq becomes <= 5.7 km. From this, one realizes hov shallov the space- 
ship must ascend in order to get into the horizontal at the atmospheric 
limit in this way. 



- 239 - 



Nevertheless, another thing must be considered t Ve had aimplj set 
fj^ - y^" 100 km; actuallji we do not have to give (yj - y^) a definite 
value; ve are really only inquiring about y^. Accordingly, in (153), 
•we can express y^ by v^j, sin OC o» ^'''^ ^^ then, after a feir transforma- 
tions, ve get I 



1 / T"'^^ 

I 2"(a= - g^y 



(154) 



Opposite (153), this formula basicly shoirs us nothing aev. It 
follows (assuming the atmosphere y^ >= 120 to 140 km high) from (l53) 
as well as (154) that this type of ascent can only be considered for 
space-ships that are able to fly through the zone between 7 and 12 km 
altitude at an angle of less than 35". A rocket should never fly faster 
than at the most advantageous velocity following from (3l), which 
here would be very high; i.e. (according to p. 118), the apparatus would 
have to be very big and heavy. If the question is pursued by calculation, 
it is found that when starting the ballistic coefficient would have 

to be *> 8 kg/cm*. But with very big machines, only hydrogen will 

F 

be used, and hydrogen rockets have a specific weight of ca 0.293. 
In order to have a ballistic coefficient of 8 kg/cm^, such a machine 
would have to be over 280 m long. Such machines will not be built in 
the foreseeable future. It is doubtful whether it will be possible to 
build them at all. 




Fig. 74 



- 240 - 



The only thing left to do vith model I) vith its ballistic coefficient 
of 1 to 1.5 kg/cm is to ascend steeply at first and then use the air 
resistance to bend doim the tra,iectory curve, as Fig. 74 indicates. 
We ascend 14 fcm high at 60*; then ire incline the axis 55" to the hori- 
zontal and, in the sequel , continue to keep it inclined a feir degrees 
less than the direction of flight until it has an inclination of 20". 
From there on, the ascent continues in a rocket line up to the horizontal, 
at which the space-ship leaves the atmosphere entirely. 

This domirard inclination of the axis causes an aerodynamic drift A. 
It must compensate for a difference in direction A^ T»hich is smaller 
than the difference betireen the angle of 20* and the angle at irfaich 
the space-ship Tould have travelled after tfie same period of time if it 
had continued, on a rocket line, its tray begun at the end of the first 
section (irhere its angle of travel was 60") and greater than the dif- 
ference between 60" and the angle at which the space-ship would have 
had to travel at the same time in order to reach a flight angle of 20" 
on a rocket line at a specific point in time. In general, for space- 
ships weighing 300-5000 tonB, ^CC lies between 33" and 20", with model 
£, we can set 

AOQ = 0.524 (155) 

(expressed in arc measure). 

As is well known, the force k, which a body of mass m with a velocity 
V opposes to a change in its direction of motion, amounts to t 

k ° mv . (l56) 

dt 

Now, when the axis is set on a slant, the air resistance increases 
by a certain anouui L which, according to present aerodynamic research, 

lies between —— and — -. That causes a loss in ideal propulsion (v^), 
10 6 



- 241 - 



irhich is obviously given by the formula i 



'xk 



r 4_L- dt. 
m 



(157) 



If Tre here set Ars/k and /j L = , and designate an average value 

o 

betireen the initial and final velocity on this curve as v^, then this 
fol loirs from (l56) and (157) i 



^xk" 



f _I_ dOC = -l5_AcC (158) 

U 8 8 



For example, for Vg, « 1200 m/seo and > 0.524, ve get 

Vjjic » 79 m/sec. (l59) 

For this part of the curve, I first calculated the loss in mass 
trithout taking v^j, into account according to formula (lOO), In so doing, 
I used the graphic method to represent v and y by t; the same with 
the succceeding integration. From that, I calculated the ideal propulsion 
and, finally, added v , to it i 

°o 
v^ = cln + ''^xk • (l59a) 

In the flight fx^OBi. OC' 20* up to the horlBontal, I again detemined 
the lost Ib b%«« aooording to (lOO). In so doing, I replaced v according 
to (l44) and (146) by x, likewise t according to (l50) and y according 
to (l5l). Finally, I again integrated the irhole by the graphic method. 

I have examined twelve different cases in this way. With model E, 
I found quite consistently that, at the end of the second section of 
the synergy curve, Vy. Tas 700 to 1100 m/sec (with the three-stage space- 
ships, 300-400 m/seo) greater than Vn. How large we made the first and 
second sections makes little difference; the same with the actual final 



- 248 - 



velocity (8-4 bm/sec). The result also depended less on the magnitude 
of the counter-pressure than I had expected. That may be because, irith 
high counter-pressure, the space-ship oiust ascend more stdeplr at the 
start, and then loss in propulsion occurs nhen it bends over . 

3) In the third section of the sjnergy curve, the distance from the 
centre of the earth does not change. We use the same fonmila quantities 
as those of formulas (188) to (l34) on p. 233 and refer to (128). We 



find I 



v* 

- P - — - g f 



VT 



r (g - p), 

Vr.dp ^ ^ 

dv . (160) 



' It has been pointed out to me that the space-ship irould ascend best on 
a pure rocket line since, in so doing, oosOC>= 1 is constant, iriiereas, 
vith the synergj curve, the nozzle must repeatedly make an angle with the 
direction of travel. 

This question is easily clarified, if ire visualize the synergy formula 
(118). As can be seen, the utilization of the fuels does not depend only 
on cosOcbut also on v, and (especially at the beginning, iriiich is the 
main thing here) v increases faster if ire let the vehicle ascend less 
steeply. This is based on the fact that, for small values of CsC , the 
costoe differs little from 1, -whereas, -rith a given counter-pressure, the 
deceleration due to gravity increases as the sine of the angle of ascent 
(which is considerably faster). 

It is true, in this part of the vay, the most ideal line of ascent 
would deviate somevhat from the horizontal, and that in the direction of 
a pure rocket line. But, as I found by the graphic method, the deviation 
is so small (greatest altitude difference 8 km, gain in velocity 1.8 m/sec) 
that I assumed this part of the way as horizontal off-hand, in order to 
make the matter feasible. 

Concerning the apparently illogical reorientation by the use of drift, 
I have already stated what is necessary on p. 2''i2. Actually, it is not 
connected with losses because, in so doing, cosCCbecranes considerably 
greater. 



. 243 - 



Furthermore, the folloving is analogous to (l32) t 

dT - b.dt- -Va* - P^'dt . (I6l) 

From (160) and (i6l), by eliminating dv and integrating vlth respect 
to t and p, this fol loirs t 



jiC _ dp_ 



(162) 



Since the flight takes place in air-free space and a is constant, 
here t 

^« = ^t--|^^Jy™^=r (163) 

Unfortunately, this integral cannot be calculated in a closedl form, 
but it is very easily evaluated by graphic or mathematical means. 
(With potrer series expansion, it is advantageous to introduce a nev 
argument ^ » ij g - p.) 

Depending on the counter-pressure and the initial velocity (v2), 
I found the ideal propulsion in the third section of the synergy curve 
to be 80 - 140 m greater than the actual propulsion. If Vg is the final 
velocity, then 

(▼g - Vjj) + 80-/ v^g^(vg - Vg) + 140 m/seo. 

4) The fourth section of the synergy curve is a rocket line again. 
As ire shall soon see, hovever, it differs but little from the arc of a 
circle, and ire make no great mistake if -re use the folloiring considera- 
tion as a basis t We designate the altitude of the space-ship above the 

dh 
ground as h, the vertical component of its velocity as h' •• — — , its 

di 



- 244 - 



horizontal velocity as v, and, following (l28), we set 



dh» 
'dt~ 



(164) 



at irhich ggj is supposed to be the meem value of the acceleration due to 

gravity. We noir designate the circular velocity as v , the horizontal 

z 

acceleration as b, and the time that has passed since circular velocity 
iras reached asT. 



We can nov regard b as approximately constant, then 



v^ + b r ; 



furthermore, 



(165) 



(166) 



and from (l64) to (166) ve obtain 



dh» 
dt 



V? 2 v^bY- b«r* 



Noir 



— + — — 
r r 



am 



+ g^ 

r 



and since dt » dT", therefore 

dh»^^(8 T^b'^+ b'r*) 1 . 

The single dh are not all parallel to each other (although the cosine 
of the angle -which they make vith each other alvays remains close to l). 
Therefore t 



A'<J(2..6t + 6=t=)^ = ^(('.t=+|x'). 



(167) 



- 245 - 



If ire designate the altitude at which circular velocity iras attained as 
hgj ire find t 






(168) 



If, in the first approximation, tre here set b >= 35 m/sec^ (that is a) 
and integrate up to the parabolic velocity, ve get : 



<X " (Va gr - .^ilr) J a - 94 sec, 



h^ - hg ■ 12.99 km. 

If ire had assumed b « 34 m/seo , which is definitely too little, we would 
have obtained i 

^ = 96,7 sec, 

h. - h„ « 14.4 km, 

/ 2 
For b - 39 m/sec , we would have obtained a mere 9,5 km as altitude 

difference. 

As a result of this type of ascent, the final velocity would have 
become 12,6 m/sec (with a 14,4-km ascent) or 9,3 m/sec (with 9.5 km) 
smaller than if the rocket had remained on the horizontal; yet this loss 
in velocity in itself is not connected with a loss in energy. That is 
apparent in the fact that, 14,4 km higher up, the parabolic velocity 
is also 12.6 m/sec smaller. Nevertheless, according to (ll2), as a 

result of the reduction of velocity, there is a loss in energy which 

1 d A 

finally amounts to about — - — « -. In all, however, the loss in 

1000 dm ' 

work conditioned thereby is still considerably less, so that the loss 
in propulsion from the circular up to the parabolic velocity amounts 
to scarcely I m/sec. 



- 246 - 



On the other hand, vith final velocities of 15 - 17 km/aee, vhich 
could occur in flights to distant heavenly bodies (although thej might 
not have to; in this connection compare Chapter 2l), this loss in 
propulsion could no longer be ignored. But here ire could fulfill the 
requirement of burning at high velocity by the folloiring artifice t 

Vfhen the rocket travels at about 10 km/sec, ve shut off the fuels. 
Then it describes an elongated ellipse i«faose perigee is not far from 
the place irhere circular velocity iras attained. When, after its return, 
it is still about 1000 km avay from the perigee, ire give gas a second 
time. Noir the second thrust also occurs as close to the earth as possible. 
I have found by the graphic method that, -rith a counter-pressure of 
35 m/sec*, the loss in propulsion betveen the circular and the final 
velocity rouains beloir 8 m/sec in this tray; in any case, it can be 
neglected. 

It still remains to be examined -whether we have the right to set 

the horizontal acceleration aa constant and equal to a, vith flight up 

/ 2 

to the parabolic velocity. For b •» 35 m/sec and <^ = 95 sec, according 

to (167), »e find 

h' = 446 m/sec. 

If Tre designate the angle of inclination of the trajectory curve 
as OC and the last value of OC as cCj» then obviously 

a^b «. a - g sinCiC^ a - g sincC , . 



Not 



g^' sin ^i: 1 - -~ 



- 847 - 



For h' ° 450 m/sec, this results in t 

a>-b >a»0.990 . 
So ve irere actually able to assume b as being constant. 

Now we are in a position to answer the question concerning the most 
advantageous curve of ascent for space-ships. In the first and second 
sections of the synergy curve, the losses in propulsion together amount 
to 700 - 1100 m/sec $ in the third 80 - 140 m/sec; together 780 - 1840 
m/sec. Since, in most flights, the trajectory can be inclined toward the 
east, a propulsion gain of 850 to 460 m/sec must be subtracted, so v 
must be 380 - 1000 m/sec greater them the final velocity . This, for 
the same flight goal, is greater so near to the earth than farther up. 
For example, at an altitude of 138 km, the parabolic velocity would be 
11,140 m/sec; whereas, at an altitude of 1400 km, it amounts to only 
10,010 m/sec, and at 1850 km a mere 9800 m/sec. 

Yet, the saving on fuel is extraordinary. In order to attain para- 
bolic velocity on the synergy curve, a space-ship requires an ideal 
propulsion of 11,500 - 18,040 m/sec; in order to attain it in vertical 
ascent, according to (70) and (80), with a counter-pressure of 40 m/sec , 
an ideal propulsion of 18,700 m/sec is required, with a counter-pressure 
of 35 m/sec*, an ideal propulsion of 13,500 m/sec is necessary. So we 
save 960 - 2080 m/sec with ascent on the synergy curve. The saving is 
still greater with hyperbolic velocities. 

Another advantage of the synergy curve is the fact that we can go 



NOORDUNG, Kho has also examined this question, gets a figure roughly 
800 m/sec higher. The reason could be because he has made no use of the 
possibility of bending over the flight curve with the help of air 
resistance. Concluding from his discourse, he appears to have assumed 
that the space-ship ascends vertically at first and then, above the 
relevant part of t^e atmosphere, is given a new thrust perpendicular to 
the previous one. 



248 - 



much lower Trith the counter-pressure. We can greatly reduce it especial- 
ly in places (for example, near the circular velocity and in the second 
section), irhereas, in vertical ascent, every second that the ascent 
lasts longer than necessary is connected with a loss in propulsion of 
3-8 m/sec. 

There are tiro more important advantages, one of irfaich is that, irit^ 
elliptical velocities, the perigee, i.e. the point of the trajectory 
near the earth, lies just above the atmosphere. Then, a small, hardly 
to fail, retro-shot in the apogee (distant from earth) suffices to 
shift the perigee so far into the atmosphere as is necessary for landing 
(cf. Chapter 14). On the other hand, irith vertical ascent, considerably 
larger differences in velocity have to be made, irhich is just as dis- 
advantageous from the standpoint of security as from the standpoint of 
the use of fuel. If, hovever, a retarding shot is fired in the apogee, 
the space-ship can here be brought into the circular velocity with a 
minimum use of fuel, (important for reaching ether stations that are 
rotating about the earth. It follows from all this that it would not 
cause a loss in propulsion if fuels were brought on the synergy curve 
to a station rotating about the earth and here space-ships were refuelled 
which continue to fly in the direction of rotation. Cf. p. S""*.) 

As a further advantage of the synergy curve, I am mentioning that, 
on it, the space-ship can easily be brought into a trajectory which 
allows it to circle the earth and remain in the ether any length of 
time. With steep ascent, however, it either soon falls back, or must 
fly far away, or must make very r^narkable directing shots in the apogee. 
(Besides, we shall see in Chapter 14 that, with every steep ascent, 
directing shots have to be fired in the apogee in order not to be 
exposed to too high counter-pressure when landing.) 

With future flights to distant heavenly bodies, the following 



- 249 - 



advantage of the synergy curve irill be very important. Here, the launch- 
ing location may be in the temperate zone, irhereas vertical ascent 
irould have to start in the tropics. - If, irhen circular velocity is 
reached, the burning is interrupted, the space-ship travels vithout 
further loss of fuel around the earth on a great circle vhich touches 
the geographic parallel of latitude of the location of ascent. The plane 
of this great circle cuts the plane of the ecliptic at tiro points. 
Thus, for every location of the temperate zone, the case occurs twice 
in the course of 24 hours that a star found near the ecliptic lies in 
the plane of this great circle. If one starts at this moment and travels 
on the great circle with v ■■ 7890 m/sec until the earth's centre is 
approximately between oneself and the goal and then applies the remaining 
propulsion, one reaches that star. I used this property of the synergy 
curve, for example, when I did the math^natical preliminary work for 
the film, "The Woman in the Moon". Required was a start in central 
Germany and a landing on the moon. 

These comparisons made between vertical ascent and ascent in the 
synergy curve are also valid for oblique ascent, even though not to so 
great an extent. Oblique ascent becomes more economical, the more it 
approaches ascent in the synergy curve| this represents the ideal case. 

I have discussed the synergy problem here because various critics 
are making awkward assumptions concerning the ascent from the synergy 
standpoint and later claim I have estimated the matter too optimistically. 

For example, one says t In order to get a rocket to circle the earth 

1) propulsion is required to carry it up vertically to the desired 
altitude (let us say 660 km). This first thrust would require 3100 m/seo . 

2) Gravitation and air resistance destroy an additional 1200 m/sec and, 
when the rocket has come to a stop at an altitude of 650 km, 3) a lateral 



^ 



am giving the figures as stated by the critic. 



- 850 - 



thrust of 7800 m/seo is needed. Together that makes 12,100 m/see. But, 
in realitj, the same goal can be reached vith an ideal propulsion of 
8600 m/seo if one ascends on the synergy curve until one travels on 
an ellipse vfaose apogee is 650 km high and then fires an accelerating 
shot in the apogee. 

I need not mention first that this critic »as quick to judge 
that I could not be taken seriously as a scientist, for I did not even 
knov trtiat propulsion is required to lift a body to an altitude of 
1000 km and give it circular velocity after that. I believe, hoirever, 
the presumption that I could not be taken seriously as a scientist was 
again of no avail. 

The irell-knoim ballistics expert, H. LORENZ, Danzig, has mad© similar 
errors. 

DlLLWITZ-VffiCaJER, again, elucidates in "Umschau" (Look Around) j 
In order to lift a vehicle out of the earth's sphere of gravity 
one irould have to impart 6,370,000 mkg per kg to it. But our most 
effective explosives and fuels (if the oxygen needed for burning is 
figured in) hardly contain one million m/kg of thermo-chemical energy 
per kg. Therefore, according to DiLLWITZ-WECSfER, a vehicle which must 
itself take along its fuels is impossibly in a position to leave the 
sphere of attraction of the earth. 

In reality, however, it is not a matter of the rocket taking along 
its fuels. It ejects th«n near the earth and only takes along part of 
their energy which was converted into energy of motion by the rearward 
thrust. But this energy of motion (even according to EINSTEIN and 
HASEJBrl) weighs as good as nothing. Beginning, at the latest, from 
the 8 th minute, the rocket flies into interplanetary space like a 
shot projectile. If only, at the beginning, it can be provided with the 



- 851 - 



necessary quantity of fuel (this must naturally be a multiple of ihe 
final mass)) it can make the trip to interplanetary space. 



In "Maschinenkonstrukteur", HOLZHAUSEN, on the other hand, attanpts 

to prove by similar considerations that the final velocity of a rocket 

can never be greater than 2.o. Namely, if the initial mass equalled m 

and the final mass equalled 0, then the average mass vould be — m. 

2 
If the mass is hurled dovmrard irith the velocity o, its impulse downward 

is m«c. The impulse upirard must be Just $,b great, and S o«-~^ m is simply 

2 
m>c. But he forgets that this cannot be done by siumnation but here the 

formula e*dm ^ m>dv must already be integrated and the vork performed by 

the fuels ejected last no longer only equals -g-^dm-c) irith the velocity 

finally increasing to infinity, the Tork likeirise becomes relatively 



infinite. 


2C 

rs 

10 

s 
1 
























f 








j. 


— 


— 










1 








HIq 














m, 




















1/ 

1/ 





























/ 

-yi 

\- 

1 






















— 






— 




























— 


1 / 

7 


i 


















1 

1 
























— 


/ 

/ 
/ 


1 
1 

1 


— 





































/ 




/ 


1 












--- 












1 

1 
1 



























— 


— 


— 




/ 
/ 






/ 


1 

-1 - 

1 











/ 




/ 
f 


' 






/ 


1 


~'~ 


I 







:. 


=:i:; 






/ 








/ 


1 

1 

1 




— 




^' 


7 









10 Km, 



%et. 



Fig. 75 



- 852 - 



It is in no iray splitting hairs if I seek to account exactly for 
every m/sec that could perhaps be saved. - I have drann tvo curves in 
Fig. 75 Those abscissae represent the velocity vfaen burning stops. The 

ordinates of the dash-dotted curve (—•—.—•) correspond to the mass 

•"o 
ratio — — required for model E to attain the respective velocity when 

the burning is shut off. The ordinates of the solid curve ( ) 

correspond to the altitude (measured in earth radii from the centre of 
the earth) to irhich the respective velocity is able to hurl the space- 
ship. The dash-dotted curve is a harp line; the solid curve is a 
hyperbola of the third degree which has the vertical v =-^2 gr (broken 
line :----) as asymptote. From the ever faster increase in the 
last km/sec are the most gainful. For example, if I add 200 m/seo to a 
velocity of 500 m/seo, the altitude reached increases from 12.8 km to 
25.6 km; thai is, it doubles. On the other hand, if I increase the 
velocity from 11 km/sec to 11,2 km/sec, I increase the altitude reached 
to infinity, for, in so doing, it increases from a finite to an infinite 
figure. From the rapid rise of the dash-dotted line with higher velocity 
we see, however, that here the increase in velocity is gained by a 
rapidly increasing loss in substance; that is, we must also work the 
hardest for the last km/sec. 

Certainly, I cannot actually calculate the mass ratio or the final 
velocity as accurately as it might appear from these formulas. We do 
not exactly know the exhaust velocity and it need vary by only 10 % to 
result in differences in propulsion, with the same mass ratio, that 
would be greater than the difference in propulsion between vertical 
ascent and ascent on the synergy curve calculated here. 

The exact development of the theory, however, has a high relative 
value : I can compare the single types of ascent with each other and 
give account to myself how such a flight can best be carried out, apart 
entirely fr<Hn the "inner ballistics of the rocket", i.e. from the exhaust 
velocity and the propulsion apparatus. 



- S53 - 



Chapter 13 

Questions of Control . 
Letter index for Chapter 13 

g t force of attraction 

h J altitude above the centre of the earth 

Tn : mass of rocket 

r t radius of the earth 

s : centre of gravity 

X, 7, z t space coordinates 

A : rearward thrust 

L ! centre of the air resistance (centre of resistance) 

P : centre of reanrard thrust 

OC : flight angle 

1 ) Stability of the Arr ott 

To begin vith, I am considering the rocket as a rigid body in nrhich 
the effect of acting forces can be thought of as being concentrated in 
one point. By the letter L and the phrase, centre of resistance, I am 
designating the point on irhich the resultant of the air resistance acts, 
by S I designate the centre of inertia or centre of gravity, and by 
the letter P and the phrase, centre of reanrard thrust, I designate the 
point on which a force can be thought of as actings which is as great 
as and has the effect of the rearward thrust. 

1) I brought this chapter in normal print since it is easily understood. 
The layman, however, may skip it. 



- 854 - 



Let us l&j a, light, rigid staff (say a cane stalk) on the sine\r of 
a boir and shoot it. It Till not keep its direction but describe peculiar 
loops similar to a spinning leaf. It would also describe this curve if 
ire did not shoot it but dropped it from a sufficient height. 

AerodTnamics explains this as follo-nrs (ve can disregard the effect 
of the acceleration due to gravity) : The centre of inertia S lies in 
the middle of the staff (cf. Fig, 76). For the sake of clarity, I have 
draim the staff in this figure excessively short and thick. The centre 
of resistance L, on the other hand, lies in the first fifth nhen the 
staff flies in the direction of its axis and moves dovn the dotted line 
the farther, the greater the angle between the axis of the staff and 
the head wind becomes. When the staff is at right angles to the direc- 
tion of flight, the centre of resistcuice lies in the middle and in front 
of the centre of inertia. The forward-pushing force acts at S and the 
backward-pushing force can be thought of as concentrated at L, As can 
be seen, the whole staff is continually in an unstable state and hence 
begins to rotate. To prevent this, there are basically two methods i 



A 

W 



s 



\i 



V 



\ 



Fig, 76 



Fig, 77a 



Fig, 77b 



- 855 - 



l) We shift the centre of graviij aheekd of the centre of resistance. 
We make the front of the staff hearier, aay by attaching a hea°v7 metal 
point or a piece of elder in front (of. Fig. 7ta). 

8} We shift the Centre of resistance back of the centre of gravity 
by fixing suitable light fins to the rear end (of. Fig. 77b). 

If ire shifted the centre of gr&vity of the staff someiihat farther 
forward but not as far as indicated here, then it could occur, vith 
flight in the direction of the axis, that the centre of resistance lies 
in front of the centre of gravity; irith flight perpendicular to it, 
it could lie behind the centre of gravity. In this case, it -would not 
be possible to shoot the staff from a sinev, but if ire dropped it, it 
vould glide dovuvard at a certain angle, namely the steeper, the farther 
forward the centre of gravity lies. This is the state of an aeroplane. 
So here the basic condition for stable flight is that its centre of 
gravity must lie in front of the middle and behind the first fifth 
of the aerodynamic supporting surface. 

If we had shot the arrow in air-free space, its inclination would 
have been entirely incidental, since there is no air resistance. It 
would have followed the rotation impulse received when shot with a 
constant ntimber of revolutions} if it had received no rotation Impulse, 
it would have kept its axis direction independently of form and weight 
distribution* 

If we had shot it in atmospheric, but gravitation-free space, it 
would have continued flying in a straight line and the direction of its 
axis would not have changed. 

On the other hand, if we shoot an arrow in atmospheric and gravita- 
tional space, it always sets its axis in the flight direction and flies 
with the tip upward at first and downward at last. 



- 256 - 



S) Stability of the Rocket 

What iras said concerning the arroT applies to the non-burning rocket. 
With the burning rocket, a feir other things must be noted. If the rocket 
were absolutely rigid and the resultant of the rearward thrust could 
be thought of as acting at one and the same point, there would be no- 
thing to add to our explanations concerning the arrow. Then the rear- 
ward thrust would only reinforce the respective motion in the direction 
of the axis. 




Fig. 78 

But now the gases stream from nozzles, and if the rocket in Pig. 78 
turns in the direction of the arrow, -Uie gas stream strikes at a and 
produces a pressure which works against rotation. But this pressure 
naturally stops inmediately as soon as the turning motion stops, and, 
if one wanted to turn the rocket from the new position back to the old, 
the nozzles would not only be a help but even a hindrance, whereas, 
for example, air rafts would again automatically put ihe rocket eccis 
into the direction of flight. 

So, in this respect, the nozzles have a stabilizing or at least 
rotation-impeding effect, and that the more, the longer they are. 
(Most with models A and D, and least with models 6 and £,) 



- 257 - 



Otherwise,, the gas in the nozzles will never bum quite uniformly. 
That -rill causes rotation impulses, so that, even in air-free space, 
ire must provide safety devices, al.though they would naturally be super- 
fluous with nozzles working theoretically correct. 

In spite of this effect of the nozzle, however, there is no essential 
difference between a rigid rocket and an arrow. Hence, I will call 
such a rocket an "arrow rocket". If such an arrow rocket flies obliquely, 
it is deflected by the force of gravity parallel to itself and drawn 
out of its direction of flight. Pig. 79a indicates the forces by arrow 
segments which occur when the rocket flies de facto in the horizontal 
direction H. The letters are explained at the beginning of this chapter. 





Fig. 79 



Fig. 79a 



Hence, the head wind no longer strikes it in the axial direction (cf . 
Fig. 79). Now the aerodynamic uplift of the fins will be stronger than 
that of the tip. The tip will turn downward farther and farther (just 
as with the arrow) until the rocket shoots downward steeply, i.e. in 
case it has not already left the atmosphere. If this rocket were suddenly 
turned downward by an outside force, immediately an opposing forcle would 
arise tending to set the «ixis into the flight direction again; but, in 
fact, this flight direction itself will bend donnward in time and, to 
prevent this, we must affix special steering mechanisms ufaich, with 



- S58 - 



inel illation of the rocket, act on the fins so that they steer opposite 
to the inclination (cf. Fig. 80a-e). 




Fig. 80a-o 

The difference between rocket and arroir becomes basic if the rocket 
does no_t represent a rigid system and if it travels under acceleration 
until its fuels are exhausted. (What I have to put forth now appears, 
on the irholei to be unknoim to the rocket manufacturers. The reason 
could be because the customary rockets usually ascend under accelera- 
tion for only a few tenths of a second. In this connection, also 
compare "Die Rakete", Vol. 1988, p. 3.) Such a rocket will still ascend 
vertically even if we tie a chain or a heavy weight G (Fig. 8l) to the 

A, 



w 



Fig, 81 



- 259 - 



end of the guiding staff w. Now, if the connection is sufficiently- 
flexible, the front rigid piece simply indicates the trajectory and 
the rear pieoe is being tored along similar to a vagon drawing 1 or 2 
trailers by the pole. The -weight G can be heavier -than the entire rest 
of the rocket. As soon as the connection is rigid, straight-line ascent 
here is impossible for aerodynamie reasons, just as with a tail rocket 
no arrow-like flight with the tip forward is possible as soon as it 
no longer bums. In the tail rocket in Fig. 81 we distinguish the head 
K, the rigid guiding staff w, the flexible connection B, and the tail 
weight G. 




Fig. 88 Fig. 83 

With the tail rocket, the tendency to turn the tip downward is not 
aa marked as with the arrow rocket. Once it flies on a slant so that 
the head wind no longer strikes it in the axial direction and if the 
weight is heavier than the head K, obviously a torsional moment arises 
which tends to set the rocket vertically (fig. 82) . Naturally, if 
the upper rigid part is suddenly turned from its flight direction, it 
returns to its former position like an arrow; in this connection, 
compare Fig, 83. 

According to this, I do not consider it impossible to build tail 

Therefore I have provided my model C with only very small steering 
fins. 



- 260 - 



rockets that react to sudden deflections of the front part like an arroT 
but to long-lasting ones in the opposite iray (especially if the tail 
itself is also constructed like an arrov but is larger and heavier than 
the head and the guide piece). I believe I have also observed this 
phenomenon »ith sone powder rockets constructed by myself in which long, 
flexible villoir siritches served as tail ', I do not wish to say €uiy- 
thing about it, however, before concluding exact experimental research. 
Neither do I wish to follow the matter theoretically any further in 
this place, for mere theory appears to me to be somewhat gray here, 
What is involved is opposing an exactly given and continuously acting 
quantity to an average value of various instantaneous deviations. That 
is a task of the type of the Petersburg problem in which the probability 
theory has not yet spoken the last word. 

If this my supposition should find confirmation, that would be a 
most favorable condition for the construction of meteorological rockets 
of the type of my model C because, in so doing, the immediately to be 
discussed and, in any case, quite expensive active steering by gyroscope 
could be dispensed with. 

3) Active Steerinti; (Steering by Gyrocompass ) 

If the arrow rocket is to burn longer than a few seconds, the steer- 
ing must be active, i.e., depending on the position of the axis, the 
fins must by themselves execute suitable movements somewhat in the way 
indicated in Fig, 80a-c. 

Perhaps, it will be objected here that the flight of an aeroplane 
at the same angle is quite stable, if only the front end is weighed 
down a bit more and stands steeper than the rear end. Among other 



1) 



Only thereby did this idea occur to me. 



- 261 - 



things, children's paper airalloirs are loio'wn as irell as gliders and 
similar derices iriiich fly completely by themselves vithout turning the 
tip do-wnTord. But, in the first place, the models mentioned fly at 
almost uniform speed, irfaereas, vith the rocket, the velocity changes 
extremely fast; it is erroneous to think that the ascent angle of an 
aeroplane is independent of the velocity (i.e., in this case, of the 
propeller traction). Secondly, vith a rocket, ve are usually dealing 
vith a round body irbich can rotate about its axis; this makes aeropland- 
type flight still more difficult. Thirdly, irith an aeroplane, the centre 
of gravity must remain in almost the same position vith reference to 
the theoretic aerodynamic supporting surface} vith a burning rocket, 
hovever, this Till be difficult to realize for rea^ions of construction. 
Here, security in flight Is guaranteed only if the centre of resistance, 
from the very beginning, is placed so far to the back that, even if it 
shifts, the centre of gravity still does not change, which is possible 
only vith arroir-type construction; in this case, the geometric position 
of t^e centre of gravity has play room equal to l/5 of the vfaole theoretic 
length of the axis vithout changing the glide angle. Finally, in the 
fourth place, it vill hardly be possible for reasons of constiniction to 
make the reanrard thrust act othervise than in the rocket axis. In this 
case, vith rearvard thrust vhich can amount to a multiple of the veight, 
stability is naturally assured only vith veight distribution of the 
arrov or veather-vune type. For these reasons, I favor arrov-type 
veight distribution and active fin control vith fin rockets. 

We can achieve active steering by automatic means if ve install a 
gyrocompass on the rocket, vfaose position controls the position of the 
fins. A gyroscope, whose axis can freely adjust itself vith reference 
to the rocket, vill seek to keep its position in space even if the rocket 
rolls. The steering apparatus of model E and the larger forms of model 
B, for example, could look as follovs t 



- 262 - 



(in case the reader is not acquainted with mechanical drawing, 
I will explain : The upper figure shows the apparatus as if we had 
bisected it from top to bottom and looked at it from the side; the 
lower figure shows the apparatus as seen from above if the top cover 
of the gyroscope chamber is thought of as lifted off.) 



S> I n I N 




Fig. 84 

Gyroscope K rotates in a horizontal, vacuum casing H, which can 
rotate about the axle g, ^2? rotation about this ea:le starts an electric 
current} g, and g_ are suspended in a ring which itself can rotate 

1 as 

about the axle g„ g. and, in slanted position, starts electric currents; 
these currents affect the position of the fins; at the same time, the 
extent of steering required can also be registered, U is an electric 
motor which turns the gyroscope. 

With vertically-ascending model B, only one such gyroscope is 
required; with the models that are to ascend on a slant, two gyroscopes 
are needed whose axles must stand perpendicular to each other. 

Here, the regulation of the electric current by the gyroscope is 
thought of so that at g- and gg, depending on the position of the 
gyroscope axle or the ring, a wire dips into a tube with mercury to 



- 263 - 



varying depths (cf. Fig, 85 a). In so doing, the outside forces affect- 
ing the gyroscope are minimal in any case, so that it irill scarcely 
make any precession oscillations. Another possible solution (cf. 
Fig, 85b) would be to send the current through a poorly conducting 
■rire a, rigidly connected to the rocket, -where it -would then continue 
to floir through the copper bracket b, connected -with the gyroscope. 





Fig, 85a 



Fig, 86b 



Here, the resistance due to friction and the precession oscillations 
would be more marked. Nevertheless, the frictlonal resistance could be 
compensated for by, in addition to the firm bracket b, attaching any 
movable bracket c which, depending on -whether the bracket rotates ir 
one direction or the other, closes an electric circuit in one direction 
or the other. By electromagnetic means, this current could exert a 
force on the gyroscope which is equal and opposite to the frictional 
resistances. 

These control mechanisms can be tested beforehand by labilely sup- 
porting a suitable model of a rocket with adjusted steering apparatus 
and placing it into a wind tunnel (cf. Fig. 85c). 



Here, the critics have largely misunderstood me. It is thought that 
I had the intention of solidly connecting a large, heavy gyroscope to 



- 864 - 



the rocket, by irhich the axis of the rocket irould be held fast in space. 
As is already knoim from similar experiments irith aircraft, that is 
impossible, l) A gyroscope that is to really noticeably retard the rol- 
ling moTements of the rocket vould be too heavy to take along. 2) Such 
a gyroscope vonld continuously perform prece'<>sion oscillations and 
make exact steering impossible. Well, that vas not my intention, and 
I recommend that the gentlemen concerned read the books irhicb discuss 
the matter more carefully. 




-^ d _ 



R " model of rocket; d >= thin steel 
rods; S = support replacing P; f = spiral 
spring serving to balance the front partj 
B - registering apparatus. 

Fig, 85c. 

GAIL also does not see clearly in the question of the control 
gyroscopes. In "Stone from the Moon" (Bergstadt Publ , House, Breslau, 
1st to 6th edition) he writes verbatim (the underlining is mine) t 
"The docking maneuvers were about to begin. The control gyroscopes 
began to hum and whine; the space-ship turned slowly until the rocket 
nozzle pointed exactly to Astropol, Then , a few brief discharges — 
braking shots that more and more reduced the flight of the ship and 
adjusted it to the motion of Astropol. 



Apart from the fact that I would never have allowed the control 
gyroscopes to stop, tiiat, for various reasons, I would never have set 



- 265 - 



the nozzle exactly in the direction of Astropol, that the discharges 
-would hare had to be accelerati on s hota , ajid that, hopefully, my 
gyro-compasses will not hum and irhine, I would, above all, like to 
remark concerning this that the control gyroscopes alone cannot turn 
the space-ship at all. It can only rotate if either, according to 
HOHMANN, the occupants climb along the walls in a circle (cf. Fig. 59) 
or if another object inside is rotated or if the nozzle works. The 
gyrocompasses, on the other hand, are in oardanic suspension and can, 
therefore, never rotate the body of the space-ship by counter-pressure. 

Correctly, the passage concerned should have stated : " The gyro- 
scopes operated, a few brief discharges followed, while that took 
place, the nozzle turned toward Astropol. Finally, a few himdred metres 
before the destination, the equalization was completely achieved, and 
so on". Naturally, GAIL'S representation is more impressive. 

For the rest, it is not a bad idea to rotate the space-ship to a 
new position by the counter-effects that arise when wheels are made 
to rotate. As far as the space-ship no longer performs any rotating 
movements, this method of rotation is definitely preferable to rotation 
by nozzles, for example, as HOEFFT suggests, for they easily cause 
rotation to continue if the thrust is not completely equalized and, 
besides, always work with a loss of substance. —This method is also 
better than the method of climbing about along the walls suggested 
by HOHUAM (cf. Fig. 59), for, in the latter case, precise adjustment 
would be possible only if the space travellers remained hanging at 
■the right place until the nozzles had worked, (if there were two, it 
would be theoretically possible for both to reach the hammock without 
rotating the space-ship, if they finally crawled toward each other; 
in practice, however, that would hardly be completely feasible.) 
In our case, they can, from the very beginning, position themselves 
as they wish. 



- 866 - 



I -would not make tJiiese irlieels as heavy as GAIL auggeflts, only out 
of a metal rim and bicycle spokes, and let the navigator set than in 
motion by hand by means of a crank with cog-wheels. This will suffice 
for the small mass of the space-ship. Rapid rotation, as could perhaps 
be necessary near heavenly bodies, will not be achieved in this way; 
in this case, one can use the gas fins and the nozzle connections . 

4, Gas Fins 

Fins projecting outward, as in Fig. 79a, for example, can only work 
in the atmosphere. In air-free space, on ihe other hand, only fins 
like those in Fig. 78 or Fig. 80 are of use which run parallel to the 
gas streom and, vith rotation, exert pressure on the gas stream. Fins 
of this type are mainly used in hydrogen rockets which must operate in 
the highest strata of the atmosphere or in completely air-free space. 
Concerning the question irtiether these fins do not bum up, the following 
can be said : 

If ihej contimiously exerted too much pressure on the gas, they would 
bum upf if, on the other hand, they stood off too far from the gas 
stream, the air fould cause friction and, hence, in the upper strata of 
the atmosphere, ittiere the rocket already flies very fast, they would 
likewise bum up. Now, in ihe elongation of the jacket of the rocket 
(as research with flying missiles has taught) only little air is encount- 
ered, and ibe gas stream again spreads out so much as to touch the air 
only farther behind the rocket. Usually the fin lies between gas and 
atmosphere in relatively cool space where the air is strongly rarified. 
Besides, with dynamically-cooled nozzles (of, pp. £ , 4l) the upper 
layer of the gas stream is cool and somewhat less in motion. Nevertheless, 
such gas fins will have to be supplied with a certain quantity of cooling 



^' In the film, "The Woman in the Moon", the space-ship was furnished 
with such Kneels at my suggestion. 



- 267 - 



fluid since they villi at timeS| be immersed more deeply in the gas or 
the air. 

Even in the highest air strata, at an altitude of about 100 km, the 
model B alcohol rocket has a velocity of only 2440 m/sec. Here, there 
is little dauiger of well-cooled air fins burning up, but, because of 
the low air resistance, air fins alone would be ineffective; hence, 
I planned to use a box-type frame similar to the former box kites, which 
can exert pressure on the gas stream. 

Nothing in particular can be sairt about the activ e steering by means 
•f gas fins. If they are pressed agains the gas stream, they actually 
produce haphazard rotatory movements. 

Concerning passive steering by means of gas fins in completely air- 
free space, it can be said that they actually represent tui elongation 
of the nozzle wall. What was said in p. 256 about stabilizing the flight 
by the nozzle wall (also compare Fig. 78) applies in still greater measure 
to gas fins. 

In air-free space, there are no such strongly deflecting forces as 
in the atmosphere. There, gas fins connected with a control gyroscope 
are sufficient. Yet, here deflecting forces will not be completely 
absent (cf. p. 257 ). Besides, the occupants will never be quite motion- 
less. With models B and E, the centre of gravity lies above the centre 
of rearward thrust, from which follows a certain tendency to roll 
which can only be combatted by the use of gas fins. 



Naturally, only because of the mentioned irregularities in the burnings, 



- 268 



5. Other Steering Possibilltiea 

At one time, HOEFFT suggested dispensing -with fins entirely and 
instead fixing four or more swivel ing nozzles to the rocket and 
variously opening or closing the ranaining ones by means of the regulat- 
ing rods described on p. 47, which can be projected to various distemces. 
These regulating rods could be manipulated by a gyrocompass. Vlhen one 
nozzle is closed somewhat, the rocket must turn to that side similar to a 
boat irtiichis rowed more weakly on one side. 

For rockets that can travel in air-free space from the start, as the 
model £ hydrogen rocket, for example, this steering should suffice. 
Besides, it has many nozzles which can be closed by means of rods anyway 
and these can actually be employed for active steering. That is why 
I also provided them for the manned model E space-ship sugcested in 1923. 

Several things must be observed, however. In the first place, the 
rocket would hardly bum as steadily if the regulating rods had to be 
advanced to various distances now here, now there. Secondly, my gas 
fins are nothing less than ballast. They represent an elongation of the 
nozzle wall and if we set than slanting outward we can, by using th^n, 
accomplish the artifice of making the nozzle outlet larger than the 
largest cross-section of rocket (which, taking into account air resist- 
ance in ascent, must naturally remain limited). Third, and finally, 
the fact must also be considered that landing on water by parachute, 
which we must pre-suppose today before we can see clearly regarding 
the transfer of heat due to friction of the air (cf. Chapter 14), could 
be considerably less dangerous if the thin, elastic gas fins struck 
the water first. Striking the surface of the water will be considerably 
more dangerous, however, if the rocket immediately touches down on the 
water with the entire broad nozzle surface. 



- 269 - 



I cannot cherish the thought of also applying this steering to 
rockets that are supposed to bum irithin the atmosphere. The gyroscope 
can always Tork only if the rocket has already been turned from its 
position. So, a rocket irould be doniitantly hurled to all sides, al- 
though it -would always return to the flight direction again; I am 
afraid this will happen at a tempo which will hardly be beneficial to 
the space-ship. For example, the liquids in the tanks will rise in 
such violent wares that the work of the pumps will be seriously endanger- 
ed. And such rolling will certainly not be exhilarating for the occupants. 

The idea might sooner be feasible if, beside a gyroscope, an instru- 
ment similar to a pendulum or seismometer were used for regulating the 
nozzles, liiich influences them as soon as the first indications of a 
rolling motion appear. The detailed calculation of such an instrument 
and the preliminary experiments in this respect would, however, pose 
incredible difficulties. I happen to itnow because I myself am intensely 
interested in the theory of the seismograph. Naturally, I would be 
honestly delighted if this type of steering proved successful, I do not 
find the air fins on my rocket especially suitable . 

Other Stabilization Suggestions 

UNGE and GODDARD had the idea (in this connection, also compare 
Vol. Il) of first driving the rocket from a gun. In so doing, it is 
naturally difficult to attach fins. Complicated control gyroscopes 
would likewise not endure the high counter-pressure during the shooting, 
nor are they at all within the intention of the gunners concerned. 
Hence, they propose to give the projectile itself (GODDARD) or a turbine 
wheel built into the nozzle a rotation about its axis. Naturally, just 



T) 
' For that matter, HOEFFT has recently suggested models which, beside 

regulatable nozzles, are also furnished with fins| unfortunately, 

however, theae are also unrealizable. Cf. Vol. II. 



270 - 



as vith a cannon ball, such rotation cannot prevent movement of the 
axis, only retard it. The air resistance, namely, has the tendency to 
set the rocket at right angles to the direction in irfaich it is shot, 
and the spinning effect only causes the axis to turn aside and relativ- 
ely slowly describe a cone. In so doing, at least the setting horizontal 
of the rocket is being considerably slowed down. How great the firing 
accuracy of such missiles can be naturally only numerous experiments 
can show. I am not posted in the matter; the last experiments I know 
of are those in Meppen in 1907. But I cannot call those experiments 
encouraging. 



TS 




Fig. 86 

Liquid-propelled rockets do not come into consideration for shoot- 
ing from a cannon for reasons of resistajice. Yet, even if I wanted 
to shoot an explosive rocket from a gun, I would not choose the method 
of stabilization by rotation but would attempt to stabilize the 
missile by a fin-like appendage. I would fix a pipe to the jacket 
of the rocket of a length to fit into the cannon barrel and four times 
as long as the rocket. I would pack the powder required for the shot 
into this pipe, so that it would also serve as a cartridge, and the 
rest of the space I would fill with a metal bolt projecting up from 
the base of the cannon. I would fire the rocket from a smooth barrel 
(Fig. 86). 

fi ) Con trol of the Vel oc i ty 



As already stated on p. 1^3, the acceleration can be directly 
measured by the counter-pre=sure produced; the counter-pressure again 



- 271 - 



is proportional to the pull or pressure irtiich any body exerts against 
its support. 

With simple, vertically-ascending meteorological rockets, for 
example with model C, ire need only register the counter-pressure. Here, 
the counter-pressure has nothing to do with regulation of the velocity 
or with the steering. We will simply fasten a weight to an elastic 
spring and, by means of a pointer, register its respective position 
on a roller rotated by clockwork. After the return, from the curve for 
the acceleration, the curve for the velocity can easily be found, and 
from this the altitude. Here, an error occurs because the trajectory 
bends now to the ^ight, now to the left, so that we are calculating 
the distance travelled and not only the altitude with this measurement. 
In order to eliminate this error, this acceleration indicator could 
be fastened to a gyroscope whose axle turns freely. If this gyroscope 
were adjusted exactly horizontally, we would actually obtain only 
the vertical component of the acceleration. Naturally, before finding 
the velocity, the gravitation would have to be subtracted from this 
acceleration; in the first approximation, that oan be equated to 9.81 
m/sec . If, under assumption of this deceleration due to gravity, the 
altitude reached hns been found, from that it can then be calculated 
more accurately, etc. With long-distetnce rockets and manned rockets, 
we will not only record the vertical acceleration but the acceleration 
in the north-south and eaat-weat direction as well. Furthermore, we 
will not only register the data of the acceleration indicators, but 
we will utilize them for automatic steering of the rocket. For the 
purpose, we shall attach three raercuiT' acceleration indicators (cf. 
Fig. 47), placed at right emgles to each other, to a gyroscope in 
Cardanic suspension. These acceleration indicators provide currents 
which are proportional to the acceleration in the respective direction 
and which can be registered by means of current meters. The accelera- 
tion indicators must work very accurately; fortunately, they can be 



- 272 - 



checked on a whirling arm beforehand. In addition, these currents can 
influence needles Thich register the acceleration on a uniformly 
moving paper strip. The reading on the current meter again xrould be 
proportional to the velocity. If thia current meter, for its part, 
so influenced a current as to make its strength proportional to the 
velocity, then, in the same way, a second current meter could integrate 
the course. The various current meters and electricity sources must 
naturally no longer hang from the gyroscope apparatus. They could be 
connected to the mercury apparatus only by light, thin wires. 

Here we at first obtain the single coordinates of the course ( I call 
them z, y, z); they could be registered again. Besides, 3 tin strips 
could be moved forward on rollers r (cf. Fig, 87); the fonrard motion 
could correspond to x, y, z. The lower edge of the tin strips is 
horizontal, the upper forms any curve; the axle of the wheel z which 
runs on the upper edge is being drawn against it. Since this wheel can 
only move up and down vertically, the distance of its axle from the 
lower horizontal edge will represent a very definite function of the 
course x, y, z. Roller z again could influence rheostats, etc. 
Naturally, in this way, fvmctions of the velocity and the acceleration, 
among other things, could be formed. 




^~w(ir 



Fig. 87 

These strips could serve a great variety of purposes. For example, 
with their use, an apparatus could be constructed which indicates 



- 273 - 



exactly vhere the rocket is situated. Nainelj, in this vay, the accelera- 
tion due to gravity could be found and the acceleration indicator could 
be used for correcting the data. Assuming that, in some tray, ire have 
obtained the three space coordinates with reference to the centre of 
the earth (i, y, z), then we let x^, y*, «8 form. We can do that, 
for example by shifting tin strips under a roller in the right rela- 
tionship to X, y, z. Then, we mechanically add these effects (say by 
sending three currents of the intensity x^, y*, z* through a joint 

current meter; x^ + y + z = h ) and, corresponding to the total effect, 

run an equilateral hyberbola imder a roller; this gives the effect : 

a 1 
g = So' ~W' '^^^'8 effect must then be divided in the ratio of the 
h ' 

three direction cosines, that is in the ratio x : y t z; for example, 

we can divif^e a current proportional to g into three branches and 

insert resistances proportional to -;-, ""y~» ~- which are simply 

activated by the space components. With that the problem is solved, 

for the three currents can easily exert effective forces proportional 

Sx> Syr S OQ ^^^ three weights. Naturally, numerous other solutions 
are also possible. This apparatus could be used only near the earth. 
It becomes considerably more complicated if the change of the field of 
gravity due to the movement of the earth and the rest of the heavenly 
bodies is to be taken into account. From the general theory of relat- 
ivity of EIKSTEIN and the theory of RliMMN'S curvatures, it can be 
concluded that, in this case, ten different functional strips will 
be required. 

Aim ing with Long-Distance Rockets 

Naturally, that type of apparatus could also be used for the 
automatic steering of rockets. For example, with long-distance rockets, 
remarkable firing accuracy could be achieved by the use of similar 



- 274 - 



apparatus. The rocket irould have to be steered so that it ascends in 
a straight line under a specified angle (not in the synerj^ curve; 
an apparatus making the latter possible could be constructed, but it 
is too complicated and heavy for smaller unmanned rockets). 

For straight-line, oblique ascent, the acceleration indicators 
irould have to be adjusted before the flight so that one of tbo space 
coordinates, i, y, z, falls exactly in the direction of flight. 
The other tiro would have to be perpendicular to it. If the respective 
pointers indicate a course differing from 0, the controls would 
have to be influenced by the produced current so that the rocket 
returns to the 0-position again. Here I would like to obviate a 
misunderstanding. After what I have said about the fins, it could be 
assumed that only rockets of the aeroplane type with carrying surfaces 
can ascend obliquely on a straight-line trajectory. In actual fact, 
any rocket with fins can observe a linear, slanted trajectory; it is 
only that, in this case, the rocket axis may not be in the direction 
of flight but must point somewhat upward, so that a component perpen- 
dicular to the trajectory arises which just cancels out the gravita- 
tion component (cf. Pig. 74, 80). That is easily achieved with 
gyroscope steprirg, as I have just described it. Naturally, by that 
type of gyroscope apparatus, the place of descent of a rocket with 
carrying surfaces can be regulated quite accurately. In addition, 
with such long-distance rockets, a type of electromagnetic balance 
could be installed between the current proportional to the velocity 
and that corresponding to the altitude, which, depending on Its 
position, opens or closes the supply cocks between propulsion 
apparatus and fuel tanks so that the propulsion increases when, at 
a certain altitude, the velocity has not yet reached a prescribed 
amount and decreases if, at the respective altitude, the velocity 
is too great, and finally stops completely, when a certain 



275 - 



velocity has been reaehed. If this balance irere built in, the rocket 
could be made to continue flying at a specified altitude vith a 
specified velocity in a specified direction. The accuracy of fire 
of this rocket irould be as great as desired If only the accuracy of 
these control appnratus irere sufficiently freat. 

Another way voul d he to have the fvels shut off somewhat earlier 
if a higher velocity was already reached farther down, and vice versa. 
In any case, in this way the rocket can be made to begin its free 
flight at the prescribed altitude under the prescribed angle of 
flight with the prescribed velocity. In the steering of rockets, a 
number of fortunate circumstances coincide which are lacking with 
aeroplanes emd torpedoes. In the first place, with my liquid- 
propelled rockets, the lift-off is free of impact. Moreover, the 
b\iminf^ of on unmanned rocket lasts only two miniites, so the 
appfiratus have no time to get out of order (for example, that such 
apnarati!s fail on aeroplanes is attributable, first, to the dura- 
tion of the flij|;ht arid, second, to the vibration of the apparatus, 
by which the secondary accelerations are very great in comparison 
to the useful acceleration , 

In the return, in any case, deviations occur because of the air 
movement. How great they are depends, in the first place, on the 
type of landing. With parachute landin;^, they are smaller than some 
flyers ni^ht expf>ct, Tn +.'ae I'ir^t rWof^, descent froin an alfituf'o 
of 100 '•?" f're.s not epsentinlly last longer then descent from an 
al + itude of 10 1^\, for the upper air strata only offer little 
resistance to the rocket and nre quickly passed through. Secondly, 
the movement of the upper air strata could be extremely uniform. 



■ 1 -— ** II -- 

Hence (apart from the inaccuracies caused by the landing), I am 
fi,<nirinfr with a steering of 5 per thousand in the direction of flir^ht 
and 2 per thousand perpendicular to it. 



- «76 - 



It urill already be known nfter a few meteorolojrical rockets have 
ascended, and then a correction can he raaile. For theie reasons, I do 
not reckon with a gre-i.+ er divergence than at the most 5 km with 
landing by parachute. 

The deviation of the rocket projectile when landing is still much 
smaller because it pafses through the relevant part of the ataoaphere 
in less than 15 seconds and because, in any care, it will be larger 
and heavier than a mail rocket. E\iirthermore, here a very special 
circumstance Is added : If the payload of the rocket projectile is 
placed in the head, the empty tanks after the fuels are exhausted and 
the fins act like the tail of an arrow. If the rocket is struck by 
a strong side wind, it mainly drives off the tail. Hence, it turns 
the hend somewhat into the air stream, and the aerodynamic drift 
produced therbby in part compensates for the effect. The deviation 
is not even as great as that of a body of the size and specific 
▼eight of the payload alone would be and, even in the strongest 
hurricane, will at the most amount to tens of metres, I could produce 
the mathematical proof of this statement only after a thorough 
development of the arrow theory, and that I do not wish to do here 
for reasons of space. 

Therefore, the rocket projectile will be feasible at the moment 
in which we succeed in aiming accurately enough at the launching 
itself. 

7) The Rocket Projec tile 

Herewith, I come to speak about a topic concerning which not niuoh 
is said but about which one appears to think more. Various parties 
have already asked me whether I consider a rocket feasible which, 



- 277 - 



in case of irar, could carry 2000-3000 kg of prusaic acid or any other 
poisonous gas into enemy citie.s or positions. 

I, personally, irould not be wholly averse to the development of 
such a weapon. And that, becau«>e I de.^ire justice and peace. 

l) In the present technique of war, it is usually the case thnt 
those who declare war or cause the government to declare war stay 
far from the fire themselves (Honor to the exceptions'.), and I 
certainly believe wars would not occur so easily if those concerned 
kn«w t "The first one to get hit is you yourself". And if they 
actually were the first. Naturally, the enemy would rather save its 
rockets and turn to the govemcients and financiers of the opposing 
country itsflf, without which the nation concerned would, in a 
short time, be a leaderless mass asking for peace. In any case, the 
enemy would not waste millions of rockets on the army widely scat- 
tered in trenches and, for the most part, still armed with gas 
masks. It would rather send its rockets against munitions factories, 
railway interchange points, etc. 

Here a communist countered by saying that one crow does not pick 
out the eyes of the other, and the 200—300 people which are to ml e 
the world according to RATHEN^AU would not kill each other. It is 
certain that, in case a revolution broke out anywhere, they would 
still assist each other. — I am not enough of a politician to be 
able to express a Judgment concerning this statement. I, for my part, 
do not believe that the solidarity of the leaders (if such existed 
at all) could prevent them from destroying each other. It is still 
possible that leading circles do not like to see a revolution in 
countries governed in a way similar to theirs, from where it could 
also spread to their own country. In our case, it is not a question 
of danger from revolution but only of increasing their own power. 



- 278 - 



It has also been objected that such a weapon could not be used in 
accordance with the Geneva Convention. I believe, however, that expe- 
rience teaches sufficiently clearly that states care very little 
about the Geneva Convention if only they themselves are in possession 
of a weapon not permitted by international law, (Perhaps, with the 
exoeption of Germany, but even that only "perhaps." It was the German 
chancellor himself niio, in 1014, spoke the words, "A{!;reements are 
scraps of paper when a nation is faced with a choice of belnr or not 
being".) 

8) JOHN C, LIVENS has shotm that war with metal weapons is in no 
way more humane than gas warfare. 

a) When attacking the armies of the enemy with the latter, there 
is more opportunity of just paralysinp; the enemy soldiers. 

b) Gas warfare causes less wounds and pain than weapon warfare and 
makes fewer invalids. Most gases never make a life-lonj^ cripple of 
any on e . 

c) A gas war will presumably be decided very quickly. The nations 
will suffer fewer privations on account of it than in a positional war 
and, because of the shorter duration, not as many values will be 
destroyed and fewer people will perish, 

3) As I see the political situation today, a certain probability 
exists that a new world war will break out in 10-20 years, in which the 
western powers (France, England, Amorica, and perhaps also Germany 
and Scandinavia) will fiffht on one side and Russia, Japan, China, and 
eventually India onj the oth«r. In so doinjT, vith the hitherto eyistinn; 
methods of warfare, the Central European states would have no choice 
but to join one of the parties tuid therewith serve them as concentra- 
tion area and theatre of war, for they are too weak to ranain neutral 



- 279 - 



and defend themselTes against both parties. (l came to this rievpoint 
through studying the pamphlet on geopolitics.) 

Noir, in order to save the states concerned from this fate, there 
appears to me to be only one mRans, namely to put war on a basis on irfaich 
no anay and no concentration area at all are required for iraging Tar. -*• 
Such a means vould be the rocket projectile, for exaisple. If the Central 
European states themselves possessed it, the others irould be afraid to 
violate their neutrality; if the parties vaging var theciselves possessed 
it, they irould already have settled their differences before their 
amies had concentrated and begun to shoot. 

4) I desire this veapon because I desire peace. In ny opinion, irar 
can be prevented only by creating veapons irtiich the public respects 
and vith vliich it does not wish to become acquainted. 

Unfortunately, some port of romance clings to warfare with fire- 
arsis, (To be sure, the pref?ent r^enerntion had enough from tbe last 
Tj^ar, The coming generation, however, will know war only from books and 
cinema pieces ond will acain be in a mood to wage war.) But it makes 
a difference whether one attacks the enemy on a noble steed or a 
masterly aeroplane and, in so doing, earns medals of bravery and per- 
forms deeds of heroism, or whether one waits in some cellar at home 
whether the enemy's poisonous gas will enter or not. This form of 
waging war is void of all romance and, hence, will not praised and 
not desired. 

5) Besides, I would welcome the replaceaent of the present— day 
costly ar?nies by the cheoper construction of rockets, which does not 
keep so many people away from productive work. 

For the rest, I must again and again answer such inquiries by 



- 280 - 



saying that, at present, I myself consider the use of my rocket as a 
lonp-distance missile as excl uded . Although a large jas missile need 
not, by far, hit the target as accurately as a shrapnel or a frreaade, 
today precision mechanics is still not in a position to build the 
steering apparatus vith the accuracy required. I believe the goal can 
never be achieved by perfecting hitherto existing methods; as far as 
the accuracy of current registration and gyroscope adjustment is 
concerned, completely n«ir inventions irould have to be made. Even if 
the problan of accurate registration of the acceleration components 
were completely solved, the whole acceleration indicator would still 
always have to be attached to the ST-roscope; I will be happy if I can 
attain a firing accuracy of 10-80 km with long-distance rockets on 
shooting distances of 1000-2000 km, 

I have been approached with the statement that gyrocompasses 
already exist today which can be adjusted more accurately (for example, 
the one by SCHCTZ) and that large plants are engaged in manufacturing 
gyrocompasses on a large scale. The economic results of this industry 
make possible the erection of well equipped factory laboratories and 
the payment of skilled personnel who can dedicate themselves exclusively 
to improvements in this area. 

Whoever finds himself outside of those circles and hence can use 
only a small fraction of his time for the study of the gyrocompass 
ccmnot easily enter into competition with the specialists. I also lack 
the knowledge of many details and practical experiences made with th«a. 
Hence I cannot say whether and on the basis of what physical laws 
sufficiently accurate control gyroscopes could be built. Neither can 
I invent anything in this field because I lack the necessary prelimi- 
nary knowledge. I can say only this much with certainty that the 
control gyroscope described here is, in any case, not suited for that 
kind of precision. So I consider my rocket unsuitable for artillery 
purposes at present. 

Possibly it will be different in 1-2 decades. As stated, that is 
my wish. 



- 281 - 



8, Orieait ation of th e Et her- Ship in Space 

On this topic, I naturally need not tell the astronomer anything. 
The layman can think of the matter as foil ova i Axiy round object, for 
example, an apple, is placed on the table to represent the earth and 
the objects farther mtoj in the room are supposed to represent the 
stars. If the observer bends doim, because he is closer to the apple, 
he sees it higher in comparison to the other objects, and that the 
more, the loirer he bends doma. If he stands on tip-toes, he sees it 
lover. If he bends over to the right, the apple apparently moves to 
the left. If he comes closer, the apple appears bigger to him, and 
so on. 

The space traveller finds himself in the very same situation irith 
reference to the earth and the near planets. The fixed stars appear 
to move along vith the space traveller like the moon moves with the 
walkers, for they are so far away that the "slight" shift of position 
in the solar system cannot produce any visible shift of their apparent 
location. 

Before the flight, the astronomer cab now calculate very accurately 
where and how large the earth must appear at a given moment (cf. Fig. 88), 
If it looks larger, one is too closei the velocity was too low. If, on 
the other hand, the earth appears smaller, one is already too farj one 
must put on the brakes. If it appears to have shifted to one side, 
then one has moved to the other side of the direction of flight 

etc. The size of the error can be exactly estimated. from the extent 
of displacement or enlargement of the earth. 

^) ffle a utom at ic observa nce of the mos t adv anta^eoua velocity can 
be achieved as follows t 

As I showed on p. 8^, the rocket travels with the most advantageous 



- 282 - 



velocity yrhen the air resistance equals the drift. Now, v& can take 
the total air resistance as being proportional to the pressure iritb 
which a movable piece of tin b at the tip is forced doimvard. The 
■weight depends mainly on the level of the fuels in the tanks. If, on 
the one hand, we install floats in the fuel tanks which manipulate 
an electric resisteuice so as to create a current proportional to the 
weight and, on the other hand, let the piece of tin b similarly 
influence an electric current so as to create a current proportional 
to the air resistance, cuid if we let both currents act on two electro- 
magnets attached to a balance which manipulates the fuel cocks, then 
we can cause the nozzle to bum faster when the velocity is lower 
than the most advantageong velocity, i.e. when the gravitation is greater 
than the air resistance, and the fuel supply to be shut off when the air 
resistance is greater than gravitation. 



Jl 



Fig. 88. Correct 






Figi 89. Too far west 



Note the size of the earth's disc and its position with reference 
to the fixed stars. 



Figs. B8-90, According to the Fritz Lang film of Ufa, "\yoman 
in the Moon". 



- 883 - 



' j! 






/ i 



Fig. 90. Too close and too far north 



With the manned machines, the acceleration could be refrulated in 
a similar way by means of the accelpration indicator so that the 
coTinter-prpssure never becomes too great nor the acceleration to« small. 
In fact, Tirith the manned machines, the aim should be to make them vork 
automatically as much as possible, so that the astronaut need intervene 
from time to time, at the most, l) There vould be so much to do 
(regulating the fufil, steerinp:, determining altitude, etc.) that even 
two astronauts could not manage everything; so the greatest part would 
have to be done automatically. Therefore, one rather has the whole work 



- 284 - 



done automatically; then the astronaut has his hands free and can make 
his observations undisturbed. Naturallj) the mechanisms must be so 
arranged that the astronaut can at any time and in any iray influence 
the operation of his machine. 2) The fact must not be forjjotten that in 
general) especially in the situations to which man is unaccustomed at 
least at the beginning, the machine will very likely work considerably 
■ore accurately and cold-bloodedly than man. 

Chapter 14 
The Land ing 
Formula quantities of Chapter 14. 



e 

h 

P 

P 

^o 
r 

s 

t 

T 

H 

L 

Q 
s 

T 



base of the natural lofrarithms 

depth of atciosphere usable for the braking flight 

parameter of the curve described by the space-ship 

air pressure after compression 

air pressure before compression 

earth's radius 

altitude above the ground 

apparent air temperature caused by the motion 

velocity 

7300-7400 m. Cf. (34) 

air resistance 

quantity of heat absorbed through conduction 

quantity of heat given off through radiation 

overall absolute temperature 



- 285 - 



t^ t absolute temperature after compresaion 

Tq I absolute temperature before compre$<sion 

X : ratio between the specific heat vith constant pressure 
and with constant volume 

^ I barometric pressure 

Q g : air pressure at altitude s 

f^ t absolute temperature of a body heated by friction against 
the air 

LU : technical mass of 1 m 

Q^ t radius vector (with reference to centre of earth) 

<X « STPTAN-BOLTZMANN radiation constant 

f^ I true air temperature 

05 : angle of direction (with reference to centre of earth) 

When laeteors fall, we notice that i 

1) The meteor does not strike the earth with cosmic but only with 
terrestrial velocity. The air resistance increases as the square of the 
velocity and is so <rreat that small bodies? can reach the earth's 
surface with velocities counted at the most in a few 100 m/sec. 

2) The meteor isrlows up in the zone between the 100 and 75 km altitude. 
(Apparently because its \eloc7ty was converted into heat due to the air 
resistance.) Fallen meteors are red-hot on the surface and ice-cold 
ineiide. The surface shows clear traces of the fact that the outer layer 
has melted and is blown away by the air. Larger meteors always form a 
bright tail irtiich often remains visible after the meteor itself 

is for long out of si<:;ht. In one case, a tail was observed which 
remained visible for over an hour. The color of tiie tail is that of 



- 286 - 



of gloving iron vapour or gloving earth metals. This supports the 
assumption that it consists of the same matter as the r^eteor itself 
and is actually the tom-avay upper layer of the neteor. Spectroscope 
examination of the tail is naturally extrenely difficult since it 
is usually only visible for a few seconds. Hence, as far as I knov, 
no faultless spectroscopic examinations have been made, 

3) On the basis of direct observations, it can be said that the 
tenperature of gloving meteors must lie betveen 10,000* and 30,000°. 
If their temperijture vere lover, ve could see thara shine brightly 
only if they vere very large. But in this case, larger pieces vould 
fall to earth. Especially, the fact could not be explained that vith 
peteor shovers often very vivid usually not a single piece reaches 
the earth. If, on the other hand, their temperature vere higher than 
30,000", a piece of vhich something is to remain vould hfve to shine 
considerably more brightly than is actually observed vith fallen neteors. 
In one case, a meteor of 63 kg fell vhich shone so brightly that it 
vas seen in broad daylight. Its temperature vas certainly over 40,000°. 

These temperatures are so-called "effective" tenperatures. That 
means : A blecif, solid body vould have to be that hot in order to 
shine just as brightly as the meteor. Hov hot the meteor is In 
reality we actually do not knov. We can only say that it is soinev''at 
hotter. Fortunately, vith the folloving calculations, ve do not need 
to knov. 

Perhaps such accuracy of statement will seem deceptive to the 
layman. Hov can such accurate statanents be made of things vhich are 
incidental ly seen for a f ev seconds? 

This can be countered by saying that, vith such high temperatures, 
the illuminating pover of an absolutely black body increases Tfitl> the 4th 
to 6th pover of tho tecaperature. IWien the absolute temperature doubles 

it shines 



- 287 - 



18-64 times as brightly; irhen it triples, it is 81-729 timea as bright. 
And meteors can be observed that accurately enable one to say 
aftervardi it w»» not^ hundred times brighter or darker. 

At somenrhat lover temperatures, the illuminating pover increases 
relatively even faster; for example, around 1000* it increases as the 
lOiii to 12th poyer. At 2000" a body shines several 100 times brighter 
than at 1000». 

As thermodynamic' teaches, a fast-flying body in the air must 
heat up; hov strongly it heats up, about that ire can say but little 
today. The applications and formulas -which I have been able to find, 
in scientific literature so far do not bear serious examination, 

a) In calculation, the following application is often met :If the 
air in a wind gun or pneumatic lighter is compressed, the tenperature 
rises. If T^^ is the absolute temperature before compression, p^ the 
pressure before compression, and x the ratio between the specific 
heat of the air with constant pressure and with constant volume, then 
we know that ^_4 

T, " T te^ (172) 



'. - ^ [W 



The air in front of a fast-flying body is being compressed. The impact 
pressure ariounts to 

^ 2iO 

Here, v indicates the velocity and yL(/ how many technical units of 
mass are contained in 1 m^ of air at atmospheric pressure. For example, 
for atmospheric air nenr the earth's surface /^ = 0.132. The actual 
pressure p^. *^^'* ^® from to 2 times as great as the impact pressure. 



- 888 - 



According to this application, one obtains 






and 



T^T^a 



T-1 X-1 



(173) 



It is easily seen, however, that the figure obtained for the air 
temperature must be too low according to this example. If we have 
nolecules whirring about in a closed space A (cf. Fig, 9l), the 
velocity with which they strike the piston increases but little if 
the piston is slowly moved in the cylinder. Here, the heat of 
compression only rise« by the amount of work that was required to push 
the pinton forward. If, on the other hand, we hurled the piston into 
a space with freely floatinir molecules (Fig. 92) until they were as 
stropgly compressed in front of the piston as earlier in the cylinder, 
they would obviously strike the piston with considerably greater 
velocity} the heating' is basicly greater. 



• ■•c 



X'.' 



i: 



Fig. 91 



Fi(T. 98 



- 289 - 



The heating of the meteor again may be considerably lover than the 
calculated heating. Because of the extreme rarification, the air 
quantitatively contains but little heat energy in spite of the high 
temperature; hence, it cannot give off the heat that would be needed 
to heat the meteor to the apparent air temperature. 

b) Basically, the following application is completely inadmissable : 
The quantity of heat that is transferred to the neteor is equated to 

a certain fraction of the heat of friction that arises; then the attempt 
is made to determine the latter factor from the fact that meteors have 
an average temperature of 20,0000. In the first place, we naturally do 
not know at all how much of the halted motion was converted into heat 
energy and how much continues to exist as kinetic energy (air currents, 
etc.). Secondly, we do not know how much of the heat produced remains 
in the air and how much is transferred to the meteor. In any case, 
those are figures which change very rapidly with the velocily of the 
neteor and can in no way be used as constant figures. 

c) \?hen calculating the tranperature of the air in the hollow 
surface of a parachute, I formerly reasoned as follows. I told i^yself t 
All the air striking the parachute must be heated to the extent that 
the mechanical equivalent of tliis heat equals the difference between 
the energy withdrawn from the rocket by braking and the energy implanted 
to the air by being dragged along and by the formation of currents plus 
the light and h«at energy radiated forward by the incandescent air. If 
the air stream were completely halted by the parachute and did not 
glow, its temperature could be easily calculated; but such heated 

air radiates much heat and, besides, we actually do not know what 
part of the energy of motion is lost. I assume it would be about 99 ^. 
Naturally, this assumption is extremely arbitrary. This calculation 
does not make the slightest claim of being sci^tifically accurate. 



- 290 - 



d) Another application is based on the assumption that an air 
stream vfaich meets a b«dy must affect the body at the places irhere it 
strikes it as though there the air vere so much warmer than it irould 
be if it contained heat energy instead of energy of motion. 

As is irell kaoim, a technical unit of mass contains 9.81 kg. In 
order to heat 1 kg of air 1" , 0.24 cal . are needed, and one calorie 
corresponds to vork of 426 mkg. Therefore, to heat one technical 

unit of mass 1**, say by friction, requires 1000 mkg. If the air moves 

v* 

with a velocity v, each unit of mass contains mkg of kinetic 

2 ^ 

energy. The approaching air vill meet the body as though it irere ' ' ■ - 
degrees Celsius ■warmer. For slowly moving bodies, this figure is 
certainly too high. According to that, gyrostatic thermometers rapidly 
revolved in a circle by a thread should show several tenths of a 
degree more than if suspended at rest. That this is not the case 
I attribute to the fact that the thermometer bulb is strijck by the 
air molecules from behind relatively slower, so that the space behind 
the thermometer has a corresponding cooling effect. It would be 
instructive to experiment with three equally-senaitive thermometers by 
leaving the bulb of one completely free, providing the bulb of the 
second with insulation on the back, so by applying pitch, and placini^ 
the bulb of the third inside a spherical shell which 4s turned toward 
the wind (cf. Tiga. 93-96) and then erposing the thermometers to an 
air stream of known strength and comparing tbeir readinj:a. So far, 
I have not been very anxionp to do this ex:)eriment, ?or we shall soon 
see that a formula obtained at the usual tanperature is not very useful 
for heat transfer with fast-flying bodies. 



- 291 - 




Fig. 93 



Fig. 94 



Fig. 95 



Fig. 96 



The faster a body moves, the more strongly vill the air behind 
the body be rarified and the leas vill cooling by the rearvard air be 
possible. Hence, one often finds the following equation in scientific 
literature : 

2000 



T-r^ 



(175) 



There, T is the temperature of the projectile or meteor, and '^ 
the temperature of the air. Applied to meteors, this statement results 
in much too high figures. The heat of the approachinr- air is expressed 

by (1^+ "BrjnTJ") '^^^y with reference to friction and transfer by con- 
duction. With reference to the rndiant heat, on the other hand, the 
frontal air naturally behaves lifre cold air of temperatiire "7^. If we 
designate the temperaturp of the meteor as ^ , then the transfer of 
heat per cinS, according to ST'H^.W BOLTTMANN'S law, is Icnown to be 



s=<^(^' -r'). 



(176) 



Naturally, that is prciunposing t'lat STEFAN B0LT7MAWS la^r is correct 
for metal sapors att7 • Let us take an absolutely black body, for 



298 - 



which it is correct. ARcordinp' to KUnLBAUM, for the absolutely black 
body, 

C « 5. 38*10"^^ Tratt'cm"^* degrees"^ . 

In our calculation, ire are sufficiently accurate if we net 0^= 5«10~^*, 
even if the color is considerably brighter, for, in return, the radiat- 
ing surfaces are larger than their pro.jection in the direction of 
motion; the two errors could compensate for each other. Since 'T^ 
vanishes becide tr ", ire finally retain 

5= 5- 10"^^^* vat f cm"" . (177) 

WAMSLER and HINIEIN have foi'nd the heat transfer between a vertical 
metal wall and static air, with slight temperature differences, to be 

Q = Z,P»iQ-'^{t -^) watt«cm-2 . (178) 

Therewith, t is to represent the temperature of the air, in our case 
2 2 

V o V 

C^- ) . If V is very high, we con ignore 'Tf beside — and 

2000^ £000 

set t » . In addition, accordinp; to metallurgy, the heat transfer 

2000 

proves to be proportional to the root of the air density, i.e. it is 
inversely proportional to the root of the absolute toaperature and 
directly proportional to the root of the air pressure. With large 
temperature differences, another factor is involved which, according 

to NUSS^T, is about proportional to'V'^-'^. I believe, however, 
this member only originates from certain phenomena of flow, which do 
not interest us since, in any case, they are lacfcin": here. That, 
other things being equal, the heat transfer is inversely proportional 
to the root of the absolute temperature can be understood if it is 



Here, the reader must clearly distinguish between absolute tempec- 
ature and temperature difference. 



- 293 - 



remambered that, irith equal prpssure, the decrease in air density is 
proportional to the absolute teniperat'ire, iriiereas, at the same time, 
the velocity of the molecules only increases as the root of the 
absolute temperature. The number of blows irtiich the plate wall gets 
from flying molecules and by itrhich it is heated up is, other things 
being equal, proportional to tHe averafje velocity of the molecules. 
So it increases only with the velocity, i.e. as the root of the 
temperature, but, at the same time, decreases as the temperature; 
now 

V^ 1 

a " ya"- * 



At first sight, it is astonishing that the heat transfer is sup- 
posed to be proportional only to the root of the density. It should 
be assumed that the wall is struck by a times molecules if there are 
a times more molecules in front of the wall. We must not forget, how- 
ever, that there can be transfer of heat when the air touching the 
metal has a different temperature than the metal. For the air to give 
off heat to the metal, the cold must again and again be conducted away 
from the metal and heat flow in, and these phenomena of conduction 
and flow obviously proceed relatively slower in dense air, 

When calculating the heating of the meteor by approaching air, 
instead of the actual barometric reading, we will have to use only the 
root of the barometric reading, for the rest, however, we will have 
to set the heat transfer proportional to the number of molecules that 
actually strike the meteor. If s is the altitude of the meteor above 
the earth, yO the air pressure at the respective altitude, andi^^ the 
air pressure of one atmosphere, then, according to (94), 

- — •= e , at which we must substitute H « 7.4 km. Accordingly, 



- 894 - 



ire will get t 




B 

2H 



The number of molecules struck increases with the velocity. We can 
equate the averajje velocity of the air molecules to the velocity of 
sound. Accordingly^ the ratio of the number of molecules struck when 
the velocity is v to the number of molecules striking a stationary 

wall will be -yj 330 + v* « 330. For v^- 330 m/sec, this ratio amounts 

■y 

to rr-. We must multiply the equation by this factor. Finally, we 
330 

must set the heat transfer inversely proportional to the root of the 

absolute t«nperature, that is, we must multiply our equation by 

888 

, thus obtaining : 




^=)/M-.3,.0..0-..e-.^g^^.) 

= )/?...oe.o-..;-..(4-.). 



(179) 

Here, is supposed to be the absolute temperature of the meteor. 

If we wish to know how much the meteor heats up, we must equate Q of 
this formula and S of formula (177), We then obtain 



.^H]/f 



'^■2.10^. o.e-^".!-'- 



\2000 



»)■ (180) 



If we apply this formula to a meteor flyins at 36 km/sec, we indeed 
get values f or -j^ vhich are 5-7 times too small. Therefore, the heat 
transfer must be considerably grreater than we had assumed, approximately 
a thousand times as great. So we must still multiply the right side 
of our formula by a factor wfaich, at 0', equnls 1 and, with^ = 20,000", 



- 296 - 



equals 1000. The simplest factor of that type -would be ( f 9 - 253") . 

80 
This factor is likely too large for average values. More suitable 

TTould be a factor which, to be^in with, like NUSSHT'S formula, is 

proportional to the 4th root of t and later increases faster, so that, 

for t = 20,000", it takes on the value 1000. I believe, however, this 

whole calculation is not worth such accuracy. 

Note : It could also be thought that the error of 1000 occurred 
in connection with radiation. Perhaps SfFFAS BOLTZfilANN'S law is not 
valid for glowing metal or rock vapors at 20,000*. On the ripht side 

of the equation (180), "Cy occurs only ^e'''*<i®«7;t7;j and, with meteors, 
that no longer plays a big role. I can assume it to be about l/25 of t. 
The crucial point is that the amount of radiation and therefore the 
effective temperature itself is some 1000 times as great as it should 
be accordinp; to our stateaient, and that (however hiph the true 
tenperature may be) can occur only if 1000 times as much heat is 
absorbed through friction with the air than we assumed. 

From the fact that we can actually say something only about the 
observed radiation and have made no assumptions about the actual temper- 
ature of the meteor, it follows that /^ is only the effective temper- 
ature of the meteor, that is, the temperature an absolutely black 
body would have to have in order to glow just as brightly as the 
neteor. In fact, we need only this temperature, for we only wish to 
know what heat was radiated forth, or better, what heat was absorbed. 
Thus we j^et 

Since we nre not calculating with great accuracy, we can set 



- 296 - 



Then ire obtain 



^ *" ® 2000 



or 



s 



^r^^~ «« y /^. (183) 

As already stated, f^e factor (t^ - 2"i3)--- is some-what too large 
for rocket velocities. We can correct this error by dropping >j/5. Then 
ve pet I 

B 

t^ ^N^e" "^-v . (184) 

Since Vis the effective temperature, the heat of radintion S ".^27 , 
and the heat absorbed through friction Q must approximately equal it. 

If the surface slants into the air strenia andOCis its angle of 

inclination to the direction of flight, the number of striking molecules 

trith on angle betireen 45* emd 90° will be approximately proportional 

to sin (X , the heat absorption likewise; so we must take Q " ^$* sin 0C» 

Here we can ignore the error we may have made with respect to <^ . 

If the surface moves parallel to the direction of flight, the ratio 

of the rnunber of air molecules still striking it to the original 

number will equal the ratio of the velocity of sound to <r. Here, we 

330 , 
find the heat transfer to be Q' = fl (I am equating the velocity 

of soiuid to 330. How great it actually is in the highest layers of 
the atmosphere we can conclude only from experiments with meteorol- 
ogical rockets; the error is not large, at least not in its effects). 
For angles between 0° and 45° we can set ; 



/ 330\ , V 

Q' = Q sinloC+ arc sin I. (185) 



Stating OC in arc measure, that is approximately 

/' 330 \ 
()» » Q sin {0C+ ~- J. 



- 297 - 



If, on the other hand, ire express OC in angle measure, we pet 

/ 1900oV / \ 

Q' = fl sin (0C+-™-j . (186) 



Therefore, 



-Ih ( , igoooywau 



Nov, this is indeed a very rough estimate and can very irell be ten 
times too large or to small; but at least it is an indication of ^at 
magnitude the transfer of heat incidentally can be irith irliich ire are 
dealing here. 

With a velocity between 5000 and 15,000 m/sec, the temperature of 
an uncooled surface struck by the air stream at an angle OC could be 
given by the fonmila 

O " "VH . ~3~/ 1900oY /.„o\ 

^= e V sin (oCh -— ) . (188) 

e) I am deriving these formulas so accurately because, of all the 
applications known to me, they seem to come closest to the truth. — 
In addition, there is another application based on thermodynamic and 
physico-chemical considerations which seeks to calculate the occurring 
vibration of the meteor molecules from the number ajid force of the 
molecule collisions. But the result is nearly 100 times too large. 
It would still be much too large even assuming a pure hydrogen atmos- 
phere, apparently because, with such high velocities, the laws of 
classical mechanics are no longer valid for the electrons. (Precisely 
considered, they are no longer quite valid even for "BOHR'S model of 
th e atom . ) 

With rockets, this temperature is much above 5000*. If we wish to 
prevent the respective surface from heating up so stronjrly we must 



- '?98 - 



provide enouf^h coolant to carry away "the heat quantity Q' , 

In spite of the high temperature ^J^, the heat transfer is not 
very great. For evampl r, consid^irahly more heat can he withdrawi from 
a metal wall by neana of coolinp -water. As stated by the thermal 
engineer, ve are here dealing only with qualitatively high not 
quantitative heatinp. ConcerninfT the use of coolant, I would like to 
say the following i 

If we want to save on cc-lant, re p'list aim to expose hollow 
surfacesto the n?r 9^[^;^ijn{cf, Fi^, 97), Namely, if we expote slanted 
or arched surfaces to the air stream, the layer of air ne^t to the 
wall, iriiich has cooled off to the terperature of the wall, will be 
continually blown away; ,1"st as little do we succeed in letting the 
coolant hept up to a temperature no longer beneficial to the wall. 




Fir. 97 



- 299 - 



Supposing -we take along ice as coolant, pass the heated coolirg trater 
over it so that it thairs, 2;et all the cooling water to vaporize, and 
finally let the steam pass along the vails to be cooled and release 
it into the open when it has the highest temperature permissible for 
the walls. With 1 kg of ice ire can absorb ca 750 cal. If, on the 
other hand (cf. Fig, 97), we conduct the steam into the hollow space 
of a surface hollowed out like an umbrella, it will here heat up 
further by the impact of the molecules. If the air stream hits this 
umbrella in a sufficiently a:xial direction, it will not be able to 
blow away the steam. So there will always be a steam cushion in front 
of the ur.ibrella which will finally be brought to overflow the ede;es 
of the umbrella only by following steam. In so doing, the temperature 
of the overflowing steam will be scarcely lower than the temperature 
which the air must take on in such a hollow umbrella. At 10,000 m/sec, 
that is certainly over 15,000". Likely even over 80,000". With this 
heat, 1 kg of water vapor absorbs over 9000 cal,, counting in the 
dissociation; that is 12 times as much as with oblique or convex 
surfaces. The colossal heating of the vapor in the hollow space of 
the parachute need not cavse tis concern. The still cool vapor behind 
it itself constitutes the most effective protection against heat ab- 
sorption by conduction or radiation. For example, it is almost 
impos;sible to burn a model of my parachute from the concave side wi+.ii 
a gas burner (with parallel flow). 

Raving determined the above, we wont to see whether the retarda- 
tion by air resistance can be utilized for landing purposes with our 
machines. 

To begin with, what is concerned here is not a pivotal question. 
Apparatus could be built which in part decelerate their velocity out- 
side of the earth's at-^osphere only by rearward thrust, and enter 



- aoo - 



the earth's atmosphere only vith terrestrial velocity. Then, however 
(figurinjf in t'le increase in -weight due to division), -jj?' irould have 
to be 80 to 40 times as great} that is, if the machines are to carry 
the same payload, they must be 20 to 40 times as larp;e and heavy before 
the ascent as they need be if ire utilize the air for purposes of 
deceleration. 

Unmanned rockets can land in any direction. Manned rockets, hoirever, 
mxtst not strike the earth in a vertical drop since the braking distance 
trould then be too short. Since the manned rocket has lateral motion 
anyvay, t'^e nore no if it has ascended in the synergy curve, it ap- 
proaches the earth on any curve of the second order which can easily 
be influenced so that its perigee falls in the upper layers of the 
atmosphere. Even if tbe layer within which the parachute can operate 
is assumed to be only 7 km (above that the air becomes too thin, 
below that the stronj^ debel ©ration endanj];ers the passengers) and the 
rocket approaches the enrth on a parabolic trajectory, the braking 
distance (more precisely, the way covered in the assumed layer) is 
over 800 km. 

Proof : polar equation of the parabola i 

p . P , cos (27 « -^ " 1 . (18«) 

^ 1 + cos 0? ' I Q 

(g t radius vector, 03 i anp^le of direction, h : depth of atmo- 
sphere layer in question for brakinp^ flijrht, r : earth's radius, 
p : pararaeter of t>ie parnbola.) 

P 

For ^ = r, we obtnin coBQy 1; 07 c: Q. 
Forg » r + h X 



- 301 - 



L-_. _i=--.?-_-^2-(l-0,00!l-l) = 0,997S. 



^ •' r ^ 6370 



Op = + 3.8" 
Braking distance t s = 2'Q?*r = 840 km. 

All that needs to be achieved over the ^ole distance is changing 
the parnbolic velocity to an elliptic velocity. Then, irhen the rocket 
parses the perigee the second time, it will pass through the atmosphere 
at the same place aiprain, at which the braking distance will he still 
longer since the ellipse conforms still more to a circle, etc. In so 
doing, however, the perigee would not essentially move closer to the 
earth. That would go on until the circular velocity would be reached. 
Then the braking distance would be practically endless and the space- 
ship would descend in a sufficiently long spiral. 

In order to achieve this goal, it was my chief aim to construct 
the apparatus so that (with the exception of a few braking ropes, 
which would naturally have to be cooled especially effectively) only 
hollow surfaces are exposed to the air stream, and that an air stream 
that is everywhere free of turbulence. Now, there is only one such 
concave surface in the surface of the rocket, namely the bottom with 
the nozzles. So all that is required is to get the bottom to come 
first. That can be achieved by attaching a parachute to the tip as 
shown in Fig. 97. Naturally, to brake is only a secondary purpose of 
the parachute, its primary purpose is to cause the rocket to land 
bottom first. (T simply called the device "parachute" because no 
better word Isecurred to me at the time. It might better have been 
called "directing umbrella" or "adjusting umbrella". This parachute 
cannot decelerate the last 80 m/sec at all; they must be dissipated 
by means of rocket propi'lsion. It makes a difference, however, whether 



- 308 - 



•we must decelerate 80 m/sec or 11 km/sec by means of rocket propulsion .) 
The holloTT surface of the parachute must naturally be cooled by ice, 
vater, or irater vapor. Now, behind the rocket a space vith air tur- 
bulence is created. This air turbulence would easily blow aside the 
water vapor in front of the parachute, so that the parachute would be 
directly hit, now here, now there, by the air stream in effect over 
80,000» hot. To prevent that, I am making the parachute circular in 
shape, so that the air turbulence does not strike it. The broken 
lines in Fig. 97 are supposed tt> visualize the motion of the air. 
I provided my first rockets, especially the meteorolofyical rockets, 
with such parachutes. In the first place, there is absolutely no 
better way of landing meteorological rockets than by means of parachute. 
Secondly, we still know too little about the actual heat transfer 
with aeroplane-type lifting surfaces; as I already said, it could 
easily be 100 times as great as our formula indicates, which would 
make landing by lifting^ surfaces generally questionable, as I shall 
show. For model E also, I plan only parachute landing. If our meteor- 
ological rockets do not make the heat transfer appear in a more 
favorable light than I expected here (l am here always working? with 
the most unfavorable presuppositions), other landing possibilities 
can be considered, 

VALIER, HOmiANN, GAIL, ZANDER, and ZIOLKO^VSKI visualize the land- 
ing in this way t the space-ship is built similar to an aeroplane 
and lands in gliding flight upon returning. HOHMANN and GAIL seek to 
to achieve this goal by means of aeroplane-type lifting surfaces. 
HOHLUNN wants to attach them to the observer's nodule, which, in his 

' NOOKDUNG basicly rejected parachute landing because here ilhe ideal 
propulsion is increased by this amount. In order to clarify the 
question from this viewpoint, however, one only needs to figure out 
for what purpose more mass must be carried along i Is it to achieve 
this change in velocity of 80 m/sec or to keep the lifting surfaces 
sufficiently cool. 



- 303 - 



syatemi is all that finallj remains, irhile the iriiole rocket bums up. 
GAIL thinks of the lifting surfaces as being attached to the spindle- 
shaped fuselage of the rocket. ViLIER thinks of giving the vfaole 
rocket more of a broadened-out| flat form that reminds one of a bird 
with thick vings (cf. Figs. 118, 119). HOHUANN has also thought of 
landing in a decelerating ellipse, as I described it on p. 301 . 

The most suitable altitude s of the perigee above the earth can 
be found by the folloirlng consideration t 

Assuming that, with normal air pressure and static air, the glid- 
ing flight is most economical at 108 fan/hr « 30 m/sec. (As is vell- 
knovn, the same aeroplane does not always use the same anonnt of energy 
to cover a distance of one km. If it flies too fast, the head-on 
resistance increases as the square of the velocity. Between the two 
there is a certain most advantageous velocity.) If the space-ship 
pierces the atmosphere at flOOO m/sec instead of at 30 m/sec, then 
formula (27) applies with regard to the air resistance. Therefore 

hm^L^mit (M^Y^ Pl 135000 . 

/.« Y^ Po\ 30 / P, 

Here, A is the air pressure at the edtitnde in question, andjQ 
the normal air pressure. Obviously, the aeroplane fliefl he^t nt 
9000 m/sec if L-. = ^9000* ^^^"'^ which it follows that 

rr— - 135,000. 

According to (34), the altitude at which the air pressure sinks to 
the 136,000th part is 

s » 87 km. 

Naturally, this is only a pouRh calciilation sirce, In reality, 



- 304 - 



n ia not constant. Before buildin/r the rirst space-ship, the exnct 
connection betireen ^ and s would have to he found from meteorolofical 
rockets or jet propulsion aircraft. 

In order to keep the vehicle at the desired altitude lonfier, the 
lifting: surfaces, according to HOTftlAJfN, could be placed so that they 
depress the vehicle at the beginning and it does not again tear 
itself free from the earth because of t^e centrifvf^al force. 

The idea of landing in gliding; flight has some attractive features t 

l) Descent in gliding flight assures the astronaut great freedom 
in choosing the landing location. For example, if the space-ship 
enters the earth's at'ioanhere with narabolic velocity, it must then 
cover some 20,000 km in pfliding; flight before comlnp; to a dead stop. 
It can describe curves on its ^^liding path and, in so doing, the 
pilot can land at ajiy point he pleases. With parabolic velocity, the 
possibility of describing curves is only small since, on curves with 
radii of curvature vinder 6000 km, the counter-pressure would reach 
unbearable levels due to the centrifuiral force. Nevertheless, the 
radius of this curvature decreases as the square of the velocity. 
For extimple, at 5 km/sec, the radius of currature is only 1240 km. 
Hence, toward the end, the space-ship can describe ever smaller 
spirals and so it can land exactly at the prescribed place. There is 
no place on earth which would not be accessible to it, no matter 
where it entered the ataosphere. One thinf»: is still to be considered i 
\!/hen we calculated the figure of 20,000 km, we assumed that the 
space-ship had circular velocity at the perigee of the cosmic trajec- 
tory. Precisely considered, that is not exactly necessary. It could 
also be arranged to have the space-ship ascend someithat due its 
centrifugal force shortly before attaining circular velocity so tliat 
it would then gravitate with circular velocity in considerably 



- 305 - 



thinner air. Theoretically, the path it vould cover in so doing could 
be unending; in any case, it can circle the earth and land behind the 
^oint above which it entered the earth's atciosphere. 

In his novel, "Bridges Acrosa Interplanetary Space", LUDWIG ANTON 
Trrites that, after entering the atmosphere of Venus, the space-chip 
had not responded to steering because of its enormous velocity, so 
that the occnants could not set it perpendicvlar or turn it and 
cushion it with steam in order the faster to dissipate the cosnnie 
velocity? the steer would sooner have broken. In reality, that is 
not how the matter stands s If the air is not too den.se, it is no 
more difficult to turn the steer than in flight under normal air 
pressure and with normal velocity; such aircraft can be turned as 
desired. In spite of that, however, with low air density and the 
momenlxim that it has, it can be drawn into another path only 
gradually. It is somewhat in the position of a bob-sleigh on an 
icy road : it can be very easily turned, but it does not inmiediately 
run in the direction in which it was turned. 

In parachute landings, there is basicly no frrent choice with 
respect to the place of descent. One can tighten the ropes of the 
parachute on one side somewhat so as to choose the landing place 
within a radius of 1000-8000 km, admittedly much less accurate than 
with airfoil landing. Naturally, that is entirely sufficient, the 
more so since (as also in Icuiding with lifting surfaces) one still 
has the possibility of shifting the landing point as desired by 
choosing the correct trajectory in interplanetary space. For example, 
if an elliptic flight is undertaken, the ellipse need only be 
changed somewhat in order to land at a different time and place. 
So, in both cases, one can land wherever one wishes, but landing 
with lifting surfaces has an additional possibility so that, from 



- 306 - 



this Tie»point, it is basicly to be preferred. The advantages would 
■wei^h in the balance especially, if vrong aim were taken with the 
trajectory in interplanetary space, if, for any reason, the space-ship 
veered from its path, or if, after entering the atmosphere, the 
space-ship freed itself once more contrary to expectations so that 
it described one more deceleration ellipse than was planned and 
descent by parachute were possible only outside of a lOOO-Lm radius 
in a reg-ion \insuitable for landing or at least generally unsuitable 
(more precise guiding is excluded here), let us say in the southern 
part of the l*acific Ocean, on the Tibetan Plateau, or in the polar 
regions. Finally, the advMita^es would be apparent if there were not 
complete freedom of choice with respect to the landing location on 
the earth's grid. (Assuming the space-ship has circled the moon or 
is returning from a distant planet.) 

2) In p^eneral, descent with lifting surfaces does not make as high 
demands on the space traveller's talent for mathematic-physical 
combinations and on his ability to make rapid decisions as does para- 
chute landing. With a 1 if ting-surf aca machine, he can reach most 
points of the landing sphere by simple gliding: flight; reflection 
and control adjustments that do not result from normal instinct are 
necessary only in the border regions. E\irthermore, if the pilot 
steered incorrectly in the beginning, he can usually correct the 
error at the end since the steerability increases more and more. 
With this landing, he simply flies in f'e direction he wishes as 
with an aeroplane. Since he can see a large part of the earth beneath 
him, he naturally sees exactly where the intended landing site is 
situated. Having arrived above it, he descends in a spiral. 

In parachute landing, on the other hand, the pilot must make 
precise combinations} a slight inadvertence can jeopardize the success 



- 307 - 



of the irhole flight. The connection between parachute lending and 
direction of flight is not as evident as the connection betireen 
steering and place of descent. The trajectory in interplcmetary 
space must also be calciilated more carefully with respect to landing. 
Naturally, all this can be achieved, except that, here also, landing 
•with lifting surfaces would basicly be preferable. 

3) In normal landing with lifting surfaces, with velocities below 
the circular and a certain position of the controls, the space-ship 
passively seeks the altitude for motl expedient night. For example, 
if it gets too low, the air resistance increases, and with it the 
uplift; that raises it higher again. With lifting-surface landing 

in general, it appears feasible to leave the largest part of the 
steering to automatic machines during dead travel, whereas with 
parachute londing the pilot (under high counter-pressure besides) 
must himself constantly watch everything. 

4) Landing with lifting surfaces is in general more pleasant for 
the passengers. Except when the border regions of the landing sphere 
have to be reached, the travellers are never exposed to essentially 
higher counter-pressure than the normal force of gravity. 

In parachute landing, the initial stages come off quite smoothly. 
Between 6000 and 2000 ra/sec, however, the counter-pressure must be 
high under all circumstances. In the beginning, the centrifugal force 
keeps the apparatus suspended; below 6000 m/sec, however, it de- 
creases noticeably and, in spite of the al tinted position of the 
parachute (which already presupposes considerable counter-pressure), 
the apparatus soon p;ets into denser layers. At 2000 m/sec, it flies 
at an altitude of 50 km. Oqly from there on can it freely follow the 
pull of gravity. 



- 308 - 



5) The actual landiripj is considerably simpler vith lifting sur- 
faces. An apparatus equipped -with parachute falls at about 80 m/sec 
at the end, and shortly before touching earth (more accurately, 
the trater surface on -which the apparatus descends) the pilot nrast 
give gas once more at 100-150 m above the s:rouiid in order to dissi- 
pate also this last remain injT velocity, which cannot be accomplished 
by parachute. In so doing, the rocket can only flescend on -vrater. 
If the propulsion apparatus does not f,Q on or the pilot, for some 
reason, neglects to put it into operation (it must not be forpo-tten 
that, after a strenuous and exciting space flight axid under a counter- 
pressure of 40 m/sec^ at the end of the deceleration period, the 
pilot iril 1 perhaps no longer be in possession of his normal elastic- 
ity and determination), although the travellers will not perish, 
the fuel tanks of the rocket will be squashed and wrecked. The land- 
ing of an airfoil apparatus, on the other hand, proceeds like the 
landing of an aeroplane . 



' These are my misgivings concerning the last part of the parachute 
landing. On the other hand, I cannot shar*» the miagivinn-s nf f-ER^ATO 
PUSOH-JIETDEWILXEN that a rocket hanginj^ from a parachute would begin 
to spjn if made to bum. The virtual deceleration which the parachute 
itself undergoes due to the a-ir resistance (by virtue of the air 
resistance due to the mans of thp parachTite) is, und^r nil ci' cuEstB.-' • 
ces, greater than the virtual decelerrtion of the body of the rocket 
due to the rearward thrust. Hence, tiie parnchute still pulls the 
rocket upward even when it hums. Kow, the parachute parts hold the 
body of the rocket by the tip; because of the long lever arm arising 
from a slanted position of the rocket, a strong torsional moment 
would tend to put the rocket into the correct position again. The 
centre of rearward thrust lies close to the certre of gravity; so, 
if set on a sl.-uit, the torsional moment endangering stability is 
only slight. The space-ship could spin only if the latter torsional 
moment were greater than the former. In addition, t'^ere is the pos- 
sibility of active stabilization by mean" of control gyroscopes and 
the regulating rods, 

NOOPJIWG has objected that letting the rocket bum when landing 
by parachute would cause both rocket and parachute to bum up because 
the air would bend the gas stream and nake it hit the apparatus. 



- cog - 



^Taturally, I adf^it that the rocket, while buminp -would have to 
pass through its ovra firinft gases. As fa'- as burning up froes, -we have 
seen that that is not so easy with liquid fuel tanks and with the 
parachute construction indicated above. On the other hand, for my 
part, I -would reconmend that NOO'IDUNG produce a calculation of the 
heat transfer for his sttggested trajectory with parabolic velocity 
brought about by means of lifting surfaces. 



6) As far as the altitude of t^e ne^-ir^ee of the cosmic tra.iectory 
is concerned, -with parachute landing the aim ri'ist be accurate to 
within 5 km, if one wishes to land at the prescribed point. If one 
is satisfied just to land, then the aim with the hyperbolic 
trajectory ^-.i^st be exact to about !•"> km. In case hydrogen prepon- 
derates in the upper layers of the atmosphftre, this figure will be 
considerably more favorable. In addition, hydrogen would not heat 
the affected surfaces so strongly. If the perigee were too high, the 
atmosphere could not decelerate the vehicle sufficiently and it 
would veer away from the earth a^al". If it were too low, it would 
decelerate too fast and the enormous counter-presswe would squash 
the paBsenecers. With elliptic velocities, it is sufficient if the 
space-ship skirts the earth's atmosphere altogether and does not 
pierce it too deeply. Then it will describe ever smaller decelera- 
tion ellipses and finally land anywhere. Where it will land if the 
aim is even only 20 km too high the gods know. 

Landing by means of lifting surfaces, on the other hand, is 
quite smooth even with hyperbolic velocity if the aim was up to 22 km 
too high or around 20 km too low. In a strongly slanted position, 
a lifting surface can carry 5 to 8 times as much as in a more favor- 
able position. If one should happen to get into an atmospheric 
layer 8 times as rare, that is if the aim was 15 to 18 km too high, 
by strongly inclining the tip downward the rocket could still be 
kept in the atmosphere and prevented from flying out again. In so 



- 310 - 



doings the drag is almost as great as the drift, but that does not 
Aatter. On the contrary, thereby we achieve strong deceleration, so 
that the hyperbolic velocity soon changes into an elliptic velocity, 
and the rocTtet can still be kept in the sphere of the earth's 
gravitation (here that is sufficient in order to land at the prescribed 
point) even if the aim was ar additional 7 km too hi2;h. The landing 
is still successful even if the perigee was so high that the drift 
alone was no longer able to T<eep the rocket in the earth's sphere of 
attraction, (Here I naturally only thought of hyperbolic velocities 
as could occur with space flights and which lie between 12 and 17 
km/sec.) If, on the other hand, th'^ aim was too low, the axis will 
be set so that no drift occurs. At the correct altitude, the decelera- 
tion due to air resistance would be ca 2 m/sec, Man, however, endures 
counter-pressure of more than 40 m/sec. So t^e space-ship could 
travel in atmosphere 20 times as dense without the counter-pressure 
endangering man, that is, the perigee could be over 20 km lower. 
That makes an altitude leeway of 40 km and more in which the perigee 
may lie. Yet, even if the vehicle should once tear itself away, 
because of the steeribility, there are still prospects of reaching 
the planned Imding place. 

Tn spite of all that, landing by parachute is pnssihle, oibenrise 
I would not have suggested it in a book in which I wanted to prove 
that travelling to interplanetary space by rocket is not .iust a 
Utopia. Parachute lemdinp; will only be considerably more inconvenient 
and difficult than lifting-surface landing. Pollowinf; is the reason 
why I nevertheless sug2;ested parachute landing and not airfoil landing! 



I wanted to show that my p'-oject is feasible under al.l. circumstan- 
ces, and that only applies to parachute landing. With airfoil landing, 
on the other hand, there is the dan'^er of the he^t transfer becoming 
too great. This is not just probable. If my formula were applied to 



- 311 - 



the heat transfer, quite possible fignros Trould be obtained, but, as 
I already said, this formula is extremely inaccurate and uncertain, 
and the heat transfer could easily be 100 times as great. In this 
cai^e, airfoil landing irould be impossible. Even if we succeeded in 
conducting avay so much heat by means of cooling water (even that 
is not certain) that the LEIDEMFROST state did not arise nor the 
plating; bum through or, -with hydrogen cooling, develop tears and 
breaks because of strong, imeven heating, we would require more 
cooling water by mns^ than the quantity of fuel needed to decelerate 
the cosr.ic velocity by rearward thru.ot, 

HOHllANN'S idea of not letting the vapor of the cooling water 
flow out at all I must re.lect completely. HOHLLAM (The Reachibility 
of the Heavonly Bodies) sugf^e^ts, after the cooling water has absorbed 
the heat, sinply conducting it to cooler areas of the snacevship, 
where it gives off its heat "by conduction and radiation". Against 
that I remark 5 By i'conduction" no heaf whatever can here be given 
off, only absorbed. The cooling ribs which HOffiiLANN su2;ge'?ts are 
also of no use heT^e, eind, as far as radiation is concerned, the 
temperature of the radiating body would have to rise so high as to 
be able to give off the absorbed heat by radiation, and no building 
material con stand such temperatures. 

Moreover, HOIBLAJ^' appears to hold the view that if only the lift- 
ing surfaces stood sufficiently flat, the heat transferred to them 
would be sufficie^itly small in qnantity. In opposition to that (in 
this connection, compare formulas (185 ff)) I believe that, even with 
a surface standing wholly in the direction of flight, the ratio of 
the heat transfer to that of a surface struck perpendicularly must 
at leapt equ'^l the rat^o between t>ie speed of sound and the speed 
of travel; and that can still be a very considerable fipiire. Nor is 



- 312 - 



the raaark made by someone else a ffreat comfort that the space-ship 
loses its velocity only slowly, whereas the meteor loses it in 10 sec- 
ond!'. If the meteor loses its velocity in 2 seconds, it heats up to 
30,000», If, by contrast, the space-ship only comes to a ston in 
1200 seconds, the energy absorption will perhaps be 600 times less. 
As is seen, I have allowed for quite a large difference, but actual- 
ly the meteor is only stopped in 5-6 seconds and the space-ship 
perhaps in a few 100 seconds, I say "perhaps", for even that is 
not certain. I believe, at the bepinnlng, the heat transfer will in 
no way be essentially smaller. Since the radiation Increases as the 
4th power of the temperature, we must devide 30,000' by yfeoO; then 
we get 6000', which is more than sufficient to destroy the space- 
ship. Even if the circumstance is taken into account that the space- 
ship flies three times as slow, whereby the apparpnt heat of the 
air drops to l/9, then the figure of 6000' would have to be divided 
by only VT ^ -y^S and the result would still be SSOO". 

On the other hand, HOHilAN^T'S sur^ffestion to attach a parachute to 
the tail of a space-ship nrov^ded with lifting surfacovS appears to 
me to have very p;ood prospects. There the perigee of the cosmic 
trajectory need not lie so low, the parachute already brakes suffi- 
ciently at a higher altitude, and the lifting surfaces only heat up 
little because of the thin air, I believe, in this way.it will be 
possible to reduce the heat transfer with a space-ship to l/lOO of 
the amount it would be if the space-ship flew without a parachute. 
For the purpose, the parachute would experience air resistance 
relatively 100 timen as p;reat as a space-ship built in the form of 
a streamlined body, and that is not difficult to achieve. 

Up to the circular velocity, it is mainly the parachute that 
brakes here; below the circular velocity, the lifting si'rfaces also 



- 313 - 



could be used to keep the space-ship aloft lonf^er. Near to cirowlar 
velocity, there is very little strain on the^, for there the space- 
ship appears to have no weight. Below ci**cula'' velocitj'^, on the 
other hand, the strair. increar-os b'lt now the heat transfer decreases 
ranidly. HOHI.IANN sug;;;ests completely sacrificing the parachute at 
last and landing in n^lidi^ff flight. (His RUfvge'tion is to cc^l it so 
lit+le that it finally b'lms rp by itself. There T cannot ap;rp", 
^or o"e uroi'ld have +00 little control over the ti e ivlien that would 
happen. I wovld prefer cooling the pL_r'chnte properly and somehow 
unco^^plinp it at the fijiven moment, but this is naturally only a seo~ 
ondary question.) After what was said here, I can also ^lot aprree to 
HOffilAJ^r-^'S sufygestion to use a convex forn of braIcin/» discs. 




Fig. 98 



Very lilrely, this type of landing would be possible and would 
combine the main advantages of parachute and airfoil landing. Sorae- 
thin^ similar could also be done with my model E. Namely, the 
observer's nodule could be provided with lifting surfaces and fastened 
so that it finally separates from the rocket and continues in gliding 
fliofht by itself, while the rocket lands wit^ the parachute. 

Fig. 98 represents another possibility of combining the advantages of 
both types of loading. The rear body of the rocket is relotively 



- 314 - 



long, the lifting wirfacea a, b and the tail fins c, c are double. 
The halves are connected to each other on one edge by an air-tight 
rubber band. Upon entry into the afcaosphere, the oval parachute, 
irhich here may be relatively mnall, hangs on the tip, so that the 
nozzle descends first. Hie liftinrr and tail surfaces are clapped 
apart exposing hoi loir surfaces to the air strean. As soon as the 
velocity sinks to below 7000 m/sec, the parachute ia sacrificed, 
the tail fins c, c are folded together, and b is placed on a. Ther 
the space-ship tips over in the direction of the arrow and continues 
flying tip forward like a glider. 

So much for the landing of memned apparatus. With unmanned machines, 
naturally only parachute landing comes into consideration. 

Actually, I consider it premature to write a lot about that. The 
best would be to do research on the conditions of heat transfer with 
meteorological rockets and rocket aircraft. Having obtained the 
respective figures, there is always time to reflect on how best to 
manage landing witli manned rockets. I actually wrote this chapter 
only to show the state of our knowledge in this area and to prove 
that deceleration by means of -Uie atmosphere is possible under all 
circumstances. 



- 315 - 



PART III. 

Que ation a of C onstr uction 

Chapter 15 

1) 



The Model B Alcohol Rocket 
(Cf. Plates I and II) 

Index of the most important fonai'la qna" titles and abbrevia- 
tions used in Chapters 15 - 17, 

A : total volume of gas flowing out during one second 

A.R. : alcohol rocket 

b I actual acceleration 

b i b in the first second of propulsion 

A J I have used this letter to designate both air pressure 
and air density. Confusing them is impossible. 

P I air pressure in kg/m^ at beginnine- of propulsion of 
alcohol rocket 

br I weight of fuel 

/?. I air pressure at beginning of counter-pressure of hydrogen 
rocket 

'Y * ballistic resistance coeff ic-l ont 

d : diameter of outlet; d as index, e.g. F, , r , c, : whatever 

.^ 

I brought Chapter 15 - 17 in normal print 3iT>ce they are not 
exactly difficult to understand. The layman, however, can skip them 
without loss if they should become too tedious for him. 



- 316 - 



is related to the outlet 

e : base of natural logarithms 

F : largest cross-section of rocket 

F^ ! width of outlet 

Fju : neck of nozzle 

G : irelght of rocket as force 

g ; acceleration due to gravlt7 at altitude h or s 

gg : acceleration due to gravity at earth's surface 

H.R, : hydronren rocket 

-, spec, heat at constant pressure 
spec, heat at constant voliune 

L : force of the air resistance 

L* J force of air resistance T»hen velocity ia less than v 

In I natural logarithm 

log ! coaunon logarithm 

m t mass of rocT<^et in general 

Oq I mass of filled rocket in general 

mj I mass of empty rocket in general 

m : as index, e.s. P.p. o , d , referring to neck of nozzle 

' ■• m '^m m m 

J^^ mass of alcohol rocket 

Tjl,: mass of hydrogen rocket 

t oven; o as index, e.g. T^, p^, d , referring to oven 

P 1 total requisite rearward thrust 

p J pressure 

Pq : pressure in oven 

p, : pressure at outlet 



- 317 - 



q : indicates hoir many times one kind of fuel is heavier 
than the other 

Q : total force impeding the ascent 

r : earth's radius 

s : altitude to which a certain rocTcet would have to ascend 
for a required velocity to becone the most advantageous 
velocity 

T : temperature; if nothing else is expressly noted, T is 
always related to absolute zero 

Tjj : absolute ot'tlet temperature 

Tq j absolute oven temperature 

t I time 

V i velocity in general 

v^ I ideal velocity 

v : most advantageous velocity for s and ds 

Vg J V at beginning of propulsion 

vj i V at end of propulsion 

Vq : specific volume of gas in oven 

l) Preliminary Remarks 

I shall briefly repeat the main requirements with respect to 
model B which we arrived at on the basis of our formvlas. 

a) as high a ballistic coefficient as possible 

b) highest possible altitude from which to ascend 

c) as thin walls as possible; as few metal parts as possible; 



- 318 - 



highest possible value of — j not too high inside pressure, 

especially not in the liquid tanks; avoidance of jerky 
acceleration 

d) combination of a number of rockets 

e ) highest possible outflow velocity; highest possible tepiper- 

ature in the combustion chamber; use of specifically light 

Pd 
propiilsion ^ases; low value for — , irhich should be kept 

Po 
as constant as possible 

f) small apparatus must ascend vertically 

ff) the velocity must be regulatAble; the most advantageous 
velocity m"st be observed as accurately as possible 

These requirements largely stand in opposition to each other. 
The task of construction is to find the ontimiin between all of them. 

In Chapter 8, ve derived the theory of model B. It is valid for 
the case in which l) c is constant; 2) the rocket flies -with the 
velocity at which the air resistance becomes equal to the force of 
gravity and the resistance coefficient is constant; 3) the rocket 
ascends vertically; 4) liquid fuels are used; and 5) the rocket gets 
its firmness mainly through rigid filling. We were able to make 
these restrictive conditions since these requirements are all met 
with model B. 

In order to show that reachinn; interplanetary space hy rocket is 
possible, it will be expedient to describe such nii apparatus. As I 
said at the beerinning, I will not go into detail. In my drawings 
I have only indicated the most essential. I simply drew one long- 
itndinal section through both rockets seen from the cut surface and 
two cross-sections. The horizontal daah-dotted (•,._._......-») lines 



-. 319 - 



betireen longitudinal and cross-section marked by Greek letters indicate 
where the cross-section lies. What belongs to the alcohol rocket (A.R.) 
I have draim in black ink, what belongs to the hydrogen rocket (H.R.) 
in red ink. 

The purpose of model B is for research into the height, composi- 
tion, and temperature of the earth's atmosphere, for learning to knoTf 
the curve for -v" more accurately, and for confirming and improving 
our ceilculations about c, T, p, etc. (especially for the hydrogen 
rocket). 

As already mentioned, the actual apparatus consists of the alcohol 
rocket and the hydrogen rocket. It is 5 m long, 55.6 cm thick, and 
weighs 544 kg. Of that, 6.9 kg fall to the hydrogen rocket. In addi- 
tion, there is an auxiliary rocket (cf. p. 337). 

Relative to the question of material, I have said what is neces- 
sary on p. 16 ff. In this section, I based the stress calculations 

o 
on materinl of which a wire 1 mm in cross-section can be weighted 

with 6.7 dcm of the same substance. (Expressed with use of the 
concept of specific tearing strenprth, that would mean : the material 
may be subjected to the same stress as a 6700-m-long wire of uniform 
cross-section hanging vertically is strained at the upper end by 
its own weight.) As I already explained, at such low temperatures, 
iron and steel could be sxibjected to up to five times the strain; 
from that, according to our elplanations in Chapter 7, would follow 
a mass ratio five times as Rood. With the brittleneas of iron at low 
temperatures, however, its utilitj^ is questionable. In this section. 
I wanted to prove that flying to interplanetary space by rocket is 
feasible un d er all c ircu nstances. That is why I based ray calculations 
on so<'t but toufh alloys of copper and lead. 



- 320 - 



In order to show that my rocket can be built under all circum- 
stances, I an choosinp- a mixture as propellant which only produces 
a temperature of 1400' to 1500" C to 1700* absolute, whereas we 
can actually go to almost 4000*" (cf. i*. 40 ff). 

I am here describinr a more complicated apparatus than would 
actually have to be built. In the first place, I want to show wliat 
kind of machine parts are possible in principle, their mode of 
operation, their purpose and use. Later I will show by how far 
these apparatus can be simplified. Secondly, I described the com- 
plicated model B and not model C (which, as the reader may already 
have noticed, is considerably '■iTnpler and more useful), for that 
does not conc«?rn s^iarded intellectual property. T do not rlsh to 
di-tijlfce the exact plans of model C. 

Ir? rpporel, my aim ir this hoolc was +o show that T know something; 
about the matter ard yet not to say much as to become disper.sible 
thereby, I predicted that, soon after publication of this booTcj 
specialists and non-specialists would come and ir-mediately affir all 
sorts of improveraeuts. If I had said everything I know, the end of 
the matter would have been that they wo"ld have said they had better 
mastered the material and hence they should be cons'.ilted. 

For this reason, I intentionally left the plans so that my 
machine cannot well be built according; to them. (Hence I ask that 
I not be judged by my constrnction drawings. Perhaps the unembar- 
rassed reader will believe me if I say that the person who was able 
to technically think through all these thinf^s can, if necessary, also 
make drawinpfs according to regulation.) In this edition, I only said 
about a third of what T could have said, described unnecessarily 
complicated and little suitable apparatus, etc. 



- r)Bi - 



TTov veil advised the^e tactics were cbji be recognized if my 
model C, Fig, 17 (irtiich cannot be built exactly according to the plans 
friven here for reasons, at present, only known to me) is compared 
with R.H. I, Vol. II, or my assembled jet propulsion aeroplane, 
Plate III, -Hrith R.H. T, Vol. II, and VALIER'S space-ship, Figs. 116 
to 120, or, for aught I care, the simple rocket aircraft, Figs. 121 
to 123, desifrned by rryrself with R.H. 6, Vol. II. 

Sspecially HOEFPT inmediately forced himself upon me as excdcuting 
practitioner. In all the newspapers with which he is associated (and 
that is quite a number, for he is technical reporter) it can be seen 
that he has "improved" my sketches pretty well in every point. — In 
so doing, he lacks one thing i 20 years of thorough penetration 
(supported by the necessary gift of c<Mnbining) of this material, 
today spread over all the disciplines of technology. Tn the funda- 
mentals, he has still kept slavishly to the information I gave him. 
With R.H. I, for example, the iraprovem'^nt in contrast to ii^y model B 
consists of the fact that he has his apparatus borne aloft not by 
2 air-ships but by a single meteorological balloon. — Certainly a 
colossal improvement; only it is unfortunate that my model C, invented 
in 1912, shows the very same performance using the same fuel and 
having the same mass but ascending from the ground! Besides, it is 
considerably simpler and cheaper than R.H. I. Concerning the other 
examples, I will say what is necessary later, I could [^ive meuiy more 
such examples, I would only be in danger of saying too gmfih. I hope 
that what I have said here, together with what I still have to 
report about VALIER and HOEFFT, will suffice to show that I am not 
entirely dispensible even yet. 

2. The Alcohol Rocket 

General t s^ • 7700 m (the apparatus is lifted to 5500 m by means 
of air balloons (cf. Fig, llO); the auxiliary rocket requires 2200 m 



- 322 - 



to attain the velocity v ) 

16.5 cm/sec^ Pq ^^^^0 ^k/cvT. 

F uels : 341.5 kg of water with 45.8 kp; of alcohol mixed in; 
l.'^T kg of rectified alcohol; 98.8 kp; of liquid oxyfjen or the cor- 
responding quintity of liquid air containing nitropjen. In this 
case, less water is needed. As regards the ignitability of this 
mixture, it in^st be considered that it is supposed to burn under a 
pressure of 16 to 20 atmospheres. For that matter, upon ignition 
(cf. p. 323) pure alcohol vapor is added to the oxypcen, 

1700»C^T /~17''-0*C, 
o ' 

V.07.z\e ratios : 

F F ^ 

-p- = 0.32fl; =-=5.80? -r- = ^{XsC - S.-^g, 

m T2i 

, 90, q 

d = 55.fi -\ro7329 - «.0.0 cm; d„ = 12.35 om, 

^ ' ■" 2.48 

Exhaust velocity : Acordinff to Chapter 5 (l), we would find it 
to be somewhat mce than 1800 m/sec. Because of iraperf actions in 
execution, e is lively reduced to somewhat above I'iOO m/sec. In o^der 
to find a lower limit of performance, I only set c equal to 1400 m/sec; 
in reality c, and wit'i it the performance, is decidedly 'greater. 

T.a»"gest dianiet«>r of rocTret s 55.6 cm. The alcohol -water tank has 
em excess pre" sure of 3 atm; likewise the apnce in it set aside for 
the hydro2;en rocket. The press\T-e in the oxypen trnk is p^ + 1."; atm. 
With the removal of liquid, the pressure is maintained by pnrt of 
the liquid vanori7injr. 



- 323 - 



Weight of propulsion apparatus 16,2 kfr, weight of fins 4 kg, 
■weight of oxygen tank 10 kg, weight of pumps 8 kp^, weight of tip, 
etc. fi kjj, thickness of wall approx, 0.4 mm, weight of atomi/er 3 kg. 
All other parts together weigh 4 kg. 

-On-i +-«lo = 56.2 kc 

* ; m « 9,7 . 

0% +n. 52,2 

We will equate this ratio to 9, 

Ballistic coefficient of filled rocket i 0,225 kg/cm^. 

To - =)00 m/sec; v. -= 2800 m/sec to 2P00 m/sec. 

Ballistic coefficient at the end j 0.0232 kr^/cm . 

The leigth of the bum is 36.to 40 secords; during the first 15 
to 20 seconds, v is observed exactly, later the apparatus falls behind 
this value, so that p '^80 atm remains true. From that (for c = 
I'lOO m/sec), it follows that F/U^ »= 34 m/sec. In or>e second, the fol- 
lowing mass is ejected : 

dm , 

12,01 kg/.«ec^-- <::^13.21 kg/sec. 
dt 

Combustion occurs as follows (cf. Plate Tl) : Tn space A, the 
pipes C, 2.5 cm wide at the bottom and 3,fi cm wide at the top, do not 
reach quite to the cover. Between these pipes there is rectified 
alcohol which is made to boil by having a pump, indicated by m n, 
pump hot n-as containing oxygen into a sni + nble network of pipes, 
which risep in the alcohol in fi^e bubbles. The alcohol vapor escapes 
through the pipes C, Into these, cone-sha'.^ed pipes D project froii 
the oxytren chamber, whose wall is pe>'fornted, as T stated on p. 8 . 



- 324 - 



The p'^espure in A is somewhat over p^ atm; in the oxvgen cha-Tiber it 
is p + 1.5 atm, so that the osygen squirts o"t in fine jets or 
drops^'. The ends of these pipes have a" ignition mechanism G to set 
the mixture on fire. Since mnoh more oxygen flows out than is 
needed for combustion, ve obtain a ras that contains 95 ^ oxygen and, 
at 20 atm., is about 700* hot. The pipes C continue in space B (e). 
Here they are surrbimded on the outside by the alcohol-Tvater, irhich 
is forced in in thin spray through narrow pores. 

Description of the Al coho l Rock et (of. Plate l) t The tip a forms 
a special part of the apparatus. It is turned upsi<le down 1 iire a 
hat over the two rockets and is held in place by elastic springs 
(the dyneunometers b, b'). It consists of two or more parts whose form 
resembles the peeling of a disected orange or the patches of which 
a leather ball is seim together (cf. Fig. 99). They are glued together 
by means of collodion, V/hen the fi'els of the alcohol rocTfet are 
exhausted, the collodion is ignited (how need not interest us here) 
by the same spark that ignites the hydros-en rocket; thereupon, the 
tip falls apart (better to say, the gases which surround the hydrogen 
rocket force it apart; they could also force open a parachute placed 
here) and the hydrogen rocket is released (cf. Fig. 100), 





Fig. 99 Fig. 100 

' This contradicts irfiat is said on p. 346. The fuel pores should 
lie exactly in the lee shelter of the oxyiio^ pores. This idea was 
not yet patented when I described model B for the first time. 



- .125 - 



On the TPside, these tin shells have air-filled cavities (c) 
Ttrhich are to keep the tip from sinkina; in case it falls into the 
vater. Since, at 2000 to 3000 m/sec, the air in front of the tip 
already heats up stron.n-ly, some simple cooling device (say a wind 
Trtieel) must be placed ii space c (not shown). Its work is facilit- 
ated by the fact that fie inside of the air cavities comes in 
contact with .iust-vaporized hydroo^en which ascends alono; the 
hydrofren rocket from its nozzle, here bends around the thin wall 
and escapes into the open thronfth a type of safety valve at K, 
The space provided for the hyd'-cren rocket is 30 cm in diameter, 
whereas the hydroger^ rocket is only 2!^ cm in diameter; so a 2.5-cm- 
wide space remains all around, which is filled with hydrogen fjas 
and is once more divided by d. The air space wonld exactly fit 

the tip of the hydrosren rocket, if the latter- did not 1 ie 1 cm 
lower, (f) are cushions made of especially supple material (say 
solidified natural gas, which, shortly before solidifying, was drawn 
out to threads or beaten foamy by means of a paraffin rod in a 
hydrogen environment). Between the cushions apace mist naturally 
remain for the escaping hydrogen vapor, e is the tank for the alcohol- 
water. In it there is a float r^, the purpose of which we will discuss 
lator. The nrfifls'^re in e is 3 atra and is maintained by the pumps m n 
pumping hot gas into the double bottom h; the gas rises from here 
through numerous smal') operir/rs. The p'-epsure is ^'enri'.l ated automatic- 
ally. If it should rret too hl^h, a safety valve allows gas to flow 
off through K. Through valves y auid pipe" o, the alcohol -water 
mixture flows alternately into chambers pj and p^, both of which 
have a second outlet to K on top nnd a third one at the bottom to 
pipe k, which ^'s connertod to the atomizer Z. These chnnhers like- 
wire have a douM e floor i. through whose pores likewi.ae "ras cominnr 
from m n ri'r'^s. Thepe chambers p^, p2 act af niimps. The valves open 
and close in n way always to cause one cha'nber to be replenished 



- 326 - 



from e wbil* the other, under a pressure of 20 to 23 atm. , pumps the 
alcohol -water to the atomizer. (Naturally, before lift-off, both 
are full in order to increase the tvel content of the apparatus.) 
Since the pre^'sure in p , pg fluct"atea considerable and the lowest 
pressure is no lonfrer sufficient to p;ive the apparatus its rigidity, 
and also because of their form, these chambers "mst be rigid; in 
co^tra^t to the rn^t of the Bocket, they nxist be made "igid by means 
of metal wipport*;. The oxyrren strenm s is under a pressure of 18 to 
SI a+m. The press^ire in room A is 1 a+m. lower; neverthelesa, the 
partition between the two must be straight and thir, hence it is 
supported by the wirps q which hanj^ from the reinforcecif'nts of p. 
The upper surface of the oxygen room resembles a hori70i^tal elonp:ated 
ellinsold. Since the cross-sectio" of the rocket is circular, the 
space pg extends down farther at two opposite points, at which points 
the valves o- are situated wiiich conduct the dilute alcohol frnia p„ 
to the atomizer. The liquid p. accumulates in the r-Jddle at fc. — The 
oxyge" must be kept at a pressure of 21 ataa. by va'^orization. It 
vaporizes, in the first place, because the mxich hotter room A is 
situated below it (cf. Plate II), But this alone would not be suf- 
ficient. Secondly, hot pns must be blown in, in the way stated, by 
means of the pumps m n. This hot gas contains water vapor which, on 
this occasion, forms ice crystals that float on top of the oxygen; 
hence they do not affect the pores of the atomizer, but increase ra 
somewhat. — The oxygen room also has a floating device g, whose func- 
tion it is, above all, to make the fu^l consumption keep pace with 
the oxyp-en cons^'mption. Through coordination of the floats in the 
alcohol and in the oxygen room, the safety valve as well as the vapor- 
ization of the oxyjfen is being influenced by electrical means, (it 
is likewise situated at K.) If the level of the oxygen falls too 
slowly, the pressu^'e in the oxygert room increases and ao more oxygen 
is forced into the atomizer. 



- 327 - 



The -vrind tank W is connected vith the dilute alcohol in the atom- 
izer by the pipe k. Its purpose is l) to ensure thnt the whole space 
bet>een the pipes E is filled -with dilute alcohol and 2) to maintain 
the pressure at a certain l^vel. Both conditions could not be achieved 
^7 Pi> Po ttloie* The pressure in W is also maintained by the pumps 
m n pumping hot gas into it. In addition, it has a float g irfaich, 
ttbove all, regulates the action of pumps p., p.. W is situated belov 
the nozzle of the hydrogen rocket and must therefore be protected 
against transmission of heat. W is ee^-shaped. A space I remains 
between W and p. irhere, likewise protected against heat fluctuationi 
are found the instnuneatF that regulate and register the work of the 
alcohol rocket. Furthermore, the^'e Is a source of direct current 
electricity as constant as possible and a small generator. 

The pumps m n operate as follows (cf. Fig. lOl) : A small piston 
pump m, piimps alcohol alternately into the two tcuiks m„, m„ and 
steadily into tank n. The tanks m., m„ (as p., p. the alcohol) pump 

oxygen to n. Pieces of sodium are place on the bottom of m„, m . 
When the valves m., m. and m„, m_ resp, are opened, oxygen enters 
and raises the sodvim pieces. As soon as tank m^ or m„ is full, 
these valves are closed nnd alcohol flows over the oTiiyen throrgh 

m„ or m^. IjTiition follows by electrical neons. The combuat'on is 

l) 
assisted by the presence of suitable porons bodies (cf. p. 2^) ', 



' I nust make some r«W!arks regarding t'lese pumps. As can be seen, 
with models A, C, and D, I have altogether dispensed with these 
dangerous and unreliable apparatus, I bronjrht then with models B 
and E becnuse otherwise I would here have had to describe entirely 
different models. But that did not appear worthwhile to me. These 
models are not meant to be taken very seriously (to express it 
drastically). As T have repeatedly said, thereby I would only like 
to show the possible equipment of a rocket that uses liquid fuels. 
For that purpose, it need not be as well constructed throuffhout as 
it could in a serious case. 



- 328 




Fis;. 101 



The oven (in this connection, also c<Mipare Plate II) does not 
border directly on the jacket surface; rather, there is a thin wall t 
in between irtiich is connected to the jacket bv cieans of rietal braces 
(not sho-wn) and is thus held in the correct position. Liquid from 
the atomizer flows between t e«id the jacket, vaporizes here, and so 
protects the wall of the oven af»ainst burning. The vapor escapes 
into the oven at L between the atomizer and the jacket. In so doing, 
it remains close to the walls in the oven, and so, with strong 
vaporization, the walls themselves are insi'lated aj^Fiinst the hot 
gas. To prevent too much liquid from vaporizing and the wall t from 
burning np he^rinning at the top, a thermocouple element is situated 
at T^ which causes more liquid to flow in whe" the temperature here 
rises too hip:h. The space between t and the jacket is wider at '*ome 
places. Here the lio"id runs Hown; here also is found a float which 
iBipedes the supply of liquid when it rises too high, t'"'s preventinfr 
the liquid fron overflowing in the oven. — The apace between the 
jacket and the surface t is once more divided into two parts, Q and 
R, by a wall u which runs a little below Fj^. When the fuels are 
exhausted, first the liquid in R and then that in 2 is vaporized 
by hot gases from ra n. By this arrangement, m^^ becomes nnoh smaller 
than it would he if oven and nozzle were lined with fireproof material 
on the inside, and (accorf'ling to Chapter 7) that is a considerable 



- 329 - 



advantage. That also makes it nossible to let tHe erases poss alonia: 
the netal, nrhich retards them less than say asbestos or fireproof 
clay. 

The nozzle of the alcohol rocket is either simple and round as 
a circle, as indicated in the sketch, or it is divided into 7 or 
more parts (cf. Fifr. 18) nrhich rise from a common oven. With small 
apparatus (sncli as model B) the former is preferable.- with 1 arper 
one" (cf. Plate IV) the lattpr. 

The fins are only Indicated in the sketch, Altop^efier there a''e 
four systems of 2 fins each, vhich are interconnected by cross walls. 
They are attached to V^e p'-opulsion apparatus. The ends can be rotated 
about the axle X. Tn ascent, the fins are folded doim and in this 
way effect stabilisation and control, since they can be manipulated 
from I, In descent they fold back and th^is carry the apparatus (cf, 
Fiff, 102). In this way, the parachute is superfluous. The fins and 
fittinrs weigh 4 kg. 




Fipr. 102 

After the jettisoning, the alcohol -water tanT<^ can be filled with 
air. First, the cocks m^'st be opened and air allowed to pass through 
to dry and cl enn the tank. ^Vhen filling later, necessary precautions 
must be taken. The olr must first pass through the oxygen room in a 
pipe to cool it off properly. Otherwise, with high hydrogen content, 
an explosion could occur because of the hent of compression. In this 
way, it is possible to have the rocket brinr down air samples. A 
mark on the registering strip (cf . p. 271 ) must correspond to the 
time of the filling. 



- 330 - 



It might be worth mentioning hoir I envisage findinj^ the rocket 
parts after descent. The launching site must be chosen so that the 
auxiliary rocket and the alcofaol rocket land in the water and the 
hydrogen rocket in inhabited areas. The outer wall is fitted with 
circular doors whose edges engage the outer wall| as Fig, 103 shows. 
Behind them is a container with a balloon b (cf. Pig. 104) suspended 
by a rolled-up cord s. Since the inside pressure of the contai.rer 
is 9-10 atin., the halloon is quite compressed; in the open it becomes 
10 times as large. The door turns on the hinge A (cf. Fig. 105); on 
the opposite aide it is soldered shut from L to L' . For the rest, 
it is closed airtight. Behind the soldered joint, in K, there is 
acid; the space K is divided irito chambers by meems of cross walls. 
The r>cid corrodes the solder, by which the door swings open after a 
few hours, since the inside pressure is grenter; thereupoi the balloon 
slips into the open. 







'"^ 








Fie. 103 Fig. 104 Fig. 105 

From the place of descent of the alcohol rocket, conclusions can 
be drawn regarding the mntion of the higher layers of the aianosnhere, 
and from that regarding descent of the hydrogen rooTcet. 

The following regulating devices and precision inatrnrnents are 
found on the alcohol rocket s 

1) An efficient and constant so'^rce of direct current electricity 

2) The f-o' t^ol gyroscope. 



- 331 - 



3) The acceleration indicntor. 

4) The floats which register the level of the alcohol an(l the 
oxygen. They also rolen.se pleciric currerts rhich, in part, refill ate 
the proportion of alcohol and oxygen and, in part, i^re uped for 

the apparatus describet' under P, 

5) Pressure gauges iriiich re<;ister the various inside prcs?!ures. 
One Fivst also be placed under the tip, 

6) The inside pres,=ur«> which tint's to blow off the tip is nat- 
urally greater than the resistance of the outi^ide air L, So the 
sprin^^s b are under tension. This tension activates currents and 
is registered. If the currents of 5 and 6 are ni'itablj' added, they 
give lis a picture of the air resitance L. 

7) These currents apd those corre'spofldinfr to the state of the 
liqi^id act in el ectromaf^ets which are suitably attached to the 
ends of a balance beam (naturally, lilre poles stand opposite each 
other). This, by its position, strengihetis or weakens the action 
of the pumps m n and thereby the accel eratior . Since, near the 
ea^'th, weif'ht is a linear function of the state of the liquid and 
since v is beinf3 observed if L ■= (r (cf. p. 88 ), therefore this 
apparatus causes the rocket to observe v. 

f) "Several ther-iofraphs (best of all ther-^ocouple elenents) also 
bel onr; to the alcohol rocket; one of thera is placed in front of the 
tip in order to register the heat of compression of the air. 



- 332 - 



Chapter IR 

The Model B Hydrogen Rocket 

l) General 

s s With the alcohol rocT'et, the acceleration at last is some- 
o 

what smaller than vould correspond to v. Thus the altitude at which 

the alcohol roclret attains the final velocity is somewhat greater 

than the altitude we would obtain according to ^orm-'la (47). 

(I estimate the altitude at 3 — fi fan n;reatpr.) Advantapjes : l) With 

the alcohol rocket, p becomes constart. 2) With the hydrof^en 

o 

rocket, the ballistic coefficient can be lower. - In the arrangoTnent 
of the alcohol rocket, s. and (Sj - s.) depend on how (Treat c actual- 
ly is. For c = 1400 m/sec, we find that S< - 8.P2 kg/m^. An altitude 
s, of ca 56.2 km would corre-'pond to that. 

p equals 3 atm. 

Fuels : 1.36 kg of hydrogen, 1.04 k^; of o^gen, T^ == ITOO" C, 

Noz7;le proportion : F = F^ (since P^'> ^^)i ^ 1.388. F^/f^ = 

10.95; d = 25 cm; d = 7.5?) cm; d/d = 3.31. 
' m ' ' m 

Ssrhaust velocity i We would find c = 4400 m/sec. For the same 
reasoD as with the alcohol rocket, I here estimate c too small s 
c » 3400 m/sec. 

Up above, the hydrogen is under mi excess pressure of 0.12 atm. 
(therewith the hydrogen rocket would naturally buckle from the air 
resistance at the beginning, if it were not situated inside the 
alcohol rocket). While the hydrogen rocket works, the ground pressure 
of the hydrogen amounts to O.H atm. in the first second, later 



- 333 - 



some^at less, So the hydrorfen tank must endure excess pressure of 
0.84 atflj. Its wall could be made extremely thin, 

^/eight of the hydrogen room and the tip t 33 (r. 

Oven and atomizer : length 1,05 m; inside pressi^re 3 atm. ; 
weight 0.466 kg. 

Instruments s 1.5 kfr. 

Piimp, oxygen ri'nfr, PJid reinforcements i 0,5 kg. 

Nozzle and its jacket j 0.3 kg. 

Fins I 0.3 kff. 

Parachute : 0.5 kg. 

m, = 3.60 kg; m =6.90 kgf fuels t 3.30 kg. 

^ - 1.9155 log -j;^ - 0.2R255 In — = 0.650. 

v^ = 3400 '0.650 = 2210 m/sec. 

Acceleration during the first second : 

o dm aOO m/sec , 

b = 200 m/sec*t — = 8.90 kg* .—■ « 0.406 kg/sec. 

o dt 3400 m/sec 

Since the innide pressure and the outlet pressure remain constant, 
this figure also remains constant. 

3.80 kg 

Burning period t , - - — = 8.15 seconds. 

'^ *^ 0.406 kg/sec 

t^ *" 

C Q«dt = 64.3 m/sec) ^I.»'dt = 7 m/sec 

*1 ■''2 

^1 "^ ^i - )Q'^^ - 5^**^*' •= ^*^^ " "^^'^ " 5.139 m/sec. 



- 334 - 



With this initial velocity, the rocket Trould rise roughly 1960 km. 

Outlet pressure : p, = 0.0196 atm, , from irtiich the nozzle ratio 
is calculated since Po = 3 atm. p^ is best found from the formula i 



Po \J^i/ ' 



Here 

''d - " *d ' '^o - at 



dn 
A. = c-F, , A„ - -j~.Vo. 



9.) Description of the Hydrogen Rocket (Cf. Plate l) 

The tip a is constructed similar to that ■with the alcohol rocket. 
In descent, it unfolds and alloirs the parachute found in space f 
under the tip to open np. Here the tip later renains connected to 
the hydrogen rocket. On the inside, the tip is lined vitb porous 
canvas behind vhich vater runs doTm. This irater is situated at c and 
pump e squirts it through a pipe to the tip, where it runs down along 
the walls. 

The letters on the diagram correspond to those of the alcohol 
rocket. The oxygen is enclosed in a circular ring similar to that in 
Fig. l"^, where it vaporizes and then flows through the pipes E, It 
is under a pressure of 3.1 atm. The hydro^eTi is put imder a pressure 
of ca 5 atm. by the pumps p., p_ and surrounds the pipes E on the 
outside. Serving as wind tank is the hollow space inside the oxygen 
ring, within which the oxygen pipes also branch out. — Here the 
oxygen room can be used for taking air samples similar to the alcohol 
room, provided l) air or any other gas (coronium ?) is found there 
and 2) this gas can be filled into tanks, which can be disputed on 
the basis of the atomic theory. Inside the pumps p., Pg the pipes 



- 335 - 



vhich conduct the fuel gas (i) lie in a type, of filter S, ifhich almost 
reaches to the ceiling. Reason : the heating gases contain irater, 
"■ifhich precipitates as soon as it comes in contact irith the hydrogen. 
Since ice is heavier than liquid hydrogen, these ice crystals irould 
sink to the bottom and plug the nores of the atomizer if the filter 
did not detain them. For this reason also, the outflow from the pump 
room is somewhat higher than the lowest level of p q* »hich in this 
way never empties completely and accu"ii'lates the ice crystals contained 
in the hydrogen in spite of all precautions (cf. Fif». 106), 




Flpr. 106 

Here oven and nozzles are surrounded by liquid hydrof^en. The fins 
w are built according to the principle of the [^na fins (p. 266 ff). 
They con slide up fmd down along the wall and nre held by hinges a, 
a' (cf. Fig. 107). 



Fig. 107 



- 336 - 



Construction should make allowance for the fact that jettisoninia; 
should take place while the alcohol rocket is still working. Ot'^er- 
wise counter-pressure would occur upwards. In so doing, the liquids 
would be lifted after leaving the valves and not reach the propulsion 
apparatus. On Plate I, tbe pumps m n have in part have in part been 
omitted because they would confuse the diagram. 

3) Precision Instruments of the Hydrogen Rocket t 

1) Electric battery and 

2) Control gyroscope as with the alcohol rocket, only appropriately 
smaller and lighter. 

3) Similarly acceleration indicators. 

4) Apparatus to indicate the level of the liquid. Here their 
only significance is as registering devices, for, with the 
hydrogen rocket, regulation of the velocity ia done only by the 

5) Pressure gauge. 

6) As in the case of the alcohol rocket, the pressure to which 

the tip is subjected is taken up by the springs b and registered. 

The apparatus mentioned under 7 is lacking here, for the velocity 
V is not observed. 

8) Thermographs, etc. 

9) On the hydrogen rocket, the device for jettisoning the tip is 
similar to that on the alcohol rocket. Here it is not released 
by the float, however, but only in descent by the chronometer. 

Chapter 17 

Discussion of the Operation and Performing Capacity of 
Metaorologioal Rooketa with Liquid Fuels 



- 337 - 



l) The Auxiliary Rocket of Model B 

As I already said on p. 269 ^ it is not advisable to shoot rockets 

■with liquid fuels from a cannon. Becftuae of the counter-pressure, it 

is better to launch them by rocket propulsion. Also, it is well for 

model B to reach the most advantageous initial velocity as soon as 

possible, othemriae the apparatus would have to irork against its omx 

weight too long. For rocket conditions, the Initial acceleration must 

also be ffreat. The best ratio of P/mj, for the start while observing v 

would be about 2,6 i 1, Naturally, p would also fluctuate aroimd the 

same value, which would be a disadvantage after what was said in 

Chapter 5. From (2) we read off : With a given chemical composition 

Pd ^d 

of the outflowing gases, the ratio -r- is given b;^ -rt— . Moreover, if 

Pd ^d ^'> . ^ 

'**- is to become smaller, — must become larger, and from (l) it follows 

Pd ■» 

that, with given ~ and "^ the exhaust velocity is the greater, the 

"o 

pjreater p •V is. p 'V Is independent of p and the greater, the 
■^ "^o o '^o o o ^ ' 

smaller by nature the specific weight of the outflowing gas and the 

higher its tenperature. Hydrogen flows out fastest. 

Finally, this follows from (l) j c becoracn the greater, the smaller 

Pd 
we can make vf-. A way would be 

Ho 

a) by nozzles with regulating rods (cf. fig. 25), 

b) or by setting the alcohol rocket on top of another alcohol 
rorket with an additional nozzle and greater rearward thrust. With 
raoHel B, the latter Is preferable. I need not r,nj much here about 
this auxiliary rocket. If the alcohol rocket of model B works, the 
auxiliary rocket is surely feasible. Concerning its construction 

cf. Fig. 108. It is 1 m in diaiaeter, reaches approximately up to the 
pump rooms of the alcohol rocket, and has 4 recesses for the fins of 



- 338 - 



the alcohol rocket. The oxygen is found in room a, -which fits into 
the nozzle of the alcohol rocket. The construction must be as simple 
as possible. The auxiliary rocket weighs 220 kg when filled, and 
-works for 8 seconds; the acceleration which it imparts to the alcohol 
rocket at the beginning amounts to 100 m/sec^, but later becomes 
less because of the increasing air resistance. Perhaps worth mention- 
ing are metal rings laid around the outside of the alcohol tank of 
the alcohol rocket and consisting of 4 pieces held together by hooks 
b; they are jettisoned together with the auxiliary rocket (Fig, 109). 



/C3£>\ 





Fig. 108 



*) The Aacent ojT Mo del C 



If V is observed, for v^ = 500, s = 7000, c = 1700, the curve 
which represents P/m^ as a function of s looks as follows : 

JD 
ft- 

to- 

J- 



Je/Cm 



If the rocket is allowed to start couipletftly on its own power, it 



- 339 - 



must first attain the most advantageous velocity. Ini so doing, the 
acceleration and, therefore, the rearirard thrust and with it p must 
naturally be greater. If the rocket is later allowed to fall behind 
V some\fhat, the cnrve for P and irith it for pg runs as follows > 



As can be seen, the rearward thrust here is almost constant and 
the velocity is close to the most advantageous velocity. (The propulsion 
lasts 18 seconds, which is 10 seconds longer than with the use of an 
auxiliary rocket; the propulsion becomes smaller by 76 m/sec and natural- 
ly also by v^.) This circumstance is very I'seful to us in the construc- 
tion of simple meteorological rockets of the type of model C. For 
manned apparatus, this kind of ascent is not suitable since the counter- 
pressure would be too high at the end. Mtuined apnaratt?s rust have 
rejjulatinp; rods. 

^^ ^^^^ an d Air Reaiatance 

We saw that the greater the ballistic coefficient, ihe better the 
rocket is able to pe^^etra+e the atmosphere. The ballistic coefficient 
is larp-e 

1) If the rocket is large in absolute size, or at least lopr. 

2) If the specific weight of the fuels is great. 

If we meJ'B the rocket long, we rmst take ca^e that the air resist- 
ance does not buckle it. We ean achieve that if 

a) As with model C, we let the fuels flow otit on, to£ ard let the 
fuel tanks hang down like a tail. 

b) If, on the other hand, we let the fuols flow out at the bottom, 
we must ma^'e the apparatus correspondinply thic'f, as I explained on 

p. 31. 



- 340 - 



c) Mother means of achieving a favorable relat'onship between 
ballistic coefficient a"d air resiRta'^ce would conaist of carryirtg 
the rocket up to a suitable altitude before starting it. That -would 
also favorably influence the mass rn+io, for the fuel tanks would 
not need to be under so high a pressure. 

Wit>i models C and E tbis is not necesaary, but model B is calculated 
to start from an altitude of 5500 m above the surface of the water. 
The apparatus is lifted to this height beforehand by a cable suspended 
from two dirip-ibles (cf. Fig, llO). If it is supposed to sta^-t from 
sea level it nuat he twice as long, i" other words 8 times as lo.rge 
and heavy, since here p is twice as large. 




Fig. 110 

If, in both cases, the gas flowing out at F^ were of the snme 
temperature and composition and if it flowed out with the velocity c, 
the ratio between the largest cross-section F and the cross-section 
of the outlet F^ would not change (cf. p. 44). Now, F ia n times 

smaller, c is to retnain the same, f^ and p, are n times .smaller, hence 

dm 
the specific volume of the exhaust <2ja.^ is n times greater, -j^ is 

n times smaller, and the absolute volume is n /n times smaller. 
F^ would also have to become n times smaller (Just like F). 

But, with p remaining the same, — is actually n times smaller, 

Pd ° ^° 

K- (opt) likewise (since P^ remains the same), and F^i must become 



341 - 



smaller. If T reraairs the aa:ne in botVi cases!, the ab'^oliite temperature 

x-1 
and the specific volume of the exhaust pas are n times smaller in 

Pd ^ Fd 

the second case; — would thus have to become still smaller, r^- would 
F Fm 

F F F 

m d d 
become greater and ~ •» — s— uronld definitely become smaller. That 

* ' ■''m 

gives us an advantaf'e : The fuels remain in the oven lon"-er, and the 

oven (taken absolutely) can be shorter. 

Pd 
If the advantage of makinp- •—- smaller -were not made use of, p and 

"o 

■with it the ■weight of the propulsion apparatus would becoae smaller. 
Indeed, c wor'ld then also become some^w'hat smaller since, with g;iven T, 
less coolant would be needed (cf. p. 4l). There i."» nn opti^mra between 
the two ways, which can be found by nsinp^ the criterion on p. 59. 

4) Comparison of the Alcohol Rocket and the Hydrogen Rocket 



Now I want to indicate, although only roughly, irtiy, with very low 
air density, the hydron^en rocket proves to be superic. 

m 
We saw that £- can become the greater, the smaller p becomr>a. 

If we designate the weifrht of the fuels as b r and that of the empty 

br k 
rocket as m , — = -^ is approximately valid, at which k is a propor- 
tionality factor. Now, with a pure alcohol rocket, the filling is 
specifically q times her.vier. If I use capitals for the alcohol rocket 
and small letters for the hydrogen rocket, according to wJiat was said 
under 8, I can write : 

Br b r 



M^ H mj • 
Furthermore, in thin air, according to (9) 

(Vj - vj^v^ , 



- 342 - 



and according to (6) 



(Pl- f'o)~'*'x, 



br\ 



If V ^v , 10 is J 



\ TO,/ 



c 



— is a civen figure. So, i" this case, by ejecting all fuels, the 
C 

hydrogen rocket assvimes a hif^her velocity. In discusriir^ t^>is fomula, 

b r 
■re note that, for small ^— t 



^>^ q , 



4+iE 
'»('-'^) 



Since I^T") +ho nlcoboi fjMin^ i >'- +o be "ecor-'otuief' here. 
Furthermore j 

\ ^ my ) \ mj I ^ Ing 

,„(i + 4 ,n(i+*j:) ^i„(i + *-^)- 

v mil \ mj \ mj 

br hr 

Here Inq is a cor,siB,n+., In M + ^pi ■'rcrerries from - cO yhen ^ 

ircrna'ps; i.e., a3 2— incroa^iep, ■■rhicl' monrs t'int y*5 decrea^os, 

the T^hole expresRlor approaches the value of 1 and thus in^'st become 

c 
smaller than - ^ 1. This natuiallv anplies oil the rrore to the smaller 
C 

expression 



- 343 - 






So for this reason, the hydrogen rocket increasir^fly reconunends itself 
the smaller ^ becomes. 

In ^his connection, Fig. 44a-c is instructive. From Fig. 44a 

"•o 
ire recognize +l\at the greatest possible ratio ™ depends on the pres- 
sure. With a specified velocity and the same form (of rocket), hoM-ever, 
the inside pressure increa'^es proportionally with the outside pressure. 
So, the thinner the outride air, the srailler are the forcer whic'i 
tend to cause the rocket to buckle or collapse and the smaller is the 
inside pressure necessary for rigid filling. Accordinf;^ to, Chapter 8, 

— represents a nearly linear function of the reciprocal value of 

the air pressure. At the same time, "we see that, with the hydrogen 
rocket, the mass ratio in .'>;eneral and especially at the beginning is 
much smaller. The solid curve refers to the alcohol rocket and the 
brohen curve to the hydrogen rocket. 

Fifc. 44b shows the connection between the nasf' ratio and the ideal 
propulsion. With the hydroo'en rocket, this curve naturally rises more 
abruptly since, with the same mass ratio, its performance is hin;lier 
due to ■the high exhanst velocity. 

Since the greatest laass ratio depends on the out-side air pressure 
and the ideal propulsion on the mass ratio, in the final analysis, 
o+her thing's being equal, the idebl propulsion depends on tl^e outside 
air pressure. Fig. 44c shows the dependence of the ideal propulsion 
on t'le outside pressure dirnctly. Fr<Ha that we gather that the alcohol 
rocket performs better with high outaiHe pressure and the hydrogen 
rocket perform.s better with low outside pressure. 



- 344 - 



Th«s* enrT«Sy hoT«T«r, only relftt* to tho ideal propulsioii. Vithin 
the fttaoaphoro, tho ale^ol rockot natorally rvialna luptrior longer 
b*e«n«o it ia !•■• ii^odod hj the air roaiataneo. 

b) Boeana* of th* lav apoeifie voigfat of tho filling of tho hjdrogan 
rookoti iho aido praaaoro ia mall. Thia ia an iaiportant advantago 
boeanao tharofa7 iha aoeoloratiMi can boeooio groator (of. pp. 125, 269 ) 
and tho prapulaion laata for a ahortor period. 

c) If ■. m If , than ^.> ■.• Tbi* eireamatanoe baa tho follotring 
effeet t If, for ezanplO) the rocket ia to earVj regiatering inatrnmenta 
of a certain vei^t and jot ia to bo bono aloft by another rocket 

and haneo not to be too heavy, hydrogan filling ia to be roeaamandod, 
OTtn thooi^ an alcohol rocket of eqaal anpty veight vonld perfonn 
better. If, vith model B, we replaced the hydrogen rocket by an alcohol 
rocket of the aaaie toIobo, iho latter would perfom better. With oqnal 
total perfomanee, hewerer, the new apparatna would bawe to be at 
leant 5 tiaea aa hea-vy aa nodel B, and with ewery kg of ^drogan we 
are aaVing reni^ly SOO kg alcohol and 4t0 kg ej^gan. 

d) Finally, tho bi^aTier of the notala at the t«aq[>erat«re of liqaid 
hydrogen onat be noted. n»ey beeaoo hard and brittle (ef. Figa. 9>ll). 
If I lay a cmbe with an edge of t ea an the table, lay a glaaa rod 

1 m thidk and 60 cBi long on it at the niddlo, and attaiapt to band 
the two anda down ae thay tench tho table (ef. Fig. Hi), the glaaa 
rod breaka. With a glaaa thread 0.1 an in diweter (it ia obtained by 
rapidly atrotohing ineandeaeant glftaa) the esverinant ia eaaily 
aaeaapl idled. With the roeket, eonatant banding will eeenr boeanao of 
the ehanging air roaiatanee and inaido preaaare. Theoretieally, thay 
eonld be alnoat aeaipletely avoided by cerroetly ealenlating the 
atrength ef the natorial at OTory point, yet, in tho teehniaal canatme- 
tian, eertain iaporfoetiona wenld alwaya raaiain. The nain floetiana 
atand in a definite rolationahip to the total aise of the apparatna and 
are the leaa dangorena with brittle natorial, the thinner the walla. 



- 845 - 



Fig. Ill 

If th« utterl*! !• pr«t«ci«d •gaiast brtakiag, ih* l«v tinpArAtar* 

has •• MTWitag* t th« twail* •traiigtli aad with 14^ iacr««aM •«•- 

"l 
aiiwtMj, Thcrt «r« «!■• acft materiiJ. lik* p«r« laaA. Th« lass ili* 



fl •Sibil itj that is r*^ir*4, th« hi^ar •tm b« th* Amumdm «• t«i«il« 
•troigth. 

6) I»»ida fr*Mamr9 i» tha Ona «»* C— baati— 

It ia paaaibla far liqalA ta ba avapt alaag fraa tha awabaatiaa 

ahaabar af aadal B, bj abiah a baa«ttaa aaallar. Thia dravbaak 4.9*r%»u*» 

Pa 
tha u»Vf tha graatar p baeaaaat far a) iff ia »• Aaingf ~ iaeraaaas, 

vith tha sMia air«wafar«aiea af tha a«abB«tia> ehanbar, tharaby tha 
Talaeil^ af tha gaa daaraaaaa. Tha ralaaity afth irtiiah tha gaa flava 
thraai^ F^ ia (alaaat) iadapaadrnt af p aad p., aad, with p iaaraaa- 
lag* Tm b****** eaaaidarablj aaallar. Ia »• daiag, aaall drapa af 
lifald Tapariaa battar aiaca thaj raaala ia tha aaabaatiaa ahaabar 
laagar. b) Hiay al aa Ti^arisa battar baoaaaa daaaa gaa giraa aff aara 
haat thaa rara gaa. a) Alaa baaaaaa, vith hi|^ p,, th«j aaad aat 
abaarb aa aaah haat ia ardar ta Tapariaa. d) Tha aiaia qpaatity af 
liquid awapt alaag datraata laaa fraa tha axhaaat ralaeitj a with 
hii^ar iaaida praaaora p baaanaat ia »• ^iag* tha diffaraaea batvaat 
tha apaaifia waight af tha liqaid aad that af tha gaa baaaaaa iaallar. 
That ia ta »mj t tha gaa flawa thraagb F_ with tha ralaaity aj^y lAiah 
ia dap«ad«at aaly «a p^*T«. Ia tha firat plaaa, a drap af liqaid af 

a aartaia aiaa iapadac a atraan af d«aaar gaa laaa thaa a atraaa af 



- 346 - 



thia g«« aad, (fe*m41jt it i* nrept «l«g f»«ter. If *• eu g* t* the 
higheat eritie«l pr«aa«re ef the Bixtwr* vith p , v* veold miIj be 
imtereeteil is the tenpereture md cheHicel CMipesitieii ef the BAtter 
thst fleve threngfa F^, and the qveatieB vfaether it is liquid er gaaeeus 
vevld be irrelerent. 

6) Fern ef the Ateaiaer 

The ateniser Z veold be lif^ter if the liqnida ea veil ea the 
exjrgaa vith aedel B fleved evt ef heagiagi eeae-ahaped pipea. I de 
Bet beliere (fer the reeaena neatiened ia Chapter 3), heverer, that 
the eeaibiiatiea veald be aa thereu^ ia thia -wttj aa it ia vhea the fuel 
ia breag^t ia frea the periphery. Ia the latter caaej the imperfeetieaa 
ef eeabuatiea are amtaally eqaalized. Ihat la -thj, with the aerienalj 
eeaeeiTed aedela C aad D, I plaaaed eeadactiag the fvel ia ealj fren 
the aide. 

Actaally thia qaeatiea ia aet tee imperteat vith apparataa ia vfaich 
ei^gea aad fuel are breu^t ia alteraately^ fer here ve eaa aet up the 
aezxlea fer aaterial A ia the lee ahelter ef the aesalea fer material 
B. Thua the eeabuatiea gaa ia hemegeaeua uader all circuaateacea aad 
there veuld be difficultiea te eTereene ealy vfaea) fer the firat time, 
briagiag liqpiid frea ceae-ahaped ataaisera iate a het atreaa ef exygea 
heated bj aeaaa ef a gaa flaae. 

It ia aa aidnrard axraageaeat ef aedel B vhich alaultaaeeualy oaea 
aeae-ahaped ateaixera aad ateaizer aezzlea attached ea the aide. Siace 
I de aet iataad te build aedel B but ealy vaated te ezplaia the aeat 
iopertaat arraagaaeata bj it^ I uaed the eppertaaitj te ahev beth. 

T) Lapertaace ef the Puapa 
la the fuel reaa, the preaaure ia auppeaed te be hifl^i ia the fttel 



- 847 - 



tasks, lfW9T%T, l*ir pr*«mire mnst preTail. The pvaps p., p^ u** iap«r- 
ttmt h9*tm»» th«7 h«ni«aiz« tliea* tm repair aaamta. The iapartaaca 
•f th> pmp* ia«r««a«s vitb th« size af th* apparattts t large apparatva 
iahereatly hare the repaired balliati* eeeffieiaat, ae ve ea» Imild 
th«i wider. Im ae 4eiBg» the imaide preaamre ef the f«el taaka re^ireA 
te keep thea rigid aocerdiag te Chapter 7 deereaaea. la apparataa vith 
a balliatie ceeffieieiit ef erer i.l kg/ea', it is alee iapertaBt that 
p^ beeeaea large, aad that the aere, the greater the balliatie eeef- 
fieioit. With the hrdregaa recketa, the puipa lese ia inpertaace if 
the weight ef the i&stmments carried along is great ia relatiea te 
the weight ef the fuel teaks. Ia the aedel B hydregn reeket, fer 
exaaple, I drew thea enly fer the sake ef the priaeiple; thej de aet 
erea iaerease the prepolsieii bj 400 a/see. If the weight ef the 
iastnuieBts is relatirely saall, the pimps en hj-dregea reekets beeeae 
especially effeetire. I eemsider the pressure-ehauber puaps p., p. a 
rather fertaaate techaical selatiea ef this preblen. Pistea poaps 
eeanet pessibly de the jeb. 

8) DiTisiea ef the Neazle 

■, 
1 farther reasea why, with large reekets, ^ (er, if we dispease 

witb that, ---} eaa be greater is the fellewiag t Vith reekets ef this 

Pd 
^7P*» V* c<A diwide the aezzles iate 7, er 19, er acre parts (ef . Fig. 

is). That dees set raise the erm, nezzle, aad paap seetiea aaj higher 

thea with aaall apparatus. Bare, hewerer, it has less weight because 

its relatiea te the fuel lerel is saaller. (it is ef the seae iaper- 

■e 
taace fer the ratie — as if we had succeeded ia sherteaiug erea, 

aezzle, aad puaps ef aedel B.) With aedel E, the bydregen racket is 
aet eaclesed iu the alcehel recket but sits eu tep ef it (cf. Plate 4). 
The upper wall ef the alcehel reeket has exteasieas that fit iate the 



- 348 - 



B*zzl9 •£ the h7dr*g«iB r«ek«t. Pvanlbly, « ap^oial tip eoa be placed 
•T«r the hyAregea reckei fer the •aeeatf vhleb inereftsei its reaiat- 
•aoe im the lever lejere ef the ataesphere eBii ie Jettieeaed tegether 
Tith the aleehel reeket. Here, it ie better te plaee ehenber I abere 
the hjiregea reeket, ^et nader the pairaehute. The aaia reasea fer 
placiag it se lev ia medel B vae te preveat the hydregea teak frea 
aaggiag nailer ^e effeet ef aoeeleratiea. That deee aet apply here. 
The regal atiag reila take ever the rele ef the aoxiliary reeket. 

9) Lanachia^ Manae<L Reeketa 

We eene te eneh giaat reeketa vfaea aa ebject ef epeeifieally larger 

B 

veight ie te be berae aleft; --- vaat hare a defiaite miaimm redae. 

If ■. le large, u^ saat aeMaaartljr al ee be large. Saeh a large reeket, 

a) beeaaee ef its high ballistic eeefficiwat, alrea^ has a very hig^ 
adTsatageeas Telecity te begia vith, vhieh perhaps it dees aet attaia 
duriag the vfaele flight, b) The iaside pressure ef the tanks is rela- 
tirely lev aayvay. c) Fer F . - F vith the aleehel reeket, p. is clese 
te eae ataesphere, if aet mere. Aecerdiag te vfaat vas said ea p. 339, 
a), b), aad o) vere the aaia reaseas fer hariag aa elevated laaaUtag 
site; that aeaas that it is aet inpertaat fer this reeket te start 
frem a hi|^ leeatiea. It starts mere eeareaieatly freai sea level . 
If the taaks are rigidly filled vith air, th^ eaa veil staad the 
dash ef the vaves. The reeket lies flat ea the vater, the rear siakiag 
seaevhat deeper (ef. Fig. llS). Thus a ship eeuld easily take it ia 
tev, vhich, at tJie saae tiae, veuld have te carry the liquid gases 
ia vell-iasulated CMttaiaers siace they ceuld ealy be filled ia 
iaaediately befere the ascoit. Ia the filled state, the apparatus 
takes a vertical pesitiea rea^y fer aeceat (ef. Fig. 113). Te prereat 
ice frea feraiag ea the hydregea reeket, it sheuld be eaclesed ia 



- 349 - 



a e*T9r af paper which is m«t t« reaaia bat is palled apart at the 
memeut ef laoaehiag. At the nmeat vfaea this racket emerges fren the 
-rater, it irill reek Tioleatly, hat that sheulA aet matter nraeh siace 
the gTrescepe eeatrel vlll seen steadj it. 





Fig. Ill Fig. 113 

UeAel C alse can easily be bailt ia a leagtii that eaables it te 
start frea the greoad (cf. Peiat 3 ef this lOiapter). Ihat I vrete 
ceaeeraiag takiag a racket aleft by aeaas ef airships applies exclu- 
siTely te metlel B. I ealy meatiea this beeaase, ia stne aeirspi^er 
articles, ny verk vas preseated te neaa that erery apparatas, evea 
me4el E veighiag 888000 kg, is te be lifted 5000 ■ by neaas ef 
ballewis. 

10) Racket Space-Ships 

If the reeket -vere aet subject te the attraetiea ef the earth aad 

te air resistaace, ve veuld be perfectly free te make the ratie -«-^ 

■l 
aa large as ve pleased. The lever the air pressare aad the ferce ef 

gravity, the mere efficieat is the racket. The reeket is the appra- 

priate apparatas far advaaeiag te iaterplaaetcuy- space. 

11) Filliag the ^dregem Reeket 

Wboi filliag the hydregea reeket, aecessary preeaatieas most be 
takea. The iaside excess pressare ef the hydregea taak aust first 



- 860 - 



b* br«tig^t t« « 1«T«1 «fa«fl« rati* t* that vbioh it vill be ^:p»aed t* 
later ia aqaal t* the rati* tt its prevent mvAoloa •£ elasticity t* 
that at the tenperatare ef liquid hjir*gea. Thca it nast be o**leA eft 
hj pvapimg ia aere aa4 mere freflhly-Taperized hjdr^gem. Omlj irttaa 
it apprazlaately has the teaperatore ef the liquid hjirtgem, aej it 
be filled ia. 

1«) Startiag Medel B 

15 seeeads befere the actual start, the small puiip ■. is made te 
eperate. 5 seeends b*f*re the start, the geaerater must begia -wvrkiag. 
The reeket starts as s**b as the axygea aad the alcehel aixture ia A 
aad B hare begua t* bura, 'which is achieved by neaas ef th* igaitioa 
plug a. 

it^j^f jlscettt 

F*r h. B r + 70 la, '\l1«g.«h. aJB*UBtB t* 11,160 a/sec| f*r h. - 

r + 140 ka, 11,106 n/sec. From that, the parabolic Telocity for 
altitudes betveai 70 aad 140 Imi is feuad by iaterpolatifta. It vill 
be sewn froa iriiat vas said s* far that it is possible t* reach this 
▼elecity. F*r example, if the alcehel rocket gives the hydrogen 
rocket a propulsion ef 3000 a/sec (a large alcohol rocket propels 
the bydregea rocket at over 4000 a/sec) aad c « 3400 a/sec irith the 
hydrogea rocket (actually, the exhaust relocity could amount to 
4300 a/sec), thea the fol loving applies te the hydrogea rocket t 

, "e 11,000 - 8000 "o 

la =- - — s . B.Mat w- - 12.78, 

■l 3400 1 ' 

that ralue caa be exceeded by adding another stage. So oty apparatus 
can very veil attain eosnic velocity. 



- 851 - 



^'*) Evaluation of the Riel« 

Concerning this, the literature on rocketry is morfcedlj rague. 
Veiriotts authors are making repeated attempt* to set up siople criteria 
for the evaluation of fuel*. HOE^TT and a number of mechanical 
engineers, for example, hare a predilection for inquiring into the 
inner energy eontmt of a kilogram of a fuel composition; N00IU3UNG 
again holds the Tlev that tite fuel vhich contains the most energy 
per liter is the best. Other authors use other norms of evaluation, 
but it is not irorthidiile to discuss them. 

To begin with, the knowledge of the tuol energy alone is no use to 
us. We must know hov much of this ener^ can be converted into exhaust 
velocity. X combination of acetylene and oxygen, for e::afflple, contains 
considerably more chemical energy per liter as well as per kilogram as 
say a combination of alcohol nnd os^gen, yet, within the atmosphere, 
alcohol results in a higher exhaunt velocity. Namely, in the acetylene 
flame we have two parts of carbon dioxide and one part of water vapor. 
But, at the same tenperature, carb<m dioxide is more than twice as 
heavy as hydro^^en; so it would have to be heated conviderably nore in 
order to produce the same ov.t-flow velocity. TaJren by itself, because 
ot its lower heat absorbing capacity (which follows from its greater 
molecular weight), the carbon dioxide would heat up correspondinijly irore 
with the same supply of ener^, but water vapor is also present. At 
such high temperatures, the water vapor disintegrates. In so doinpr, it 
again absorbs the greater part of the developing heat, i5o that the gas 
is not as lin;ht as the combustion gas of the alcohol flame, which con- 
sists mainly of undissociated water vapor. 

This situation would not chaofre evpn if we "nf.de the noi^le wider 
at the bottom than we assumed in Chapter a. If, in air-free space, 
we have i^uch a greatly widened nozzle, that will cause a ctron;; 



- 352 - 



r*4aeti«B af the g** presaur* frwa the •t«b up t* the catlet t»i with 
it « decline in diBseciatien, m PIRJJCJEr (cf. LEX t "The Pessibilit^ 
ef InterpI eBetarj- Travel ") ha» shevn seme tiae age. A* leng a« the 
reekei travel ■ irithin the atveaphere, heireTer, and as leng aa its 
Telecity deea net exceed the ezfaanst Telecity, tiie preasure at the 
eutlet eannet aink belev the presanre ef the entaide air beeaase the 
entire apace behind the reeket ia filled by the exhauat gaaes. 
Aeeerdinglj) the degree ef diaaeciatien at the entlet vill alvaja be 
bi^. It ia net eur intention te aelt the vail ef the nezzle bnt 
te achieve high ezhanat relecitieai hence ve vill prefer alcehel te 
acetyl «ie. 

The hi|^ diaaeeiating capacity ef vater Taper alae ezplaina the 
peculiar fact that, vith aa epen blevpipe, the acetylene flaae ia 
hetter, vhereaa, when bvming in a cleaed, preaanrized even, the 
flame ef the ezyfaydregen blevpipe ia better. The acetylene fleaie 
eenaiata ef 81.5 % earben diezide, vhich la nere difficult te dia- 
aeciate, and enly 18.5 fi vater Taper, vtaeae diaaeciatien here deea 
net carry aa aach vei^^t as vith the ezyhydregen flame vfaich delivera 
pure vater Taper. If ita diaaeciatien ia inhibited by higher preasure, 
the higher energy eentoit ef 'Uie ezyhydregen ia mere eTident. 

It is true, NOORIWNG says quite cerrectly, "With the oenditien 
that the fuels can be utilized equally veil**. (A cmditina <rtiieh, fer 
the reasens already explained in oennectien vith acetylene, dees net 
apply te the flnulsien ef eeal dust in gaseline er benzene suggested 
by him.) Assuming, hevever, that it dees apply te tve different 
fuels; er, still better, let us ceapare the fuels enly vith regard 
te the exhaust energy centained in a liter. This is prepertieaal te 
the specific veight <^ and the square ef the e^anst veleeity. Se, 
aceerding te NOORIXTNG, tve fuels veuld be ef the same value vhese 
^'•o are eqpial. 



- 853 - 



L«t us ««stUBe v« have a ftiel ifa«8« 



1 
(3^* — ; c - S8S8 ■/a*e. 

S 



Herft 



cr.«* . 4.10®. 



With this fuel, ve vant t* fill a siaple racket Vbicb caa h»H vatar 
•qua! t« 9 tiaea its anpty vaight. We eavld pvt half af 9 h^ ar 4 l/S 
■^ af thin fuel into ita fuel taaka ani, aaeardiag ta (6), it« ideal 
prapvlaias vaald be 

^|"l^-l 
T - S888*lB - 4880 ■/•ac. 

Z Bj 



If, ea the ether head, ve had a fuel vith apeeifie veight S aad 
eshanat Telecitj 1414 ■/■**! here alse 

CTc* - 4.10®. 



Aaeardiag ta NO0RIX7KG, this fnel vauld equal the firat-««ntieaed ia 
Talue. The 
aad here > 



Talue. The taaka af eur racket Yeuld held 8*9 - 18*m. ef this fael 



18 mi + B^ 
T^ - 1414*1b - 4170 a/sea. 



The difference venld be still greater if ve did aet werk vith a 
simple but vith a tve-staga racket. — Assaaiag that tiie eopty lever 
recket is 10 tiaes as heatj as the tmptj mpper eae aad e«eh helds 
9 tiaes its em veight ef vater. The capital letters refer te the 
lever aad the onoll letters te the upper recket. With the lighter ef 
the tve assumed fuels t 



> 354 - 



T - 4S30 n/»»iit 

U^ - 10 .J, 

■^ • 5.5 m^ - 0.56 M^, 

M^ - Mj + 4.5 Mj - 6.5 M^, 

• • 6.05 ill , 

TT + T - 8900 ■/»»«• 

Vitb the heavier fuel, ve veul«l hftTe i 

T^ • 4170 m/»99f 

Mj - 10 Bj, 

■« - 19 a^ . 1,9 U^, 

M + ■ 18 M. + U. + 1.9 M 

V - c«U TT ^ - 1414'la „ ^ . a V, - WOO ■/■•«» 

X M, + B M, + 1.9 M. 

1 11 

V + ▼ - 6970 n/eec. 

Therefere, with the eeeenA fuel, »e ebtain 1930 m/eec - 87.7 J6 less 
than vith the first-Mentiened. 

The reasea nhy N00&IXJNG*S criterien iii. aet vork eut is because 
net 

9 e 

cS~c*, but c*ln ;r- 

"l 
▼eulA have had te be oeustoat; er, since 



- 366 - 



at vhich k (th« filling factor) repreaents a e«nstant that depends en 
the atniotare ef the racket, ▼• vould hare had the criterien 

c»ln (k<r + l), 

Nev, the filling faeter k is tetaUr different irith different 
reekets, se that, vlth different rackets, specific weight and ettt-fle-r 
Telocity carry totally different veight vith respect to each other. 
For this reason alone, there is no simple oriterion vbich, eren thongfa 
only vith respect to tiie ideal propulsion, vould tell ns iihether one 
type of fuel is basiely preferable. 

The natter beeeaes still sore ooaplieated if the penetration of 
the atmosphere, the ballistic coefficient vhieh depends on the sise 
md shape of the rocket, and the degroe of dissociation of the 
osditHist gas, vhich depends on the nozzle ratio, the OYen pressure, 
the speed of traTol, and the pressure of the outside air, are al^-o 
takttn into calculation. The description of the model B alcohol and 
hydrogen rockets and their comparison above already provided us vith 
a sample. 

The dissimilarity 

-o ' 

end say the fonmlas (43) and (lOO) should be compared. There is 
simply no fuel vfaich, vlth suffieittit variation of all the formula 
quantities, vould be superior to all other fuels* Such a fuel vould 
at once have to be the heaviest, highest in energy content, least 
dissociable, and, if the matter is to be practically feasible, also 



- 356 - 



tha cbe^«st| aoat atabl*, an4 laaat dMngaraua) it voald hara ta aaka 
tha lavaat deuanda an tha caaatruotlmi aatarial. B«t aaoh af tha 
lotamk'H*!* i* axoallad h7 athars in aoaa paints, and ainca thasa 
prapartias earry diffarant vaight vith raapact ta aaah athar with 
diffarant apparatua, tn» typa af fual Till ba aara snitabla vith the 
onai and tha athar aara snitabla vith tha athar apparatus. 

Tha malj raasraiAla thing the racket bnildar can da is tiia follaviagt 

Ha first skatabas tha plan af a roaket in rough autlina, taking 
inta cansidaratian tha ganaral basie raquiraniants af canstmotian 
arising fraa tha thaary af reakatry and vfaiah I hare alsa in part 
darirad in this beak (high aass ratio, aroidaDca af rainfareanants, 
snitabla boiler poaps, appropriate ballistio aoefficieat, etc.). 
The qaestion ef the sise and construction of the fuel tanks and of 
the finer aeasuroaaats ef the eombustien apparatus is left open for 
the presmt. Than ha calculates the perforaauce of the upper rocket 
with Tarions fuels. Baring found the best fuel, ba calculates the full 
veight ef the rocket and noir considers it as the payload of the next 
largest rocket, vith vfaicb he proceeds in the saae aanner. iboTo all, 
the fuel for the different rockets aust be tested separately, for 
va already sav vith aodel B that the daaands on the fuel are quite 
different for the upper and lover rockets. On top va vill abore all 
(although not exclusiToly) strire for high energy content, vbereas 
belov ve vill aia for higher speoifie veight. (in so doing, it can 
happen that, after calculating the fuel ef the lover one, ve vill Mice 
aero ohanga the fuel for the upper one taking the whole into aeooont.) 
Finally, ve vill design the -ahole i^paratus. 

The aatter becoaes still acre oaraplicated if the cost aust be 
takaa into account. The aecbanical engineer and heat teohniaian will 
ba prene to choose the fuel which is cheapest per calorie. Nov, the 
aheap fuels usually result in a lev eahaust velocity, and since the 



- 857 - 



l*garithia vf the naas rittio la approziaately iinTersely proportional 
to the oxbftaat rolocity, the maso oxpmditar* with higher Aeaaada 
▼ill increase to anch an extent that the matter as a whole will be 
cenaiderablj mere ezpenaiwe in spite ef the low specific cost of the 
fuel. The ascent ef a crude-oil rocket, for example, whieh perfonns 
as well as Model C would be roughly 4 times as expensire. 

NererthelesSy eren if the exhanst Telocity ef the fuels is equal- 
ly hij^) care must be taken in the calculation, for the liquid o^gen 
must also be paid ferj that means taking into account whether the 
ascent is to take place near the oj^gen factory and hew mnch time 
the factory needs to produce the required quantity ef o^^gttii, in 
ether words, how mnch ojqrgea waporiaes unused before the rocket is 
filled. — In the troposphere, benzine, 40 ^methyl alcohol, and 30 % 
ethyl alcohol, for example, result in nearly the same exhaust Telocity. 
(In the stratosphere, the conditions could shift somewhat in faTor 
of the benzine.) Of these three liquids, benzine is the cheapest and 
•ibjl aleohol the dearest. So we will use bsmzine ? 

If the molecules ef bwizine contain en the awerage 8 atoms ef 
carbon, combustion occurs according to the formula t 

CgHjg + «5'0 - 8 COj -f- 9 H^ 0. 

One kilogram of eur fuel combination will contain 82.1 % benzine and 
77*8 % oxygen. With methyl aleohol we would haTe 85 % alcohol and 
97 1/8 % oxygen, with ethyl alcohol 18 l/8 ^ aleehel and 38 l/S % 
ejqrgen. With today's lewel of prices, wood alcohol would be the 
cheapest* (The fact would also hawe to be considered that the nozzle 
walls are not affected as strongly when alcohol is used; with benzine, 
a certain surplus of oxygen would hawe to be used to make certain 
that the heavy benzine Taper bams up completely.) But the question 



- 358 - 



Arises vfaether iixb present prices voold rem&in in effect vith Tigoreus 
mail rocket traffic. Methyl aleohol, for exeaple^ is actuall/ so 
cheap only because it is not being used in large quantities. With 
greater demand, the price vould rise considerably, so that finally 
ethyl alcohol, -which can be produced in any quantities, or (if 
alcohol tax is calculated) fuel alcohol, methylated by means of some 
wood alcohol, would be the cheapest. 

If, with my first meteorological and long-distance rockets, I will 
noTertheless use benzine, the reason is because it makes the prelim- 
inary esrperir'dnts more convenient and cheaper. In the first place, 
with benzine certain questions are already cleared up which, especial- 
ly with methyl alcohol, would still have to be investigated. Secondly, 
with ifche experiments on atomization and combustion, the color of 
the flame indicates whether the benzine is well burnt up, which is 
not ih9 case with alcohol . 

15) Simplifications in Model B 

We cotild simplify the oven considerably if we placed less value 
on achieving high final velocities. We can let the oven border directly 
on the Jacket and simply line the latter with asbestos, which we 
moisten before ihe launching. A further simplification would consist 
of simply lining the nozzle with material titat can endure the fire 
for d/4 of a minute. 



' For similar reasons, it is impossible to state simple criteria for 
for the optimum division with multiple-stage rockets. If one applies 
criteria published on the topic to concrete eases, they do not 
prove themselves. There is only one way out t calculate a number of 
possible cases. I will write in detail on the topic in the second 
volume. 



- 369 - 



If, irith the alcohol rocket, instead of the folding fins, solid 
fins provided only vith a control vere used, a parachute vould be 
needed and the propulsion be reduced by another 100-800 a/aee. in 
apparatus irith all these simplifications irould still reach an alti- 
tude of over 250 km. Such an apparatus cannot, hovever, give us any 
information about iiie movement of the hi^er layers of the atmosphere, 
for the time during vhich it has ibe tangential motion of the higher 
layers of the atmosphere is relatively too short in comparison to 
the time during irtiich it has the lateral motion of the lover layers 
of the atmosphere. 

Ve could also dispense vi^ t^e pumps p., p. and the vlnd tank 
if ve kept the alcohol -vater tank at the pressure betveen the atomizer 
pipes. In so doing, its walls vould naturally become thick, but ve 
vould have the advantage of being able to moke the rocket narrover 
in shape. With tiie some fuel consumption, the ballistic coefficient 
could be greater; vith the some ballistic coefficient, tlie fuel 
conaumption could be lever. — If this simplification vere carried 
out, V. vould equal 1800 m/sec and the rocket (figuring in s.) vould 
rise somevfaat over 100 km. In order to ascend, it vould nov need 
nothing but the pumps m n , the atomizer Z, the alcohol tank vith 

the double floor h and a pressure gauge, vhioh regulates the supply 
of fuel gases, and a safety valve, and an oxygen tank vith the same 
accessory ports. In addition, there vould be the control gyroscope, 
the parachute somevfaat moistened beforehand and the jettisoning 
device. Cooling the tip is no longer necessary here. The period of 
ascent and fall of this apparatus vould not be quite 6 minutes. 
It vould descend at the most 10 km from the place of asc«nt| hence 
it vould be easily found, the more so since the approximate direction 
in vhich to look for it vould be knovn. So ve can dispense vith 
every additional aid in locating it. We vould obtain a relatively 



As is seen vith models A, D, and C, the pumps m n can also be 
dispensed vith. 



- 360 - 



•ii^pl* apparAtu* (altbons^ using 6 tlmec more fuel) viUi the s«me 
perforaano* aa nodel B (viiieh, beeauae larger, eaa asomd from aa 
altitude ot i — 3 Im) if ve placed three aimilarly simple rockets 
one aboTO the other as follovs t an alcohol-vatsr rocket at the 
bottom, a rocket vfaich uses liquid methane gas as fuel and vater as 
coolant in the middle, and a hydrogen rocket en top. 

Models Jl and C are basicly still simpler. In C even the fins ean 
be dropped. 

16) The Advantages of Liquid Fuels 

The advantages of liquid fuels over the proTieusly used explosives 
are the following t 

a) The velocity can be regulated. 

m 

b) — becomes greater. 

c) The «chanst velocity (especially vith Uie hydrogen rocket) 
becomes greater. First, because the out-floving gases are lighterj 
second, because the propelling force of the fuels is better utilized 
by suitable nozzles; third, because the nozzles are under balanced 
pressure. 

d) The operation is less dangerous. 

it) Division of iii* Rocket 

Advantages i 

a) Less dead material is toired along. 

b) The single rockets can be built differently in accordance vith 
their varying purposes. 



- 361 - 



I also r«gard the folloving as my inreations s the Telocity 
regulator! the jettisoning deTicO} the pump ehamber! vaporization by 
forcing in of fine liquid bubbles. The formulas (36) to (5l) and (6l) 
te(l7l) also i^>peeu* to be neir. Likevise the research into natural 
phenomena in connection irith eounter-pressure and the research cen- 
eeming the synergy problem. 



- 368 - 



P»rt IV. 

P*«*iblliti<» of U«« 

Ch«pt*r 18 

Podslbtlitiea »f U«ing th» R»ck«t H»«»lo 
y , or LlqttlA ftfl» w Bwth 

Foranl* qamtiti«« of Chaptor 18 

Tbo indox figsro* rofor to point* indio«tod by brsekotod niuibora 
in Fig. 184. 

t out-flow Toloeity 

o I ba*o of n»tarol logaritbaa 

g t «ecflor«tioB due to grari^ (cwtotmt at 0.81 a/soo ) 

b t altitado aboT* tho gronnd 

■ t ■«■• 

p t drag 
p t oToa proomro 
p. t oatlot pro««are 

t t tiao 

T t TOloOitj 

C t diotoneo eororod dnring diioipation of tbo enorgy 

E I totol onorg7 

H 1 oonatant fron (34) (7400 ■) 

K I m*TtX of Botion 

K' I Apparont ratio of J& 

*^o 



- 363 - 



P t energy due to poaitloa 
^ t air denalty 

I ahall write about the bietory of the rocket and the areas of ita 
ap|>lieation mo far in To}. II. Here I vould like to report only en 
the areas of applieatios of the rocket vfaich can etill be opened «p. 

l) The Vertical ly-Aecending Rocket 

») The meteorological rocket ie used for research into the higher 
layers ef the atmosphere. 

The acceleration of a rocket is so small that it can carry vith it 
sensitive precision instruments. With small meteorological rockets 
vhioh are to simply ascend vertically past the limits of the earth's 
atmosphere the fol loving measurements can be taken t 

The acceleration indicators (cf. p. 123) give us a curve indicat- 
ing the relation betveen counter-pressure and time both during ascent 
and descent. From that, by integration, ire can derive the velocity 
at a specified mimttit of the flight. From that again ve conclude 
the altitude attained at the time (cf. p. 272). In so doing, ve 
have a certain check on the data of the acceleration indicators, 
for ve must obtain the same value for the highest altitude reached 
from the data recorded during ascent as from those during descent. 
A further check vould consist of observing the rocket by telescope 
during flight and recording the angle of observation . 

That can be done vith the zeni'Ui telescope of ZEISS 



- 364 - 



On a body in rapid motion, a baronoter vlll hardlj shoir the trua 
•ir preavuro becaase of the turbuleaco. Nor do the readings of a 
thermometer correspond to the true air temperature. On the other 
hand, an empty meteorological rocket borne by a parachute falls rela» 
tirely sloirlj belov 50 km, so that pressure and temperature of the 
air can here be measured directly. Abore, the rocket naturally falls 
too rapidly in spite of the parachute. During ascent, the air 
resistance against the tip of the rocket could be measured (cf. p. 331 
apparatus No. 0). Naturally, with the barometric readings during 
the deseoit, the Telocity relatire to the air irould also hare to be 
taken into account} it could be found by means of a type of vind 
irbeel. (its blades vould have to stand almost in the direction of 
flight lest it turn too fast.) By o<»tparing tite barcHnetrie readings 
during descent vith the air resistance to vfaieh the tip vas subjected 
at the same altitude during ascent, the resistance coefficient for 
relocities abore 100 m/sec oan be obtained vith great accuracy. 

Up above, the empty fuel tanks can be filled vith air. Vhile the 
air samples are being taken, iti9 piston strokes of the pump are 
counted, and from that and the readings of the pressure gauge ef the 
tank conclusions can be dravn as to the air density. In this ray it 
could, above all, be determined vfaether the composition of the air 
above is sirailor to that belov or vfaether the peromt ratio betve^x 
its single components is different. Many astrimmners and meteorologists 
assume that there must be relatively acre hydrogwi and less oxygen 
in the higher layers of the atmosphere. Substances could even exist 
in the upper layers of the atmosphere vhich are not found ou the 
ground, as, for example, certain nitrog«is and nitresyl cmtpounds 
vhich eon form only under the influence of strong ultra-violet rays 
and soon disintegrate again, or ^e hypothetical coronium gas* The 
pipe through vhich the air samples are dravn in voald have to point 



- 366 - 



exactly Aovn; only th«n vould it be possible to calculate from the 
falling speed v^ith •uffieient aceuracj «hat relative compression the 
air undergoes in front of the mouth of the pipe. The pipe vould also 
hare to be cooled careful I7, In an atmosphere vith relatirely much 
hydrogen, the compression vould cause the hydrogen to unite vith 
the esygen. Because of this combustion, the figures obtained vould 
be completely irrong. 

If, on the ether hand, this pipe Yere cooled mere effectively 
than the air in front of the parachute, oxidation vould occur here 
and the retardation of the fall due to the suddttx increase in the 
volume of air in front of the parachute ^ould itself be the best 
guarantee against the air in front of the pipe of the pump being 
compressed and heated beyond the conducive measure. 

I Tould like to coraaent on an objection here. Fear has been 
expressed that this inflanyaable atmosphere could catch fire due to 
the hot ezboost gases of the rocket and cause very peculiar catas- 
trophes. At least the composition of the top layers ot the atmosphere 
▼ould be basically changed thereby, perhaps causing a not incon- 
sequential intervention in nature. I do not vish to give any further 
explanation in this place vhy that is theoretically impossible. 
Proof that this actually does not happen is shown by the fact that 
meteors and shovting stars pierce this layer almost daily without 
ignition occurring, although the tail of these formations is con- 
siderably hotter than the e:diaust gases of my rocket. 

From the air resistance readings at the tip during the ascent 
▼e vould at first be able to find the resistance coefficient for 
very hig^ velocities only inclusive of the hydrogen effect. After 
various ascents to different altitudes, hovever, ve -vould be able 
to separate the actual resistance coefficient from the hydrogem 



- 366 - 



effect. (The hydrogen effect could make the air appear up to 4 times 
as dense as it actually iSj although, according to p. 101 ff, that 
scarcely changes the performing capacity of the rocket.) 

Since all these quantities nutually support and cooplement each 
other, they can later be yery accurately determined by indirect 
cadcttlation. To me it appears as an especially fortunate circumstance 
that -re are making direct measurements of exactly those aspects 
▼hich are of special interest to us irhen building rockets. 

Naturally, during the ascent, state of the liquid, inside pressure, 
toaperature, etc., are also recorded; in so doing, it appears especial- 
ly odTontageous to me that the out-flov Telocity c, increased by the 
force of grarity and the air resistance, can be found from the liquid 

decrease and the acceleration and that, moreover, troa the inside 

Pd 
pressure and the acceleration, on apparent ratio K' between -r- can be 

"o 

constructed as it vere, vfaich, for the construction of rockets, is 

Pd 
more important than ihe actual —^. This is also obtained if the 

Po 
composition, temperature, and excess pressure of the out-floving gases 

are compared vith c and the friction etc. is taken into account. 

Place of descent t Although this rocket appears to rise vertically, 
it does not fall at the same place from vfaich it ascended. In the 
first place, the layers of air moving sldevays influence it (the 
horizontal component of its motion is as good as exactly equal to 
the lateral motion of the higher layers of the atmosphere)* Secondly, 
a deviation occurs for cosmic reasons. Tieved from the intersection 
of the vertical vith the earth's axis, due to the earth's rotation, 
the rocket moves en a great circle drawn about the celestial sphere. 
At the beginning, this circle runs exactly from west to east but 
later deviates toward the equator, unless the place of ascent itself 
was at the equator (of. Fig. 114). 



- 367 - 




O' 



5 

Fig. 114 Fig. 115 

Furthemore, the a&gul&r Telocity of the rocket irith reference to 
the centre of the earth is smaller than the angular relocitj of the 
point on the earth's surface abore ufaich the rocket is just situated. 
That causes a deviation tovard the vest. In Fig. 115, the arrow 
connects the geographical points orer vfaich the rocket flies. This 
curve is easily calculated, vfaich facilitates locating the rocket. 

FroB the difference betveox the calculated and the actual place 
of desoent, the movement of iii9 hl^er layers of the atmosphere is 
found) vitb the condition that the c<mtrol vas correct. This can be 
tested beforehand by loosely supporting the model vith the same 
gyroscope carefully tul justed earlier and placing it in a uniform 
stream of air (cf. Fig. 85c}. 

Similarly, many questions still xmclarified today could already 
be ansvered by the use of such simple meteorological rockets, for 
example the question regarding the heavyside layer, regarding ct^rtain 
short-vave rays in sun or starlight, and others. 

Since the rocket can better be sent where one wishes than a 
meteorological balloon, unanswered questions in connection with the 
formation of thunderstorms, the oecurr^ice of barometric maxima and 
minima, and the like could be investigated with the use of rockets. 
Naturally, it cannot be predicted today whether this research will 
also lead to control of the respective natural phmomaaa, but it is 



- 368 - 



pr«bi^l«. Until nov ther* ▼«■, as a rale} enlj one it«p from ih« bnev^ 
l*dge of a natural proeeii to its control. 

Not only model B eeuld eerre as a Terticallj-aseending neteoroleg- 
ical rocket) bat enaller apparatus like models A and C would be atill 
better salted for the purpose. 

b) The Reconnaissance ftocket. A rocket ascending 30 — 40 km 
could be equipped vlth a motion-picture camera to make It photograph 
the landscape before it. In case of var, such a rocket could replace 
especial Ij the captlTO balloonS| vlth the adrantage oTor then that 
the enemjr could not shoot It down. 

S) The Lo ng-Dlstance Rocket 

As I alreadj said on p. I'i-l, such rockets can net only fly hl^ 
but far as veil. Concerning c<nitrol I hare said vfaat is necessary 
on pp. 260 to 280. 

a) The Geogrqphtoal Rocket. This rocket could be equipped with a 
photographic camera and made to fly orer unknown^ hardly accessible 
areas and photograph or surrey them photograimaetrlcally. For ezample> 
much would be gained for the exploration of inland Africa, the Tibetan 
plateaU) Uie polar regions, Greenland, etc., if one had a cmsplete 
bird's-eye-riev photograph of the respectlTO region, it could serre 

as a map and preliminary guide for the research expedition. 

b) The Mail Rocket. Long-distance rockets could be used to 
dellTor fast mail. For example, such a rocket flies from Berlin to 
New York in less than half an hour. The place of descent can today be 
determined exact to within a radius of ca 10 km, the more so if 
before the start l^e launching center is telegraphically informed 

of the wind conditions at the place of arriral. 



- 869 - 



Let vfl aay 'Uie rocket ia aimed for the Nev York harbor. Then an 
aeroplane vould hare to take to the air at the deetination in order 
to obeerTe vfaere the rocket descends. Naturally, the rocket eurrirea 
exactly on the second aad| together vith its parachute) is visible 
fron a long distance. If the aeroplane itself cannot bring the rocket 
in (should it drop <m the ▼ater), that is readily aeoupl ished vith 
an aquaplane, for the rocket floats easily with empty fuel tanks 
and is relatlToly light after losing its fuelsj at least it can, in 
a short time, indicate where it fell so that mail Tehicles can drive 
up and fetch it. 

Ihe delivery costs vill in no vay be high. The propellants used 
will be kerosene and liqpiid oxygen, and about 30 — 40 pence can be 
figured for 1 kg of this propellent. If, vith a 4000-Ira-flight, the 
propellant is figured as amounting to 10 times the payload, ve get 
3 — 4 pf . of propellant per decagram of payload. According to tbj 
calculation, the total cost of delivery (figuring in depreciation 
and amortization of toe machine, vages of functionaries, guarantees 
against loss, etc.) with undivided mail rockets is not q[uite 1 pt, 
per gram, with two-stage rockets 4—10 pf . per gram. 

Since, according to what was said in Chapter 11, the aail rocket 
can make its flight in less than l/S hour, the cable and radio sta- 
tions will not offer it any serious eempetition, quite apart from 
the fact that the rocket delivers the writing in the original and 
preserves the secrecy of correspondence. 

The machine also is quite cheap. What is involved is essentially 
the simple work of a copper-smith. Besides, if properly handled, it 
can ascend ever 100 times. Per example, with a correctly-built oxy- 
hydrogen nozzle, I achieved a bum lasting SI minutes. With a large 
rocket nozzle SO — 30 times as large, this figure can easily be 



- 370 - 



maltiplied bj 10 because the dTnaoic cooling (of. p. 41 ) can be carried 
out much more eff ectivelx. Since a mail rocket bum* at the most for 
8 minutea at a time, the calculation results in 100 ascents. 

The onlj ezpensire part of these mail roclcet vill be the control 
doTice, but that could be transferred froa one rocket to the other. 

On this occasion, I nust comment on a grave error of VALIER and 
GAIL. In the book, "Into Outer Spae* bj Rocket Poirer", p. 76/77, thej 
describe a mail rocket that is to carrj a payload of tvo hundredweight. 
To prevent it from causing damage upon landing, it ia to burst apart 
beforehand, so that the letters land separately by parachute. 

But the empty rocket scarcely veighs as much as the payload. So 

if ve had sent only 50 kg of letters instead of 100, we could hare 

saved the rocket, according to ihis, (The delivery costs per deoagram 

of payioad vould be essentially no higher even vith smaller apparatus, 

for, vith a giv«ii eidiaast velocity, the performance of a rocket aainly 

°o 
depends on the ratio — } so a smaller rocket would use correspondingly 

loss fuel.) 

I only mention this incid«itally. I am figuring vith a paylead of 
30 kg and a landing weight of Just under 60 kg. 

Furthermore, these two authors state that a normal letter would 
cost less than 50 OU, which is correct. Twenty p«inies ture actually 
less than 60 DM. I find this estimate much too cautions, not least in 
eooparisen to ViLtER'S predilection for propagating ideas on ether 
occasions, 

c) The Rocket Projectile . Concerning the use of the rocket as a 
projectile, I have already said what is required in Chapter 13 . 



- 371 - 



S) The Rocket Airplane 

It i« ▼ell-knovn among experts in aeronautics that the perforoanee 
but also the dimensions and veight of the propeller airplane are 
fast approaching their llait. If ve disregard the possibility of a 
fantastio, thorougfalj rerelutionary inTentioUi the aeroplane in its 
present form t rigid vings, fuselage or boat fuselage, and netor 
▼ith propeller has liaited possibilities of development. We can hardly 
expect to get carrying surfaces irith a better ratio betveen uplift 
and drag, and propellers are difficult to improTe. The effect of 
inproving the profiles and forms of the wings, the foru3 of the fuse- 
lage, and the efficiency of the motors and propellera is to improve 
the flying perfomance only by a little ^ar thousand. Something can 
still be achieved by doiu^ avro^' vith vhole parts of the aeroplane) 
thus, for exaaple, by throTing avay the fuselage, ve get the "irings- 
only aeroplane" or "single-ving aeroplane", among others. But even 
this, in its present form, could already be near the limit of its 
perfecting capability. 

Only the aeroplane velocities eould still be increased if the 
path of flight could be moved to higher and more rarified layers of 
the atmosphere. 

Nevertheless, a propeller is not suitable for driving such aero- 
planes. First of all, it might be difficult to build propellers that 
could convert an acceptable aaount of the fuel energy into notion 
of the aeroplane in such thin air. Building motors that irork veil in 
such thin air could also cause some difficulties. Uoreover, the 
working capacity of the motor would have to be increased «aonnously. 
Namely, with supersonic speeds, the ratio between dr«kg and uplift 
becomes worse; therefore, the pull of the propeller would have to be 
greater while carrying the same load. Since the distance covered in 



- 372 - 



•ne second i» to bo considerably increased, such a motor would hare 
^to produce an unearthly number of horsepoirer; vith a gasoline motor, 
that votxld naturiJly entail an enormous veight. 















,»^ 'S"'^" 









k 






i • . ( <» f 

'? J' -1 

d r- 



Fig. 116 
(Munich Illustrated Press) 



Abore all, achioTing velocities considerably hi^er than those 
we have reached until today with propellers will hardly be possible 
because of the centrifugal force. It is easily shown that, with too 
high tip velocity, the propeller blades must simply tear off. In so 
doing, propeller size plays no role; improving the material only a 
very small one. Hence, for aircraft that are to fly more than 550 km/hr, 
other means of propulsion will have to be sought. 



Such a means of propulsion is the propulsion apparatus of liquid- 
propelled rockets described in this book. The well-knovn inventor, 
CLANSVnNDT, was the first to think of using the rocket motor. He made 
his first suggestions before 1870. GMSWINDT thought of making 
compressed air flew from steel cylinders and, later, of using dynamite 
cartridges; that as well as the opposition of a few scholars (cf. 
Vol. II) wrecked his plans. The suggestions of the engineer, GA£DICKE 



373 - 



(in 1912 he pnbliahed the then popular journal, "Uan Flies Without 
Hazard**! in the Haephestos Pub. House, Hamburg 86, under pseudonTis 
of CSJSSOS) still do not appear feasible in their form at the tlae. 
At present, cspeciallj ViLIER is attracting much attention vith his 
plan, "From Aeroplane to Space-Ship" (l already related something of 
the history of his invention on p. 208). TALIER'S plan is first to 
build simple aeroplanes idiich, beside the propeller, ilao have liquid- 
propelled rockets built into the carrying surfaces. Then the propeller 
is to be dropped altogether, tb« carrying surfaces are to become 
smaller and smaller, and the structure is to become more and more 
compressed until finally a space-ship similar to i^ model C takes 
shape (of. Figs. 116— 120). 



fr> 



r 



" ji^Vti^ -^T J^'* 















-> 



' \ 



«• * ■'i^-i -."kiA, 






Fig. 117 
(Monieh Illustrated Press) 



VALIER'S plans are rery attractive to the layman. The step-by-step 
change from the knovn (the aeroplane) to the unknomi (the space-ship) 



- 374 - 



■eema natural. Beaides, vith an inTention serTlng, abor* all, practical 
porposaa, obtaining funda for preliminary experimenta and deTelopmenta 
aeama to b* eaaier than vith a pure rocket apace-ship aerring rather 
more acientifie purpoaea and today appearing;: fantastic to moat people* 






-ar ^ ssr «>'^"' 



. -/^ 



7^ 









Jill' '»'!? 

I y 'J if j h n : 



v-<,* 



4 <r 



? .i \ 



Fig. 118 
(Uuich Illnatrated Freaa) 



X ggraelf did not take that courae but, from the firat, reatricted 
myaelf to -Uie apaoe-ahip that had amerged from the meteorological 
rocket. I vaa guided by the following conaiderationa t 



a) The qneation ia iifaether the change from the aeroplane to apace- 
ahip Till be poaaible at all. Aa I already ahoved on p. 285 ff, in 
rapid flight the rocket may heat up ao atrongly by friction of the 
air aa to make the change from terrestrial to coamio Teloeitiea vith 
longitudinal aurfaeea vhithin the aimoaphere altogether impoaaible. 
I am not a^ying that it mnat be ao, only that it could poaaibly be ao. 
I vaa anxioua to prore, hovever, that the apace-ahip ia certainly 



- 876 - 



po««ibl«. Mor««T«ry if on* t«k«« » closer look at Figs. 119 and ISO, 
en« *••« that tills i^parataa oan actually be used neither as aeroplane 
nor as space-ship. Is an aeroplane it laeks the correct aerodynamic 
font of the carrying sarfaoes and the right proportion of its parts. 
For a space-ship again its noxile surface is too small (that is 
recognized if it is eo«pared vith mj model E, Plate IV, or a^ model 
C, Fig. 17). Besidesi the construction of the apparatus is not suit- 
able for Tortioal ascent. Tet| it -vould haTo to ascend from the vater 
Tortically at first (ef. p. 348 ff). Starting from a launching ^[ttarter 
deck as represented in Fig. ISOb is entirely impossible. The air 
resistance vould be too great and the control could not be uniform. 
Final ly^ it irould be difficult to install fuel tanks in this apparatus 
that can be Jettisoned, in undirided, liquid-propelled rocket cannot 
reach interplanetary space and, hence^ cannot represent a space-ship. 
It is also precarious to have a manned space-ship alvays borne by 
the same propulsion apparatuSf whether it vei|^s aOO|000 kg or 3000 kg. 



r—^-^-^- --^ --■-" — -■■• —*r 



1 * /:i -■ I 



< I ■ 



■ ■' >\ 






;1 



■ t: ' ' 'if; ^ 



Fig. 119 
(Uunich Illustrated Press) 



- 376 - 



ViLIER did not have a ivo-stag* rockst in mind. This apparatus 
is to earry out space flights vithout jettisoning the empty parts (l). 
But eren if he had thought of dividing the rocket, that vould have 
been difficult to do vith this machine. The tail, for example, oould 
not be divided farther because it is too short. For setting the irfaole 
on top of a second rocket, the air fins would be coapletely useless 
•nd in the waj. They cannot vork as gas fins (cf* p. 266) and the 
last rocket of a space-ship no longer needs air fins, for it begins 
'Torkittg only at altitudes above 150 km. 

It is not exactly a recoouendation for VALIER'S technical abilities 
that he still has not grasped -Uiese things after occupying himself 
vith tiiem for three years, after studying the vritings of QODHARD, 
HOffiUNN, and myself, and after a correspondence vith me about them 
that could veil comprise 120 typed pages (cf. Vol. II). 

Assuming that the development fr<HB the aeroplane to the space-ship 
•eeurred relatively smoothly and by steps, except perhaps for one 
preliminary stage of this vehicle (I vill shov later that even that 
does not apply), that vay voxild have to be abandonned completely 
and tiie actual space-ship built on the basis of the theory only . 
The rocket airplane is not the preliminaxy stage of the space-ship 
but a side invention, although it vill perhaps be practicable. 

Concerning safety in the change from the aeroplane to space-ship, 
I vish to make the following remark : There can naturally be no talk 
of my rocket burning up since it only reaches its full velocity out- 
side of the eartii's atmosphere and later descends by parachute. That 
can be said on the basis of reflection. For the rest, the fol loving 
can be said on the topic of safety t 

At present, astronoiT' is the most certain and best known natural 



- 377 - 



science of all. Thait caanot be orer-eiaphaalzed vitb reference to laj- 
ra«i. One need only compare a physician's prediction concerning the 
occurence of an eel ipse of the sun or the appearance of a comet. 



m-, 






Fig. 120a 
(jLceerding to an adTertisement of ViLIER) 



With a space-ship in ether space, the mathematical conditions are 
precisely given and the connections betveen the lairs of nature are 
simple and calculable. And actually no unknown element enters into 
the prediction regarding the vorking of the single machine parts. 
(With exception of the atomization and eoabustion of the liquid in the 
propulsion apparatus. This is still not adequately knoim, at least 
in part; that is "wbj 1 place so much veight on its exact research 
before building the first rocket.) The air resistance -with Tertic«tl 
ascent is relatiTely veil knovn by the obserTation of projectiles; 
besidesi it only plays a minor role vith larger rockets. Hence, my 
predictions concerning the space-ship in interplanetary space irill 



- 378 - 



come true as surelj as a prophesied eclipse of the sun, and aj state- 
msQts Goncaming the technical details are, in the mala, about as 
reliable as the stataaenta «f a machine builder concerning a planned 
locoMotire model. 







Fig. 180b 
(According to an adTortisement ef ViLIER) 

On the ether hand, irith the rocket airplane ve are dealing vith 
the uplift of carrying snrfaoeS| etc.| in short, vlth aerodynamics, 
in vfaich the aathematical conditions are alwi^s given only as 
experiential average values of processes that are extremely coiplicat- 
ed and are difficult to survey in detail. They may not be transferred 
eff-hand to ether relationships of sise and velocity. Hoice, a demise 
in the expectations placed on the rocket airplane is naturally possible 
just as it was vitb the first aeroplanes. What do ve know today, for 
example, about the behavior of a carrying surface at supersonic 



- 379 - 



velocities or about the doTelopment of beat due to friction of the air? 
To Be, the -rtkj from the aeroplane to the space-ship does net appear 
to be a step-by-step noTemeat from the kaovn to the unlmoen but, at 
besty a detour across the unknom to the knovn. 

Hence I vas careful not to stix up the question of the rocket 
airplane with that of the rocket to interplanetary space, for, if 
the rocket airplane fails, the nnfeasibility of the rocket to inter- 
planetary space itself is still far fr<»i proved. I vas content to 
let ViLIER stimd as the sole inventor of the rocket airplane, although 
I have likewise collaborated in the worlting out of this idea. Other- 
vise the two Tould be constantly confused. I en leaving the whole 
responsibility of propagating this idea to him. As a writer, it is 
naturally nuch less harmful to him if one of bis ideas does not 
prove feasible. On the other hand, as a physicist, T must keep from 
making rash claims and strive to make only suggestions whose feasi- 
bility is established. 

All the same, I am supporting VALIER in his work. Since he is not 
a specicdist, I worked out the theory of the rocket airplane at his 
request and, among other things, calculated a model for him. For 
even though I do not regard the rocket airplcme as preliminary stage 
of the space-ship; I still expect various advantages for space-ship 
construction to come fr<»i developing this side invention. 

a) As I already said, the propulsion apparatus or the rocket motor 
is actually the only part of the space-ship whose operation we cannot 
completely predict on the basis of our present experiences. On the 
basis of our atomization and combustion experiments with combustion 
engines, we have maturally come to the point where we can say that 
it will certainly work, this waj or that wi^. But how it will work 
best we Just do not know yet. It would be desirable to have several 



- 380 - 



hiiDdr«d saaqil** of thia machine and operate it daily under obsezTation 
of the ^ilot. Thns nnich more experience could be gathered and coitlj 
prelininary experimenta avoided. 

b) We can only hope that, in so doing, a<wiething can be learnt 
regarding the behavior of carrying surfaces at supersonic speed, 
heating of the vails by friction of the air, etc. Perhaps ihe results 
▼ill shov that air-foil landing (cf. p. 304 ff) is possible, vfaieb, 
as I shoved there, vould considerably facilitate space flight. 

c) The idea of the rocket airplane is better able to popularize 
rocketry than is the idea of the mail rocket. 

Unfortunately, VALIER has not folloved all my advice, nor does 
his propaganda activity appear to have been suitable at all times. He 
has not penetrated the material very deeply (I vill shov that 
repeatedly). Vboever doubts l^e feasibility of the rocket airplane 
or the rocket space-ship merely on the basis of VALIER'S representar- 
tions Tonld do veil not to throv out ib9 baby vith the bath. Again 
and again I vas able to disperse engineers' and physicists' objections 
to ViLIEB'S project. 

First, I vould like to shov here hov I conceive of -tiie rocket 
airplane and then shov vfaat ViLIER has suggested and vfay I do not 
agree vith his suggestions. I can only give a general viev here| hev- 
ever, I vould gladly provide interested persons vith exact detailed 
explanations at any tiae. 

The fol loving conditions applj to the mode of operation of the 
rocket airplane t 

l) It can fly much faster than the propeller airplane. 



- 381 - 



8) In g«aeral| It waBt also tlj faster. According to vfaat was said 
on p. 207 ttf only in this iraj can the utilization of fuel be half- 
-v«7 efficient. 

3) So the aia must be to aehiere considerable relocities quickly. 

4) The main portion of the flight must be covered at a considerable 
altitnde. For, according to vfaat vas said on p. 83 ff* considerable 
Telecitiea can be attained only in thin air* 

6) Hence, it anst ascend in a Tery steep curre (similar to the 
rocket lines in Figs. 7S, 184) in order to reach the necessary altitude 
quickly. 

6) Consequently, the rocket nozzles Bast be so strong that 8—3 
times the tvll veight of the Tehicle could still hang frooi then. 

An importaat advantage over the propeller airplane fol loving from 
that, among ether things, is the fact that the rocket airplane cam 
ascend and descend vertically vfaile hanging by its nozzles. 

7) With regard to starting and landing, W9 need not keep slavishly 
to the example of the propeller airplane. The abrupt change from 
ascent in gliding flight to vertical ascent vould have to be made 
sooner or later anyvaj. With smaller machines, the idea could be 
considered of having the airplane stand on four vheels before the 
start (cf. Fig. 18l), to each pair of iriiich the elevators could be 
attached. If these studs are long enough, the apparatus can ascend 
from this position. During flight the studs veuld th«a have to be 
folded back, as shown in Fig. 182. 

If this start should not prove good due to the turbulence prodaced 
by the ezhanst gases, the ascent would have to be made from a launching 
pad as represented in Fig. 183. (Obviously, an aerodyuMiic problem 



- 382 - 




Fig. 181 



e^ 






Fig. 18S 




Fig. 183 



la iavolTed h«re alao. iMta eould b* conducted vith amftll 0od«ls 
idwtical in shApe.) The launching pad finally •taads almost Tortical. 
This tjpe of ascent anat be coneidered vith larger rocket airplanes 
because it is ispossible to Bake the feur studs on vfaich such aass is 
to stand sufficimtly light. One of the errors found in Fig. 180 is 
that the launching pad is too shallow, nie tip of the gigantic space- 
ship would flop dovn at the «ad of the pi at f era. (FroTided it veuld 
reaeh the end of the platform at all vitheut leaTing the glue.) For 



- 383 - 



that Batter ) it eonid iapoasibly hare the speed at the end ef the 
platfem required te make it fleat in the position indicated. With 
Tery large aachinee, asceok. fron the -rater voold be most expedient* 
Here the eloTator vith the etnde venld hare to be held dovn hj means 
of chains (ef* Fig. 183a); the chains vould also be required because 
they alone can hold the apparatus in a vertical position if the 
nozzles do not ignite at the same time. As soon as all the nozzles 
bum, the apparatus vould lift itself from the mter together vith 
the chains^ ufaich could then be Jettisoned. 




Fig. 183a 

I cannot recommend the type of ascent suggested hj HOEFFT (cf. 
Vol. II). In the first place, that vould require completely simultan- 
eous starting of the nozzles. Secondly, oTsn in the most faTorable 
case, the ckpparatus vould glide on the surface of the vater far some 
time, at vfaich larger vaves vould shatter the thin vail, and the 
machine could not become air-borne at all because, at the instant in 
vfaich only the rear edge touches the vater, a torsional moment vould 
arise vfaich vould burl the tip into the vater. 

In landing, the aeroplane vould float at lover velocities because 
of the smaller veight and hence it could land in gliding flight. 



8) The need of attaining a higher velocity and the possibility of 
ascending vithout a take-off run put a greater load on the carrying 



- 384 - 



•nrface* and necesaitat* compact conatmctlon. Tha relatirely light 
baild of today' ■ propeller-drirata airojtlanea resnlta from the necea- 
aity of alretkdy floating at a lov Telocity. Hence I aoggest building 
the rocket airplane vithout a fuaelage, eaaentially eonaisting of 
only a single thick carrying surface. This carrying surface is to 
accommodate the nozzles provided -with regulating rods, as indicated 
in Fig. 25, as veil as the pilots' room. The intervening space is to 
be filled irith propellants. It might also be feasible to fill the 
surfaces of the elevators H irith fuel and use it first (cf. p. 266). 
That facilitates vertical ascent^ but the horizontal control becomes 
more unstable than vi-Ui unveig^ted elevators. The control cabin must 
be airtight and, if possible, permit a clear vieir on all sides; 
hence, the bott<HB must be of glass plate. That can be covered vith 
vire uetting to protect it. 

9} With this compact type of constiniciion, t'le mechaaical advantage 
is lost w?iich birds aud lightly-built aeroplanes drair froa velocity 
differttiees in p^atj irind (cf. e.g. WIENER i Science of Flying Foirer). 
At higher altitudes, this mechanical advantage would be lost anyvay, 
for the air aovecieni becoues unifonn higher up. Besides, here the loss 
favorable uplift conditions at superscmic speeds must be taken into 
account. Even in the best instance, I only figure 'urith an angle of 
glide of 1 > 5. The greater expenditure in fuel is the price ve must 
pay for the increase in velocity. 

lO) The fli^t would proceed someirfaat as follows : 

A. Steep ascMtt in a curve similto* to the rocket lines descrjLbed 
on p. 227 ff. At an altitude of 80 to 40 km, the curve changes to a 
horizontal line; during this part of tlie flight, the acceleration 
should be as high as possible. At the end of this part of the way, 
full velocity of tiie magnitude of the exhaust velocity c should be 
reached. 



- 385 - 



B. Horizontal flight wliii a velocity close to e '• 

C. Shutting off the motor) descent in gliding flight. 

D. Starting the Jets once aore, uprighting the apparatus^ 
decelerating the Telocity, and landing rertieally. Fig. 184 sehena-- 
tically ahova the trajectoiy of a rocket airplane. I did not draw 
it true to nature, othcrvise l) it vould have been too lev, 8) the 
nature of the portion C vould not have been apparent. Actual lyi it 
ia a curTed line that hardly dropa at the beginning. 3) The portion 
D vould not hare been Tiaible. 




ll) Gaaoline, keroaenei or alcohol could aerve as fuel. Beaide 
that, liquid oxygen vould have to be carried along. If one vanted to 
utilize the atmoapheric air in combustion, the pumps required vith 
the lov d«iaity of the air and the enoraous quantity of fuel to be 
burnt vould be too large and too heavy. The injection and combustion 
of these stuffs vould be similar to that vith my rockets. 

The fuel tanks vould have to be under excess pressure. Hwace, 
vith coopaet censtraction of the rocket airplane, the principle of 



' I hare likevise investigated this part of the flight, since this 
book is supposed to contain a complete theory of the rocket airplane 
in vhich this ease anst also be taken into account. According to the 
synergy principle, it is to be expected that the rocket airplane vill 
vork better if the fuels vhich it still has at point 1 are immediately 
utilised under the highest possible acceleration, because it thus bums 
at a higher velocity. I vill return to this later. 



- 386 - 



rigid filling (pneutaatic str«ngth) ooald also b« applied. In thia wvjt 
alBoat aa nmeh fnel could be taken along a« with a liquid-propelled 
rocket) about 5—7 tiaaa as uuch hj weight as the aaobine. 

is) When calculating the fuel consunptiMii the following are 
approxiaate guide lines i 

On distance Af the initial acceleration is 10 m/see « Tith werj 
large aachines^ it could be somewhat higher. With those being consider- 
ed, it cannot be higher, for here the relocitj vast not exceed the 
▼alne t (cf. Chapter 8). At the altitude of 10 ka, the air resistance 
(cf. p. 170) would be noticed as most inconvenient. Here the aero- 
plane would hawe a Telocity of 8IM) a/see and the flight direction an 
inclination of about 50* toward the horizontal* In this ascent, 4/lO 
of the total ideal propulsion would be lest through air resistance 
and grawitatien. If, at the md of tJils stretch, the Telocity is sup- 
posed to be 





▼l - «» 


then 






T « 1.67«c, 


at which 





m must equal 4*5* m. (cf. p. 60 )• 

On the map, the place of ascent would be a distance of 50 — 150 km 
from the end point of this curre. Fomulas (l35) to (l59) apply to 
the flight Ml stretch A. 

With the reaaining fuel, the rocket airplane then traTels the 
distance B so that t is constantly kept equal to e* Here only the drag 
is OTorcome. At the same time, the rocket airplane is still being 
lifted so that it always remains at the altitude in which, with a 



- 387 - 



Telocity of c ka/seci th« ratio betvoen drag and uplift i« tho Boat 
advaatageoua. Since the uaae ia ateadilj decreasing} it nnat steer to 
OTor higber lajera of the ataospberei yet thia rise of a few km plaja 
no role irorth mentioning on such a long stretch. 

Since the drag p emoiints to l/S of the Teigbty according to the 
lav of impulae, the following must be true t 

p dt ■ — 'm'S'g'dt - dB*e. (190) 

5 

From that follows 

^ - JL.dt 



6c 



or 



^"•S5"5T^-^*a"V <**^) 



or 



»1 5?^-(*fi-V 



5-0 « * (19a) 



We can find the l«igth of diataace B, if ve talce B — (t^ — t.)*e. 

The calculations for distance C are made easy by the fact that} 

with non-operating nozzles^ we maj use the theorem of the eonserwation 

of energy (cf. Chapter 18). At the beginning of this stretch C, the 

1 8 

rocket airplane has the kinetic energy SL ■ -^im^'C and the potential 

« 8 * 

energy P^ - Bn'g'h^i where b^ represents the altitude of the y^icle 

abore the ground. So its total inherent energy is 

Eg - K, + P,. (198) 



- 388 - 



A* I CAid on p. 307, vith the controls set corroetlj, the aoro- 
plan* milt sink ao that it aliraya fli«t in that lajAr of the atnosphore 
in vhich tlio uplift ratio ia the moat farorablo -ri'Ui tho T«looit7 it 
has at the time. If p ia the force needed for propnlaien and C the 
diatance eorered during diaaipation of the Mergj E^t then obrioualy 

Eg - p'C 

(here ve maj eqpiate the diatance en the mt^ vith the actual diatance 

eorered;. If "we aet p ■ ■ ■ i ire obtain 

5 

We calculate the period of flight on thia atreteh aa follova t 

Obrioualj 

dE - - pT.dt. (195) 

fVirthermore) according to (193), 

dE - dE + dP - m^T'dr + m^'dh (l9d) 

and 

ryi^ - «"jg. (iw) 

Therein ^ ia any conataat dependent on the conatmotion of the 
aeroplane. & ia the air danaitj. Thia follova (19T) t 

mg - 
Ing ■ In — ^- - * luT. 

' it 

If|S deaignatea the air denaitj on the earth' a anrface, from 
(34) thia follova > 

h - H (ln8 - Infi ) - H (in^^ - In ^^ + 8 In t). (198) 



- 389 - 



FroB that, this follov* bj differentiation t 

dh - a H ^. (199) 

From that, using (195) and (l96) in the elimination of d£ and dh, 
thia follovs t 






dl = 



(201) 



m.2 i , „ „ / 'J. 1 






If ^e mibatitate the exhaust velocitj c « 1500 m/sec, assume the 
lest attainable mass 

p > ^ m^g, ve find that 



mo 
highest attainable mass ratio to be =- - 7.2, and finally substitute 

^ ma 



"i "a 

Then, for the longest flight distance, ve find that 
A B 100 km; B - 450 km; C - 800 km. 

So the farthest attaincUile flight distance vould be A + B + C > 
1350 km. 

For the period of flight ve vould obtain : 
t, — t - 860 sec, 

10 

t^ — t. ■ 300 see. 
If ve set T. m 50 ra/«ec, t. — t. - 8250 m/sec. For t. « 30 m/sec. 



- 390 - 



to - ta * 3330 sec. This flight voald laat roughly •& hour. 

As I alrsady said on p. 385, the fli^t on the stretch B contrwiicts 
the requirement of burning at a high reloeitj. Let us suppose ire had 
continued fljing vitb the hi^^est acceleration at point (l); taking 
the jsachine into account, tiiat could be quite considerable, for, 
at this high Telocity, the rocket airplane vould quickly reach higher 
altitudes eren -wiib a shallow angle of ascent and, other things being 
equal, vith cm altitude increase of 10 to 11 ka, the value of t 
doubles. Therefore, the acceleration need be restricted 
only on accotint of the passMigers. 

/ 8 
Assuming the acceleration amounts to 30 m/sec and, for our calcula- 
tion, ve estimate the decelerating influences to be 8 m/sec' (perhaps 
that is too low a figure since at the beginning the rocket airplane 
flies on a trajectory inclined 8* upward. To compensate for the error 
I will round off ▼* downward). In this case, b^^ - 38 m/sec*. Since 

T - - 750 m/sec, ▼j - ▼i - ^^^ m/sec. Namely here 

^"^1 ^8 

^x8 " ^za * 

Thus, T. would have equalled 8160 m/sec and 

*8 - *1 - ^1 «^ ■«» 

8 

and the stretch B of the wvj would have become i 

B - (t- - tj -* = - 88. 1.83 - 40 km. 

■ * 8 

Tbe aeroplane would have had to climb another 9 — 10 km in order to 



¥> 391 - 



tlj under the moat adTantageous conditions vith the nev Telocilj- and 
the amaller mass. If, in the preTioua example, point 1 had an altitude 
of 50 kn, point 2 has an altitude of raa^ilj 80 Im. Therefore, the 
potential energy i« 

P. * 600,000*ai. micg, 

the kinetic energy would be 

Kj, - |*"a'^a " *»»>0»OOO.mj mkg, 

and, according to (194), ve find that 

2,900,OOO.S.m2 

c - — -rx -* - 1450 *■• 

10 •m^ 

Thus, the idiole flight distance Tould be expressed in figures rounded 
off to hal res of 100 Ian { 

A + B + C - aOO + 50 -t^^ 1450 - 1700 fan. 

In this case, the rocket airplane flies farther with the same quantilj- 
of fuel. In addition, the same flight distance vpuld be coTered in a 
shorter time. 

Nererthel ess, one remark may not be altogether superfluous here. 
Vith such high Teloeities, ve do not fa&ov hOT great the heat formation 
▼ill be due to the air friction and whether ve irill be able to control 
it* I am not afraid of minor heat formation; en the contrary, it has 
two adrantages t 

l) It makes artificial heating of the observer's cabin at higher 



- 39a - 



oltitodes vnnecsuy '• 

t) The ateMi derired fr«a th« eooliag v^ter provide* • good lot 
of propoleloa if vo let it flow out throoi^ tlie nosile. Ihat (• 
•iq>eei»ll7 conToniefat ie the eirevuuteace that va can let the oooliag 
v»ter Tttporize at rooei temperature. So ve can iaTo eoae fuel at least 
a* far the econoay is concerned, although not vith regard to the 
theory of rocketiy. 

iaother fseation vfaich 'rill likewise have te be onawered in the 
future ia whether the nosKle* can actually stand burning for 9 ainutea; 
the aolution nay be to have the rocket airplane bum for a short tiae 
only and repeatedly let the nossles cool off for sone time or to equip it 
▼ith alternately vorking noszles. 

Bie flight distance increases as the square of the exhaust velocity 
and directly as the uplift ratio. Using kerosene ve vould obtain esdianat 
veloeitiea around 1800 m/sec and flight distancea of 8450 Iob} using 
giaseline or ethyl alc^ol esdiauat veloeitiea of up to SOOO a/sec and 
flight distancea of up to 3000 Ion. But that vould be the utnost that 
could be achieved vith a siaple rocket airplane. If visionaries here 
and there dreaa of crossing the Atlantic Ocean (ViLI£R| for ezaaple, 
mrites in a proelaaation t "Such aaohines ... would aanage distances 
. . . equal to that frwi Europe te iaerica . . ."} HOXFFT daiaa the 
saae for his R.H.V.)| that anst be relegated to the reala of fables. 
Without propulsion rockets wfaiob can be Jettiaoned later or siailar 
auxiliary aeana that can certainly not be achieved. 



f One caU) at the aost, suffer from cold during Uie last quarter to 

half hour before landing. But the problea of freesing will not be 
acutO} for, in any case, the flight will be undertaken so as to land 
in daylight, and above 7 loa the sun is already quite warn. 



. 393 > 



For l«ng*r dlataacea, it vill procuaably be best to conetmct the 
whole apparatofl of t jet propulsion aeroplene* (of. Pl»te III, Fig. C), 
the larger (Fig. b), rear one of iriiich playa the role of a propulsion 
rocket aiailar to the alcohol rocket of Bodel B. When ita fuela are 
eadliaaated, the co-pilot stationed at H guides it to earth in gliding 
flight while the foremost aeroplane (aain aeroplane, Fig. A) continues 
in aole flight. 

Fig. D ahova one aide of the aain aeroplane •viiHx the upper vail 
remoTed and the outside nocsle out in the middle. Fig. E ahowa the 
aame nachine part in profile. P repreaenta the puop chaobera, here 
having the fom of ejlindrical pipes and, at the aame time, aerving 
to reinforce the front e^ea. are the erena, v the collecting and 
feed pipes, F the nozzleai theae viden tranareraally, at firat, until 
they touch each other and then they -wiim. Tortically. Therefore, all 
the nozslea end in a aingle nozzle ehenber abated like a triangular 
priaa into iriiich the front edge of the auxiliary aeroplane fits. Aa ia 
seen, the rods of the main aeroplane, irtiose function it ia to bold the 
atabilizing aurfacea during free flight, are conToniently laid orer 
the front part of the auxiliary aeroplane and faatened there. That 
makea a aolid connection poaaible (for contraat, cf. R.H. 6 or E.H 7, 
Vol. II). 

I have left out regulating roda becauae here they do not meet 
the retirements of the criterion on p. 30 , 

True, the vide aperture angle of the nozzle chamber ia avkvard. 
I do not believe, hoverer, that it vill ham the effect of the rear- 
vard thruat. If the nezzlea operated in a vide vaeunm apace, the 
out-*flov Telocity vould likely be 10 — 80 ^ lover than vith 7* nozzlea. 
Here, hoverer, the gase* merely enter a cylindrical vacuum caused by 
the rocket airplane, at vfaose edges they are stopped. In so doing. 



- 394 - 



they directly serre mi a prop for the on-coming gases. Fig. F shovs 
that the air jacket here plays a role similar to that of the less 
conTergmt extension of the nozzle and the gas fins of the hydrogen 
rocket of laodel B. I have only drami the flov lines haphazardly here. 
At present, their ceurse is actually not yet knovn. According to vfaat 
vas said on p. 267 concerning gas fins, this effect could be strength- 
ened if the el orators vere brought forward to the edge of the nozzle. 
Hence, I do not consider this form — rery conT«nient for reasons of 
construction — as compelling. 

For the rest, the last word here is naturally reserTod to experience 
Tith nozzles of this form. If it should not prove itself, the solution 
sketched in Fig. G is still possible. Here the nozzles are placed one 
abore the other in pairs. 

This form has the disadvantage that the apparatus cannot carry as 
much fuel. Perhaps, bovever, one circumstance helps us outt I believe, 
vitfa such long pipes, the ot^ can be dispensed vith, since here the 
fuels have sufficient time to bum. In this case, the natural thing 
to do vould be to consolidate atomizer, ovens, and nozzles in a single 
cone-shaped appcu-atus and install it as shonn in Fig. G. 

As is apparent, I am leaving the solution of the problem vith this 
apparatus open in part. I consider it prei&ature to irork out construction 
plans in detail before the natural lavs vfaich oust be observed are 
thoroughly knovn* 

I have not indicated the construction of the auxiliary aeroplane 
here, since ve do net see too clearly on this point. In principle, 
it should be conceived of like the alcohol rocket of model E (cf. 
Plate IV). 

Now the question arises whether, after the fuels are edausted, 



- 895 - 



such a large and coi^aetlj-imilt aeroplaa* a« th« wixiliax7 aeroplane 
can still land in gliding flight* If this ahould not auoceid (here 
it ia Mice again eTident hov problenatie the vhole idea of the rocket 
airplane atill ia todiqr) one eould naturally think of a paraehute 
landing vith a retro~rocket (aa 'vitb the alcohol rocket of nodel E). 
Nerertheleaa, I find it more coaaendable to use numerooa) aaall} 
unmanned propulaion rockets which land singlj hy Beans of parachute t 
a eolation vbieh could also be considered vith space-ships. *<■ Then 
the launching site Tould naturally have to meet certain conditions 
(large vater surface or at least aa area suitable for the descent 
of the secondary rocket, large aeadov, not too much forest or culti rat- 
ed land, eto.). The place of descent of these secondary rockets itself 
could also be controlled only to vithin a radius of 10 km, 'which vould 
still farther limit the usability of the overseas rocket airplane. 

Such a machine could eonfortably cross the Atlantic Ocean, and, 
if liquid hydrogen were also used in the main aeroplane (indeed only 
beside acetylene, lAich will prove to be better higher up than in the 
lower atmosphere, or gasoline), it could reach any point eA earth 
since it could attain circular velocity. 

If one does not w4sh to fly as far as an undivided rocket airplane 
eould go in the eztretae ease, the stretch B must be shortened first. 

If it drops out completely, then --^ - 4.5 and, for e > 1500 m/see, 

the flight distance is approximately 1000 km. 

Still shorter flight distances are achieved if, from the very 
beginning, the velocity is not forced up to v > e. Then especially 
the distance covered daring the dissipation becomes correspondingly 
shorter* 

Even -with rocket airplanes which are not supposed to fly far, 



- 396 - 



heavy frontal area loading should be aimed for in order not to lose 
too much fuel to air resistance at the beginning. — Here the welgbt 
of \he motors, iifaich make up most of the ireight of the propel ler-driren 
aeroplane, hardly plays a role; the propulsion apparatus are very 
light and increase the weight by scarcely 200 — 500 kg. 

Utilization of the fuels t A rocket airplane -reighing 4000 kg -with 
payload but without the propellents irould require 24,000 kg of propel- 
lants to fly 1700 km. As stated, I believe that ■with -ttie peculiarly 
compact construction and the pneumatic rigidity as well as the relat- 
ively high specific weight of the propellants it can accommodate so 
much fuel. — With the propellant, one can figure 1 kg gasoline to 4 - 5 
kg oxygen. So the flight would require 4000 - 4800 kg gasoline and 20,000- 
19,200 kg oxygen. This fuel would cost 3000 - 5000 M. The payload could 
araount to 600 kg, so that the cost of the propellants alone per kg of 

payload would be 5 — 8 M. Since the delivery is rapid, that would still 

""o 
be a reasonable "3um. For a SOO^on flight, ^ = 4.5. The vehicle just 

described (provided there is sufficient available space) could carry a 
payload of 3200 kg beside 21,200 kg of propellant. Here the cost of 
the propellant per kg of payload would be only 1.20 M. 

Naturally, if I were the builder, I would not immediately build a 
vehicle with a capacity of 28,000 kg (although, in length and width, 
the vehicle would hardly be larger than a middle-sized monoplane of 
today). I would first experiment with the atomization and combustion 
of liquids (cf. Vol. Il) and examine the eadiaust velocities of rocket 
nozzles. Then I would build the mail rocket ant' rith it acquire the 
necessary experience. Only when the mail rocket works satisfactorily 
would I build wide, flat rockets similar to JUNKER'S all-wing airplane 
in order with it to obtain the needed experience concerning the behavior 
of such apparatus at supersonic velocities. 



- 397 - 



Only vhen everything functions faultlessly ' in all these prelia- 
inarj stages vould I build a small pilotless, autoaaticallj-controlled 
model for the sole purpose of doing research on the starting and 
landing of rocket airplanes (length of the studs, rapidity of ascent| 
etc.)* Then I vould build a large aeroplane according to this pattern 
irfaich can carry a man aloft and rise some 50 km. Instead of iiheels, 
I TOttld use 4 pontoons at the beginning and (so as not to hare to 
make t^e pontoons too large) set the irtiole on a r«ift vhen starting. 
Later I vould try landing vith vheels on land* With this aeroplane 
I would, above all, investigate the behavior of the carrying surfaces 
at velocities upwards of 100 m/sec. 

fiasietdly, this experience can also be acquired by ot^er means. 
JOHiNNES WINKLER, Breslau, suggested letting air from a funnel -sliaped 
nozzle floT against a carrying surface at supersonic velocity. Natural- 
ly, -Uiat is possible only up to 460 m/sec; the air cannot be forced 
out faster that that* Dr. BUSE&UNN is at present conducting these 
experiments at the Aerodynamics Institute in GSttingen. I do not knov 



' It is evident from Fig. 184 that the jet-propelled aeroplane must 
ascend like a rocket (othervise ve vould have ve^8 r S. Cf. p. 92 ), 
so ve cannot build it before ve have the necessary experience regard- 
ing the ascent of rockets. 

In addition, the propulsion apparatus using liquid fuels is 
indispmsable for rocket airplanes, (in the first place, the required 
mass ratios cannot be obtained vith povder rockets and, secondly, it 
is impossible to build a povder rocket that is safe to operate, as 
the numerous rocket explosions this year have taught. Cf, also Vol. II.) 
Before it is used in rocket airplanes, however, it must be adequately 
tested in unmanned apparatus. 



- 396 - 



the results at tiiis time ', 



A.B. SCHERSCHEVSEY vould like to increase our k&oirledge in this 
area by shooting hea-vy plane models from catapults «ud photographing 
them during flight in the same vay as is customary with projectiles. 
From these photographs, conclusions can be drawn regarding occurring 
forces. 

Nerertheleas, I beliere we will be able to dispense with experiments 
with manned models of the rocket airplane itself. 

I would alter the rocket airplane with one occupant in so far as 
that mi(^t prowe necessary. I would then inmediately build the 88,000- 
kg refaiele according to this model, for I do not beliere in the practice 
ability of a rocket airplane iriiose most adwantageous relocity is t<400 
m/see. We can achieve such a high most advantageous Telocity only if 
the weight in relation to the profile is wery great, and that can only 
be the case with heaty machines. Nor would it be a great help if we 
made the carrying surfaces thinner, for here the air resistance does 
not depend only on tiie cross-section but also on the linear coefficient 
of friction against the wing surfaces . During ascent, the rocket 
airplane must be regarded as a flattened-out li^id-propelled rocket 

8 r S 
and if, with the latter, t. is not much greater than — — , it remains 

* c 

stuck in the air, so to speack. Anymy, the dead weight would also 
become too great. 



'In the meantime I have been informed ef measurements at sonic and 
supersonic Telocities (Reports of National idwisory Committee Aeronautics 
U.S.A. -No. 807, 1984, and No. 855, 1987). They were conducted on thin 
profiles and resulted in a lift-drag ratio down to n - 0.1. This was 
a Tery eantions estimate of mine. 

'^ Strictly speaking, this consideratim would no longer be walid for 
supersonic speeds; we are here simply dealing with a small value of t. 



. 399 - 



Caaoftring th« rocket ^irpiaa» «md the proprilw-driTcn airplip* i 

A. Idrantages of the rocket airplane t 

l) High Telocity 

S) lomenfle operating efficiency of the noior in cogq>ariaon to 
iti veigbt. 

3) llakea poaeible heaij ving loading and thereby eoapaet 
conatmction. 

4) Fliea at high altitude*, at vfaieb irregular ■OTonent of the 
air Carrie* lea* vei^t end, in ease of var, the rocket 
airplane ia unaaaailable by oneogr veaiioiia (and, beeanae of 
ita apeed, unaaaailable alao fay rooket airplenea of the 
eneoy). 

d) Largely independent of the veather. It doAa not matter to 
the rocket airplane, for example, what the veather ia like 
in region* over ufaich it mnat fl^. What i* dangerou* i« 
only air hl^ly charged vith eleetrieity (thunder a tonw) 
at the place of aaoent or fog at the landing place. Pre- 
caution* can be taken against that by telegraphic -veather 
report* from the place of landing. 

0) The rocket airplane can hang by ita noislea, ia thua aecored 
againat a tail alide, and can aacend vertical ly. 

B. Siaadvantage* of the rocket airplane * 

1) Neceaaity of hermetically aealing the pilot'* cabin and 
artificially producing the air he breathe* (because of the 
nitroeyl compound* present in the etratoaphere) . 

a) Bicker flij^t coat*. 

3) Vertical aacent vith a connter-prearare of SO m/aec • 

4) Liquid oaygen muat be available at the place of aacent and 
naturally alao at the normal landing place. 



- 400 - 



Objection* to the Idea of th« Boeket Airplane 

Most of them are based on misapplications of the energy concept 
and are refuted hj vfaat was said in Chapter IS. Of ih« rest, I need 
onlj aention a single one at this place. OARSiDX and Major BAVER 
point out iha,t a fast-flying aeroplane cannot describe any cur res 
because of the high counter-pressure. That can be countered by saying 
that the rocket airplane need describe no curres as long as it flies 
»o fast. In any casoi the involuntary rotary movements vill only be 
small) for it flies above the cirrus clouds where turbulent air 
movements are scarcely to be expected. Besides, the air is so thin 
there that it only gradually follows lateral air motion (cf. p. 304) 
or an awkward set of the controls. In ascent and landing it does 
indeed get into denser, turbulent layers of air, but here again its 
velocity is only of tiie same magnitude as that of the usual aeroplanes. 
Shortly before landing, for example, it will hardly exceed SOO ka/hr. 
And with its compact construction, turbulent air movements cannot 
harm it as th«y do a lightly-built propeller-driven aeroplane. Since 
it <mly flies slowly at last, it can describe curves and spirals at 
the oad of stretoh C, so that it can descend at the intmded landing 
place just as well as an aeroplane. 

Vi^IER'S suggestions . I would now like to subject them to a 
critical examination. 

Figs* 116 and 117 represent aeroplanes with propellers and rockets. 
These rockets can facilitate starting the aeroplane since they quickly 
bring it to a high velocity. Besides, th^ can be of value when tiie 
motor fails. In high flying, they can raise the ceiling of the aero- 
plane by 500 — 1000 m and increase the flying speed (at the cost of 
the flying range, it is true) by a few km/hr. In mom«ats of danger, 
such nozzles represent an effective help for the motor provided th^ 
have not already used up their fuel at the start-off (danger of side- 
slipping, etc.). 



- 401 - 



All in all these nozzles represent a convenient secondary apparatus 
of the vehicle. I can really not see it as some kind of preliminary 
stage of the rocket airplane. Also, they will likely help to extend 
our theoretical knoTrledge but little. The only thinp that can be learnt 
from practice is the mode of operation of these nozzles (provided the 
laboratory experiment preceded it) . All the other innovations, such 
as increasing the number of nozzles, vertical starting, etc., are not 
made gradually but abruptly, 

VALIER conceives of effecting the gradual change by only naking the 
fuel -carrying irings thicker and first doubling the number of side noz:ales 
and then triplicT them. He forgets, hoirever, that he thus arrives at 
unusable intermediate forms. Fig. 118, for example, could no longer 
really start in the way aeroplanes do. I c^self suggested to YALIIH 
starting from a platform (cf. Fig. 123) since he iroTild have nothing to 
do irith starting as I represented it in Figs. 121 and I23a. But in this 
case also, the fuel consumption -would increase by so much and the velo- 
city so little (the construction is still too light) as to make one 
doubt whether this vehicle will ever be built. Concerning Pi's^ 118, YALIER 
writes i "One again the rocket motors are being strengthened ard increased 
in number, so that the propeller can now be dispensed with. We obtain 
the so-called rocket airpleme, a machine that still starts off like an 
aeroplane and flies using the effect of carrying surfaces". It is not 
quite clear to me how he conceives of the "aeroplane-type start" of a 
machine that weighs in the neighborhood of 500 kg per ai* of wing surface. 
It would be possible to start off with the use of a starting platform. 
Yet, the machine is still not quite suitable as a rocket airplane, for, 
as is seen at first sight, here v^^ is scarcely 100 m/sec with vertical 
ascent, which, as we saw, is much too little. I do not believe the 



The numerous experiments with powder rockets are as good as useless 
scientifically. 



- 408 - 



nachine would flj ftren 100 ka. VALIESl thinks of flying at yelocities 
of 500 a/aoe with thia machine. Naturally, it can fly that fast, but 
than 4.t Till moat auraly gat atoandad in the alaoaphere. Besides, 
with T - 500 m/seo, the utilization of propel lasts is still rery un- 
satisfactory. Discussing minor avkward details of the construction 
forms suggested is not necessary. VALIGR is no engineer, he only lets 
himself be called that. Since any engineer could naturally aroid 
these drawbacks of construction, they are not essential to the ques- 
tion whether the rocket airplane is possible. (Here I am thinkiiig of 
^e w^y the nezsles are attached, for example, in vhich connection 
I refer the reader to what was said on p. 397. It is difficult to 
reconcile the way the turbulence of the exhaust gases in the oven is 
represented with the principle of dynamic cooling, etc.) Concerning 
Figs. 119 and 180, I hawe already said what is necessary. 

All in all, it can be said that the rocket airplane does not lead 
froa the aeroplane to the space-ship, but it is a promising side 
iarention. 

Recently, HOEETT of Vienna has ctlso caused much talk with his plans 
for a rocket airplane. I will report concerning HOEFFT'S suggestions 
in context in the second volume. 

The idea of the air tank is related to that of the rocket airplane. 
It is a large, thick-walled war rocket with or without armor plate 
that is to fly into enemy air fleets in order to destroy them by gun- 
fire, impact, incMidiary, and turbulence. 

Since, today, nothing certain can be said about the rocket air- 
plane, naturally still less can be said about such a war rocket. Hence 
it is superfluous at this place to do more than mention the idea. 

Before I oonolude this chapter, I cannot help but emphasize that 



. 403 - 



the first stages of 1117 iuTention of the rocket will certainlj 7ield 
a reveane. We learn abont the financial significance of tiiat fact 
from LEI'S popular compilation) '*Tbe Possibility of Interplanetary 
Travel" (Hachmeister and Thai, Leipzigyl928). In it, the vell-knovn 
Vienna mgineer, GUIDO t. PIRjJDET writes (p. 320 ff) ; 

"If, for the solution of mj problem, a method prowes effective > 
it will not be applied isanediatelj, but first a con9>arison with other 
existing methods will be undert^en and the one chosen which proves 
the most advantageous with respect to performance, expenditure and 
risk. 

In this connection I must make a short excursion into the field 
of technical eeonoiqy* In general, we can subdivide technical structures, 
whether machines, buildings, bridges or highways, factories or trans- 
portation facilities, etc., into two large groups. 

Group I. 

Group of the indivisible units or the unfinished futile works. 

For example, if the construction of a tunnel or bridge is begun 
but cannot be completed, the whole expenditure for the half-finished 
tunnel or bridge is wasted because the serviceability of half a bridge 
tiiat reaches only to the middle of the river or of half a tunnel 
equals zero. 

Group IZ. 

Group of the divisible units or the completed active works. 

If, for example, a highway 100 km in length is to be renewed and 
the work is discontinued at 50 km, that does not represent a useless 
expenditure of the cost of the 60 km, since an improvement has beoi 
made in the transportation facilities of the respective region, etc. 



- 404 - 



Guided hj th« Ti«vpoiat of indiTiaible and diyisible technical 
vorke ire dnce nore vant to consider the presmt problem of space 
narigation . 

In «o doing, -w naat atate that three or four different etagee 
can be dietinguiehed vfaieh can be attained in sncceseion. 

i) The meteorological aggregate. Concerned ie a projectile that 
makes it possible to lift a meteorological apparatus to an altitude 
of some 100 — 800 km and let it return to earth again undamaged by 
means of a paracbute^uch a projectile can be used at any point desired 
on the earth's surface. Requirement t Telocity v^ of ca ISOO to 1800 
km/ see at an altitude of ea 30 km. 

8) The long-distance projectile ' is usefnl for coping ^ith 
further stretches of the earth's surface — say 500 km and higher. 
Requirement t relocilj- r^ of 4 — 7 km/sec (depending on the range of 
the oTer-spaaniag are). 

Naturally I the use of this aggregate is likeirise not to be restrict- 
ed to any specific point on the earth's surface. 

3) The moon aggregate is supposed to be suitable for circling the 
mooui for example, and is thus the preliminary stage to point 4. 
Requirement t ca 11 km/sec outside of the atmosphere* 

4) The manned interplanetary aggregate. Requirement t ca 18 to 17 
km/see - t^ (see par. l). 

If we had found, for example, that the so-ccaied *n)ROUET Tunnel 
Plan" is suitable for leaTJng the earth, ve vould hare had to ask 

^' I do not si^ 'haeteorological rocket" and "long-distance rocket", 
etc., delj.berately since I want to make another attea4>t to leave open 
the choice of method. 



- 406 - 



oiira«lT«« in the lig)it of oar foregoing stadj- on •eononica t I« tbi* 
■olntion an indiriaible or a diriaible tochnieal vork ? 

We find that it ia entirely unauitable for aolTing problena I and 
II ainee ita Applicability to the meteorological aggregate and eapecial- 
ly to the long>diat«nce projectile is reatricted to the atarting 
tunnel vfaich haa a fixed location and ia not oTon aringable. 

If I hoverer, one proceeda according to the principle of the multipli 
atage rocket, it ia quite a different natter. It ia then a diriaible 
technical irork and can alao be uaed for atagea I and II. Thia econonic 
adTantage of the rocket cannot be emphaaized and underlined enouj^ 
aince thereby the actualization of the rocket ia atripped of erery 
economic riak. 

Uaing the rocket principle as abasia, each of the atagea mentioned 
haa practical Talue and paya for itaelf. 

Thereforoi in contraat to onr example of tunnel or bridge conatruc- 
tion, it doea not matter from the atandpoint of interest on inreatoienta 
if tlie meteorological rocket project ia halted for a fev yeara or 
perhapa the long-diatanee rocket bogs dovn for aereral yeara because 
they are aelf-eontained and economically independent unita and yield 
roTenne by themaelrea. 

f^irthermore, it is also clear that the credit balance of the aingle 
atagea considerably facilitates carrying out the neceaaakry experimental 
and construction ^ork for mastering the next atage! 

WiUi thia another emphatic appeal ia made to the public to 
energetically support the actualization of the meteorological rocket, 
vfaieh really prerents no technical difficultiea, the more ao aince 
it repreaenta the firat vnuig of the daring ladder to apace flight. 



- 406 - 



As haa just b«en proved «ad «mphs8ized, that goal can 0&I7 be reached 
in this vaj Tithottt aD7 economic risk vorth m«ationijigt"< 

Thus for PIRjpJET. His statements imply a certain accusation of 
ViLIER vho Tould like to iooediately implenent the expensire and, 
in financial -technical respects, problematic rocket airplane. Actually, 
even fflotoi>-povered air transportation is not yet profitable today. 
— Vhether the meteorological rocket irould yield revenae as 

PIRQOEr assumes, I do not dare decide. The mail rocket, hoiroTer, will 
certainly be profitable. Just think what it means to be able to send 
letters in the original in less than half an hour from Berlin to 
Moscov for not quite a penny per decagram or from Europe to imerica 
for not quite 8 pence |>er decagram. As for the preliminary experiments 
that would still have to be made, I vould definitely require less 
than 10,000 U to finance them (cf. epilogue), vfaereas until noir 
hundreds ot tiioasands have been blown into tiie air at VALIER'S 
instigation without essentially bringing us closer to hawing a rocket 
airplane. 



Chapter 19 
The E Model 



Formula Quantities 

g : acceleration due to gravity 
go » 9,81 m/seo 
b : height above cmitre of eartit 
p : paraoieter of the trajectory curve 
s : distance covered 



- 407 - 



t t time 

T t Telocity of rocket 
T. I reciduol Teloci'ty t. ■■ i \t - 2gh i 

r : Telocity at neutral point betireea earth and moon 

▼ - tg J 

F t eurface of triangle paaaed through bj the radius Teetor 
M. } mass of earth 

Mg I mass of moon 

T t absolute temperature 
^ : angle between the direction of motion and the horizontal 
(S t numerical eccentricity of the trajectory curTe 
fS. I radius Teetor of the trajectory curTe 
^ : angle of direction of tiie trajectory cnrTe 

Concerning the prospects that are opening up for bqt inventioni 
-Rhat is talked about most today is the project to shoot a manned 
rocket into interplanetary space or eTsn onto distant celestial 
bodieS} although this question is actually less up-to-date than the 
question of the meteorological rocketS| the rocket airplanes, and 
the unmanned long-distance rockets. 

I haTO already said something on pp. 156 ff, 230 ff, and 305 ff 
regarding the requirements of size and Telocity that mast be made 
for a manned space rocket. Hate IV shows a picture of such a rocket. 
The nomenclature of the machine parts and their operation Till be 



- 408 - 



clear to the reader if he reads the explanations of model B '. 

The apparatus pictured here would veigh 288,000 kg before the 
departure. The empty hydrog«a rocket together irith the observer's 
cabin, the parachute, and the two-part hoi low tip covering the para- 
chute vould weigh 5000 -> 7000 kg. Figuring in the propulsion losses 
due to air resistance and gravitation, this model would attain a 
final velocity of 9000 m/»ec. So it would not have the capacity to 
fly beyond the attraction of the earth, but, according to what was 
said on p. 249 concerning ascent on the synergy curve, it could 
ascend so as to gravitate continuously in orbit around the earth like 
a moon after propulsion has ceased. In so doing, sufficient fuel 
would be left in order, finally, to decelerate the velocity by rear- 
ward thrust so far on one side of the earth as to cause the orbit 
to change to an elliptic path vfaich dips into the earth's atmosphere 
on the other side of the earth so far as to make uso of iixo parachute 
possible (ef. Chapter 14). On such a rocket, the observations and 
measurements enumerated on page 453 ff could be made. 

I would like to remark titat, with the model pictured here, 
I thought of using the same fuel combination as with the model B 
described earlier. I simply wanted to show that building a rocket for 
reaching interplanetary space is by all means possible and hence 
planned using a fuel mixture that results in relatively low tempera- 
tures. Otherwise the objection could have been raised that the 
nozzle mi^t bum up and the affair would be impossible anyway* In 
fact, I hope that even the highest temperature attainable will not 
ham the rocket thanks to the principle of dynamic cooling (cf. p. 41 ), 
vhich is the easier to inqplemmt, the larger the absolute size of the 



' Landing the alcohol rocket after its fuels have been exhausted would 
have to be done with a parachute under ihe guidance of an assistant 
pilot H. Well, the paper is patient and, in this book, certainly no 



- 409 - 



accident nill happen', I explained on p. 299 ff nhj I suggested para- 
chute landing vith this "demon8trati<Hi model". I have also declared 
(p, 302 ff) that I vill actual I7 do everything possible to arrive 
at a machine similar to Plate III or at least Fig. 98 vfaose rockets 
can land in gliding flight. 



nozzle. Concerning the consequences of using stronger fuels I have 
already said irhat is needed on p. 56. Here I need only add that a 
machine of the model E pictured here could reach hyperbolic velocities 
and Toald be capable of orbiting the moon and the nearer planets 
(vithout landing on them, to be sure). The only change in construc- 
'£ion that irould be necessary is that the oxygen room S and the oaygen 
pumps Pa and p^ vould have to be relatively larger. The rest ranains 
as on Plate IV. 

An apparatus siailar to nodel E in its essentials -«rith a consider- 
ably higher performance vould be one vitb tvo hydrogen rockets built 
in instead of one,iifaich are borne by one alcohol rocket. The initial 
▼ei^t of such an apparatus vith the same final ireight of 5000 — 7000 
kg -vould be ca 4,000,000 kg. For that it could advance to distant 
celestial bodies. Of course, landing the alcohol rocket vould be a 
problem vhich, today, is in no tray solved theoretically. But I -wanted 
to prove that reaching interplanetary space by rocket is definitely 
not just a dream of Utopia. Hence I pres^ted model E, -which is 
definitely realizedtle. For that matter, ve vill see in the sequel 
that interplanetary space can also be e<mquered vitli such tvo-stage 
rockets, although they eannot fly to distant stars or even dovn and 
back. 

As can be seen, U\e observer's cabin on Plate IV is strikingly 
small. It must be our aim to have the final wei^t as small as possible. 
Hence ViLIER'S drawing (Vol. II ) in no vay corresponds to mj plans. 



> 410 - 



Before I proceed to the eeientifio dieeuaeion of nodel B, I vould 
firat like to give • Ti-rid deaoription of rocket flighta through 
iiiterplanet«r7 apace. Z hope the reader vill fiad the diaeaaaion of 
the technical detail a later eonaiderablj eaaier to nnderatond. Here 
I am firat preaeoting an excerpt fron a ahort atory- I oonpoaed in 
'vfaich the participant is a rocket flight relatea hia trip around the 
moMi I 

"... Mechanical engineer MQller vaa aupposed to pilot the 
rocket^ I vaa to carry out the aatronomic obaerrationa. 

In FebruaxT', 193Sf the rocket vaa ready; it vaa cbriatened "Luna"} 
irfaich ia Latin for moon. Firat it waa aent aloft unmanned to 4200 Im 
in order to teat ita control and recording apparatus. All theae rocket 
are built ao that they can also fly uuntonned. That coffle about as 
follovs i At first only small apparatus had been constructed lAich 
could carry a load of l/S to 1 kg. Here no pilot could go along, ao 
that it was necessary to invent doTicea by meana of -which the rocket 
could find its vay by itself, e.g. a gyrdacope which influenced the 
position of the tail fine, and aimilar inatrumenta .... These 
devices irere also installed in the larger machines) for it appeared 
advisable to free the pilot of many natters -which he could have taken 
care of himself, a) To give him the freedom to make astronomic observa- 
tions, b) Because a machine vorks without emotion and more accurately 
than a man. 

Naturally, the pilot can at any time influence the course of flight 
by firing rockets. The results of thia firat unmanned aacent were 
satisfactory, and in the beginning of Uaroh, MQller undertook a 5000- 
km ascent in order to test the maneuverability of the rocket by the 
pilot «... He looked me up in order to tell me of hia intentiona 
to fly around the moon in mid-June. 



- 411 - 



So ve made preparatioas for the trip .... In order to accustom 
persons to high counter-pressure , . , th^ are suitablj placed on 
a cart ifhich rotates in a circle at the end of a metal ana 200 — 400 m 
long (cf. Fig. 55). 

By mid-June I vas ready to ascent vith "Luna". I had already gone 
to India in the middle of Uay, for ve vere to ascend from the jndlan 
Gulf. In early June I sav "Luna" for the first time. It vas a stately 
machine, 35 m long and 10 m in diameter , and consisted of one alcohol 
and -bwo hydrogen rockets. It was equipped for attaining a relocity 
of 13 km/sec in all. (Note t Today I vould already be in a position 
to build sueh a rocket only 17 m long and 7 n in diameter, since 
considerable improveoientB have occurred to me in the meantime. Uodel 
E on Flate III is also considerably smaller.) Naturally, it only 
required an initial Telocity of not quite 11 km. First of all, hovever, 
it could not reach this Telocity immediately but only in the course 
of fiTo minutes, during vhieh it lost 1 kn/sec to air resistance and 
graTitation. Then it iras good also, after hsTing attained the fall 
Telocity, to haje some fuel in reserTO for the purpose of influencing 
the direction in case it veored from its course. 

IVhen I arrlTod in Calcutta I vas surprised to see the many auto- 
mobiles which caused neither fumes nor noise and, in spite of their 
flcmetimes considerable speed, seemed to hare extremely sme^ll and 
light motors* 

''Well, remember", 11011 er said, **'re haTe liquid hydrogen and o^gen 
factories on the Upper Brahmaputra, ill these automobiles have hydrogen 
motors . . . ** 

"Yes, but is not all the hydrogen produced by the plants needed for 
the rockets f" 

"At first, often no larger rockets vere launched for months. To 



- 4ia - 



prevent our hydrogen plants from being completely idle in the meantime, 
ve aoa^t to utilize at least part of the liquid hydrogen in industry* 
— Today ve can hardly fill the demand. We are obliged to enlarge the 
plants almost every month ..." 

On Jime 12, the steamer "Tagore" arrived vith the fuels for eur 
fli^t. We vent aboard, took "Luna" in toT, and departed accompanied 
by the vell'-^ishes of thousands. 

On the morning of the 14th, the Tagore" beared to and ve vent 
about to fill our rocket. First, freshly vaporized hydrogen vas blown 
through the fuel tanks to cool them off. If they had immediately been 
filled vith liquid hydrogen, the metal containers vould probably 
have burst liks a hot glass into vfaich cold vater is directly poured. 
Also, the so-called Leidenfrost state could easily have set in . . . 
For example, if a metal boiler is made gloving-hot and cold vater 
is poured in it, at first a layer of steam forms betveen the metal 
and the vater, so that the vater cannot touch the metal. Hence, the 
vater cannot eoel the metal at first. Since steam is a poor beat 
conductor, the metal cools off very slovly. Only after its temperature 
has dropped by a certain amount is there any contact betveen vater 
and metal at any place. Here the metal suddenly cools off rapidly and 
the drop in temperature rapidly spreads over the whole container. 
The vater, nov suddenly touching the metal, boils violently and isi- 
mediately forces the dosed boiler apart. We observe the same phenomenon 
wbm filling a metal container at normal temperature vith liquid air 
or liquid hydrogen, in explosion vould have been inevitable if ve had 
suddoily put tite liquid gases into the tanks. At 10:30 our rocket vas 
covered vitb a thick layer of ice and cold «iough to be filled. 
Ebormous hoses vere laid from the ship to the rocket, first to the 
alcohol rocket; as soon as it vas almost full, the hydrogen rockets 
»lso began filling. "Luna", vfaich so far had lain flat on the vater 



- 413 - 



(ef. Fig. 118), nev sank erer deeper Titb the rear end, vfaile the 
tip soon stood in rertieal position (ef. Fig. 113). At 11:05 it vas 
completely filled and IfiULler end I got into the obserrer's cabin and 
closed it air-tight b^ind us. It vas not con^letelj dark inside; 
some light entered through the periscopes* I looked tiirough one of 
them and Just sav the "Tagore" leaving full steam ahead. The exhaust 
gases of the rocket cause large irares, eren vater spouts. 

U811er manipulated something on the irall. I heard a veak metallic 
hum and an electric light bulb lit up. 

I started the generator, vfaich is naturally driven Toy a hydrogen 
motor* Nov vas the time to put the control gyroscopes into operation. 
He turned a svitch, took a small, precision-built gyroscope, and, using 
a micrometer gauge, compared the positions of the control gyroscopes. 

"They are nov accurate to three seconds of an arc, is that suf- 
ficittit ?** he asked me* 

''If the error leads avay from the moon, fine. But if you can 
adjust them more accurately, naturally that would do no harm". 

UQller vorked on the gyroscopes again. After a few minutes he said, 
"Nov the error is close to a second of an arc". 

"I believe that will suffice". 

Uailer also adjusted the remaining instruments. "When do ve start ?" 
he asked '. 



Note I Here the astronomer does not thoroughly faaov the machine nor 
the machinist the flight plan, but that is a "dramaturgical" error. 
Cf. Vol. II. In reality, I would naturally insist that each be able to 
pilot the vehicle around the moon alone if necessary. Then, however, 
the layman would not be able to understand their conversation and I would 
have to escplain all these things n^'self, which would be a terribly 
tedious job. 



- 414 - 



"At 30 ninutes and 46 seconds after li o'clock, tJie rocket amst 
be at an altitude of 1830 ka and have a velocity of 10,700 a/'*c« Can 
ve made ^t ?" Ufiller adjusted the acceleration indicators. "Certainljl Can 
700 help me -rith the instmnents ? We mst start at 11 o'clock) 
25» 30" 



1)„ 



It was litis. After a farther 5 minutes, ve had set the instruments 
rig^t and started the big pumps of the alcohol rocket. Only the gas in 
the oren needed to be ignited. Ve took the haomock from one comer, 
fastened it in the middle of the obserrer's cabin and lay down on it 
(Fig. 185). 




Fig. 185 

It gave us a peculiar feeling to lie there in that position. Due 
to the temperature of liquid hydrogen, the metal of the liquid tanks 
had become as hard as glass. Ihe boiling of the liquid gases caused 
a sound as of a hundred bells; in addition, the vaves beat against the 
rocket and rocked us. At 11(85 the gases belov us began to boil more 
vigorously, the rocket began to vibrate vfaile nov and then a larger 
quantity of air rose beside it. At 11 o'clock, 85' 84" there was a 
jolt. The electric ignition had begun to vork and the rocket rose from 
the water. A feir seconds later a rapture occurred like the sheet of 



' Note t It is apparent that I did not knov the synergy curve at the 
time. Today, I vould begin such an ascent quite differently. 



- 415 - 



ice on a river breaking up; a suitable mechanism had burst the lajer 
of ice that covered our rocket and cast it into the sea. ind nov, at 
li* 25' 30", exact to the second, our ro»ket ascended at full force. 

The powerful counter-pressure pressed me to the hammock. It would 
hardly have been possible for a person to stay on his feet. Through 
the periscope I could see a hole at the water's surface resembling a 
crater that was surrounded by a circle of white foam. That was where 
our exhaust gases had struck the water. After 25 seconds we already 
passed through the fleecy clouds, and after another minute I saw the 
peaks of the Himalayas rise on the horizon, although we were over 1000 
km away. After a minute, the fuels of the alcohol rocket had been 
edansted and it was jettisoned} vith it also the first covering 
which had drawn over the tip. 

Now the hydrogM rocket operated. It rolled a bit. It seemed as 
tbough we were on the back of a huge beast that was trying to get up. 
Also comparable to the breath of a hvLge beast was the sound of the 
pumps forcing the fuels into the atomizer. At one instant, their nozzles 
ejected a dull, hoarse roar that made everything in the observer's 
cabin rumble and rattle. Fortunately, MOller was able to turn the 
thing off again. In so doing, lie expressed maledictions concerning 
man's un trustworthiness in general and his chief assembler in part- 
icular. Namely, descent rockets must not roar. They mc^ at the most 
puff and hiss like an old tea kettle . . . (ef. p. 31 ). After two 
minutes, the fuels of this rocket also were used up and the upper 
hydrogen rocket began working. Uore depended on ihis one than on the 
other two (cf. p. 470 ).. . . Failure of the other two would only 
have meant that the flight had failed and that we would have dropped 
back to earth. Failure of this rocket, on the other band, could put 
our life in Jeopardy. Therefore, the best German engineers and mechanics 
had worked on it for almost a year, making it a master-piece of 



- 416 - 



technologj. It worked superblj. I no Itmger had the feeling that I vas 
on an accelerating bodj. I felt a« thoii|^ I wai remarkably hea'vy and 
thin. After another 2 minutes, the ftoele vere shut off and 2 seconds 
later all connter-pressure ceased and I iras floating freely in the 
aiddle of the observer's cabin feeling as though I had avakened from 
a dogsleep. I noticed that -what I thouj^t vas the left side iras actual- 
ly the right and that I lay in an entirely different position that Z 
had believed. 

"So, noir let us put avay the hanmock and make ourselves cKHnfortable," 
irailer said. 

We rolled up the haonock and UQller activated a device that Jet- 
tisoned the tip and separated the parachute, observer's cabin, and 
fuel tanks from each other. Our cabin had numerous irindovs. . . « 

Althou^ I knew to a certain extent vfaat I would see and experience 
up here, still I was confounded by the view that presented itself to 
me. I floated freely in the middle of the cabin { a slight swinming 
motion vas sufficient to take me vbere I vished. Only nov did I 
notice a number of leather loops attached to the vail everywhere. 
If ve hadn't cravled along by means of th«n it would have been impos- 
sible to get a firm hold. 

The sunlight falling through the windows was extremely glaring. 
Still, the windows did not have a bright but dark effect; they looked 
as thou^ they consisted of Jet-black glass. They directly radiated 
cold and darkness, vhereas outside where tiie sun shme it soon turned 
hot. This was a result of the fact that the sun is not able to illum- 
inate clear ether space . The sun stood as a blinding disc in a 



^ Actually, I would cover the windows with plates of frosted glass 
on the inside, which can easily be removed if <me wishes to look out. 
Thus the light in the observer's cabin would be more diffused and 



- 417 - 



aimilor to di^light, not straining the eyes. (NOOBDUNG has mad* a 
cimilar suggestion, onlj be vould give the irindoirs a shape resembling 
a lens. I cannot reallj agree to this suggestion; I believe plane 
pe^allel Tindoirs afford a better Tietr.) Here I am dispensing viih 
frosted glass plates (likevise for "dramaturgical" reasons); I vanted 
to shotr the reader vhat interplanetary space really looks like. 



completely black sky. If I screened i^y eyes from the sun for a vbxi*, 
I gradually began to distinguish single stars in the sky; finally they 
shone brighter than in the darkest night. The sky did not appear blue^ 
black as in oar nights but peculiarly broimish like a sooty porcelain 
plate. Near the Millgr Way it was somewhat bri^ter than in more distant 
places. It is not completely dark because of the presence of numerous 
fixed stars that are not risible to the naked eye. The brovnish color is at-j 
tributable to the fact that the reflection of our atmosphere is missing. 
We appeared to be floating at the centre of an immeasurable sphere. 
On one side iras the arch of the earth like an enormous boiler. It oc- 
cupied approximately one third of the lower celestial hsnispher*. On 
the other side vas the burning sun surrounded by a peculiar bright 
aura that reminded me of an elongated quadrilateral. This is the so- 
called zodiacal light which, aa is believed todiqr, is caused by minute 
grains of dust flying around the sun. inien I screened the sun vith 
i^ hand I noticed that it vas surrounded by peculiar beams. This is 
the so-called corona iifaich can be observed from the earth only vith 
a total eclipse of the sun. Not far from the sun stood the moon like 
a round frosted-glass Tindow, quite a bright disc. Its nij^t side was 
turned toweurd us; it was illuainated only from the earth. It was to 
take two days before we were to observe it by sunlight. This was the 
first time I had seen the new moo n! . . . 

Nevertheless, we did not want to let the time pass unutilized. 
Under the parachute we had a large concave mirror which could be moved 



- 418 - 



into place from the obserTer's cabin bj means of three elastic steel 
vires vound on drums. That served as the lens of a large telescope* 
JL small telescope in the observer's cabin served as eyepiece. We did 
not need a pipe dark on the inside, for the s&y vas completely black; 
Jtist as little did ve need heavy supports on irhieh to fasten the 
telescope, for the single parts had no veigbt; they remained in rela- 
tion to each other just as ve put them. Here the mighty installations 
vere superfluous Uiat are needed on earth to support and carry the 
vfaole. The telescope magnified 100,000-fold t a ma^ification ve could 
afford, for there vas no flickering atmosphere. 

UQller suggested i "It vo\ild be veil if you put on your diver's 
suit and stepped out vith me to learn to move about in space". We both 
put on our diver's suits vfaich vere made of rubber coated vith thin 
strips of shining tin to prevent thai from bursting. Half of tlie head-piece 

vas of an elastic, transparent material to allov free vision <m all 
sides. Ve carried containers vith compressed air on our backs that 
provided breathing for approximately 1—1 1/2 hours. We blev the air 
ve breathed out through a tube containing caustic potash idiich vas 
to absorb the ceirbon dioxide. We could also let it escape to the open 
tiirough a type of valve; the rearvard thrust propelled us in the op- 
posite direction, thus being a means by vfaich ve could move about. 
In order to get back to the observer's cabin again ve fastened our- 
selves outside by means of cords. These cords vere of hemp vith tele- 
phone vire voven in to permit the diver to talk to the person in the 
cabin or, as in our case, permit the tvo divers to talk to each other, 
although sound is not transmitted in air-free space. MQlIer let ae 
carry out a fev simple maneuvers first; then he let me eaq>erinent 
vith some instmments still found under the parachute. Next he explain- 
ed the outside arrangement of the cabin to me. 

"JLs you can see, one side of the cabin is covered vith thin black 
paper vbich clings to it closely. Yon also knov that the sun does not 



- 419 - 



heat air-free space, but it doe?! heat bodies -which are struck by the 
sun's reiyaj and black surfaces more so than shiny ones. For that, 
black surfaces radiate more heat. Now, in this country, the pun's 
heat is not great, therefore we turn the black surface into the sun 
and the shiny surface Into the shade. If ■vre should later make trips 
that bring us closer to the sun we will do the opposite. In this way 
■re can always have e::actly the omount of heat in our cabin we wis''.. 
The windows of onr cabin can be covered with reflecting tin plate 
which can be clapped hack and forth fron within. The rerson for th it 
is first of all because we could easily ^et inflammation of the eyes 
if we are exi^osed to the bright sunlight day and night. It is also 
useful for flying through the shade of a larger celestial body. Then 
we can jettison the black paper and close all sut;erfluoua shutters. 
Mr. Professor, you know the principle of the thermos bottle, don't 
you ?" 

"Certainly, a shiny container is surrounded by a vacuum; it can 
give off no heat by conduction because there is no matter in the vacuuin 
that can conduct away the heat. The heat could be given off by radia- 
tion. But very little heat is given off by radiation, for a Fhiny con- 
tainer allows no heat to radiate; thus the contents remain hot". 

"Fine, here we have the very sa-^e thinp i the shiny obs»erver'8 
cabin surrounded by air-free interplanetary space. Now let me explain 
the black pipe to you which makes a number of windings along the 
shaded side, then makes the seme niuaber of windings <m the sonny side, 
and finally returns inside the cabin again. As you can see, here 
there is a sraall pump wliich pumps the air from the cabin into the pipe 
on the shady side". 

"Ah, that must be the air distiller ?" 

"Indeed. On the shade side, the air cools off, for, in interplanet- 
ary space, Trtierever the sun does not shine directly, there it is just 



- 420 - 



as cold as it is dark. All impurities that the air may have condense 
at a higher tenperature than the main components of air, namely 
nitrogen and oxygen. The imparities precipitate in this pipe and 
only the nitrogen and the oaygen reach the sun side. Here they are 
heated to room temperature again. As soon as IJie pipe on the shade 
side is completely filled with impurities, »e very simply unserev it 
and torn it to the sun side. There the contents vaporize and floirs 
out. Nov, please look at the clock inside; I cannot see from here. 
Hov late is it ?" 

"12:30. The time is approaching for me to take the bearings". 

"Fine, and I vill prepare lunch. Let us cravl back in again". 

The earth had rapidly decreased in size. Nov it no longer gave 
the impression of a boiler, nor the impression of a sphere; it had 
the shape of a disc. With the moon, the impression of curvature is 
produced by the fact that, from certain moimtains, e.g. Copernicus 
and Tycho, straight -white ri^s spread over a large part of the spher- 
ical surface and shoir up the curvature in perspective. 

For the rest, it vas a splendid vieir of the earth. Since the 
atmosphere appears red in the transmitted light and blue in the 
incident light, the edge of the earth iras an intense red, and round 
about there iras a fine blue border. Above the poles floated the polar 
lights as croTns. The blue oceans, the deep-green tropics, the yellov 
deserts, the black tundras, the pale-green steppes, the irbite polar 
regions : all stood out against the deep-black, star-studded back- 
ground. Snoir-irfaite clouds floated over the whole. From our vantage 
point, they looked like mere dust, reminding one of the pollen on a 
colorful flower, 

I did not have too much time to admire the view. I had to determine 



- 421 - 



oar position, for this vas the best time to correct any deviation 
fron the trajectory* I consulted the table vith my calculations of 
the position and apparent size of the earth at every moment of our 
flight. I found that the earth could be seen exactly idiere it should 
be seen and that it had the calculated apparent size. Therefore^ our 
bearings vere correct. Then I checked the data of our recording 
instruments and found that th^ were accurate. 

After that ire had lunch. First ve had soup vhieh, boveveri ▼• did 
▼e did not eat with spocms from a plate but ve sucked it through vide 
aluminum tubes from spherical , almost completely closed containers. 
Then there vas etc. 

UBller developed a healthy appetite, but I could hardly svallov 
a bite. I felt as thou^ an iron hcmd gripped my chest and clamped 
■By esophagus shut. Still I did not actatJly feel bad. On tiie contrary, 
never before had I been so free of listlessness, nausea and pain. 
I carried a pin vith me. I pricked i^yself vith it, but no matter vfaere 
I pricked I didn't feel the slightest pain. 

"Hm, yes, professorl Tou had best take scopolamine or bromural. 
Later you should try to get some sleep. That is tiie effect of the lack 
of counter-pressure combined vith the excitement during the first 
flight". 

MQller stuck a pill into my mouth. Then he took a bottle of rasp^ 
berry Juice from our food box, first put it to his ovn mou-Ui and took 
a big gulp. He viped the neck of the bottle vith his hand tvice and 
then stuck it into b^' mouth, calling, '*Nov you must svallov". 

I svalloved vith all the force I bad and finally got the pill dovn. 
But then I said, "Do yon know, Ur. USller, veil and good, but have ve 
no tumblers ?" 



- 422 - 



"Tumblera ?•• Miller laughed. "Hfhy yes, even tiro. But how do you 
■want to pour ?" 

'^ell, that should -work s(Hnehov'*. 

"Please, here is a tumbler and here (irait a minute, it is too bad 
to waste the raspberry juice for this experiment), here is a bottle 
of water". 

I turned the bottle over; naturally, not a drop came out. I was 
annoyed and so I waved it a bit. The water gushed forth, but alas, it 
did not stay in the glass in which I tried to catch it; the water sprang 
out again as though it had struck a rubber wall. Just a few drops stuck 
in the glass. The rest of the water formed mimerous spherical drops 
which flew about in the cabin and bounced off the walls. Here and there 
one stuck to the wall and broke up further. Finally the whole observer's 
cabin was filled with flying water-drops like a swarm of mosquitoes, 
which gradually remained hanging somewhere. 

"I must acknowledge the fact", I said. 

"Well, there you are. Vho would ever fill a tumbler so wildly ? 
But now please look here, professor. The lack of counter-pressure also 
has a ^ood side. You will drink from a tumbler often enough yet, but 
what I will show you now you will perhaps not see so often". 

He moistened the fingers of his left hand by squashing a few water- 
drops that hung on his suit. Then he took the water bottle in his right 
hand and slowly and xmsteadily drew it back while holding th«> fingers 
of his left hand in front of the neck of the bottle. It .seemed as though 
he drew a ball of water frron th© bottle. Then he suddenly opened his 
hand; the ball remained floating freely before him. 

"This is the model of a celestial body", he said. Then he took his 
rubber comb, passed it through his hair several tiaes to electrify it. 



- 483 - 



and held it doae to the drop« Thereupon the drop moved around the 
comb in an elongated ellipse. ''Here joa have SEPLIR'S planetary lava" 
(Fig. 186). 




Fig. 186 

Then I vent to aleep, that is I suspended n^self by one am and 
one leg in tiro leather loops on the trail of the cabin so as to hang 
still. Natural l7) the straps caused no pressure, for I had no weight. 

I did not sleep veil. I dreamt I vas an antediluvian monster that 
had sval loved the earth. Nov it repeatedly rose to my throat no matter 
hov hard I svalloved, and -vhenever it came up I felt I vould suffoc- 
ate. Nevertheless, vhoi I avoke about 4 o'clock, I felt considerably 
better, miler vas already sitting in his diver's equipment outside, 
experimenting vith electric rays. I should mention that, simultaneously 
vith our rocket, another rocket vas flying in interplanetary space. . . 
It had contacted us by means of light signals and vas seeking to pro- 
duce electric rays and tlransmit them to us. 



Nov I began vorking as veil. It vas not yet possible to observe 
the moon, but there vere enough other things to do. On that day I ob- 
served Uars and Jupiter. Evening around 9 o'clock ve dosed the shut- 
ters and vent to bed. Of course, the vord "evening" is (mly conditional' 
ly correct, for our position to the sun had not changed. We vere no 



- 424 - 



longer part of the earth but a small, independent celestial body. 
Astronomically speaking, it vas day on our sun side and night on the 
shade side. Ifhen I say "evening" I only mean that it was nov evening 
at our place of ascent; ire irould have had eveninj if ve had not flown 
airay. 

... On the evening of the third day (-tiiat is, it vas evening 
in India, not ufaere ire irere) ve had approached the moon to vithin 
several 50,000 km. Only nov did ve see a narroir crescent illuminated 
by the sun, -which soon became bigger and wider. I determined our 
location according to the position of tite moon; ve vere 500 km too 
close to the moon. We easily corrected the error by giving the rocket 
a propulsion of 1.35 m/sec. For that purpose, ve pulled the telescope, 
parachute, and tip up close to the cabin, alloved some gas to flov 
fr<Nn the rocket, and then spread out the parts of the rocket again* 

The whole maneuver had taken hardly a minute. 

Yet, it left an impression with me that vas to remain during the 
nttire flight period. Had not tJhe earth been belov the whole time and 
the moon above at first and then on the side ? Nov the moon vas sud- 
denly belov and, the earth off to one side above; yet notiiing had 
rotated I Neither had I turned myself. Everything had reaained as be- 
fore and everything had been this -way the ifhole time. Hov could I have 
erred so badly ? I had that feeling again of lapsing into a dream or 
avaking from a dream. One does not turn, nor does the vorld turn and 
yet one notices one has had a different position than one thought* 
For me the earth stood "belov" again only at the moment vh^i "I^una" 
rocked on tiie ocean after landing . « •" 

Here I quote a fev excerpts from GAIL'S novel, "The Stone from the 
Uoon", at the same time as .a sample of GAIL'S brillant style and his 
abili-t^ to imagine himself in unusual situations and to present them 
true to nature and fascinatingly. Concerned is a visit to a small 



- 425 - 



body gravitating irith circular Telocitj on the edge of the atmosphere 
of Venus and the description of a not quite voluntary airfoil landing 
on Venus. Some of GAIL'S claims are incorrect; I vill correct them 
on this occasion. That naturally does no harm to the value of the book. 
I vill speak about the matter in Vol. II. 

"The decrease in the distance from the sun began to make itself 
fait. The rays of the gloving disc, nov three times larger in size, 
shone through the vindovs of the ''Ikaros" vith scorching heat; all 
the passengers Tore dark glasses to protect the eyes from the excess 
of light » The strongly-reflecting vhite layer of fog on Venus con- 
siderably increased the brighiness. After tvo days Venus hardly looked 
like a star suspended in the aJsj anTinore. Its mass spanned the fir- 
mament in a vide arc and, if all sensation of above and belov had not 
been destroyed by the veightlessness of tlie free flight, one vould 
have had the impression as though the "Ikaros" vere dropping obliquely 
dovn to land from an infinite heig^ht. 

The suaJl orbiting satellite had long been spotted in ihe telescope. 
With concern, Korf had found that its distance from the surface of 
Venus had decreased to scarcely 150 km. Its orbit shrank rapidly and 
had changed to a fine spiral vfaich took the body closer and closer 
to the planet. 

The landing plan vas fixed. First, a connection vas to be made 
vitA the moon of Venus. Since the "Ikaros" vas very large, not at all 
built for overcoming atmospheric resistance, and had no carrying 
surfaces, it vas impossible to come close to the surface of Venus, 
Similar to Astropol, it vas to gravitate as a permanent ether station 
in a constant orbit. 

' On Venus, the apparent diameter of the «un in 1.4 times as great as 
on •krth. Therefore, in area, the disc is scarcely tvice, in any case 
not 3 times, as great. 



- 4S6 - 



For ibe aeiual •xpeditimif a aaall mo<m rocket hcul bean taken 
along as a dinghy. Its carrying surfaces folded up $ 'Uiis 8-Bi-l«ig 
steel torpedo ^ vas kept in a side-chamber of the "Ikaros" especially 
installed for the purpose and sealed air-tight. It could be reached 
froB the pilot's stand through a snail pneumatic door. A larger door 
of the chamber led directly to the outside. 

The auxilifury rocket could only acccwmodate 3 men. ... 

The planet came oyer closer. 

From time to time, Korf measured the Tisual angle of the crescent 
of Venus and from it calculated the distance. When the *'Ikaro8" came 
to vithin 50,000 km, the nozzles vere set to operate in order to de- 
celerate the speed of fall and force the space-ship into an orbit. 

The reavward thrust, not felt for veeks, upset everything. Sud- 

dMily the passengers felt the veight of their limbs again - 

2) 
and groaned under the counter-pressure ' , After a fev minutes, the 

rocket motors stopped. The "Ikaros" freely orbited the planet at an 

altitude of 45,000 km '. Venus had suddenly gotten a second satellite 

— and the state of irei^tlessness was restored. . . . 



The five sailors remained on board the "Ikaros" under command of 
the senior with strict instructions under no circumstances to change 



' I vonld never make a rocket out of steel (cf. p. 16 ff). No more 
Tould I make the vings retractable. I vould rather have fastened the 
dinghy in front or on the side of the space-ship. 

' I vould have arranged it so as to connect the observer's cabin to 
the rocket body only by a long cable and have it rotate about the 
rocket at least periodically during flight in order not to completely 
disaccustom ibe passengers to counter-pressure (cf. p. 140). 

3) 
' I vould have descended to the edge of the atmosphere of Venus vith 

the space-ship. 



- 427 - 



the gravitating path of the space-ship. 

The rocket -was examined closely once more and supplied vith pro- 
pellants and food conserves for five dajs. llien Korf, Bums, and 
Isabella cravled through the hatch at the tip of the auxiliary 
rocket. • . . 

The slender torpedo emerged slovly from the vomb of the space-ship. 

For a vfaile it remained close beside the "Ikeiros". Since both 
ships vere freely left to the effect of the star close by, they floated 
relative to each other in peace and apparent ireightlessness. 

The irings of the rocket unfolded to their full span. Another moment, 
then the nozzles speired streams of gloiring gas into space and the 
boat shot airay in slanting flight toirard firm ground. 

The three persons lay close beside each other in the hammocks of 
the small, arched pilot's cabin of the small rocket. The springs 
tensed) creaking under the pressure of the vorking rocket nozzles 
and the passengers, disaccustomed to gravitation, heavily sensed the 
weight of their bodies. 

Through the upper lookout irindov, one could see the shiny crescent 
of the near plannet spread out. It became visibly longer and narrover. 

"We're ascending to the tvinkling moming-steu>! Into heaven! Hoir 
ironderful!" Isabella shouted for joy, shaking irith excitement. 

For a second £orf turned his eyes from the levers and dials. "Tou 
are wrong. Miss Isabel! Not up — we're going doim to solid ground — 
in an oblique f«ail " 

"But there, see the glittering sea of stars above — high up — 
there! " She pointed with her hand through the upper round windows 



' What is referred to are the springs of the hamnocks and the counter- 
pressure produced by the nozzle of ihe rocket. 



- 428 - 



through vfalch flooded bright light. Her hand fell back suddoilj and 
■truck her body vith a -Uiud. The counter-pressure made the simplest 
moTeotent a test of strength. 

"in illusion! Produced bj the motors, which for us are at the 
bottom alirajs and in every situation, as soon as they vork. Only irhm 
th^ don't work, then - "^' 

Isabella cried out. "Wiat's that ? The vorld is sinking!" 

It bad become dark 'vithout any transition, as though a cosmic 
monster had sral loved the sun. The dormer irindovs vere a menacing 
black. Nothing vas risible anymore, even the mass of Tonus had dis- 
appeared. 

*5re have entered the shade of Venus, but ve vill soon emerge again 
- Tith this velocity!" 

The boat rushed on, lover and lover. A light hum made the mats 
vibrate — the control gyroscopes vere operating. ... 

Ifter half an hour, the shade of Venus vas past. The passengers 
closed their eyes for several minutes against the recurring glaring 
light. 



' It is presented very vividly here tiiat a planet appears to be 
above vfaen the rearvard thrust acts in a direction tovard it. This 
description naturally gives the r^spectilre place a peculiar poetic 
fascination. Tet, if I had to do the act not in fiction but in vitality, 
I vould never have let the rearvard thrust act tovard the planet, 
but only in the tangmt of the orbit, so that the plan«t vould have 
appeared to be off to the side. I vould have decelerated the flight so 
■nch that the orbit vould have changed to an elliptic one, vfaose perigee 
vould have fallen in the ataosphere of Venus. 



> 489 > 



Now iee fog ' billoved on the side — like a Tertical vail ascend- 
ing from unfathomable deoth up to heayen* It aeeoed a« though the ahlp 
■hot up along this vail ' — ever farther — ever hi^erl Olietenning 
vfaite fog einking dovnvard vfaereyer the eje tamed! 

... Single flhooka corrected the flight. Nov etrong counter- 
preeenre coupreaeed the chest, nov the three jolted veightlessly froa 
their hanmocks. 

Hours passed. The ship, circling the b«^l of Venus ever closer, 
entered the shade tvice more and emerged to the light again. 

Isabella could no longer stand the sight of the ice-fog forma- 
tions rushing by. She closed her eyes. 

... The gitmering point up ahead floating above the ball of 
Venus vas becoming larger. 

... Eorf • » • looked at the pointer vliieh indicated the 
reading of the outside barometer. 

"There, do you see t A fifth of a millimetre of outside pressure! 
Ve are already skirting the outer edge of t)ie atnosphere of Venus'*. 

••Danger ?" 

d) 

'%'ot to us. But to that over there '. The resistance of even the 

most rarified layers of air can so accelerate the slorlnking of the 



' Bj contrast, cf. p. 552. 

n) 
' Here the rearvard thrust has a decelerating effect. The flight is 

in the direction in which a plummet pulls on the line. The impression 

is not that of flying up along a vail} it is the opposite, that of 

going dovn beside the vail. 

3) 
' That is, the moon. 



- 430 - 



trajectorT' that it quickly enters the deuaer layers, and then there's 
n<) stopping it. I do not knov hov far — no exact meaaureinents can be 
carried out on the bil loving svaths of ice". 

The rocket came closer and closer to the tiny satellite. The 
telescope ▼as already superfluous. 

"It is time to slip into the space diving suits, j^iickl I vill 
soou hare to firo the retro-rockets and then the cou&ter-pressure 
sets in". 

Pale, but steady and irith vigor Isabella donned the shapelesss 
covering of rubberized leather « Bums placed the massive helmet 
irith the air cartridges and the microphone over her head and screwed 
it to the metal collar. In another minute he hiiriself had the equip- 
ment on. ... By Tay of trial, the telephone cables vere connected. 
Jny other iray of cnnmunication betveen the occupants, now in air 
tight jackets, iras no longer possible. 

"Everything ready ?•• 

8) 
The voices of Isabella and Sir Williams ' resounded in the receiver. 

••We trill proceed as ploiuied", said Kbrf, "as soon a* ire have 
completely adjusted our speed to that of tlie satellite both of you 
Till slip out. There is absolutely no danger. You vill gravitate 
side by side freely uid without weight. I vill stay vith the c<mtrols 
of 'Uie rocket and promptly meet any fluctuations in the velocities 
that occur. — Bra! ~ The tiny moon cannot be more than 20 metres long* 
— We Trill have to brake! Otherwise ve will shoot past. On your toes!" 

The nozzle already pointed in the direction of flight. A blue 

' In contrast, cf. p. 450. 
' I.e., Bums. 



- 431 - 



stream of gaa shot oat three or four times. The awesome satellite 
moved up very close — jet the distance heiireen us reduced at a sloirer 
and slower rate — emd then it stopped a tew metres <m one side of 
the rocket. 

The nozzles irere silent . 

Bums and Isabella cravled out ^trough tlie double hatch. 

On the outside of the rocket, the fiiglishman plugged in the strong 
cables irhose ends vere fastened to their belts, frosi there leading 
to the speakers in the helmets. 

The girl vas almost overcome vith dizziness and she vas gripped 
by a choking dread of 'Uie fearful abyss separating the rocket from the 
cosmic formation. Bums guiclcly grasped her leother-covered hand and 
together vith her pushed himself avay from the steel irall of the ship. 
The tvo shapeless forms floated freely like inflated rubber balloons. 
The cables curled behind ihea like iridescent vipers. 

Eorf ' s eyes moved to and fro betveen his companions and the 
indicators of the measuring instrurients. He saw Bums holding on to 
the jagged edges of the central crevice, crawling into the crack, 
and pulling Isabella in after him. 

"The satellite is hollow!" Eorf uombled to himself, and confused 
thoughts and suspicious shot through his brain. ... 

Korf's voice sounded in the receiver. 

"Back! It once! The air is becoming denser! We're in danger of 
crash-landing! " 

... Korf's voice again : "Get back— quickly! For Crod's sake! 
Trajectory disturbance! — Ve're falling— crashing! Not a second to lose!** 



' It would have been ici^oasil)!* to hear the nozzles, even while working. 



- 432 - 



... A dreadful, silent struggle for life! 

The vails turn hot. A slight pressure dovnirard is beginning to be 
felt. Sloirly the force of gravity returns '. 

Korf speaks into the microphone ^mi^terrupedl7, hurriedly, vith 
frantic concern. The iron nerves of the Svabian begin to vibrate. 

"Get back — at once! For heaven* s soke! It is almost too late — 
too late! The satellite is crashing — ipadly ~ the rocket trith it — 
destruction —1 ' 

Bums lets go of the girl. It is useless Tithout a firm support. 
He cannot free her. 

"Should they all perish — or only she alone ?" 

It is a matter of making a desperate decision. 

A thought! The cable! Back to the rocket! Get a hold and pull! 

He glides back as fast as he can. 

Outside the air pressure forces him sideways. The atmosphere is 
still t^in. The rocket is floating nearby as before. 

One leap! — Bums is standing between Oxe double doors tugging 

3) 
vildly at the cable by irfaich Tuztla hung. 



' What is meant here is not the gravitation of Venus but the counter- 
pressure becwiing noticeable on the satellite due to the air resistance. 

' I would not have been disconcerted, I would simply have stuck the 
tip of the rocket into the crack of the satellite and then opened throt- 
tle, accelerating the motion and lifting the whole form together with 
the rocket out of the atmosphere of Venus. A rocket tiiat has the cap- 
acity to llmd on Venus with three persons, being decelerated only by 
meems of rearward thrust, and fly away from Venus agaiq is htmdred 
times strong enough, at circular velocity, to lift itself several kilo- 
metres higher together with a formation weighing 30-40 tons. Of course, 
if Korf bad done that the impressive drconatic ending would have been lost. 

3) 
'i.e., Isabella. 



- 433 - 



Korf had hia band on the gas lever. 

The rag of cloud riaes up fr<Mi belov. If he acceleratea the rock- 
et, the cable vill anap and Tuxtla la lost. 

Just a fe^ minutes and they -rould «iter the dense layers of the 
ataoaphere; that vould be the end. 

He jerks open the inner door. The air eacapea from the apace-ahip. 
He paja no attention to it. Everything depends on the protective auita. 

He pulla Buma inside and grasps the cable. Both pull on it •wiih 
all their force. The cable must have gotten stuck in the cracks of the 
satellite. 

Already a whitish mist surrounds the ship. They have reached the 
ice clouds. The steel vails of the rocket hiss for heat. 

Suddenly -- there is a whizzing over there around the satellite — 
the cruat of ice is vaporizing '. 

And now— it is disintegrating! The fragments glow brightly I Smoke 
trails behindl 

The cable slackens, Tuxtla hanging by its end, tightly holding the 
small case in her anos. 

Another five seconds! The body of the girl is pulled inside. The 
hatch covers are slecmed shut. At the sarte instant Korf's hand grips 
the gas 1 ever. 

Full throttle! 

Five streams of fire rush downward -~ bent back like the hood of 
a coiaet under the air pressure. 



— p 

' I do not believe that, in air-free epace at the distance of Venus 
from tiie sun, a crust of ice can form around a body or remain intact 



at all. 



- 434 - 



The fx'ee fall !■ getting sloirer. 

Far belx>v the gloving ruins of the Venus satellite are burning up. 
The star is no more. 

Korf looks dovn -with burning eyes. The surface of Venus is ap- 
proaching at a raving speed. The ship is falling — still falling! 

Is the altitude sufficient to ccnnpletelj stop the fall and then 
ascend again? 

The nozzles are operating effectively — but will thej' master the 
mad falling velocity? Korf's brain irorks like lightning. Thirty Esetree 
of velocity are decelerated in every second. The nozzles have vorked 
for three minutes — that already makes 5 sec/km of velocity by irhicb 
the free fall has been decelerated so far. 

Again he gazes below him. ... 

Below glistening idiite surfaces are spread out interspersed by 
dark lines. There is a black spot witli sharp edges exactly in line 
vith tlie vertical . It is eajlargiiig extremely rapidly. 

A lake ? Water ? 

Hope shinaaers in the steely eyes of the engineer. He presses his 
lips togetlier, What if he dared the uttensoet — 1 

lie waits two seconds more — then he sviugs the gas lever around 
to its linit. 

The nozzles have stopped crocking — they give a hoirl — screorjing — 
thunderously spewiu^^ cosmic power in the direction of the mainland. 

The hammocks rip under the enormous pressure. 



' Vhat is likely meant here is the plumb line* 



- 435 - 



The lungs can no longer lift the ireight of the chest''' . 

The maneuver is successful. 

The terrible rearward thrust decelerates the fall in the last 
second and almost brings tl\e rocket to a standstill just above the 
surface of the vater. It slovlj falls the last ten meters — like a 
spinning leaf. 

The stream of fire frran the nozzles violently agitates the vater. 
Giant clouds of steam ascend. Then a slap-bang. 

No one is there to feel it. Unconscious — struck doim hy the 
enormous counter-pressure ~ the three space travellers lie on the floor. 

7ater laps high ogains the vindovs, A greenish film covers the 
glass. The nozzles are extinguished in the enveloping irater". 

Thus for GAIL. 

This could in a measure have introduced the reader to the thought 
patterns of space travel; nov I -would like to proceed with the discus- 
sion of model E. 

The Observer's cabin . The observer's cabin is best designated as 
an "aquarium for earth dwellers" placed into interplanetary space. As 
a sea aquarium enables sea creatures to live in a totally different 
environment far frmn their home under conditions almost natural to theoi 
just so the observer's cabin is to enable the astronaut to live in 
interplanetary space under almost terrestrial conditions. 



The front chest wall (at least that of a man or a girl) does not 
weigh over. 5 kg. Therefore, with a counter-pressure of 6 g, the effect 
would, at the most, be as though a 25-kg weight were distributed 
evenly on the chest. At that, the intercostcvl muscles could still lift 
the chest. 



- 436 - 



The question of temperature . One often reads about the "loir 
temperatare in interplanetary space." Other authors again (e.g. LUDWIG 
anion) let their space travellers suffer from heat. The truth is that 
interplanetary space has no temperature of its own whatever. As is 
well known, heat is concurrent with a state in which the nFTf\l}rRt particles 
of a body strike each other and whirr about more or less rapidly. 
Hence, only a body consisting of molecules or atoms can have tempera- 
tures, not empty space. The energy that is transmitted from one star 
to the other does not penetrate it as flowing or conducted heat, but 
merely in the form of electromagnetic ether waves. Here a body cannot, 
as in the atmosphere, be brought to the temperature of bodies found 
in its neighborhood by conduction or circulation of the surrounding 
medium. 

The bodies flying in interplanetary space themselves naturally 
have some level of toaperature; it may be just absolute zero (- 273* C)« 
This temperature depends on what kind of ether waves strike the body, 
what fraction of the ether convection it absorbs and converts into 
heat, and finally how easily it, on its part, again gives off its 
heat to interplanetary space as radiant «aergy. Of two bodies flying 
side by side, for example, one can be glowing; hot in the sunlight 
while the other remains ice-cold. It may be that one is located in 
the shade of the other, it may be that the one reflects the light 
striking it onto the other like a mirror, and finally it may be that 
the tro bodies have different surfaces. 

Wlicn the sun shines on a body from a distance of 100 — 200 million 
km, it radiates the energy to it in relatively short waves due its 
high temperature. Now the body heats up and itself begins to radiate 
heat, but in long waves. JL balance is reached when it radiates just 
as much energy as it absorbs. Black bodies permit much energy to mter, 
but they also radiate it easily again. White bodies absorb little 



- 437 - 



heat, but these do not let it eacape so easily again. If all body 
sorfaces vere equally permeable for ahort-trave as for long-vave rays, 
all small spheres in interplanetary spacei for example, vould have to 
heat up to the same extent irith equal exposure to radiation. (On ear%b 
the black bodies become warmer than the vfaite ones because the nain 
part of ihe absorbed heat is given off to the air by conduction. This 
part, boTever, is just about independent of color, so that with a 
irtiite body there is the same loss of heat but relatively loirer heat 
absorption.) Nov, there are materials iifaich are relatively veil perme- 
able to short waves but not to long ones (e.g. glass, carbon dioxide, 
sodium chloride). These allow the short-wave sunlight to enter but 
retain the long-wave raya which, with its low temperature, are the 
only ones the bo^ can emit. Such a body must be warmer than cm 
absolutely black body (e.g. a salt pond or a glass bed). — Other matter 
such as fog, snow, or tincture of iodine are more permeable to long- 
wave than to short-wave rays. In interplanetary space, at the same 
distance from the sun as the earth, these could be up to 50* colder 
than a body of the category mentioned earlier. 

Moreover, much depends on the form of the body. A sphere receives 
the sunlight from one side only, but it freely radiates its own beat 
to all sides. On the other hand, a long cylindrical wire, relatively spooldi^, 
radiates infinitely little heat in the direction of its axis. Finally, 
a broad plate has only two radiating surfaces irtiich must be taken 
into account in calculations. 

Finally, the surface of a body mast not be of the same brightness 
everywhere. A plate or sphere, for example, whose black surface is 
turned to the sun end the shiny surface to the shade will heat up much 
more than when the shiny half is turned to the sun and the black to 
the shade. 

Let us imagine a sphere as far away from the sun as the earth. If 
its diameter is 1.128 cm, the circle of light striking it -will be exactly 



- 498 - 



o 2 

1 ca and its total surface irill be 4 cm . The heat inside is to spread 

■0 Rapidly hj conduction or flux that its surface can be regarded as 

evenlj varm. The surface is to absorb all the rays striking it| it 

must be absolutely black. Then, according to ABBOT'S measurements, 

which at present eire considered as the most exact, ihe sphere receives 

energy amounting to 



3^ «*1 



sec~^»cm~* 



2 

(that is, in one second the sun radiates onto an area of 1 cm > per- 
pendicular to the sun's rays* a quantity of heat equal to l/SO of that 
necessary to heat 1 g of vater from 15* C to 16" C). If the absolute 
teraperature of this sphere is T, according to research by STEPHiN, 
BOLTZliUNN and KUBLBJUm, it itself radiates 

i.27'10""^* cal sec-^'cm"* T* . (202) 

In this connection, also compare p. 292 ff. The irarmer the sphere, 
the more heat it radiates, and if 

4* 1.27 -10-12 t'* - ^p , (203) 

the irradiation is just as great as the radiation. Then the sphere 
neither beats up nor cools off. From that, this fol loirs i 

T = 285*. 

That is 12* C above 0. (On earth, the average temperature is some- 
irtiat higher because the earth is still hot on the inside and that 
contributes something to the heat of its surface. Why it is not still 
considerably hotter is because of the cover of clouds; extended 
desert areas, the Sahara, for example, are much hotter.) Naturally, 
a spherical observer's cabin also has a temperature of 12* C if it 
is uniformly permeable to the radiating energy at all places and to 
all sides. 



- 439 - 



On the other heund, vith a lonf, thin, round \fire irhose axis is 
perpendicular to the sun's rays, the radiating surface is onlytt'^ 3.14 
times as great as the surface of incidence. Here we irust irrite 

3,14«1.27«10~^^«t'* = —. (204) 

30 

From that, this would follow : 

T = 302» abs. = 29» C. (205) 

If its axis were parallel to the aun's ruya, the radiating 
surface would be very much greater than the irradiating surface. Its 
tffinperature would then be very low, especial ''y at the shale end. 

Thus, the temperature of the egg-shaped observer's cabin is between 
12' and 29* C if it" axis is perpendicular to the sun's rays. If it 
is parallel to the sim's rays, it will be somewhat below 12". This 
only applies if the surface is the same at all places. 

For a broad, thin plate perpendicular to the sun's rays, the 
surface of incidence would be half as large as the surface of radiation. 
Here we get t 

T =. 350» abs. = 77"» C. (206) 

Finally, with a thin disc which is bright on the shade side and 
black on the sun side, the coefficient of radiation is 9 times as great 
on the sijn side than on the .<?hade side. Here, almost only the front 
wall is in question when it cones to radiation; so we can equate the 
surface of incidence with the surface of radiation, and we obtain a 
disc temperature of 147* C above 0. This value coincides approximately 
with the Values that have been measured with the bolometer on the 
moon's surface. At noon, at the equator of the moon, the surface 
of incidence is also as large as the surface of radiation. 
On earth, the bodies never get that hot in the sun because 



- 440 - 



•ir currents arise which conduct the produced heat avaj again (Flick- 
ering of air oTer objecta standing in the sun.) 

On the other hand, Uie effect of inrerting tiiis surface vonld 
be as thon^^y keeping the same color, the radiating surface had be- 
eeae 10 times as large as the surface of incidence. The temperature 
venld be onlj 

T > 835* abs. . - 38* C beloir 0. (207) 

A vhollj bright bodj in interplctnetary space is in the same 
position as the contents of a thermos flask. It can absorb or give 
off heat hj radiation only vith difficulty. So it is not necessary to 
•quip a diver's suit vith double walls like a thermos flask as has 
often been sum;ested to me and VALIEK apparently had in mind for 
some time '. On earth, thermos flasks must have double walls only to 
pemit forming a Tacuum around the inside container. In interplanetaiy 
■pace, hovewer, ewery body is surrounded by air-free space anyway, 
•nd it is entirely sufficient to make the diver's suit out of shixty 
metal plating in order, in great measure, to protect the direr against 
heat and cold. 

HOmiANN'S suggestions (The Reachibility of the Celestial Bodies) 
with respect to the observer's cabin are also not thou^t through 
oenelusively. HOHUAMN assumes that the shade side of the observer's 
eabin will have a tesiperature of 0* abs. - - 873* C. Accordingly he 
thinks of lining the inside of the wall with a strong insulation 
•gainst the loss of heat and heating the observer's eabin with kerosene. 
But that is not necessary, as ve shall see immediately* 

ilj idea is to simply make the observer's cabin out of i to 8-( 

' He had misunderstood the story related at the beginning of tiie 
•zeerpt. 



- 441 - 



thick •lominm plftting vitbout igij «p«cial protection ag»iniit froat 
(cf. Plate IV| I). Am maaj vindors of quArts plate as posaible are to 
be inatalled om all eidea. The oataide aurface la to get a apecular 
coat and the vindova are to be fitted out ao that thej can be corered 
vith apecular plating oo the ontaide. One half ia to be covered vith 
black paper or ailk cloth, which ia to cling ti^tly to perait it 
to giTe off ita heat to the metal by conduction. Inaide tiie obaerver'a 
cabin} the heat quickly apreada to all aidea bj air circulation. 
Depending on hov much of the black or ahiny half ia turned torard the 
auttf the tenperature can be regulated. With model E, the tip can alao 
be Jettiaoned and the parachute can be noved off aa from cabin I of 
the obaerver. Since I ia connected to the hydrogen rocket only by 
electric -rirea, I can be moved amy a good diatance) allowing a free 
Tiev to all aidea in apace (Fig. 187). Since their ia no coimter- 
preaaurey the objecta can easily be given any poaition with respect 
to each other. 




Fig. 187 

In ao doing) aa in Fig. 187 , it is possible to have the holloT, 
reflecting inner surfaces of the tvo tip sections a likevise reflect 
the sun's rays on cabin I. Thereby «idurable temperatures can be 
maintained inside the cabin oven in the zone of the asteroids. 
Conversely, the observer* e cabin can be moved into the shade of the 
tip and turned toward space vith ihe black side so that the bright 



- 448 - 



aide reflects Uie heat rftyi ufaich the tip alloired to pass through and 
the black side gives off into space vfaat the bright side may hare 
alloired to pass through. In this vay, the rocket could travel on the 
edge of the sun's atmosphere iritbout causing the occupants to suffer 
from the heat* 

We must keep the containers for the liqmid gases cool. So ire must 
do the opposite t We Till place them into the shade of the observer's 
cabin, the parachute, and the tip sections, leave them polished on 
the sun side and paint them black on the shade side. 

It has been pointed out to me that the liquid hjdrogen irould, 
nevertheless, vt^orize on the son side and freeze on the shade side. 
I do not believe the latter irould happen since cold and irarm liquid 
is constantlj being mixed due to diffusion. — Unfortunately, I do not 
knoir vfaat is the actual rate of diffusion of liquid hydrogen and 
wfaetiier it vill suffice vith large rockets. It does not appear to be 
knoTO even today; at least I vas not able to find out. This does not 
present a basic problem, hovever. In the irorst case, a type of agitator 
could be attached to the tank vfaich mixes the liquid occasionally or 
a number of electromagnets could be built into the vails, ufaich are 
STitched on alternately as in the three-phase motor, and a perforated 
hbllov sphere of iron plating or the spherical float of the liquid 
indicator is all owed to roll about in the gas tank. 

All this research only applies as long as the space-ship travels 
in sunshine. With model £ that is mostly the case, for its trips take 
it into the shade of distant celestial bodies at the most for 1 l/S 
hours. 

The surface area of the observer's aabin is roughly 10 m'^. If it 
reflects and the irindov covers are possibly kept shut, it radiates 
45 cal. per second, vith an inside temperature of 17* C above 0. 



- 443 - 



In an hour that vould make 188 cal. It vonld lose that much through 
radiation in the ahade of a large celestial bodj. This heat loss in 
itself could b» made up hjr burning 18 g of kerosene. As is veil 
knonn, the passengers also derelop heat (over 100 cal. per hour per 
person); the alkalis carried along for absorbing the carbon dioxide 
likevise, so that it Till likely not be necessary to heat at all* 
No more does space diving equipment need to be heated. 

It has also been objected that space dirers vould roast in the 
sun on <me side and freeze on the other, I hope the reader Till re- 
alise from these extremely low figures for heat loss that the shade 
side of the obserrer's sabin must feel nearly just as irarm as the 
light side. 

Only vith large observers' cabins that enter the shc^e of the 
earth very often (let us say with a station constantly rotating 
about a celestial body) vill special precautions against heat loss 
perhaps be necessary, say lining the vail vlth a poor heat conductor, 
Ifuch can be gained. by this measure) for the radiating capacity of 
reflecting surfaces decreases almost as the 5th pover of their absolute 
temperature, 

Short^^rave r^rs in interplai^etary space . As laboratory experi- 
ments teach, short-'vare rays (light rays on the other side of the 
ultrar-Tielet spectrum, roentgen rays, and y -rays) only pass throu^ 
our atmosphere wiih difficulty. The result is that sunlight on the 
top of high mountains contains more ultra-riolet rays. Hence ve irill 
probably meet up vith strong short-nray radiation in interplanetary 
space. Their energy content cannot be great. For example, if, in his 
novel, "On Tvo Planets", KURD LISSWITZ writes about ultra-violet 
radiation that contains 30-40 times more energy than the sunlight 
that reaches us, I see that only as poetic licence. Our atmosphere 



- 444 - 



could not ref 1 ect auch radiation | it could only absorb it) for tiie 
atmoBph«re has no reflecting surfaces vith reference to interplanetary 
space, as does vater, but the air is grt^lually lost in the Tacuun. 
Hence, the air would not reflect rays striking it as a glazed clay 
surface reflects light, but it vould absorb them like a dug garden. 
But if the uppermost layers of the a-tmosphere absorbed such a quantity 
of energy it vould have to be considerably vamer on earth that it 
actually is. 

The KOHLHORSTER rays . Nov, in interplanetary space, ve find very 
hard (i.e. short-vaTe) radiation emitted by certain mist patches, 
irfaich has the effect of very hard roentgen rays. This radiation itself 
has too short a vaTe^l ength to harm the htsoan organism, but it causes 
the bodies it strikes to emit a somevhat longer radiation, the so- 
called secondary radiation. It iras with regard to this that fears vere 
expressed that an insurmountable hindrance to space flight could arise- 



This radiation is too weak to hcurm man in a measure -worth mention- 
ing. The inhabitants of regions where radium is produced (not to 
speak of workers in uranium mines and X-ray doctors) are constantly 
exposed to stronger y-rays without suffering harm. For that matter, 
I can here ref^r to the discoverer of these rays, Prof. Dr. WERNER 
KOHLHORSTER himself, who, when asked about this, declared that he saw 
in any case only the smallest hindrance to space fli^t in this radia- 
tion. 



The ultraviolet light could not penetrate aluminum walls and glass 
windows. But I chose quartz. glass just for the purpose of not complet- 
ely shutting out the ultraviolet light. 

i) It accelerates the oxidation of the disintegration organic 



- 445 - 



matter vfaich perhaps ia not completely eliminated by the air purifying 
apparatus still to be discussed. One ia easily convinced of that by 
the foil owing experiment t 

The air in a small, dark room is polluted nith hydrogen sulfide, 
ethyl hydrosulfide, rotten meat, or the like, the small remains for 
ireeks. If, hovev^r, an ultraviolet lamp is left burning in this room, 
the air is pure after a feir minutes. 

2) I do not vish to dispense completely vith the refreshing and 
blood-purifying power of ultraviolet rays, especially for longer flights. 
I here have the choice, as it irere, between submarine air and mountain 
air| naturally I choose the latter. 

Corpu scular rays . Beside the electromagnetic ether waves, electric- 
ally-charged atoms and electrons are also flying through space. We can 
measure their penetrating power by our northern lights. Where these par- 
ticles strike the air molecules they cause thoa to give off light, and 
that ia known to be the basis of our northern lights. They begin at an 
altitude of about 500 km and suddenly stop at an altitude of 95 km 
above the ocean as if they had struck against an invisible wall. This 
wall is the atmoi^phere of the earth. The momentum of these small bodies 
is sufficient to drive them into the earth's atmosphere up to the ninety- 
fifth kilometre. If one placed a layer of air of normal density in their 
path, they would not advance 10 cm in it. Namely, at an altitude of 
95 km, the air is at the most under a pressure of the 200,000th part of 
one atmosphere. That figure is rather too high than too low. 

That the corpuscular rays already shine there, while still being 
invisible in equally rarified GEISSLER tubes, is based on the fact that, 
in the first place, the space passed throup;h is longer. Naturally, 
*.he lonser the tube, the greater the probability that the radiating 
particle will strike a molecule on its way eoid cause it to shine. 



- 446 - 



Secondly^ it is based on the fact that the space i« oucfa vider, so 
that turbidity caa be seen which is not discerned vith a depth of 
5 — 20 (an (ve do not hare QEISSLER tubes much thicker than that). 
This is the same natural phmiomenon that makes a li^er of air 10 en 
thick appear clea^ irfaile one 80 — 100 ka thick appears cloudy. 

If tiie lover edge of the northern lights lies in an atmospheric 
layer that has a pressure of 0.05 kg/ra , that is the same as if the 
corpuscular rays had passed through a layer of air of normal density 
4 cm thick. The distance they cover in any medium depends on the mass 
of the matter that vas passed through. The specific veight of normctl 
air is 1.29 kg/m^. If it stood 1 m high abore a surface, it irould 
exert a pressure of 1.29 kg/ en . But here it has a pressure of only 

0.05 kg/ cm I irfaich vould correspond to a height of ^ ' ■ m a 4 cm. 

Nov, these electrons naturally do not alvays enter the atmosphere 
perpendicularly, yet, •with the spherical shape of the earth and the 
ri^id decrease in the air density irith higher altitudes, this dif- 
ference is relatively unimportant. These rays vould penetrate at the 
most 0.0042 cm into aluminum or glass} and disintegration of the 
glass or aluminum is nbt to be feared. As a rule, GEISSLER tubes are 
made of glass and their electrodes of aluminum, yet they endure radia- 
tion of quite different intttisity for the longest of periods. 

The air supply . The supplying of air could be arranged similar 
to the case of submarines. Another vay vould be to only renew the 
oi^gen in general, since breathing does not change the nitrogen, and 
somehow to remove the aspirated carbon dioxide from the air. In so 
doing, the oi^gen could be produced from potassium chlorate or taken 
along compressed in cylinders or in a liquid state and vaporized 
either by the sun or by the use of fuels. Taking along liquid oxygen 
in the rocket would prove best, for larger quantities of liquid 



447 - 



oxygen would b« carried along anjwaj and they can be stored for anj 
length of time in the shade of the rocket. For reasons I will not 
discuss further here, I v-ould take along the supply of liquid oxygen 
intended for breathing in a separate container. (l did not shov it 
on Plate IV in order not to confuse the picture.) 

In general I -would replace only the oxygen and reoowe the ccu*bon 
dioxide. Newertheless, beside mainly oxygen - containing liquid, I 
would t«tke along about half that quantity of liquid nitrogen in a 
separate tank, in the first place, in order to renew the ^ole air 
supply occasionally and, secondly, in order to make up for possible 
loss of air, about which we will speak later. If, with loss of air, 
we only continually replaced the o^^gen, the air would soon be so 
enriched with oxygen as to be undesirable. The liquid air vaporizing 
apparatus would hare to be arranged so that they automatically keep 
the air pressure inside t^e cabin at a certain level and alarm the 
pilot in case it suddenly drops. On longer trips, the pilot can 
easily determine the composition of the air chemically and regulate 
it by correctly adjusting the apparatus. 

'>n shorter flights and in the shade of the earth, I would use 
alkali hydrates (sodium hydroxide, potassium hydroxide, or slaked lime) 
for elimination of the carbon dioxide. These absorb the carbon dioxide 
according to the formulas t 



and 



NaOH + C0|| - NaHCOg 



8 NaOH + CO^ - Na^CO^ + H^O. 



These alkalis would, at the same time, absorb some water vapor, 
which could be supported by adding some quicklime. They would simultan- 
eously absorb the sulphur dioxide and the nitric oxide which are formed 



- 448 - 



from disintegrating organic aubstancea under ^e influence of the 
ultraviolet light. 

For purification of air on longer trips I irould use the air 
distiller discussed on p* 418. That naturally vorks only in sunshine; 
but one does, as a rule, flj in the sun. I irould like to mention 
that I would also put thd air coming from the air distiller through 
alkalis before leading it into the observer's cabin; the alkalis, 
hoTever, -would scarcely be used up with air purified in that way. 




Fig. 128 



Wastes can be conveyed from the ohaerTer'a cabin in the following 
way (cf. Fig. 128). The object a, which is to be thrown out, is 
brought in front of a shutter b; the latter rotates outward about hinge 
c and is held shut by hoop e and roller d. The hoop is tensed by hold 
g which can be suspended from hook i; i can be tightened by a specitJ. 
lever hot pictured here. Usually, shutter b is pressed firmly against 
a rubber ring. Then a dish-shaped container f, whose flat edge clings 
firmly to the wall and is likewise lined with rubber, is turned upside 
down over -Oie object. When shutter b is opened, the air under f 
escapes outward and, at the same time, draws the object with it, 
while the air inside the rocket firmly presses dish f to the wall. 
If dish f is to be opened again, air is allowed to enter underneath 
it throng the cock b-. Obviously, in so doing, the air flows obliquely 
inward causing a wind by means of which, with shutter b open, the 
object can still be expelled even if it should cling to the shutter 
or the dish. 



- 449 - 



FELIX LINKS suggests that vastes and faeces not be flung into 
interplanetary apace at all but be takes along until landing becauaey 
at the hi^ relative velocities vith irfaich ve are dealing here, flying 
pieces can later constitute a danger to space-ships once th^y becMie 
numerous I the more so since the space-ships vill repeatedly travel 
only al'U^ certain paths, on which matter will then accumulate. 

Well y I am not saying one or the other to avoid being accused 
later of having said so and so. One thing is certain. Interplanetary 
space is large and can hold a lot. It is finally more or less a matter 
of our world view whether we already want to iiimer«e ourselves in 
expenditures for the sake of our posterity over 60,000 years. In any 
case, we are not as pedantic in many more iimnediate questions (e.g. 
depracating our estate by marriages of convenience, unhygienic mode 
of living, etc.). Besides, because of their water and gas content, 
faeces, for example, immediately disintegrate into minute pieces, so 
that we are, at the most, concerned with cosmic dust whose grains are 
too snail to harm a space-ship. — On the other hand, encountering a 
half-rotten beet or a broken control gyroscope could, in fact, 
have unpleasant results and it should actually be considered whether 
such things should not at least be ground up beforehand. That is 
easily done if they are kept in the shade of the space-ship for some 
time, where they freeze to -873* and become brittle. 

The question of wastes would have to be considered seriously in 
connection with the observer stations rotating about the earth, as 
I will describe them in the next cht^iter. Fortunately, this disposal 
device gives the objects a certain propulsion and it can well be 
arranged to make the wastes hit the earth's atmosphere due to their 
disturbed trajectory and thus end their existence as indepmdent 
celestial bodies. Naturally, in the upper layers of the atmosphere, 
they immediately bum to dust like meteors, so that, for the people 
living below, the matter would only represent a pretty spectacle 
without further consequences* 



- 450 - 



Space diTers . When the motor is shut off, there is no counter- 
perssTire on the flying space-ship and so the passengers can put on 
divers' suits (cf. Fig, 129), leave the observer's cabin, and float 
near the space-ship. The divers' suits -rould have to stand an inside 
pressure of 1 atmosphere. I vould make them of thin polished tin and, 
in principle, similar to the deep-see divers' equipment already in use 
today. For hands, I -rould attach clavs. The feet could have hooks with 
niiich the diver can hold on to the cables or rings especially attached 
for this purpose to the projections of the rocket. For the rest, the 
diver's equipment could be considerably lighter and thinner than 
equipnent that is to stand an outside pressure of 10 atmospheres. 
I would embed the joints in a balloon of canvas lined irith a thin 
layer of rubber on the inside. The whole diver's equipment could be 
tested before the ascent by sticking it into a somewhat large deep-sea 
diver's suit and using the air hose of the deep-sea equipment to 
evacuate the space betweoi the two suits. 




Fig. 129 

It appears impractical to me to supply the diver with air through 
a tube from the observer's cabin, I would rather let him carry 
compressed or liquid air in a cylinder P. The diver could breath the 
aspirated air into a second tanjc L which expands like an accordian 



- 451 - 



and is kept at atmoapheric pressura by spiral springs. From time to 
time» the diver can empty this tank to the outside hj means of cocks 
H, H.. That causes a slight reanrard thrust ufaich gives the diver a 
certain pover to influence his raovem^its, for example, during free 
flight. As LAFFERT has suggested, for special purposes the diver 
could take along reanrard thrust pistols similar to those of BROWING. 

For the rest, the diver is not supposed to float entirely free 
but is to be connected to the observer's cabin by a cable F. Telephone 
-wires can be vound into this cable, for air-free space is known not 
to conduct sound and it appears desirable that the diver be able to 
speak to the persons in the observer' g cabin. 

In contrast to GAIL, I ▼ouldl like to have the head-piece screved 
on not on the outside but on the inside by the diver himself, but it 
is also supposed to have a flap K that can be opened frcm the outside 
for any eventualities. To enable the diver to get out vithout causing 
too great a loss of air, the observer's cabin has a passage irhich 
can be closed airtight both front and back (Plate IV, T). This also 
serves as entrance to the observer's cabin before the start. The 
diver gets in irith the outside door shut; then the inside door is shut 
and the air from the passage is vithdrami to the observer's cabin or 
into a compressed air tank. Then the diver opens the outside door, 
cravls out halfvay, and fastens the end of his lead cable to a screv 
affixed here for the purpose. This screv also provides the contact 
for the speaker. Nov the diver can move out into space. 

The precision and control instruments of model E in geuere^ cor- 
respond to those of model B already described on p. 331. Concerning 
the acceleration indicators and the control gyroscopes, I have already 
said vhat is needed on p. I23and p. 271 ff. Concerning position find- 
ing by the pilot, the reader Till find -what is required on p. 281. 



- 452 - 



The instniment described under 7 is not needed here since the laost 
adTantageoua velocity ▼ is not observed. Here, the velocity is regala1>- 
ed by a ireight vhich hangs by an elastic spring and keeps the counter- 
pressure on the same level, mien the pilot changes the suspension of 
this spring (the regulating resistance mentioned above by the use of 
mercury tubes), the acceleration changes, 

7a) Here, the hydrog«) rocket must not simply bum out; it can be 
shut off by the pilot and turned on again later. The folloiring ni{^t 
also be mentioned i Ifhen the observer completely turns off the fuel 
supply to puBips P., Po and m, n (cf. Plate IV), free fli{rht begins 
and the rocket is not subject to any counter-pressure. Since the 
▼alls of the tank are vet from liquid oxygen and especially liquid 
hydrogen, the lipids accvmiulate along the vails and force the vapors 
tovard the centre (cf. Fig. 57). Nov, the vents -which bring the 
liquid to the pumps are situated quite close to the floor (on the 
vail, therefore). They vould still be covered vith liquid even if 
th^ extend far invard. ^ea these vmta are opened, the inside pres- 
sure forces liquid through and not gas, even vhoi there is no counter- 
pressure. (The safety valves are another matter, but th^ are not 
being used nov.) So, vith free. flight in ether space, the rocket can 
actually be started at any time, <mly the counter-pressure may not 
act in the direction from the outlet to the tip. Where this is in 
danger of happening, the rocket must have special liquid vents. 

Finally, mmtion should be made of the periscopes p (Plate ZV) 
vfaich permit an open vlev on all sides during the ascent. As soon as 
free flight begins, as is represented in Fig. 187, the tip is jettison- 
ed and the vfaole machine is spread out to give a free view to all 
sides of space. This is possible since these pcurts appear as though 
th^ had no vei^^t and are connected only by cables and electric vires* 



- 453 - 



Little can be said about the rentaining parte of model E} thej 
oorrespond to the machine parte of model B labelled vith the same 
letters oa Plate I sad discussed in Chapters 16 — 17. 

Purpose and tHmctions of the E Model 

a) Space telescope (cf. p. 418) 

As is vell-knonii astronomical telescopes consist of a large lens 
of considerable focal length, the so-called objeetire, vfaicb produces 
a relatively largei inTerted, real image of a distant object in front 
of the obserTer. B^ means of a l«is serving as metgnifying glass, tlie 
so-called eyepiece, the observer can thm approach ihe image as dose 
as he ▼ishes. — A reflecting telescope has a concave mirror instead of 
the object glass, which likeirise projects inverted, real images of 
distant objects '. 

Building astronomical instruments on earth is fraught with great 
difficulties. The first consists of the fact that there is alvays 
diffused light present on earth. That is disturbing -when one vishes 
to simply fasten two lenses one behind the other, let us say on a 
stick. Hence the lenses must be attached at either end of a pipe which 
is coated black on iixe inside. 

Naturally, that would be the least. The disadvantages resulting 
from the force of gravity are more inconvenient. The telescope bends 
easily and it must be mounted <m firm footing. But no absolutely rigid 
bodies exist and so telescopes of too light a build vibrate when they 
are touched. Moreover, no accurate angle measurements can be made 
with too light and bendable instruments since the effect of gravitation 



■^^^7^ 



writing this section also for laymen and ask the opticicua to 
excuse me for making some things sound nomewfaat amateurish. 



- 454 - 



bends them somevfaat from the direction they should have according to 
the position of suspension mechanics. Vlth very strong magnification, 
the holding of the pipe due to gravitation easily has an unfavorable 
effect on the sharpness of the image. These dravfoaeks can be offset t 

1) By making ihe stand of the telescope as massive and strong as 
possible; the pipe likevise. Naturally, that makes the instrument 
very heaiy. 

2) By not making the telescope too long. As is veil known, small 
bodies are relatively more rigid. I can hold a thread 6 cm long and 
1/5 mm thick stretched out horizontally. A rope 10 m long and 4 cm 
thick resembles the thread in form but, upon stretching it out horizon- 
tally, the end hangs dovn limply. Now, the length of the telescope 
mainly depends on the focal length of tlie objective, but the magnifica- 
tion equals the figure obtained by dividing the focal leigth of the 
objective by that of the eyepiece. If one makes both focal lengths 
short one arrives at a relatively short instrument which still enlarges 
well. But this is like a two-edged weapon. Apart from all other dis- 
advantages, this requires painstaking accuracy in toe manufacture of 
the instniraent, since the eyepiece considerably magnifies an error in 
the objective image. That is why really good telescopes are so rare 
and expensive. 

A further disadvantage of the telescopes on earth is that they 
must be kept directed at the stars and that it is never possible 
always to observe the same star when one wants to. Observation depends 
on time of day, weather, and region. 

Once having overcome all the difficulties connected with the 
construction of the terrestrial telescope, we come to ibe main problem. 
As is well known, a star always flickers a little due to the earth's 
atmosphere, as can be observed with the fixed stars. For this reason, 



- 455 - 



more than 8000-fold magnifications can only be used under especially 
favorable conditions. Vith such strong magnifications one simply cannot 
see anything defined. The large telescope in Chiceigo, for example, 
is "too strong" for the canals on Mars! 

In interplanetary space, any magnification can be used, since the 
stars do not flicker. In his norel, "The Stone from the Uo(m", GAIL 
describes a telescope vith a 10,000-fold magnification. I vont to 
surprise the reeuier vith the remark that GAIL iras much too timid. 
I am expecting million-fold magnifications. The irell-knomi astronomer 
FLASS&IANK has objected "that . ... it is not enough to have escaped 
from the earth's atmosphere since at least on Mcurs, of vfaich most 
▼ill think first, the atnosphere cannot be removed". This statement 
has largely been understood to mean that an atmosphere still exists 
irhoae flicker vould make observing the surface of liars just as diffi- 
cult as does the earth's atmosphere. I am not certain vhether that is 
how FLASSIiUNN meant it} at any rate, the conception just mentioned is 
not valid. If the telescope is situated at the bottom of our atmosphere 
and the rays coming from the stars are diffused, let us say, by only 
l/S second of arc, the impression made is as though ve had set up the 
telescope in air-free space and were observing an object irtiose points 

6 1 

make fickering movements of 60*10 '-gi an expansion of more than 100 km. 

That is the case in especially clear weather. If, on the other hand, 
the telescope is placed in air-free space and the surface of Uars is 
viewed throng a flickering atmosphere 60 km thick, the effect is only 
as thou£^ the points made flickering movement of 60«^ - 10 cm. It is 
the same phenomenon as when a picture is clearly visible through trac- 
ing paper lying on top of it but nothing can be seen when the tracing 
paper is held before the eyes. 

Furthermore, the background is completely dark, so that the pipe 
of the telescope is superfluous. The parts holding the objective 



- 456 - 



reflector (because of the size of the objective, only reflectors 
C(»ae in question here) can be much simpler since there is no counter- 
pressure. In general, it is sufficient to distance a large, moderatelj- 
shaded parabolic concave reflector from the space-ship hj three steel 
vires. The length of this telescope is not important at all. If ve 
wish ve can dispense vith the eyepiece entiroly and get a real image 
of the objective projected into the observer's cabin, for that matter, 
on to a glass plate on 'iliich ire can then make our measurements vith 
protactor and rule. jLccordingly, the reflector need not be vorked out 
so very accurately. It need not even consist of a single piece. It can 
be packed in several pieces vith the parachute and assembled by divers 
vfaile aloft. Only the joints betveen the pieces must be smeared vith 
a reflecting paste to prevent diffraction. Because they are of such 
light construction, the mass of these telescopes is so small that 
they can be carried aloft by a rocket. 

Opposite all these advantages of the ether telescope there is 
actually only one drawback. The earth gives a telescope firm support 
vfaile the observer's cabin of the rocket is affected by every movement 
of the passengers. This dravfoack could be offset by somehov connecting 
tiie objective to a control gyroscope and using an eyepiece (or an 
isinglass plate) vfaich is attached similar to a seismometer so that 
it does not follov the movwiaits of the observer's cabin. 

For the rest, contrary to the fears of PLASSfiANN, the sighting, 
holding, and photographing of celestial objects could sooner be easier 
than on earth, for the rocket maintains the position <mce given it in 
space as long as the motor does not vork and is easily focussed on a 
point vith precision by use of the rotating wheels mentioned on p. 266. 

Greater angular distances can be measured by using ihe large arc 
meter, vbich is presently finding application at the Babel sberg 



- 457 - 



ObserTatory* Such an apparatus (contraiT- to espressed fears) vill 
sooner be easier to handle on the rocket than on the earth. Actuallji 
vith more precise measurements, ire usually need only the angle betireen 
the object and any given point nearby ^ not the exact location of the 
object in degrees, minutes, cuid seconds. On earth, the parallaxes of 
the fixed stars, for example, are not determined vith the use of the 
horizontal and vertical circles of the telescope; rather, the respect- 
ive star is brought into relation to a distant fixed star visible 
nearby. In a similar vay, it -vill be possible to make measurements 
concerning the diameter of planets, the distance of strange planers 
from their fixed stars, etc., by a relative angle measurement and by 
linking them to neighboring fixed stars. 

These instrunents vill function perfectly vhen ve succeed in set- 
ting up such a space telescope on an asteroid (e.g. on the small planet 
Eros). The mass of a star i — 2 km in size is sufficient to give 
completely solid support to the telescope and bring all uncontrollable 
movements belov the limit of the perceptible. Such an asteroid is so 
small that no trace of air is found on it and its force of gravity has 
no noticeable effect. Krploring Eros, vhich, after the moon, comes 
closest to the earth, is quite possible vith model E. No doubt, valu- 
able research could be done vith telescopes attached to a rocket, 
e.g., vhether our planets are inhabited or at least inhabitable, 
vhether larger meteorites could endanger the flight to our planets, 
irtiether distant fixed stars have planets, vhether various objects 
vhich appear to be sioiple stars are not actually star clusters infinit- 
ely far avay. 

b) Since the sby is completely dark, it is sufficient to screen 
the disc of the sun for freely observing the surroundings of the sun. 
It follovs from EINSTEIN'S general theory of relativity that, for 
example, the light of fixed stars near the sun must be deflected by 



- 458 - 



its gravitational field. But the deflection ia so small that, even 
vith a total eclipse of the sun on earth, it is difficult to prove 
its existence at all or even to say that it was actually brought 
about by the gravitational field of the sun or by other causes. 
LMARD, for example, assumes that the deflection could also be caused 
by the outermost atmosphere of the sun. If, in the completely dark 
interplanetary space, having screened the disc of the sun, ve examine 
the surroundings of the sun spectroscopically and then observe the 
fixed stars near the sun with a screen before the sun disc, we can 
later state exactly whether the deflection of the fixed star was only 
as great as must foilow from the atmosphere mentioned or greater, and 
by how much. 

c) We can observe the solar eoroaa, on earth for a few minutes 
only during absolute eel ipse of the sun. Then it appears to us as an 
immovable circle of rays. Actually it is not that, as we learn from 
the fact that it looks different at every eclipse. From the rocket, 
we can observe Hie solar corona as often and as long as we wish. In 
so doing, we can scrutinize it and determine the connections between 
the solar corona and ihe processes on the visible surface of the sun 
as well as the meteorological phenomota on earth. 

d) Uany fbysicists assume that, in its movement, the earth sweeps 
the ether with it. That is why, for example, MICMLSQK'S experiment 
cannot succeed. Others argue the point and explain the failure of 
MICBBLSOK'S experiment by a certain short«iing of the bodies, which 
we cannot perceive only because the criteria must be lengthened or 
shortened in the same proportion (LOR]ENTZ, EINSTEIN). TOMASCHEE of 
Heidelberg has tried to determine whether there is ether wind relative 
to the eartii on high moim tains where perhaps the ether is no longer 
swept along by the eartb in the same measure. So far the results were 



- 459 - 



negative. The question vould be ittsnediately clarified if TOMASCHGK*S 
apparatus irere talcen into interplanetary space on a rocket, for, as 
(O^IVIBR LODOE already shoved in 1899, the ether is not borne along 
by such small masses. 

e) During free flight, the machine is not exposed to any counter- 
pressure. Hence, many physical and physiological experiments can be 
conducted ufaich are impossible on earth because of gravitation. 

For reasons I irill not discuss further here, I presume, for example, 
that the cells of algae or infusoria vill enlarge enormously irith the 
lack of counter-preasure. From that and from a possibly different 
behavior of the celln, an insight into the physiology of the cells 
could easily be von irfaich could not be obtained otherwise. 

f) We can determine the magnitude of the radiating energy coming 
from different regions of the sty. If, by means of shiny tin platesj 
▼e protect a body against all greater quantities of riidiating energy 
(above all from the sun's rays), let it float freely behind them| 
and take care to alloir it to radiate its own heat to the colder parts 
of space, ire can bring its tonperature extremely close to absolute 
zero, many 1000 times closer than the temperature of solid helium, 
for example. The possibility is not excluded that, in so doing) in 
part entirely nev phenomena (e.g., in the behavior of electrons, 
etc.) could arise. At least, it would be irorth the trouble making this 
experiment. 

g) GAUSS has thought of the possibility that light maj not be 
transmitted in a straight line in interplanetary space or, expressed 
in EINSTEIN'S vords, inscribed in four-dimensional space our three- 
dimensional space would not behave like a plane surface in space, 

but perhc4>s like a spherical surface in space. This question has again 
been raised by EINSTEIN'S general theory of relativity. According to 



- 460 - 



that, it could happen that the three angles of a triangle together do 
not make 180 degrees (non-Euclidian geometry). At the time, three 
observation stations irere built for GAUSS at distances of 30-50 km 
from each other and at each the angle betveen the other two was measur- 
ed as accurately as possible. No deviation from 180* was foimd. This 
ezperiu^it xrould have greater prospects of success if three space- 
ships were used as stations that are many million kilometres away from 
each other. Z do not believe the experiment would be successful, but 
it would be worth trying. According to certain assumptions concerning 
the curvature of space, the possibility is not excluded, with sufficient- 
ly sharp instruments, of again seeing our own }>Iilky Way at a distance 
of 100 million light years, but at the place where it stood 100 million 
years ago and .in the state it had at the time. 

i) The intensity of the sun's rays and the albedo (reflecting 
ability) of the earth could be perfectly determined only from inter- 
planetary space. This would be valuable because important conclusions 
regarding the intrinsic heat of the earth can be drawn from it. Like- 
wise, by observing the clouds from above, important meteorological 
information could be obtained, as HEIN has shown. 

k) I now ask the reader not to be frightened if I touch on the 
controversial field of parapsychology. As is well known, many psycho- 
logists and doctors (serious researchers like OESTERREICH and LOUER, 
among others) assume that suggestion, for instance in hypnosis, or 
the suggestive power of certain personalities is based on the fact 
that ether forces or even substances are transmitted from the influenc- 
ing person to the one influenced, Naturally, I do not wish to decide 
whether and to what extent this view is correct, for, as a physicist, 
I am working in a totally different field. As I see the matter from 
my standpoint, I believe it will be difficult on earth to determine 
anything concerning these forces or whatever they are, even if they 



- 461 - 



Actually exist. According to the theory, such rays emaaate from almost 
every person and these forces all imp in '^e on the experimental person 
simultaneously and cross and obstruct each other. In my opinion, ve are 
somewhat in the position of a man vho, irhile standing near the Niagara 
Falls, irants to examine the overtones of a violin string by the use 
of tuiied resonators. We do not know irbether these rays can somehov 
be screened out. On the other hand, perhaps it would not be impossible 
to determine something positive about it if the hypnotist and the 
experimental person vere taken several 100,000 km from earth in a 
rocket. 

Of course, it might be difficult to find persons vfao are, at the 
same time, useful objects for telepathic experiments and good engineers 
and rocket pilots. But the problem could be solved. A rocket pilot, 
parapsychologist, and experimental person simply ascend in a rocket. 
Then the rocket pilot puts on the space diver's suit and flies some 
100 — 1000 km out into space, using a small rearward thrust apparatus 
that could be easily accommodated under the parachute, while the 
other two experiment. 

l) Here I would like to mention further experiments which are 
possible only in a large air-free space, e.g., transmitting parallel 
anode or cathode rays over long distances; I will say nomething regard- 
ing that in Chapter 28. Th3 8 experiment is much more than mere scientific 
sport; for example, the attempt could be made to set up solar generators 
in space and in this way send electricity to earth. Furthermore, in 
this way the flight to strange plandts might be made possible, etc., 
as we shall see in Chapter 22. 

m) Finally, with an initial velocity v. « 10.4 km/sec, such a 
rocket cotild, at new moon, fly around the moon and examine the back 
side. Uany have suggested equiping an unmanned rocket with a movie- 
camera and letting it fly around the moon this way. I believe, however. 



- 462 - 



that irould not be successful because the accuracy of focus irould be 
too small. In this connection, compare p* 508. Oalj vfaefn the rocket 
has a pilot vho constantly controls and corrects its course is it 
probable -Uiat it vill return safely. 

Naturally, numerous other experiments ecm be conducted vith model 
£, but I do not vish to go into that any further. 

Duration of Space Flights 

(Here, the formula quantities have the same meaning as in Chapter 
10.) 

A. Duration vith vertical flight : I am often being asked how 
long a space-ship would be underway on certain flights. Hence, I will 
say a few things about flight duration. I cannot deal with the question 
exhanstiToly here; in this book I am only proving that space travel is 
possible at all. I must leave the ret^pective literature to deal with 
special questions, llhoever is interested in the detailed calculation 
of the flight period is referred to textbooks on astronomy. They have 
the disadvantage of setting up flight calculations for purposes of the 
a8tron<»ier (locating asteroids, comet movoaents, trajectory disturb- 
ances, etc.) and not for the special purposes of the space navigator. 
The latter usually has a pile of work to do oonpiling what is appro- 
priate for him. 

In this respect, the works of FOHMANN and PlR^Sl are more con- 
venient; they are quite adequate scientifically at present, although 
they would have to be thoroufrhly improved and c<Hnpleted if space 
flight sboild becone a fact. 

I myself would only like to say the following : 

l) In vertical flight upward with parabolic velocity, this follows 



- 463 - 



from (59) and (60) i 

Vagr - 

(The formula quantities are the saoe as those in Chapter 10.) 



V = 

P 




Not 




dt 


dr 


Therefore, to get 




dt 


Yr.dr 




y>v% 


and 








With h7perbolic vel 


ocities in vertical 



(208) 



is not completely dissipated even at infinity; it retains a residual 
velocity vjj. At infinity, its kinetic energy is 

1 2 

^ = a " ^h • 

The irork required to take it to infinity from any point on its 
trajectory is ogr , and its entire kinetic energy is 

E o -5: m V • 

Obviously, it must be as great as the sua of these tiro energies. 
Therefore, 

i 2 I o 

5BIV o-xmv? +mgr. 



- 434 - 



From that, this fol loirs t 






(I (c- — Vk) 



(With dr and dt, the minus sign naturally means nothing more than 
that, in a given case, v is the snaller, the greater r or t.) By 
integration -we find 



*^i> '- fn. ^Vi — v^ i>^ + v-J. 



(209) 



Therein, t. designates ths velocity at the lower end r. of the 
section of the trajectory under consideration, Vg and r^ refer to the 
upper end, and 



^h 



a/7 2 6o^ 



With elliptical velocities, the energy of motion inhereut in the 
body is not sufficient to lift it to infinity, from irtiicb it follovs 
that 



2 



m V 



- mg r ^0, 



Formally, our calculation is very similar if ire set i 



^ go % 2 



- 485 - 



Then 



2 go rl 

^^ - „• + .r 



' = ",p U' + «'? <'. ''• ■' U (aio) 



Formulaa (SOS) to (810) natarally merge one into the other depending 
on -whether the quantity takin{]; the pl&ce of t. or t is assumed as 
being real, equal to zero, or imaginary. 

With elongated ellipsesi the flight duration is almost the same 
as vith rertical ascent. For example, a flight to an altitude of 
800,000 km would take 15 days and the descent Just as long; so the 
space~ship vould be undervay a month in all. 

With a flight to the moon, the ti-ne can be calculated vith great 
approzimatioT) if the spnce-ship is t^en as flying in a strai^t line 
front the earth to the mocm. In the case of a vertical flight, 



..y:r;.,,[A:i^(j:_.j^^. 



Therein ▼ is the Telocity at the point vfaere the tiro attracting 
forces are balanced. M^ is the mass of the earth and ll~ that of the 
moon, d is the distance betveen ihe two stars. Here the formula 

dr 



^¥ 



leads to elliptic integrals, but th^ are easily evaluated irith the 
use of TAILOR'S series. 

For the flight irith the lowest posnible initial velocity (ca 10,380 



- 466 - 



Bi/sec), irith the average distance io the moon, one obtains 

t « 97 hrs., 30 min. 
That is ca 4 days. 

With velocities over v. ■> 11 km/sec^ the formulas for elliptical, 
parabolic, and hyperbolic velocities can be used irithout causing 
errors worth mentioning. For v. ■ 15 km/sec, ve get t " 9 hours (cf. 
LORINZ J "The Possibility of Flight in Interplanetary Space", Journal 
of the Association of German Ihgineers, TV, 1927, and PLANA t Dis- 
sertations of the Turin Academy of Sciences, Ser. 8, Vol. 20, 1863, 
pp. I - 86). 

B, Flights on Strongly-Bent Curves . 

It is most convenient to hold to the formula quantities of Chapter 
10. 

For example, if the space-snip travels on an ellepse (Fig. 130), 
this folloTS from formula (v) s 







Fig, 130 
In the case of a hyperbola, SL^ I* After several immediate 



- 467 - 



transformations, ve get the foil owing from (213) i 



, w 



i 



w 



£- - 1 \(\ +s) «'="-;- (f- 6) * 2- iF-t " '"■ 



... -1^^ 



(814) 



In the case vbere the trajectory curve is a parabola, S, ■ 1* 
Then ve ciia apply the method of indeterminate forms to f omul a (813) 
or (814); our calculation is still more conrenient if ve apply the 
same method -which famished us irith the ellipse surface in Chapter 10 
to parabola 



1 - cos(p 



The result is the same in all three eases t 



4 l^w 37^»3 



(216) 



Then the flight duration, according to Chapter 10, is 



t - 



2.F 



T. rj cos a^ 



Vith interplanetary space flights at greater distances from the 
earth than 1,000,000 kn, the influoxce of the earth* s attraction can 
be ignored in the first approximation and later incorporated into 
the calculation as a correction together vith the trajectory disturb- 
ances caused by the rest of the planets, as is done by HOHMANN, for 
example. Then, instead of the formula quantities of Chapter 10 relative 
to the earth, the corresponding values relative to the sun must be used. 

For example, r would be the distance from the centre of the sun, 
g the acceleration due to gravity of the sun, oC the complement of 
the anjle between the trajectory curve and the radius vector drawn to 
the centre of the sun, etc. 



- 468 - 



Here, the astronontf specialist's calculatione are naturally more 
convenient and more elefant, according to the methods of calculating 
trajectory disturbances set np by LEVEiaiEP. and BESSEL, which are 
also essentially based on the developed train of thought. 

In the transition of the space-ship from one gravitational field 
to the other and from one type of motion to the other, the calculations 
of the non-astronomer are most elementary and surest if he divides the 
flight into small sections in vfaich the attracting forces can be 
regarded as constant and parallel. In my boob on three-body calcula- 
tion already mentioned I vill state methods irhich rapidly lead to the 
result. 

Depending on the velocity and the direction of the ascent, a trip 
from earth to Mars, for example, would take 3 — 8 months (I will write 
about this in greater detail later). A trip to Venus would take 2 — 5 
months. A flight circling the earth 500 km above the ground takes 5470 
seconds b 1 hour 31 minutes 10 seconds. A trip on an ellipse whose 
perigee dips into the earth's atmosphere and the height of whose apogee 
above the ground is equal to the diameter of the earth would require 
4 hours 17 minutes 30 seconds. The period of a flight arovmd the moon 
at new moon would be 5 to 6 days. 

D angers of Space Flights 

The ascent is much less dangerous than might at first be thought. 
The reader is asked to examine Plate IV. 

The pilot occupies chamber I; its walls are of aluminum 1.5 — 2.5 
cm thick and, during the, ascent, the windows are covered with similar 
alximinum plates. To me the possibility of the cabin bursting appears 
quite renote. Above the cabin we find the parachute. The tip can be 
jettisoned at any time, at which the parachute spreads out in the air. 



- 469 - 



Only three dangers threaten the pilot during ascent t 

l) Failure of the pumps. 

8) Failure of the control device. 

3) Explosion. 

If possible, the machine ascends over a large body of irater (even 
if just for the sake of the jettisoned alcohol rocket). If the pomps 
mentioned on p. 325 fail, the rocket drops into the vater) since it 
floats, no harm is done. Vith respect to S), if a) a tail fin breaks 
or b) the control mechanism fails, the pilot need only turn off the 
pumps and the rocket drops. —With respect to 3), four types of explo- 
sions can occur : a) in explosion can occur in the combustion chamber 
or the punq) chamber of the alcohol rocket only at the start of the 
flight. It is the more to be feared the greater the required reanrard 
thrust (P). Since the acceleration may not exceed a certain maximum 
value, as the mass decreases, P also soon decreases (at the beginning 
P increases someidiat because of the increasing air resistance). No-v 
attention is dramx to Plate IV. For itself, it is improbable with such 
an ezplosi<m that metal parts are hurled in the direction of I. With 
fev exceptions, only an explosion in the top pump chamber could have 
this effect. Nevertheless, if it should occur, the (filled) liquid 
tanks of the alcohol rocket and the hydrogen rocket would act as buf- 
fersf the thick-valled purap chambers of the hydrogen rocket likeirise* 
b) in explosion of the pump chambers of the hydrogen rocket irould, 
in effect, be less violent than the t>revion8 cme. The liquid tanks of the 
hydrogen rocket vould suffice completely as buffers, c) The explosion 
of a liquid tank under its own excess pressure is, first of all, 
improbable and, secondly, its consequences for the pilot irould scarcely 
be more serious) not with the alcohol rocket, because there the 
hydrogen rocket shields the pilot; nor with the hydro(;en rocket, for 
its excess pressure is too low. It would likewise not have serious 



- 470 - 



consequeucefl for the pilot if the head triad caused the hydrogen rocket 
to collapse (irfaich can only occur at the beginning). Nov, irith every 
explosion, liquid -rould escape iffaich presumably vould catch fire. But, 
on one side, I is covered by the parachute, iriiich is kept moist in 
the beginning} on the other side, insulation is required anyvay against 
tlie extremely cold liquid hydrogen. As long as the hydrogen itself 
does not bum inside the hydrogen rocket, it ybtj effectirely protects 
I against the fire; if it bums, hovever, the tip is bloim avay together 
irith I because of the weak walls of the hydrogm rocket. Even if this 
should not occur, what would happen in this case (vfaich is possible 
only if liquid oxygen enters the hydrogen chamber) is that the hydrogen 
would be forced out of its tank in 2 — 3 seconds and, because of its 
low specific weight, renain behind the motion of the rocket, ao that 
no disadvantage to the pilot would arise from this. So it is evident 
that no other dangers threaten him within the earth's atmosphere than 
those that could result from too high counter-pressure. Also compare 
p. 415. But this danger is only slight. In flight on the synergy curve, 
the rocket attains high velocities only in tangential direction. If 
the propelling force should fail, a distance is covered in ihe atmosphere 
that suffices for deceleration. 

Meteorites and cosmic dust doubtless constitute a danger for the 
space navigator. Due to tiieir average speed of 30 — 40 km relative to 
the space-ship, th^ have a considerable piercing force. For example, 
a shooting star of the specific weight of iron would still pierce the 
1 to 8-cm- thick aluminum wall even if it were only 3 nm thick. Are we 
in great danger of being hit by such shooting stars ? 

Size of the meteorites . If an effective temperature of 10,000 — 
30,000* is ascribed to them (cf. p. 286^, the astonishing result is 
arrived at that the shooting stars vhich we see on clear nights are. 
in general, less than 3 cm in diameter. The smallest shooting stars 
visible with the naked ^e would be somewhat unfler ■? cm in size. 



- 471 - 



Obviously, the shooting stars and meteorites risihle vith the naked 
eye are quite rare. It vould be e^ heavy meteor shoirer in viiichi on the 
average, one shooting star lights up every second. 

Froia that part of the atmosphere in vbich shooting stars flash up 
ve can see a circle at least 1000 km in diameter. In this circle, 
vith an average forrard motion of the earth relative to the shooting 
stars around 40 km, one shooting star is picked up every second. 
Therefore, there is one shooting star to a cylindrical space 1000 km 
in radius and 40 km high. In order to determine hov many seconds, on 
the average, the rocket must fly until it is hit by a shooting star 
ve must divide this space by the space which the largest cross-section 
of the rocket must de^tcribe vith an average velocity of 40 km/sec. 
The ratio of these tvo volumes is equal to the ratio of a circle 1000 
km in diameter to the largest cross-section of the rocket (ca 50 m^). 
The rocket vould have to fly 10 '0.78 t 50 - 1.6>10 sec - 530 years 
for it to be hit by a shooting star. The observer's cabin, -whose larg- 
est cross-section is scarcely 5 m^, would, on the average, only en- 
counter a visible shooting star every 5000 years. 

Of course, the supposition vould have to be considered that scialler 
shooting ntars which can no longer be perceived with the naked eye 
are more frequent. Tet, they cannot be much more numerous, otiierrise 
shooting stars would be seen much oftener during astronomical observa- 
tions than is actually the case. I continue to hold to the view already 
expressed in the 1st and find editions of n^ rocketry book t If I have 
hdd luck, a meteorite can hit me in the first half minute. According 
to the law of probability, however, a space-ship can fly through inter- 
planetary space for hundreds of years without having such an accident. 
In this respect flying a sT^ace-ship is not as dangerous as say drivlT'g 
a car. 



- 172 - 



For thftt matter, s)?ialler punctures in the irall of the obfjerver's 
cabin need not necepsarily be fatn.l to the observer. The air restorator 
autoGiatically keeps the air pressure in the observer's cabin constant 
and sijpnala the pilot if air escapes anjnvfaere. The pilot can easily 
close the hole by covering it irith a rubber plate. The Inside air 
pressure presses it against the opening and seals it. If the space- 
ship is to land on vater, this rubber plate <iust aomehoir be fastened 
to the vail, say by gluing, in the course of the flight. 

Concerning the descent, I have said what is necessary in Chapter 14, 
As is seen from the chapter, landing in the vater need be no more 
dangerous than landing vith a hydroplane. All in all, one can say that 
space flights vill be much less dangerous than the layman pictures 
their to himself. 

I would here like to discuss several objections to space flight 
in so far as they relate to what has been said hitherto. 

A number of laymen cannot understand hov it is possible to knoir 
so exactly what vill be met up vith in interplanetary space. In res- 
ponse, I refer the reader to what is said on p. 377, 

In literature, a danger is frequently pointed out irfaich, in short, 
might be characterized by the question t "Vill the natural lawa be 
subject to the same conditions in inter>ilanetary space as they are on 
earth ?" (German Newspaper ) "It is not certain -whether the natural 
lavs iihich ve have discoTored on earth vill also be valid in inter- 
planetary space". (South German Daily Paper) "It could be possible, 
for example, that a vire qo longer cimducts an electric current in 
interplanetary space" (STEIN), or that hydrogen and oxygen no longer 
combine, among other things. It is actually just a "postulate of 
practical reason" (vfaat that means in a scientific context, of. p. 537 
ff ) to say that the same conditions must alvays and everywhere have 
the same result. 



- 473 - 



Frankly speaking^ I have no feare idiateTer in this regard. The 
extra-ordinary accuracy of astronon^r in predicting natural phenomena 
nakes it probable to the highest degree that everything happens 
according to the ssme lairs in interplanetary space. It must further 
be considered that, since the earliest time of irhich history informs 
us, the earth has moved at least 8 -s billion kilometres from its 
original location in the universe, if the calculation is based on a 
velocity of 17 km/sec for the -whole solar system. 

If, hovever, the fact postulated by COURVOISIER i» taken 'into ac- 
count that the vfaole Milky Way is rushing through space at about 700 
ka/sec, then ire have travelled at least 100 billion kilometres since 
the beginning of recorded history. 

Yet the observed natural processes have always occurred according 
to the same lavs; Vith the exception of the reduction of the speed of 
light (still largely questioned). 

The correlation betireen our sun and the most distant fixed stars 
is still more striking. It really cannot be assumed that the fe-r million 
kilometres by irtiich the space-ship is distanced from the earth irill 
suffice to bring it into a irorld irith other natural lavs. In the opinion 
of most physicists, the ether is ultimately the bearer of all physical 
processes. At the moat, one might say that the proximity of the earth 
affects the ether in a certain sense and that, at a greater distance 
from the earth, this effect irould be lacking. That can be countered by 
saying that we have observed absolutely nothing on comets, for example, 
irfaose mass is often no greater than that of a space-ship, that irould 
allow us to conclude that other natural laws prevailed in interplanetary 
space than on the surface of the earth. On the contrary : Some natureJ. 
laws (e.g., radiation pro!3sure) have first been observed on comets 
and only latsr confimed in laboratories on earth, just as the speed 
of light and meny other things were first found from astronomical 



- 474 - 



obserrationa. At most, beside the natural lairs ire already kaov today, 
there is the possibility that ve vill find one thing or the other 
that ve have not yet had the opportunity to obserre on earth. As far 
as being a dangerous nnderttiking) I do not believe it* The first rock- 
ets vill ascend tuuaanned. Then manned rockets vill be sent aloft 
according to the data obtained, at first only a feir hundred, ihea. a thou- 
sand, and finally «, hundred thousand kilometres. One does not blindly 
rush into danger but step by step learns to knov the Torld into vhich 
one is advancing. 

Other authors again fear the rocket will be deflected 1^ the radian 
tion pressure of the sun. But, according to UACWQl. and SCHEINM, at 
the earth's distance from it, the radiation pressure of the sun can 
never exceed 0.8 mg/m ; at the distance of Venus from the mmt it would 
amount to less than 1.6 mg/m*. Otherwise the energy radiated to us by 
the sun irould be greater than it actually is (cf. p. 444). As is well 
known, the formula 

1 i- force 

acceleration » _. ' 
mass 

gives the acceleration of the rocket due to radiation pressure. 

Since one force gram imparts an acceleration of 981 cm/sec^ to one 
mass grara, the acceleration that a rocket weighing 5000 kg, for example, 

o 

undergoes when it exposes an area of 50 m to the radiation of the sun 

0.0008. 50* 981 , 2 

is certainly under "" ■-T r r' T,^^ " 0.00000784 cm/sec . In one day, 

5000*1000 "" 

that makes an acceleration of 0.34 cm/sec^, an infinitesimal figure 
beside the kil(Hnetre-seconda in which we have to calculate here. Even 
if it were a matter of hurling a space-ship from earth to a nei{;hboring 
planet, the trip would take scarcely 100 days. In so doing, the radia- 
tion of the sun would result in a velocity error of 34 cm/sec*. I figure 
that, beside the propellents required for ascending and landing, the 



- 475 - 



space-ship vill take along enough propellant for correction purposes 
by which it could change its velocity by 500 m/sec. Thus it could 
very easily cope with this slight trajectory disturbance which is 
not even added to its velocity lineally but according to Pythajjoras? 
theorem (cf. p. 52l) and can be incorporated in the calculation 
beforehand. 

Other authors fear a diflection of the rocket by the world ether. 
That would be extremely interesting for the physicist. So far, it has 
not been proved that the world ether puts up opposition to a moving 
body at all. We do make the observation that small comets are deflected 
from their path, but this deflection no doubt has other causes. For 
the rest > Comet heads and meteorite showers probably consist only of 
widely-scattered dust and the ratio between their mass and the surface 
they offer to the "ether streean" is more unfavorable than with a rock- 
et. Yet we never observe deflections of a magnitude with which a good 
space-ship could not cope easily. 

Finally, different advocates of Uie theory of relativity fear the 
relativity theory could make my calculations worthless. (I have natural- 
ly based nry calculations on classical mechanics.) That I counter by 
saying : The deformations of the rocket airplane and its trajectory 
posited by the theory' of relativity, with its low velocity compared 
to that of light, would be so small even in absolute terms that we 
could not measure them at all. But that exactly is the main character- 
istic of the theory of relativity whon it holds that these deforma- 
tions, in general, cancel out again because the scales according to 
which we measure and calculate change to the same degree. Apart from 
a few special cases, with which we are not yet dealing directly in 
flights to interplanetary space, everything appears to the observer 
as though ke stood in the absolute world and measured with absolute 
measurements. Processes of oiotion and technical devices, for example, 
must be considered just as though the theory or relativity were un- 
known. 



- 478 - 



Ifanj authors cannot Tisualize haw the rocket can be guided whmi 
there is no static medium. Here I simply refer to p. 5. In general, 
the rocket flies like a shot projectile. Deviations from the course 
are corrected hj means of rearrard thrust and that does not require 
a static median. 

The danger of the space~ship deviating from its course has often 
been described in vifid colors, but I cannot take that seriously. The 
danger that the space-ship might get hung up in the sphere of attrac- 
tion of a strange heavenly body is completely excluded. Provided it 
does not directly hit it, it must, according to the lav of the conser- 
vation of energy, vithout further agency leave its sphere of attraction 
agair irith the same velocity vith vfaich it entered it. Nor do I fear 
a deflection from the course. The trajectory is determined beforehand 
vitb astronomic accuracy and eirors of control can be checked and 
corrected vith the same accuracy. 

In general, one can see that the first space flights vill not be 
as dangerous by far as vere the first air flights. 



- 177 - 



s 
t 

X 

V 

z 
A 
D 
L 
R 
V 
V 
oC 



Chapter 20 
Stations in Interplanetary Spac£ 
Formiila Quantities for Chapter 20 

distance of reflector from point illuminated 
acceleration 
revolving speed 
diameter of the sun's image 
vertical component of the light-pressure 
sagittal component of the light-pressure 
acceleration due to gravity at the altitude examine 
altitude of reflector above the ground 
outlet pressure 
pressure in oven 
earth's radius 
radius of reflector 
' direction toward the svm 
direction perpendicular to the s - x - plane 
direction toward centre of earth 
velocity with reference to centre of earth 
centrifugal acceleration 
distance of reflector from the sun 
diameter of the sian 
light-pressiire 

distance of the earth from the sun 
potential (without light-pressure) 
potential with light-pressure 

tension of net due to differences in gravitation 
precession accelerations due to differences in gravitation 
differences between the gravitational and centrifugal acceleration 



- 478 - 



^h /j h : altitude differences 

^ y : difference in potential without light-pressure 
^ y i difference in potential with light-pressure 
w : angular velocity 



Space vehicles on the largest scale can be put in orbit around the earth. 
They then represent a sinall jnoon, so to speak. They need not be provided with 
landing facilities. Communication between them and the earth can be maintained 
by means of smaller rockets so that these large rockets (we will call them 
observer stations) can be progressively rebuilt for their actual purpose 
vrtiile aloft. 

Such a station could consist of two observer cabins which would be 
connected by a cable 10-20 km in length and would rotate about each other 
(cf. p.Hl)"'^. 

"^he remark is often found in literature that the observer station 
shoiild gravitate near the zone of weightlessness between earth and moon. That 
is wrong. The closer to earth the observer station rtins the smaller the 
trajectory disturbances due to extraneous stars become and the easier it is 
to correct them again (e.g., with the help of the pressure of the sun's rays, 
cf. p. 497). Some authors have also thought of placing the station just at 



1) As already stated at that place, 1 consider such a long connecting cable 
necessary for psychological reasons. V/ith a smaller radius of curvature, the 
number of revolutions would become too great^ with coimter-pressure similar 
to that on earth, Ihe passengers would notice the rotation and become sea- 
sick. For the same reason, I cannot agree to NOORDUKG'S in itself very 
beautiful suggestion of a passengers 'wheel with a radius of scarcely 100 m 
and still less to G/lKS»vII>JUT'S suggestion to build the observer's cabin of the 
space-ship itself as a rotating drum. 



- 479 - 



the point of weightlessness between earth and moon. This is altogether impos- 
sible. Without the effect of gravity, a body in space would continue on its 
course in a straight line and not remain near the earth. On the other hand, 
it is basicly possible to bring the observer station somewhat closer to earth ; 
namely, to the place where the attracting force of the earth is weakened 
by that of the moon by just so much to make it equal to the centrifugal force 
that arises when the space-ship orbits the earth in one month. Here the space- 
ship would always gravitate between earth and moon. But this set-up would 
not be advisable. If, for some reason, the observer station should move down 
or up from this point, it would be hurled from its course. So that position 
is unstable. On the other hand, the position of an observer station near the 
earth is stable, for here performance d" work is required to move the station 
either farther from the earth or closer to it. Finally, I expressly point 
out that the centrifugal force of the station suffices in itself to prevent 
it from falling to earth. The moon does not fall to earth although there is 
no body above it to draw it upward. I woiold let such a station gravitate 
700 to 1 ^ 200 km above the earth. 

The purpose of these observer stations would be the following : 
l) With their precise instruments they cotild pin-point every detail on 
earth and, with suitable reflectors, could send light signals to earth. 
They make possible telegraphic communication with places that are cut off 
from normal contact by telegraphy because of operational distvirbances . Since, 
with a clear sky, they can recognize a candle by night or a pocket mirror 
by day, if only they know where to look for them, they can contribute much 
to navigation, etc., in helping expeditions establish contact with the 
homeland from far outlying colonies. By observing and photographing unexplored 
covmtries and peoples (Tibet) they naturally benefit geography and ethnology. 
Their strategic value, especially in theaters of war with low average 
clouding, is obvious, whether the state that owns them is at war itself or 
sells their reports to nations at war at a high price. With small plane 



- 480 - 



reflectors, if the station is not too far, the reflector signal is recogni- 
zable on a limited area only. Furthermore, the station notices every iceberg 
and can warn ships indirectly by reporting the iceberg to a naval observa- 
tory, which publicizes the location by telegraphy, or directly if its reflectors 
are strong enough for the ship to notice them through the usx^ally foggy 
atmosphere. The tragedy of the Titanic in 1912, for example, could have 
been prevented in this way. These stations can also contribute much to the 
rescue of ship-wrecked people, to newspaper services, etc. For example, 
IJUNGESSJjR and COLI coiJ.d have been rescued in this way, probabl^r also 
EOALD AKUlffiSiiN and I'AMGREEK. 

I do not consider it an impossibility recognizing, with the use of a 
telescope, the change of barometric maxima and minima, the direction of the 
wind, etc., on optical indications, ^n this way, the vreather conditions of the 
vrtiole earth could constantly be kept in view, considerably promoting our 
knowledge of meteorological processes. 

Fiurthermore , 1 would like to mention here that the observer station 
could, at the same time, be a fueling station ; if the hydrogen and oxygen 
are protected from the sun's rays they remain in a solid state for any length 
of time. A rocket that is refuelled and leaves from the observer station 

suffers nothing from air resistance and only little from retardation due to 

^d 
the force of gravity. Its acceleration and, therefore, ___ may be very 

Po 
small, whereby, according to (l), the propelling force of the fuels is 

powerfully utilized, "^f the rocket need not pass through the atmosphere nor 

be subjected to counterpressure, we can build it as we please as regards 

form and rigidity ; b may be shhII (cf. p. 246) and we can make the tanks of 

mo 

sodium plate, -"-n so doing, -jjr — will be very large. In addition, the rocket 
need have no very high initial velocity in order to leave the earth's 



- 481 - 



sphere of attraction for, in the first place, the potential of the earth 
is smaller at the observer station and, secondly, the propulsion of this 
rocket need only compensate for the difference that exists betvreen the 
required final velocity and the roughly 8\aa/sec velocity of the observer 
station. For example, if a large sphere of sodium plate, manufactiu'ed on 
the spot and filled with fuel, is connected to a small, solidly-built 
rocket so that the latter pushes the sphere before it and is constantly 
refilled from it, we have an extremely efficient machine that is easily 
able to fly to a distant celestial body. There the rocket is lowered to 
the siorface of the celestial body while the sphere with the fuel gravitates 
about the respective body. After ascent of the rocket they are connected 
again and the machine makes the return flight. J'jbre about this later. 




Fig. 131 



2) A circular wire net (Fig. 131) could be spread out about its centre 
by pivoting. In the gaps between the single wires (here exaggerated in size) 
movable reflectors made out of light metal sheeting could be fixed so that 
they can be given any position to the plane of the wire net from the station 
by means of electric currents. The whole reflector would gravitate about 
the earth in a plane perpendicular to the plane of the orbit, and the net 
would have an inclination of 45° toward the sun's rays (cf. Fig. 132). By 
suitably adjusting the single facets, all the solar energy reflected by the 



- 48S - 



sun coiald be concentrated on a single point on earth or also spread out 
over wide stretches of land as needed or, if there is no use for it, 
allowed to radiate into interplanetary space. 




Fig. 132 



For example, if the reflector were ], 000 km wide, the sun's image of each 

facet would be 10 km in diameter ; if they coincided, the enerfy would be 

2 
concentrated on an area of 78 km . Since the reflecting surface can be of 

any size, colossal effects can be achieved, ^or exan^jle, the way to Spits- 
bergen or to the ports of Northern Siberia could be kept ice-free by means 
of such concentrated sun's rays. If the reflector were only lOO km in dia- 
l) V.'e are here dealing with a phenomenon similar to the dark room. As long 
as one of these facets is smaller than 10 km it produces, independent of 
size and shape, a circular Image of the sun. According to the laws of geonetric 
optics, viewed from the position of the facet, the sun's image must appear 
at least just as large as the sun itself, ■'■f d is the diameter of this image 
of the sun, a its distance from the reflector, D the diameter of the sun, and 

A the distance of the earth or the refictor from the sim, then 

d s. D 

"T^T" (216) 

It is impossible, for example, to concentrate the light of a 
100,000 km-wide reflector on the space of one hectare, as GAIL describes it 
in his novel, "The Stone from the Moon". Fere the sun spot would be at least 
1 000 km in diameter, i'or achieving strong heat effects, we must aim to bring 
the reflector as close to earth as possible. 



- 483 - 



meter, vrlde stretches of land in the north could be made habitable hy means 
of dispersed light ; in our latitudes, the feared sudden drops in temperature 
(ice men) in spring and the night frosts, in fall and spring could be prevented, 
thus saving fruit and vegetable crops of entire provinces. It is especially- 
significant ihat the reflector is not fixed above one point of the earth and 
so can perform all these tasks at once. 

In the question of the material of this reflector, it is clear that 
l) no oxygen must be present, and 2) it must heat up but little itself, ■'"t 
will remain colder if we leave the back side rough or even paint it black. 
As material, I would suggest sodium which, under the respective conditions, 
has a specific weight of 1, considerable tensile strength, and a siL^ery 
lustre. It can be taken along in large pieces by the single rockets and, 
since it still has the usual temperature up above, can there be rolled out 
to sheeting or pressed out as wire or strap from the rocket. Joining of the 
single pieces as well as polishing can be done by men in divers 'suits. If 
the reflecting plate is 0*005 mm thick and the wires, etc., have the same 
mass as the plate, the whole weighs 10 g per square metre or 100 kg per hectare. 
With regular rocket traffic to the observer station, the ascent of one rocket, 
vAiich, beside all else, can carry up 2,000 kg of sodium, costs P^OOO to 
60,000 I-^rk all told. Thus, one hectare of reflector costs at tlie most 
3, 500 I-feirk altogether. Jf we figure that 1 hectare of reflector sxu-face 
coiold make 3 hectares of polar land arable, we see that a time may come when 
this reflector and the whole invention becomes a paying proposition. 



- 484 - 



In this way, a reflector 100 km in diameter would, at the most, cost 
3 billion Ilark and, if 100,000 kg of sodium were taken aloft every week, 
it woxild require ca 1; years to build it . Since such a reflector could, 
unfortvmately, also have high strategic value (munitions factories can be 
exploded with it, tornadoes and thunderstorms produced, marching troops 
and their reserves destroyed, whole cities burned, and gener lly the greatest 
of damage done) the possibility is not excluded that one of the civilized 
states will make use of this invention in the foreseeable future, the more so 
since a large part of the invested capital could also bear interest in peace 
time. 

I must make a 'remark here : I coiild have restricted myself in this book 
to only the most sober physical calculations. But in order to create the 
necessary respect for ny idea (otherwise a realization of this idea ia un- 
thinkable), I felt impelled to drax a few pictures of the futxire at the end 
of the book, and I have set up some fantastic claims. Naturally, here also, 
I have said nothing that might not be possible by present scientific standards, 
and I will now show that I am abo on completely scientific ground with this 
idea of a reflector. 



l) The calcTolation would be considerably more favorable if the material 
could be delivered by the use of electric space-ships from the moon or from 
an asteroid. Then the reflector coxild possibly be built for several hundred 
million I'lark in less than a year. 



- 485 - 



Construction of the Reflector 

A rocket with the necessary equipment is sent aloft and there given a 
lateral propulsion which puts it into an elliptical orbit around the earth. 
I will call this rotation about the earth "revolution". Major axis perpendi- 
cular to the ecliptic, perigee in the south 1,000 km above the earth's surface, 
apogee in the north f^^ 000 km above the earth's surface (cf. Fig. 133). 



In spite of its proximity to the earth, this rocket and everything in and 
around it is not exposed to any counter-pressure ; the force of gravity is 
compensated for by the centrifugal force in every atom. So the single parts of 





Fig. 133 



Fig. 134 



the rocket are related to each other almost as though the earth were not there. 

Now the axis of the rocket is turned perpendicular to the future plane of 
the wire net and, by means of side nozzles, the rocket is made to rotate about 
this axis 4-5 times per hoin-. This motion I will call "rotation", -"^f now 
wires are let out which are attached to the rocket on one end (Fig. 13A-), they 
will in a short time take a position perpendicular to the rocket axis due to 
centrifugal force and the lack of air ; and that the more promptly, the longer 
they are and the greater the rotative speed (Pig. 135). ^f course, until they 

have erected themselves, that takes place at the cost of the rotative speed 
of the rocket, so the side nozzles must sometimes be used. Finally, as the 
dianteter of the net increases, the rotative speed should decrease in order not 



- 486 - 



O^ 




Fig, 135 

to put tinnecessary strain on the material. Now the workmen -naturally weighing 
nothing here- can move along these wires, if they do not prefer to use rearward 
thrust machines to move about, and draw the cross wires, etc. ^he rigidity of 
the net is based on the absence of a force that could bend it or, more precisely, 
on the minuteness of these forces as compared to the centrifugal force due to 
the rotation about the centre. (More details below.) 

Adjusting the reflector surfaces is done electrically (Fig. 136). There are 
very many ways of, for exajnple, producing a deflection on pointer B that corres- 
ponds to the defiction on a pointer A. It is possible to install miniature 



<5^ <$^ 

CX^ 



Fig. 136 



facets in the control room each of which is connected with one of the actual 
reflector surfaces in such a way that it must follow the position of the 
miniature facet -the electric current could flow through the wire net-. The 
matter is complicated by the fact that there are two rotating axes and the 
reflector surfaces cannot follow the motion of the miniature facets ijranediately 



- 487 - 



because of their size and fragility (they must have little reinforcement and 
may not be too small because of diffraction). 





Fig. 137 

It will take 10-15 minutes to adjust them. Provision would also have to be 
made by which to give them an impulse contrary to their motion at the right 
time to prevent them from moving too far due to inertia ; compared to the 
forces which can act on them, their inertia is very great. This, however, is 
basicly feasible. 



The miniature facets are adjusted by hand ; they are attached to a flat 
bar grill (Fig. 137) which is in the position which the reflector net will 
have in 15 minutes due its rotation. Beside it is a globe which is placed in 
relation to the grill aa the earth will stand in relation to the reflector 
after 15 minutes (that is very easily seen from a table, while making a 
few corrections resulting from position findings ). It is sufficient to simply 
let the sun shine on the miiiiature reflector and then to turn the facets so that 
the reflected light strikes those parts of the globe corresponding to the 
region to be irradiated. In so doing, even the bending of thenetdue to ra- 
diation pressure and precession forces, still to be discussed, could be taken 
into account. Either the grill bars could be pliable and be bent beforehand 
at the discretion of the reflector pilot (the error occurring in this way is 
not large), or, at the adjusting mechanism of the reflector surfaces, directional 



- 488 - 



gyroscopes could be sitiiated according to which the reflecting surfaces adjust 
themselves, at which the gyroscope would naturally not serve as support but the 
wire net. 

^t takes 10-15 minutes for the reflector surfaces to follow the facets, 
so there is plenty of time to test the thing while making the adjustnient, ^f 
one wishes to continue illuminating the same region, one moves the facets a 
little farther from time to time. Because they move so slowly, the reflectors 
only follow the adjustment gradually, so steady motion of the reflector siu*faces 
can be achieved in spite of the jerky motion ofthe facets, '^aturally, this would 
be only one possible solution ; there are a hundred others. 

According to MAXWELL, the light-pressure at the distance of the earth with 
the rays striking a completely black surface perpendicularly amounts to 
0,4 mg / m , with a completely reflecting surface twice that. With a sodium sur- 
face standing at an angle of 45" to the sun it will amount toca0.5nig/m = 
0.5 kg / km .In any case, it does not increase tolkg/km =lmg/m even 
when the reflector is perpendicular to the sun. Now, the reflector together 
with reinforcements, observer's cabin, etc., weighs 10 gr / m . So the radiation 
pressure gives it an acceleration of less than 0.1 cm / sec . (The exact value 
can be found experimentally when rocket ascents are made ; beside the pressure 
posited by MAXVffiLL'S theory, all sorts of other factors are involved. Here I 
want to show what is Lnvolved in principle only. ) The reflector does not rise 
higher than two earth's radii above the centre of the earth. In so doing, the 
acceleration due to gravity remains over 240 cm / sec . rut even 10 earth's 
radii high, it would still be about 10 cm / sec . whichde hundred times greater 
than the acceleration due to the light-pressure. 

I am now introducing three new designations relating to direction. The 
direction to the sun I call sagittal (s-direction), the direction from the 



- 489 - 



centre of the reflector to the centre of the earth vertical (x-direction) the 
direction perpendicular to the s - x - plane transverse (t-direction). We will 
txegin .our considerations vdth the following assumptions : The orbital plane is 
to be perpendicular to s, at the same time foiTidng the t - x - plane ; the 
reflector surfaces are to be perpendicular to the s - x -plane. They are to be 
inclined at 45° to the other two fundamental planes, so that the reflected 
light falls on the earth vertically. When the reflector revolts about the 
earth, the s-direction is maintained in space while t and x rotate once with 
reference to a fixed system of coordinates. VJhether we must seek to constantly 
reflect the light on the earth vertically or are, in fact, able to is another 
question. I will assume that we can in order to stiidy the single elements which 
determine the path of the reflector, (imaginary numbers are also r^aed in cal- 
culations, although it is known that they do not exist.) 





Fig. 139 

Fig. 138 

Let AB represent the earth (Fig. 138), CD the path the reflector rocket 
would describe without the reflector (seen from the side it appears as a 
straight line), irst, 1 will assume it to be a circle, and then proceed to 
more complicated cases. The radiation pressure L (Fig. 139) breaks up into 
2 components e and f, one of which (e) tends to lift the reflector vertically. 
We compensate for it by taking the revolving speed of the reflector 
1 - 2 m / sec less (more is unnecessary) than it would have to be if there 
were no' .radiation pressure. -^ is simply as though g were 0.01 % - 1 % smaller 



- 490 - 



than it is. he second component f presses the reflector toward the earth's 
shadow so that the radius vector from the centre of the earth to the centre 
of the reflector no longer describes a plane but a conic surface. In so doing, 
g breaks up into ? components (Fig. 138), one of which acts in the direction 
of the orbital centre and compensates for the centrifugal force z and for 
the light-pressure component e. The second acts toward the sun and compensates 
for the light-pressure component f. Because the light-pressure f is so 
small, the quantity (r + h) , by which the reflector is pushed away from 

O 

the sun, is inconsiderable. So there is no possibility of the reflector being 
"blown away", as has largely been feared. 

I wrote that it is simply as though g were 0.01 - 1 ^ smaller. It follows 
from that that the reflector gravitates approxinately as it would about a body 
whose mass is somewhat over 99 % of the mass of the earth. If, for example, 
iiiipact disturbs it in its orbit, it describes an oval which is very nearly an 
ellipse. likewise it can be shown that here f simply acts as though the centre 
of this body were not situated at the centre of the earth but 40 - 100 km 
sagitally behind it. 

Let us move on. 'I'he reflector is supposed to work as hitherto, but only 
above the northern hemisphere. We are assvPing we have nothing to do in the 
southern hemisphere. As before, above the southern hemisphere, (but now only 
under the influence of gravitation), the reflector is to describe a circle in 
tiie direction B - A (cf , Fig. 140 ; let AB be the equatorial plane seen sagi- 
tally). VJhen it passes A aind begins to work, the force of gravity seems to 




Fig. 140 



- 491 - 



decrease ; but its velocity is too great for this smaller force of gravity, 
so that it begins to rise, reaching its apogee at B' on an approxinately 
elliptical trajectory at the cost of the excessive kinetic energy. At B' 
its velocity is too small again to constantly keep it in an orbit at this 
altitude. (Vore details can be learned from the laws of the rotion of planets.) 
Even if g were reduced by the amount of the radiation pressure, the reflector 
would return to A on the geo^tric continuation of this ellipse ; but now g 
increases because the light-pressure ceases, '^'he result is that the reflector 
approaches the earth still more, let us say to A*, at which, of course, its 
velocity far exceeds circular velocity (which it should have at this altitude). 




Pig. 141 

Because of the light -pressure, the circular velocity from A' to B would be 
still smaller, so the ellipse becomes still wore elongated from A* to B" than 
it was from B' to A' ; B" liers still farther out than B', but for that the 
following perigee would lie still nearer than A', etc. he final result would 
be that the reflector would either get hunpupin the upper layers of the 
atmosphere on the A - side or fly out of the earth's field of gravity on the 
B - side. 

The inherent energy increases with every revolution. In Fig. 141, on both 
sides of the line ACB, one can speak of a potential vAich ne.turally changes 
by bounds as this line is crossed ; the locations of equal potential form 
semi-circles on both sides. of the line. 

I*uring the whole run above the line ACB, the sum of the kinetic and the 



- 492 - 



potential energy of the reflector must reinain constant, during the run belovr 
the line ACB likewise. 

Corresponding to the difference in altitude il h, there is a smaller diffe- 
rence in potential (i? V ) above the line AB» than below it {4v). The reflector 




Fig. 142 

nakes the ascent^ h from A (perigee) to B (apogee) (cf. Fig. 142) at the cost 
of the loss^ V in kinetic energy, but in return it gets back more kinetic 
energy when, on the way back, it arrives at C at the altitude of A again ; if, 
in addition, it sinks by the distanced h', for that it likewise wins more 
kinetic energy than it would use to make this ascent on the other side again. 
The action is similar to that of a merchant who buys cheaply on one side and 
sells at a high price on the other, getting rich in the process. 

To prevent that we can do various things. For example, if we accelerate 
the reflector at B' so that it does not travel the dotted ellipse to A' but 
the dash-dotted ellipse to A and decelerate its velocity at A so much as to 
cause it to continue flying in the field of less attraction on the curve 
AE again, this state can be constantly maintained. Ke would get this result 
in practice, for example, if we did not reflect the light rays vertically 
but, as much as possible, to the north pole. 



- 493 - 



In the example discussed, there iras an increase 
in energy because the body ascends in the veaker 
field of gravity and falls in the stronger one. The 
opposite would be the case if it reached its perigee 
at B and ascended from B to A (Fig'. 143). Then its 
energy content irould decrease at first. Yet, in 
so doing, the trajectory ellipses irould become 
rounder and roiuider until attaining the circular 
shape , and then the opposite case irould arise 
again. In order to keep A (md B as points on the trajectory, we 
have to decelerate at A and accelerate at B here also. 




Fig. 



143 
would 



In a similar way, it can be proved that a body cannot permanently 
gravitnte in a centred ly-oriented field of gravity which varies in strength 
in different sectors (cf. Fig. 144) unless it is decelerated upon passing 
over into weaker sectors and accelerated when passing over into stronger 
ones, or is elevated so strongly in the stronger sector as to just cancel 
the difference in gravitation thereby. 

So much concerning the vertical component of the light-pressure with 
one-sided operation of the reflector. With one-si(^ed-operation, the effect 
of the sagittal component tends to rotate the trajectory plane about an 
axis perpendicular to the ecliptic (revolution precession). In Fig. 145, 
the plane of the paper represents the ecliptic, ACBD the earth; the 
trajectory AB would be seen as perpendicular to the ecliptic if the radia- 
tion pressure did not act. The arrows desicnate the velocity pare-l- 
lelogram; AB' is the actual path of the reflector, A' B' the 





Fig. 144 



Fig. 145 



- 494 - 



new trajector;;' plane. (The theory of the gyroscope and the science of the 
trajectory disturbances of the moon provide further details.) If we proceed 
aptly, we can arrange to have the trajectory plane rotate about this axis 
once a year and always stand perpendiciilar to the s-direction. 

Derivations similar to those mentioned above also apply to the case in 
which the light-pressure is not equally strong over the whole stretch A~ B 
but gradually increases from A to the pole and decreases from F — B. This 
case corresponds to reality for, in general, the reflector net is inclined 
to the earth's surface by 45° only above the pole and the reflector does not 
work above the hot zone. (Several facets could be used for illuminating 
large cities at night.) Decelerating at A (Fig. 142) and accelerating at B 
can naturally be done only with use of the light-pressure. In so doing, the 
reflector surfaces must reflect the light in the transverse direction. Here 
likewise, sagittal components arise which, however, cannot completely halt 
the rotation of the trajectory plane, for they in part mutually cancel out 
their effects ; nor do they act as far south as Ihe first-named sagittal com- 
ponent in the north. But we can easily suspend the revolution precession 
completely or reverse it if, in the south, we set the reflector surfaces 
perpendicular to the sun. If we wish to do little work with the r. fleeter 
in the south, we can here carry out a large number of light-pressure maneu- 
vers, changing the revolution and the rotation of the reflector as we vrish 
and taking it nearer to or farther from the earth. 

F recession movements . I wrote above that, at the centre of the reflector, 
gravitation and centrifugal force are almost in equilibrium in every atom. 
I^at is correct only for the centre, not for the edge. If the reflector has 
a 45° inclination tovraird the earth, with a diameter of 100 km, the lower edge 
is ca 25 ' V2 =35.3 km nearer to the earth thian the centre ; the upper 
edge is respectively farther. As is well known, the force of gravity decreases 



- 105 - 



as the square of the distance from the centre of the earth. If the whole 
is just kept in balance by the revolution centrifugal force, a pull down- 
ward ( 2*-') is exerted on the lower edge and an equal pull upward ( j*- ) on 
the upper edge. In part, these forces cause a tension (•<, "< ) in the net 
and, in part, they tend to set the plane of the net perpendicular to the 
earth {jS */9 )• The latter does not come about because of the rotation of 
the reflector, instead the rotation axis shifts perpendicular to the direction 
of the force similar to a gjrroscope axle. In figure 147 I have represented 
r 





Fig, 146 Pig. 147 

the conditions in a gyroscope. The arrows v indicate the velocity of two 
opposite points on the circumference. AB stands for the propulsion of a pair 
of forces tending to turn the axis off the paper, v'v' are the resulting 
new velocities, C'C* is the new direction of the axis resulting Jrom v'v'. 
So the axis has not turned in the direction of the pair of forces AB but 
perpendicular to it, and we obtain a precession of the rotation axis. The 
acting forces (compared to the light-pressure) are considerable : thus, 
in the previous example, wl.en the centre of the reflector is 1 000 km 
above the earth's surface, for the outermost point, each of y* and v< is a 
force equal to 11 cm / aec tiroes the mass on which x% acts. Fortiwiately, 
the forces do not bend the net. They are proportional to the mass on which 
they act (i.e., the acceleration imparted does not depend on the mass) ; 
moreover, they are proportional to the distance of the mass from the line 



- 496 - 



on which the centrifugal force (z) due to the revolving speed c and the 
earth's attraction g mutually cancel out (i.e., apF roxLmately the horizontal 
straight line through the centre of the net). This also applies to every 
r.dtation of the net as long as the dir ction of revolution lies in the plane 
of the net. 

for economical guiding of the r^Ilector, care vd.ll have to be taken to 
place the net in the best possible position for the vrark to be undertaken. 
(A region to be illuminated must not lie in the plane of the net nor the 
s-direction fall in the plane of the net, and the like.) The reflector 
should naturally be put to as full use as possible. 





How, the idea is reasonable to arrange the rotation of the reflector 
so that the precession keeps pace with the revolution and the trajectory 
plane is always perpendicular to the s — x-plane and makes an angle of 45° 
with the s-direction (>'ig. l48). Unfortimately, this cannot always be achieved. 



■i|97- 



>breover, we can considerably influence the relation between precession 
and rotation if we set the net on a slant or perpendicular to the direction 
of revolution. That should not adversely affect the angle of the net to the 
sun a.nd the earth, since we can also correspondingly set the trajectory plane 
on a slant to the s-direction (Fig. 149). This figure exaggerates the matter. 
Here the s-direction falls in the trajectory plane. That could natiorally not 
be achieved during the whole year. Nor does the figure take the lateral motion 
of the rotation axis into account. The picture shows, however, how the loss 
due to the unfavorable positions (at u) is again equalized by the fact that, 
as a whole, the position of the net is more favorable than with 4 5 "-guidance. 

hi certa:ln purposes, types of guidance can be more advisable in which the 
periods of precession and rotation do not coincide. They have the advantage 
of making it possible to illuminate certain regions more strongly than with 
the methods of guidance just described. These methods are extremely manifold. 
4'hen studying them one has a feeling similar to that when examining the question 
of how best to begin a game of chess. This is an extremely productive field 
for mathematicians who would like to work on something new. 

All these possibilities of guidance I would like to combine as the 
group of guiding methods with mechanical precession of rotation. The radiation 
pressure, however, is also a means by vjhich to influence the rotation speed 
and the rotation axis. 



-i;98- 



Precess ion-Free Gtddance 

Peculiar to all the guiding methods mentioned so far is the fact that 
the rotation appears as a function of the revolution. Still another method 
of guidance is possible in which the net plane, rotation plane, and trajectory 
plane coincide and are perpendicular to the s-directioh. Steering is done 
solely by means of the light-pressure, which is especially strong here. 
Pig. 150 shows the conditions for a reflector 200 km in diameter at an 

ml 



I 

I 
.1 



Fig. 150 

altitude of 800 to 1,000 km ; m, n is a plane through the centre of the 
earth parallel to the rotation plane. Here the period of rotation is 
irrelevant. If the reflector is to orbit close to the earth, this method of 
guidance is superior to all the others ; it is unsuitable if the reflector 
is to ascend several 1, 00 km, vrtiich would be indispensible if the reflector 
is to float over one half of the earth longer than over the other. 

With use of the light-pressure, the reflector can be placed in all possible 
positions in the course of several days. 

A few words could be said about the tension of the net. It is based in 
I part on centrifugal and in part on gravitational forces. 



-i^.99« 



If the ratio between mass and reflector surface were the same on the 
whole line, in other words if the tin surface reflected uniformly, the 
light-pressure would accelerate all points equally. Then the light-pressure 
could cause no bending whatever, and, since the other forces can likewise 
cause no bending, there would only be one type of tension, and that very sraall. 
At the centre, however, there is a heavy observer and control station, which 
may also have to serve as pier and fueling station for rockets. Naturally, 
this would hardly be affected by light-pressure, but the reflector round 
about would. The latter is bent back as far as corresponds to the parallelo- 
rrsim of forces between the light -pressure and the tension of the net (Fig. 151). 




Fig. 151 

If, on the other hand, we have many stations distributed over the whole net 
(Fig. 152), as will be the case with large reflectors, there is much less 



o- — 



-— c— 



-O-^ 



-O 



Fijr. 152 
bending. So the angular velocity can also be smaller. And that is necessary 
The highest value for w is given by the fact that r'w^lOO m / sec. Other- 
wise the bracing wires would have to be thick in the middle and thin on the 
edge, which woiild again give occasion for bending due to the light-pressure. 
So, with large reflectors, w can only be small. 



-5oo-< 



Actually, these are all only introductory remarks. In regard to the 
adual guiding of a reflector, I have only the following to say : 

In the south, sjnaller reflectors wotild scarcely be used, larfer ones 
almost not at all. Here, the main task of large reflectors, that of naking 
polar regions arable, is not feasible. If the glaciers of Antarctica were 
melted, the level of the ocean would rise uncomfortably (6-8 m). Hopefully, 
by then nan will be sensible enough at least to leave a cold zone for the 
protection of nature. So for the southern hemisphere and the tropics there 
would only remain the illumination of large cities at night and perhaps 
supplying solar plants vrith more light as well as the influencing of the 
weather. In the north, on the other hand, outside of Greenland, there are 
no such masses of land-ice (however much ice there may be, no danger arises 
from melting ice that floats in the water), and the glaciers of Greenland 
will renain because of their high location and because there will be more 
snowfall on Greenland if the polar sea melts. Since the reflector is to work 
mainly over the northern hemisphere, it is reasonable to plan the trajectory 

so that it gravitates mainly over the northern hemisphere ; according to 
KEPLER'S second law, that occurs if the reflector follows an ellipse whose 
perigee lies in the south. The perigee is determined by the fact that the 
reflector is not supposed to enter the atmosphere even with unforeseen 
disturbances in the trajectory : meteors, inadvertence of the pilot, the 
eff :ct of extraneous fields of gravity not calculated beforehand, etc. An 
altitude of 1,000 km should suffice. (V/ith large reflectors, the perigee 
is also given by the fact that the net must not tear under the influence 
of the difference in gravitation. ) 

The apogee is determined by the fact that the light reflected to earth 
must have the necessary concentration in order to fulfill the purpose of the 
reflector. The light patch of a reflector 6,000 km high, for example, cannot. 



-501- 



according to (2l6), be smaller than 56 km, no matter how well the reflector 
works. In order to concentrate the radiation energy more strongly (in case of 
war) the reflector would have to be brought closer to earth by decelerating 
its revolving speed at the perigee so that the reflector gravitates in a 
circle near the earth ; the deceleration would occur by means of the light- 
pressure, if one has time (it would take 2 to 3 months), or by means of rear- 
ward thrust, if one does not have much time. —With low guidance, precession- 
free guidance would be in place. 

With the trajectory ellipse described at the beginning, which is perpen- 
dicular to the s-direction, the reflector would be situated south of the 
earth's orbital plane for 44 minutes &nd north of it for 1 hour 51 minutes. 
Since the light-pressure acts longer in the north, it tends to depress the 
plane of revolution in the north. But that does not happen, instead there is 
a precession of the plane of revolution about the main axis (north-south axis) 
which, with correct guidance, takes exactly one year. Furthermore, there is 
a rise of the reflector which can easily be offset by suitable braking 
above the hot zone and in the south. That is possible, in spite of the short 
flight period in the south. Since the velocity here is considerably greater 
than in the north, a smaller thrust in the direction of motion results in a 
greater energy change (cf. Chapter 12), Directional change, on the other 
hand, is strongest exactly with small velocities. It could easily appear as 
though the reflector would have to be extremely thin and light for the light- 
pressure to have such an effect. That is not absolutely true. With appro- 
priate guidance, the reflecting surface could be 10-20 times as thick, yet 
this precession of the plane of revolution could always be effected in the 
course of one year. 

The trajectory disturbances caused by sun, moon, and planets in general 
tend to rotate the plane of revolution about the north-south aocis, while the 



-502- 



axis itself is preserved. In their total effect, they produce a precession 
ncment which, in general, is opposite to the light-pressure moment, but 
smaller. Of course, with suitable guidance of reflectors, which, in relation 
to the reflecting surface, are 100 times as heavy as the one described, this 
precession moment could be greater than the light-pressure moment. These 
trajectory disturbances are extremely diverse and, in part, can hardly be 
investigated mathematically ; so it might appear as though they pose insur- 
nountable difficulties to the reflector guide. Actually, he need pay no atten- 
tion at all to smaller trajectory disturbances ; he must simply re-adjust 
the reflector in the south each time with the use of the light-pressure. 
Determining the position is likewise very simple ; and, if everything else 
comes off, I believe that any 6th-seiiiester student of astronomy could be 
instructed well enough in 2-3 months to be entrusted with the reflector 
without concern. 

Here I want to discuss several objections to the reflector idea. 

For example : The slightest pressure would shatter the reflector like glass. 
I already spoke about the temperatures of different bodies when exposed to 
solar radation on p.iQQtf. It will not be difficult to paint and guide the 
reflector so that it alvrai.vs has a temperature at which the sodium is firm 
yet alwa; s elastic. As we just saw, it need not pass through the earth's 
shadow at all, for the light-pressure causes an annual precession which 
al^^'ays keeps it above the edge of the earth's shadow. Besides, we must not 
forget that the forces which act on the reflector are so small that, although 
we still determine them mathematically, we can really no longer visualize 
them at all. 

Another objection is : The energy reflected by the reflector will not 
be sufficient to achieve the required effect. Vie must first ascertain what 



-503- 



kind of effects we are cfealing with. The strategic effects can be achieved 
with the reflector tinder all circumstances. Even the thickest clouds reflect 
at the most 3 A °^ the striking rays. l/4 -is absorbed and, with closest con- 
centration of the rays, the heat generated thereby is sufficient to produce 
a tornado in a few minutes that can destroy enemy forces, -^^or the sarce 
reason, the objection is invalid that the cloud cap that must necessarily 
form above the rising air stream makes fxirther action of the reflector impos- 
sible. But this cloud cap would be no hindrance for another reason. In a 
calm, it forms at an altitude of 3-10 km vertically above the affected area. 
With precession-free guidance of the reflector (Fig. 150), as in the case of 
war, the light falls in on a slant. When no calm prevails, west wLnds usually 
blow in the cold and moderate zone, and stronger in winter than in summer ; 
in the hot zone, on the other hand, apart from the monsoons, it is usually 
north-east or south-east wind. This wind blows the cloud cap farther and 
farther away, so that the attackf-d region becomes open to further influence, 
("■'xcept vdien the reflector is situated exactly in the wind direction behind 
the region. But, with the rapid north-south movement of the reflector in 
precession-free guidance, that can be the case only for a few minutes.) 

The cultural tasks are also possible to fulfill • For example, if a 
sea route to the ports of Siberia is to be kept ice-free, a route must only 
be chosen that runs approximately in the direction of the winter wind from the 
Gulf Stream, that is 1-2 points of the compass to the north. In so doing, 
light is thrown on a relatively narrow and short strip running from east to 
west, beginning in the east and moving westward to the extf^nt that the sky 
clouds over at this place. What stands us in good stead here is the fact that 
the direction of the wind and the direction of the earth's rotation coincide. 
Hereby the earth always rotates as we need it during the work. Kow there is 
a fog strip above the melted ocean which protects it from cooling off further 
and which the wind cannot effectively blow away because it blows parallel to 



'50k- 



the strip. By the time the light patch has passed along the whole stretch, 
the fog at the beginning vdll either have settled or been bi-own avra,;', since 
the vrind cannot permanently blow in the direction of the shipping lane. Then 
one can bej^in at the beginning again. Since the clouds hold the heat above 
the shipping lane for a long time, a reflector lOO km in diameter is completely 
sufficient, it has also been objected that the heated air would simplj'' rise 
and cold air rapidly rush in from the side and cool off the whole. In the 
first place, because of deviation to the right, the air cannot so easily 
penetrate a minimum of a few points of the compass running from east to. west. 
Secondly, another thing must be considered : If the air in the irradiated 
area rises, only the air from the immediate surroundings will be able to rush 
in (again because of deviation to the right), and that must again be replaced 
from atmospheric layers higher up, not from those on the side. As is well known, 
when air is forced down from above it warms up. It acts like the foehn and does 
not cool off the affect'-d place. 

\ihen illuminating a strip of land on a clear, frosty nig! t, the reflector 
likewise has a considerable effect because a layer of fog develops over the 
heated area which keeps it from cooling off. The chinook, for example, can 
blow only when there is a considerable difference in the air pressure above 
North ;vmerica and the Pacific Ocean. If one illiminates a strip running say 
from the 48th parallel of latitude and the 95th meridian to Lake Athabasca 
and moves farther west as the sky clouds over, the result is a warm night 
under a cloudy sky at the U.S. -Canadian border. Since the fog settles by the 
next morning, the sun has the opportxmity to further warm the area, causing 
a warm day ; thus a minimum pressure arises which sucks in the air across the 
Rockfes and releases the chinook. If in a simllsr way the K'orthern Pacific is 
irradiated, a chinook blows on tl e west coast of America. (Cf. JULIUS HAHN, 
Textbook on Climatology I, p. 304. ) 



-505- 



Jn the same way, only much easier, the bora or mistral can be prevented 
from blowing by illiaminating Yugoslavia or Korthem France during the preceding 
cold winter night. likewise, night frosts can be prevented. 

Illuminating the Caspian Sea continuously for several days could produce 
a low pressure area .here and bring rain to Southern Russia ; in so doing, 
the water evaporated from the Caspian Sea would condense in Southern Siberia. 

Here a number of circumstances are in our favor which permit us to achieve 
considerable effects with relatively small means. 

Another objection is that the sodium plate would quickly lose its luster 
due to the cosmic dust or the short-wave rays of the sun. I would like to 
answer in short that, with their apparent weightlessness, it will be very 
easy to bring the reflector facets to the station occasionally and pass them 
throUi?h the rollers once more after first ttjming their rough side to the sun, 
thus making them soft by heating. In this way, a km', of the reflector, could 
be repolished without expenditure worth mentioning ; I hope, however, that 
the reflecting capacity of such a reflector facet v/ill not require renewal 
for at least 30 years. The objection that the reflector would be pushed from 
its course by cosmic dust I have already refuted on p, 905. 

Finally, 1 was told that sodium plate 0.05 mm thick wo^^ld allow the light 
to pass through and not reflect. T have done an exp-eriment in this regard b;;^ 
rubbing wood with a piece of sodium under kerosene. I hope a thickness of 
1 / 20 mm will suffice. No basic problem would arise in the construction of 
the reflector even if it had to be made • mm thick, for the radiation pressure 
is so great that, efven in this case, a precession of the plane of revolution 
about the north-south axis in one year would be possible. 



-506- 



Enough of this, ihey are only dreams of the future. Bold ones ? Perhaps, 
but we have already experienced the realization of bolder ideas. V.'ho woiild 
have believed in 1894 that, a few years later, one would see through a person 
by means of roentgen rays ? PHILANDiiR'S statement (Medical Fairy Tales), 
"tSan will be made transparent like a Jelly-fish", was bolder than this dream 
of the future ; that required f i'-ding something completely new, \diile here 
we are only dealing with laws of nature already known, —Accomplishing these 
things will certainly require the conversion of enormous energies. But were 
not hundred times greater energies and thousand times greater sums of money 
expended diui'ing the VJorld War ? In one year, the nations of Europe spend 
more on smoking and drinking than the whole sodium reflector would cost. 
V.'ar and narcotics are quite unnecessary things, yet more money is sp^t 
on them than on something useful. Should not mankind, in an exceptional 
case, also save something for constructive work ? 



-507- 



Chapter 21 
Trips to Strange Celestial Bodies 

Formula Quantities (pp. 507- 518) 



m : mass of rocket 

p : parabolic velocity with reference to the earth 

r : residual velocitj'- with reference to the earth 

V : velocity in general 
V, : residual velocity 

V : parabolic velocity with reference to the moon's surface 
V. : tangential velocity of the moon 

'^o much is spoken about it today that I would also like to say something 
concerning it here. Thereby I would also like to answer various inquiries by 
letter in greater detail. 

Essentially, there are two questions to be answered : 

1) Are flights to strange celestial bodies (and back) possible at all ? 

2) If so, do these flights have a purpose ? 

In giving an answer we must above all, clearly distinguish between suppo- 
sitions, ascertained knowledge, and bayic considerationp- 



-508« 



1. The ::oon 

To shoot a rock t to the noon we must give it an initial velocity of 
at least 10,380 m /sec at an altitude of 230 km above the ground. Then, if 
the aim was correct, it could reach the point at which the moon draws it to 
one side just as strongly as the earth to the other side, so that it would 
later fall on the moon. 

The flight period would be about 97 hours (cf. p.465)' JJ^ W opinion, 
a rocket that is to really hit the moon must have a somewhat higher velocity 
for the following reasons : 

If p represents the velocity with which the rocket must start off in 
order, with wholly correct control, just to get past the neutral point, 
V the actual velocity, and if v = p, thei?, at the neutral point, the rocket 
retains a residual velocity r which, according to (120), has the value : 

r = V'v2 - p2 

Here r appears as a function of v, and by differentiation we find 



dr 



(219) 



dv, V-^— 7 



P 



For the limit of v = p, this expression becomes infinite. The flight 
period, in large measure, depends on r, and near v = p a difference in 
velocity of millimetres per second would suffice to cause time differences 
of hours in the flight period. Then the probability of the rocket hitting 
the moon at all would be minimal. Since the mo&n revolves alout the earth, 
we cannot avoid giving the rocket lateral motion to the moon and, since the 
moon runs roughly 1 km / sec and is 3 . yOO km wide , it covers' the distance 
of its own diameter in just under an hour, rhe rocket will probably not meet 
it because the velocity regulators of the rocket operate exact to a thou- 
sandth at the most, which makes an error of between 10 and 100 m / sec. This 



-509- 



circumstance would weigh in the balance especially heavily if we wanted 
to shoot an immanned rocket to the moon. With a manned rocket, the pilot is 
in a position to correct errors later when they beconie clearly visible. 
3ven then, it will be better to give the space-ship an initial velocity of 
at least 10,5CX) m / sec' 

'^'hus the time differences become considerably smallef". According to 
P«246» the ideal velocity must be about 700 m / sec greater. So to start 
from earth we need an ideal propulsion of 11,200 m / sec. Left to its fate 
after lavmching, the rocket would fall increasingly^ faster on the other 
side of .the neutral point and finally hit the moon v;ith a velocity that 
would destroy it, in any case. In the first place, the moon already has 
a velocity relative to the earth of on the average 1025.25 m / sec due to 
its motion about the earth. The rocket would already strike the moon with 
this velocity (vt) if, relative to the earth, it stood still on the moon's 
orbit, "urtherroore, the moon imparts a velocity v = 2370 m / sec to a body 
falling from very high. 

1;^ relative to the nraon, the rocket ejcactly stood still at the point 
of weightlessness, it would strike the moon with th:'. s velocity. If, at the 

point of weightlessness, it already had a velocity v^., then, according 
to (120), the velocity Vg with which it strikes the moon xrould be given by 
the forffiula 

Vs = Vp + vr {P20) 

Since the residual velocity r with reference to the earth and the tangen- 
tial velocity v^ with reference to the moon stand perpendicular to each 



l) ^n the film, "The V.oman in the "oon", I have, for this reason, applied 
a still greater initial velocity (10,700 m / sec)« 



-510- 



other, therefore 

v/ = vt^ + r^ (221) 

and, according to (?18), 

? 2 2 

r = V — p 

consistent with (l20), from (218) to (221), we find 

vg = ^v^ - P^ + vt^ + v/ (222 ) 

For V = 10,5oo m / sec (the other quantities are astronomic constants), 
that results in 

Vg = 3027 m / sec, 
which is roughly 3 km / sec. 

To keep the rocket from crashing, this velocity jrajst be decelerated 
shortly before it reaches the moon*s surface. Since the moon has no atmos- 
phere, that can be achieved only by rearward thrust that counteracts the 
notion, which means a further increase of 3 km / sec in the required ideal 
propulsion. 

But Just somehow decelerating these 3030 m / sec is not enough. The 
rocket must land as gently as a snowflake. It consists of thin plate which, 
by contact with the liquid hydrogen, has become at least as brittle as 
steel plate at usual temperature. No fissure or break is to arise. Certainly 
strong, resilient supports can be fixed to the bottom of the rocket; never- 
theless, it will have to land very carefully. 

Apparently, the moon is covered with fine sand and dust similar to the 
deserts on earth. With the temperature differences on the moon (up to + l80° 
where the sun shines and to — 273) where it does not), more brittle rocks 
must be shattered like a glass into v*ich hot water is poured. Accordingly, 



-511- 



it is probable that the horizontal areas of the moon's surface are cover- d 
>rith fine sand. It is also probable that the exhiaust gases of the rocko;t vdll 
siniply blow this sand aside at tl^e landing place, so that the rocket will 
finally touch down on naked rock ar^n-,^y. (^t least, that possibility rnust 
be figured vrith for the pr- s-nt.) 

I cannot Imagine that a rocket pilot would let the rocket fall freely 
u/itil the last ^iioment and dec-lerate it only at the very last with the 
highest perrn:'Gr:!.ble counter-pressure, so that it loses its velocity comple- 
tely, just at t;-.e moment when it touches the surface of the moon. Irobably 
he will decelerate the greatest part of its velocity consider bly earlier 
and then descend at almost uniform velocity, constantly compensating for the 
acceleration due to gravity by rearward thrust in order, finally, to stop 
completely one meter above the ground and then land centimeter by centimeter. 
The disadvantage of this method is naturally th t the rocket must work agairst 
its own weight a very long time or, as we described it in Chapter 12, rau£t 
bum at a low velocity. 

•-Ti the moon, the acceleration due to gravity amounts to about 1.62 m /sec . 
If the first deceleration of the velocity of 30''? m / sec occurs with a 
counter-pressure of 3' m / sec", it would take 1 i- minutes (if the direction 
of motion is not perpendicular to the moon's surface, even somewhat less). 
But the careful landing now following could easi],y take <V-5 times that, 
so that altogether a burning period of - minutes = 540 seconds must be 
planned for. V'ith the 1.62 m / sec"' acceleration due to gravity, that makes 
a loss in propulsion of 873 m / sec ; still equal to the velocity of a good 
rifle bullet. 

Our space navigators have arrived on the moon safely. Na+urally, they 
want to get back again. They can do so only by lighting the rocket once more 



-512- 



^ ^ arc sine 



so that it can ascend from the moon and fall to earth. ' his ascent is the 
exact reverse of the fall to the mDOU, for a throw upra.rd is plr sically tVe 
op-rxjsite of a free fall. So, by quantity, wf. would have the same as in formula 
(131). In other words, what is required is the actual velocity of the ascent 
Vg = 3027 m /sec. The rocket can start with full throttle. According to 
V'rtiat was said on p. 2^2, with an ideal acceleration of :;5 m / sec and 
horizontal starting, the floating angle 

1.62 

= 2.36° 

35 

Here we can altogether ignore the losses in propulsion that would occur during 
steep ascent, ^'he rocket need only rise high enough to avoid the mountains 
on the moon. Therefore, 

Vx ^^021 • sec 2.63° = 3030 m / sec 

■^ need figure only with horizontal starting, for the rocket can start 
horizontally wherever it stands, so that, with circular velocity, it first 
deacribes a circle about the moon in whose plane lies the direction of the 
velocity with v/hich it would have to leave in order to hit the earth. Then, 
as soon as it moves parallel to the desired flight direction (approximately ; 
I am not discussing finer differences here), the circular velocity is 
increased to the requisite 3027 m / sec by rearward thrust. As far as that 
goes, even id-th vertical ascent, the rocket would sacrifice only 160 m / sec 
of its ideal propulsion because the gravitation on the moon is so small. 

Depending on how the carrying surface and parachute question is solved, 
landing on the earth world require an additional ideal propulsion of up to 
200 m / sec. 

Since the pilot is only a human being and can commit inaptitudes, he must 



-513- 



take along fuel for about IjOOO m / sec for correction purposes (I believe 
this will certainly be quite sufficient). The total ideal propulsion would 
equal the" sum of the single required items : 

Ftinction Ideal Propulsion 

Starting velocity from earth 11,200 m / sec 

Deceleration of the velocity upon arriving at the moon 3»027 m / sec 

Braking losses 873 m / sec 

Leaving the moon 3,030 m / sec 

Corrections 1,000 m / sec 

Total : Vx = 19,130 m / sec 

If we set the exhaust velocity c = 4000 m / sec, according to (6) 
(Chapter 6) we obtain an ideal maris ratio o f ^ _ 134 for this machine. 
According to what was said •np.97,a machine composed of 3 hydrogen rockets 
could make this flight ; because of its size, it would naturally have the 
required ballistic coefficient in spite of the light specific weight of the 
fuels, ierhaps it would not even have to leave the 'Hull of a rocket on the 
moon. 

If the first expedition should find a sufficient quantity of water on 
the moon (the light color of some areas on the moon as well as the peculiar 
changes of color at the bottom of the crater of Ilato, and other things 
are being attributed to hoar-frost), the next expeditional rocket, instead 
of fuel, could take a sunlight motor, a water-decomposing apparatus, a re- 
frigerator, and a large insulated container in the fuel tanks of the last 
rocket in order to produce the fuels for the return trip itself. Ihese instru- 
ments would remain on the moon and likevrise serve the succeeding expeditions 
for the manufacture of fuel and in their place they could bring along other 
equipment and little by little build a station on the moon. I do not think 
it probable that sufficient water vdll be found there, in which case the roc- 



-514- 



kets would always have to take along fuels for the return trip and be cor- 
respondingly larger. 

Actually, I do not believe that pure fuel rockets will achieve the state 
to ever attempt the trip to the moon ; I rather hope that will be reserved 
for the electric space-ship which 1 will describe in the next chapter. I still 
cannot say for certain whether such can be built, hence I have based m^ 
research on hydrogen rockets in order to show that travelling to the moon 
is possible under all circumstances, 

Furpose of the flipiht : We saw that the trip to the moon is possible. 
Now the second question must be answered : ^oes the trip have a purpose ? 

I cannot agree with the view that stranj'.e celestial bodies should be 
visited only if living conditions similar to our o\m. are found there. For 
exarnple, people cannot live at the north pole, and yet the region is being 
visited and explored. Kor do we have in mine pits what we find on the earth's 
surface and iiiust designate as our normal living conditons. And although other 
things are found in mines, indeed exactly because other things can be obtai- 
ned there than above the earth's surface, thousands of miners daily repair 
to them. 

A visit to a strange celestial body should be discouraged only if, with 
our technical means, we were not at all able to stay alive there for a few 
hours or days, as, for exapple, on the sun or on Jupiter. On the other hand, 
we can protect ourselves against the cold of the moon night by reflecting 
metal surfaces (cf. p. 41o), against the lack of air by divers'suits and 
artificial air, aP3.inst the high rock -temperatures by insulated soles, 
against the heat bj- refrigerators, and against the sun's rays by suitable 
umbrellas. Dr. VvEBER, for example, forgot that when, from the supposition 



-515- 



that living conditions similar to our own can perhaps be found on none of 
our neighboring planets (that is not certain, as I shall soon show), he drew 
the conclusion that it was impossible to land on them. If it were true that 
we must use no technical auxiliary means, we could not even spend the winter 
in Europe. 

A visit to the moon would have great scientific value. We are here 
dealing with a celestial body that, in the main, consists of the same subs- 
tances as the earth, although, relatively speaking, the earth has somewhat 
more of the heavier and the moon somewhat more of the lighter substances. 
The surface of the moon consists of the same basic elements as the earth's 
surface, but it has been preserved from the effects of air and water. % 
conparing the two, we can see what, on the surface of our earth, is attribu- 
table to the effect of air and water and what is not. Furthermore, on the 
mDon,we could make mine shafts and drill holes up to four times as deep as 
on earth. l)Tk« small force of gravity and the expected hardness of the 
rock would prevent the drill holes from collapsing as easily as on earth. 
2) Presumably the noon is not as hot on the inside as the earth, hence the 
temperature in the deep shafts would be better endurable than on earth, ^ut, 
on the moon, a drill hole fo\jr times as deep would, relatively, not be 
foiir times but 10-1? times as deep as on earth, for the diameter of the moon 
is three times smaller. Prom that we could obtain geological knc>^ledge of 
incalculable importance, for example, concerning the causes of the rising and 
sinking of continents, concerning the profound." reasons for the difference 
between sial and sima, and other things. :'oreover : Bark, moving spots are 
supposed to have been observed at the bottom of the Pratosthenes crater from 
which the existence of animals has been concluded. PlCKxiKilMG claims to have 
found traces of chlorophyl in the spectrum of certain crater floors, 'i do 
not believe that any sort of life can exist on the moon. Still it would be 
interesting to investigate whether, in the course of millions of years. 



-516. 



life has gaiiied a foothold on this world, so completely uninhabitable for 
earthly creatures. 

In addition to these more theoretical reasons for travelling on the 
moon, there covild be a practical, in 1-2 decades perhaps an actual one : 
According to a recent theory/, the moon's craters have been caused by numerous 
larger meteorites falling on the moon after it had already solidified. 
Percent-wise, these meteorites consisted of the sajne stuff as the whole 
celestial body, that is in large part of heavy jnetals. Ihe larger part of 
our earth also consists of heavy metals. Earthquake research teaches that 
the relatively light layer that forms the earth's surface suddenly stops 
at a depth of ], ^00 km, where a layer begins that has the specific weight 
of iron. Tum&rous meteorites also fell on the earth when it vras still in 
the stage of formation. At that time,^ however, t?ie earth was still r.iolten 
and the heavy substances sank below the surface. Ivith the moon, on the other 
hand, the heavy substances reimined at the surface and here it is relatively 
easy to mine and transport them to earth. In so doing, only the small 
attract!- g force of the moon has to be overcome. Reside ^■n.th the use cf 
rockets, the transporting could be done with the use of electromagnetic 
cannon, which would have to be only l/l6 as long as on earth. Perhaps it 
would be possible to drive missiles from the moon to the, earth. Setting up 
electromagnetic guns and the cannon would be facilitated by the fact that seen 
from the moon, the earth alwa;'S remains at the same place in the sky. 

It is self-evident that the electric space-ships already jrentioned could 
be very useful in the mining and transporting of moon ore. 

Here I would also like to say a few words about the science of inter- 

I' 

planetary ice as formulated byHORBIGER and FAUTH, since it is widely confused 
with the problem of space flight, for example, bv VALIER and GAJL. 9he 



-517- 



book by HORBIOiJl and FAUTH, "Glacial Cosmogony", represents a grandiose creation 
of ideas, and I can recommend it to every specialist who has the capacity 
to read it vdth the necessary critical faculty. It contains an almost depres- 
sing wealth of facts and suggestions. Besides, it represents a valuable 
exercise in reason-^ ng for the specialist, forcing him to reflect on why 
he holds to exactly our scientific world image and not that of HUiiBICER. 
The layman, however, I would urgently advise not to study this work, for the 
false notions of HORBIGER are just as forceful as his achievements. I do 
not believe, for example, that his conclusions concerning the state and destiny 
of our planetary system apply to a single one of the closer celestial bodies. 

■"•he moon, for example, can impossibly be com] letely covered with ice. 
Here is just one reason (I could name 10) : 

^f any area of the moon's equator is examined with a diffraction spec- 
troscope and bolometer while the sim rises over it, it is found that it 
reflects any percentage of the received light. TfJith every color of the spectrum, 
the percentage of the total light can be determined which makes up the energy 
contained in this part of the spectrum. VJhen the sun rises higher, the radia- 
tion coming from the respective area becomes richer in infra-red light (in 
heat rflys, therefore), his heat radiation is greatest when the sun has 
passed the zenith by 10-20°. Later it decreases again. S.nce all areas of the 
moon's equator show this phenomenon in the same measure and the heat radiation 
depends almost alone on the height of the sun above the respective area, there 
is, in my opinion, only one explanation, viz., the r spective area has heated 
up under the influence of the week-long radiatr'on unmitigated b- an atmos- 
phere. From the increase in this infra-red radiation, one can quite accu- 
rately derive the temperature of the moon's landscape and finds its maximum 
to be between 150" and 1P0° above OC. (Cf. M. WILHLLM MEYjiR'S "The Moon", 
Cosmos, Prankish lubl. House, Stuttgart. I am intentionally citing a popular 



-518- 



science book, since all specialists in astronomy are fandliar with these 
and similar facts, and these discussions are only meant for non-astronomers.) 
That is what must theoretically be expected according to the formulas set up 
on p. 439. At such temperatures, there can naturally be no talk of ice. At 
night, the tenperature of the moon sinks very low, which would brthe occasion 
for existing water to freeze. If, however, there were water on the moon in 
quantities worth mentioning, the changes on the moon's svirface as we actually 
peraeLve them near Plato, Eratosthenes, and at other places wovild have to be 
much more extensive. 

2. The Asteroids 
Fonnula quantities used on pp. 518-556. 

Viiere f.pplicable, the letters designate scalar values of a velocity ; 
underlined letters refer to the velocity as vector quantity. 

g : acceleration due to gravity toward the sun 

r : distance from centre of the sun 

V. : initial velocity with reference to any planet 

V : parabolic velocity with reference to the sun 

V : residual velocity with reference to the planet from where flight started 

w : velocity with rfference to the sun 

w. : circular velocity at the examined distance from the sun with reference 
to the sun 



o<^^: 



m, lit 



Between the orbit of the fourth planet in the solar system (I-iars) and the 
fifth (Jupiter) there are the orbits of numerous small celestial bodies, t e so 

called planetoids, asteroids or small planets. So far, roughly 1,000 
have been discovered, but probablj"- there are more. They are only so srall that 
they can no longer be seen or photographed. 



-519- 



Their orbits extend over a circular space that is wider than the diameter 
of the earth's orbit. On the average, the asteroids are 3 radii of the eaiiih's 
orbit from the sxan, but some almost reach the orbit of Jupiter (5 radii of the 
earth's orbit) and others that of Mars (1.5 radii of the eairth's orbit). 
One (Eros) even covers the large, t part of its orbit within that of Mars, so 
that the orbits of the two planets appear like two concentric links of a 
chain. 

"^he largest asteroid (Ceres) has a diameter of just under 900 km ; the 
smallest ones are hardly visible even in the best telescopes and are c ertainly 
only a few kilometres across. The albed© (which is the ratio between the quan- 
tity of light which the star reflects and that which it receives) differs 
widely with the asteroids. With Ceres it amounts to 10 %, so that Cer s is 
almost black in color. The albedo of Vesta, however, is over 60 ^ ; so Vesta 
must have a pure white or shiny surface. This difference leads to the conclu- 
sion that different asteroids are composed of diffirent stuff. 

The mass and the attracting fores of the asteroids are scarcely known ; in 
any case, because of their small size, they are only small. Thus, on Cerps, the 
acceleration due to gravity would hardly exceed 5O cm / sec and the parabolic 
velocity scarcely 800 m /sec. With the smallest asteroids, the effects of 
gravitation can be ignored. V.Tiether s^me asteroids have an atmosphere is not 
known. In any case, because of their sirall attracting force, the majoritj' 
can letain neither airnor water. Some asteroids show periodic light fluctuations. 
The assumed explanation is that they are not spheres but irregularly-shaped 
splinters which turn now w^ider, now narrower surfaces to the sun. 

In flying to an asteroid, we have a new task before us in so far as it is 
a matter of taking the space-ship to a different distance from the sun* 



-520- 



If the space-ship leaves the earth with the hyperbolic velocity v, and 

if V had been the parabolic velocity at the point where propulsion ceased, 

p 
then, outside of the earth's sphere of gravitation, according to (120), the 

space-ship retains a residual velocity with reference to the earth of 

Y — V . -"-n SO doing, the earth's sphere of gravitation theo- 
r 1 V 

retically never stops ; in practice it can be applied as equal to 

1 million km. Beyond this limit, the attracting force of the earth appears 

so small compared to that of other stars, especially the sun, that it can 

be ignored in the first approximation. On p,208 I spoke about a subsequent 

trajectory disturbance by the attracting force of the earth. On a flight 

.to an asteroid this is in general smaller than on a flight to Mars. 

On these flights, the space-ship describes an extremely complicated 
trajectory curve, although.it can be exactly determined by mathematics. I 
will write about that in greater detail in n^y treatise on three-body calcu- 
lations. Meanwhile, especially PIRQUET and HOffi-LiNN deserve the merit of 
having showi-i that, at least by approximation, the matter can also be approa- 
ched with relatively simple methods of calculation. 

In the earth's field of gravitation, the space-ship describes approxi- 
mately a hyperbola. Beyond it, it continues flying (cf. also p, 466 ff) with 
a velocity w, which vectorially consists of the tangential velocity of the 
earth with reference to the sun w^^ and the residiial velocity of the space- 
ship v . ^nder the influence of this motion it then describes any ellipse at 
one focus of which the sun stands. The calculations of Chapter 10 combined 
with what was said on p. 466 ff apply here, at which ^V' w, jj^ must be taken 
for <^ . -^ 

If we designate the radius of the earth's orbit as r^^, the distance of 



-521- 

the asteroid from the sun aS fg* *he attracting force of the sun rt 
the distance of the earth AS g^ and at the distance of the asteroid 
as gg, and the velocity of the rpace-shlp at the distance of the 
asteroid as v/, then, according to (59) 



»!-»;~2„i.(i-A). ^^^ji 



IfOCis the angle of inclination to the horizontal with reference 
to the sun, then, according to (55a) t 

r, It'i C03 7, = Tj t»'j COh K2 • . . 

(224) 
From (223) and 224), this follows : 

.„/,_('x.?5i»^Yl = 2ff,r,.(i-A). (225) 

' L Vj C03 a^/ J Vi r-i' 

With the use of this formula we can calculate the angle which 
the trajectory makes with the horizontal at a certain altitude r, or 
r^ as well as, having a given angleOC^, the altitude rg at which 
the trajectory encloses the respective angle with the horizontal. 

If we regard the orbit of the earth and that of the planet to 
be visited as circles, the space-ship will travel with the least 
fuel consumption if it flies on a semiellipse whose perihelion 
(point closest to the sun) touches the earth's orbit and whose 
aphelion touchesthe orbit of the planet. (Of course, with the 
condition that the planet passes the respective place at the right 
time. With this method we cannot fly whenever we like.) In this case 



<«. = -X*i = 0- (226) 



-522- 



Here the space-ship at first passes the earth by and its residxoal velocity 
V ^ is simply added to the tangential velocity w. ^ of the earth. (Sumnation 
of impiilses, p. 221 ), Therefore 

Ifihile the space-ship rvins ahead of the earth, it at the same time moves 
farther away from the sun due to its greater centrifugal force. Jn so doing, 
its velocity is retarded (Just as if it travelled up a mountain). In the 
aphelion its velocity is smaller than that of the planet, otherwise from 
there on it would have to describe a circle and not an ellipse. If w. „ is 
the tangential velocity cf the planet, the residual velocity of the space- 
ship with reference to the planet is 

^t7 ^ ^t2 ' ^2 (228) 

From {225) and (2?6), this follows ; 



A 


= 2 . 


Si • ^ 

• 


^2 -^1 


2. 
^2 


< 


^2 



2 
As is well known, w. . = gj^ . r. . Therefore 

2 2 



or 



^2-^1 
2 


= 


2 


^tl 
• 2 


^2-^1 
^2 


M 






2-^2 




"t: 




r 


1+^2 





(229) 



-523- 



■^hen, from (22?) and (229), this follov;s 




- 1 



(230) 



From (22?), (226), and (228) we, in a similar way (with analogous permu- 
tation of letters and signs, likewise from (230) find : 




(231) 



For example, if it were a matter of reaching a body which is gravitating 
with circular velocity at a distance of three radii of the earth's orbit, 
then, according to (230) (assuming that w, = 29.7 km / sec), v = 6,S^5 km / sec. 
Summing up the imptilses (cf. (l20)), v = 13.1 km / sec. In so doing, the 
ideal propulsion would be just under lA. km / sec. According to (231), the 
velocity upon arrival on the asteroid would be v „ = 4.95 km / sec. 



As a rule, the increase in the residual velocity v ^ due to the attracting 
force of the asteroid can be neglected because of the small mass of the asteroid 
and the high residual velocity. — Since the asteroids apparently have no 
atmosphere, this velocity would have to be decelerated by rpcket power, at 
which we can apply v = v „. V.'hen departing, the same propulsion would have 
to be given once more in reverse. Additional fuel for Ij "^00 m / sec would 



-524^ 



have to be taken along for landing and correction purposes, although there 
would be less chance of missing the asteroid than the j-oon because the 
space-ship travels in the same direction and not perpendicular to the celestial 
body. In all, this space-ship would have to produce an ideal propulsion of 
roughly 2^ km / sec. 

A four-stage hydrogen rocket would be capable of such perfomance, but, 
with the present state of technology, the possibility of building such rockets 
-is doubtful J, fortunately, that is not necessary. Before the actual space 
flight (cf. p. 480 ), we can take the fuels on STnaller rockets to a fuel station 
which orbits ti;e earth in a circle with circular velocity. The circle must 
have a position that enables the direction of the departure to be imdertaken 
later to fall in the plane of the circle. 

If this fuel station gravitates at the altitude at which, with ascent 
in the synergy curve, the rocket attains circular velocity, that is if it 
flies above the edge of the earth's atmosphere, then the docking and refuel- 
ling of rockets theoretically represents no loss of work, for, on departing, 
the new propulsion is the synergetic continuation of the propulsion so far 
imparted to the fuel. In a sense, the circular velocity is a resting point where, 
without disparagement to the principle of the summation of impulses and the 
flight, the ascent can be interrupted for any length of time with possibly 
high acceleration. 

In so doing, it is not absolutely necessary (at least with regard to the 
trip up) that the fuel station gravitate above the equator. If, in its time, 
the station rocket rose in the temperate zone (say in Germany), it will describe 

l) Unless, in the lower stages, {)\amerous smaller rockets are used which are 
combined in bundles and are so light that they can Just land singly hanging 
from a parachute (cf. p. 395). This was assumed, for example, in the film, 
"The Koman in the 2'oon" (cf. Vol. II). 



-525- 



circles about the centre of the earth which are inclined toward the equator 
by as much as the latitude of the place of ascent. Just when it is over the 
latitude of the place of ascent, it will fly exactly from west to east, so 
that it can be reached by a rocket in the synergy curve. 

The departure of the space-ship from the fuel station, however, is the 
synergetic continuation of the journey out and transportation of fuels out 
only if the fuel station gravitates at the pice where the synergy.' curve runs 
horizontally. If, for example, as NCXDRDUNG suggests, the station is set up 
so high above the earth that it exactly circles the earth once in 2k hours, 
it wovild always be above the meridian of the same location , which would 
certainly be convenient for communicating with the earth ; as a fuel station, 
however, that would in no way be the be t position, according to Chapter 12. 
Even if, as PIR^iUET suggests, the observer station were allowed to revolve 
above the earth's surface at an altitude equal to the radius of the earth, 
that would be very suitable for observation purposes, but, if this station 
were also tobeosed as fuel station, several 100 m /sec in ideal propulsion 
would be sacrificed.-AlmDst as great would be the loss if the reflector 
station described in the previous chapter were at the same time used as fuel 
station. That the loss Is not still greater is solely because the reflector 
station constantly gravitates above the shade limit and so, with each revo- 
lution, there are two points from which, by increasing i+s velocity, the 
space-ship can just run ahead of or stay behind the earth, vi^iich resij-ts 
in the best flights to strange planets. 

■^hua, synergetically considered, it is best to establish the fuel station 
separately from the observer and reflector station. ''Nevertheless, that is not 
absolutely necessary since, at most, it is a mattered several 100 m /sec in 
propulsion losses. 



-526- 



On the other hand, synergetically considered, putting a fuel sphere into 
orbit around a planet that has an atmosphere which could be used for braking 
purposes would naturally represent an energy loss vriien compared to departing 
with the use of a fuel station, although this is not meant to disparage such 
orbiting. 

If an asteroid that describes an elliptic orbit is to be reached, the resi- 
dual velocity is mathematically found as the vectorial difference between 
the velocity of the space-ship and the planet. Incase the latter is not 
known from some annual, it can naturally easily be found by using the formulas 
(225) to (229), provided the orbital elements of the asteroid are known. 



^ere I will set up only the formulas for reaching asteroids in the peri- 
helion and the aphelion. If the earth's radius is designated as r. , the 
distance of the perihelion r„, the distance of the aphelion of the asteroid r-, 
the velocity of the asteroid in the perihelion V^, its velocity in the 
ai helion V„ , the velocity of the rocket with ref er'--:nce to the sun with 
semielliptic flight in the perihelion w„, that in the aphelion of the asteroid 

the associated residual velocities with reference to the asteroid v 



w 



3, 
and V o, then by logical substitution in form.ula (229) we find : 



r2 




(232) 



-527- 




^3=^3"^3 



(233) 



'^he residual velocity with reference to the earth v is found from 
(230) by there substiti'ting the distance of the perihelion or aphelion 
for r^' 

•^rprisingly enough, atmosphere-less celestial bodies with strongly 
elliptical orbits are more easily reached in the aphelion than in the 
perihelion because, in so doing, v „ decreases vrfiile v^ increases but little 
(because of the rythagorean addition of the velocities accordirg to (l20) 
to the considerable potential velocity of the earth v ). 



Of course, this flight on a semi-ellipse has a considerable drawback ; 
it takes very long. If we desirrnate the radius of the earth's orbit as r. , 
and the distance of the flight target from the sun r„, we are here dealing 
with a semi-ellipse and, therefore, according to KEPLER'S third law. 



;(-«^> 



years 



(234) 



^ the first -mentioned case, for example, the journey out alone would 
take 1 year, 4 months, and 28 days. Then the space navigators would have to 
wait on the asteroid for two months for an opportunity to return, which would 
naturally take as long as the journey out. So the whole trip would take up 
3 years. 



-528- 



The only remedy is : fly faster . In so doing, much can be achieved at 
first, especially because the flight ellipse rises more abruptly v;ith s 
higher velocity and hence the flight distance is shortened considerably. 
Of course, that means giving up the advantage of being sure of one's target. 
%mely, if the orbit of the planet is reached in the aphelion of an ellipse, 
the planet is hard to miss. On the other hand, we already saw in the case 
of the moon how easy it is to miss a aslestial body if the trajectory of the 
space-ship makes a considerable angle with its direction of motion. 

"■'ith the electric space-ships to be discussed later the whole trip could 
be made in 1-2 months. 

As I already said, several asteroids are considerably closer. After the 
moon, Eros may be the closest to us of all the celestial bodies. With lowest 
fuel consumption, the flight to ^iros would take l/2 to 3/4 year (the whole 
trip vrould take somewhat over 3 years). Including the losses due to braking 
and corrections, the flight would require a total ideal propulsion of 17 km / se c. 
From the standpoint of the question of fuel , of all the bodies of our solar 
system including the moon, Eros is the easiest to reach with a space-ship. 
A fuel concumption of v = ?,0 km / sec cotild shorten the duration of the trip 
to two years. 

Flirpose of the ^ 'light 

A visit to these celestial bodies which, because of their small size, 
are today still as good as unknown to the astrophysicist vrould in itself 
be interesting and instructive. In addition, there is the value that sma,ller 
asteroids (e.g. Eros) could have for anchoring space telescopes (cf. p. 457). 

V'ith regard to the geological results of such expeditions, what was said 
concerning the moon is ^ill more applicable here. Vfith asteroids less than 



-529- 



300 km in diameter a shaft could be sunk to the centre, making it poaible 
to completely explore the inside of a celestial body -which, although consi- 
derably sjiialler than the earth, is still similar to it in a certain respect 
(spherical form, stratification, etc.). 

lixploring the asteroids vrould be of especially high scientific value 
because all the transitions are represented from the planet (I'Jars, Ceres, 
Pallas, Psyche, etc.) to the comet (Eros, laicke comet) to the meteor block. 

iNith today's technology, the question whether earthly creatures could 
settle on the asteroids must be flatly negated. On the other hand, finding 
livjng beings or at least fossils on the lar<';;est asteroids is not completely 
excluded . 

"^he asteroids are fragments of a planet which, for some rason, could not 
combine into asi- ,":le mass. Single ones may consist of those substf-rces which, 
with the planets, sank invrard ; at 1 ast in part they will b® e as ;i]y extricated 
from t?je inside of the asteroid. If the electric space-ship shov Id prove itself 
mining these substances could be considered. 

3. Fars 

f^rs moves around the sun in an ellipse. Half the major axis of its 
orbit equals 1.^236914 radii of the earth's orbit ; its numerical eccentri- 
city amounts to 0.0933574. If we want to reach liars in the semielliptic flight 
discussed above, the differences in the residual velocities are considerable 
depending on whether w ■ want reach I'lars in its perihelion or in its aphelion. 



-530- 



In the perihelion, at departiire the residual velocity with reference to the 
earth would be v = 2.l6 km / sec (cf. (234)) and upon arrival the r'sidua] 
velocity with. reference to Mars would be v ^ — 3.2? km / sec* 



in the aphelion, the corresponding figures would be v . = 3.50 km / sec 
and v p =2.00 km /sec. ^ince the earth as well as Mars have a consideible 
mass and hence a high parabolic velocity, these residual velocities only 
contribute little to the ider-l propulsion, orever, we must not forget that 
the two planets have atmospheres which we can utilize for braking purposes , 
so that, upon arrival, the residual velocit?- is irrelevant. landing on 
>1ars may be facilitated by the fact that apparently there are open bodies cf 
water on it, as 1 ICKERIKG discovered by the use of polarized light. Never- 
theless, we must still figure on decelerating t}:e last 400-700 m /sec by 
rearward thrust, for the l-Sars atmosphere is quite thin, in any case. If 
we wanted to exr^ore J'iars when it is in the perihelion upon arrival of the 
space-ship, the ^nal velocity at departure would be v = 11.3 Ion /sec. Upon 
arrival on J'iars, at the most 700 m /sec would have 'o be decelerated by 
rearward thrust ; including losses during ascent of roughly 700 m/sec and 
the 600 m / sec to be provided for correction purposes, the total ideal 
propulsion for the journey out would amoioht to 13,300 m / sec— For ■''^rs, 
the parabolic velocity is 4.96 km /sec, the acceleration due to gravity only 
3.50 m /sec , and the air in general thinner, although pierhaps reaching sorae- 
wliat higher tiian on earth, for these reasons vre will lose but little in 
ideal propulsion when ascending from ^\rs, perhaps 300 m / sec. On the return 
flight Vp = 5.94 km / sec, and, if we agaiji allow 500 m / sec for correction 
purposes and presuppose braking by means of the earth's atirosphere, we would 
need at the most v = 6.7 km / sec for the return trip, 'ihe whole trip would 
require rou.^rhlj'- 20 km / sec, somewhat more than a trip to the moon. 



-531- 



If, on the other hand, ^lars is in the aphelion, v = 19.8 km / sec, as 
is easily found hj .calciJ.ation. 

It would require the least fuel if the trip were undertaken to Ifers in 
the perihelion position and tr.e expedition could remain thereuntil it is 
possible to return from the aphelion position. In theory, that can be appro- 
ximately accomplished since for a minimum f ill expenditure trip the expe- 
dition must wait almost l/2 Miars year for the date on which to return. 
(Whether the fuels can be kept in a liquid state for one year is quite another 
matter. ) 

The duration of the trip to Vats caij, however, easily be shortened by 
increasing the velocity, for, with the high parabolic velocities of the earth 
and i'Jars, a small increase of the initial velocity already considerably 
influences the residual velocity and, since we are decelerating by using the 
atmosphere, we need give the same propulsion orijjr once. Kith v = 25 km / sec, 
for example, the round trip can be made in 4-6 months without having to 
travel around the sun. The flight period from the earth to Mars especially 
can be considerably shortened without a propulsion increase worth me-'itioning. 

'^'he flight to ":ars is greatly facilitated by the fact that very likely 
there is a sufficient quantity of water on Mars and the sky is mostly clear. 
The machines for raanufa'cturirig the liquid fuels already mentioned on p. 513 
could be safely set up there. In so doing, in the first place the expedition 
could remain on Mars any length of time without being concerned about the 
fuels vaporizing and, secondly, no fuels would have to be taken along for 
the return trip. Thereby at least 6 km / sec can be saved. Once such a station 
were established on ^'lars, from the standpoint of the fuel question it would 
be the easiest to reach of all the bodies of our solar system. 



-532- 



Furixise of the Flight to I jara 

Ivith regard to the purpose, I an afraid •'■ will disappoint many a reader 
who expected too much. The only thing that can be proirised with certainty 
is the solution of most of the riddles which our neighboring planet sets 
us. Often the hypotheses concerning liars are advanced with great force of 
conviction and hence the layman only too easily considers them as proved 
facts. By contrast, it must be stated that we know nothing certain today, 
for example, concerning the geologic or climatic conditions on Mars. To 
the layman I especially recommend the book "Astrophysics" by SCHEIKER and 
GRAFF (Leipzig, '^eubner) for inspection. H is possible that the exploration 
of Itars will open up undreamt-of possibilities of development for human cul- 
ture, technology, and science, -^t is also possible that the first expedition 
to t'iars will be the last for centuries. 

Mars is farther from the sun than is the earth. From that it can be 
concluded that it consists of lighter elements (confirmed also by measu- 
rements of its diameter and its mass) and that in its formation it retained 
iTore air and water. The circumstance again that its mass is only 0.1078 of 
thf>t of the earth and is older makes it probable that it has lost a relati- 
vely large part of the atmosphere, especially water. Formerly, there was the 
tendency to regard the atmosphere of Mars as extireraely thin (at most a pres- 
sure of 1-2 cm of Trercury) and to deny almost completely that it had water. 
The astronomer JOHNSTONE G. STONEY, for example, completely denied the 
existence of water and sought to attribute to liqaid carbon dioxide the 
phenomena that speak for the presence of large quantities of liouid. (He 
forgot, however, that carbon dioxide can occur in liquid state only with 
a pressure of over i atmospheres, otheiwise it immediately changes from the 
firm to the gaseous state.) The latest research, especially during the last 
close approach of l-Jars, agaifi speaks for a higher and denser atmosphere and 



-533- 



higher water content. From the research I have become acquainted with I 
have the impression that there is a greater percentage of specifically 
heavier gases in the Mars* atmosphere than in the earth's atmosphere and that 
the atmosphere reaches higher on Jiars than on earth ; in spite of that, 
because of the small attracting force of l*iars, it is not under as high a 
pressure. The barometric pressure will be about half as high as it is here. 

^%rs' period of rotation is 24 l/2 hours. So days and nights are almost 
just as long as on earth. The inclination of the axis toward the elliptic 
almost corresponds to terrestrial conditions, but the seasons contrast 
more strongly climatically since the I-krs year is almost twice as long as 
the earth year. 

The assumption that the mighty canals on ^'^rs might have been produced 
by thinking beings .appears to be definitively disproved, "^he question is 
even being asked whether most of the canals on Mars are not simply based 
on an optical illusion. Thej' are hard to see through the largest telescopes 
and, if we look at our moon through a reducing lens, with a concerted effort 
we can discover "I'iars canals"on it as well. 

According to PICKERING, the large, yellowish-red patches seen on l^ars 
are deserts. They are more extensive than those on earth because there is 
less water on '^rs. Tj^e gray and bluish-green patches are vegetation areas 
according to HCKERIKG. in the light of some of these places, PICKERII^G 
believes he can even point out the absorjAion banos of chlorophyl. '^his 
research is difficult to carry out and Interpret clerrly. So it will be well 
to regard the question whether there are plants on Kars as unclarified for 
the present. 

By day, the temperature on %rs is a few degrees above zero only in the 
tropics. At night it sinks under -30° at every point. The reason why, in 



-534- 



splte of that, there is liquid vmter in the cold zones is because the Mars 
seas have largely lost their water with time and the salt has remained, so 
that today the water on l-lars has a high salt content. Strong salt solutions, 
however, freeze only under -20°. 

The low temperature of Kars would in itself not exclude the presence of 
plants. Plants in Northern "^iberia and on the Arctic Archipelago endure 
temperatures of upder -40° for months. Theie is linotber important factor : 

The sap of plants growing in cold regions on earth must not contain 
too much salt. Otherwise, when the snow melts, the cell walls would break 
due to osmotic pressure. On the other hand, if there are plants on Viars, 
they are likely to contain miich salt. Since salt water does not freeze as 
soon, especially wl en under pressure within the cell, the sap of Mars plants 
is already fluid much below 0° and capable of living activity, ■^n no way 
do the plants on l^rs lack light. Although the sun scarcely appears half 
as large as on earth, the air is clearer. Haze or dust has been obs rved 
on Mars but never real clouds. 

i'iars plants are already viable at temperatures at which our polar plants 
are still in the dormant winter state. So, by all appearances, the pre-conditions 
for a type of life on 'ars are given, ^n the other hand, we must not forget 
that life need not necessarily be present wherever life could occlt. In a 
sterilized tin can, for example, decay-causing bacteria could well live, yet 
there are none in it. 

Perhaps it is objected that according to SVANTE ARRHENIUS'S cosmos- 
permism hypothesis there must be life on Mars if only there is life on earth. 
SVaNTE ah .HENIUS said : 



-535- 



If a planet vdth a small attracting force is situated near a bright 
sun and there are encapsulated bacteria floating in the atmosphere of this 
planet, the light-pressure of the sun's rays must blow them out into inter- 
stellar space. Such bacteria germs mut be floating about in all interpla- 
netary space and, according to AHRHEMIUS, the cold of interplanetary space 
would not only not kill them but in a measure conserve them causing them 
to remain alive much longer than at normal temperature. According to 
ARRHEKIUS'S calculations, three such bacteria germs would have to fall 
on the earth every year . Of course, only in the rarest case could they 
live long on earth, for the earthly creatures are eminently adapted to 
living conditions on earth by a long struggle for existence and among them 
the strange monocells would play about the same role as a lion among 
polar bears at the noi'th pole or a polar bear among lions in Africa. 

I do not wish to enumerate all the arguments here that have been 
advanced for and against the cosmospermism hjrpothesis. In our case, it seems 
out of the question to me that life should reach Infers from the earth in this 
way. The radiation pressure of the svm today is far from sufficient to drive 
any body away from the earth. That is found to The true indirectly by calcu- 
lating the radiation pressure and direc^■ly by observing the comet's tail. 
■4. is difficult to believe, however, that the earth was already inhabited 
when the pressure of the sun's rays was not as great. If such a gerr^ arrived 
on Wars, it would strike it with a velocity of at least 5 km / sec. In so 
doing, according to what is said in Chapter 14, it would burn up in the 
atmosphere of %rs under all circumstances. For this reason, earthly life 
can in my opinion have originated only on the earth itself. Just as for 



l) To me, this figure seems too high. According to my calctilation, one v;ould 
be closer to the truth if one assumed that one such germ fell to earth every 
100,000 years. 



-536- 



the earth, one can assume original generation for %rs • one can naturally 
also reject it as, for example, for the conserving can. 

Let us suppose there are living beings on ikrs. In what way have they 
developed ? About that we can state still less. People who believe that 
there are inhabitants on foreign celestial bodies usually imagine them as 
more or less similar to the earthly creatures. I would like to counter that 
with the following reservations. 

■4/ can scarcely be otherwise tten that all living beings on earth developed 
x'rom a single, unicellular primitive form. 

But how differently did the various creatures continue in their develop- 
ment. Australia has approximately the same cliniatic conditions as the old 
world, but it was cut off from the mainland for "only" 2-3 million years 
and yet Australian natural life looks entirely different. (Naturally, we 
are not considering certain plants and species of birds as well as the 
Australian negroes because they obviously immigrated later. ) How diffe- 
rently life can develop is realized when various forms of life are compared. 
Let us compare, for example, a human being, a bee, a crayfish, a tapeworm, 
an an»eba, a fungus, a lichen, a lycopod growth, a fern, a gingko, an 
evergreen tree, a grass species, a V^'elwitschia, a palmr-tree, or a fruit tree. 
■H. must also be remembered that the development of these organisms was 
in part identical for long periods of time and that the struggle for 
existence and oertain incidental catastrophes nipped much development in 
the bud. The bird of paradise, for example, could develop only where no 
beasts of prey existed to h\mt down these conspicuously-colored creatures. 
Several species of hvonming birds have been exterminated by a storm in one 
day. V/hen the ice-age arrived, only a few species renained of the living 
organisms of the Tertiary period. Only when we logically reflect on all this 



-537- 



do we get a notion of how different from ovtr living world will be that of 
other celestial bodies where life developed along other lines right from the 
start. 

Perhaps it will b&objected that often under similar living conditions 
very similar forms arise even though the course of development was basicly 
different. If we place a dolphin, an ichthyosaurus, and a shark side by 
side, the external similarity will likely be greater than that between a 
whale and land mammal, an ichthyosaurus and a lizard, or between a shark 
and say a sea-horse. — '^'he marsupial wolf of Australia, a carnivorous kangaroo that 
runs on all fouiSis iiiuch more like a wild dog than a kangaroo. Further- 
more, I remind the reader of the similarity between palm trees and tree 
ferns at similar locations, between the orang-utan and the sloth, between 
ants and termites, between swallows and swifts, between pseudo-acacias 
and acacias, between certain plant leaves and phylloclades, between sea 
snails and nummilites. Certain cactuses and spurges growing at the same 
location are externally similar beyond recognition. Naturally these examples 
could be multiplied hundred-fold especially if one does not look for overall 
similarity of single organs as, for example,' the similarity of the fossorial 
forefeet of the mole and the mole cricket. 

I do not doubt that there will be creatures on distant celestial bodies 
that look very similar to creatures known to us. (^^at^^rally, the course of 
development of these creatures would be entirely different from that of our 
forms.) Beside them will also be forms vfhich we can no more imagine today 
than anybody who has never heard of an amoeba or a cuttlefish will get the 
idea that such creatures exist. 

I do doubt, nevertheless, whether there are human intelligences or at 
least such similar to human beings anywhere in the cosmos. 



-538- 



The fundamental condition for human intelligence is the ability to gather 
personal experiences and by oneself to learn and take note of something one 
does not already possess as ready knowledge from birth. ■'■ cite the following 
as examples of innate knowledge of man : 

If the number A is larger than the number B, and the number B is larger 
than the number C, then A is also larger than C. — If A is a part of B and 
B a part of C, then A also is a part of C. —The straight route is the shortest. 
— "^he straight line has the same inclination throughout. —Straight linos 
that have the same inclination cannot intersect. —All that happens happens 
in space and time, and space and time end nowhere. ^Taken as a whole, the 
earth is a horizontal plate. — ^ian has a free will, and many others. 

The advantage of this inherited knowledge is, in the first place, that 
it does not have to be learned ; it is inherent. Animals with much inherited 
knowledge (e.g., chickens) can look for food just after emerging from the 
egg ; an ant or termite is fully capable of intelligent performance imraedia- 
tely aftsr slipping from the pupa shell, Secondly, this knowledge is usually 
better assimil ted than learned knowledge, and the latter can be easily in- 
corporated into it, so that it does not hang in mid-air. According to ^ant, 
with whom I in no way agree on the whole, this innate knowledge are the 
categories into which the world of phenomena can be integrated. 

The drawback of this inherited knowledge is tl^t it does not adapt 
itself to the special needs of the individual concerned and hence is not 
only superfluous but a downright hindrance. — In ngr work in astronomy, 
I can well imagine a planetarium in which the single models of stars seem to 
freely rim on invisible rails about a large, shiny sphere ; but as soon as 
I want to visualize the action of a space-ship I nust resort to other 
represent-.tions, say a piece of iron that is hanging from a magnet and, by 



-539- 



the impact of a billiard stick, is to be impelled ayray from it to another 
magnet. Then, as soon as I want to imagine the feelings of the passengers, 
I must again revert to other concepts, say an empty, black, hollow sphere 
10-20 km in diameter. Without "up" and "down" I cannot visualize such a 
picture at all, although here these concepts are perfect nonsense. Then, 
when I occupy jnyself with other things, the earth is naturally no longer 
a "celestial body" but just the "earth", the opposite of the "sky". This is 
a source of considerable difficulty in all work in the field of astronomy. 
— Wow, by century-long work in astronomy we have to a certain extent mas- 
tered these difficulties. Today the faculty of philosophy in Turin would not 
answer Columbus in this way : ^ine, you can sa^l over the edge of the 
earth ; thpt we want to believe, if need be. But how will you sail your ship 
back up again ?. '^oday we have invented all sorts of astronor.lc images 
and diagrams and worked out a casuistry as to when one or the other thing 
applies. —But who would claim, for example, that, in our present day 
adjiiinistration of justice, the concept of causality has been fully digested 
and that a proper distinction is always made between innate notions of 
revenge and retaliation as well as freedom of the will and mitigating causes, 
on the one hand, and the concepts of causality and the requirements of crime 
prevention, of sparing the innocent, of deterrents, and of correctly influencing 
public action, on the other hand. 

'^here is about the same difference between acquired knowledge and inhe- 
rited knowledge as there is between the art of printing books and the me- 
diaeval art of cutting whole plates. (Perhaps later^n * philosophic book, 
I will write more about these and similar things.) A further drawback of 
inherited knowledge is that it only changes very slowly and so it takes long 
for an animal species to achieve intelligent action half-ways worth mentio- 
ning by means of inherited knowledge. 



-540- 



Acquired knowledge is in no way as great a necessity as say the fish 
form, the fossorial forefeet, or the feathered leaf. Kiandreds of thousands 
of species and millions of subspecies get along without it. If we examine 
the genealogical tree of the earthly creatures, in my opinion we find acquired 
knowledge only in a very small brancli, thct is with the r-ptiles and the 
creatures which later developed from the reptil s. ;"'ain worms have something 
akin to the ability to remember. Beheaded worms also show it, so that we 
are likely not dealing with conscious rational activity. V. ith amphibians 
no trace of it has been found so far, just as little with any other animals. 

That the "clever" bee, for example, is not able to take note of any- 
thing and draw conclusions from it can be seen from the following observa- 
tion : 

If a bee flies into a room through a half-open window and when flying 
away strikes the window-pane, it often exerts itself for hours without no- 
ticing that it cannot get through there and getting the notion to try by 
another way, say by the way it came. Yet it by no means lacks the sense of 
locality. Bees have been packed into cases, whirled around by a cord, and 
taken by car 5-10 km away from the hive. They always found their way home. 
Obviously the boe knows only that, if one is loaded with sweets, one returns 
to the hive by the straightest way and that one can fly through wherever 
one can see through if one exerts oneself a bit ; from personal experience 
it learns absolutely nothing. 

■^he results of research concerning the intelligence of ants and the 
remaining invertebrates are similarly crushing. Their experiences simply 
do not influence th'iir knowledge ; they obviously lack all remembering and 
combining ability* 

^ere perhaps someone will think of the Munich flea circus or the training 



-541- 



of spiders. In this case, I believe only the human trainer "learns" any- 
thing, not his pupil. 1 have ryself watched a spider keeper who was firmly 
convinced of the intelligence of his horrible pets attempt to train them. 
he training consisted of carrying the spider away from the web, after which 
it returned to it, or producing certain huimning and piping sounds and, vdth 
the hand or a straw, causing vibrations on a thread spun by the spider ; 
there upon it thought there was a fly and approached. 

In the flea circus either a piece of the flea's ankle-bone is cut off, 
so that it can only crawl, and is irade to draw a wagon or crawl along a v/ire, 
and the like ; or the aim is achieved by setting the flea into a shallow 
box with a glass cover, where it jumps against the glass until it is tired 
out. 

To make the flea ao springing gymastics, certain light and shade effects 
are produced with the hand, the flea is blown at, etc. If one is adept at 
it, every flea (not just the "trained" one) will jump exactly as one wishes. 
Here also, it is not the flea learning to jump correctly but the man learning 
to induce it correctly. 

Of course, I do not wish to conceal the fact that such an important 
entomologist as FABUE assumes that the wasp ants have the ability to gather 
recollections, at 1 ast with reference to location. It seems to me, however, 
that the phenomena which FABRt interprets in this sense could be explained 
differently ; neither should it be forgotten that recollections of location 
(just as the entire sense of locality) do not necessarily represent conscious 
knowledge • 

'^0 clarify the question for nyself , I sketched the plans of 2 machijies. 
Both were to be driven by clockwork and, after having been guided about on 
any desired curve, were to return to the point from where they had staHed : 



-542- 

one by the shortest way (sense of locality without ability to remem- 
ber), the other on the same curve on which it was guided away (register- 
ing recollections of location). As can be easily shown, the latter 
machine is by far the more complicated. Accordingly, sense of locality 
without the ?ib;:iity to remember could be by far the simpler. The 
wasp ants 'flying to and fro in front of the hole after crawling out, 
w^ich PAB5-E interprets as though they wanted to impress the environ- 
-ent of the hole on their minds precisely, could also be taken as play 
for practicing the sense of locality without memory. 

In siimmary we can say: Acquired knowledge is not necessary for 
life; it is only an incidental property of a small group of animals, 
the number of species or individuals of which certainly does not 
make up a thousandth part of all animals. V/ith the diversity of living 
forms, it is highly improbable that this property should repeat itself 
anywhers else in the cosmos. For this reason it is just not probable 
that there are creatures resembling human beings or at least such 
possessing human intelligorce on any other celestial body. 

V/riters of Mars novels especially write about highly cultured 
Mars i^eople. Contrary to the idea is, among other things, the 
circumstarcG that they have not yet come to earth by space-ship. They 
would actually have enough reason at least to bring air and water 
to their planet from earth. Measured by the period of development of 
a star, the time from the appearance of the first man to the construc- 
tion of the first space-sbip is so extremely short that it would be a 
downri^^ht miracle if the deveJopment of two celestial bodies within one 
planetary system stopped at exactly the same point. 

Perhaps the retort could be made th^-t possibly the inhabitants of 
P'^rs did send space-ships to earth several hundred million years ago, 
but they 



-543- 



had become extjjict In the m'.antime. According to OSivALD SFENGDJl, ruin 
awaits the western world in an uncanny short period of time by cosmic 
standards. Here I wish to say only this much : 

I believe that once humanity has reached the point where we are, it 
will no longer become extinct at all. Through science it will find ways 
and means to redress all threats of harm. With sharp observation we notice 
a number of indications of that. (For example, the movement for race hygiene, 
for biologically and hygienically correct living, for moral purity of 
public life, for NIEWKA>IP»S Freybund, etc. The last idea in this connection, 
compare NIENKAI>fl'S "irinces Without Crowns " and "irinciples of the Princes 
Without Crowns" — I consider just the most important thing man has thought 
up so far.) iifter these few sentences, it is naturally more or less a matter 
of opinion whether or not one wants to believe in the ruin of mankind on 
the basis of such and similar observed facts. Some tinre in the future, on 
approximately 300 printed pages, I hope to produce convincing proof of my 
claim. 

The possibility should also be considered that the inhabitants of Mars 
may well be able to build space-ships but that they have kept away from the 
earth because of the strong force of gravity, "n itself, this assumption is 
improbable. Cuite apart from the fact that, with so high a level of culture, 
the nature of the force of gravity could perhaps be tmderstood and means 
fotind to overcome itj in the course of millions of years the inhabitants of 
Mars, if they really had such a high cij-ture, coizld have developed a voca- 
tional caste that can endure counter-pressure of more thain 9.81 m / sec . 
i^en we human beings can get accustomed to 3-4 times the earth's gravitation 
in a relatively short time. — ^ut entirely irrespective of this, Mars would 
likely have quite a different appearance if its inhabitants really had such 
high culture. 



-544- 



V.'e cannot even say whether possible living beings on ■''-ars have had a 
Ioniser period of development than those on earth. 1 ) Me have enough examples 
on earth of biological speci s that have either scarcely advanced in deve- 
lopment or directly retrogressed in development. 2) The living beings on 
r'ars, even if older in an absolute sense, need not also be older relatively 
speaking. Apparently, life processes on i'hrs are slower. That is conditioned 
by the low oxygen content of the atmosphere on i-iars, by the little heat 
derived from the sun, and by the circumstance th t the force of gravity is 
lower on i--ars than on earth. If a creature on tlars is to move about vdth 
the same dexterity in relation to the force of gravity as an earthly crea- 
ture in a similar state, all its movements need be only 0.35 times as fast. 
The whole teirpo. of life could be slovrer and, in P. 4 earth years, all other 
things being equal, the living beings of 'Ma.rs would only advance as far as 
the living beings on earth advance in one year. I'ot to forget another matter. 
DevelopiTent can take place only where there are creatures to develop. The 
greater the number of jjidividuals, the greater the prospect of something 
new developing. (In a city, for example, more new things happen than in a 
vill "e.) Fow the nuirber of individuals on I'-iars is likely smaller than the 
number of living beings on earth, l) The earth is bigger. 2) On earth land 
and sea are inhabited in the same way, whereas 2/'J, of Mars' surface is a 
desert. 3) According to GAUSS, the living beings on Icars could, on the average, 
be larger than those on earth, so that relatively fewer individuals would 
have room in the saxf:e space. Tecause their number is small, the probability 
of a mutation occurring is naturally correspondingly smaller. Since Australia's 
separation from the mainland, its actual living world has not developed as 
far, relatively speaking, as the living world of the other continents. 

So we can affirm with a good conscience that we can say absolutely 
nothing about the living world of l-Iars. 

I do not agree with the view that holds that ^^ars is a boundless ocean 



-545- 



of ice, the seas open places, the continents ice-floes, and the canals 
fissures in the ice sheet. In such a case the atmosphere of JJars vrcnild have to 
give more indications of the presence of water, (-.ven the mists that are 
frequently observed could actually be dust clouds, libcperiraents conducted 
to determine the water vapor content from certain diffraction phenomena 
indicated an extremely dry atmosphere.) Besides, the edges of tie continents 
show considerable change in form depending on whether the season is moist 
or dry, but as a whole the form and position of the continents appears too 
constant for ice-floes. As a wl'^ole, the map of I'iars has not changed demons- 
trably since at least 70 years. It seems to me the red color of the continents 
especially speaks agaii.st the theory of ice in inter rlanetary space. Ihis 
red colorirg is xost easily explained b the occurrence of the hydrate 
of ferric oxide, to which the desert sand on earth also owes its red color. 
Naturally, a snow and ice surface could in time become red in color from 
ferric dust which, let us say, fell on it in the form of meteor fragments. 
If, however, it actually v;ere a water and ice surface, hoarfrost and snovr 
would soon be deposited over the red layer of snow and cover it. ('.e must 
not forget that the sun certainly heats up the equator of I'lars so strongly 
at noon as to cause large quantities of water to evaporate.) To adequately 
explain the red color an uninterrupted shower of iron dust would have to 
be assumed, in v;hich case space around Ifeirs would contain so much iron dust 
that it vjould, under all circumstances, be visible as a bright ring in our 
night sky. 

In conclusion, we can say : 

Pluman beings vri.ll probably not be able to breath the air on I-iars. I would 
already be satisfied if the air pressure were great enough to make space 
divers' suits dispensable and the space navigators only had to carry air 
tanks on their backs. 'ecause of the small force of gravity, the tanks mil 



-546- 



fortunately not be a very heavy burden. The needed oxygen could be produced 
with the use of suitable machines by distillation of the atmosphere on i%rs, 
which likely contains oxygen* 

The space-ship does not need to take along fuel for the return trip ; it 
is sufficient to take along machines for manufacturing the fuel on I'lars itself. 
The necessary conditions (simshine, salt water) are given. The total duration 
of an expedition is 1-2 years. Because of the clear atmosphere on Mars, the 
space travellers can remain in contact with the earth by means of light 
signals almost the whole time if, on an observer station near the earth, 
there is a sufficiently large space telescope and a sufficiently large 
reflector. Provided these are available, an eight-inch telescope and a 
reflector 1-2 m in diameter on liars would be sufficient. 

'^he space navigators would have to take precautions against cold nights. 
They would have to take along provisions, for l) we do not know at all whether 
Mars is inhabited and P.) the plants on Viars would not be suitable for human 
nourishment presumably because of their salt and potash content. L'rinking 
water could be produced on I'feirs. 

Concerning the purpose of the trip only this much can be said today : 
the first expedition would clear up the old points of controversy about ^^ars, 
'.■."hether further trips have a purpose one will be able to say only after the 
first trip. The first trip would pay financially under all circumstances. 
First of all, the : rix Gusmann could be won : About ?0 years ago, I-ine Gusmann 
bequeathed 100,000 franks to the Paris 'cademy with the specification that 
they be given to the physicist who succeeds in establishing contact with a 
planet of our solar system. At that Venus and ''ercury have the preference, 
but since both are more difficult to reach by space-shir^ than Tars the prize 
will probably be paid out after the trip to 'ars. Jf the money were soon 



r547- 

invested profitably (at present it is still in an envelope locked up 
in the treasury of the French academy), it would likely cover the 
cost of the I'ars expedition by the tiro it materializes. Besides, 
with the great interest the public has exactly in I''ars, any objects 
brought from Kars (even if only samples of air, water, and rock) 
v/ould represent such a hi^;h value (they could be placed in museums or 
sold to collectors) that the cost of the trip would be covered by far. 

In case K'ars were uninhabited, it would be the task of the first 
expedition to make colonization attempts with organisms from similar 
climates on earth (e.g., from Central and Northern Asia). Apart from 
the basic consideration of opening up all areas accessible to life, 
it would be of scientific interest to see whether and hov; these living 
organisms acclrlmatize on Mars, Nor is the possibility e>:c].uded that 
they would develop other properties in the course of a few decades, 
the study of which could be of importance from the scientific and 
perhaps also pract.'"?,! standpoint, e.g. pharmaceutics. 

On the other hand, if Mars were already inhabited, its natural 
life would have to be guarded and preserved unchanged. Its research 
v;ould become of downright epoch-making importance to the biological 
sciences. 

Ij., Venus 

Venus could be the most difficult but also the most rewarding 
celestial body for the space navigator to explore. 

Its size and chemical composition is almost completely like that 
of the earth( diameter ca 12,300 km). Its atmosphere appears to be 
10-20 km higher than the earth's atmosphere. Hence the air pressure 
at the visible surface is 2-3 times as great as normal air pressure 
on earth. (That has been found by observing how far the twilight 
overlaps the unilluminated part of the planet.) 



-548- 



The albedo amounts to 0.71-0. 76. Therefore, the regions of Venus on 
which the sm shin-s absorb only 2/j.-29 ,• of the light radiated upon them. The 
renaining 71-76 / they simply reflect. This is a very high figure, corres- 
ponding to the rf fleeting ability of say a thick layer of clouds or snow. 

\^Ihen clearly visible in the telescope, Venus appears as a small half- 
noon. v.Tien very near to us, it stands between earth and sun and we cannot see 
it at all t, so-called lower conjunction). l\?hen it is situated so that the 
sun is between Venus and the earth, it stands in the so-called upper conjunction. 
In this position we cannot observe it either. When it is close to the upper 
conjunction we see it as a small disc, but then it is unfortunately quite 
far from the earth. 

In the telescope, the observer sees Venus as a uniform bright, white 
surface on v.ihich not the slightest detail is recoprti^able. he dark spots 
which are allegedly seen after long observation and can also be photographed 
with poor apparatus are only based on a glare effect. They appear on every 
brightly-illuminated, uniformly-white sphere and demonstrably disappear the 
more, the better the instruments with which Venus is being observed. So, for 
the observer, it is truly a thankless object. 

It is difficult to say anything definite about the temperature of Venus. 

2 
The light or heat energy which the sun transmits to an area of 1 cm -■lith 

perpendicular radiation (the so-called solar constant) on Venus is 

4-^^.3 cal / cm'^ min., which Is 1.9-2 times that for the earth. Since Venus 

absorbs only ?%-?.'' ;=' of that, whereas the earth, being considerably darker, 

retains 42-46 4 of the sionlight, Venus actually retains only 0.99-1.38 as 

much energy as the earth. 

If we designate the heat that Venus absorbs as C;^' and the heat that the 
earth absorbs as Q$ , then the ratio 

C:^ : Q6 = 1.9 *24 ! 1.46 to 2.29 : 1.42 



-549- 



Naturally, in the final analysis, Venus does not "retain" this quantity 
of energy, but this heat must be irradiated again together with the heat 
which the planet radiates out from itself (as with the earth, that could 
amount to l/3 to l/4 of that designated as Q j ). So the surface of Venus 
must be so warm as to give off this whole quantity of heat in the form of 
heat rays. 

If the reflecting ability of Venus were just as great for long-wave 
as for short-wave rays, the calculation according to p- 438ff would be quite 
simple. 

If, on the other hand, the dense atmosphere of Venus contains much 
carbon dioxide it can be considerably warmer than we found it to be just 
now. Of course, I do not consider the atjnosphere of Venus to contain much 
carbon dioxide. T believe, as on earth so also on Venus, there must he re- 
gions whose temperature is up to 40° below the average temperature of the 
planet. (Certainly, plants can exist here (we are familiar with species 
of algae occuring in 60° hot springs), but such plants would in a short 
time reduce the carbon dioxide content of the atmosphere. Thereby, accor- 
ding to what was said on p. 437, the temperature as a whole would drop 
somewhat, making formerly warmer regions accessible to life ; that would 
cause more carbon dioxide to be absorbed, reducing the carbon dioxide con- 
tent of the atmosphere to a minimum. 

Visible light penetrates other substances less easily than do heat 
rays, e.g. mist, 'he white layer that we see on Venus is very likely mist 
and hence the cloud cover of Venus will sooner be colder tl an we calculated 
above. Jf Venus is uniformly white everywhere, I would assume its average 
temperature to be f:-15°C, 



- 550 - 



But noTT, more than ever, various thingn must be considered, As is 
irell knonn, our atmosphere is cold above and, moving doirmrard, the 
teriperature increases a^out 1* every 200 m. One should also be able 
to assume this figure for Venus. So the actual surface of the planet is 
likely iramer ^han the cloud cover. The question is how far it lies 
belOTT the cloud cover. I personally believe 6-8 fan. Of course, what 
surprises ne is that even the stron/^est telescopes reveal no si^ns of 
nountain ranjjes rising above the cloud cover. Venus is a relatively 
young plaret and likely hfts higher nountains than the earth. 

Finally, there is +he possibility that the reflecting ability of 
Venus is (different on the ni^ht side than on the day fide. For oxaaple, 
if the night side vere absolutely black, t'le average temperature of the 
cloud cover irould be about 20* belov 0, 

Vniethcr Venus (like the earth) rotate'; about its axis or whether 
it always turns the sarie ride to tho sur a-a does the moon to the earth 
is atill not known today. SCHIAPARELLI assumes the latter is true. 
Othor astrononers, B?? Cpot '^^'^X , to name one, believe that Venue rotates 
aboi-t its axis once in 20-36 hours. 



The clv'ate of Venus win vary gre vtly depondinn- on whether it ro- 
tates about xts a'ris or not. If it always; turns the saiae side to the sun 
(cf. Fig. iri-j), the air rises at the place direcfy facing the sun (l will 
call it the day pole). In so dolnf;, as on earth, a den-<^e layer of clouds 



fonns 



4 



L 



/- 








\^ 




FifT. 153 



-551- 



in the ascending air current while the surface of Venus itself remains 
free of nust. Below, cold air flows in from the night pole. 

The sphere req" ires 20*-' days to once rotate about its axis in relation 
to the stellar system. Hence the deflecting forces which are noticeable 
to so high a degree with. our trade and monsoon winds can only be small on 
Venus, for they are merely the r suit of the rotation of the celestial 
body. The air simply flows from day pole to night pole and vice versa by 
the shortest way. n so doing, the upper layers of air likely develop 
hiu'ricane-t;'T5e velocities. (According to mj'- calculation, 400 to 1,0C0 km 
per hour.) 

In our latitude, the fleecy clouds driven by the west wind develop an 
average velocity of ^-20 m per second. Our west-vands develop from the fact 
that the air heats up at the eqioator and seeks to flow towaid the poles. 
Therein the air is hijidered by the deviation to t he right due to the earth's 
rotation (by the so-called coriolis force) and only slowly winds forward to 
t?e poles (in the course of 1-2 years). But if these fleecy clouds fly 8-20 
per second, one gets an Idea of what velocities must occur on a star 
on viiich the day pole obtains 1«9 'Jt to 2 ^ times the heat of the earth's 
equatorial region, on which furthermore, in contrast to our cold zones, the 
night hemisphere receives no heat from the sun at all, and on which there 
is hardly a deflecting force to hinder the straight-line motion of the air 
between the hot and cold regions • 

V.'ith this velocity, the upper layer of the atmosphere could cover the 
distance from the day pole to the night pole in about 1; -50 hours. 

The lower layers of the atmosphere will likely move considerably slower, 
although the prevailing climate will be quite windy even there. I estimp-'e 



m 



-55?- 



tlat the air will require 10-20 days to return from the nig' t pole. On the 
surface of Venus it would be relatively cool, for the winds would constantly 
bring cold air from the night hemisphere, 'he temperature could be even 
lower than that of a imiformly-white sphere situated as far froiti the sun as 
Venus. There would likely be niuch fewer clouds over the night hemisphere 
than over the day hemisphere, l) Fart of the water vaix^r carried along like- 
ly falls as rain on the way. 2) Over the night hemisphere, the air is in 
descending motion ; on the earth, however, vre make the observation that 
areas with air in ascending motion (e.g., the doldrums) are heavily clouded, 
whereas areas with air in descending motion (as the deserts, for example) 
have blue skjes. So the albedo of the night side woiild be smaller than that of 
the daj'sLde. Heat WDuld be absorbed with difficulty but readily radiated. 
The effect woxLLd be the sare as if we turned the observer's cabin of our 
rocket with* the bright side toward the sun and with the dark side toward 
inter planetary space or as if a beautiful woman shaded herself against the 
sun's rays with a parasol and fans herself on the shady side. 

Nevertheless, temperatures under 0'^ would be rare. Tn this case, the cold 
areas v.ovild be covered with snow or ice. (Dark ice surfaces do occur, but on 
water ai ove which such storms rage as above the night side of Venus not 
dark but light ice is formed.) If a sufficiently large part of the night side 
cooled off to below -j", Venus wpuld be uniformly vrtiite on both sides. But then, 
as we already saw, its average temperature could not be below 0° but, 
according to STi^rHAN BOLTZa- ANN'S law, would have to be at least 8-20" above 0. 

Since, in the upper layers, the atmosphere moves tovfard the night side 
but in the lower layers in the opposite direction, eddies occur in the Inter- 
mediate layer which cause a temporary and irregular rise and- fall of the 
barometer. Dut these barometric fluctuations are evened out more rapidly 
than on earth due to the lack of the coriolis force, and the barom.etric 



'55^" 



minima are likely also carried away faster, so that the." do not lie above one 
and the same region as long. In cortrast to our land rains, which often last 
for weeks, on Venus barometric depressions will seldom last longer than a 
matter of hours. 

If Venus always turned the same side to t.e sun, the climate would look 
somewhat as follov/s : 

First of all, great similarity of climate at the same poJnt. The sun is 
alv;ays in the same position in the sky, the wind blows uninterruptedly from 
the same direction and with the same force, barometric fluctuations are 
generally equalized again in fractions of an hour, there are no times of the 
day or seasons. 

In -a narrow zone ar'-und the day pole, humid-warm, tropical climate, caljn, 
heavily-clouded sky perhaps with violent, continuous thvinder. 

For the rest, the climate on the day side is moderate, perhaps 10°C on 
the edge of the day side, very windy. Cloudy sky, the clouds begin 2 km 
above the ground, below that clear atmosphere. The cloud cover reach s to 
an altitude of some 6-7 km. Sunlight strongly reduced by the cloud cover, 
illumination as strong as on a dull day on earth. Mkely not as bright as 
when the sun shines on earth. 

In general, the air is dense but not so dense as to prevent one from, 
breathing • 

This climate vrould be bearable for earthly creatur'-s, the more so of the 
temperature zone, in which case one could think of settling on Venus. Unfor- 
tunately, it appears more probable that Venus rotates about an axis appro- 
ximately perpiendicular to tlie orbital plane. I believe that the sion's attracting 



-554- 



force has not been sufficient to niake Venus stop rdtating. Of course, with 
the assumption of axial rotation, it is difficult to explain the uniformly- 
white color of Venus. Actually, cloud-free zones would have to form as on 
earth, for example, or the clouds would at least have to show varying shades 
as, for example, on Jupiter or "Jars. Assuming, however, Venus did ivstate 
about its axis like the earth, then the climate would look somewhat as 
follows : Quite uniform clouding over on both sides, hence a temperature 
at the visible surface of 8-20°C and a ground temperature of at least 45''C. 
Humid-warm, foggy weather, very much rain, frequent thunder (in agreement with 
this is perhaps the lighting sometimes observed on the night side). 

In this case, settling on Venus would naturally be out of the question, 
except if man of later ages found waj'S and means of keeping part of the 
sun's rays away from Venus say by rotating umbrellas made of sodium plate. 
On the other hand, a scientific expedition might be able to protect itself 
against such temperatures for a time (say by taking along refrigerators). 
A visit to Venus would have a high scientific, 1 would like to sajr, almost 
philosophic value. Here one would find the climatic conditions that prevailed 
on earth when life began. V^ny a hint could be obtained for answering 
quesiioit? which concern the origin of life and the development of the animal 
world, and which our theory of fossils does not answer today since we have 
no fossils from those first dajf^s of life. 

Finally, a last possibility would be that Venus rotates about an axis, 
but this axis is strongly inclined tovreird the orbital plane, perhapslying 
entirely in the orb,ital plane. In this case, all life on Venus would be 
ejd-uded. ! ut this case is not probable, for such an inclination of the axis 
coiild have been brought about only by an outside acting force and the great 
regularity of the Venus orbit militates against such a force having acfed. 



-555- 



Direct landing by means of a rocket space-ship would be possible only 
if Venus does not rotate about its axis. If there is axial rotation, landing 
on high mountains ndght be possible, but they would have to be found before- 
hand. Iiow hopes exist of photographing the surface of Venus through the 
cloud cover from a space-ship gravitating about the planet b; using a method 
invented by BAIRD and in this way answering the questions concerning its 
axial rotation, habitableness, and possible landing sites. 

In itself, reaching Venus would not be difficult. Acccrdirg to (230), 
V . =2.5 km / sec and, according to (120), an ideal propulsion of 13 km / sec 
would be sufficient by far to reach it. "^'he trip out would take at the most , 
4-5 months, '■'he return trip woiild likewise be relatively easy ; v „ =3.3 km/sec J 
v^= 10.5 km / sec. For the return trip, an ideal propijlsion of 12.5 km / sec 
would suffice. 

Here the difficulties lie rather in the landing and the re-ascent. 

The dense Venus atmosphere is unfavorable for rocket space-ships. Its 
perhaps high temperature makes it almost impossible to keep the fuels in a 
liquid state, and today we can i ill say absolutely nothing as to whether 
and with what kind of machines we might be able to produce the fuels on 
Venus itself. 

On the other hand, with a total ideal propulsion of v <^20 km / sec, 
it would be possible to let a rocket orbit Venus and photograph its surface 
by BAIRD'S method. 

On the possibility of reaching Venus with an electric space-ship I will 
write in the next chapter. All in all, one can say that a visit to Venus 
would be revra.rding under all circumstances but that so far considerable astro- 



-556- 



physical research has still to le done and enorraous technical difficulties 
vdll have to be overcome. 

*:■. The Remaininp: Bodies of Our Solar System 

These cannot be reached with rocket space-ships. 

'fercury, for example, is too close to the sun and here a difference in 
potential wovild have to be overcone of which the rocket space-ship is no 
longer capable. For example, the total ideal propiilsion for a landing would 
be V = 39 km / sec, for orbiting v = 3? km / sec. 'hat would result in a 

X X 

minimum mass ratio of— _2_ >> 13,200, a completely indiscussible figure. H 

would be possible to reach I'ercury br electric space-ship, but the question 
is v/hether one could land. Since it always turns the same side to the sun 
and has no atmosphere, the areas illiominated by the sun must have a tempe- 
rature below 0, and it is more than questionable whether we can cope with 
such extreme temperature differences with our present-day technical means. 
Besides, we woiLLd presumably find nothing else on Jlercury than on the moon. 

The comets occasionally com.e very close to the earth, but in this case 
they have so high a velocity with reference to the earth that landing with 
rearward thrust deceleration in oUC/ of the question. (VJhether the atmosphere 
of comeis is suitable for bra)>ing purposes we do not know, but it is unlikely.) 
They can bo reached by electr'c space-ship, but nothing can be said about the 
p\irpose of the flight since too little is known about them. 

Finally, Jupiter and its moons can be reached by electric space-ship. 
To bef^'in with, Jupiter itself is eliminated as goal of a visit because it 
is surrounded by a very dense atmosphere of at least 400°C. l/e can say 
nothing about the moons of Jupiter since they are not sufficiently known. The 
three outer planets (Saturn, Uranus, ^eptune) and their moons cannot be 
reached even with the elf-ctric space-ship, since the best machines cannot 
work so far from the sun. 



'5'^' 



Chapter 22 
The lectri c '^pace-Ship 

^nce we have set up a rotating station outside of the earth's atmosphere, 
neither air nor counter-pressure disturb us and we can here build nachTnes 
which are related to the fuel rockets as an ocean liner to a boat. V.'c ran, 
by electrical means, increase the radiation velocity to double 1, . ie?>-l'old. 
Thereby, according to formula (6), we reduce the loss in propell,j.r;l very 
considerably. 

If we connect one pole of an electrifying machine or an induction coil 
to a pointed metal body, v/e notice that the air is hurled avra' from the tip. 
This is the so-called dectric v/ind. As Fig. 15/+ shovfs, it can blow out a 
candle flame. 



8 




Fi^:. 154 

As I already said on p- 3, a force never acts on one body alone ; it 
always acts between two bod-i s. "'he electrically-charged air nrolecules on 
their part push back the tip with the same force vdth which they are being 
pushed forward by the tip (electric wind-wheel). :n dense air, this electric 
wind blows only slowly, although in comparis n to the energy expended it 
has considerable percussive power. In thin air, on the other hand, its 
velocity is c nsiderably greater, but its percussive power decreases in 
relation to the work performed. 



-558- 



That is easily understood : The work of the influence-machine is being 
used to charge and set in motion the air molecules. If the air mass m^ moves 
with velocity Vj, its momentum (and with that also its percussive power) is 

Jj = m^ ^i (235) 

On the other hand, the work required to set it in motion amounts to : 

If we have the mass m^ and the velocity v^, then 

1 2 
Now, if the influence-inachine performs the same work in both cases, then 





h 


= 


^'2 




1 

7 ^ ^i' 


= 


^ 2 


From that. 


this follows 


• 






2 
m, v, 

1 i 


= 


2 


or, since 










mv 


XK 


J 




'I'l 


= 


•^2-2' 




jfy 


= 


^2-^ 



(237) 



^'oday, the electric wind is being explained as follows : All matter 
consists of molecules, these of atoms, and the atoms of positive nuclei 



-559- 



about which the so-called electrons whirl in determined circular or ellip- 
tical orbits. V hat these electrons actually are we still do not really 
know ; in most cases we prefer to visualize them as small material bodies 
with a strong negative charge. If a molecule has one electron too few, it 
appears to have a positive electric charge ; if it has one too many, it 
appears negative. 

If a molecule breaks up say because the molecules whirl about due to 
the heat and str:;ke against each other, tVen one part is often negatively 
and the other positively charged (ions). Such ions occur in every gas (most- 
ly in very small numbers), also in the air. Mear a strongly electrified 
body ions with the sar'.e charge are repelled. Kow thej'- fly among the other 
uncharged molecules and sweep them along, while they themselves are retarded 
in their initially very rapid motion. If there is much air around the ions, 
a large mass is set in motion but only at a low velocity. On the other hand, 
if the air is thin, the ions strike only few air molecules, but for that they 
impart a higher velocity to them. In a highly evacuated (evacuate = empty 
out v/ith an air pun^) glass tube (with less than l/lOOO of an atmosphere) 
the molecules and atoms flying away from the + pole (the so-called anode) 
already develop average velocities of tO to 400 km / sec. I'hese are the 
so-called Csc , canal, or anode r.-ys. From the - pole (the so-called 
cathode), for the most part free electrons fly away which, due to their 
small mass, reach velocities of up to 90,000 km / sec and over ( /O or 
cathode rays)'^. 



l) Fig. 155 shows a Gf^lSSIER tube (a hii;;h3y-e,-acuated glass tube) through 
which passes a high-tension electric current, he lighting is caused by 
the collision between the air molecules and the electrically-charged 
particles. 



-560- 



The rearward-thrust effect on an electric wind-wheel is likewise the 
greater, the denser the air. We can understand that if we consider that in 
dense air the dectrically-charged particles being hurled away remain near 
the tip longer and hence have more time to impart their repelling force to 
the tip. In return, with the same loss of substance, a considerably stronger 
rearvrard-thrust impulse can be produced with higher rarifications due to the 
high repelling velocities. 

Mention should also be made of the fact that, with high rarification , 
the bodies from which electricity is to flow need no longer be pointed ; 
the OC andyO-rays also flow from wide surfaces , in which case they run 
perpendicular to the surface, in a straight line and parallel to each other. 

with a complete vacuum,usually noQC or/T-rays can be produced. Rsr them 
to occur, ionized molecule's appear to be absolutely necessarj'. Vfe cm produce 
these ra3-s in a completely-evacuated glasstube only if we ionize the material 
of the anode or cathode itself (e.g., by heating : glowing cathode ; making 
the anode or' a roxi-.ure of fused salts according to the method of GEHRCKE 
ar.H ;'.:rcn:KIi.'iI>" ? i saving the electrodes hollow and filling them with any 
gaser; -..hich seep through the fr^ nt wall, and the like). 

If c is the velocity in cm / sec of the hurled-away particles, V the 
difference in tension between the two electrodes in volts, e the quantity 
of electricity ca ried along by the gas mass m, then this formula is valid : 



•TIT 



(238) 



■tAnsde 




ri? 



155 



-561- 



With the electric space-ship, it would be a matter of utilizing the 
radiation of the sun (in space this is truly vigorous) for driving steam- 
engines. These steam-engines would hav«to propel some sort of electrifying 
machines which in turn vrould supply the current for strong electric radiation 
by which the space-ship is propelled forward. 

Since we are probably dealing with a vacuum, we can achiere our goal 
only by the use of the hollow, salt, or glowing electrodes mentioned above 
(cf. Fig. 156). The electrode which emits the radiation delivering the rear- 




Fig. 156 

ward thrust would have to be a broad surface (main electrode). In front of it 
would have to be an auxiliary electrode of" wire grid with an opposite charge. 
At the cathode, enough gas would have to seep through (concerned wouJd be 
chlorine, oxygen, or the like) to fill the space between 

the main cathode and auxiliary anode so strongly with gas so that what would 
be emitted in the main would not be rapidly-flying electrodes but a relatively 
more slowly-flying electric wind mainly carrying gas particles. 

A pure stream of electrons would only consume much work due to the all 
too high velocity of the electrons without delivering a discussible rear- 
ward thrust (cf. (23?)), i.e., if a pure stream of electrons delivei s a rear- 
ward thrust at all. his is very probable but has not been proved experi- 
mentally and hence is largely being questioned. So the charges directed 



-562- 



against ULINSKl because of his stream of electrons do not affect me, since 
I am thinking of a relatively slow electric vdnd. But, for the roai, I must 
reject the "earth-related" objections by engineers because of the low utili- 
zation of energ^^ following from formulas (23') to (?37). On earth supplying 
energjr in general costs more than mass, so here we must save on energy 
at t!'..- cost of mass. With the electric space-ship, on the other hand, we 
attain energy much more easily than mass and hence vre must aim to save mass 
at the cost of energy"/' 

The positive wind could be mainta:ir''--d clth-i- ~'3y ;i salt anode facing a 
glowing platiniwn grid or by a hollow electrode filled with hydrogen or sodiim 
vapor. — Chlorine, oxygen, sodium, and mineral salts would have the preference 
as propellants since they are also contained in the rock of the moon and the 
asteroids, from where they are more easily obtained than from the earth. Hy- 
drogen, on the other hand, will be difficult ta obtain from the moon or the 
asteroids, for here there are in any case oi;ly traces of water or ice. 

The machine . A steam boiler operat-s at the focus of a concave reflector. 
H drives a steam turbine which in turn drives an influence-machine. The exhaust 
steam passes through pipes situated in the shade of the reflector, wl ere the 



l) By the wgy, this reirark is purely academic, for, according to what was said 
on pp.515 - 216, the radiation velocity of 10-40 km / sec which I aim for actvial- 
!'.y just (incidentally) corresponds to the requirement of the best total utili- 
zation of energy, for it is of the magnitude of the space-ship velocities for 
interplanetary traffic, whereas here e = 4 km / sec would be decidedly less 
favorable. 



-563^ 



^ 



water precipitates and is again returned to the boiler through feeder pumps.-' 




Fig. 157 

Details : The boiler A (of Fig. 157) has the form of a cylindrical pipe. 
>/ater is found only in the space between the outer and inner surfacr^s of the 
cylinder. The whole is built as though the wall of a pipe were hollovred 
out and filled with water. Eoth cylinder surfaces are connect-xi after the 
fashion of Fig. 37. Inipneral, I have not drawn connecting pieces in Fig. 157 
in order not to confuse the drawing. For this reason T have only dravm 
the feeder pipe for the cooling water simply, actugll - a,syinmetric»lly. 



Inside this hollow cylinder is a steam turbine B mounted on the saine 
axle with an influence-^nachine C. The influence-machine is built on the 
model of Vy'OI-i>iELSDORF'S condenser-machine, but if possible I would like to 
make it out of more h at-resistant material ; otherwise it would be neces- 
sary to conduct the feed water of the boiler for cooling purposes around 
th^'s -a chine first instead of, as indicated in Fig. 157, leading it directly 
to tho boiler at K. 'I he middle of the axle of B and C must be so strong as 
not to twist. On the other hand, at the ends D and E it can be very than 
and flexible because of the low counter-pressure, "his considerably facili- 
tates balancing t;ie oscillating parts (as in ijAVAL»S steam turbine). 



l) Here I took water as feeder liquid, but I am leaving the question open 
whether another liquid (say mercury) Hiight not be more suitable. 



^h- 



The idler vrtieels of the turbjjie and the condenser plates of the influence- 
nachine are firmly connected to the boiler, hen the turb'^ne starts, the idler 
wheels together vith the boiler get a rotational momentum in the oprosJte 
direction according to the lavf of the conservation of the centre of gravity. 
Thereby l) the water in the boiler is pressed firmly against the boiler wall. 
(Lecpuse of the lack of counter-pressiH-e, this could b e achieved in no other 
way» ) 2) "^hat has the additional advantage that tl.e relative velocity between 
the rotating parts is increased while the centri f ugal for e , which depends only 
on the absolute rotative speed, does not need to rise to an imroderate level. 

For this rason . hope, for example, to get by v/ith 1-2 pressure stages 
It; the steam tur'- '• e. 3) Vie eliminate one, feeder pump ; the centrifugal force 
is suffici'^r,'. to drive the water from K into boj.ler A, since its outer 
velocity is aloui. m / sec. 4) ""'he whole outer side of the boiler is irra- 
diated to the same degree by" the sim, at v;hich light and shade change so 
rapidly that -M-r ere dealin^j I'iih almost uniform transmission of heat over the 
whole surface. 

Due to the strong centrifugal force, vapor bubbles very easily tear them- 
selves free from the boiler wall and liquid particles swept along soon settle 
again, so that before the vajor reach, s B it is tolerably dry, although satu- 
rate d. The exhaust steam fills the space between B and D. At D, guide vanes 
are attached which deprive the steam of its rotary motion before it enters 
the exhaust-steam pipe Q. The steam leaving the turbine is "wet", i.e., it 
carries along partly condensed water. Now most of the fog particles are carried 
into pipe ''^ by the rest of the steam, but part of the condensed water settles 
on the guide vanes, etc. This water is in part driven against the boiler wall 
by the centrifugal force, where it vaporizes, for the temperature cf the boiler 
is considerably higher than the boiling point of t' e water at D ; by suitable 
spiral-shaped guide channels (not shown), the greater part of the water can 
also be drawn directly into pipe K or at least into pipe Q. Part of the boiler 



-565- 



wall can be insulated aginast giving off heat. Fipe Q makes several turns 
in the shade of the ef lector, -where the steam condenses. Due to the lack 
of counter-pressure, the steam still uncondensed drives the water before it. 
At K it again enters the machine. 

Since the boiler rotates, the pipes at G and H must interlock in Dutch 
fashion. Here this connection is quite frJctionless since both the irside 
pressure and the counter-pressure are malL At axle I, by which the boiler 
is fastened to the outer jacket on the other side, the friction is still 
much smaller. Nevertheless, the friction cannot be entirely eliminated, 
which in time would cause the boiler to impart its rotating motion to the 
outer machine. That can be prevented by attaching an influence-machine at I 
that acts like a motor and gives the axle a rotational momentum opposite 
and equal to the friction. Side M of the outer jacket is turned away from 
the cbhcave reflector and has a reflecting overlay for the purpose of reflecting 
back on the boiler the heat it radiates. Side N is turned toward the concave 
reflector and must consist of some type of transparent substance. This jacket 
completely surrounding the boiler is needed- because it will probably be 
impossible to seal closure I entirely hermetically and we do not v/dsh to 
lose the steam escaping here to interplanetary space. Cn the other hand, no 
rotating machine parts extend through the jacket " , K anywhere ; hence it 
is more easily protected against the loss of ,'•,-; s. 11 that is needed is a 
pump (not shown) to bring the steam escaping at G back to pipe K. and P 
are sliding contacts for taking off the electric current. By means of electric 
currents conducted over sim:.lar contacts the work of the t achire can be 
controlled , 

1) This naturally has the condition that the electricity does not flow from 
to I , which can perhaps be achieved by keeping the space between the boiler 
and the jacket "• , 1: sufficiently free of air. The insulation could also be 
achieved as follows : Here it is best to have the contact points run in mercury 
cfiannels. Kow one would simply have to pour oil over the mercury and insulate 
everything else correspondingly. 



-566- 



R and S are the rods that connect the machine to the reflector. The 
operation of the machine can be regulated by letting the influence-machine 
at I run faster or slower. In this case, a slight rotation occurs which 
brings the boiler partly or completely out of the rays of the concave 
reflector. 

Fig. 158 shows an electric space-ship vrith 6 machines. They are connected 
to each other by cables (insulated in case of need) so that the pilot can put 
them in any position in relation to each other. To me this appears necessary 
so that no mach're gets into the shade or the electric rays of another. R desi- 
gnates the actual space-ship about which rotate the two gravitational cells S 




Fig. 158 

fastened to a strong cable. The space-ship and each oi^ the single nachines 
has two electrodes. 

As the SO' rce of electricity I vroiild suggest the influence-machine, which 
has the advantage of a considerably higher tension compared to the dynamos, 
•'■o achieve approxLiiately the sarr.e effect, a great number of direct current 
dynamos WDuld have to be connected in series, resides, the inf luence-mach ' ncs 
have the advantage that their voltage is independent of the rotative speed 
within wide limits. 



-567- 



One might also consider using a combjTiation of dynamos and induction 
coils, ^n comparison to that, the ir^fluence-irachine has the advantage l) of 
lighter weight-, he dynamos and induction coils built today are relatively- 
lighter than infjuence-machin'^s, but I believe that is only because special 
lightness has not been aimed for with the latter, .'.ccording to iry calculation, 
it should be possible to reduce the weight of an influence-machine to below 
0.2 kg per kilowatt. 2) Inluence-machines produce a direct current (whereas 
the voltage of an induction coil changes between and the maximum point 
with every stroke of the hammer). Thereby the repelling velocity becomes 
uniform and we can achieve the same rearward thrust with the sarr-.e loss in 
substance and a smaller ex enditure of energj"-, by which the machines become 
correspondingly smaller and lighter. 

The percussive effect is proportional only to tne linear mnan value of 
the velocity. Here is a simple example : 

If 1 have two gas molecules of mass 1 and impart the velocity to one 
and velocit,y 2 to the other, the total impulse is 

+ 1*2 = 2 
■""he work >o be expended amoxints to 

+ -^ • 1 • 2^ = 2 

On the other hand, if I impart the velocity I to both molecules, the impulse 
here is : 

1 • 1 + 1*1=2 

But the energy of motion required is only 

1 2 1 2 
•^ ,1.1 + —r- .1.1 — 1 

That is only half as great as in the former case. 



-568- 



3) Because of its constant voltage, the influence-machine can be connected 
in parallel as well as in series, which has the advantage that, in the fornier 
case, we achieve slower but forcefully-percussive currents and in the latter 
case, by contrast, rapid cxirrents and relatively small loss of substance. 

U]:,li bl'I, who has come up v.dth a similar project, suggests thermocouple 
elements as source of propulsion ; he wants to Ist the sun shine on one side 
and expose th other side to the temperature of interplanetary space. As a 
source of current, these thermocouple eletnents certainly have some advantages, 
but they have a defect which I do not know whether and how it could be 
remedied. Since the required high voltage can be achieved only by connecting 
in series millions of themocouple elements, we obtain an extremely long 
thermopile whose ends are strongly charged. (ULIl.SKI figures with voltages 
of up to 250,000 volt ; I hope to^t along with voltages of 50,000-100,000 volt.) 
'^ince interplanetary space is certainly no absolute vacuum and the existing 
gases are probably strongly ionized, I fear that this thermopile covering 
a wide area would emit electric rays in all directions, r.o t'lat it would be 
impossible to bring the required quantity of electricity to the electrodes. 
Of course, one might think of coating the thermocouple exements with a 
transparent and diathermic material that holds back electricity. I am afraid, 
however, this would reduce its performing capacity too strongly and greatly 
iicrease the weight of the machine (one should consider what tvro glass plates 
2-3 mm thick and covering in the neighborhood of 40 hectares must -relgh). 
Admittedly, it is not eud-uded that in this point chance might somehow come 
to ULIlvSKI'S aid, in vihich case (with sufficient lightness) the thermopile 
would naturally be preferable to the movable machines. 

^Jagnit^lde of the propulsion : %turally, the Capacity of the machines is 

the greater, the stronger the radiation of the stin ; at the distance of Venus 
from the sun, for example, they vould have twice the capacity they have near 
the earth. 



-569- 



^t the distance of the earth, the sun radiates 2 g.cal. / min. on a 

2 
square centimeter of surface. So, with the heat energy that 1 cm receives 

in the course of a minute, 20,000 g, that is 20 liters of water, could be 

heated by 1". With a good steam engine (and here we may presuppose good 

steam engines) we can count on a efficiency of 1? %t i.e. 72.5 mkg per 

kg / cal. 7hus, corresponding to a square meter of reflecting surface, our 

machine delivers ! 

^° IJ^'"^ = 2.; mkg / sec. 

That is roughly l/3 metric horsepower. If we designated the irradiating 
mass falling to a m of reflecting surface as dm, the average radiating 
velocity as c, and the velocity increase of th space-ship as dv, we obtain : 

dt m dt ^'^^^' 

'■'■'he work (the effect) performed in one second amounts to : 

"= (240) 

If, for example, c-= 10,000 m / sec, then 

dA 11 r in? dm , / 
"dt"^ 5.10' ^ mkg /sec 

2 
We found the share of work falling to a m" of reflecting surface to be 

24 mkg / sec. So, per m of reflecting surface, 

■ . = c ^^y (tech. mass units), 

2 
which is 4.7 milligram per second per m' of reflecting surface. 

»^ith the electric wind, however, it is known that tlie gas particles do 
not fly equally fast ; hence, with an average velocity of 10 km / sec, we 
wiU. do well to apply only 3/4 'to 4/5 of this figure in our calculation ^* 



-570- 



^^hat would be 3-4 mg / sec . m . If the space-ship weighs 1 km / iri^ (to some 
this figiire will appear too low, but I submit that steam engines under 
1 kg / kp have already been buJlt, which would thus weigh only about 300 g 
per m of reflecting surface. The infuence-machine woiild be all of half as 

heavy and the reflectors could likewige be made extremely light because of 

2 
the lack of counter-pressure ; therefore, the weight per m remaining to 

be carried along would be 400 g), the following calculations apply with 

reference to the acceleration : 

dm . . _ ... dv 



or in figures 



^ 



10 



dt 



From that we find the acceleration of the space-ship to be up to 4 cm / sec , 
which means that after one day the space-ship would have a velocity of 
3-3^ km. The loss in substance we can find according to formula (5) : 



_ -^ _ 

■nr- - e ~ 1.43 ; m^ _ m. = 0.43 m 

1 'Oil 



m 
o = 



(here e is the base of the natural logarithms). 

That is, in order to attain this velocity, the space-ship would use up 
43 % of its final mass. Naturally, it could take along nrach more propellant, 
but then it would be heavier at the time of launching and could not attain 
this velocity as rapidly. 



1) ■''he more so since part of the work is lost through the electric charging. 
For, obviously, the hurled-away gases could, due to their charge, deliver 
work even after having been mechanically brought to a stop, that is after 
already having given off the kinetic energy, vfhich alone has been applied to 
our calr^ulation. 



-571- 



VJith a radiating velocity of n*10 km / sec, 

dA» = l.dm' .2 8 

"dT ^ dT " • ^° 

Since with the same machine performance 

dy'v* _^ dJv 
dt dt ' 

therefore 

dm* _ dm . 1 
dt dt ~f? 

I'he acceleration, however, would sink only to — : 



=' = (h? • ^) • ^'^•^^ = k ' 



dv' _ dm* , _ jfdra 1 1 / \ 1 dv 
■dT -dT • '=' - Idt • i2 . (n.c) = - . H^ 



During a period n times as long, the space-ship would attain the sariB 
velocity but with considerably less loss of substance. For example, to reach 
a velocity of 3 l/? l<m / sec v.'ith a radiation velocity of 100 km / sec vraiJ.d 
require 10 days, but the loss in substance would amount to only 4 /o of iil . By 
the way, these calculations have been kept amply pessimistic . Tor example, if 
we assume the machine to weigh only r kg = O.C^ technical nass units per 
horsepower (this value is just at the limit of the attainable), we obtain : 

^ • f • ^^ = 75 (mkg). 



from which follows 



and from that 



dt * ° °-"^ • dt ' 



dv _ 3^000 , / 2 ^ 



For example, for c = 10 km / sec. 



dv _ „ / 2 
TT" = 3o cm / sec 
dt 



-572 



for c = 20 km / sec : 



•rr 15 cm / sec 
at 



In one respect, this rachine justifies great hopes. It permits very con- 
siderably shortening the trip to strange celestial bodies and, more important, 
visiting these planets in almost every configuration, r.ocket space-shaps, 
on the other hand, can visit distant celestial bodies only when they are in 
esrecially favorable positions and, in so doing, a trip to the distant 
celestial bod^ and back almost always lasts years. With the use of this 
machine, the asteroids, comets, and moons of Jupiter could easily be explored 
and perhaps especially valuable pieces of rock brou{^ht to earth. 

They still do not facilitate explorijig the rlanets or the moon in itself. 
Because of th^ir friagiJe i.rd light build, the unavoidably large reflectors, 
and tJe low accelerating capacity, they must stay away from the large celestial 
bodies ; landing on the larger asteroids (like Ceres, Fallas, or Vesta) would 
even be questionable. A s we saw, with planetary flights the trip o\it and 
back is the least. The difficulties lie in landing and ascending. 

I hope for the follovring : I believe that, with a high voltage as can 
be achieved by connect ng in series the influence-machines of the space- 
ship, it will be possible to produce electric rays that run approximately 
parallel and in a straight line for seve-al 1^000 km (in contrast to electro- 
magnetic waves, with which this is naturally impossible). V/hen they enter 
a grid cage covered with metal foil they charge it to a high potential. Due to 
their great velocity th y have, according to formula (237), as good as no 
percussive force in spite of their high energy content. Now, these rays 
can^rve as sources of energy for smaller space-ships. These space-ships could 
be built on the model of the rocket airplane. The carrying electrodes c. 



-573- 




Fig. 159 

d (cf. Fig. 1^9) coild be profitably attached to the imder side of the 
carrying surface. 

^he 'positive electrodes a, b, which would natiorally have the form of 
the above-mentioned cages, would have to be as far apart as possible, 
that Is hang b: the wing tips ; the positive electrodes and the auxiliary 
electrodes, the latter consisting of wire grid, would have to be arranged 
so that they could be rolled up and stored away before the atmosphere is 
entered. If one aimed at simplifying the mechanism one could oonsider simply 
leaving these wire grids to their fate when entering the atmosphere. I 
believe that, with the use of the hard and rapid rays generated by the 
energy-producing space-ship, it will be possible to produce a relatively 
slow but massive and percussively forceful electric wind on the flying 
space-ship, and that by simply making the electrode of the energy-producing 
space-ship very little permeable to gas but that of the flying space-ship 
s^.ronfly permeable to gas and by simply connecting the positive receiving 
electrode of the flying spa(£e-ship to its negative (emitting) electrode. Let 
us assume the energy-producing space-ship gravitated at 3-5 radii of the 
earth's orbit and its reflectors covered a surface of 10 km (we already saw 
that constructing such large reflectors in space out of sodium flate presents 



-574 



no further difficulties) ; furthermore, that the total energy irradiated by 
the space-ship were utilized by a rocket airplane weighing 10,000 kg (if 
we figured 1 kg / m as the weight of the reflector surface of the space-ship, 
that would be a thousandth part of the weight of the space-ship). VJith a 
radiation velocity of 10 km / sec, this vehicle couJd develop an acceleration 
of 1000.3 to 1000.4 cm / sec , vAiich is 30-40 m / sec . As a rocket, this 
space-ship would have to be impelled up only to just above the earth's 
atmosphere, let us say 120 km high. Here it would spread out its wire-net 
electrodes and, at this acceleration, it could easily connect up to the 
energy station. The return would be managed in a very similar way. 

When landing, this rocket airplane drops only from the imment in ivhich 
it can no longer be supplied with energy by the space-ship until the moment 
when it is borne by the earth's atmosphere. In so doing, no velocities over 
I km / sec occur. So there is no danger of it burning up ; accordingly, it 
is not necessary to land by parachute, but one can also vjork with carrying 
surfaces. Of course, one w uld have to count on decelerating 500 to 600 m / sec 
of the flight velocity by means of rearward thrust at an altitude of 50 km. 
But we would gladly take that into the bargain because, in so doinp, the 
safety of landing increases exceedingly, landing and ro-ascending from Venus 
or I'ars would be very similar to ascending from the earth. Ascending from 
%rs would even require only a third of the fuels. landing on the moon would 
be still simpler, wl ere the space-boat could remain in the rays of the 
energj'' station to the last. 

If, at some time, regular transportation should be established between 
the earth and any other celestial body, the matter wovild be still simpler. 
Tl'.in one such electric space-ship each could simply gravitate constantly as 
energy station about the earth and about the respective planet and upon 
departure and arrival, the rocket space-ships would simply be received by 



-575- 



its energy rays and supplied ^rith the needed energj'-. For the trip they would 
only need to take along enough fuel for correcting possible deviations from 
the course by means of rocket propulsion, which however would here be extre- 
mely small. Assioming that the energy station could still supply the space- 
ship with energy at a distance of 42,000 km, then, on a trip between two 
planets, with an acceleration of 30 m / sec', the space-ship would reach a 
velocity of Y 2.42,000,000 . 30 = 51,000 m / sec and cover the stretch, 
for example, between Venus and the earth in 10 days. 



^n the meantime, the energy station could be used for other purposes, 
ler for reflecting sunlight to earth 
near the earth with electric radiation - 

The following solution would be still simpler : 



either for reflecting sunlifjht to earth or supplying smaller energi* stations 

,1) 



*-*ne could use only a rocket airplane to carry on communicati.'n with the 
surface of the planet. This need only be strong enough to lift itself above 
the atmosphere. Here it is received by the electric space-boat and cairied 



l) If the principle of the electric space-ship should prove feasible, there 
would be, beside the rocket and the solenoid projectile, a third theoretical 
possibility of reaching interplanetary space. An energy station on earth v.'ould 
have to operate a number of influence-machines. (Indeed, of several million 
horsepower, which, in practice, would probably wrettk the matter. Outside of the 
earth, for example, an eqiially strong plant coiold be an "indivisibly reali- 
zable" invention. Cf. Chapter 18) The current would be conducted into a ver- 
tically-rising cable which, from kilometer to kilometer, has devices which pro- 
duce an electric irind directed downward, thus bearing up the respective piece 
of cable, "^he upper vnd of the cable would reach above the earth's atmosphere 
and serve as buildin^;; and docking station for electric si)ace-ships as well as 
energy station for the space-boats described above. 'Ihe intercommunication 
could be man&ged by means of elevators. 



-576- 



farther or unloaded and sent back. (This principle could also be applied 
in long distance transportation of rocket aircraft on earth.) 

VJhether all this will work, I do not know. Rut nothing is impossible 
on earth ; one must only discover the means with which it can be carried 
out. 



EFILOGUE 



The Soci^te Astronomique de France has distiguished this book with the 
REF-HlHSCH-Prize. Beside the tangible advantages which this tribute has 
already brought and will likely still bring nie, it has also had a moral 
effect which must not be under-estimated. Frankly, I did not believe that 
ir. PraJice one \irauld award such a prize to a C-erman, the more so since 
good Krwich, :,ussian, Italian, and English vrorks were at h;!,nd. H is en- 
coura£;ing to see that science and education are able to bridge national 
differences. —I believe I can thank the French Astronomical Society in 
no better way than by promising in this place to work for science and educa- 
tion on my part and to judge man only by his achievements. 



- 577 - 



Alphabetical Index 

iSBOT, 438 

Acceleration! most advantageous, 100 

— ideal, 63, 100 
Acetylene, 351, 35t, 395 
Acquired knowledge, 538 ff 
Active steering, 261 ff, 867 
Activity of the heart, 144 ff 
Adjustable parachute, 301 
Adaptation, biological, 536-538 
Aiming, 878 ff, 508, 528 

Air density, 88-89 

Air passage, 458 

Air resistance, 80, 83-86, 166 ff, 348 

— maximum vith space-ships, 170 

— vertical, 184, 339, 340 
Air samples, 3G4 ff 

Air tank, 403, 445 

Albedo, 459, 519, 548 

Alpha rays, 460, 557 ff 

A method of reaching extreme altitudes, 4, 115 

Anchoring, 14-16, 21, 64 ff 

Angle of ascent, most advantageous, 87, 160, 830 ff 

^ode rays, 460, 560 

Ants, 540 

ARRHBMIUS, 534, 535 

Arrov, 853 

Arroir rocket, 856-857 

Artificial composition, 9 

Ascent, oblique, in straight line, 83, 160, 165, 187 ff, 273 ff 

— synergetic, 87, 151, 830 ff, 584, 585 

— vertical, 101 ff, 164 ff 



- 578 « 



Ascent irith carrying surfaces, 87 

JLsteroids, 457, 518, 572 

Astral light, 417 

Astronomic safety, 376, 473 

Atomizer, 10, 51-52, 310, 346 

Automatic steering, 2H1 ff, 270 ff, 281, 330, 336 

Auxiliary rocket, 337, 395 

Axial rotation of Venus, 550 ff 

Babel sberg, 457 

BAETZ, 54 

BAIBS, 555 

Ballistic coefficient, 92, 112 ff, 165, 338-340, 348 

Basin gondola, 128 

BAUER, 400 

B£X:KER, 83 

Bees, 540 

BHLOPOLSKJ, 550 

Bending dovn of the trajectory curves, 234 

BESSEL, 468 

BOHR, 297 

Bolometer, 439, 517 

BOLTZiUNM, 291, 438, 552 

Bora, 505 

- rays, 529, 56 Off 
Braces, 15, 71-72 

Braking flight, 178 ff, 299 ff, 428 

Braking parachute, 268, 299 ff 

Bridges across interplanetary space, 144, 148, 304, 435 

- rays, 529, 560 ff 
BUSBIANF, 397 

Ceunera obscura, 482, 500 
Canals on Mars, 454, 534 



- 570 - 



Cathode rays, 460, 560 ff 

Charge, 5 

Chinook, 505 

Chlorophyl, 533 

CLAUDE, 14 

Clouds, 419, 437, 438, 549 ff 

COLI, 480 

Color of the ether sky, 416 

COLUlfBUS, 539 

Combination of impulses, 221 

Comets, 474, 475, 535, 556 

Comet flight, 222 

Communication, 417, 430-433, 449 

Conditions of the natural lavs, 473 

Cooling, 10, 16, 40-41 

Coriolis force, 502 ff, 551, 552 

Corona, 417, 458 

Coronium, 334, 365 

Corpuscular rays, 445, 560, 573 ff 

Cosmic dust, 204, 206, 417, 470 ff, 475, 504, 505 

Cosmospermism, 534 

Counter-pressure centrifuge, 136 ff 

Course of deyelopment of life, 536 ff, 544 

COURVOISIER, 195, 473 

CRiNTZ, 83 

CRASSUS, 373 

Criteria, 60, 92, 341 ff, 350 ff 

Cross braces, 15, 71-72 

Crude-oil, 366-357 

Curvature of space, 459 

Curvature of the stars, 419 

Cylinder (mass ratio), 64-68 



- 580 - 



DALLv/iTZ-\ra:(r^En, aso 

Dan/rers of space flight, 489 ff 

Dark room, 482, 500 

Day pole, 551 

Deaf-4nite8, 145 

Deep-sea divers, 451 

Deflection to the right, 367, 50 H ff 

Deserts, 552 

DetenninatioQ of locatior, 281 

Detonator conposition, 9 

Deviation froci the trajectory (see also trajectory 

disturbances), 475 

Diffraction spectrum, 516 

Diffuser nozzles, 45 

Directing parachute, 301 

Dissociation, 39, 351 ff 

Distance, 100 

Diatnncinc the observer's cabin, 416, 440 

Divers, 417, 430, 441, 449-452 

Divisible units, 403 

Divisior of nozzle, 350 

- of the rocket, 94 ff, 359, 395, 584 

Dizziness, 134 

Doldrums, 552 

DOMINIK, 147 

DOIT, 51 

DoTm nnd up. 117, 144 

DrMnn+ureical error, 414, 418, 426, 43« 

DBILI, 159 

DEOIJET. 404 

Dust, cosmic, 204-206, 417, 470 ff, 475, 504, 505 

Dynamic ballistic coefficient, 113 

Dynamic cooling, 9-10, 41, 266, 369, 408 

Dynamic heat of a gas stream, 11, 26, 266, 299 



581 - 



Bar, 131 

Econon^, technical, 403, 411 

Effective tenperature, 886 

Efficiency, £08 ff, 218 

EINSTEIN, 194, 250, 273, 467, 458, 459 

Electric space-boat, 574 ff 

Electric space-ship, 215, 461, 514, 628, 529, 556, 557 ff 

Electric wind, 557 

Electric vind -wheel, 153, 557, 575 

Electromagnetic gun, 153 

Ellipse trajectory, 154 ff 

Enormous grovth of cells, 459 

Eratosthenes, 516 

Eros, 457, 538 

Ether divers, 417, 430, 441, 449-452 

Ether space, 144, 416 

Ether telescope, 417, 453-457 

Explosion, 469 

Excessive calculation, 114-115, 251-252 

Extent of presssure, 36 

EyEre.LW>r-scHui.z, 5i 

FJlBHE, 541 
Faeces, 446-448 
Failure of pumps, 469 
Failure of the controls, 469 
FAUTH, 516, 517, 544 
Filling, 350, 412 
Filling factor, 76 
Fireworks rocket, 5-7 
Firmness experinents, 77 
Flap j/arachute, 183 ff 
Flea circus, 540 



- 582 - 



Flickering of the stars, 454-5 

Flight period, 162, 462 

Floating an(>:le, 233, 242, 512 

Foehn, 504 

Fog, 437, 549 ff 

Force of rearward thrust, 62, 99 

Forms of braces (mass ratio), 70—72 

Freezing of the fuels, 441 

Freybund, 543 

Friction against the air, 11, 86, 867, 287 

Fueling stations, 248, 449, 477 ff, 525 

Fuels, 48, 216, 351 ff, 360, 386, 396 

Fuel utilization, 208 ff, 375, 55T-558, 568 ff 

GAEDE, 37 

GAEDICKE, 372 

GAIL, 8fi, 141, 188, 189, 2'34, 302, 303, 424, 425, 435, 451, 

455, 516 
Gamma rays, 444-445 
aWSWINDT, 372, 478 
GABSAtlX, 150, 400 
Gas fins, 256, 266-268 
Gasoline, 357, 385 
a«JSS, 117, 459, 460 
GEHRCKE, 560 

GETSSLER'S tube, 445, 446, 559 
GILLHIT, 130 

Glacial cosmogony, 517, 544-545, 552 
Glowing cathode, 550 
GODDA'ID, 4, 50, 208, 269, 376 
GIUFF, 532 

Gravity, 83, 116 ff, 172 ff 
GRTIftt, 130 

Guidance, precision-free, 498 ff 
Guidance, see Steering and Stations, 
Gun, electroiaagnetic, 153 



- 588 - 



Gyroscope control, 216 ff, 280, 3?0, 336 

IIANN, 504 

HASENORL, 250 

Heat conducting, 16 

Heat of compression, 39, 47, 287 

Heat of the sun, 437-438, 548, 569 

Heat tone, 208 

Heat transmission, 10-11, 16, 41, 29.1 ff 

HEIN, 122, 460 

Height of ascent, 157 

HINLELN, 29S 

HOEPFT, 56, 149, 265, 2'58, 269, 321, 351, 383, 392, 402 

HOmiWTN, 60, 148, 149, 221, ZZZ, 224, 225, 265, 302, 303, 304, 

311-313, 376, 440, 462, 467, S'iO 
HOLZHAUSIK, 251 

HOHBIGER, 516, 517, 544-545, 552 
Hovl of jets, 31 

Human beings on distant celestial bodies, 537 
Hjdrogen atmosphere, 365 

Ifydrogen effect on the resistance coefficient, 366-366 
Hyperbola trajectory, 157 

Ideal acceleration, 63, 100 

Ideal propulsion^ 53 ff 

Ideal velocity, 56 

Ignition, 10 

Indivisible units, 403, 575 

Influencing of treather (also see meteorological rocket), 480, 504 ff 

Innate characteristics, 538 

Inner ear, 131 

Interplanetary space-reflector, 304-206, 449, 477 ff, 526 

Jet-propelled aircraft, see rocket aircraft 
Jupiter. 515, 656 



- 584 - 



Tan>T, 128 

KANT, 144, 538 

ICAPPSLtlSYEl, 210 

rCEPLER, 156, 161, 208, 423, 533, 527 

Kerosene, 385 

Knowledge, innate and acquired, 537 ff 

KOHI.HO'ISTER rays, 367, 444, 445 

KOLBE, 14, 16, 17 

KUHLBAUJI, 292, 438 

LADSJAW:, 150 

LAFPEIRT, 45.^ 

Landing, 178 ff, 28 t ff, 366 

Large arc meter, 457 

LASS'»yiTZ, 117, 147, 443 

Lair of impulse, 62-63, 196 

LENARD, 458 

LEVERRIER, 468 

LEY, 144, 153, 403 

Life on distant planets, 533 ff 

Lighting, 10, ^50 

LINKE, 449 

LIVENS, JOHN C, 278 

Locating, 330, 386, 369 

LODGE, 459 

LOMER, 460 

Long-distance rockets, 175 ff, 260-280, 368-370, 404 

LOaENTZ, 458 

LORENZ, 61, 96, 203, 250, 466 

LoTT temperatures, 14-16, 459 

LUDWIG ANTON, 144, 147, 305, 436 

Machine builder, 250 

Mail rocket, 175 ff, 260 ff, 270 ff, 404 



- 585 - 



Uar«, 117, 454, 466, 589 ff , 574 

Uars olimat*, 538 iff 

Mars people, 637 ff 

Uaae ratio, 54, 55, 60, 61, 64 ff, 93, 113, 341 ff 

Uattrees forme, 15, 71-78 

UAXWiaLL, 474, 488 

Ueaeurenent of acoeleratioa, 183, 870, 331, 336 

Ueniere'e bodiee, 131 

Meniere's disease, 133 

Ueppen, 869 

Mercury, 556 

Uetol foil, 574 

Meteorological rocket, 81, 86, 87, 115, 876, 338, 349, 

368 ff, 404 
Meteorology, see Veatiier and Meteorological rockets 
Meteors, 885-886, 470 ff, 475, 516 
Methyl alcohol, 357 
MEy£R, M. WILH., 517 
HICHELSON, 458 

Military iinportance, 818, 876 ff, 388, 479, 498, 503 
Minerals, 516, 517, 531, 578 
Mistral, 505 
Model A, 8, 86, 185 

- B, a, 87, 89, 41, 116, 315 ff 

- C, 8, 87, 30, 115, 805, 815, 858 

- D, 81, 185 

- E, 87, 41, 140r 350, 351, 404, 406 ff 

- F, 8, 398 ff 
Monsoon, 551 

Mood, 411-434, 439, 460, 468, 463, 508 ff, 575 
Most, adTaataceoufl velocity, see Velocity 
Ifatatious, 544 



- 586 - 



Natural lavs, certainty of, 376, 473 

Neck of jet, 9, 34 ff 

Neptune, 556 

NEWTON, 44, 148 

NIEMUMP, 543 

Night frosts, 505 

Night pole of Venus, 551 

Nitrogens, 365 

Nitrosyl c<»npoands, 365, 399 

Non-Eocl idian geometry, 459 

NOORDONG, 56, 138, 210, 847, 302, 308, 309, 351, 352, 354, 417, 478 

Nozzles, ovenless, 394 

NUN6ESSER, 480 

NUSSELT, 292, 295 

Oblique, straight ascent, 83, 160, 185, 187 ff, 273 ff 

Observation of the sun, 458 

Observation Ptation, 140, 248, 449, 477 ff, 525 

Observer's cabin, 399, 412-435, 439-453 

OESTERHEICn, 460 

OPEL, 133 

OptimuEi division, 358 

Orbiting of planets, 5S5 

Organ of equilibriun, 131 

Orientation, 281 

Original generation, 535 

Outside stations, 204, 206, 248, 449, 477 ff, 525, 657 

Oven, 10, 47 ff, 328 ff, 334, 345 

Parabola trrjectory, 157 
Parabolic velocity, 156 ff 
Parachute, 176 ff, 208, 299 ff 
Parachute flaps, 183 
Parallax, 381 



- 587 - 



Parapsychology, 460 

Passive steering, 233-261, 267 

PEGOUD, 123 

Period of flight, 162, 462 

Periscope, 413, 453 

PICKERING, 515, 530, 533 

Pilot's cabin, see Observer's cabin 

PTrCDET, 153, 178, 358, 403, 406, 462, 530, 525 

Place of descent, 366 

PLANA, 466 

Planetoids, 458, 518 ff 

Plato, 513 

Plumbline, 123 

POISSON formula, 47, 286 

Pores, 9 ff, 324 

Precession-free fpiidance, 498 ff 

Precession moveuents, 495 ff 

Precision instrvnentS} 331, 335, 452 

Preservation of the centre of {gravity, 56 ff, 196 

Pressure, 83 

Pressure of lig-ht, 474, 488 ff, 535 

Principle of relative work, 193 ff 

PROLL, 45 

Propeller, 372 

Propulsion apparatus, 14 

Protective jacket, 78 

Pump chambers, 21, 23, 325 ff, 349, 393, 469 

Purification of air, 418, 419, 442-448 

PUSCH, 308 

Pythagoras of velocities, 200, 223, 509, 527 

Question of material, 16 ff, 64 ff, 344, 415 

Radiation intensity, 437-438, 548, 569 
Radiation pressure, 474, 488 ff, 535 



- f588 - 



Rain worms, 540 
Range, 154 ff 

Reachibility of the celestial bodies, see HOIC.UKN 
Refurard thrust, 3 ff 

— specific reaiTrard thrust, 100 
Rearward thrust pistols, 449 
Rearward thrust principle, 3 ff 

Reflector stations, 204-206, 449, 477 ff, 535 

Regulating flaps, 183 ff 

Rei^lating pin, 46, S68 

Refralation of temperature in the space-ship, 418, 435-444 

Regulus, 198 

REICHENHEIM, 560 

REIMER, 10, 11 

Relativity principle of work, 193 ff 

Residual velocity, 200, 283, 508-510, 521 

Resistance coefficient, 83-86, 164 ff 

Revolution, 484 

REIM, 4 

Rigid filling, 16, 81, 77. 343, 350, 386 

Risk, 403 

Rocket aircraft, 371, 575 

Rocket lines, 227 

Rocket projectile, 211, 276 

Rocket space-ship, see space-ship 

Rocket, vertical, 184 

— Journal of the Society for space-flight, cert, assoc, 130, 144 
Rotation wheels, 265, 456 

Ruin of the Tfest, 543 

Safety of space-flight, 376, 468 ff 

Safety valves, 141, 325, 452 

Sagittal direction, 489 

Saturn, 556 

SCHEINER, 474, 488, 523 



- 589 - 



SCHESSCHEVSKT, 18, 83, 398 

SCHIiPARSLLI, 550 

Scopolamitie, 142, 147 

Sea-aickness, 135 

Sealing, 14, 19-20 

Security factor, 74 

Seismograph, 269 

Sense of locality, 540, 541 

Shooting distance, 158 ff 

Short-wave rays, 367, 443, 445 

Shot into t^e universe, 141 

Siberian ports, 503 

Similar living beings, 536-538 

Simplifications, 358-359 

Sleeping in the space-ship, 423 

Small planets, 457, 518 ff 

Smithsonian Institute, 5 

Solar constant, 437-438, 548, 569 

Solenoid gon, 1^3, 404 

Soldered Joints, 18 

Solidity, 16 ff, 84 ff, 341 ff 

Solidity, pneumatic, 16, 21, 78, 386 

Space-boat, electric, 575 

Space curvature, 459 

Space diver, 417, 430, 441, 449-452 

Space-ship, 27, 41, 140, 350, 351, 404, 406 ff 

— electric, see electric space-ahip 

Space telescope, 417, 453-457 

Speed of light, 473 

Speed of out-flow, 34 ff, 337 

Speed of out-flow, effective, 45 

SSWGLER, 543 

Spiders, 541 

Spinning, 307 



- 690 - 



STMOSmSTEIT,, 146 

Starting, 10, 340, 350, 351 

Stations in interplanetary space, 140, 205-206, 248, 449, 477 ff, 

525, 657 
Steering automatic, 260 ff 
— in interplanetary space, 5, 341 
STEFAN BOLTZiUNN'S lair, 291, 295, 438, 552 
STEIN, 472 

Stoichiometric factor, 38 
Stone from the moon, 144, 264, 424 ff, 454 
STONBY, JOHNSTONE G., 632 
STOPPEL, 140 

Strategic inportarce, 212, 276 ff, 368, 479, 498, 503 
Subdivision of propulsion rocket, 395, 524 
Support, 45, 118, 189 
Supporting mass, 189-190 

Synergetic ascent, 87, 88, 151, 230 ff, 524, 525 
Synergetic continuation of propulsion, 248 
Synergy curve, 88, 230 ff, 609 
Synergy problem, 80, 217 ff, 524 ff 

Tail rocket, 27, 114, 259, 260 

Tapevorm rocket, 31 

Technical economy, 403 ff, 576 

Telepathy, 460 

Telephone, 417, 430-433, 449 

Telescope, 417, 430-433, 449, 453 

Tension of net, 497 ff 

Theory of ice in interplanetary space, 429, 516, 544 

Theory of natural descent, 536 ff , 644 

Theory of relativity, see EDISTEIN 

Thermal efficiency, 208 

Thermopile, 568 

Thermos flask, 418, 439, 441 

Three-body calculation, 194, 207, 467, 521 



- 591 - 



Tip, 26 f 78, 384, 414 

Titanic, 480 

TOHASCIIEK, 458, 459 

Toroid (mass ratio), 74 

Trade-vind, 551 

Trajectory curves, 154 ff, 

Trajectory disturbances, 208, 220, 467, 474, 602 

Transverae direction, 489 

Turning -wheels, 265, 539 

ULINSia, 56, 562, 568 

Ultraviolet rays, 444-445 

UndertoT, 84-86 

X]NGE, 269 

Ifcits, divisible and indivisible, 403 ff 

Up and doim, 117, 144 

Uranus, 556 

Utilization of fuels, 208 ff, 218, 396 

YALIER, 74-75, 86, 93, 145, 150, 188, 189, 205, 209, 216, 302, 
303, 321. 370, 373, 376, 377, 378-380, 392, 401, 402, 406, 
409, 440, 518 

Vasano tablets, 146 

Velocity control, automatic, 270 ff, 281, 330 

Velocity, «o«t favorable (v), 78 ff, 164, 275, 281, 338, 339, 

350, 396, 397 

— most favorable, sinpl e velocity (vg)* 88-90 

— ideal, 56 

— parabolic, 151, 156 ff 
Venturi tubes, 45 
Venus, 547, 576 

VEEOTE, 122, 147, 199 
Vertical ascent, 101 ff, 164 ff 
Vertical direction, 489 
Virtual rocket, 184 
Virtual speed, 55 



- 5M - 



Wj^SSLER, 298 

Wasp ant, 541 

Vastei, 446~44n 

VEBER, 84, 41, 182, 514 

WIVKLER, 130, 397 

Viteh'8 ointmoit, 143 

OTTTKUHN, 133, 146 

WOLF, 49, 50 

Woman In tlie moon, 84P, 265, 881, 288, 509, 585 

VaimSBOBF, 563 

Work, relativity principle of, 193 ff 

World other, 196, 457, 473 

ZAFDSR, 308 
ZEONER, 42, 43 
ZIOLKO^Sia, 150, ail, 308 
Zodiacal li<;ht, 417 



-593- 



MISSING 



ELATE I 



-59^- 



Plate II 




Atonizer 



•595- 






.ijt^:iiJ:iVi^'ypj,^ 



Plate III. 








■596- 



Plate IV 




/X|~^ 



— e;- 








/ 







ifiMspfflir'^" 



a I tip of the alcohol rockot and the hydrosen rocket 

f i parachute 

T I entrance to I 

e s tank for the hydrogen or for the alcohol-Toter 

S : oxygeu tank 

I t cabin for the observer and for the precision instruments 

P ( periscope 



-597- 



m, n : heating gas pumps 
V*i n * PWi>P chambers for the fuel 

Pg, . I pump chambers for the oxygen 

Fq, : smallest cross-section of nozzle 

z i atonizer 

1 ; re/»ulating rods 

t : nozzle vail 

V : inflow behind t and regulatin;^ deTices for the inflow 

w : fins 

o I oven