4
MAP READING
FOR
AVIATORS
INCLUDING
AERIAL NAVIGATION
BENSON
EDWIN N. APPLETON INC,
NEW YORK
MAP READING FOR
AVIATORS
WITH A CHAPTER ON AERIAL NAVIGATION
BY
C, B. BENSON, C.E.
Instructor in Cornell University
School of Military Aeronautics
EDWIN N. APPLETON, Inc.
Publishers and Booksellers
Military and Naval Books Exclusively
1 BROADWAY :: :: :: NEW YORK
Copyright, 1918
BV
L - EDWIN N. APPLETON
This little book has been prepared with a
view to providing a brief reference in Map
Reading and Aerial Navigation for Aviation
Students in the United States Army.
The author acknowledges with thanks the
suggestions and advice of Professors L. A.
LAWRENCE and ERNEST BLAKER of Cornell
University.
392299
CONTENTS
PAGE
MAPS 1
MAP SCALES — Three methods ; Changing from one to another
method ; Changing from English to Metric, and vice versa ;
Standard Scales, Metric Table, Problems 4
CONVENTIONAL SIGNS , 14-
THE FORM OF THE GROUND — Degree of Slope, Contours, Profiles,
Visibility, Hachures, Problems t 19
DIRECTION — Orientation, Methods of Orientation, Resection and
Intersection 32
AERIAL NAVIGATION — Bearings, Variation, Deviation, Map, Magnetic
and Compass Courses, Correction for Wind, Changing from
Map Courses to Compass Courses and vice versa, Problems 37
PREPARATION OF MAPS — Examining a New Map; Cross-Country
Flying ; Co-operation with Artillery 53
CHAPTER I
MAPS
A MAP is a graphical representation of a portion of the
earth's surface. Information of the natural and artificial
features is conveyed to the reader by means of lines, symbols,
words, and abbreviations. It is drawn to scale — that is,
there is a definite relation between the space on the map
and the ground distance represented.
The amount and character of the information given on a
map depend upon the use to which the map is to be put and
the size — or the scale — of the map. It is obvious that more
detail can be shown on a large than on a small map of the
same area. The features to be left off the map are deter-
mined by the use which is to be made of it. For instance,
the ordinary County Map shows only property lines,
streams and dwellings. Its purpose is to enable the County
Clerk to keep track of the taxes, etc., and it is immaterial to
him whether there is a hedge or barbed wire fence between
John Brown's property and William Smith's. The map found
in a railroad time-table does not show types of bridges along
the line, or whether the highways are metaled or not, but it
does show the sequence of the towns and villages passed
thru, the large streams crossed, and connections which can
be made with other railroads. Maps of these two types
rarely show differences in elevation. That information is
not essential to their purpose. The topographic map, on the
other hand, goes into detail as to the exact form of the
ground, the location of buildings, fences, highways, rail-
roads, and other natural and artificial features.
A military map is an elaborate topographic map. There is
nothing on the surface of the earth which does not have its
1
military significance, and therefore a good military map
shows all the information which is compatable with its size.
For instance the "Trench" or "Position" Map (See page 15)
shows, first, the exact form of the ground — hills, valleys,
ridges, etc., whether the railroads are single or double track,
steam or electric ; whether the highways are metaled, ordi-
nary county roads, or simply trails ; whether the fences are
stone, hedge, barbed wire, smooth wire, rail, or board ;
whether the bridges are truss, arch, suspension, ponton, foot
or aqueducts, whether the buildings are dwellings, barns,
factories, post offices, churches, telegraph offices, or military
headquarters; where the telephone and telegraph lines are;
the electric power transmision lines ; whether the streams
are fordable ; where the woods are ; where the different mili-
tary units are located, etc., etc.
However, all maps have a military use. A map which
shows only large towns, streams, railroads, and highways
will be useful to the aviator in cross-country work, and to
the staff in working out strategic moves, because the details
of the movement of small bodies of troops must be left to
the officer in immediate command in any event. Even the
county map will enable a commander to make plans for con-
centrations of bodies of troops.
The term "Map" implies an accurately made drawing
from a survey in which the distances and directions have
been carefully measured with instruments. The name
"Sketch" is given to the map which has been hastily made in
the field by measuring the distances by some crude method
such as counting paces, timing the trotting of a horse, or
counting the revolutions of a wheel. Sketches are rarely
used in modern warfare, except in minor operations. Topo-
graphic maps obtained in time of peace are converted into
military maps by the use of aerial photography and data
2
gotten by secret agents in the enemy's country. Extreme
accuracy may be gotten from aerial phcko graphs "when the
altitude of exposure is known, the focal length of the lens,
and the size of the negative. Even when this data is miss-
ing, if two or more features can be identified from a good
map, the relative distances of other features may be easily
and accurately filled in.
"Map Reading," or the art of translating and understand-
ing the information given on maps, may be said to consist of
only four things: First, the scale, or relation between the
size of the map and the ground represented ; Second, the
symbols or conventional signs used to represent different
features; Third, the representation of differences in eleva-
tion or contour of the earth, and Fourth, the direction.
Each of these problems will be taken up in turn.
1 ' " •'•« CHAPTER II
MAP SCALES
THE DISTANCE shown on a map between two points is
always the horizontal distance. The map is made as tho the
observer were vertically above each point. This will be
made clearer when the study of contours is reached.
The scale of a map is the ratio between the
Kinds of length of the lines on the map and the length
Scales of the lines they represent on the ground.
There are three ways of showing the scale
of a map : The Graphical Scale ; the Words and Figures
Scale; and the Natural Scale or Representative Fraction,
commonly spoken of as the "Scale" or the "R. F."
The Graphical Scale is the most common
The Graphi- and best known, and usually appears in con-
cal Scale junction with one of the other methods. It
is simply a line or graph marked off in some
common units, such as miles, yards, meters, kilometers. In
Figure 1, the distance from A to B is 200 yards. It means
that a space A-B on the map represents 200 yards on the
ground. Similarly CD is 540 yards.
SCALE OF YARDS
C ^ B p
100 50 0 IOO ZOO 300 400 5OO 6OO
When speaking of the scale of a map or cal-
The "Words culating distances on it the "Words and
and Figures" Figures" method is usually used. "6 inches
Scale = 1 mile" obviously means that 6" on the
map represent a distance of one mile on the
ground. "10 cm. = 1 km." (See Table II on page 11)
means that a space of 10 cm. on the map represents a dis-
tance of one kilometer on the ground. It is awkward for a
man trained in the English system to use a map in the
Metric system, and vice versa, and for that reason most mili-
tary and topographic maps have their scales given in the
"Natural Scale" or "Representative Fraction" method.
The "Natural Scale" or "R. F." of a map is a
The "R. F." fraction, the denominator of which shows
the number of times the line on the map is
contained in the line it represents on the ground. In other
words, it shows what fraction of the ground the map is. The
R. F. does not depend upon the system of units used. It
may be found by writing a fraction having in the numerator
the number of units on the map and in the denominator the
number of the same units on the ground, which is repre-
sented by the numerator. For convenience this numerator
is usually written as 1.
If the scale of a map is given as : "6 inches
Changing = 1 mile," the R. F. may be found as fol-
Words and lows : (One mile contains 63,360 inches)
Figures to R.F. 6 inches on map 6 inches on map
1 mile on ground 63360 inches on ground
6 units on map 1 1
or the R. F. is
63360 units on ground 10560 10560
which means that the lines on the map are l/10560th as long
as the lines they represent on the ground. If one line is
5
l/10560th as long as another it is easy to see that it is im-
material whether you measure them in inches, feet, miles,
yards, centimeters, meters, or kilometers. As long as you
measure then both in the same units, the result for one will
be 10560 times as large as the result for the other.
If "4 inches = 1 mile," the R. F. is:
-I inches on map 4 units on map 4 1
63360 in. on ground 63360 units on ground 63360 15840
or the lines on the map are 1/1 5840th as long as the lines
they represent on the ground.
If the scale is given as "10 centimeters = 1 kilometer," the
R. F. is, since there are 100,000 centimeters in 1 kilometer,
10 cm. on map 10 cm. on map
1 kilometer on ground 100,000 cm. on ground
10 units on map 10 1
100,000 units on ground 100,000 10,000
or the lines on the map are l/10000th as long as the lines
they represent on the ground.
If the scale is given "1 millimeter = 10 meters," the R. F.
is found in the same manner. There are 1000 millimeters in
one meter.
1 mm. on the map 1 mm. on the map
10 m. on ground 10,000 mm. on ground
1 unit on the map 1
ID p
10,000 units on the ground 10,000
When the scale is given in the R. F. form,
Changing R. F. it is usually necessary to change it to the
to Words and , "Words and Figures" form before reading
Figures the map. Most of us would have difficulty
in imagining 21120 inches on the ground
6
but \vhen we know it is 1/3 of a mile it is easy. Therefore,
i
if the scale is given as , it will be convenient to know.
21120
the number of inches on the map which represents one mile
on the ground. Remembering that to find the R. F. from
the "Words and Figures" scale, the number of inches on the
map which represented one mile on the ground was placed
over the number of inches actually in a mile, the "Words
and Figures" scale can be found from the R. F. by finding
the number, which, when placed over 63360, will give a
fraction which may be reduced to the given R. F.
Let X = the number of inches on the map which repre-
sents a mile on the ground. Then
1 X 63360
== -, or 21120 X = 63360 and X = = 3
21120 63360 21120
which means that 3 inches on the map represent a mile on
the ground.
If the R. F. is 1/7920:
1 X 63360
X =r = 8, or 8 inches on the map
7920 63360 7920
represent one mile on the ground.
If it is desired to have the scale in the Metric system, re-
member that to find the R. F., the number of centimeters on
the map which represented one kilometer on the ground was
placed over the number of centimeters actually in a kilo-
meter and the fraction reduced.
Given a scale of 1/20,000. To find the number of centi-
meters on the map which represents one kilometer on the
ground :
Let Y = the number of centimeters. Then :
1 Y 100 000
_ — from which Y = — = 5, or 5 centi-
20000 100000 20 000
meters on the map represent one kilometer on the ground.
7
Reduced to simple terms, the rules become,
(1) TO FIND THE NUMBER OF INCHES ON THE MAP WHICH
REPRESENTS A MILE ON THE GROUND FROM THE R. F., DIVIDE
63360 BY THE DENOMINATOR OF THE R. F.
(2) TO FIND THE NUMBER OF CENTIMETERS ON A MAP WHICH
REPRESENTS ONE KILOMETER ON THE GROUND FROM THE R. F.,
DIVIDE 100,000 BY THE DENOMINATOR OF THE R. F.
Since the R. F. is independent of the system of units used,
it offers the most convenient method of changing scales from
the Metric to the English system and back. If a map is
made in the Metric system it will be difficult for a man
trained in the English system to read the scales in centi-
meters, meters, and kilometers. A single operation will
change the scale to "Words and Figures" in the English sys-
tem, and then a graphical scale may be easily constructed.
Suppose the scale is given as "10 centimeters
Changing from = 1 kilometer." Reducing to the R. F. :
Metric to 10 cm. 10 cm. 1
English Scale J^ = 100>000 cm =
Having the R. F. proceed in the manner
described above to find the number of inches on the map
which represents one mile on the ground :
1 X 63360
X = - = 6.33" or 6.33 inches on the
10000 63360 10000
map represent one mile on the ground, which for practical
purposes of map reading is 6 inches = 1 mile.
If the scale is given as "3 inches = 1 mile,"
Changing from to find the number of centimeters on the
English to map which represents 1 kilometer on the
Metric Scale ground, first, find the R. F. :
3 inches 3 inches 3 1
1 mile ~ 63360 inches "" 63360 '"21120
Having the R. F. proceed as above for finding the number of
8
centimeters on the map which represents one kilometer on
the ground :
1 Y 100000
— or Y = = 4.73+, or 4.73 centimeters
21120 100 000 21120
on the map represent one kilometer on the ground. For or-
dinary map work this may be called "5 cm. = 1 kilometer."
This method is much simpler and less liable to error than
the one of remembering the number of centimeters in one
inch and the number of miles in a kilometer, etc.
If there is nothing but a graphical scale on a map and it is
in the wrong system, it may be easily' transferred to the
other system.
For instance, upon measuring a graphical scale, it is found
that 0.80 inches on the map represent one kilometer on the
ground.
There are 2.54 centimeters in one inch.
Therefore, there are 2.032 centimeters in 0.80 inches.
Or 2.032 centimeters on the map represent 1 kilometer or
100,000 centimeters on the ground.
2.032 1
The R. F. is = , and since 1/50,000 is known
100,000 49,212
to be a standard Metric scale, it is probable that the map is
made on that scale. Then proceeding as above, Rule 1, we
find that 1.26 inches (1^4") on tne maP represent one mile
on the ground.
If a map is in the English system and upon measuring the
graphical scale it is found that 10.2 centimeters on the map
represent one mile on the ground, to change to the Metric
system :
There are 0.4" in one centimeter.
Therefore there are 4.08" or 10.2 centimeters.
Or 4.08" on the map represent 1 mile or 63360 inches on
4.08 1
the ground. The R. F. is = . 1/15840 is a
63360 1S529
9
standard scale for maps in the English system, so allowing
for a slight error in measuring, it is probable that the map is
on that scale. Proceeding as above, Rule 2, it is found that
6.32 centimeters on the map represent one kilometer on the
ground.
It will be found convenient, when measuring distances by
eye, to use yards or meters as units. A mile is 1760 yards
long, approximately 1800 yards. Where the scale is 3 inches
= 1 mile, 1/21120, (or 5 cm. = : 1 km., 1/20000), one
inch on the map represents approximately 600 yards on the
ground. If the scale is 6 inches = 1 mile, 1/10560 (or
10 cm. = 1 km., 1/10000) one inch on the map equals ap-
proximately 300 yards on the ground. The error is probably
less than that made by estimating the distance on the ground
by eye. The number of meters is a little more than 9% less
than the number of yards.
There are a few standard scales for military maps. At the
present time both England and the United States have
adopted the Metric system for their armies, so the scales
given are Metric : TABLE I
R. F.
Cm.
per KM.
In.
per mile.
1. "Siege," "Fortification," or
"Local" Maps
1/5000
20
1267
2. "Infantry," "Position," or
"Trench" Maps
1/10000
10
634
3. "Artillery" Maps (Some-
times Road Sketches)
1/20000
5 -
3 17
4. "Tactical" Maps
1/40000
2 u
1 58
5 "Strategical" Maps
1/100000
**/2
1
063
6. "Emergency" Maps (for
Aviation Service)
1/250000
04
025
10
TABLE II
10 millimeters (mm.) = 1 centimeter
100 centimeters (cm.) = 1 meter
1000 meters (m.) = 1 kilometer (km.)
25.4 mm. — 1 inch
2.54 cm. = 1 inch
1 cm. = 0.4 inch
1 meter = 39.37 inches
1 meter = about 3*4 feet
1 meter = 1 yard, 3 inches +
1 kilometer = about 1100 yards (1093 yards +)
1 kilometer = about 0.6 mile
\z kilometers = 1 mile.
11
PROBLEMS ON MAP SCALES
1. The R. F. is 1/316,800. What is the scale in inches per mile ?
Answer, 1" = 5 miles.
2. The R. F. is 1/200,000. What is the scale in centimeters per kilo-
meter ? Answer, 1 cm. = 2 km.
3. The R. F. is 1/31,680. What is the scale in inches per mile ?
Answer, 2" = 1 mile.
4. The R. F. is 1/5280. What is the scale in inches per mile ?
Answer, 12" = 1 mile.
5. The R. F. is 1/50,000. What is the scale in centimeters per kilo-
meter ? Answer, 2 cm. = 1 km.
6. The R. F. is 1/10,000. What is the scale in centimeters per kilo-
meter? Answer, 10 cm. = 1 km.
7. If the scale is 8" — 1 mile, what is the R. F. ? Ans. 1/7920.
8. If the scale is 24" = 1 mile, what is the R. F. ? Ans. 1/2640.
9. If the scale is 20 cm. == 1 km., what is the R. F. ? Ans. 1/5000.
10. If the scale is 5 cm. = 1 km., what is the R. F. ? Ans. 1/20,000.
11. A is 4 miles from B. How many inches is A from B on a map
whose scale is 5 cm. = 1 km. ? Answer, 12.68".
12. X is 10 kilometers from Y. How many centimeters is X from Y
on a map whose scale is 4" = 1 mile ? Answer, 63 + centimeters.
13. A is 38 inches from B on a map whose scale is 20 cm. = 1 km. How
many miles is A from B? Answer, 3 miles.
14. X is 40 centimeters from Y on a map whose scale is 6" = 1 mile.
How many kilometers is X from Y? Answer, 4.22 kms.
15. A is 4" from B on a map whose scale is 1/120,000. On another map
of the same territory, A is 12" from B. What is its scale?
Answer, 1/40,000.
16. X is 36 inches from Y on a map whose scale is 1/21120. On an-
other map of the same territory, X is 6 inches from Y. What is
its scale? Answer, 1/126,720.
12
17. A map is 40" square and represents country 10 miles square. What
is its R. R? Answer, 1/15840.
18. Upon measuring a graphical scale it is found that 0.4" = 1 km.
What is its scale in inches per mile ? Answer, 0.633" = 1 mik.
19. Which is the larger scale, 1/10,000 or 1/50,000 ? Answer, 1/10,000.
20. M is 24" from N on a map whose R. F. is 1/633,600. How many
miles is M from N ? Answer, 240 miles.
21. If the scale is "1 inch — 8 miles," how many kilometers is X from
Y if they are 20 centimeters apart on the map ? Answer, 101.38 kms.
22. How many inches on the map would represent the distance covered
in 20 minutes with a ground speed of 120 miles per hour on a
1/250,000 map ? Answer, 10.13 inches.
23. Construct a graphical scale of yards for a map whose R. F. is
1/20,000.
24. Construct a graphical scale of kilometers for a map whose scale is
"1 inch = 4 miles."
25. Construct a graphical scale of miles for a map whose scale is
"1 centimeter = 5 kilometers."
13
CHAPTER III
CONVENTIONAL SIGNS
THE SYMBOLS used on maps to represent the objects on
the ground are called "Conventional Signs." Unfortunately,
there is no standard set of conventional signs for all coun-
tries, and for some features, different signs are used even in
the same country. The following pages give some of the
signs in most common use in the United States.
It is necessary at times to draw the signs slightly out of
scale. On a small scale map an ordinary house would be a
mere speck, and the symbol is usually drawn a little larger
so it may be seen easily. This also applies to highways,
bridges, etc., etc.
14
RAILROAD5
Single* Track
Double Track
Single Track.
Double Track.
Electric . .
European
R. R. ip Cut.
RR In nil
R R. in Tunnel..
2 Railroads
R R Station
HIGHWAYS
Metaled Surface
Improved Surface
Unimproved but cut out..'
Trail or path '
Incline,.- — :
FENCES
G-er»eral
Wlre._ x * *-
Smooth W<r«. • « •
Worm.
Stone.
Boord... '..
(vsvallj in 9reen).._<
Ahny roads-arrvall ;>ca\e Mops
Electric Power
tr«r»sml3Sion line
FEATURED
Ditch
Dry Lake
Tidol Flats (salt ponci)....
Arroyo fstreom in
Dom (In block).
Sand Oun<?s(in brown)....'^vrv'*i','rr-v'
WATER CROSSINGS
FORDS
Infantry t- Covolry_
Cowalry only
YVogon •»- Artillery j
FERRIES
TREES
LAND
Corn.
Cot+on...
BUI LDl NG5
Barns
Chvrch
Hospital ________________________ m
Post Office ........ _ .............. tt
Teleqraph Offi<e __________________ db
Factory (show Kindl ........... *&"
Electric Power Plont.... _____ -*
City, Town, or Vi I lo<?e M'Sft'*
City. Town, or V/illa^p-
16
MILITARY SIGNS
HCADQUARTCR5
Corps
Divivor,
STAFF CORPS
Commissary. ...... ______ _____ ._([
Medical ........ ' ......... ..J*>
Ordnooce ............ _ .......... O
E no !r> ef. ______________
THE LINE.
Infantry in line __________
Covolry (Ob obOvf)
Ar-t'i|le«-y.
" Tro'r>
cn ry
Viderte ____
Int. Pi'cKef
Cov. PicH«-t
Inf. Support
A A A A
..A A A
Trencn.
Fort (show t'oe plon if
Redoubt (tro* plan
Gun Battery. -«f.\.
Mortor Bofter
Battle
Good Ld<? Ptoce for Airplanes.-!
Possible Ld Ploce.
OB5TACLC5
_y Xf
Chevoux de frise
Paliso.des_. I
Wire Ent-an'jlement_
Dcrnolitlons.
SSi
Mi
Controlled Mmtfs
Mine Croter.
Mine Croter Fortif i
f"* * »
17
AUTHORIZED ABBREVIATIONS
A.
Arroyo
Mr.
rioun t di n
abcf.
Abutment
Mti.
hountaina
AK
Arch
N.
North
b.
Brick
T..{
Not Fordable
as.
BlocK5mi fh Shop
bot
Bottom
P
Pi/rr
Br.
Branc h
Pk
Plonk
br
Bridge
PO.
PosV Office
Pt.
Point
C.
Cope
cem
Cemetery
q-p.
Queen Post-
con.
Concn? re?
cov.
Covered
R.
River
Cr.
Creek
RH.
Round House
cuL
Culvert
RR.
Railroad
d.
Deep
SL
oouth
D.S.
Druv 5*"Ore>
S
5*e*l
5.H.
ochool house
C.
Cast-
5.M.
Sowr"iH
fit.
Cstvtfry
3ta.
Ototion
M.
o^one
f
Fordable
Str.
Streo^vi
rt
Torr
TG.
Tolloate
CrS.
Genero I Store
Tr*$.
Tr«3tle
<ji«r
Oird«?r
+ r.
Trosi
G-.M
Gristmill
k
Iron
I
Island
W.T
Water TopK
V* W.
Wot«r Works
Jc.
Tune t ion
W.
W«st-
k.p.
K,n? P05t
w.
W(de
|_.
Loke
Lot
Latitude
Ld!:s.
Londin^
Life Saving 5tot\or
L.H.
Li^ht hou5^
L*,,
Lon^i tude
18
CHAPTER IV
THE FORM OF THE GROUND
THE SLOPE of the ground is the angle be-
Degree of tween the surface of the ground and a hori-
Slope zontal line. In military work this angle is
measured in degrees and is called the "de-
gree of slope." A rise of one unit in 57.3 units (horizontal)
is a one degree slope. A rise of 2 units in 57.3 units is a two
degree slope. Up to about 20 degrees this method is quite
accurate. In ordinary engineering practice the slope angle
is measured in percent. It is the number of units rise divided
by the horizontal distance in the same units. A rise of
1 foot in 100 feet is a \% slope.
A steep slope is one with a large angle between the sur-
face and the horizontal, and a gentle slope is one with a small
angle. An even slope is one where the angle is constant,
and an uneven slope is one where the angle changes. A level
piece of ground is one which has the same elevation at all
places. A flat piece of ground is not necessarily level, — the
surface of a board for instance is flat in any position. The
terms valley, ridge, gulley, etc., are well enough known so
description here may be omitted.
There are two methods used on maps for showing the
form of the ground. The most common is the Contour
method, and the other, now very seldom used except on very
small scale maps, is the Hachure method.
Contours should be thought of as lines cut
Contours from the earth by a series of imaginary level
surfaces, with equal vertical distances be-
tween them. The French call them "courbes horizontales
reprcsentant le terrain." The vertical distance between the
19
imaginary surfaces is called the "Contour Interval" or some-
times the "Vertical Interval." (Abbreviated
Contour C. I. or V. I.) Since a contour is a line in a
Interval level surface, all points on it are of the same
elevation — or contours are lines joining
points of the same elevation.
Fig. 2 represents a conical hill, with a gulley down one
side. The first imaginary surface passes thru points which
are 5 feet above the bottom of the hill. It will cut out a line,
shown on the map below, which represents points which are
5 feet above the bottom of the hill. The next surface is 10
feet above the bottom of the hill, and cuts out a line which
shows places 10 feet higher than the bottom. The map can
only show the horizontal distance from X to Z, but at point
Y one can tell that the ground is 5 feet higher than it is at
X, because all points on that line are 5 feet above the bot-
tom of the hill.
The slope of the hill is even — the angle between the sur-
face and a horizontal line is always the same. Since the sur-
faces are equally spaced, angle ACB (See Fig. 2) is equal to
angle CDC, angles CC'D and ABC are right angles and side
AB equals side CC', so triangles ABC and CC'D are equal
and side CB is equal to side DC', Therefore, it is seen that
the horizontal spaces between the lines cut out by the sur-
faces (the contours) are the same, where the slope is even.
This horizontal space on a map between
Map Distance the contours is called the "Map Distance."*
This establishes the first principle of con-
tours: (1) WHERE THE CONTOURS ARE EVENLY
SPACED, THE SLOPE IS EVEN.
Fig. 3 represents a hill shaped lige a semi-sphere. Near
the bottom where the slope is steep the lines cut out by the
* The term "Map Distance" is seldom used in any other sense.
20
imaginary surfaces are closer together than at the top where
the slope is more gentle. Fig. 4 shows a reversal of this
form — the gentle slope is at the bottom. These two figures
show two more principles of contours: (2) WHERE THE
SLOPE IS STEEP THE CONTOURS ARE CLOSE TO-
GETHER, and (3) WHERE THE SLOPE IS GENTLE
THE CONTOURS ARE RELATIVELY FAR APART.
(1), (2), (3), may be briefly stated by saying that the spac-
ing of the contours shows the degree of slope by varying
inversely with the steepness.
From these principles it naturally follows that when the
steepness reaches a maximum — or the ground becomes a
vertical cliff — the contours will coincide. Since a contour
connects places on the ground of the same elevation, if two
or more contours of different elevations lie one over the
other it means that places of different elevation on the
ground exist one vertically over the other. On the other
hand when the ground is level there will be no contours at
all, because one level surface passed over another level sur-
face will not intersect it.
Contours never cross one another, except in the very rare
case of an overhanging cliff.
Fig. 5 shows the way contours always bend toward the
source of a stream. A stream must have a depression to flow
in and must flow down hill. Therefore when the contours
get to the edge of the depression, they will have to bend up-
stream to reach points of the proper elevation, because a
contour can only connect places of the same elevation. The
same figure shows that on a ridge or hill the contours bend
down stream, and establishes two more principles of con-
tours : (4) TO SHOW A VALLEY THE LOWER CON-
TOURS BEND TOWARD THE HIGHER ONES, and
22
23
(5) TO SHOW A HILL OR RIDGE THE HIGHER
CONTOURS BEND TOWARD THE LOWER ONES.
Fig. 6 shows a landscape with hills, streams, steep and
gentle slopes, vertical cliffs, and flat places, and the map
below it shows the way it is represented by contours.
It is sometimes possible to get a clearer idea of contours
by imagining a contour to represent the shore line of a body
of water. All points on the surface of a still body of water
24
are of the same elevation, so the conditions of a contour are
satisfied. Now imagine the surface to be lowered a certain
amount. It is apparent that where the ground is steep the
new shore line will be closer to the old than at a place where
the slope is gentler.
Contours are usually drawn in brown. When you decide
to make a map, you choose the contour interval as soon as
you have fixed the scale. Suppose you decide to have a
contour for every 20 feet of elevation : Then the first contour
on the map if you are mapping country near the sea, will
pass thru points 20 feet above mean sea-level. (Mean sea-
level is usually chosen as reference or datum.) The next
one will pass thru points 40 feet above the sea, the next thru
points 60 above, etc. It is customary to number only every
fourth or fifth contour — in the U. S. generally every 5th —
and those bearing the numbers are made several times
heavier than the others. If the C. I. is 10 feet, the 50, 100,
150, etc., contours will be numbered and heavy. If the C. I.
is 20 feet, the even hundreds will be numbered and heavy.
Having only a few of the contours numbered sometimes
makes it difficult to tell whether several concentric contours
represent a hill top or a depression. See A, Fig. 7. Unless
there is some information to the contrary, it is safe to assume
that such a feature is a hill top. Depressions are shown
sometimes by drawing short lines perpendicular to the con-
tours, on the inside. Sometimes the exact elevation of the
deepest and highest points are shown in figures.
On some French maps, none of the contours are num-
bered. Prominent points have their elevations shown in
figures and the contours simply show the form. Their ele-
vations must be figured from the elevations of the nearest
known points.
Contours, being cut out by surfaces passed thru the earth,
25
are closed lines and therefore contours never end on a map.
They either close on themselves, or run off the map.
Since a 1° slope is a rise of 1 unit in 57.3 units horizon-
tally, the slope (S), in terms of horizontal distance (D) and
difference in elevation (H), may be stated:
H
S = — x 57.3
D
i. e., if we had a 4 foot rise in 114.6 feet, we would have a 2°
slope. But contours are lines on a map, and it is more con-
venient to use the "map distance" (Page 20) and "contour
interval" when working out slopes from a map. The map
distance (M. D.) is equal to the ground distance (D), times
the R. F. (See Page 5). Letting "H" in the above formula
be limited to one contour interval, and since D = M.D./R.F. :
S x D = H x 57.3
M. D.
S x = C. I. x 57.3
R. F.
S x M. D. = R. F. x C. I. x 57.3
It is convenient to measure M. D. with a ruler graduated to
inches or centimeters and to use the C. I. in feet or meters as
given on the map. In the English system the formula be-
comes: (Since 12" — 1 foot)
M. D. (in inches)
S x = R. F. x C. I. (in feet) x 57.3 or
12
(1) S x M. D. (inches) = R. F. x C. I. (feet), x 688
(57.3 x 12 = 688)
In the metric system, (since 100 cm. — 1 meter)
M. D. (in cm.)
S x = R. F. x C. I. (in meters) x 57.3
100
or (2) S x M. D. (cms.) = R. F. x C. I. (meters) x 5730
26
If two adjacent contours are J4 mcn apart on a map whose
scale is 4 inches = 1 mile, C. I. — 15 feet, the slope may be
found as follows :
1
S x y4 — x 15 x 688
15840
4 x 15 x 688 688
S = = = 2.6°
15840 264
To find the distance apart in centimeters the contours will
be on a map whose scale is 10 cm. = 1 km., C. I. = 3 meters,
for a 4° slope :
M. D. x 4 = 1/10000 x 3 x 5730
3 x 5730
M. D. = == 0.42 cm.
4 x 10000
Some maps have a "Map Distance Scale" which may be
used to find the slope graphically. The scale is made by
using the formula to find the M. D. for several different
degrees of slope.
The normal system of map scales prescribed
Normal by the U. S. Army for field sketches is based
System of upon the above formula. The spacing of
Map Scales contours for a 1° slope is 0.65 inch. After
the scale of the map is decided upon the
proper C. I. is found from the formula, since all the quanti-
ties except the C. I. are then known. The spacing for a
2 degree slope is 0.32 inch, for a 3 degree slope 0.22 inch, etc.
This is of great value in teaching men to read maps in the
field, because the same contour spacing means the same
slope on all maps no matter what their scale, if the C. I. is
chosen according to the Normal System. A simple rule to
remember is that if the C. I. = 60 -i- scale of the map in
inches per mile, the map is in the Normal System, i. e., Scale
6 Inches = 1 Mile. C. I. = 10 feet (60 -*- 6 = 10).
27
It is sometimes desirable to know the form
The Profile of the ground along some definite line. A
drawing which gives this information is
called a profile. It is made from a contour map by taking a
sheet of paper with equally spaced parallel lines, and num-
bering the lines according to the contour interval, starting
with the number on the lowest contour along the line under
consideration and continuing to the highest. This sheet is
placed along the line on the map (Fig. 8). The line crosses
the 810 contour at (A). Drop a perpendicular from (A) to
the line numbered 810. The line crosses the 800 contour at
(B). Drop a perpendicular from (B) to the line numbered
800. Continue this throughout the length of the line of
which a profile is desired and connect up the points so found
with a smooth curve and the exact form of the ground will
be shown. A study of the profile and map will show that
the map simply shows the horizontal distance between two
points, while the profile shows the true distance (of course
to scale).
(The sheet of parallel lines need not be parallel to the line
of which the profile is desired, as long as the perpendiculars
are dropped to them. If they are askew, it will have the
effect of making the scale smaller, but the relations will re-
main the same. For the same reason the spacing of the lines
is immaterial.)
It is very desirable to know at times whether
Visibility one point is visible from another or whether
a certain line of march is concealed from the
enemy, etc. This information may be easily obtained from
a contour map in several ways:
1. The Profile Method. (Fig. 8.) Draw a profile of the
ground between the points in question and then draw a
straight line from one point to the other. This line repre-
28
29
sents the line of sight. See whether it passes thru a hill. If
it doesn't the points are visible one from the other. E is
visible from A, but not from B.
2. By Proportion : An inspection of the map will show
which high points are liable to interfere with the line of
sight. In Fig. 8 suppose it is desired to find whether E is
visible from A. The ridge D is the only point that is liable,
to interfere with the line of sight. The line of sight will
XE' AE'
have to pass over D. Therefore (see Figr. 8) = ,
DD' AD'
and if XE' is greater than EE', E will be invisible from A ;
and if XE' is less than EE', E will be visible from A. The
distances may be scaled from the map and the differences in
elevation may be obtained from the contours.
3. By Proportion : From a map we find that X has an
elevation of 600'. Y, a point which might interfere with the
line of sight, is 2 miles from X and has an elevation of 700'.
Z is 5 miles from X and has an elevation of 800'. Is Z
visible from X?
At Y the line of sight has risen 100' above X or has gone
up at a rate of 50' per mile. Therefore 5 miles from X it will
be 5 times 50 or 250' above X. Since Z, 5 miles from X, is
only 200' above X, it will lie below the line of sight and be
invisible.
4. By Proportion : O has an elevation of 200'. P, a point
which may interfere with the line of sight, is 800 yards from
O, and has an elevatiori of 450'. Q has an elevation of 1400'
and is 2400 yards from O. Is Q visible from O?
Q is three times as far from O as P is, so therefore the
line of sight will have risen three times as much above O at
Q as it was at P, or 750'. But Q is 1200' above O, and there-
fore lies above the line of sight and is consequently visible
from O.
If more than one high place exist along the line of sight
30
they are taken one at a time until all are eliminated or one
is found to interfere.
The second method of showing the form of the ground is
the Hachure Method. It is very little used in the United
States and most of the European countries have abandoned
it. However, it is still used to a very slight extent on small
scale maps, particularly in Germany. A contour map gives
not only exact elevations but a much clearer idea of the
ground form than a hachured map. The spots on a hachured
map where no hachures are found are either the tops of hills
or flat, low places. It is often very difficult to tell the flat
areas without reference to other features nearby. The
steepness of the slope is roughly indicated by the varying
blackness and nearness of the hachures. As a rule, figures
show the heights of important points in feet or meters.
PROBLEMS ON SLOPES AND VISIBILITY
1. The scale is 6" = 1 mile, C I. = 10 feet. The 910 contour is (U2"
from the 920 contour. What is the degree of slope ? Answer, 2°.
2. What is the M. D. on a map whose scale is 4" = 1 mile, C. I. = 20
feet, for a 5° slope? Answer, 0.17".
3. What is the M. D. on a map whose scale is 3" = 1 mile, C. I. = 20
feet, for a 6° slope? Answer, 0.11".
4. Scale is 12" = 1 mile, C. I. — 10 feet. If the 800 contour is yS from
the 810 contour, what is the degree of slope? Answer, 2.6°.
5. Elevation of A is 200'. B, in line with A and C, is 3 miles from A,
elevation 400'. C is 9 miles from A, and its elevation is 1000*.
Is C visible from A? Answer, Yes.
6. In Problem 5, how high could C be, and still be invisible from A?
Answer, 799'.
7. Elevation of A is 800'. B is 2 miles from A, elevation 1000'. C is
5 miles from A, elevation 1500'. D is 9 miles from A, elevation
1900'. (A, B, C, & D are all in line.) Is D visible from A?
Answer, No, C interferes.
8. The scale of a map is 5 cm. = 1 km. C. I. = 5 meters. What are
the M. D.'s for the following slopes: (a) 1°? (b) 3°? (c) 4°?
(d) 6°? (e) 9°? Answers: (a) 1.43 cm., (b) 0.48 cm., (c) 0.36
cm., (d) 0.24 cm., (e) 0.16 cm.
31
CHAPTER V
DIRECTION
WHEN AN aviator wanted to make a cross country flight in
the early days of flying, he usually made arrangements to
have a special train (engine and caboose), with a white sheet
behind, to guide him, or he at least followed a regular train.
But when one is flying over the enemy's country he won't
find a train to guide him and probably not even railroad
tracks running to the places he wants to see. He must keep
his direction by a compass, the stars or the sun, and a map.
Side winds cause the plane to drift out of its course and the
compass is liable to be disturbed by local magnetic in-
fluences, such as metal in the plane, electrically charged
clouds, magnetic ore deposits, etc. Therefore, the aviator
must know how to keep his course and check his progress
by the use of his map.
It must be remembered that from a great
Orientation height in the air a large number of objects
can be seen. For this reason, at times it is
very difficult to identify particular places on the map, but if
one notes carefully the directions of railroads, highways,
streams, forests ; the angles of intersection of railroads and
highways; and the bends in streams, railroads, and high-
ways, and so forth, he can locate his position by finding a
similar place on his map. To be able to do this quickly it is
necessary to have the map in such a position that the lines
on the map are parallel to the lines they represent on the
ground. When a map is in this position it is said to be
ORIENTED. Then it represents the ground in miniature —
North of map is North on ground, South of map is South on
ground, etc. A map should never be used without first
32
orienting it, because it not only saves time, but greatly
reduces the possibility of error.
The top of the map is almost always north — the printing
reads from west to east. It is usual to have a prominent
arrow labelled "Meridian" or "True Meridian" (Fig. 11) to
show the direction of north, especially in the rare cases
where the top of the map is not north. In addition to this,
maps are usually divided by horizontal and vertical lines,
lines of longitude and latitude, in which case the true north
is the direction of the longitudinal lines, or by lines which
divide the map into conveniently sized squares for reference
in artillery work. On a complete military map an arrow,
less elaborate, usually, will be found, at an angle with the
true meridian, which shows the direction the compass needle
points in that locality, the angle being the angle of varia-
tion. (See Page 39.) This arrow is labelled "Magnetic
Meridian." _, . .
The easiest way to orient a map is to turn it
Orienting by ^ t^ie ^ne snowmg the magnetic north is
Compass parallel to and pointing in the same direc-
tion as the compass north-south line. This
will make one line on the map parallel to the line it repre-
sents on the ground and therefore all the lines on the map
will be parallel to the lines they represent.
Without a compass the map may be oriented
Orienting in the daytime with the aid of a watch. Take
with Watch the number of hours since midnight, and
divide by two. Hold the watch face up, in
such a position that a line from the center thru the resultant
hour will point toward the sun. Then a line thru the center
and the figure "12" will point north, i. e., it is 4 P. M., 16
hours since midnight. Point the figure 8 at the sun and the
figure 12 will be north. (See Fig. 10.) It may be easily done
with the watch strapped to the wrist. If an accurate deter-
33
initiation is desired, a string with a weight on one end may
be held so it casts a shadow across the face of the watch and
the watch turned till the proper hour and the center o£ the
watch are in the shadow. After the north is found, the map
is oriented by pointing a line on the map which is known to
be a true N-S line toward the north.
At night without a compass the map may be
Orienting oriented by the stars. The North Star is
by Stars easily located by its relation to the Big
Dipper, Casseopia, or the Little Dipper.
(See Fig. 9.) If a line on the map which is known to be
N-S is pointed toward the North Star the map is oriented.
The more usual methods of orienting are by
Orienting by lining up the symbols on the map with the
Known Points features they represent on the ground. For
instance, a long straight highway is seen on
the ground and the symbol for it is easily found on the map.
If the map is turned so that this symbol is parallel to the
road, it is oriented. (Care must be taken not to turn the
map thru 180 degrees, by checking by other features in the
vicinity.) If two prominent hills can be seen and the sym-
bols for them found on the map, the map is turned so that
an imaginary line between the symbols on the map is par-
allel to an imaginary line between the hills on the ground.
When one is on the ground, if his position is known, the
map may be oriented by sighting along the map, over the
symbol for his position and the symbol for some other
feature, and turning the map till the second feature is seen
as he sights over the two symbols. If his exact position is
not known but two objects can be seen in line, the map Is
turned so that a line of sight across the symbols for the two
objects passes thru the two objects on the ground, and it is
oriented.
34
35
After a map has been oriented by some method, the mag-
netic meridian may be put on, if it is not already there, by
placing a compass on the map and drawing a line in pro-
longation of the N-S line of the compass. (If the angle of
variation is known, the magnetic meridian may be put on by
drawing a true N-S line, and putting the lubber line of the
compass along it. Then turn the map with the compass on
it till the lubber line points to the figure corresponding to
the variation.)
When on the ground, one's exact position
Resection may be located on the map in the following
manner: Orient the map. Then pick out
an object which can be seen easily on the ground and the
symbol for which can be found on the map. Hold a ruler on
the map with its edge touching the symbol, and turn the
ruler, using the symbol as a pivot, till, as you sight along it,
you see the object. (The map is kept oriented during the
entire process.) Draw a line along the ruler toward your
body. Pick out another object on the ground and repeat the
process. The point at which the two lines cross will give
your exact position. This is called location by RESEC-
TION.
The position of an object in the distance
Intersection may be located on the map as follows : Find
the symbol for your position. Orient the
map and lay your ruler on the map with its edge touching
the symbol. With this point as a pivot turn the ruler till as
you sight along it you see the object you wish to locate.
Draw a line along the ruler. Repeat the operation from
some other point and the intersection of the two lines will
give the proper position of the object in question. This is
called location by INTERSECTION.
36
CHAPTER VI
AERIAL NAVIGATION
To DESCRIBE the direction or bearing of a
Bearings line in aviation work, the angle, measured
clockwise from the north, which the line
makes with a north-south line, is given. This angle is mea-
sured with a protractor, a semi-circular instrument grad-
uated in degrees from 0° to 180°, and also from 180° to 360°.
(Fig. 11.) To find the bearing of a line a meridian or north-
south line is drawn thru the initial point. If the line lies to
the east or right of the meridian, the protractor is placed to
the right with its back along the meridian and its center
over the initial point. The graduation on the arc between
0° and 180°, under which the line passes, is the bearing. The
bearing of line AB is 135°, and of AC is 47°. If the line lies
to the west or left of the meridian, the protractor is placed to
the left, with its back along the meridian and its center over
the initial point and the graduation on the arc between 180°
and 360° under which the line passes is the bearing. The
bearing of XY is 195° and of XZ is 315°.
In navigation in the air or on sea, one usually speaks of
the bearing of the line along which he is travelling as his
"course." In engineering practice the bearing is sometimes
spoken of as the "azimuth."
It is better to speak of a true north course as 360° instead
ofO°.
The magnetic compass does not always
Variation point toward the true or geographic north.
This is because the magnetic north pole is
located considerably to the south of the geographic north
pole. The VARIATION of the compass, or the angle be-
37
tween the direction the compass points and the true north is
different for different parts of the world. In the state of
Washington the compass needle points over 20 degrees east
of north, points true north in some parts of Michigan, and
over 20 degrees west of north in Maine. The variation also
varies slightly from year to year. Maps are published show-
ing the variation in different parts of the country. They
have lines on them called "Isogonic" lines
Isogonic and which connect all points which have the
Agonic Lines same variation. A line on such a map which
connects points where the variation is zero,
or where the compass points true north, is called an
"Agonic" line.
The ordinary compass has a needle which moves over a
dial, and when one wishes to find his direction the box is
turned till the north-south line is directly under the needle.
The airplane compass has its needle fastened to the dial,
which -moves under an indicator. This indicator is called
the "lubber line." The compass is mounted in the plane in
such a manner that when the longitudinal axis of the plane
is north-south, head of the machine north — the lubber line
is directly over the N or 360 of the compass dial. If the
plane is pointed northeast, or 45°, the dial does not move,
because it is fastened to the needle, which always points to
the magnetic north, but the lubber line moves along till it is
over the 45 degree mark of the dial. The aviator can always
tell the direction his machine is pointing by finding which
figure the lubber line of his compass is pointing to.
The air compass is subjected to a second error, caused by
the proximity of the metal parts of the machine. This error
is called deviation, and is different for each direction the
machine is pointed, and for each machine and compass.
38
39
At places where machines are assembled a
Deviation large platform is usually found with a mag-
netic north-south line marked across it ; a
line at right angles to it which is east- west ; and two lines at
45 degrees with it which are northwest-southeast, and
northeast-southwest. The airplane, with its compass
mounted in it, is placed with its longitudinal axis over the
magnetic north-south line. The lubber line should indicate
360 or N. But due to the metal parts of the machine it is
found that it points to some other figure. In this case the
dial is drawn toward the west 10 degrees by the metal parts
of the machine, and the lubber line shows 10 degrees when
the machine is pointing toward the magnetic north, and the
deviation is said to be 10 degrees west. (If the error is
very large, small magnets are placed near the compass to
compensate for the effect of the machinery. The error can-
not be totally removed because too many magnets may
effect the compass differently when the machine is pointing
in some other direction.) Then the machine is placed over
the northeast-southwest line. Now it is found that the lub-
ber line points to 36 degrees when it should point to 45 de-
grees, since the machine is pointing northeast. This shows
that the dial has been drawn 9 degrees to the east by the
metal parts, so the deviation for this point is 9 degrees east.
The machine is placed successively in each of the eight po-
sitions (N, NE, E, SE, S, SW, W, NW), and the deviation
for each point noted in a table. (The table should be checked
at least once, to be sure the placing of the small magnets
hasn't changed the deviation for some previous point.) A
typical table follows, which of course only applies to a par-
ticular machine with a particular compass in it :
40
TABLE III
1
2
3
Direction
Plane
Points
Magnetic Bearing or
Direction Compass
ought to show.
Compass Bearing or
Direction compass
actually shows
4
DEVIATION
N
360
10
10W
NE
45
36
9E
E
90
88
2E
SE
135
150
15W
S
180
185
5W
sw
225
215
10E
w
270
267
3E
NW
315
317
2W
N
360
10
10W
Map, Magnetic,
and Compass
Courses
(Column 3 is not always given.)
When a bearing is taken from a map and
referred to a true north-south meridian, it
is called the "Map Course." When this
bearing has been corrected for the varia-
tion in the region, or in other words, when
it refers to the angle made with the magnetic meridian, it is
called the "Magnetic Course." When it has been corrected
for deviation, or when the bearing is the reading the com-
pass must have to keep the plane going in the proper direc-
tion, it is called the "Compass Course."
Before the conversion for compass work is
Correction made, the correction to the map course for
for Wind the wind is figured out. The wind causes
the plane to drift out of its course an amount
per hour equal to the velocity of the wind, and in the direc-
tion the wind is blowing. For instance, if one wanted to fly
from east to west, and a wind was blowing 30 m.p.h. from
41
the north, at the end of one hour the plane would be 30 miles
south of the line along which the aviator wanted to fly, un-
less he made allowance for the wind. To counteract this
wind effect, the pilot must "crab" his machine into the wind.
The amount of correction is usually found graphically from
the map. Suppose it is desired to fly from A to B in Fig. 12.
The map course or track is 90 degrees. The wind is blowing
at a rate of 25 m.p.h. from the northwest. The air-speed of
the plane is 75 m.p.h. Choose some unit, say M, Fig. 12, to
represent 5 m.p.h. Beginning at A, lay off a line from north-
west to southeast, or 135 degrees, and on it mark out 5 times
M, or 25 m.p.h. This line represents the velocity and direc-
tion of the wind. In other words, the end of the line will be
the point to which the plane would be blown at the end of
an hour if it made no progress in the direction AB. Let this
point be called P. Now, with P as a center, and radius of
15 times M or 75 m.p.h., describe an arc cutting AB in C.
A line from A (AX), parallel to PC, will show the direction
in which the plane will have to be pointed in order to keep
on its course. The actual flight of the machine will be along
the line AB. The corrected map or heading course is then
76° The rate of progress along the line AB can be found
by measuring AC and finding how many times M is con-
tained in it. In this case it is 18 -f x M, and since M is
5 m.p.h., the rate of progress is 91 m.p.h. To find the length
of time required to get to B, divide the distance AB by 91.
To get back from B to A, the uncorrected course is 270, the
wind direction 135 as before, and a new chart is constructed
with the data.
The direction of the wind is obtained from a weather vane
on the aerodrome, and its velocity from an anemometer. It
must be remembered that at higher altitudes there is a ten-
dency for the velocity of the wind to increase and for its
direction to change.
42
•%>
43
The following table will give an approximate idea of the
prevailing wind velocities in the latitude of the United
States and France. There is a tendency for the direction of
the wind to change in a clockwise direction as you go up in
the lower flying levels, but local conditions vary so much
that it is difficult to give any set rules. You will have to
learn the conditions to be expected in the region in which
you are flying, but you must always be careful to watch for
variations from the ordinary.
Height in Feet I 9"0 | 1300 | 2000 | 2000 ' 5600 | .660.1 | 7000 | 9800
Velocity in
Miles per hoar
Summer
Winter
6.5
10.3
8.4
11.7
10.5
13.2
10.5
14.3
10.5
14.8
11.2
15.2
13.0
18.8
15.9
18.8
16.8
19.2
20.4
22.4
24.4
26.4
Add Westerly
Variation, Sub-
tract Easterly
Variation
After the map course, with allowance for
the wind, is found, it must be corrected,
first for variation, and then for deviation.
When the variation is known, if it is west
it is added to the map course to get the
magnetic course, and subtracted when it is
•east. Figure 13 shows that when the variation is west, or
the magnetic needle points west of north, the angle between
the line of flight and the magnetic meridian is larger than
that between the line of flight and the true north meridian.
The map course is 85 degrees. The variation is 8 degrees
west, so the magnetic course is 93 degrees. If the variation
had been 12 degrees east, the angle between the line of flight
and the magnetic meridian would have been less than that
between the line of flight and the true north meridian, or
the magnetic course would have been only 73 degrees.
The same reasoning applies for deviation
errors, but it must be remembered that the
deviation is different for each direction in
which the machine is pointed, and therefore
must be calculated separately for each case.
44
Changing the
Map Course
to Compass
Course
The following problems illustrate the method usually used
for finding the compass course from the magnetic course.
PROBLEM 1 : The map course, corrected for wind, is
35°. The variation is 10° west. What is the compass course?
Since the variation is west it is added to the map course
to get the magnetic course. This makes the magnetic course
45°. From Table III it is found that when the machine is
pointing in a direction 45° from magnetic north, its compass
is drawn 9° toward the east. Then to get the compass bear-
ing, the deviation must be subtracted from the magnetic
course. Then the compass course is 36°. This means that
when the compass in the machine shows 36°, the plane is
really headed in a 45° line (Mag.). In other words, to fly a
map course of 35° in a locality where the variation is 10°
west, with this particular machine, the compass must
read 36°.
PROBLEM 2: The map course, corrected for wind, is
145°. The variation is 5° west. What is the compass
course?
The variation being west, it is added to the map course, to
get the magnetic course, which becomes 150°.
Table III does not show the deviation for 150°, but it
gives it for 135°, and for 180°. At 135° it is 15° west, and at
180° it is 5° west. In other words, between 135° and 180°,
magnetic, the deviation has changed 10°. We can assume
that the deviation has varied at a uniform rate, or (since
180 — 135 = 45) at a rate of 10/45 or 0.22° per degree change
in magnetic bearing. Since at 150° the magnetic course is
15° more than it is at 135°, the deviation will have changed
15 x 0.22 = 3.3° (It is difficult to read a compass even to
the nearest degree, so fractions of a degree are dropped).
Since the deviation is diminishing from 15° west, at a mag-
netic bearing of 135°, to 5° west, at a magnetic bearing of
45
180°, the deviation at 150° will be 15 — 3 = 12°. As the
deviation is west, it is added to the magnetic course, and the
compass course becomes 150 -f- 12 or 162°. The work may
be neatly arranged as follows :
Map Course 145
Variation 5 West
Magnetic Course 150
Point under 150 at which dev. is known 135 Deviation 15\V
Point above 150 at which dev. is known 180 Deviation 5\Y
Change in deviation between 180 and 135 10
Change in deviation between 135 and 150
(A) (150 — 135) x 10/45 = 3.3
Since the deviation is diminishing from 135 to 180, at 150
it is 15 — 3 = 12 west. Therefore it is added to the magnetic
course and the compass course is 162°.
(The deviation table shows the deviation for each angle of
45 degrees, so statement (A) may always be written :
(Magnetic course — nearest 45 point below it) x (Change in
deviation between nearest 45 degree points above and below
magnetic course in question) /45 = change in deviation.)
PROBLEM 3: Map course, corrected for wind, 340°.
Variation 5 degrees east. Find compass course.
Map Course 340
* Variation 5 East
Magnetic course 335
Point below 335 at which dev. is known 315 Deviation 2W
Point above 335 at which dev. is known' 360 Deviation 10W
Change in deviation between 315 and 360 8 degrees
46
Change in deviation between 315 and 335:
(335 -- 315) x (10 — 2) /45 =
20 x 8/45 = 160/45 = 3.5
The deviation is increasing from 2° west at 315°, to 10°
west at 360°, so at 335° it will be between 2° west and 10°
west, and as the change is 4°, at 335° magnetic, the deviation
is 6° (2 + 4), and since it is west it is added to the magnetic
course and the compass course is 335 plus 6 or 341°.
PROBLEM 4: The map course, corected for wind, is 30°.
The variation is 5° west. Find the compass course.
Map course 30
Variation _5_ W
Magnetic course 35
Point under 35 at which dev. is known 360 Deviation 10W
Point above 35 at which dev. is known 45 Deviation 9E
Change in deviation between 360 and 45 19
(The deviation decreases from 10 W to 0 and then in-
creases to 9 E. Total change is therefore 19 degrees.)
Change in deviation between 360° and 35° :
35 x 19/45 = 14.8 = 15°.
The deviation is decreasing from 10 W at 360 to 0 and
then increases to the east. Therefore the deviation will have
become zero and increased to 5° east by the time a magnetic
course of 35 degrees is reached. (Change from 10° W to 0°
is 10°, and then from 0° to 5° E is 5° more, so the total
change is 15 degrees).
Since the deviation is east, it is subtracted from the mag-
netic course and the compass course becomes 35 — 5 = 30°.
Another method of rinding the Compass
Another Course from the Magnetic Course which
Method does not require the deviation to be figured,
may be used :
47
PROBLEM 5: The map course, corrected for wind, is
150°. The variation is 5° west. Find the compass course.
The magnetic course is 155°. From the Deviation Table
we find the compass course is 150° for a magnetic course of
135° and 185° for a magnetic course of 180°. In other words,
for a change in magnetic course of 180 — 135 =45°, there
is a change of 185 — 150 = 35° in compass course. There-
35
fore there is a change of — = 4/5° in compass course per
45
degree change in magnetic course. From this it follows that
when the magnetic course has changed from 135° to 155°,
or 20°, the compass course will have changed from 150° to
[150° + (20 x 4/5 = 16)] = 166°. Therefore the compass
course is 166°.
If we call : The compass course — "C"
The magnetic course — "M"
The nearest magnetic course in the table be-
low "M"— "A"
The compass course corresponding to "A"-
"B"
The compass course for the nearest magnetic
course above 'M" in the table— "D"
Then:
C = B +
[D — B
-_X(M-A)J
PROBLEM 6: The map course, corrected for wind is
200°. The variation is 10° west. Find the compass course.
"M" is 210; "A" is 180; "B" is 185; "D" is 215.
[215—185 "I
• x(210— 180)
45 J
— 185 + (30/45 x 30) = 185 + 20 = 205°.
The compass course is 205°.
48
It is sometimes necessary to change compass
Changing Corn-bearings to magnetic bearings and magnetic
pass Course bearings to map courses. In aerial sketch-
to Magnetic ing, for instance, one method of getting the
Course bearing of a line is to point the plane along
the line, and then read the compass bearing.
Being a compass bearing, it must be corrected before it is
put on a map.
It is very simple to change magnetic bearings to map
courses. When the variation is west it is added to the map
course to get the magnetic course, and consequently it is
subtracted from the magnetic course to get back to the map
course. Similarly, variations east are added to the magnetic
course to get the map course.
A slightly different method is followed to change from
compass bearings to magnetic bearings than that used to
change from magnetic bearings to compass bearings.
PROBLEM 7: The Compass course is 170°. Find the
magnetic course.
From the table we find that for a magnetic course of 135°,
the compass course is 150° (Deviation 15 W), and for a
magnetic course of 180°, the compass course was 185°
(Deviation 5 W). Or the compass course has changed 35 a
while the magnetic course changed 45°. Therefore the
magnetic course has changed at the rate of 45/35 = iy3°
per degree change in compass course. When the compass
course is 170°, it has changed 20° (170—150), from the last
point at which the magnetic course is known, so therefore
the magnetic course will have changed 20 x \y$ = 27°, from
what it was when the compass course was 150° (135°), or
the magnetic course is 162 degrees, when the compass
course is 170.
49
Using the same abbreviations as on page 48, this state-
ment may be made :
45
M = A +"
f
PROBLEM 8: The compass course is 30. Find the mag-
netic course.
"A" is 0; "B" is 10; "C" is 30; "D" is 36.
[45
-x(30— 10)
3<>-10
M = 0 +
= 0 + (45/26 x 20) = 0 + 35 == 35.
The magnetic course is 35, when the compass course is 30.
An excellent thing for the aviator to do if he has time is to
plot the deviation against the magnetic courses, as shown in
Fig. 14, or to plot compass courses against magnetic
courses, as shown in Fig. 15. The first method is an easy
one to find the deviation at all points, but it is believed that
the latter is better because the compasss is found directly,
and there is no adding or subtracting to be done. It is not
necessary to bother to draw the curves smoothly, because
in the first place there is hot enough data to justify it and in
the second place, a compass cannot be read closer than
1 degree and the straight line table will give results within
1 degree in most cases.
J
MAGNETIC COURSE:
H 5
S«
in
•fl 44 -> i
!
f * * *
ff
if
^
In
f
fa
I\
M
i
fH
::
DEVIAT
WEST
10 5 O
K n
MAGNETIC
a 8
So
M 3
PROBLEMS ON BEARINGS
(Use table on page 41, or charts on page 51)
1. The map course is 150°. Speed of plane 100 m.p.h. Wind is from
the northeast, 40 m.p.h. (a) What is the corrected map course?
(b) What is the speed of flight? Answers, (a) 124°, (b) 102 m.p.h.
2. The map course is 285°. Speed of the plane is 120 m.p.h. Wind is
from the southwest, 30 m.p.h. (a) What is the corrected map
course? (b) What is the speed of flight?
Answers, (a) 273°, (b) 102 m.p.h.
3. The variation is 5° east. Wrhat are the compass courses for the fol-
lowing map courses : (a) 30°? (b) 150°? (c) 300°?
Answers, (a) 24°, (b) 157°, (c) 295°.
4. The variation is 10° west. What are the compass courses for the
following map courses: (a) 40°? (b) 250°? (c) 315°?
Answers, (a) 42°, (b) 256°, (c) 329°.
5. The variation is O°. What are the compass courses for the follow-
ing map courses : (a) 96°? (b) 230°? (c) 197°?
Answers, (a)96°, (b) 221°, (c) 197°.
6. The variation is 5° west. What are the map courses for the follow-
ing compass courses : (a) 330°? (b) 210°? (c) 80°?
Answers, (a) 321°, (b) 212°, (c) 78°.
7. The variation is 8° east. What are the map courses for the follow-
ing compass courses: (a) 285°? (b) 170°? (c) 25°?
Answers, (a) 294°, (b) 169°, (c) 33°.
52
CHAPTER VII
PREPARATION OF MAPS
A REGULAR method should be followed in
Examining a examining a map which is new to you. The
New Map first thing to become familiar with is the
scale. This will give you an idea of the
detail of the information to be expected, the area the map
covers, and enable you to make rapid mental calculations of
the distances between points. If the scale is given graph-
ically, become familiar with the spaces given. If it given in
words and figures or in the natural scale convert it into units
with which you are familiar. Remember, for instance, that
"5 cm. = 1 km." is 1/20,000, which is approximately 3 inches
to the mile.
Next find the contour interval. It is usually printed on
the map ("Contour Interval 20 feet"; "L'Equidistance est
de 5 metres"). If it isn't shown, find the numbers on the
contours and take the difference, if every one is numbered ;
if every fifth one is numbered, divide the difference between
the numbered ones by 5 ; if none are numbered, find the
number of intervals between two places whose elevations
are given, and calculate it. This will give you a relative
idea of the differences in elevation — heights of hills and
depressions of valleys.
Now examine the conventional signs, if a list is shown on
the map. When such a list is given it is usually an indica-
tion that there has been a departure from the usually ac-
cepted standards.
Find which side of the map is north, the position of the
true and magnetic meridians, and the amount of variation.
53
You are now in a position to make an intelligent use of
your map.
If there is time, it will be found a great help to study the
features shown on the map. Pick out the streams and follow
them out. The streams are the framework of the country—
they are put on the map first, and should be looked for first
in forming an idea of the terrain. They show where the low
places are, and then it is easy to imagine the approximate
location of the hill tops and ridges. When the streams,
ridges, and valleys are in mind, it is astonishing how quickly
the features of the ground seem to stand out on the map.
Pick out the towns and villages, and get their names and
locations with respect to each other in mind. The railroads
and highways should be traced out and their relative im-
portance estimated.
If the map is to be used for cross country
Cross Country flying, it will be of small scale. The course
Flying should be marked out on it, with the com-
pass bearings written on the different lines.
It will be found convenient if lines are drawn across the line
of flight at intervals of about 10 miles. The scale will of
course be too small for emergency landing fields to be picked
from the map, so they should be found from maps of larger
scale and marked on the map with the proper conventional
sign. In this connection, remember that smooth, nearly
parallel contours represent flat country, and rough uneven
contours show country which is cut up by little ridges and
valleys, because when a high contour bends toward a low
one, there is a ridge, and where a low contour bends toward
a high one there is a valley. A safe landing may be made
on a slope of about 9 degrees, if the ground is smooth and
flat, and such a place will be preferable to a field which is
nearly level, but cut up with little bumps and depressions.
54
The features used for guides in cross country \\ork are large
woods, lakes, towns, highway intersections with railroads,
highway and railroad intersections with streams, bends in
large streams, and mountains or prominent hills. These
landmarks should be marked with a heavy pencil and the
approximate time they should be passed written near them.
It is well, if color is not used on the map, to color either with
grease pencils or ink, the woods in green, the highways in
red, and the streams blue. Even if nothing else is done, it
will be found a great help to have the streams colored, so
they will not be mistaken for contour lines. A fountain pen
will do for this in an emergency.
The map will usually be too large to be placed in the plane
so it is all visible at once. For this reason it is necessary to
cut it up into convenient-sized squares or rectangles.
The pieces are numbered, a north arrow marked on each,
and the pieces mounted on cardboard or a continuous strip
of cloth. If the first method is used, the cards are arranged
so when the country represented on the first is passed over,
the card is removed and the next in order is found under it
and so forth. If the continuous strip method is used, it is
arranged to roll from one roller to another, and the part with
which you are finished is simply rolled up. It requires con-
siderable practice to use a map cut up in such a manner, so
the arrangement of squares should be carefully made.
If the map is to be used for cooperation with
Cooperation artillery, it will be of large scale (1/20,000
with Artillery or 1/40,000, sometimes even 1/10,000). The
outline of the area to be observed should be
marked out on it, the roads marked in red, the streams in
blue, and the woods in green if they are not already colored.
Fields of peculiar shape will be helpful if they are colored.
55
For work of this ' kind the reference points are fence
corners, bemls in small streams, corners of woods, highway
intersections, small ponds, separate houses, and other small
features which stand out well on the ground and are shown
prominently on the map.
When the map is to be exposed in the plane in wet
weather, a couple of coats of wing dope will make it water-
proof, without producing any visible effect on the paper.
Pencil marks may be made on this surface and erased with-
out injuring the map.
56
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