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Aeronautical  Engineering 

and 

Airplane  Design 

Klemin 


Engineering 
Library 


Aeronautical  Engineering 

and 
Airplane  Design 


Aeronautical  Engineering 


and 


Airplane  Design 


by 


LIEUTENANT  ALEXANDER  KLEMIN 

n 

Air   Service,   Aircraft   Production,    U.  S.  A.,   in   charge   Aeronautical   Research 
Department,  Airplane  Engineering  Department. 

Until  entering  military  service,  in  the  Department  of  Aeronautics,  Massa- 
chusetts Institute  of  Technology  and  Technical  Editor  of 
Aviation  and  Aeronautical  Engineering. 


Based  on  a  series  of  articles  in  Aviation  and  Aeronautical  Engineering  by  Alexander 

Klemin  and  T.  H.  Huff,  S.B.,  chief  aeronautical  engineer  for  the  Standard 

Aircraft    Corporation,  formerly  instructor  in  Aeronautics, 

Massachusetts  Institute  of  Tecimology., 


Published  1918 


Engineering 
Library 


CopyriKlit.  in]  7 

Alexander    Klcniin 

All    KlKlits    1!.-.  r\cii 


'J'he  (ianlnor-MolTat  <'"..  Inc. 
New    York 


PREFACE 


In  submitting  the  series  of  articles  appearing  in  AVIATION  AND 
AERONAUTICAL  ENGINEERING  in  book  form,  only  minor  corrections 
have  been  made. 

No  attempt  has  been  made  for  obvious  reasons  to  include  new 
material  at  hand,  and  under  stress  of  urgent  war  work  no  systematic 
revision  has  been  attempted. 

It  is  felt,  nevertheless,  that  as  the  articles  contained  matter 
mainly  regarding  fundamental  principles,  that  they  will  still  be  of 
assistance,  particularly  to  younger  designers  and  draftsmen,  .while 
they  should  be  of  value  as  a  reference  to  more  experienced  men. 

The  author  has,  unfortunately,  not  had  the  advantage  of  Mr. 
Huff's  valuable  collaboration  in  this  production  in  book  form.  He 
thanks  Mr.  G.  M.  Denkinger,  instructor  in  aeronautics  at  the  Massa- 
chusetts Institute  of  Technology,  and  Mr.  Clarence  D.  Hanscom 
for  valuable  assistance  in  corrections. 


ALEXANDER  KI.EMIN. 


Dayton,  Ohio, 
October,  1918. 


INTRODUCTION 

This  work,  practically  a  course  in  aerodynamics  and  airplane  design,  is  subdivided  into  two  parts:  Part  I, 
Aerodynamical  Theory  and  Data;  Part  II,  Airplane  Design. 

In  PART  I  it  is  proposed  to  deal  briefly  with  the  fundamental  ideas  and  theories  of  aerodynamics  in  a  simple 
yet  comprehensive  manner. 

It  is  important  for  the  aeronautical  engineer  and  for  every  student  of  aerodynamics  to  have  at  his  disposal 
exact  definitions  of  such  terms  as  lift,  drag  or  resistance,  center  of  pressure,  wing  cord,  angle  of  incidence,  and 
other  well  known  expressions. 

Although  the  exact  nature  of  viscosity,  skin  friction,  eddying  or  density  resistance,  stream  line  flow,  turbu- 
lent flow,  the  sustaining  action  of  cambered  wing  surfaces,  and  the  principles  of  comparison  for  forces  on  bodies 
of  varying  dimensions  still  present  many  difficulties,  it  is  hoped  to  give  a  simple  and,  above  all,  practical  sum- 
mary of  these  points.  The  more  difficult  theoretical  demonstrations  will  be  reserved  for  special  articles. 

The  authors  propose  also  to  give  a  brief  description  of  the  chief  aerodynamical  laboratories  and  of  experi- 
mental methods  there  employed.  Without  a  knowledge  of  such  methods,  appreciation,  and  application  of  the 
laboratory  data  available  is  certainly  not  easy. 

Considering  the  comparatively  recent  growth  of  aerodynamics,  the  amount  of  material  now  available  is 
extraordinary.  It  is  unfortunately  scattered  through  a  variety  of  publicatons;  English,  French,  German,  Rus- 
sian and  Italian,  presented  in  varying  ways  and  in  varying  systems  of  units.  Nor  is  all  of  it  entirely  wor.thy 
of  credence. 

In  this  course  it  has  been  attempted  to  reduce  this  material,  particularly  that  of  English  and  French  origin, 
to  one  system  of  presentation  with  forces  measured  in  pounds,  areas  in  square  feet  and  velocities  in  miles  per 
hour  or  feet  per  second,  so  as  to  be  more  readily  applicable  in  American  design ;  to  include  all  the  material  which 
is  trustworthy  and  of  immediate  and  pressing  utility  to  the  designer,  in  carefully  classified  form. 

The  Economic  Laws  of  Flight  will  be  fully  dealt  with,  in  horizontal  and  ascensional  flight.  The  consideration 
of  the  performance  curves  of  a  machine  will  be  particularly  useful  to  those  engineers  and  students  to  whom  the 
subject  is  comparatively  new. 

Throughout,  illustrative  problems  will  be  worked  out  on  important  points,  especially  to  facilitate  comparison 
between  wing  sections. 

PART  II  will  include  a  discussion  of  available  aeronautical  materials,  timber,  steel,  alloys,  rubber,  etc. — 
with  trustworthy  values  for  stresses;  a  variety  of  diagrams  and  scale  drawings  representative  of  modern  design, 
and  a  classification  of  the  most  important  modern  machines,  with  their  main  data. 

At  this  stage  of  the  art,  it  is  impossible  to  say  that  any  method  in  design  is  standard,  but  a  systematic  pro- 
cedure of  design  will  be  fully  developed. 

Particular  stress  is  laid  on  the  evaluation  of  factors  of  safety.  The  dynamic  factor  of  safety,  the  material 
factor  of  safety,  the  worst  loading  possible  in  the  air,  the  worst  possible  shock  on  landing;  nothing  offers  so  many 
possibilities  of  confusion  and  untrust worthiness ;  and  nothing  is  in  more  need  of  definite  and  accurate  statement. 

Complete  strength  calculations  will  be  presented  for  body,  chassis,  wing  girders,  and  controlling  surfaces,  and 
1he  design  of  a  standard  machine  will  be  carried  through,  with  consideration  of  motor  and  propeller  problems, 
weight  distribution  and  balancing. 

Throughout  the  course,  the  most  elementary  mathematics  arc  employed,  and  nothing  beyond  a  knowledge  of 
the  first  mechanical  principles  is  presupposed. 

It  is  hoped,  therefore,  that  the  course  will  be  easily  understood  by  any  engineer  or  student  approaching  the 
scriuis  study  of  the  airplane  for  the  first  time.  At  the  s;ime  time  it  is  felt  that  much  will  be  of  service  even  to 
the  expt  rt  aeronautical  engineer. 


TABLE   OF   CONTENTS 


PART  ONE 

Aerodynamical  Theory  and  Data 

CHAPTER  I 

MODERN  AERODYNAMICAL  LABORATORIES 

Early  Experimental  Aerodynamics — General  Requirements  in  Airplane   Design — Difficulties  of  Full   Scale 

Experiments — Towing  Methods — Wind  Tunnel  Methods — Laboratories  of  the  Wind  Tunnel  Type 15 

CHAPTER  II 

ELEMENTS  OF  AERODYNAMICAL  THEORY 

Liquid,  Fluid  and  Perfect  Fluid — Density  of  Air — Variation  of  Density  of  Air  with  Height — Principle  of 
Relative  Motion — Bernouilli's  Theorem  for  Fluid  Motion — Total  Energy  of  a  Fluid  Applied  to  the  Theory 
of  the  Pitot  Tube — Definition  of  Angle  of  Incidence,  Resultant  Pressure,  Lift,  Drag,  and  Center  of  Pres- 
sure in  a  Plane  or  Cambered  Wing  Section — Definition  of  Lift  and  Drag  Coefficients — Position  of  Center 
of  Pressure  or  Resultant  Vector  of  Forces — Forces  on  a  Flat  Plate  Immersed  in  a  Fluid  and  Normal  to 
the  Direction  of  Motion — Forces  on  Flat  Plates  Inclined  to  the  Wind 23 

CHAPTER  III 

ELEMENTS  OF  AERODYNAMICAL  THEORY — Continued 

Skin  Friction — Viscosity — Coefficients  of  Kinematic  Viscosity — Reynolds'  Number — Prandtl's  Theory  of  the 
Boundary  Layer — Density  Resistance  to  a  Plate  Moving  Edgewise — Total  Skin  Friction;  Dr.  Zahm's 
Experiments — Curves  for  Computaions  with  Dr.  Zahm's  Formula — Turbulent  Flow,  Eddy,  or  Density 
Resistance — Comparison  of  Forces  Acting  Upon  Similar  Bodies;  the  Importance  of  Kinematic  Viscosity 
and  Reynolds'  Number — Stream  Line  Bodies — Energy  Considerations  for  a  Perfect  Fluid  Flowing  Past 
a  Stream  Line  Body — Stream  Line  Bodies  in  a  Viscous  Fluid — Resistance  of  Wires,  Cables,  and  Cylin- 
ders— Fluid  Motion  Around  Wing  Surface.  . -1 

CHAPTER  IV 

FLAT  PLATES.     SIMPLE  PROBLEMS  ON  SUSTENTION   AND  RESISTANCE  OF  WING   SURFACES 

Coefficients  of  Resistance  for  Circular  or  Square  Plates  Normal  to  the  Wind;  Varying  Sizes — Coefficients  for 
Rectangular  Flat  Plates  Normal  to  the  Wind ;  Varying  Aspect  Ratio — Coefficients  for  Flat  Plates  In- 
clined to  the  Wind — Preliminary  Application  of  Data  for  Flat  Plates  in  Rudder  and  Elevator  Design — 
Problems  on  Flat  Plates — General  Considerations  of  Sustaining  Power  and  Resistance  of  Wing  Sections 
— Problem  of  Sustention  and  Resistance  of  Wing  Surface 32 

CHAPTER  V 

COMPARISON  OF  STANDARD  WING  SECTIONS 

Representative  Wing  Sections  Selected — Complete  Data    Presented — Points  of  Interest  in  Considering  a  Wing 

Section — Consideration  of  a  Few  Sections  in  Common  Use 37 

CHAPTER  VI 
EFFECTS  OF  VARIATIONS  IN  PROFILE  AND  PLAN  FORM  OF  WING  SECTIONS 

Effect  of  Variation  of  Position  of  Maximum  Ordinate  in  a  Wing  Section  of  Plane  Lower  Surface,  and  Con- 
stant Camber  0.100  for  Upper  Surface — Behavior  of  Wings  with  Reverse  Curvature  at  the  Trailing 
Edgi — Effect  of  Thickening  the  Leading  Edge  of  a  Wing — Effects  of  Thickening  Wing  Towards  the 
Trailing  Edge — "  Phillips  Entry  '  —Effects  of  Varying  Aspect  Ratio — Choice  of  Aspect  Ratio — Effects 
of  Raking  the  Plan  Form  of  a  Wing-Swept  Back  Wings — Negative  Wings  Tips  of  Swept  Back  Wings; 
Effect  on  Longitudinal  Stability 41 

9 


10  AERONAUTICAL    ENGINE BRING 


CHAPTER  VII 
STUDY  OP  PRESSURE  DISTRIBUTION 

Methods  of  Obtaining  Pressure  Distribution — Comparison  of  Results  from  Pressure  Distribution  and  from 
Force  Experiments — Effect  of  Variation  of  Speed  and  Scale  on  Lift  and  Drag  Coefficients — Distribution 
of  Pressure  at  Median  Cross  Section  of  Various  Surfaces — Distribution  of  Pressure  Over  the  Em  in: 
Surface  of  a  Wing;  Lateral  Flow,  Its  Bearing  on  Aspect  Ratio — Distribution  of  Pressure  Over  the 
Entire  Surface  of  Wing  and  Curves  of  Equi-Pressure — Relative  Importance  and  Interdependence  of 
Two  Surfaces — Distribution  of  Pressure;  the  Principle  of  the  Dipping  Front  Edge;  "Why  a  Wing  Sec- 
tion Is  Advantageous  as  Compared  with  a  Flat  Plate 46 

CHAPTER  VIII 
BIPLANE  COMBINATIONS 

<  h-tliogonal  Biplane  Arrangement)  with  Varying  Gap  Between  Planes — Distribution  of  Forces  Between  the 
Upper  and  Lower  Wings  of  a  Biplane — Distinction  Between  Static  and  Dynamic  Stability — Stable 
Biplane  Arrangements — Results  of  Experiments  on  Biplanes  with  Staler  and  Decalage — Comparison 
of  Aerodynamical  Losses  Involved  in  Obtaining  Stability  by  Reversed  Curvature  Wings  and  by  Stag- 
ger; Decalage  Combinations — Aerodynamic  Comparison  Between  the  Monoplane  and  the  Biplane' M 

CHAPTER  IX 
TKIPLANE  COMBIN ATIONS— USES  OF  NEGATIVE  TAIL  SURFXCES 

Interference  in  Triplanes — Some  Considerations  for  Tri  planes — Triplanes  for  Fast  Speed  Scouts — Use  of 
Negative  Tail  Surfaces— Effect  of  Influence  of  the  Wash  of  the  Wings  on  Stabilizer  Surface— Problem 
on  the  Design  of  Tail  Surfaces  to  Give  Longitudinal  Static  Stability f>7 

CHAPTER  X 

RESISTANCE  OF  VARIOUS  AIRPI. \.\i-:  PAUTS 

Airplane  Bodies  from  the  Aerodynamical  Point  of  View — Tractor  Bodies — Pusher  Bodies — Radiator  Resist- 
ance— Resistance  of  Fittings — Resistance  of  Airplane  Wheels — Resistance  of  Wires  and  Methods  of  Plot- 
ting — Resistance  of  Stationary  Smooth  Wires — Resistance  of  Vibrating  Wires — Resistance  of  Stranded 
Wires — Resistance  of  Wires  Placed  Behind  One  Another — Resistance  of  Inclined  Wires — Suggestions 
for  Stream-Lining  Wires — Resistance  of  Miscellaneous  Objects 61 

CHAPTER  XI 

RESISTANCE  AND  COMPARATIVE   MERITS  OK  AIUPI.AM:  STRUTS 

Considerations  of  Comparative  Merit  of  Strut  Sections — Strut  Sections  Developed  bv  Oirilvie — Another 
Series  of  Struts  Tested  at  the  N.  P.  L.— Tests  on  Struts,  Length  to  Width  Varied— Two  Eiffel  Struts— 
Effect  of  Length  of  Struts— Resistance  of  Inclined  Struts— The  Effect  of  Changing  the  DV  Product  for 
Struts  65 

CHAPTER  XII 
RESISTANCE  AND  PERFORM  AM  i. 

Nomenclature — Structural  and  Wing  Resistance  for  British  B.E.2 — Theoretical  Laws  for  Minimum  Thrust 
and  Minimum  Horsepower — Effective  or  Propeller  Horsepower  Available  Curve — Minimum  and  Maximum 
Sp.-ed;  Maximum  Excess  Power;  Best  Climb;  Descent — The  Two  Regions  of  Control;  Control  by  Throt- 
tling— Variations  in  Propeller  Horsepower  Curves — Angle  of  Glide 69 

CHAPTER  X11I 
RESISTANCE  COMPUTATIONS — PRELIMINARY   WIM;  SEI.EITIONS 

Example  of  Estimate  for  Parasite  Resistance  for  a  British  Machine — Examples  of  Parasite  Resistance  Distri- 
bution in  School  Machines — Parasite  Resistance  Coefficient  for  a  Sturtevant  Seaplane — Allowance  for 
Slip  Stream — Preliminary  Estimates  for  Parasite  Resistance — Preliminary  Selection  of  Wini:  Section 
and  Area. .  7- 


PART  TWO 

Airplane  Design 


OHAPTEB  1 

<'I.\.->IFI<   \TloN    <IK    M\IN     D\T\     FOR     Mol.lUN     AlRIM.\MS:        I'x  MIMED       LAND       Rl.l  nN  N  MSS  \  \  <  I        .\I\CII1M.S;       LAND 

TRAIMM;   MUIIIM- 

The  Army  < 'lassitieation  I'liarnieil  Land  Reconnaissance  Machine  Anahsisof  Main  Data  for  R  pr.-seiita- 
tive  I'narrned  Reconnaissance  Biplanes  Moiv  Than  L'.'iOO  Pounds  (iross  Weight  Average  Values  for  Ma- 
chines More  Than  'J.'iJHi  Pounds  in  Weight  Primary  and  Advanced  Training  Ail-planes  Data  for  a 
Typical  School  Machine  Less  Than  2(KK)  Pounds  in  Weight-  Photographs  and  Drawings 77 


AND    AIRPLANE    DESIGN  H 

CHAPTER  II 
LAND  PURSUIT  MACHINE;  LAND  GUN-CARRYING   MACHINE;    TWIN-ENGINED    ALL-ROUND    MACHINE 

The  High  Speed  Scout  or  Land  Pursuit  Type — Data  for  Pursuit  Type,  100  Horsepower  Engine — Data  for 
More  Powerful  Pursuit  Types — Trend  of  Design  in  the  Pursuit  Type — Guns  on  the  Pursuit  Type — 
Land  Gun-Carrying  Machines — Twin-Engine  Machines 83 

CHAPTER  III 

ESTIMATES  OF  WEIGHT  DISTRIBUTION 

Difficulties  of  the  Subject — Weight  Schedules  for  a  Machine  of  the  Unarmed  Tractor  Reconnaissance  Type 
(Two-Seater)  More  Than  2500  Pounds  in  Weight — Summary  for  Weight  Distribution  for  Standard  H-3 
—Percentage  Table  for  Machines  About  2500  Pounds — Weight  Distribution  for  a  Typical  School  Machine 
— Summary  of  Weight  Distribution  for  JN-4-B — Empirical  Formulas  and  Values  for  Weight  Estimates — 
Some  General  Considerations  on  Distribution  of  Weight  and  Useful  Load , 87 

CHAPTER  IV 

ENGINE  AND  RADIATOR  DATA 

General  Requirements  of  Aeronautical  Engines — Weights  for  Radiators  and  Cooling  Water — Practical  Rules 
for  Cooling  Surface  for  Radiator  of  Honeycomb  Type — Position  and  Resistance  of  a  Radiator — Prac- 
tical Construction  of  Radiators 91 

CHAPTER  V 

MATERIALS  IN  AIRPLANE  CONSTRUCTION 

Special  Utility  of  Wood  in  Airplane  Construction — Weight  of  Wood — Specific  Gravity  and  Weights  of 
Woods — Factors  in  the  Mechanical  Properties  of  Woods — Tensile  Strength — Compressive  Strength — 
Crashing  Across  the  Grain — Strength  in  Bending — Knots — The  Effect  of  Moisture  on  Strength  of  Wood 
—Time  Factor  in  Tests  of  Timber — Difficulties  of  Wood  Construction  in  Airplanes — Strength  Values  for 
Timber — Wires  and  Cables — Properties  of  Metals — Strength  and  Weights  for  Wire  and  Cables — Wire, 
Strand,  or  Cord — Turnbuckles — Strength  of  Steel;  Pounds  per  Square  Inch — Strength  of  Steel  Castings; 
Well  Annealed ;  Pounds  per  Square  Inch — Strength  of  Special  Steel  Alloys ;  Pounds  per  Square  Inch — 
Strength  of  Copper,  Aluminum,  and  Various  Alloys ;  Pounds  per  Square  Inch — Strength  and  Weight 
of  Mild  Steel  Rivets  and  Pins — United  States  Standard  Bolts  and  Nuts — Airplane  Fabrics — Some  Repre- 
sentative Specifications;  Strength  and  Weight  Figures — Wing  Dope  and  Varnish 95 

CHAPTER  VI 
WORST  DYNAMIC  LOADS;  FACTORS  OP  SAFETY 

Conditions  Under  Which  Heavy  Loads  Come  on  an  Airplane:  (1)  Flattening  Out  After  a  Steep  Dive;  (2) 
Loading  in  Heavy  Banking;  (3)  Loading  in  Looping;  (4)  Stresses  Due  to  Gusts — Limiting  Velocity  for 
a  Sheer  Vertical  Dive — Worst  Loads  on  Landing 102 

CHAPTER  VII 

PRELIMINARY  DESIGN  OP  SECONDARY  TRAINING  MACHINE 
Preliminary  Weight  Estimates — Choice  of  Wing  and  Area — Position  of  Center  of  Gravity 106 

CHAPTER  VIII 
GENERAL  PRINCIPLES  OP  CHASSIS  DESIGN 

General  Proportions — Chassis  Height — Location  of  Chassis  with  Respect  to  C.  G. — Stresses  and  Structural 

Considerations — Shock  Absorbers — Types  of  Chassis — Brakes  and  Braking 109 

CHAPTER  IX 
TYPE  SKETCHES  OF  SECONDARY  TRAINING  MACHINE — GENERAL  PRINCIPLES  OP  BODY  DESIGN 

General  Requirements  in  Body  Design:  (1)  Stream-Line  Form;  (2)  Fin  Area  of  Body ;  (3)  Length  of  Body ; 
(4)  Provision  for  Pilot  and  Passenger ;  (5)  Engine  Installation ;  (6)  Gasoline  Tanks;  (7)  Engine  Foun- 
dation; (8)  Engine  Must  Be  Secured  Against  Weaving;  (9)  Strength  of  Body — Formulas  for  Spruce 
Compression  Members — Body  Stress  Diagrams — Army  Specifications  1000,  1001,  and  1002 — Army  Speci- 
fication 1003 — Another  Suggested  Method — A  Detailed  Example  of  Stress  Diagram 114 

CHAPTER  X 
Computation  of  Strength  Members  and  General  Layout  oi  Body  Cable  Terminals 119 

CHAPTER  XI 
WING  STRUCTURE  ANALYSIS  FOR  BIPLANES 

Distribution  Between  Planes — Spacing  of  Wing  Spars;  Limiting  Angles  of  Incidence — Running  Loads — Reso- 
lution of  Forces  in  Planes  of  Wing  Trussing  and  of  Wings,  and  in  Plane  of  Spar  Web — Different 
Methods  Employed  in  Stress  Diagrams  for  Lift  Truss — Bending  -Moment  Diagrams:  Theorem  of  Three 
Moments — Working  Out,  of  Bending  Moment  and  Shear  Diagrams  for  Upper  Rear  at  0  Degree 122 


12  AERONAUTICAL    ENGINEERING 

CHAPTER  XII 
Wis<;   STRICTI  KK   ANALYSIS   KOU   BUM. AM  > 

Reactions  in  Plain-  of  Lift  Truss  Due  to  I'pper  Rear  Spar  at  0  Degree  Reactions  in  Plane  of  Lift  Truss  Due 
to  Lower  Rear  Spar  at  0  Degree — Stress  Diagram  for  Rear  Lift  Truss  at  0  Degree— Stress  Diagram  I'm- 
Internal  l']>per  Wing  Hraeing  at  0  Degree — Computation*  for  J)imensions  of  Rear  Upper  Spar — A 
Complete  Example  of  Wing  Analysis  Arrangement — Computations  for  Shear  in  Spars. 

APPENDIX 

NOTES  ON  AERIAL  Pum-Ki.i.Kits 

Constant  Ineidence  Method— Value  of  Angle  of  Attack  — Efficiency  of  Elemental  Strip,  and  Curve  of  Effi- 
ciencies  Propeller  Diagrams— Ideal  Curves — Determination  of  Scale*— Computation  of  Thrust— Load 

Grading   Curve Pressure    per    Sq.    Ft.    Curve — Number     of     Mlades — Interferenee     Construction     and 

Stivngth    of    Wade—  Materials   and    Stresses      Eiffel's  Experiments— Summary  of  IVoeedure  in   Design..    l:!l 


Part  I 
Aerodynamical  Theory  and  Data 


M.  KIFKKL1N  HISLATKST  AERODYNAMICAL  LABORATORY 


Chapter  I 

Modern  Aeronautical  Laboratories 


Early  Experimental  Aerodynamics 

Aeronautics  as  a  whole  anil  aviation,  the  science  of  the 
heavier  than  air  machine,  has  from  its  earliest  conception, 
been  an  experimental  art.  When  Professor  Langley  in  1887 
started  his  experiments  on  an  extended  scale  for  determining 
the  possibility  of,  and  the  conditions  for,  transporting  in  the 
air  a  body  whose  specific  gravity  is  greater  than  that  of  air, 


measuring  these  forces  were  designed  with  the  intention  of 
correcting  the  errors  which  had  rendered  so  untrustworthy  the 
results  of  their  predecessors. 

During  the  winter  of  1901-1902  their  investigations  included 
some  hundred  different  surfaces  of  which  about  half  have 
been  tabulated  and  the  results  used  in  their  subsequent  work. 
Experiments  were  made  on  the  effect  of  varying  aspect  ratio, 
curvature,  camber,  and  the  variation  of  the  position  of  the 


Fin.  1.    WHIRLING  Ami  USED  BY  MESSRS.  VICKERS  IN  TESTING  PROPELLERS 


he  had  before  him  papers  by  such  scientists  as  Gay-Lussac  and 
Xavicr,  proving  conclusively  that  mechanical  flight  WHS  im- 
possible. 

Langley  was  not  easily  discouraged  and  by  a  carefully 
conducted  series  of  experiments  carried  on  under  very  ad- 
verse conditions,  he  was  able  to  build  a  machine  which  though 
unsuccessful  in  its  flight  in  his  day.  due  to  faulty  mechanism 
in  the  launching  device,  has  since  been  flown  under  its  own 
power  b\  Glenn  Curtiss  in  1914,  at  Haininondsport,  N.  Y., — 
possibly  with  some  alterations. 

At  the  time  the  Wrights  took  up  the  subject  in  189C,  there 
were  but  few  aerodynamical  works  of  interest  or  value  in  ex- 
istence. They  were  dependent  upon  the  meager  experiments 
and  tables  of  Lilienthal  and  Duchemin  and  the  work  of  Lang- 
ley  which  seemed  to  verify  Duchemiivs  formula.  After  spend- 
ing two  years  experimenting  upon  these  figures  of  Lilienthal 
and  Dnchemin,  the  Wrights  came  to  the  conclusion  that  the 
tables  were  so  much  in  error  as  to  be  of  no  practical  value  in 
airplane  design. 

In  1901  the  Wrights  designed  and  built  a  small  "  Wind- 
Tunnel  "  in  which  they  could  carry  on  systematic  investiga- 
tions on  the  pressure  produced  by  various  surfaces  when  pre- 
sented to  the  air  at  different  angles.  The  instruments  used  in 


maximum  ordinate  of  the  wing  section  from  the  leading  edge. 
Thick  and  thin  surfaces  were  tested  to  determine  the  effect  of 
thickness.  The  effect  of  superposing  the  surfaces,  as  well 
as  placing  one  behind  the  other,  were  measured  and  what 
was  of  even  greater  interest,  the  first  measurements  of  center 
of  pressure  motion  on  curved  surfaces  at  carrying  angles  were 
tabulated  by  them.  As  a  direct  result  of  their  laboratory  ex- 
periments and  the  development  of  a  system  of  control,  worked 
out  in  their  earlier  gliding  flights,  they  were  able  to  build  the 
first  power  driven  airplane. 

To  demonstrate  that  the  United  States  deserved  a  right  to 
leadership  in  aviation  in  the  earlier  years,  one  need  but  men- 
tion other  names,  such  as  those  of  Octave  Chanute  and  Dr. 
Zalun.  The  latter,  through  the  efforts  of  Hugo  Matthul- 
lath,  was  provided  with  an  aerodynamical  laboratory  which 
was  in  its  day  the  most  perfect  of  its  kind:  and  although  the 
experiments  extended  over  a  few  years  only,  the  results  of  Dr. 
Zahni's  labors  were  exceedingly  valuable. 

General  Requirements  in  Airplane  Design 

As  is  the  case  in  ship  building,  a  suitable  machine  for  every 
purpose  cannot  be  developed  and  there  must  be  a  special  type 


15 


AERODYNAMICAL  THEORY  AND  DATA 


with  specific  qualities  in  slow  speed,  high  speed,  weight,  arma- 
ment and  defense.  Some  of  these  factors  arc  directly  opposed 
to  others.  For  example,  the  ideal  machine  for  the  regulation 
of  artillery  fire,  would  be  able  to  remain  immovable  or  circle 
about  very  slowly  above  one  point.  The  "  chaser  "  or  machine 
used  to  rid  the  air  of  the  enemy's  planes  should  be  the  fastest 
possible.  With  the  comparatively  narrow  range  of  speed  pos- 
Mblc  in  mi  iiirplane  one  can  see  the  nselessncss  of  MM  Mitrmpt 
to  combine  these  two  types  in  one  machine.  On  the  other  hand 
from  the  productive  side,  it  is  impracticable  to  increase  the 
number  of  types  indefinitely,  for  this  would  call  for  an  enor- 
mous outlay  in  machinery  and  increase  in  personnel.  A  com- 


K!<;.  2.  FIRST  PLATFORM  EQUIPPED  FOR  TRIAL  AT  AEROTECHNIC 

IXSTITfTK  OF    S.UXT-Cvi: 

promise  has  therefore  been  made,  with  the  selection  of  some 
four  master  types  of  airplanes  which  may  lie  classed  accord- 
ing to  their  military  uses: 

1.  THE  STRATEGIC  SCOUT.    A  slow  endurance  machine  for 
use  on  long  raids  into  the  enemy's  country,  for  mapping  and 
photographic  work. 

2.  THE  HIGH  SPEED  SCOUT.     For  tactical  re. -om .-n-sanee 
and  use  over  the  lines,  and  capable  of  out-climbing  and  out 
Hying  the  enemy. 

3.  Fniimxc  OR  BATTLEPLANE.     Armed  and  armored,  for 
driving  off  the  enemy's  scouts  and  protecting  the  fourth  dm. 

4.  BOMB  DKOPPHIS  m:  WKU;HT  CARRIERS.     For  use  in  de- 
-t roving   small    bridges,    railway--,    etc..    depending    for    their 
protection  upon  the  battleplane. 

In  order  to  design  and  build  machines  to  meet  such  quali- 
fications the  designer  must  give  up  the  old  hapha/.ard  method- 
of  building  first,  and  then  determining  (lie  performance.  11, 
must  go  about  the  design  in  a  thorough  and  scientific  manner 
in  order  to  hope  to  come  within  reasonable  limits  of  his  speci- 
fication. 

The  most  important  items  in  the  performance  of  present  ..lay 
machines  are:  their  weight,  their  rate  of  climb,  high  anil  low 
-peed-,  aii'.'le  (.1    L'lidc,  propeller  ctn'ciencv,  and  endurance  at 
•'meal    --peed    for    various    loading.      These   depend    on    a 
il    manipulation    of   aerodynamical    data,    including    the 
lift    ami    rcM-tancc   of   the   main    plane*    and    control    sin •: 
the    resistance    of    stnii  wheel-,    radiators    and    ap- 

pendages, the  distribution  of  loads  <>n  surfaces,  nnd  different 
eiiiiitiiiiHlinii-  of  surfaces.  On  the  ctlVet-  of  (be  various  -up 
porting,  control  and  (in  surface-,  and  on  the  summation  of  all 
aerodynamical  forces  depend  not  onlv  the  performance,  but 
OntrollabilitV,  factor  of  -aletv.  and  -lability  of  the  :m 


plane.     To  produce  a  desired  type  the  designer  must   bear  in 
mind  every  factor. 

The  desired  type  can  be  obtained  by  the  "cut  and  try" 
process  on  the  full  size  machine.  This  experimental  flying 
is.  however,  a  dangerous  and  costly,  method  that  has  led  to 
many  an  unfortunate  accident. 

Difficulties    of    Full    Scale    Experiments 

The  real  worth  of  full  scale  experiments  depends  on  the 
delicacy  and  precision  of  the  recording  instruments,  (!.. 
pertness  of  the  pilot  and  the  interpreter  of  the  recorded  data. 
The  chief  objections,  other  than  that  of  danger  to  the  pilot,  are 
the  great  variations  in  atmospheric  conditions  and  therefore 
the  unavoidable  delays  in  tests,  the  inability  to  repeat  the  trials 
under  exactly  the  same  conditions,  the  necessarily  short  time 
allowable  for  observation  and  the  unavoidable  introductions  of 
many  variables,  when  but  a  slight  change  is  made  in  one  part 
of  the  design.  It  is  this  inability  to  discriminate  among  the 
possible  causes  of  behavior  of  the  machine  that  may  lead  to  a 
ma/e  of  conllicling  results. 

There  is  a  place,  nevertheless,  and  a  very  important  one  for 
full  si/eil  experimental  flying — that  the  machine  may  be  tuned 
up  and  minor  adjustments  mad"  for  ea-e  of  control  and  steadi- 
under  actual  llyini.'  conditions.  Such  work,  however, 
-hould  not  be  undertaken  until  the  safety  of  the  pilot  is  rea 
-oiiably  assured. 

Towing  Methods 

The  most  natural  and  logical  thing  to  do  with  model  air 
planes  would  be  to  tow  them  through  s|jl]  air  and  record  the 
forces  and  moments  to  which  they  are  subjected.  This  is  not 
SO  simple  an  arrangement  as  in  marine  work.  The  airplane 
is  free  to  move  along  the  three  axes  in  space  and  around  an\ 
of  the  same,  which  introduces  complications  in  the  recording 
mechanism  that  are  most  dillicult  to  overcome.  Very  much 
higher  speeds  are  rei|uired  in  aeronautical  work  nnd  this  in- 
creases the  length  of  track  for  testing  prohibitively  or  de- 
creases the  ti f  experimental  observation  to  such  an  extent 

as  to  spoil  the  precision  of  the  results. 

The  principal  objection  to  towed  model  tli'jht  is  the  inability 
to  obtain  still  air,  as  even  in  a  closed  room  eddies  are  con- 
stantly present,  which  are  impossible  of  measurement:  this 
may  be  observed  by  making  apparently  calm  air  visible  by  the 
introduction  of  smoke,  li'adiation  of  heat  from  the  walls  is 
apt  to  cause  such  eddy  making  to  a  verv  marked  degree. 

In  a   niea-nre  the  dillicullies  of  rectilinear-motion   are  over 
come  by  replacing  it  by  rotation  about  a  fixed  axis:  but  here 
the  radius  mu-i  be  relatively  large  and  the  building  necessarily 
of  similar  great  dimensions.     The  rotation  is  not  wholly  com 
parable  with  translation  since  along  the  transverse  axes  of  the 
body,  under  test,  the  different   parts  have  not  the  same  relative 
velocity  and  some  compromise  is  necessary   due1   to  this  differ 
enee  in  radial  length.     Centrifugal  force  is  present   which  must 
be  overcome  by  the  measuring  instrument,  as  well  as  the  dis 
turbance  -el  up  in  the  air  by  so  large  an  object  as  the  whirlim: 
arm  passing  the  same  point  a  number  of  t:1 

The  whirlim:  arm  used  by  Mc-si>.  Yickers.  Ltd..  of  F.iiL'hind. 
in  then  experimental  work  is  illustrated  in  Fig.  1. 

\\  UK!  Tunnel  Methodi 

If  we  arc  willing  to  accept   the  doctrine  of  relative  motioi 
then   the   resultant    force  on   a   solid   with   a   uniform   motion 
through  still  air.  is  the  same  as  that   for  an   immovable  solid 


AERODYNAMICAL  THEORY  AND  DATA 


17 


upon  which  a  constant  current  of  air  impinges.  A  "  Wind 
Tunnel "  test,  where  a  steady  current  of  air  impinges  on  a 
model  at  rest,  should  therefore  give  the  same  results  as  a  tow- 
ing test.  Differences  would  be  due  to  experimental  errors  and 
not  to  a  difference  in  principle. 

In  the  towing  method,  the  influence  of  the  mounting  stage 
and  unsteadiness  of  the  air  introduce  errors.  In  the  wind 
tunnel,  there  may  be  slightly  non-uniform  flow,  disturbances 
due  to  the  sides  of  the  tunnel,  etc.  Wind  tunnel  work,  how- 
ever, has  proved  far  superior  to  the  towing  method,  which  it 
has  almost  entirely  replaced  and  it  has  now  been  developed  to 
a  high  degree  of  precision  and  usefulness. 

From  wind  tunnel  tests,  the  engineer  may  obtain  data  for 
the  "balancing"  up  of  an  airplane — the  adjustment  of  the 
center  of  gravity  with  reference  to  the  air  forces,  the  loading 
on  his  wing  and  control  surfaces,  the  resistance  of  the  body  and 
appendages,  and  other  useful  information.  It  will  be  scarcely 
disputed  that  such  tests  are  of  immediate  commercial  value  to 
the  practical  designer. 

Laboratories  of  the  Wind  Tunnel  Type 

The  Institut  Aerotechnique  de  I'Universite  de  Paris,  under 
the  directorship  of  M.  Maurain  and  M.  Toussaint,  situated  at 
St.  Cyr,  some  ten  miles  out  of  Paris,  is  devoted,  for  the  most 
part,  to  experiments  on  full  size  surfaces  and  aeroplanes. 
Covering  some  eighteen  acres  of  land,  a  splendid  opportunity 
is  offered  for  ample  buildings,  as  well  as  the  seven-eighths  of  a 
mile  railway  track  used  for  experimental  work. 

The  main  building  with  a  large  central  hall  is  surrounded  on 
three  sides  with  work  shops,  laboratories  and  a  power  station. 
Within  the  hall  is  installed  the  experimental  apparatus  directly 
connected  with  aviation.  Here  there  are  several  wind  tunnels 
of  different  dimensions  and  wind  speed,  arranged  for  the  test- 
ing of  scale  models  and  appendages,  apparatus  similar  to 
Colonel  Renard's  for  the  investigation  of  stability  and  proper 
propeller  testing  apparatus.  A  motor  testing  plant  for  endur- 
ance and  economy  of  aeronautical  motors,  instruments  for 
measuring  the  propeller  torque  for  various  rotational  speeds 
at  a  fixed  point  and  the  testing  of  propellers  at  rupturing 
speeds  are  also  included. 

In  the  chemical  laboratory  investigations  on  balloon  fabrics 
and  gases  are  undertaken  with  special  reference  to  their  manu- 
facture and  purification.  The  physical  laboratories  are  de- 
voted to  the  production  of  instruments  for  aeronautical  pur- 
poses, both  experimental  and  applied.  Work  shops  are  at  one 
end  and  an  individual  power  station  supplies  energy  and  light 
tn  the  Institute  and  experimental  departments. 

In  a  separate  building,  covering  a  quarter  of  an  acre,  is 
housed  a  "  \vhirling-ann  "  some  50  feet  in  radius,  used  prin- 
cipally for  the  calibration  of  instruments.  It  is,  however,  not 
as  popular  as  the  track  and  wind  tunnel  experimental  ap- 
paratus. The  out-door  track  proper  is  of  standard  -rage, 
seven-eighths  of  a  mile  long,  level  for  the  part  over  which  ex- 
perimental data  is  recorded,  but  rising  slightly  for  some 
distance  at  either  end  to  facilitate  the  starting  and  stopping 
of  the  five-ton  electric  car,  upon  which  the  surface,  full  size 
airplane  or  propeller  is  mounted  and  carried. 

Four  cars,  each  rigged  for  one  type  of  experiment,  are  con- 
sidered necessary.  Car  number  one  measures  the  horizontal  and 
vertical  components  of  the  resultant  air  force,  as  well  as  the 
center  of  pressure  for  various  angles  of  incidence  of  the  sur- 
face to  the  wind :  two  and  three  are  for  large  and  small  pro- 
pellers in  connection  with  dirigible  and  airplane  work;  and 
number  four  is  especially  equipped  for  the  measurement  of 


the  resistance  of  appendages.  The  carriages  are  equipped  with 
appropriate  measuring  instruments  of  the  recording  type, 
readings  being  recorded  simultaneously  as  the  car  moves  over 
the  track.  The  velocity  of  the  air  is  recorded  by  means  of  a 
calibrated  venturi  tube  anemometer. 

The  testing  apparatus  is  of  such  size  that  a  full  scale  air- 
plane can  be  mounted  and  subjected  to  test  for  lift  and 
resistance  and  static  longitudinal  stability.  In  order  to  accom- 
modate such  large  forces  as  are  encountered  in  full  scale  work, 
the  instruments  are  of  considerable  size;  this  has  the  disad- 
vantage of  destroying  much  of  the  delicacy  of  the  measure- 
ment. The  results  obtained  are  said  to  be  in  error  by  about 
five  per  cent  in  lift  and  about  ten  or  fifteen  per  cent  in  re- 


! 


FIG.  3.    PLAN  OF  EIFFEL'S  AERODYNAMICAL  LABORATORY 

sistance.  The  real  value  of  experimental  work  of  this  nature 
and  its  comparison  with  results  obtained  from  model  tests  is 
as  yet  not  fully  determined. 

Eiffel  in  liis  laboratory  at  Auteuil,  in  an  investigation  to 
ascertain  the  aerodynamical  effect  produced  by  the  car,  sit- 
uated as  it  was  directly  beneath  the  surface  under  test,  reports 
that  when  correction  is  made  for  the  presence  of  the  carriage, 
agreement  with  wind  tunnel  results  is  fairly  obtained.  He  also 
notes  that  modification  is  being  made  at  St.  Cyr  in  the  position 
of  the  surface  as  mounted  on  the  car  in  order  to  reduce  the 
interference  as  much  as  possible.  A  similar  comparative  test 
made  at  the  National  Physical  Laboratory,  England,  on  wind 
tunnel  models  shows  good  agreement  with  the  lift  coefficients, 
but  the  resistance  coefficient  in  the  full  size  experiment  is  still 
unsatisfactory. 

The  Laboratoire  ASrodynamique  Eiffel,  supported  by  the 
personal  means  of,  and  directed  by  G.  Eiffel,  is  of  the  most 
elaborate  in  design.  Devoted  entirely  to  wind  tunnel  experi- 
ments, it  is  completely  housed  in  a  beautiful  white  stone  build- 
ing, fronted  by  a  formal  garden.  The  building  proper,  two 
stories  in  height,  is  100  by  40  feet. 

As  may  be  seen  by  the  accompanying  photographs,  the  lab- 
oratory room  is  rectangular  in  shape,  with  a  large  and  small 
wind  tunnel  side  by  side,  occupying  the  central  space  and 
suspended  mid-way  from  floor  to  ceiling.  The  position  of  the 
tunnels  permits  the  free  circulation  of  the  air  in  the  room. 
The  wind  tunnels  are  of  similar  character,  one  being  of  smaller 
working  diameter  than  the  other.  They  each  consist  of  a  bell- 
shaped  collector,  a  large  laterally  air-tight  experimental  cham- 
ber, used  for  both  the  large  and  small  tunnel,  and  independent 
expanding  trunks  leading  from  the  experimental  chamber  to 
the  individual  suction  blowers.  The  air  is  drawn  from  the 
large  surrounding  room  or  hangar  into  the  bell  collector. 


AERODYNAMICAL    THEORY    AND    D  A  T  \ 


through  a  honey-comb  balHe  to  straighten  the  tlow,  then  across 
the  experimental  chamber  into  the  expanding  trunk  where  it 
passes  through  the  suction  Mower  and  is  discharged  at  low 
velocity,  bark  into  the  room. 

M.  Eiffel's  characteristic  variant  is  his  hermetic  experi- 
mental chamber.  When  first  interested  in  experimental  aero- 
nautics, lie  experienced  dillicnlty,  due  to  interference  of  How 
around  his  models  caused  by  the  walls  of  the  closed  tunnel. 
In  order  to  avoid  a  tunnel  of  excess  size  and  still  not  reduce  his 
model  dimensions,  the  walls  were  removed  for  some  distance 
and  replaced  by  an  air-tight  chamber  enclosing  the  stream  of 
air.  The  pressure  in  the  hermetic  room  is  necessarily  that  of 
the  air  stream  it  contains,  so  that  a  cylinder  of  air  traverses 


obstructions  1(1  incteis.  33  lect.  in  length,  -)  mclci-.  111.! 
in  width  and  5  meters,  16.4  feet,  in  height.  A  rail  supporting 
a  sliding  floor  carries  the  observer  anil  weighing  mechanism 
above  and  clear  of  the  air  stream.  A  second  observer  on  the 
floor  is  required  to  regulate  the  wind  and  adjust  the  model 
during  a  test.  The  two  tunnels  are  of  course  so  arranged  thai 
the  one  not  in  use  may  be  blocked  off  with  air-tight  wall  plates 
so  preserving  the  low  pressure  in  the  experimental  chamber. 
In  order  to  avoid  the  possible  physical  discomfiture  often  a.- 
ciimpanying  sudden  changes  in  pressure,  an  air-lock  is  pro- 
vided for  passage  into  or  out  of  the  experimental  chamln 

The  models  are  mounted  upon  especially  designed  standards 
or  measuring  instruments,  such  a-  a   lai'.-e  and   small  ;\>  • 


FIG.  4.    LONGITUDINAL  SECTION  OF  THE  LARGK  WIND  TUNNEL  IN  Kinn.'s  I..U:C>I!.\T<>I:Y 


the  chamber  in  parallel  stream  lines  and  without  showing  any 
appreciable  eddy.  If  a  fine  silk  thread  is  held  in  the  working 
stream,  a  slight  play  up  and  down  or  to  the  right  and  left  may 
be  noted,  showing  some  variation  is  present.  The  velocity  of 
the  stream  is  measured  by  an  alcohol  manometer,  registering' 
the  difference  in  pressure  in  the  experimental  chamber  and  the 
laboratory  room  outside.  This  is  one  method  of  velocity  de- 
termination and  will  be  explained  in  detail  later.  The 
manometer  when  left  to  itself  shows  a  slow  variation  in 
velocity  with  time  of  some  four  per  cent. 

The  general  dimensions  of  the  installation  at  Auteuil  are  as 
follows:  The  large  channel  has  a  bell  collector  with  end  diam- 
eters of  4  and  2  meters,  13.1  and  6.6  feet,  with  a  length  of  3.3 
meters,  10.8  feet,  and  an  expanding  trunk  9  meters,  29.5  feet, 
long  with  end  diameters  equal  to  the  collector.  The  expanding; 
trunk  connects  with  a  suction  blower,  having  a  sectional  an  a 
of  9  square  meters,  97  square  feet.  The  small  tunnel  . 
prises  a  bell  collector,  ends  2  meters  and  1  meter  in  diameter, 
I.H.'i  meter-,  in  length  and  an  expanding  trunk  6  meters  long, 
connected  to  a  Sirocco  suction  blower. 

The  above  dimensions  permit  in  the  larger,  n  uniform  stream 
t  '2  meters,  (i.lj  I'cet.  in  diameter  to  be  drawn  throuL'h  the 
experimental    chamber  at    a   speed    varying   between   '2  and   .'!'J 
"lid,  or  (i  and  ]<>">  feet  per  second;  this  is  accom- 
plished   by    a    ">O    h.p.    electric    motor   driving    a    .">()    per   cent 
efficient    blower.      In    the    small    tunnel    of    1    meter   diameter 
air  How.  a  maximum  velocity  of   t'l  meter-,   l.'tl    feet.  ]»< 
ond,  i-  obtained  bv  a  .">(»  h.p.  electric  motor  driving  the  Sirocco 
blower. 

TI.e  experimental  chamber  is  a  rectangular  room  free  from 


namical  balance — devices  for  measuring  the  lateral  IV 
pressure  distribution  and  a  very  excellent  apparatus  for  test- 
ing small  propellers.  All  the  apparatus  is  mounted  in  the 
most  convenient  manner  and  may  be  used  for  either  the  large 
or  small  channel  as  desired.  The  accuracy  of  the  results  oh 
tained,  while  possibly  not  sufficient  for  exact  physical  research. 
are  ample,  from  the  practical  stand-point. 

'///••  Ih'utarhe  \'erstichsanstalt  fiir  Luftfahrt  :u  Adlershof, 
superintended  by  Prof.  Dr.  Hendemaiin,  is  of  the  same 
order  as  the  experimental  grounds  at  St.  Cyr,  but  on  a  much 
h-s  elaborate  scale.  The  work  is  principally  on  lull  scale  air- 
planes and  block  tests  on  aeronautic  motors.  One  building  is 
devoted  to  full  scale  testing,  another  to  construction  and  re- 
pairs and  five  smaller  ones  to  the  housing  of  motor  testing 
apparatus.  The  main  building  has  a  central  tower  some  inn 
feet  in  height  from  which  wind  observations  may  be  made  and 
other  atmospheric  conditions  recorded.  Cables  from  the.  top 
of  this  tower  are  nseil  to  support  full  si/.e  airplanes  in  the 
determination  of  their  moments  of  inertia.  A  track  ouKiile 
of  the  building  is  used,  as  at  St.  Cvr,  for  the  testing  of  full 
si/e  airplanes  or  surlaces.  In  this  instance  a  locomotive  used 
to  pu-h  the  mounting  stage  is  substituted  tor  the  St.  <  'v  i 
trie  driven  car,  a  rather  doubtful  ad.junct. 

'It',  n   .lirdili/niniiiiiil  J.nliiiriitnri/,  under  the  super- 

vision  of  Profe-sor   Praiidtl.  lias  little  of  the  ornate  as  com 

pared  to  the  KitTel   Instituti housed  as  it  is  in  a  plain  one 

-lory  brick  building.  1(0  by  -Id  feet   in  si/.e.     The  building,  as 
nmy  lie  seen   from  the  drawing,   is  about  equally  divided   b. 
tween  wind  tunnel  and  office  space.     Glass  doors  in  the  snle 
next  the  observation  room  permit  of  access  to  the  experimental 


AERODYNAMICAL  THEORY  AND  DATA 


19 


section  of  the  tunnel,  while  trap  doors  open  here  and  there 
to  allow  entrance  into  other  sections  for  the  adjustment  of  the 
honey-combs,  baffles,  etc. 

Unlike  the  Eiffel  tunnel,  the  air  follows  a  closed  circuit 
necessitating  the  turning  of  four  corners.  The  2  meter  diam- 
eter blower,  driven  by  a  30  h.p.  electric  motor,  forces 
a  steady  current  of  air  through  the  2  meter,  6.6  foot,  square 
wooden  tunnel.  At  a  short  distance  down  stream  the  air 
passes  through  the  first  honeycomb,  400  large  square  metal 
cells,  similar  to  the  pigeon  holes  used  for  post  office  boxes. 
These  cells  are  so  constructed  with  two-ply  metal  walls  that 
the  quantity  of  air  passing  through  any  one  may  be  regulated 
by  partly  bending  out  one  thickness  wall  to  obstruct  the  pas- 


passes  through  the  second  honeycomb,  much  finer  than  the 
first.  This  last  honeycomb  is  constituted  of  about  9,000  cells 
from  which  the  air,  after  passing  a  wire  mesh  to  remove  any 
foreign  matter,  issues  with  a  maximum  velocity  of  10  meters  or 
32.8  feet  per  second,  to  act  upon  the  model  suspended  some 
distance  down  stream. 


Section  Plan 

Via.  5.     THE  GOTTINGEN  AERODYNAMICAL  LABORATORIES 


sage.  The  cells,  in  many  instances,  have  been  so  restricted  to 
regulate  the  air  flow  that  it  might  be  as  uniform  as  possible. 
Vanes,  similar  to  those  of  a  turbine,  are  utilized  at  the  four 
corners  to  turn  the  current  through  a  90  degree  angle,  without 
producing  excess  eddy-motion.  After  the  second  turn,  just 
before  the  nir  enters  the  experimental  part  of  the  tunnel,  it 


A  great  deal  of  the  work  in  the  Gottingen  Laboratory  hfas 
been  devoted  to  the  resistance  of  airship  hulls,  etc.,  for  which 
work  a  special  suspension  method  of  mooring  wires,  bell 
cranks  and  weights,  has  been  adopted  with  great  success.  A 
differential  pressure  gage,  sensitive  to  pressure  changes  of  one- 
millionth  of  an  atmosphere  is  used  in  the  determination  of 


FIG.  6.    ELEVATION  AND  PLAN  or  THE  WIND  TUNNEL  OF  THE  UNITED  STATES  NAVY  DEPARTMENT 


AERODYNAMICAL    THEORY     AND    I)V1\ 


velocity.  Many  interesting  experiments  on  the  distribution  of 
pressure  have  been  conducted  upon  small  propellers,  con- 
structed by  electroplating  with  copper,  wax  models.  A  more 
detailed  description  of  the  suspension  device  and  differential 
ira-je  will  follow. 

The  Wind-tunnel  of  the  United  States  Xavy  Department, 
under  Naval  Constructor  li olden  C.  Richardson,  is  at  the 
Washington  Navy  Yard.  Washington,  D.  C.  The  tumid  is 
similar  to  the  German  liottiiigeii  Laboratory  in  that  the  air  is 
confined  in  a  closed  circuit,  in  tliis  case  eight  feet  s<|iiarc  at  the 
-I'ctiun.  The  cross  sectional  dimensions  vary  as  may  he  seen 
in  the  accompanying  print,  hi  order  to  compensate  for  the 
curves  taken  by  the  stream.  Only  one  set  of  honeycomh 
baffles  is  employed,  these  being  placed  just  at  the  entrance  of 
the  experimental  chamber  and  20  feet  up  stream.  These  04  cells. 


Fie.   7.     EXTERIOR  OF  THK   WIND   Tr.\xn.   AT   TIIK   MASSA- 

•  •Hl  SETTS      IXSTITITK    OK     TECH  XOI.O<;1  .     SlIllXVlM,     CKI.I.S 

TllROt-(iir  Winni   An;   Is  SrcKKi*  IN   II:<MI  Tin:  IJoOM 

each  one  foot  square  and  eight  feet  long,  are  equipped  with 
individual  adjustable  dampers  used  as  a  control  upon  the 
quantity  of  air  passim;  and  so  producing  uniform  How  to 
within  about  '2  per  rent.  The  balance  ami  motor  control  are 
mounted  on  a  platform  upon  the  roof  of  the  tunnel.  The 
model  is  supported  in  a  horizontal  position  in  the  wind  on  ;, 
balance  similar  to  thai  ol  Kind's  and  sen.-itixe  to  at  least 
J  1000th  of  a  pound.  Models  up  to  :t(i-inch  span  are  per- 
mitted without  nutieejihle  in1'  I  mm  the  walls  or  chok- 
ing of  the  air  flow. 

The  velocity  measurement*  are  unique  in  tluit   in  place  of  a 

-itiifle    pilot    and    pics-lire    tlllie.    placed    in    I  he    Mcimtx     n!'    th"1 

model,  a  series  of  twelve  tubes  equally  spaced,  directly  on  the 
di-chiirge  side  of  the  Mower  icconl  on  an  integrating 
manometer  the  xelociix  of  the  stream.  The  velocity  of  the 
-tream  from  the  blower  ha-  a  direct  relation  to  the  veloeily  of 
the  wind  in  the  experimental  chamber,  ntrainst  which  it  has 
••alibrated  tor  nil  speed-.  The  pilot  tubes  u-ed  have  been 
themselves  checked  with  the  standard  tubes  of  the  National 
Physical  Ijihoralorx  »:  Kiiirland  and  the  Aerodx  namical  I*ab- 
•  •ral-tiy  of  the  UMHMlnMttl  Institute  of  Technology. 

Cower  for  drivinu  the  suction  blower  is  -upplied  by  a  500 
h  p.     J.Vl     volt     direct     current     elti-tric     motor,     operated     on 


the  Ward-Leonard  system.  A  velocity  of  75  miles  an  hour 
may  be  obtainable,  but  due  to  the  heating  of  the  air  by  friction 
and  other  dillieultius  in  maintaining  regular  How  this  high 
speed  is  seldom  utilized.  Generally  tests  are  made  at  a  speed 
of  about  to  miles  an  hour. 


Fid.    8.       (A)    1'HOPELLEl:    AND    (  I !  I     A  l.l.'c  Hil  N  A  M  1C    I'.AI.ANCK    IN 
USE    AT    TIIK    M  \SSAl  IHJSKTTS     IXSTlTfTK    OK    TECHNOLOGY 

The  National  1'hiixical  Labvrator/i  at  '/ViWiH'''""  <""'  ''"' 
I\oyal  Aircraft  l-'actonj  at  Farnborough,  England,  constitute 
the  most  complete  aeronautical  experimental  combination  in 
the  world.  The  aeronautical  portion  of  the  National  Physical 
Laboratory  is  devoted  to  experimental  investigations  of  the 
I'.ritish  Advisory  Committee  for  Aeronautics.  This  committee, 
with  I>r.  I!.  T.  < ila/.chrook  as  chairman,  and  such  able  co- 


Kni.  !'.      KXTUKM  i     NH//I.I    Simxvixi;    HIIM-.M  o.xtr. 

worker-  :LS  l»r.  Stanlon  and  Mr.  I..  I'.airstow.  initiale- 
the  investigations  at  the  N.  I'.  L.  and  mersi-es  the  general  work 
in  aeronautics  throughout  the  Kinu'dom. 

The     l»o\al     Aircraft     Kactorx.    superintended     by     Mervyn 

<i'(!orman.   work-   in   close  i peiation   with  the   N.  I'.  I..      It 

hius  facilities  for  model  experiments,  but  is  more  Concerned 
xvilh  tests  on  lull  size  airplanes  and  the  application  of  the 
iiuesti'.'ation-  of  the  National  Phv-ical  laboratory.  There  is 


AERODYNAMICAL  THEORY  AND  DATA 


21 


necessarily  some  overlapping  in  the  work  carried  on  at  the  two 
institutions,  but  no  interference. 

The  Royal  Aircraft  Factory  before  the  war.  was  the  largest 
factory  then  in  existence  devoted  lo  the  manufacture  of 
airplanes.  All  the  experiments  arc  carried  on  in  the  large 
flying  field  in  connection  with  the  factory.  Machines  equipped 
with  intricate  recording  instruments  are  flown  under  their  own 
power  and  such  important  information  as:  power  utilized, 
angles  of  pitch,  roll  and  yaw,  speed  through  the  air,  altitude 
and  control  movements  are  simultaneously  recorded.  This,  in 
a  true  sense,  is  full  scale  experimental  work  and  the  results 
have  been  to  disclose  defects  and  encourage  the  improvement 
and  safety  of  the  machines.  By  the  careful  application  of  the 
model  experimental  work  of  the  N.  P.  L.  an  inherently  stable 
biplane  with  a  speed  range  of  40  to  80  miles  an  hour  had  been 
produced  by  the  R.  A.  F.  before  the  war.  Improved  machines 
of  this  type  have  been  of  the  greatest  value  to  the  Royal  Fly- 
ing Corps. 

The  National  Physical  Laboratory  has  turned  over  ample 
space  for  the  exclusive  use  of  the  Aeronautic  Committee,  com- 
prising a  large  and  small  wind  tunnel  house,  a  whirling  table 
house  and  ample  space  for  any  independent  investigations. 
The  small  and  large  wind  tunnels  are  of  similar  character,  one 
4  and  the  other  7  feet  square  in  cross-section.  Each  is  mounted 
in  a  separate  building,  the  smaller  being  included  in  the  engi- 
neering laboratory  building.  For  details  of  the  small  tunnel, 
reference  is  made  to  the  description  of  its  duplicate  in  the 
Massachusetts  Institute  of  Technology  Laboratory.  The  new 
7  foot  tunnel  only  differs  from  the  4  foot  in  its  dimensions  and 
power.  It  is  80  feet  in  length  with  an  air  flow  of  60  feet  a 
second  produced  by  a  low  pitched  four  bladed  propeller  driven 
by  a  80  horse  power  electric  motor. 

A  great  amount  of  time  was  spent  in  experimenting  with 
this  form  of  tunnel  before  the  committee  was  satisfied  with 
the  results.  They  have  the  deep  satisfaction  of  knowing  that 
the  artificial  wind  produced  by  it,  is  the  most  uniform  in  the 
world  and  adaptable  to  the  most  scientific  research.  The  cur- 
rent is  uniform  in  velocity,  both  in  time  and  space,  to  within 
one-half  of  one  per  cent.  The  velocity  measurements  and  aero- 
dynamical balance  will  be  described  in  detail  later.  It  suffices 
here  to  say  that  they  are  as  carefully  worked  out  and  results 
obtained  as  gratifying  as  the  wind  tunnel  itself.  The  work  of 
the  committee  has  been  extremely  broad  and  the  results  are  of 
untold  value  to  aeronautics.  The  whirling-arm  and  small 
water  channel,  the  former  used  in  the  calibration  of  velocity 
instruments,  the  latter  in  the  study  of  stream  line  flow,  are 
both  examples  of  high  engineering  skill. 

The  Wind-tunnel  of  the  Massachusetts  Institute  of  Tech- 
nology was  built  after  a  careful  study  of  European  Labora- 
tories, on  plans  furnished  through  the  courtesy  of  the  National 
Physical  Laboratory.  Maintained  in  connection  with  the 
graduate  course  in  aeronautics  at  the  Institute,  with  the  helpful 
cooperation  of  Professor  Peabody  of  the  Naval  Architectural 
Department,  and  under  the  former  directorship  of  Lieutenant 
J.  C.  Hunsaker,  U.  S.  N.,  the  work  has  been  of  the  most  com- 
mendable character. 

The  tunnel  is  housed  in  a  temporary  building  on  the  new 
Technology  site  in  Cambridge,  with  offices  in  the  main  Insti- 
tute building.  Enclosed  in  a  20x25x66  foot  shed,  the  tunnel 
is  suspended  in  the  center  of  the  room.  6  feet  from  the  floor, 
so  that  ample  space  is  provided  for  the  free  circulation  of  air. 
The  illustrations  indicate  the  general  form  of  the  tunnel  which 
has  an  overall  length  of  about  56  feet  and  a  working  section  4 
feet  square.  The  air  which  is  drawn  from  the  room  around  the 
cowled  entrance  end  passes  through  a  honeycomb  formed  from 
3-inch  metal  conduit  pipes  2  feet  6  inches  in  length  into  the 


experimental  chamber.     This  honeycomb  helps  to  straighten 
out  the  Mow  and  prevent  eddies  in  the  wind. 

The  experimental  chamber  reaches  from  this  honeycomb  to 
the  expanding  trunk,  but  only  the  section  midway  between 
these  points  is  utilized.  The  air  after  passing  the  model  goes 
through  a  series  of  diagonal  vanes  and  enters  the  expanding 
trunk.  Here  the  velocity  decreases  with  an  increase  of  static 
pressure.  The  expansion  in  11  feet  of  length  is  to  a  cylinder 
of  7  feet  diameter.  This  cone  expansion,  in  the  English  tunnel 
is  only  6  feet  on  the  11  foot  length.  By  expansion  the  pres- 
sure difference  maintained  by  the  four-bladed  propeller  is  re- 


FIG.  10.    INTERIOR  OP  DIFFUSER  LOOKING  FROM  PROPELLER 

duced  and  some  turbulence  in  the  wake  avoided.  The  dis- 
charge from  the  propeller  is  received  by  a  large  perforated 
d  iff  user  with  the  end  opposite  the  propeller  a  blank  wall.  The 
function  of  this  diffuser  is  to  distribute  the  air  into  the  room 
at  a  uniform  rate  and  at  a  very  low  velocity.  This  is  indeed 
accomplished  for  the  area  of  the  perforation  in  the  diffuser  is 
several  times  that  of  the  tunnel  and  when  a  velocity  of  30 
miles  an  hour  is  maintained  in  the  tunnel,  the  discharge  from 
the  diffuser  is  hardly  noticeable. 

A  four  bladed  black  walnut  propeller  of  low  pitch,  revolv- 
ing 600  r.p.m.  will  produce  a  wind  of  25  miles  per  hour.  The 
propeller  is  driven  by  a  10  h.p.  electric  motor  through 
a  "  silent "  chain.  The  motor  is  mounted  on  a  separate  con- 
crete foundation,  as  are  likewise  the  aerodynamic  balance  and 
the  tunnel  proper,  to  avoid  any  variation  in  alignment  caused 
by  vibration.  The  sectional  area  of  the  tunnel  permits  of 
models  of  18  inch  span  and  as  an  extreme  24  inch  span,  to  be 
tested  at  speeds  from  6  to  40  miles  per  hour. 

The  control  of  the  wind  is  by  sentitive  rheostats  in  the 
motor  field  and  wind  speeds  may  be  kept  constant  as  in  the 
English  tunnel  to  within  one-half  of  one  per  cent.  Measure- 
ment of  velocity  is  by  means  of  a  calibrated  "  side  plate  "  in 


22 


AERODYNAMICAL  THEORY  AND  DATA 


the  wall  of  the  tunnel,  recording  on  un  alcohol  manometer  the 
difference  of  the  pressure  in  the  room  and  in  the  experimental 
part  of  the  tunnel.  These  manometer  readings  were  calibrated 
against  a  standard  N.  P.  L.  pilot  tube  to  ascertain  the  true 
velocity. 

The  aerodynamical  balance  was  constructed  by  the  Cam- 
bridge Scientific  Instrument  Company,  England,  and  is  a 
counter-part  of  the  English  installation.  Most  model  adjust- 
ments are  possible  from  the  outside  without  stopping  the  wind, 
thus  greatly  facilitating  the  experimental  work.  The  balance 
is  arranged  so  that  complete  data  for  the  calculation  of  the 
stability  coefficients  for  airplanes  is  obtainable. 

While  the  laboratory  is  primarily  for  research  work,  investi- 
gations are  conducted  for  private  individuals  or  manufacturers 
at  nominal  charges. 

It  is  interesting  to  note  that  the  Curtiss  Company  has  re- 
cently erected  at  Buffalo,  under  the  direction  of  Dr.  A.  F. 
Zahm  a  wind  tunnel  similar  in  construction  to  that  of  the 
N.  P.  L.  and  the  Massachusetts  Institute  of  Technology. 


References  for  Chapter  1 

.National    1'liysiral   Laboratory.  Teddlngtuu,  and  ICiival   Ai 
lory.    Faruborough,    England.      Publication:    Technical    AY/»/rl    «f    tin 
Adritom   Committee  /or  Aeronautics,  for   tin-   v..n-    \'.<i<:<  1<>.    T.H'i  11. 
1911-12.  1012-13. 

•  Unltnl   States  Navy  Department   Wind  Tunnel.   Wiishlnirirui.   1>.   c 

•The  Aerodynamical  Laboratory  of  tho  UanacnowtU  institute  of 
Technology,  r.o-ion,  .Mass. 

The  LaUoratolre  Aerodynamlque  ElftVI.  Autenil.  Kraneo.  I'nlilii-a- 
tlons  :  ••  ],:i  BeaUtance  de  1'Alr  <-t  1'Avialion."  by  <;.  KIITH.  nil'-',  trans 
Intod  hy  J.  C.  Hunsnkcr.  ••  Nonvelles  lieeherehes  sur  la  i;i--i>i.-inM'  ilc 
1'Alr  .'i  1'Aviall "  l>y  <:.  Kiffi-l,  Diiiuid  aud  I'lnal.  1'arls.  r.H  I 

Jlillli'tin  </c  I'lnntilut  .!(  rui/ifiiumii/ui    (/.•  Knuli-lniio,  Mox-ou. 

t  UuttiiiKi'ii    Acroilvnainiral    Laboratory,    <:rniini:i>ii,    (irrinanv. 

t  Tin-  Dentcche  7enachaanital<  fiir  i.iifii'aiin  /.n  Adii'rsin.i.  i'..Tiiii. 
(IcTinany. 

"  Heport  on  European  Aeronautical  Laborati.rirs."  i,y  A.  K  X.ahni. 
Vol.  «i,  Xo.  I!  :  ••  Ki-port  on  Wind  Tunnel  Experiment!  In  Am- 
djrnainlca."  by  llunsaki-r  and  otJbcrs,  Vol.  ti^.  NO.  -i.  E^ibllihed  b\ 
Snillbsonian  Institution,  Washington,  1>.  ('..  in  Smith.  Uiscellaneotn 

<'i,ll<rli,,M,,    Vol.    02. 

Itullitin  dc  I'lnstitut  Afrotechniquc  dc  l'Unlrcr«il,  <1<  l'nri«.  I'.HJ 
18-14. 


•  Work  published  at  Irregular  Intervals  In  standard  periodicals  ami 
reports,  such  as:  Aeronautical  Journal,  England;  L'At'rojilani.  Paris. 
France;  Smithsonian  Institution  Keportt,  Washington,  D.  C. ;  Hni/lnnr 
ing,  London;  Annual  Keport  of  the  National  Advisory  Committee  lor 
Aeronautics,  Washington.  D.  C.,  " 


1915. 


t  Jahrbueh  der  Motorluftscliiffstudiengesellachaft,  Berlin,  years 
1908-09,  '09-10.  '10-11,  '11-12.  '12-13,  and  ZcltocMJt  fiir  l-'hiiitrrl, ml. 
und  tfotorluftschiffahrt  (semi-monthly  periodical  of  research  work). 


Chapter  II 

Elements  of  Aerodynamical  Theory 


Liquid,  Fluid,  and  Perfect  Fluid 

Both  liquids  and  fluids  may  be  defined  as  substances  which 
flow  or  are  capable  of  flowing.  A  liquid  is  incompressible  and 
therefore  of  constant  density,  a  fluid  is  compressible  and  of 
varying  density.  Thus  water  is  commonly  spoken  of  as  a 
liquid,  air  as  a  fluid,  yet  the  hard  and  fast  distinction  is  un- 
fair, since  water  itself  is  slightly  compressible. 

In  the  transportation  speeds  employed  in  aeronautics,  the 
variations  in  pressure  of  the  air,  and  the  consequent  varia- 
tions in  density  are  so  slight,  that  the  air  may  also  be  regarded 
as  incompressible.  Thus  for  a  dirigible  at  a  speed  of  100 
miles  per  hour  the  increase  in  pressure  at  the  nose  is  only 
about  one  per  cent.  It  is  only  at  the  tips  of  fast  moving 
propeller  blades  that  the  compressibility  of  air  assumes  any 
importance. 

The  motion  of  fluids  is  so  complex  that  no  complete  mathe- 
matical theory  has  yet  been  evolved  for  it.  In  hydrodynamics 
the  mathematicians  have  stipulated  a  perfect  fluid  possessing 
no  viscosity.  In  such  a  fluid  all  bodies  may  move  without 
encountering  resistance.  Although  the  conception  of  a  perfect 
fluid  may  seem  of  no  practical  importance,  yet  hydrodynamical 
theory  serves  as  a  guide  in  the  theory  of  aeronautics  and  we 
shall  have  to  make  occasional  reference  to  this  idea. 

Density  of  Air 

In  setting  forth  data  from  the  laboratories  the  air  will  be 
assumed  as  having  a  temperature  of  15°  C.  and  a  density  of 
.07608  Ibs.  per  cubic  foot  at  sea  level. 

Variation  of  Density  of  Air  with  Height 


Height  (ft.) 

0 

500 

1,000 

2,000 

5,000 

10,000 

20,000 


Density  (Ibs.  per  cu.  ft.) 
.0761 
.0748 
.0734 
.0707 
.0632 
.0523 
.0357 


Principle  of  Relative  Motion 

We  shall  assume  throughout  without  further  reference  that 
the  same  resistances  will  be  brought  into  action  whether  a  body- 
is  moving  through  a  fluid  or  a  fluid  is  streaming  past  a  body, 
provided  the  relative  motion  is  the  same. 

This  is  an  idea  which  often  presents  difficulties  and  is  very 
difficult  of  theoretical  demonstration,  yet  it  is  merely  a  matter 
of  common  sense.  In  La  Technique  Aeronautique  of  May 
15th,  1913,  M.  Lecornu  has  given  a  very  sound  discussion  of 
this  point.  We  will  venture  a  rough  illustration.  Imagine  a 


boat  propelled  through  a  river  at  rest  at  a  speed  of  5  miles  per 
hour.  The  oars  will  exert  a  certain  force  of  propulsion.  Now 
if  the  river  has  a  contrary  current  of  5  miles  an  hour,  the  boat 
will  remain  at  rest  relative  to  the  banks,  yet  exactly  the  same 
force  will  be  exercised  by  the  oarsman.  There  is  really  nothing 
more  to  be  grasped  underlying  the  principle  of  relative  motion. 

Bernouilli's  Theorem  for  Fluid  Motion 

In  the  steady  flow  of  a  fluid  the  current  at  any  point  is 
always  in  the  same  direction  and  magnitude  and  may  be  rep- 
resented by  a  series  of  stream  lines,  or  by  tubes  of  flow. 

The  energy  of  a  fluid  consists  of  three  parts:  (1)  The  po- 
tential energy,  or  the  energy  due  to  its  position  of  height 
through  which  it  may  fall,  (2)  The  pressure  energy,  (3)  The 
kinetic  energy  due  to  its  motion,  neglecting  the  effects  of  vis- 
cosity or  friction.  Bernouilli's  theorem  states  that  along  any 
stream  line,  the  sum  of  these  energies  is  a  constant,  and  if 

y  =  acceleration  due  to  gravity 
h  =  height 
p  =  pressure 
\'  =  velocity 
9  =  density* 


p       V 
-{-        —  constant 


In  considering  air  flow  in  aeronautics  where  we  deal  with 
a  fluid  ocean  of  immense  depth,  the  variations  in  height  are 
negligible,  and  the  theorem  becomes:  — 


, 
+ 


=  constant 


The  theorem  is  of  fundamental  importance  in  aeronautics; 
its  proof  will  be  found  in  any  text-book  on  hydrostatics. 

This  equation  may  also  be  written  in  the  following  useful 
form,  by  multiplying  both  sides  of  the  equation  by  p  : 

fl" 
p  -\-  -  —  =  constant 

Total  Energy  of  a  Fluid  Applied  to  the  Theory 
of  the  Pitot  Tube 

The  Pitot  tube,  so  frequently  employed  in  aeronautics  to 
measure  the  speed  of  a  machine  in  actual  flight,  furnishes  an 
excellent  illustration  of  the  principles  just  set  forth.  In  Fig. 
1  is  given  a  diagram  of  such  a  tube. 

Its  main  function  is  to  measure  the  velocity  of  flow  for  e 

*  (p)  is  used  for  Density  to  prevent  confusion  with  D  for  l)rag 
and  tu  conform  with  standard  usage. 


24 


AERODYNAMICAL  THKORY  AND  DATA 


steady  irrotational  (low  of  air,  and  it  is  unsuitable  for  mca.- 
uring  the  velocity  of  turbulent  flow,  such  as  that  occurring  in 
the  vicinity  of  a  fan  to  give  an  example. 

In  practice  the  Pitot  tube  is  finely  rounded  so  as  to  give 
the  least  possible  disturbance  to  the  air  How.  It  consists  of 
two  concentric  tubes.  The  inner  one  is  open  to  the  wind,  the 
outer  lube  is  closed  to  the  wind  and  is  only  connected  to  the 
surrounding  air  by  a  .-cries  of  tine  holes.  The  lubes  are  con- 
nected to  the  two  arms  of  a  pressure  gauge  as  shown  in  the 
figure,  and  the  gauge  measures  the  difference  in  pressure 
U-tween  them. 

The  inner  tube,  open  to  the  wind,  brings  the  air  impinging 
on  it  to  rest,  and  the  pressure  in  it  is  therefore  a  measure  of 
both  the  static  pressure  in  the  stream  and  of  the  kinetic  energy- 
head  of  the  stream.  If  p  is  the  static  pressure  of  the  stream. 
V  the  velocity,  the  total  pressure  will  be  given  by 

9V> 


Definition   of   Angle    of    Incidence.    KeMiltunt    Pres>nre. 

Lift,  Drag  and  Center  of  Pressure  in  a  Plane  or 

Cambered  Vi  in;;  Section 

Whether   for  a  plane  or  a  curved  wing  M-ction.   the  angle 


L  int  «f  mad- 

FIG.  2.     LIFT,  DRA<;,   ANIII.K  OF   |X<-II>K\CK.   AM> 
l-'i.n-   1'i.vn. 


of  incidence  is  defined  as  the  angle  i  expressed  in  decrees,  be- 
twcen  the  relative  wind  and  a  line  in  the  supporting  surface. 
termed  thu  chord,  lu  the  case  of  the  tlat  plate,  this  line  coin- 
I-H!C>  with  the  face  of  the  plate  and  is  physically  justifiable 
-ince  when  the  face  of  the  plate  coincide-  with  the  relative 
wind,  there  is  no  sustaining  force  or  lift  on  the  plate. 


The  outer  tube,  on  tlie  other  hand,  being  closed  to  the  wind. 
will,  if  the  holes  are  small  enough  to  prevent  velocity  having 


2  rifles  at  front  &•  boc/r 
02 "  diam  /'//  outer  tube 


.4.4.' JF          _»I 


FIQ.  1.     PITOT  TUBE. 

any  effect  on  its  pressure,  read  the  static  pressure  of  the  air 
flow. 

Hence  the  difference  in  pressures  read  on  gauge  will  be 


and  will  therefore  be  a  measure  of  the  velocity. 

We  shall  discuss  the  methods  employed  in  connection  with 
the  Pilot  gauge  more  fully  when  dealing  with  laboratory 
methods,  but  may  state  now  the  results  of  recent  experiments 
as  summarized  by  Dr.  .1.  ('.  Hunsaker:  — 

1.     The  precision  is  one-tenth  of  one  per  cent. 

'_'.     The   open    tube   correctly    transmits   the    total    pr« 
regardless  of  size  or  shape. 

.1.     The  nose  of  the  combination  tube  must  be  of  easy  form. 

4.  The  static  openings  should  be  clean  holes  from  0.01  to 
0.04  inches  dintm  •;• 

"i.  Slain-  opeiiuii;-  -lioiild  lie  well  hack  troni  the  no>e  ol 
(lie  instrument  on  a  polished  cylindrical  portion  of  the  tube. 

Static   opening   may    In-    from    1    to   '_'  1    in    number   ar- 
ranged in  an  arbitrary  manner. 

7.  The  tube  should  be  pointed  into  the  wind,  but  an  error 
of  two  degrees  in  alignment  will  cause  |e—  I  ban  1  per  cent 
error  on  velocity  nica»urcm< 


Line  of  ChcrW 


ii;.  :t.     LIFT,  DRAG,  LINE  OF  CHORD,  ANGLE  OF  INCIDKM  f 
FOR  DOVBLK  CAMBKRKI,  SK.  TIOK. 

In  the  case  of  cambered  surfaces,  the  posi- 
tion of  the  chord  has  been  fixed  by  conven- 
tional usage,  and  is  best  illustrated  by  the 
diagrams  in  Figs.  2.  .'!  and  4.  With  cam- 
bered surfaces,  when  the  conventional  chord 
coincides  with  the  relative  wind  there  is  lift 
as  a  rule,  although  the  position  of  no  lift 
may  be  only  a  degree  or  so  removed. 

Owing  to  I  he  relative  motion  of  the  air, 
the  wing  experiences  a  resultant  pressure 
which  we  will  designate  as  ]{.  This  resultant  is  very  nenrlv 
normal  to  the  face  of  a  flat  plate,  but  it  is  quite  wrong  to 
state  that  it  is  exactly  at  right  angles  to  this  face.  The  re- 
Miltant  force  H  may  be  generally  resolved  into  two  com- 
ponents; one  at  right  angles  to  the  relative  wind,  which  is 
termed  Resistance  or  Drag  (D).  Drag  will  he  used  instead 
of  the  term  drift,  which  unfortunately  is  capable  of  misinter- 
pretation. The  component  at  right  angles  to  the  relative 
wind.  L.  may  act  upwards,  giving  1'i^itii;  Lift,  or  downwards 


Fie;.   4.      LIFT.    HUM;,    AM.I.K  OF   Jxrii'i.s.  t     k\n   Cnoui'    >«i: 
('AMHKKKH  SCKKV  i 

L-uiiig   .Wi/n/i'rc  Lift,  depending  on   the   position   of  the  sur- 

•  lativc  to  I  be  wind. 

The    hit     mi  ;iMircs   the   sustaining    power,    the    drair    the    n 
-iRtftnce  to  forward  motion.     The  tnnirent  of  the  mitrle  In 


AERODYNAMICAL  THEORY  AND  DATA 


25 


the  R  and  D  gives  the  ratio  L/D,  lift  over  drag.  The  greater 
the  value  of  L/D  the  greater  is  the  path  efficiency  of  the  sup- 
porting surface. 

The  center  of  pressure  will  be  arbitrarily  defined  as  the 
point  of  application  of  the  resultant  force  R  on  the  plane  of 
the  wing  chord.  This  is  by  no  means  a  rigid  definition. 

Definition  of  Lift  and  Drag  Coefficients 

We  shall  employ  throughout  the  following  notation  : 
Lift  ==  L  =  K,AV.    Resistance  or  Drag  =  D  =  K^AV'. 
Where  L  and  D  are  in  pounds,  A  =  area  in  square  feet  of 
one  surface  projected  on  the  line  of  chord,  and  r  =  velocity 
in  feet  per  second,  K7  and  K*  will  represent  forces  for  unit 
areas  and  unit  velocity.     We  shall  see  later  the  justification 
for  these  expressions. 

Position  of  Center  of  Pressure  or  Resultant 
Vector  of  Forces 

It  has  become  customary  in  Aerodynamics  to  speak  of 
Centers  of  Pressure,  and  it  is  very  often  convenient  to  em- 
ploy this  term.  But  it  would  be  much  better  to  speak  of  the 
position  of  the  resultant  vector  of  forces,  a  vector  being  a 
line  representing  a  force  in  magnitude  and  direction.  For  a 
Hat  plate  or  a  cambered  wing  section,  the  term  center  of 


FIG.  5.     ILLUSTRATING  POSITION  OF  VECTOR  OF  RESULTANT 

FORCES. 

pressure  might  answer  fairly  well,  but  for  a  combination  of 
wing  surfaces,  as  in  a  biplane,  or  for  any  kind  of  airplane, 
it  is  very  unsatisfactory.  Thus  as  in  Fig.  5  for  certain  angles 
the  resultant  force  passes  right  outside  the  wing  surface,  and 
to  speak  of  a  center  of  pressure  in  such  a  case  is  meaningless. 
It  is  also  often  stated  that  the  stability  of  a  wing  depends 
on  the  motion  of  the  center  of  pressure  with  reference  to 
the  center  of  gravity.  The  moment  about  the  center  of  grav- 
ity can  be  more  correctly  stated  as  depending  on  the  position 
and  direction  of  the  resultant  vector  of  forces.  If  current 
practice  leads  us  to  speak  of  center  of  pressure,  the  reader 
will  always  bear  these  considerations  in  mind. 

Forces  on  a  Flat  Plate  Immersed  in  a  Fluid  and  Normal 
to  the  Direction  of  Motion 

Newton  was  the  first  to  consider  the  case  of  a  flat  plate  placed 
normal  to  its  direction  of  motion.  Ho  stipulated  a  medium 
composed  of  an  infinite  number  of  small  particles,  having  no 


sensible  magnitude  but  possessing  mass,  and  not  intercon- 
nected in  any  way.  A  plate  of  area  A,  moving  with  a  velocity 
I*  in  a  medium  of  density  p  would  meet  a  quantity  of  fluid 
fAV  and  impart  to  this  quantity  a  velocity  V  per  unit  of 
time. 

From  the  fundamental  equation  in  mechanics: 


Force  = 


(mass  acted  upon)  X  (velocity  imparted) 


Time 


we  should  derive  the  equation  : 


9  9 

Similar  reasoning  from  the  Principle   of   Relative   Motion 
would  apply  were  the  plate  held  at  rest,  and  the  fluid  im- 


FIG.  0.    MOTION  NEAR  A  FLAT  PLATE  N 


THE  WIND 


pinging  on  it.     The  force  as  derived  from  actual  experiment 
is  considerably  less  than  this. 

But  Newton's  theorem  is  obviously  incorrect,  no  account  be- 
ing taken  of  the  action  at  the  back  of  the  plate,  or  of  the  com- 
plicated interaction  between  the  particles,  or  of  the  formation 
of  eddies  and  whirls.  The  photograph  in  Fig.  6  gives  an  idea 


FIG.  7  FIG.  8 

DIAGRAMS  ILLUSTRATING  FLUID  MOTION  AND  PRESSURE  DIS- 
TRIBUTION ON  PLATES  NORMAL  TO  THE  STREAM 

of  the  complicated  actions  which  take  place.     These  are  repre- 
sented diagrammatically  in  Figs.  7  and  8. 

From  a  consideration  of  Bernoulli's  Theorem  it  will  be 
seen  that  the  pressure  in  front  of  the  plate  will  become  greater 
than  the  statical  pressure  of  the  stream.  At  the  back  of  the 
plate,  owing  to  the  considerable  velocity  of  the  eddies  or 
whirls,  we  can  say  again  from  a  consideration  of  Bernouilli's 
equations — that  the  pressure  will  be  less  than  the  statical 
pressure.  It  is  to  the  difference  in  pressures  front  and  back 
of  the  plate  that  the  resistance  is  due.  Fig.  8  represents 
roughly  the  distribution  of  pressure  on  either  side  of  the 
plate. 


20 


\KR(»  DYNAMICAL  THEORY   AND  DATA 


Ni-wton  was  coned.  however.  in  so  far  as  the  resultant  force 
of  a  plate  normal  to  the  wind  is  proportional  to  the  velocity 
squared.  the  area,  and  the  density;  and  if  K  denotes  the  re- 
sultant foroe  we  can  write: 


where  K  is  au  experimental  coefficient. 

We  shall  show  later  that  a  similar  law  holds  for  all  cases 
of  bodies  producing  turbulent  flow,  and  discuss  fully  the  re- 
sistances due  to  such  flow. 

Forces  on  Flat  Plate*  Inclined  to  the  Wind 

Figs  9  and  10  represent  diagrammatically  the  fluid  section 
in  the  case  of  an  inclined  plate,  and  the  distribution  of  pres- 
sure, which  are  further  illustrated  by  the  photograph  (after 
Kiabouchinsky)  in  Fig.  11. 

Just  as  in  the  ease  of  the  plate  normal  to  the  wind,  the  re- 
sultant forre  will  he  determined  by  the  difference  in  pressures 


reached.     After  this,  the  resultant  force  slowly  diminishes  to 
the  value  in  normal  presentation. 

At  small  angles  the  center  of  pressure  is  near  the  mid  posi- 
tion, and  gradually  moves  forward  as  the  angle  of  incidence 
increases.  That  the  center  of  pressure  should  be  forward  of 
the  mid  position  is  fairly  obvious  from  the  above  mentioned 
photograph.  It  is  in  the  forward  region  of  the  plate  that 
the  air  experiences  the  most  abrupt  changes  of  direction, 
with  consequently  the  greatest  variation  of  pressures.  This 
can  be  seen  also  from  the  diagram  of  distribution  of  ; 
sures. 

Numerous  efforts  have  been  made  to  deduce  expressions 
for  lift  and  drag  and  for  the  motion  of  the  center  of  pres- 
sure from  theoretical  considerations.  But  the  only  trustworthy 
values  are  those  directly  taken  from  experimental  data  ob- 
tained by  Eiffel  and  others  which  will  be  dealt  with  later. 

It  may  be  stated  here,  to  remove  a  somewhat  common  inis- 


Fio.   9.  FIG.    10. 

DIAGRAMS  ILLUSTRATING  FLUID  MOTION  AND  PRESSURE 
DI-TRIIHTION  ON  INCLINED  PLANK. 

at  the  front  and  back  of  the  plate,  and  lift  and  drag  will  vary 
as  A.V,  as  in  the  case  of  all  bodies  producing  turbulent  flow, 
with  a  different  coellicient  for  each  angle  of  incidence. 

The  minimum  resultant  force  of  a  plate  occurs  when  it  is  in 
the  line  of  the  wind.  As  the  angle  of  incidence  increases  so 
does  the  pressure,  until  a  critical  angle  of  some  40  degrees  is 


FIG.  11.    MOTION-  XKAU  A  FLAT  PLATE  INCLINED  TO  THE 
WIND 

conception,  that  the  resultant  pressure  on  a  flat  plate  is  not 
perpendicular  to  the  plate  except  for  a  certain  limited  raii'_'«' 
of  angles  of  incidence.  At  zero  degree  of  incidence  the  re- 
sultant pressure  is  90  decree-,  behind  the  normal,  rapidly 
approaches  the  normal  at  small  angles,  and  shoots  past  it 
at  10  depi 


Chapter  III 

Elements  of  Aerodynamical  Theory — Continued 


Skin  Friction 

Skin  friction  may  be  defined  as  the  total  resistance  of  a 
thin  plate  moving  edgewise  through  a  fluid,  and  is  due  to 
two  components: 

(1)  Viscosity  resistance 

(2)  Density  resistance 
which  we  shall  consider  in  turn. 

In  some  respects  skin  friction  is  a  misleading  term.  We 
shall  see  shortly  that  the  skin  of  a  body  has  nothing  to  do 
with  the  resistance,  a  moving  body  being  covered  with  a  layer 
of  fluid  at  rest.  Its  usage,  however,  has  been  sanctioned  by 
time. 

Viscosity 

Real  fluids  like  air  and  water  offer  a  resistance  to  shear, 
which  is  a  measure  of  their  viscosity. 

Let  us  imagine  two  horizontal  planes,  one  of  which,  AB, 


\\\\\\ 


I*        /y 


Jjf 


be  AT 


Z'y- 


T 

c 

.1 


FIG.  12.     VISCOSITY  ACTION  FOR  THIN  SURFACES. 

is  at  rest,  as  in  Fig.  12,  while  the  other,  CD,  is  dragged  past 
with  a  velocity  V,  with  the  viscous  substance  intervening,  the 
distance  between  the  two  plates  being  c. 

Particles  of  the  substance  nearest  to  CD  will  adhere  to  it. 
<  )ther  particles  will  be  carried  along  to  the  line  yyyyy  a  con- 
stantly decreasing  amount  xy.  If  /•'  is  the  horizontal  force 
per  unit  area  required  to  drag  CD,  it  is  obvious  that  it  will 
be  proportional  to  some  constant  dependent  on  the  nature  of 
the  substance  and  on  the  velocity  gradient. 

We  may  then  write 

F  =  [A  -     where  JA  is  some  constant,  t 

c 

II'  V  and  c  are  unity 

/•'  =  [A  and  [A  becomes  the  coetlicient  of  viscosity. 

The  simplest  case  of  viscous  drag  is  that  of  a  thin  plate 
moving  edgewise  through  a  fluid.  Length  is  I  and  breadth  b. 
There  will  be  a  thin  boundary  of  fluid  of  thickness  a  which 
connects  the  particles  adhering  to  the  body  with  the  particles 
at  rest  in  the  fluid.  This  layer  will  continually  lose  and  gain 
fluid  as  it  is  rubbed  off.  In  unit  time  a  mass  of  fluid  propor- 
tional to  the  cross  section  of  the  layer,  (bn),  and  to  the  veloc- 
ity, will  be  captured  and  have  its  velocity  partly  destroyed. 

t  fj.  is  Greek  lottcr  mu. 


The  inertia  force  required  for  this  change  of  momentum  •will 
therefore  be  proportional  to 

(p  ab  V)  V  or  p  ab  V 
The  viscous  drag  must  be  equal  to  this  inertia  force;  and  is 

V 
itself  proportional  to  p.    (bl)    X  --  by  the  definition  given 

above.    And  if 

V-  (bl)  -~9ab  F2,  then,  a  ~-\l-^. 
a  \  p  v 

\Jv 

The  viscous  drag  therefore  is  proportional  to  y.  (bl)   V  -vl 

or  to  I/.'5  6  Z'V5  vl'° 

Coefficients  of  Kinematic  Viscosity 

To  represent  the  relative  importance  of  density  and  viscosity 
a  coefficient 


is  employed,  known  as  the  coefficient  of  kinematic  viscosity. 
Substituting  from  this  equation  in  the  expression  for  viscous 
drag  we  obtain 

F~  v5b/-5pV'-5 
which  may  be  expressed  in  the  more  practical  form 

fl,.  =  dv°-M.0-"F1"> 
where  B-,  =  viscous  drag 
d  =  constant 
A,  =  area  in  shear 
A,'n  is  equivalent  to  6Z'°  dimensionally. 

Reynold's  Number 

It  is  interesting  to  note  that  the  thickness  of  the  boundary 
layer 


The  expression 


will  be  of  use  in  comparing  resistances  for  similar  bodies  in 
the  same  fluid. 

It  is  known  as  Reynold's  number  and  expresses  mathe- 
matically a  relationship  between  velocity  linear  dimensions 
and  viscosity.  We  shall  have  frequent  occasion  to  refer  to  it 
in  comparing  resistances  of  stream  line  bodies,  rods,  wires 
and  so  forth. 

Prandtl's  Theory  of  the  Boundary  Layer 

The  theory  of  the  thin  boundary  layer  is  due  to  Dr. 
Prandtl  of  Gb'ttingen,  his  hypothesis  being  that  the  velocity 
gradient  is  at  first  very  steep  but  flattens  out  quickly,  until 


27 


28 


AERODYNAMICAL  THEORY  AND  DATA 


in  the  free  stream  the  velocity  gradient  between  stream  lines 
is  negligibly  small.  Elaborate  experiments  by  Dr.  Prandtl 
bear  out  this  theory,  and  demonstrate  that  the  viscous  drag 
does  indeed  vary  as  V'\ 

Dr.  Zahm's  experiments  on  skin  friction  on  the  other  hand 
have  shown  that  for  even  surfaces,  bodies  covered  with  such 
widely  varying  substances  as  dry  varnish,  wet  varnish,  water, 
sheet,  zinc,  etc.,  all  experience  the  same  frictional  resistances. 
It  seems  therefore  reasonably  safe  to  assume  that  viscous 
drag  is  due  to  internal  fluid  friction  and  not  to  the  sliding 
of  the  fluid  along  the  surface  of  the  solid. 

Density  Resistance  to  a  Plate  Moving  Edgewise 

For  exceedingly  small  velocities,  it  has  been  found  that  re- 
sistance varies  as  I'1  indicatin;:  purely  a  drag  due  to  shear 
(Stokes).  For  small  velocities  experiments  by  Allen  have 
shown  a  resistance  varying  as  I"1'1  indicating  the  condition 
of  viscous  drag  which  we  have  developed  in  the  preceding 
paragraphs.  But  for  the  velocities  with  which  we  are  con- 
cerned the  resistance  of  a  thin  plane  surface  moving  edgewise 
increases  as  some  higher  power  of  1".  Tliis  is  probably — 
although  it  is  impossible  to  state  the  exact  cause — due  to  the 
fact  that  the  viscous  drag  not  only  imparts  translational 
velocity  to  the  particles  which  adhere  to  it  in  the  boundary" 
layer  but  the  boundary  layer  acting  as  a  species  of  gearing 
also  gives  some  eddying  or  rolling  velocity  to  particles  adjacent 
to  this  boundary  layer.  It  is  a  commencement  of  turbulent. 
eddying  motion.  As  such  this  extra  resistance  is  proportional 
to  some  area  A  of  the  body,  and  to  the  velocity  V,  squared. 
and  is  termed  density  resistance  and 

/,'„       AMI 
where  K  is  a  constant  for  the  fluid. 

Total  Skin  Friction.     Dr.  Zahm's  Experiments 

Total  skin  friction  =  R,  =  R,  +  B« 

=  viscosity  resistance  -f-  density  resistance 
Strictly  speaking  if  K,  —   I"'1  and  Rj   ~  I'3  no  one  expression 
with  V  raised  to  a  power  n  can  satisfy  this  expression.     But 


Slut  rncfion  Resist 
once  of>  Ttvi  flat 

of  My 
Area*    Unts  Lta 
p»r  Sq  rt. 


FIG.  13.    SKIN  FRICTION  CHAIJT 


for  practical  purposes  the  results  of  Dr.  Zahm's  valuable  ex- 
periments  have   been   accepted,   his   formula   being: 

R  =  0.00000778  J"  r1  "  6 
where  I{  =  resistance  for  one  side  of  board 

/    =  length  in  direction  of  wind  in  feet 

6   =  width  iii 

I"  =  velocity  in  IK  "iid. 

In  the  British  Technical  Keport  of  the  Advisory  Comn 
for   Aeronautics.    l!'l  1  -1  !'!•_'.    \>.    -M.    an    alternative    form   of 

•  •n    h:is  In-,  h    siiliinittcil.  MI   :i-   lo   iiinkr   llir  equation  con 
-i-tent   with  the  principle-  nt'  ilvi.aiiin-  -innlant 

//       o.iMiooOsj    I        I 

MIIC  »|ile  nt    tin    hi<:i 


Amongst  other  applications.  Dr.  Zahm's  formula  may  be 
used  to  compute  the  resistance  of  flat  rudders,  elevators,  and 
-taliilizers  when  neutral  to  tlit-  wind.  In  Fijr.  13  cum--  for 
the  resistance  of  plates  of  various  area  at  varying  speeds 
have  been  plotted,  to  facilitate  such  computations. 

Dr.  /.a Inn's  skin  friction  experiment-  an-  doc-rilied  in  Ilul- 
letin,  Vol.  xiv,  pages  247-276,  of  the  Philosophical  Society 
of  Washington,  June,  1904.  The  plane  was  suspended  in  the 
wind  tunnel  as  shown  in  sketch  in  Fig.  14,  with  wind 
shields  at  either  end  so  as  to  give  purely  tangential  forces. 


FIG.  14.    ARRANGEMENT  OF  THIN  PLATE  IN  WIND  TUNNEL  IN 
DR.  ZAHM'S  EXPERIMENTS. 

As  the  wind  friction  moved  the  plane  edgewise  the  displace- 
ment was  determined  by  the  motion  of  a  sharp  pointer  at- 
tached to  one  suspension  wire  and  traveling  over  a  fine  scale 
lying  on  the  top  of  the  tunnel,  and  hence  the  forces  were  de- 
duced. A  variety  of  shapes  and  surfaces  were  tried. 

Curves  for  Computations  with  Dr.  Zahm's  Formula 

TABLE  1.— SKIN  FRICTION  RESISTANCE 


Speed 

Ares    «q.  ft.) 

second) 

1 

a 

10 

15           20 

L>i 

30 

35 

30 

.0046 

.020 

.039 

.036        .074 

.091 

.108 

.124 

70 

H 

.022 

.099 

.189 

.280        .360 

.440 

.520 

.610 

90 

.036 

.159 

.300 

.440        .580 

.710 

.840 

.970 

100 

.043 

1'iJ 

.370 

.530        .700 

.860 

1.02 

1.18 

120 

.060 

.270 

.510 

.740        .970 

1.19 

142 

1.66 

TABLE  2.— ZAHM'S  FORMULA 
R-O.OQOOW7  A'»  l'"».      r-milct  ptr.kouf 


Speed 

Are*  ( 

HJ.    ft.) 

(milraper 
hour) 

1 

5 

10 

15 

H 

25 

30 

35 

30 

DOM 

.041 

.080 

.114 

.151 

.186 

.220 

HO 

40 

.0159 

.071 

.137 

.198 

JM. 

.320 

.;vi 

.430 

50 

.024 

.108 

.210 

.300 

.390 

.490 

.570 

.650 

60 

.034 

.151 

.200 

.430 

.550 

670 

.800 

.,_.,, 

70 

.045 

WO 

.390 

.570 

.730 

,. 

1  06 

1.24 

80 

.057 

.260 

.490 

.710 

.940 

1.16 

1.37 

1.59 

90 

073 

.:.'" 

„!,, 

.900 

1.18 

1  45 

1.71 

1.98 

100 

188 

390 

.760 

1.08 

1.43 

1.76 

2.06 

2  41 

In  rY_'.  l.i.  the  skin  friction  n  -Mancc  in  Ills,  per  square  foot 


AERODYNAMICAL  THEORY  AND  DATA 


29 


is  plotted  against  the  speed  in  miles  per  hour.  Since  the  re- 
sistance increases  less  rapidly  than  the  area,  separate  curves 
have  been  drawn  for  several  different  areas,  and  the  force 
per  unit  area  on  any  other  surface  can  be  found  by  interpola- 
tion. The  curves  were  plotted  by  modifying  Zahm's  formula: 

JB,  =  0.0000082. 1  -<«r..» 

where  F  is  in  feet  per  second.  To  throw  this  into  mile  hour 
units  it  was  necessary  to  multiply  by  (ff)l'"°,  or  2.04,  giving 

R,  =  0.0000167  .-I  •T'" 

In  Tables  1  and  2  similar  data  has  been  given  for  speeds  ir 
feet  per  second  and  miles  per  hour. 

Turbulent  Flow,  Eddy  or  Density  Resistance 

We  have  already  seen  in  the  case  of  a  flat  plate  normal  to 
the  wind  that  the  resistance  was  due  to  a  region  of  turbulent, 
eddying,  low  pressure  behind  the  plate.  This  resistance  varies 
as  o  .1  I"" 

where  .1  =  area  in  normal  presentation 
2   =  density 
V  —  velocity. 

It  will  be  assumed  for  the  time  being  that  wherever  there  is 
a  region  of  turbulent,  eddying  flow,  there  will  be  a  density 
resistance 

/,-  ~  Ml" 

A  fairly  complete  demonstration  of  this  has  been  given 
by  a.  French  author. 

Comparison  of  Forces  Acting  Upon  Similar  Bodies.   The 

Importance  of  Kinematic  Viscosity  and  the 

Reynold's  Number 

For  the  comparison  of  forces  acting  on  similar  bodies,  a 
knowledge  of  the  geometric  proportions  and  of  the  wind  veloc- 
ities is  insufficient.  The  density  of  the  fluid,  the  viscosity  and 
hence  the  coefficient  of  kinematic  viscosity,  and  the  compressi- 
bility of  the  fluid  all  enter  into  the  complete  comparisons. 

Compressibility,  we  have  seen,  may  fortunately  be  neglected 
in  all  aerodynamical  work. 

For  bodies  in  which  the  resistance  is  purely  of  a  density 
or  eddy  making  nature — as  in  the  case  of  a  flat  plate  normal 
or  inclined  to  the  wind,  and  as  we  shall  see  subsequently  in 
the  case  of  a  wing  section  at  large  angles — viscosity  does  not 
enter  into  consideration,  or  is  of  so  small  importance  that  it 
may  be  neglected,  [n  such  cases 

where  .1  is  the  area  of  one  face  of  the  plate,  comparison  be- 
tween two  bodies  such  as  a  full  sized  wing  and  its  model  be- 
come extremely  simple. 

But  for  stream  line  bodies  such  as  struts,  cables,  wires,  and 
cylinders  the  resistance  is  compounded  of  density  resistance 
and  viscosity  resistance  in  varying  proportions. 

Viscosity  resistance  depends,  as  we  have  seen,  on  velocity, 
linear  dimensions  and  the  coefficient  of  kinematic  viscosity. 
For  such  bodies  therefore  the  resistance  must  be  expressed  in 
a  form  involving  these  variables,  and  by  the  principle  of 
dynamic  similarity  it  can  be  demonstrated  that 

R  =  '-f  f"*/ 

where  /  is  some  unknown  function  and  f  is  of  the  same  di- 
mensions as  A.  The  5  I"  I'"'  brings  out  the  density  resistance. 

,//l'\  IV 

I  I      -  Ithe  viseositv  resistance:  since  — =  the  Reynold's  num- 

v  /  v 

ber  r,  we  can  write 


The  reader  will  now  appreciate  the  importance  of  the  Rey- 
nold's number  in  comparing  the  resultant  forces  on  the  above 
mentioned  bodies. 

It  is  quite  incorrect  to  compare  such  bodies,  making  allow- 
ance for  variation  in  f  and  V"  only  unless  the  Reynold's  num- 
ber is  the  same  for  the  two  bodies  under  comparison. 

In  practice  it  is  very  rare  that  comparisons  of  forces 
are  made  with  reference  to  two  different  fluids.  We  are  al- 
most solely  concerned  with  bodies  in  air.  The  coefficient  of 
viscosity  becomes  a  constant,  and  instead  of  considering  the 
Reynold's  number,  we  can  drop  the  v  and  compare  bodies 
having  the  same  product  IV. 

Stream  Line  Bodies 

A  stream  line  body  may  be  defined  as  one  which  has  a 
gradual  change  of  curvature  along  any  section,  and  which 
when  moved  through  air  or  water  at  ordinary  speeds  makes 
little  disturbance  or  turbulent  wake.  Such  a  body  moving 
in  a  viscid  fluid  would  experience  mostly  frictional  resistance. 

Energy  Considerations  for  a  Perfect  Fluid  Flowing 
Past  a  Stream  Line  Body 

It  is  most  useful  to  have  a  definite  idea  of  the  exchange  of 
energy  which  occurs  in  such  a  case.  The  first  treatment  ap- 
pears to  have  been  given  by  W.  Fronde. 

Imagine  the  fluid  in  the  vicinity  of  the  body  to  be  divided 
up  into  a  large  number  of  imaginary  tubes  of  flow.  Well 
ahead  of  the  body  where  the  stream  is  as  yet  undisturbed  the 
energy  of  the  fluid  will  be  that  due  to  the  static  pressure  pa  of 
the  stream  and  the  kinetic  energy  head  of  !"„.  the  undisturbed 
velocity.  In  a  perfect  fluid  this  will  remain  a  constant  along 
any  tube  of  flow  by  Bernouilli's  theorem,  and  is  equal  to 

PO        TV  __       _  '_/<        _!" 
For  the  portion  L.  as  shown  in  Fig.  15,  of  the  body,  the  tubes 


FIG.  15.     LINKS  OK  FLOW  FOI:  A  STIJKAM  Lixio  BODY. 

of  flow  widen  out,  the  velocity  and  the  kinetic  energy  head 
diminish  and  the  pressure  on  the  body  becomes  greater  than 
the  static  pressure  p».  The  nose  of  the  body  therefore  does 
work  upon  the  fluid  in  contact  with  it.  This  is  also  evident 
by  considering  the  effect  of  curvature  and  the  centrifugal  force 
resulting  from  it.  For  the  portion  31  the  tubes  crowd  together, 
the  velocity  increases  and  the  body  is  under  the  action  of  a 
pressure  less  than  pa — it  is  really  under  suction  and  the  fluid 
does  work  on  the  body.  By  similar  reasoning  it  can  be  shown 
that  the  portion  .V  the  body  works  upon  the  fluid,  and  for 
the  portion  P,  the  fluid  works  upon  the  body.  The  balance  of 
work  done  on  the  body  is  thus  found  to  be  zero. 

Stream  Line  Bodies  in  a  Viscous  Fluid 

At  slow  speeds  in  water  almost  perfect  stream  line  motion 
has  been  observed  and  recorded  by  Dr.  Ahlborn  (see  Fig.  16). 
But  at  ordinary  speeds,  even  with  stream  line  forms,  there  is 


30 


AERODYNAMICAL  THEORY  AND  DATA 


It  is  obvious  that  the  resistance  will  be  partly  due  to  viscos- 
ity over  the  front  part  of  the  cylinder,  and  partly  due  to  eddy 
or  density  resistance.  The  forces  in  action  will  therefore  be 


Fiu.  1C.    MOTION  AKOUND  A  STREAM  LINE  BODY. 

always  a  region  of  turbulence  and  eddying  motion  such  as  we 
have  already  observed  in  the  case  of  the  flat  plate,  accom- 
panied by  a  surface  of  discontinuity  between  the  main  stream 
and  the  turbulent  region.  The  eddying  motions  are  in  part 
due  to  pressure  differences  in  the  undisturbed  stream  and  the 
region  behind  the  body,  in  part  due  to  viscosity.  The  exact 
theoretical  investigations  of  the  causes  at  play  are  unimportant 
from  the  designer's  point  of  view.  It  is  more  important  to 
notice  that  just  as  in  the  case  of  the  flat  plate,  this  turbulent 


FIG.  19.    FLOW  AROUND  A  CYLINDER. 

represented  as  previously  stated  by  an  expression  of  the  form 
PfFV(r). 

And  two  wires  or  ruble's  will  only  be  comparable  when  r  is 
the  same  for  both,  or  simply  when  the  product  IV  is  the  same. 

Fluid  Motion  Around  Wing  Surface 

It  is  to  Langley,  above  all  other  men,  that  we  owe  an  appre- 
ciation of  the  value  of  cambered  surfaces.     A  good  \\iiu 


i-lG.    17.      t'LOW    FOR  A   SHORT   STRUT. 

region  will  be  a  region  of  low  pressure  and  will  introduce  a 
density  or  eddying  resistance. 

This  density  resistance  for  a  stream  line  body  may  be  said 
to  increase  with  the  extent  of  the  turbulent  region.     Thus  in 


f  lli.   20.       t  LOW    FOR  A    I'AMIIKKKII    WlMi   AT    -    . 


tion  may  give  a  lit't-drit't  ratio  of  18  as  compared  to  I  lie 
6  or  7  of  a  flat  plate,  and  it  is  the  remarkable  efficiency  of  a 
wing  surface  which  has  largely  rendered  aviation  possible. 

In  wing  surfaces,  we  recognize  two  distinct  types  of  flow. 
For  the  small  angles  up  to  6°  or  thereabout-;  a  sle.ulv  flow  as 
shown  in  Fig.  20  for  a  typical  airplane  wing.  At  this  angle — 


J'Ki.  18.     >  l.ow   KIR  r  INK  .-MI: 

17  and  18  depleting  two  standard  struts,  the  finer  strut 
has  a  smaller  turbulent  region  and  con>idorahly  less  resistance. 
On  the  other  hand,  as  the  fineness  ratio,  or  the  ratio  of  length 
to  maximum  thickness,  of  a  stream  lino  body  increases,  the 
•res  in  shear  and  the  viscosity  drag  itic-rea.se  also:  the  fineness 
ratio  niu-t  l>e  kept  within  reasonable  limits  even  from  a  purely 
aerodynamic  point  of  view. 

Resistance  of  Wires,  Cables  and   Cylinders 

111  repn-i-nt-  diagrimmticiilly  the  fluid  motion  round 
a  cylindrical  Ixidy,  such  as  a  wire  or  cable,  at  usual  airplane 
speeds. 


I'l.llU     KH<    A    (    .\.\lltKlthll    \\INli    AT    10" 


often  termed  the  first  or  lower  critical  angle,  turbulence  begins. 
At  Id',  as  shown  in  Ki-_'. '-'1.  this  turbulence  is  (piite  consider 
able.  Finally  a  second  critical  or  "  burble  point"  is  reached 
at  18°  for  the  same  wing.  Here  an  extremely  turbulent  type'  of 
motion,  as  shown  in  FJL'.  1'-  is  found,  and  the  lift  of  a.  wing 
attains  its  maximum.  Beyond  this  "  burble  point  "  the  motion 
becomes  extremely  unsteady  and  the  lift  decreases. 


AERODYNAMICAL  THEORY  AND  DATA 


31 


The  lift  of  a  wing,  as  experiment  shows,  varies  directly  as 

p  AV,  with  a  different  coefficient  for  everj  angle  of  incidence. 

Where  turbulent  flow  is  present  this  is  readily  explainable, 


FKI.  22.    FLOW  roii  A  OAMDKRED  WING  AT  18°. 

as  in  the  case  of  the  flat  plate,  on  the  hypothesis  of  low  pres- 
sure region  at  the  back  of  the  wing. 

It  is  the  lifting  power  at  small  angles  and  in  a  condition 
of  steady  flow  that  offers  theoretical  difficulties.  The  most 
likely  explanation  is  offered  by  Kutta's  theory  or  the  vortex 
theory  of  sustentation.  We  shall  reserve  the  full  treatment 


FIG.  2li.     A  KiiOPLANE  WING  WITH  TRAILING  VORTICES. 

of  this  theory  also  to  a  special  article,  contenting  ourselves 
with  the  barest  outlines: 

An  airplane  wing  in  steady  flow  gives  off  a  series  of  trail- 
ing vortices  as  depicted  diagrainatically  in  Fig.  23.  These 
vortices  are  constantly  destroyed  and  renewed.  The  circular 


motion  in  these  vortices  and  their  interaction  is  such  that — 
as  the  hydrodynamical  theory  demonstrates — they  have  a 
downward  momentum,  and  action  and  reaction  being  equal, 
the  airplane  wing  receives  an  upward  momentum. 

The  drift  or  drag  of  a  wing  is  for  all  practical  purposes 
taken  as  varying  directly  with  A  I'",  with  a  different  co- 
efficient for  every  angle  of  incidence. 

At  high  angles  of  incidence,  the  drift  is  almost  entirely 
a  component  of  the  density  resistance,  and  we  see  that  what  is 
taken  to  be  the  case  in  practice,  is  also  theoretically  correct. 
But  at  small  angles  and  steady  flow  the  resistance  is  more  of 
a  viscous  nature,  more  akin  to  skin  friction.  And  skin 
friction,  as  we  have  already  seen,  varies  as  I'1'8",  and  depends 
also  on  the  dimensions  of  the  body.  This  introduces  con- 
siderable difficulties,  as  we  shall  see  later,  in  computing  re- 
sistance in  actual  flight  from  small  model  experiments  at  low 
speeds. 

As  to  the  form  of  wing  giving  the  best  results,  no  general 
laws  are  yet  available,  and  each  type  of  wing  must  be  con- 
sidered separately. 

This  section  constitutes  but  a  brief  introduction  to  aerodyn- 
amical theory,  but  will  perhaps  assist  the  reader  in  the  ap- 
preciation of  the  extensive  aerodynamical  data  which  we  shall 
present  later. 


References  for  Chapters  2  and  3 

"  A  Krview  of  Hydrodynamical  Theory  as  Applied  to  Experimental 
Aerodynamics,"  3.  C.  Ilunsaker,  International  Engineering  Congress, 
San  Francisco.  Sept.,  I'.iir,.  An  authoritative  and  advanced  treatment; 
containing  numerous  references  for  further  readine. 

"  Aerodynamics."  F.  W.  Lanchestcr  (Archibald  Constable  &  Co., 
Ltd.,  London.)  A  valuable,  classical  treatise. 

"The  Aeroplane,"  A.  Fage  (Griffin  &  Co..  London).  A  concise  scien- 
tific study,  excellent  in  matter  and  presentation 

•'  The  Aeroplane,"  T.  O'B.  Hubbard,  J.  H.  Ledeboer,  and  C.  C. 
Turner  (Longmans.  Green  &  Co.,  London).  An  elementary  text  book 
cif  the  principles  of  dynamic  flight,  suitable  for  beginners. 

"  Loitfaden   der   Flugtechnik,"    S.    Huppert    (Springer,   Berlin). 

"  Wind  Resistance  of  Some  Ae-oplane  Struts,"  Booth  and  Eden. 
Technical  report  of  the  (British)  Advisory  Committee  for  Aeronautics, 
1911-1912,  No.  49  (Wyinan  &  Sons,  Ltd.,  London). 

"  Investigation  by  Visual  and  Photographic  Methods  of  the  Flow 
Past  Plates  and  Models,"  Eden.  British  report,  1911-1912,  No.  58. 

••  Photographic  Investigation  of  the  Flow  Hound  a  Model  Aerofoil," 
Keif.  British  report,  1912-1913,  No.  76. 

These  papers  in  the  British  report  contain  some  beautiful  and  In- 
structive photographs. 


Chapter  IV 

Flat  Plates :  Simple  Problems  on  Sustention  and 

Resistance  of  Wing  Surfaces 


Coefficients  of  Resistance  for  Circular  or  Square  Plates 
Normal   to   the   Wind.    Varying   Sizes 

Although  it  would  seem  that  the  question  of  the  forces  on 
a  flat  plate  placed  normally  to  the  wind  would  be  fundamental 
in  aeronautics,  and  although  it  can  be  shown  by  the  principle 
of  dynamical  similarity  that  similar  plates  should  have  the 
same  coefficients  no  matter  what  their  size,  provided  that  IV 
remains  constant,  yet  considerable  controversy  exists  as  to  the 
variation  in  the  values  with  the  size  of  plate,  and  with  the 
velocity  of  flow.  Those  who  are  interested  in  the  controversial 
aspect  of  the  question  are  referred  to  the  references  at  the  end 
of  the  section.  For  all  practical  purposes,  the  following  table 
may  be  safely  used. 

R  =  KA  V  where  S  =  resistance  in  pounds. 

A  =  area  of  plate  in  square  feet. 
V  =  velocity  in  miles  per  hour. 

TAIU.I.    1. 
Side  of  Square 
or  Diameter  of 
Circular  Plate, 

In  Feet.  fc- 

O  %  00269 

.     .00286 

2V!  00814 

SO     00.122 

50  00.127 

10.0 00327 

Coefficients  for  Rectangular  Flat  Plates  Normal  to  the 
Wind.      Varying    Aspect    Ratio 

The  aspect  ratio  of  a  flat  plate  is  the  ratio  of  b  to  a  a.< 
shown  in  the  Fig.  1.  With  increased  aspect  ratio  the  resistance 

coefficient  increases.  A  thor- 
ough theoretical  ilisrussion  of 
this  invol-  •  nlou-  ilif- 

fieillties,  but  the  inere.i 
probably  due  to  the  faet  thai 
with  inereaseil  aspect  ratio 
the  air  How  i>  broken  up  into 
a  greater  number  of  vortices. 
with  a  resultant  '.'iratcr  tur- 
bulence. The  following  table 


TIIK     Wisi' 


These  values  are  plotted  in  Fig.  2  and  are  assumed  to  be 
true  independently  of  the  size  of  the  plate. 


-hows   the   effect    of   inci  • 
a-peet    ratio,   accorilini;   to  e\ 
penment-  by   KilTel.     The  co- 
efficient  tor  ;i   -i|iiaie  plat.-  ol    the  -ame  aren   i-  taken  a-  unity. 


TAB1 


Anpect   Rjitln 


K  fur  lln-taiiuulnr  Plate 


ii 


1  :. 
10.0.  . 

-.0  O 


.10 

20 

.".  i 

'.47 


I;  iso 
\ 
4, 

^ 

^- 

jr^ 

Ratio  of  pressure  to  pressure  on  a  si 

$  *  §  S  8 

/ 

s^ 

/ 

/ 

/ 

/ 

Variation  with  as- 
pect ratio  of  the 
pressure  on  a 
normal  flat  plate 

/ 

/ 

2 

1    J 

r  —  -4 

0       4 

T~3 

r      o      s    - 

>o    ^s•    J 

Aspect  Ratio 

FII;.  -2.     VARIATION  WITH  AM-NT  RATIO  OF  TIM:  PRKSSI-RK  ON 
\   NORMAL  FLAT  Pi  ATI 

Coefficients  for  Flat   Plates   Inclined   to  the  \\  in.l 

Table  .'!   gives   valuer    for   A\.    A',,   anil   1.  \>.   and    Table 
the  distance  of  the  center  of  the  pressure  from  the  leading 
edge  of  the  plate  in   terms  of  the  chord,  for  flat   plate-   of 
variiiti-  Biped   ratio.-.     The  ilra-r  al  "     may  lie  calculate.! 
/.ahni's  formula  for  skin  friction. 
TAT,  i 


ratio  =  1. 

Asjii-ct  ratio 

Angle 

•»  .    , 

1  n 

K, 

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Angli 

10. 

20. 

to. 

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00010 
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OO026 

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LID 
S.2 
4.7 
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00126 

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\-|i,  it 

n.ti,,        1    ::. 

Aspect  ratio  =  1/6. 

Ang 

A 

.00007 

'-M 

Anglt.           A 
00020 

.00008 

Lin 

4.0 

.ooo.-.'.l 

OOO  1  t 

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.88 

AERODYNAMICAL  THEORY  AND  DATA 


33 


0030 

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/  / 

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ill 

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Left  Coefficients 
for  Rectangular 
Flat  Plates  of 
Various  Aspect 
Ratios.  Units:  Lbs. 
per  Sq.  rt.;  Miles 
per  Hrr 

Asp  RO.-I.  
1.5  
2  
3.  
6.  

N 

^S 

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IO'           SO"          3O"          4O'           SO"          6O'           7O~         8U~          ai 
Anff/e  of  Incidence. 

7 

e 

5 

4 

L 

s. 

t 

-j 

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3 

0 

It 
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t 

^ 

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/ 

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i 
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Rat/o  of  £.fft  to 
Drag  tn    Rectangu- 
lar Flat  P/ates  of 
Various  Aspect  Ra- 
tios. 

1 

f 

/ 

?           f          icy         L 

T'            Si 

FIG.  3.    LIFT  COEFFICIENTS  FOR  RECTANGULAR  FLAT  PLATES  OF  VARIOUS 

ASPECT  RATIOS 


Angle    of  Incidence. 

FIG.  4.    RATIO  OF  LIFT  TO  DRAG  IN 

RECTANGULAR  FLAT  PLATES  OF 

VARIOUS  ASPECT  RATIOS 


TABLE   4. 

DISTANCE    OP    CENTER    OF    PRESSURE    FROM    LEADING    EDGE,    MEASURED    IX 

TEEMS    OF    CHORD,    FOR    RECTANGULAR    FLAT    PLATES    OF    VARIOUS 

ASPECT    RATIOS. 


A.  E. 

=  1. 

A.  R. 

=  3. 

A.  R 

.  =  6. 

A.  E. 

=  1/3. 

A.  B. 

=  1/6. 

Dlst. 

Angle. 

Dist. 

Angle. 

Dlst. 

Angle. 

Dlst. 

Angle. 

Dist. 

Angle. 

.12 

.8 

.233 

5.0 

.267 

3.0 

.167 

3.0 

.289 

2.5 

.16 

1.0 

.267 

7.8 

.300 

8.0 

.267 

5.0 

.311 

7.5 

.18 

2.0 

.300 

10.0 

.333 

10.0 

.283 

6.8 

.323 

10.5 

.20 

2.8 

.333 

12.0 

.367 

12.2 

.300 

10.8 

.334 

19.0 

.22 

3.8 

.367 

13.8 

.400 

26.0 

.317 

17.5 

.345 

49.0 

.24 

6.5 

.400 

17.5 

.433 

54.0 

.333 

30.5 

.356 

52.0 

.28 

13.0 

.433 

52.8 

.467 

73.7 

.350 

45.0 

.367 

53.5 

.30 

15.3 

.467 

73.7 

.500 

90.0 

.367 

47.8 

.378 

56.2 

.32 

18.0 

.500 

90.0 

.383 

50.2 

.389 

58.0 

.34 

21.0 

.400 

52.5 

.400 

59.5 

.36 

25.0 

.417 

54.3 

.411 

60.0 

.38 

28.0 

.433 

56.5 

.422 

63.0 

.40 

33.5 

.450 

65.0 

.433 

64.0 

.42 

39.0 

.467 

77.8 

.444 

68.5 

.44 

55.2 

.483 

85.8 

.455 

72.5 

.46 

73.5 

.500 

90.0 

.466 

80.0 

.48 

84.0 

.477 

84.0 

.488 

87.5 

.SCO 

no.o 

]  n  Fig.  3  are  plotted  values  of  Kr  against  angle  of  incidence 
for  various  aspect  ratios.  In  Fig.  4  the  same  treatment  is 
applied  to  the  L/D  ratio. 

In  Fig.  5  are  indicated  the  positions  of  the  center  of  pres- 
sure for  various  aspect  ratios  and  angles  of  incidence.  In  Fig. 
6  the  directions  and  points  of  application  of  the  resultant 
forces  are  indicated  for  a  flat  plate  of  aspect  ratio  6 — the 
value  which  is  usually  employed  for  purposes  of  comparison 
— in  order  to  give  the  reader  a  more  graphic  idea  of  the 
forces  at  play. 

In  all  these  values  it  may  be  noted  that  no  allowance  is 
made  for  possible  variation  in  the  coefficients  with  size  of 
plates,  and  this  is  probably  accurate  enough  for  all  practical 
purposes. 


Preliminary    Application    of   Data    for   Flat    Plates    in 
Rudder  and  Elevator  Design 

These  curves  and  tables  give  fairly  complete  data  for  flat 
plates  and  are  likely  to  meet  all  the  requirements  of  design. 


Distance  of  C.Pfrom  leading  edge. 
<  r«  U)  -Iv 

_____ 



______  _ 

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sr-=3 

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tf 

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T' 





' 

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Travel  of  Cet 
Pressure  in 

nter  of 
ffectang- 
es  of 

it  Ratios. 
7— 

1 

ular 
Vartc 
Asp.h 

Flat  Plat 
ius  Aspec 

>a.**  
/ 

R 

•J                  10'              ,SO-              30'               40"               SO- 

-Anyle  of  Incidence. 

FIG.  5.     TRAVEL  OF  CENTER  OF  PRESSURE  IN  RECTANGULAR 
FLAT  PLATES  OF  VARIOUS  ASPECT  RATIOS 

It  may  be  useful  to  indicate  a  few  salient  points,  and  to  make 
preliminary  reference  to  the  design  of  flat  rudders  and  eleva- 
tors. 

(1)  For  plates  of  all  aspect  ratios  when  turned  from  zero 
angle,  the  lift  increases  until  the  critical  angle  or  "  burble 
point "  is  reached.  Beyond  this  angle  the  lift  rapidly  de- 
creases, and  no  rudder  or  elevator  should  be  employed  beyond 
this  critical  angle. 


34 


AERODYNAMICAL  THEORY  AND  DATA 


(2)  The  lift  drag  ratio  is  not  much  improved,  for  flat  plates 
at  the  same  angles,  by  increased  aspect  ratio.  For  all  plates 
the  ratio  reaches  its  maximum  value  at  small  angles,  6*  or  7*. 
At  angles  still  smaller  it  decreases,  due  to  the  predominating 


Fio.  6.    DIAGRAM  SHOWING  DIRECTION  AND  POINT  OF  APPLI- 
CATION OF  RESULTANT  FORCE  IN  A  RECTANGULAR  FLAT 
PLATE  OF  ASPECT  RATIO  6  AT  SMALL  ANGLES  OF  INCIDENCE 

effect  of  the  skin  friction.  Plates  of  large  aspect  ratio,  being 
more  sensitive  at  small  angles,  are,  on  the  whole,  more  efficient 
in  flight. 

(3)  On  the  other  hand,  plates  of  small  aspect  ratio  have 
the  critical  angle  much  later  and  give  a  wider  range  of  action. 
They  also  give  a  much  higher  lift  at  the  critical  angle,  which 
is  important  in  the  action  of  the  rudder  when  "  taxying  "  at 
low  speeds  on  the  ground. 

(4)  For  the  elevator,  which  is  more  constantly  used  in  the 
air,  and  from  which  great  liftine  power  is  not  required  on  the 
ground,  an  aspect  ratio  of  three  seems  a  fair  compromise. 

(5)  For  the  rudder,  the  above  considerations  seem  to  indi- 
cate an  aspect  ratio  of  one  or  two  as  advisable. 

(6)  It  should  be  noted  that,  as  the  angle  of  incidence  is  in- 
creased, not  only  does  the  force  increase,  but  also  that  from 
the  point  of  application  of  the  resultant  force  to  the  hinge, 
giving  a  greatly  increased  moment  about  the  hinge.    If  either 
the  elevator  or  the  rudder  is  placed  too  near  the  wings  it 


D     •  . 

XTN 

! 

1 
J 

E 

Rudder, 
Balance 

"7      T                  \ 

)?    Aspect 
Pi  Ratio. -g-. 


*-El«voior    Ploo«»-x 

Fio.  7.    DIAGRAMS  FOR  ASPECT  RATIO  IN  RUDDER  AND  KLKVATUI: 

necessitates  large  nn-.-i-  for  the  controlling  .-ur  fa  <•<•«,  and  the 
pilot  may  have  to  exert  tremendous  force  at  large  angles. 

(7)  To  obviate  the  necessity  of  exercising  large  forces  on 
the  controls,  it  is  possible  to  use  a  balanced  rudder;  one  in 
which  the  hinge  is  placed  about  in  the  position  of  the  center 
of  pressure  at  small  angles.  The  rudder  in  Fig.  7  is  a  balanced 


rudder.     It  should  be  noted  that  the  "  balance  "  is  only  ap- 
proximate. 

Problems  on  Flat  Plates 

A  rectangular  flat  plate  4  feet  9  inches  high  and  3  feet  a 
inches  long  is  employed  as  a  rudder,  and  is  placed  with  its 
leading  edge  at  a  distance  of  18  feet  from  the  center  of  grav- 
ity of  the  machine.  The  machine  is  traveling  at  CO  miles  an 
hour.  The  rudder  is  hinged  at  the  leading  edge,  while  the 
control  leads  are  one  foot  from  the  rudder  surface.  (See  Fig. 
8.)  Find  (a)  the  frictional  resistance  of  the  rudder  when 


FIG.  8.    RUDDER  FOR  PROBLEM  ON  FLAT  PLVTKS.     RCDPER  is 
UNBALANCED  AND  HINGED  AT  LEADING  EDGE 

neutral;  (b)  its  turning  moment  about  the  center  of  gravity 
when  set  at  an  angle  of  10°  and  its  resistance  at  that  angle; 
(c)  the  tension  in  the  control  lead  under  the  same  conditions 
as  (b). 

(a)  The  area  of  the  rudder  =  2  X  SVc  X  4%  =  30  square 
feet.    From  Fig.  13  in  Chapter  3,  we  sec  that  the  t'rictinnul  re- 
sistance on  a  surface  of  15  square  feet  at  60  miles  an  hour 
equals  .0285  pounds  per  square  foot.    Thus  tin-  total  f  fictional 

=  2X  15  X  -0-s:'      >i;-  rounds. 

(b)  The  aspect  ratio  of  the  rudder  =  1.5.     The   distance 
from  the  leading  edge  to  the  center  of  pressure  is  given  by  Fig. 

5.      Interpolating    between    (A. !{.  =  !)    illnl    (A.Ii.          3),    u 

that  the  center  of  pressure  on  a  plate  of  aspect  ratio  1.5  at  an 
angle  of  incidence  of  10  deg.  is  .L'(!S  of  the  chord  from  tlie 
leading  edge.  Thus  the  desired  distance  -  :!',-,  X  .268  =  .S.".  It. 

The  moment  arm  about  the  center  of  gravity  longitudinally 
(see  sketch  of  machine)  =  18  +  .85  cos  10°  =  18.84  fed. 

The  moment  arm  about  the  center  of  gravity  laterally  =  .85 
sin  10°  =  .14  feet. 

By  Figs.  3  and  4,  K,  =  .00109  and  L/D  =  5.5.  Then  L,  the 
rone  peipcndicular  to  ilie  line  of  ilighi.  i  A".  I  I  .nnl09X 
15X(60)'  =  5S.!I  pound,,  and  1>.  the  reM>laiicr,=  L^D/L  = 

58  9 

=  10.8  pounds.     It  will  be  seen  that  turning  the  rudder 
5*5 

causes  a  decided  increase  in  the  resistance  of  the  machine. 

The   above    work  a    basis    tor    rapidlv    computing 

the  turning  moment.     M  =  58.9  X  18.84  +  10.8  X  -14  =  1112 

pound  feet,  taking  the  movements  of  hotli  the  lift,  and  the  drag 
about  the  center  of  t;ra\ity. 


AERODYNAMICAL  THEORY  AND  DATA 


35 


(c)  The  turning  moment  about  the  leading  edge  of  the 
rudder  =  58.9  X  -85  cos  10°  +  10.8  X  -85  sin  10°  =  51  pound 
feet. 

Moment  arm  of  control  lead  =  cos  10°  =  .986  foot. 

Then,  since  the  stress  in  the  control  lead  times  the  moment 
arm  must  just  balance  the  turning  moment  of  the  rudder  about 

51 

its  axis,  tension  in  lead  =  — —  =  52.7  pounds 
.986 

General  Considerations  of  Sustaining  Power  and 
Resistance  of  Wing  Sections 

We  have  seen  that  the  equation  for  lift  is 

L  =  K7AV  (1) 

where  Ky  is  a  constant  varying  with  the  angle  of  incidence, 
A  =  area  in  square  feet,  and  F  =  speed  in  miles  per  hour. 

In  horizontal  flight,  the  lift  equals  the  weight  of  the  ma- 
chine, W,  and  the  equation  becomes 

W  =  K,AV  (2) 

which  can  be  expressed  in  the  forms 
W 


AV1 


(3) 

(4) 

(5) 

as  may  be  convenient.     The  lift  coefficient  is  small  at  small 
angles  and  increases  at  larger  angles  until  the  "  burble  "  point 


W 

-f*-.         —    ^—     -r^* 


3.0   30 
ZB    £B 
2.6  ZB 
S.4  £4 
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JL 

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Characteristic    Curves 
for  R.A.F  6    Wing   Sec- 
t/on.   Wind  Speed-  3O 
ft  per-  sec.     DV'7.5 
Units:  Lbs.  per  Sq.  ft; 
Miles  per   Hour 

3 

r 

/ 

/ 

// 

JL 

'-•      0-      a-      4-      B-      B'      tO-     /2'     14'     16-     It 

Angle  of  Incidence. 
Fin.  9.    CHARACTERISTIC  CURVES  FOR  R.  A.  F.  6  WING  SECTION 

or  critical  angle  is  reached,  as  can  be  seen  from  the  curve  of  a 
standard  wing  section  (R.  A.  F.  6)  in  Fig.  9. 

From  these  considerations  may  be  deduced  the  following 
ideas,  which  should  become  absolutely  familiar  to  every  student 
of  aeronautics: 

A  machine  traveling  fast  will  require,  by  equation  (3),  a 
small  value  of  Ky,  and  hence  a  small  angle  of  incidence.  Con- 
versely, flying  slowly  it  will  require  a  large  angle  of  incidence. 

Sustaining  a  given  weight,  we  can  vary  angle  of  incidence 
and  either  area  or  speed. 


If  we  give  a  machine  a  large  wing  area,  it  will  fly  slowly. 
With  a  small  area,  it  will  attain  a  high  velocity  if  sufficient 
engine  power  is  available. 

The  drag  equation  is 

D  =  KfAV  (6) 

The  higher  the  value  of  L/D,  the  smaller  will  be  the  drag 
for  a  given  lift  and  weight  of  machine  at  a  given  speed,  and 
the  less  will  be  the  power  required.  The  ratio  L/D  is  therefore 
a  measure  of  the  wing  efficiency.  For  the  R.  A.  F.  6,  the  maxi- 
mum value  of  L/D  is  at  about  4°  and  at  about  this  angle  a 
machine  would  fly  at  its  greatest  efficiency. 

We  have  here  neglected  all  other  resistances  than  those  of 
the  wings.  These  resistances  will  modify  the  drag  equation 
and  the  best  angle  of  flight.  We  shall  deal  with  these  modifica- 
tions under  the  Economic  Laws  of  Flight. 

Problem  of  Sustentation  and  Resistance  of 
Wing  Surface 

A  monoplane  weighing  2000  pounds  uses  an  R.  A.  F.  6  wing 
section. 

(a)  What  area  will  it  require  so  that  its  lowest  speed  may 
be  45  miles  an  hour? 


CO 


'GO        ~  SS  GO  65       .TO  75  SO  35          90 

Speed  (Miles  per  Hourj 

FIG.  10.    RESISTANCE,  HORSE-POWER  AND  SPEED  DIAGRAM 


(b)  What  will  be  the  drag  of  the  wing  at  this  speed  and 
what  will  be  the  horse-power  required  for  the  wing  alone? 

(c)  Assuming  that  the  parasite  resistance  (resistance  of  the 
body,  chassis,  wires,  struts,  etc.)  is  120  pounds  at  60  miles  an 
hour,  and  that  it  varies  directly  as  the  square  of  the  speed, 
what  will  be  the  total  resistance  and  horse-power  required  at 
this  speed? 

(d)  If  the  power  delivered  at  the  propeller  is  100  horse- 
power, what  is  the  maximum  speed  available? 

(a)  Let  A  =  wing  area 

W  =  weight  of  machine 
D  =  drag  of  wing 
P  =  parasite  resistance 
R  =  total  resistance  =  D  +  P. 

From  Fig.  9  we  see  that  the  maximum  value  of  K,  is  .00309, 
at  16°.    Then,  since  W  =  K,AV*,  and  V  —  45  miles  per  hour, 

W  2000 

—    .  =  319  square  feet. 


A  = 


.00309  X(45)2 


2000 


(b)   From  Fig.  9,  L/D  at  16°  =  6.8.    Then  D  =  =  294 

6.8 
pounds. 

Since  ~,  horse-power  is  required  to  overcome  a  resistance 

o  /  O 

of  1  pound  at  1  mile  per  hour,  horse-power  =  — 

375  375 

=  35.3  horse-power  to  overcome  wing  drag  at  45  miles  per 
hour. 


36 


AERODYNAMICAL  THEORY  AND  DATA 


The  drag  of  the  wings  can  also  be  obtained,  of  course,  by 
substituting  the  proper  value  of  A",  in  the  equation 


The  first  method  described  will  prove  the  simpler  when  a 
number  of  cases  are  to  be  worked  out.  but  the  second  is  more 
accurate  at  very  small  angles  of  incidence. 

W  9ftf>ft 

(c)  At  60  miles  an  hour  K,  =  —  =  g^SO?  =  -00174. 

Fig.  9  shows  us  that  this  value  of  K,  will  be  attained  at  an 
.•iii-;lp  of  incidence  of  5.7°,  at  which  angle  L/D  =  14.2. 

10  =  141  pounds,  and  R  =  D  +  P  =  141  +  120 


=  14.2 
=  261  pounds. 

EV       261  x  60 
The    power    required    equals  — r  =  — — : — 

OYO  O/O 


:  41.8   horse- 


power. 

(d)  In  order  to  determine  accurately  the  speed  obtainable 
with  a  given  power,  it  is  necessary  to  plot  a  curve  of  power 
required  at  various  speeds.  In  computing  points  on  this 
curve,  we  assume  the  parasite  resistance  proportional  to  V. 
This  is  approximately  true,  the  deviation  being  due  to  changes 
in  resistance  coefficients  of  body,  struts,  etc.,  as  the  angle  at 
which  they  meet  the  wind  changes.  Proceeding  on  this  assump- 
tion, P  =  KV.  since  P  =  120  pounds  when  F  =  60  miles  per 

hour,  K  =  -j  =  .0333,  and  P  =  .0333  F1. 

In  Table  5  are  given  a  few  points  on  such  a  curve,  com- 


puted as  was  that  for  60  miles  an  hour,  which  we  just  secured. 
A  student  might  carry  through  some  of  these  computations, 
checking  his  results  against  those  here  given,  in  order  to  make 
sure  that  the  method  is  perfectly  clear  to  him. 


TABLE  5. 


r 

K, 

Angle 
of  inc. 

/C. 

L/D 

D 

P 

R 

WlM 

ii.  i: 

Para- 
site 
II.  P. 

Total 

II.  P. 

U 

.00309 

16.0 

.000446 

6.9 

289 

67 

356 

34. 

8 

8.0 

42.8 

30 

.00251 

9.9 

.0(10218 

11.5 

174 

83 

257 

u:: 

11.1 

34.3 

55 

.00207 

7.4 

.000156 

13.3 

150 

101 

251 

•-2, 

1 

14.8 

36.9 

60 

.00174 

5.6 

.000122 

14.3 

140 

120 

260 

L-J 

4 

19.2 

41.6 

65 

.00148 

4.4 

.000102 

14.5 

138 

141 

279 

LM 

.0 

24.4 

48.4 

70 

.00128 

3.5 

.000093 

13.8 

145 

163 

308 

•21 

.1 

30.4 

57.5 

75 

.00111 

2.8 

.000087 

12.8 

156 

187 

34:1 

31 

1 

37.4 

68.6 

80 

.00008 

2.2 

.000082 

11.9 

168 

213 

381 

.'!.-, 

.7 

45.5 

81.2 

85 

.00087 

1.8 

.000081 

10.7 

187 

241 

428 

42.5 

H4.6 

97.1 

90 

.00077 

1.3 

.000081 

9.5 

211 

270 

481 

50.6 

64.8 

11C.4 

References  to  Chapter  4 


CONTROVERSIAL  ASPECTS  OF  VALVES  OF  COEFFICIENTS  FOR 

FLAT  PLATES  OF  VARYING  S/ZBX; 

Notes  on  the  Dlinenslonril  Theory  of  Wind  Tunnel  Experiments.  E. 
Buckingham  ;  Reports  ou  Wind  Tunnel  Experiments  In  Aerodynamic*, 
Smithsonian  Miscellaneous  Collections. 

"  Critical  Speeds  for  Flat  Disks  in  a  Normal  Wind,"  J.  C.  Hunsaker 
and  E.  B.  Wilson  ;  loc.  cit. 

Bulletin  de  I'lnstitut  de.  Koutcltino,  Moscow,  1912. 

DATA   FOR  FLAT  PLATES. 

"The  Resistance  of  -\ir  and  Aviation,"  G.  Eiffel,  translated  by  J.  C. 
Hunsaker. 

DATA   FOR  K.   A.  F.  6  WIXO  SECTION. 

Reports  on  Tests  of  Four  Aerofoils.  Report  of  the  British  Advisory 
Committee  on  Aeronautics.  l!H2-1!ii::.  Report  No.  72. 


Chapter  V 

Comparison  of  Standard  Wing  Sections 


The  National  Physical  Laboratory  has  often  been  criticized 
in  the  past  for  not  stating,  in  spite  of  its  voluminous  reports, 
what  the  "  best "  wing  section  is.  There  is  no  such  thing  as 
a  "  best "  section.  There  are  very  bad  wing  sections  giving 
abnormally  high  resistance  and  low  lifting  power;  there  are 


oratories.  German  laboratories  have  done  a  great  deal  of 
work  with  reference  to  propeller  sections,  and  also  have  car- 
ried out  tests  on  wing  shapes  of  a  great  many  forms,  but  the 
present  selection  is  representative  and  sufficient  for  all  prac- 
tical purposes.  When  a  designer  wishes  to  introduce  slight 


Each  Aspect  Ratio  6 


Eiffel  I3 


.  . 

ta 


Comber  -?|i  TyP'Cd   Plodn9   °f  Win9  S*»ra 


Eiffel  37 


Eiffel  33  M    3    ? 


Eiffel  35  .    ? 


Eiffel  36  - 


.088 


=  Cambers 


0/6 

Surface  =      ooe 


FIG.  i. 


sections  giving  high  lift  at  big  angles  of  incidence,  but  too 
great  a  resistance  at  small  angles,  others  giving  a  low  maxi- 
mum lift,  but  very  suitable  for  high  speeds;  others  give  a  very- 
stable  motion  of  the  center  of  pressure,  but  sacrifice  aerody- 
namic efficiency.  The  selection  of  any  particular  form  depends 
on  the  performance  required  of  the  machine  in  view. 

As  the  result  of  several  years'  practice,  modern  machines  all 
tend  to  a  few  types  of  wings,  although  there  are  numberless 
small  modifications  by  individual  designers.  We  shall  attempt 
to  classify  and  give  data  for  what  may  be  called  Standard  Sec- 
tions, using  the  (pounds,  per  square  foot,  per  miles  hour) 
system  of  units  for  force  coefficients. 

Representative  Wing  Sections  Selected 

These  have  all  been  taken  from  the  N.  P.  L.  and  Eiffel  lab- 


variations  in  the  standard  forms,  it  will  be  always  necessary 
for  him  to  submit  his  variation  to  a  special  test,  so  that  a  com- 
plete collection  of  every  form  that  has  ever  been  submitted 
to  publication  would  be  useless. 

The  sections  we  have  selected  are:  R.  A.  F.,  No.  3,  4.  5,  6 
and  Eiffel  13  bis.,  32,  33,  35,  36,  37.  In  Fig.  1  these  forms  are 
represented  on  a  uniform  plan,  with  complete  dimensions,  and 
values  of  camber.  The  camber  of  the  upper  surface  is  defined  as 
ratio  of  maximum  height  above  chord  to  chord  length,  and  the 
saiMu  definition  holds  for  the  lower  surface.  The  hollowing  out 
of  the  lower  surface,  as  we  shall  see  later,  has  little  importance 
— it  scarcely  affects  the  Lift/Drag  ratio  or  the  angle  of  inci- 
dence for  the  burble  point,  but  it  increases  the  lift  about  17 
per  cent  at  any  angle  when  a  plane  lower  surface  is  cambered 
out  to  a  camber  of  0.06.  An  increase  in  lift  obtained  in  this 


38 


AERODYNAMICAL  THEORY  AND  DATA 


way  involves  a  dangerous  weakening  of  the  wing.  In  Dr. 
J.  C.  Hunsaker's  opinion,  a  decrease  of  camber  below  0.05  or 
an  Increase  of  camber  above  0.08  for  the  upper  surface  is  dis- 
advantageous in  practice.  Broadly  speaking  for  the  incidence 


LJ ft/ Drag  for 
Wings  Tested 
at  the  1(1.  PL. 


B"    8~    nr   t?-    Tf 

Angle  of  fnadencf 
FIG.  2. 


/6"   16'  Scr 


giving  maximum  Lift/Drag  ratio,  the  lift  for  upper  surface 
camber  of  0.08  may  be  twice  as  great  as  for  a  camber  of  0.05, 
but  the  Lift/Drag  ratio  is  diminished  by  nearly  25  per  cent. 
We  shall  deal  later  with  the  effects  of  varying  the  position  of 
the  maximum  ordinate  of  the  upper  surface;  the  best  position 
for  this  maximum  ordinate  is  about  %  of  the  cord  from  the 
leading  edge. 

Complete  Data  Presented 

In  Figs.  2  to  8  are  given  curves  for  Lift,  Drag,  Lift/Drag 


so 
/a 
te 

14 


Lft/Drag  for 
Wings  Tested  by 
Eiffel 


a-     icr 
of  Incidence. 


Fio.  3. 


16-     Iff 


and  Center  of  Pressure  motion  for  these  wings.  In  Fig.  0  a 
comparative  table  has  been  drawn  up  giving  maximum  Lift 
coefficients  and  corresponding  angles;  maximum  L/D  and  cor- 
responding angles;  the  angle  of  incidence  and  the  correspond- 
ing L/D  for  a  lift  coefficient  of  value  .00086,  and  also  the  value 
of  V  for  the  tests  from  which  these  rr-ulN  IKIVC  been  taken. 
This  is  as  complete  data  as  the  designer  can  po^-ihly  rc<|nin>. 
The  aspect  ratio  for  all  these  sections  is  G. 

We  shall  deal  later  witli  the  effects  of  variation  of  scale  and 
speed.  At  this  point  it  is  sufficient  to  state  that  whereas  the 
lift  coefficient  is  unaffected  by  variation  in  the  product  IV- 
*f>an  of  wing  in  feet  times  velocity  of  relative  wind  in  feet  per 


second — the  drag  coefficient  and  the  L/D  ratio  are  both  im- 
proved by  increase  in  IV.  The  N.  P.  L.  tests  and  Eiffel's  testa 
are  unfortunately  not  concordant  in  this  respect.  Eiffel's  ex- 
periments were  made  in  a  larger  wind  tunnel  and  at  higher 
speeds,  aud  if  the  same  wing  were  tested  at  the  N.  P.  L.  and 
Eiffel's  laboratory,  the  latter  would  give  better  results  for  bott 
drag  and  L/D.  Since  in  an  actual  machine  the  product  IV 
will  be  very  much  greater  than  the  values  of  either  laboratory, 
the  full  size  performance  will  always  be  somewhat  better  than 


Travel  of  Center  of 
Pressure  in  Wings 
Tasted  at  the  ft/PL. 


4-     6~     8'    IO'    !£•   14"    16-    IB"  SO' 

Angle  of  Incidence 

FIG  4. 

the  one  deduced  from  these  experimental  results,  particularly 
where  an  N.  P.  L.  section  is  used.  Employing  the  exact  figures 
of  our  curves,  the  designer  will  be  proceeding  on  a  very  con- 
servative basis.  Certain  experiments  of  the  X.  P.  L. — which 
we  shall  deal  with  fully  later — permit  us  to  make  approxi- 
mate corrections.  These  have  been  made  in  the  last  column 
of  Fig.  !». 


Travel  of  Center  of 
Pressure  in  Wings 
Tfstad  Oy  Eiffel 


sr    4-    &   er   tcr   ?  w 

Angle  of  Incidence. 
FIG.  5. 


te 


^o• 


Points  of  Jiitrrr.«t    in   Considering  a   Wing  Section 

In  discussing  the  merits  of  a  section,  there  are  so  many 
points  at  issue  that  it  is  only  in  an  actual  design  that  it  is 
possible  to  enter  fully  into  all.  Study  of  the  data  submitted 
will  be  of  much  more  use  if  the  following  features  are  always 
kept  in  mind  : 

(a)   The  maximum  value  of  L/D,  and  the  corresponding  Kr. 


AERODYNAMICAL  THEORY  AND  DATA 


A  macliine  in  normal  horizontal  flight  will  generally  be  navi- 
gated at  the  angle  giving  the  best  L/D  ratio,  which  is  there- 
fore most  important  from  an  efficiency  point  of  view.  The 


FIG.  6. 

value  of  the  lift  coefficient  at  the  best  L/D  is  of  importance. 
The  greater  the  lift  at  this  ratio  the  smaller  the  area  of  the 
wing  surface  required  for  a  given  load.  With  a  heavy  ma- 
chine, such  as  a  flying  boat,  or  an  armored  battleplane,  a  big 

.00300    .0006 


LIFT  &  DRAB 

COEFFICIENTS  FOR 

VARIOUS  WINGS  TESTED 

AT  THE  N.  P.  L 


Units:   I  bs.  per  Sq.  Ft. 
Miles  per  Hour 


.00250    .0005 


•00200    .0004 


.00/50    .0003 


4"       6°      8°      70° 
Angle  of  Incidence 

FIG.  7. 

lift  coefficient  is  essential.  With  a  speed  scout  or  a  light  re- 
connaissance machine,  a  small  value  of  K,  at  best  L/D  is  usual. 
With  a  sufficiently  powerful  motor  a  small  wing  surface  may 
be  used  and  a  great  speed  attained. 

(b)   The  maximum  KT  has  a  bearing  on  a  number  of  points. 


The  greater  the  maximum  Ky  the  slower  is  the  speed  at 
which  a  machine  may  land.  If  the  maximum  Kf,  or  simply 
large  values  of  Kf,  are  accompanied  by  a  good  L/D  ratio, 
then  the  machine  will  be  efficient  and  ready  in  climbing — 
though  the  best  angle  of  climb  is  by  no  means  the  angle  of 
maximum  KT,  as  we  shall  see  later  in  considering  the  economic 
laws  of  flight. 

(c)  The  maximum  Kr  should  occur  at  as  high  an  angle  as 
possible,  so  as  to  give  a  big  range,  and  possibility  of  a  large 
speed  variation. 

(d)  The  angle  of  maximum  lift  is  termed  the  burble  point, 


.00350  .0001 


1.1  fT    ANO    OKfAG 
COEPVICICMTS     FOR 

VARIOUS        VV1MG3    TEST  El 
BV     Eifrci_ 


4°     e'   a-     to-    \ef 

AHOlf.    OF  iNCIOeMCE. 

FIG.  8. 


i*'  «r 


as  we  know,  and  also  the  "  stalling  "  angle.  It  is  very  im- 
portant to  consider  what  the  shape  of  the  lift  curve  is  in  the 
neighborhood  of  this  angle.  If  the  lift  past  the  burble  point 
falls  off  very  rapidly,  the  pilot  may  easily  stall  the  machine. 
He  may  increase  the  angle  of  incidence  too  far  and  find  his 
sustaining  power  fall  off  dangerously.  A  wing  with  a  flat 
lift  curve  at  the  burble  point  will  avoid  such  danger. 

(e)  The  L/D  ratio  at  small  angles  of  incidence  and  small 
values  of  K7  determines  whether  the  machine  is  really  suitable 
for  high  speeds.    We  have  arbitrarily  chosen  K,  =  0.00086  as 
the  value  of  comparison,  and  it  can  be  seen  from  the  tables 
how  widely  L/D  varies  at  this  point.     A  machine  with  good 
maximum  L/D  and  a  high  maximum  Kf  might  be  totally  in- 
efficient at  high  speeds. 

(f)  The  movement  of  the  center  of  pressure  is  important  at 
low  angles.     If  at  low  angles  the  center  of  pressure  moves 
steeply  back  towards  the  trailing  edge,  the  machine  will  have 
a  tendency  to  "  dive,"  provided  for,  of  course,  by  fixed  stabil- 
izing surfaces  on  modern  machines.     If  the  center  of  pres- 
sure remains  stationary,  on  the  other  hand,  as  in  Eiffel  32, 
it  will  maintain  its  attitude  at  low  angles,  and  will  not  tend 
to  dive  even  with  small  stabilizing  surfaces  and  inefficient  or 
inoperative  elevator.     Similar  considerations  apply  to  "  stall- 
ing" angles. 

(g)  In    addition    to    the    separate    consideration    of   these 
points,  there  yet  remains  the  appraisal  of  the  wing  through- 


40 


AERODYNAMICAL  THEORY  AND  DATA 


FIG.   9      COMPARATIVE   TABLE  OF   STANDARD   WING   SECTIONS 
LIFT  COEFFICIENTS  IN  LBB.  PER  Sq.  FT.;    MILES  PEE  HK. 
ASPECT  RATIO  6 


CAMBER 

Wrao 

MAX.  Ky 

MAX.  LID 

K,  -.00086 

Max.  LID 

—  corrected 

Span  of 

app.  to  full 

Wins  in 

size  mach. 

Feet  x 

in  actual 

Relatire 

Sight  in 

Wind  in 

Ft/Sec. 

Upper 

Lower 

Section 

Angle 

K, 

LID 

Angle 

K, 

LID 

Angle 

LID 

accordance 
with  eip'ts 

IV. 

at  the 

N.  P.  L. 

16 

0.081 

0.036 

Eiffel  13  Bis. 

4.3° 

0.00129 

13.6 

1.9° 

11.4 

14.5 

49                   0.079 

0.030       |         "    32 

3.0° 

0.00103 

18.2 

2.2° 

18.0 

18.2 

30                 0.092 

0.033 

"    33 

16.8° 

0.00336 

7.2 

3.5° 

0.00152 

13.4 

-0.2° 

9.5 

13.6 

37                 0.080 

0.050 

"    35 

14.6° 

0.00296 

5.2 

4.8° 

0.00165 

18.7 

0.5°       j       10.6 

18.9 

37                 "  088 

0.022 

"    36 

3.1° 

0  00142 

14  3 

0.0° 

13.1 

14.3 

37           |       0.087 

0.041 

"     37 

14.1° 

0.00288 

4.0 

-0.8° 

0.00086 

20.4 

-0.8° 

20.4 

20.4 

6.3 

0.088 

0.032 

R.A.F.  3 

15.7° 

0.00347 

7.8 

5.0° 

0.00195 

14.3 

-0.1° 

7.4 

18.1 

6.3 

0.075 

0.022               "      4            14.0° 

0.00304 

8.0 

4.2° 

0.00142 

13.8 

1.4° 

10.3 

19.2 

6.3 

0.075 

0.022 

"       5 

14.2° 

0.00288 

7.0 

4.2° 

0.00142 

13.8 

1.4° 

11.0 

19.2 

6.3 

0.076 

0.008 

"      6 

15.4° 

0.00310 

7.8 

4.9° 

0.00157 

14.6 

1.9° 

10.4 

18.5 

out  its  performance.  The  designer  must  see  how  far  one  point 
of  excellency  conflicts  with  other  requirements;  what  the 
range  is.  The  ideal  wing  would  give  great  lift  and  efficient 
climb,  high  efficiency  in  normal  flight,  and  high  efficiency  at 
maximum  speeds. 

(h)  A  wing  may  be  entirely  satisfactory  from  an  aero- 
dynamic point  of  view,  and  yet  fail  to  satisfy  as  regards 
structural  requirements.  In  Fig.  1  is  shown  a  typical  arrange- 
ment of  the  wing  spars.  It  is  important  that  the  points  where 
the  wing  spars  are  likely  to  be  placed,  the  wing  should  have 
sufficient  thickness  to  permit  the  use  of  reasonably  deep  spars 
without  exaggerated  width.  A  wing  may  indeed  have  sufficient 
thickness  at  two  points  for  good  spars  to  be  placed,  yet  these 
points  may  be  totally  unsuitable.  They  may  be  too  near  to- 
gether, so  that  a  weak  overhanging  construction  or  excessive 
spar  loading  is  the  result,  or  too  far  apart  so  that  too  long 
an  unsupported  rib  section  results. 

There  could  be  no  better  plan  for  the  reader  to  whom  the 
subject  is  comparatively  new  than  to  go  through  all  the  wing 
sections  presented  with  reference  to  these  eight  points. 

Consideration  of  a  Few  Sections  in  Common  Use 

We  shall  consider  a  few  sections  in  this  manner  ourselves. 

Take  Eiffel  37,  for  instance.  Its  maximum  L/D — the  high- 
est of  any  section  considered  here  is  20.4,  occurring  at  — 0.8°. 
which  is  still  a  good  many  degrees  from  the  angle  of  no  lift. 


though  its  center  of  pressure  motion  at  this  point  is  rapid.  Its 
iiinxinniin  AT,,  is  small  (0.00288),  with  a  L/D  of  only  4.0.  Surh 
a  machine  would  be  unsuitable  for  heavy  loading,  but  would  be 
excellent  for  a  high  speed  racing  machine,  in  which  little  vari- 
ation in  speed  would  be  required.  It  would,  however,  have  to 
land  at  comparatively  high  speed  because  of  the  low  maximum 
KT.  The  structural  difficulties  would  be  considerable,  because 
there  is  insufficient  thickness  in  the  wing  for  the  rear  spar. 

Eiffel  32  is  an  excellent  all-around  wing.  Its  maximum 
L/D,  unconnected  for  scale,  is  high  18.7.  It  has  fairly  good 
values  of  L/D  for  high  lift  coefficients.  Its  center  of  pressure 
motion  is  almost  nil. 

E.  A.  T.  3  has  the  highest  value  of  K}.  (0.00195)  at  maximum 
L/D.  It  would  be  suitable  for  a  heavy  flying  boat.  At  small 
values  of  K,,  on  the  other  hand,  its  L/D  is  very  small.  It 
would  be  unsuitable  at  high  speeds.  Structurally  it  is  ex  col- 
lent. 

R.  A.  F.  6  would  also  be  a  good  all-around  wing,  noi  ciipa- 
ble  of  sustaining  the  heavy  loads  of  R.  A.  F.  3,  or  given  the 
high  speed  of  Eiffel  37.  but  compromising  usefully. 


References  for  Chapter  5 

les  Recherches  Sur  la  Resistam v 
British   Report.   1011'  nil::.    No.    TL'.    i:<>p<>H    ,,n    the   Results  of   'IVsts 

"if    I'lilM'    AiT'il'nils. 


Eiffel:   "  Nouvclles  Recherches  Sur  la  Resistance  iif  1'Air  et  1'Avln- 
tlon." 


Chapter  VI 

Effects  of  Variation  in  Profile  and  Plan  Form  of 

Wing  Sections 


As  we  have  seen  in  Chapter  5,  numberless  variations  are  pos- 
sible in  the  profile  of  wing  sections.  A  slight  variation  in  the 
profile  may,  however,  introduce  considerable  changes  in  the 
aerodynamic  properties  of  a  wing,  and  necessitate  a  wind  tun- 
nel test.  Experiments  conducted  at  the  various  laboratories  on 
variations  of  camber,  of  position  of  maximum  ordinate,  on  the 
thickening  of  leading  and  trailing  edges,  and  so  forth,  have 
therefore  rather  a  qualitative  than  a  quantitative  significance. 
But  the  results  obtained  deserve  attention,  and  may  serve  as  a 
guide  to  useful  modifications.  The  most  important  of  these  ex- 
periments are  summarized  here,  and  a  fuller  reference  list  is 
appended. 

Effect  of  Variation  of  Position  of  Maximum  Ordiuate  in 

a   Wing   Section   of   Plane   Lower   Surface,    and 

Constant  Camber  0.100  for  Upper  Surface 

These  experiments  of  the  N.  P.  L.  are  mainly  interesting  be- 
cause they  indicate  where  approximately  the  maximum  ordi- 


RATIO 
.500 


B 


.163 


FIG.  1.    SECTION'S  USED  IN  INVESTIGATING  VARIATIONS  OF 
POSITION  OF  MAXIMUM  OIJDINATE 

uate  of  a  section  should  be  to  give  the  best  possible  L/D  ratio. 
In  Fig.  1  are  shown  a  selection  of  three  of  the  sections 
tested.  They  were  all  developed  from  one  section  by  altering. 
the  position  of  the  maximum  ordinate  and  compressing  or  ex- 
panding the  other  ordinates  to  correspond.  The  Lift  and 
Lift/Drag  curves  for  these  sections  show  considerable  varia- 
tions in  values  as  can  be  seen  from  the  following  table: 


Wixu 


TABLE    1. 

SECTIONS   Pi,  AXE   LOWER   SURFACE.      UWEII   SURFACE   CAMBER 
0.100.     POSITION  OF  MAXIMUM  ORDINATE  VARIED. 

Ratio 
of  position 
of  maximum 
ordinate  to 
.  chord  length. 

500 
332 


168 


Maxi- 

mum 

L/D. 

11.2 

13.G 

11.0 


Angle 
for 
maxi- 
mum 
L/U. 
8° 
4° 
4° 

Maximum 
K:i  in  Ibs., 
sq.  ft.,  miles/ 
hour,  units. 
.00317 
.00338 
.00206 

Angle 
for 
maxi- 
mum 
K" 
18° 
16° 
8.5° 

We  see  that  the  maximum  L/D  for  section  B  with  a  ratio 
.332  is  as  high  as  13.6,  while  for  section  C,  where  the  maxi- 
mum ordinate  is  well  forward,  it  sinks  to  11.  Again,  the  max- 
imum lift  for  B  is  about  50  per  cent  greater  than  that  for  C. 
The  angle  of  maximum  lift  also  appears  much  earlier  when 


the  maximum  ordinate  is  nearer  the  leading  edge.  A  further 
inspection  of  the  N.  P.  L.  curves  also  shows  that  at  the  point 
of  maximum  lift,  a  slight  variation  in  the  ratio  changes  a 
smooth  burble  point  into  a  dangerously  steep  one. 

The  main  result  of  the  investigation  is  to  show  the  care  re- 
quired in  altering  even  slightly  the  position  of  maximum 
ordinate  for  a  given  section,  and  also  to  indicate  that  the  best 
position  is  about  one-third  from  the  leading  edge. 

Behavior  of  Wings  with  Reverse  Curvature 
at  the  Trailing  Edge 

This  constitutes  a  far  more  important  question  than  that  of 
the  preceding  paragraph.  It  would  considerably  simplify 


NO.  OF  TAIL 

1 

Z. 

3 

4 

Amount  ta.il  is 
r<xiseii  0.3  a- 
fnxction  of  chpra( 

DOO 

0.011 

0.027 

0.057 

Fi.;.  2. 


MODIFICATIONS  OF  THE  R.  A.  F.  6  WITH  UPTURNED 
TRAILING  EDGES 

airplane  design,  from  the  point  of  view  of  statical  and  dy- 
namical stability  if  the  position  of  the  centre  of  pressure  or 
of  the  vector  of  resultant  force  on  the  wing  did  not  vary  its 
position  so  rapidly  with  change  in  the  angle  of  incidence.  It 
may  be  said  that  as  a  general  rule  for  the  usual  angles  of 
flight  that  when  the  angle  of  incidence  decreases  the  centre  of 
pressure  on  a  wing  moves  far  back,  and  the  resultant  force 
tends  to  dive  the  machine,  decreasing  the  angle  of  incidence 
still  further.  When  the  angle  of  incidence  increases,  the  centre 
of  pressure  moves  forward  and  the  resultant  force  tends  to 
stall  the  machine,  increasing  the  angle  of  incidence  still  fur- 
ther. "We  shall  deal  fully  with  this  important  point  when  con- 
sidering the  general  statical  equilibrium  of  the  airplane. 

Among  other  means  of  attaining  stability,  wings  have  been 
designed  with  a  slight  reverse  curvature  at  the  trailing  edge, 
\\-\ncli  have  been  very  successful  in  keeping  the  centre  of  pres- 
sure motion  within  narrow  limits.  It  is  important  to  us  to  see 
what  sacrifice  of  sustaining  power  and  efficiency  reverse  curva- 
ture entails. 

At  the  N.  P.  L.  a  section  (No.  1)  very  similar  to  that  of  the 
R.  A.  F.  6  was  employed,  and  three  reversed  curvature  forms 
2,  3,  4  were  developed  from  it  by  turning  up  the  trailing  edges 
through  successively  increasing  distances  while  keeping  the 
thickness  of  section  unaltered.  The  point  of  inflexion,  at 
which  the  reflexing  began  was  in  each  case  0.4  of  the  chord 


41 


42 


AERODYNAMICAL  THEORY  AND  DATA 


from  the  trailing  edge,  though  this  could  be  varied  to  0.2 

without  much  effect.    These  sections  are  illustrated  in  Fig.  2. 

The  trnvol  of  the  centre  of  pressure  is  shown  in  Fig.  3  for 


•<*   o 

0 

f    . 

^ 

MOD)FICATtOM60f 
R.A  F.    6 

"^^_ 

I 

U       a 

--^, 

~-^^. 

'—  — 

2  

0       -m 

— 

— 

*^ 

XJ 

3  
4  

/ 

"1^ 

*=: 

=rzn 

5^~ 

Eiffel<32  

K 

^^s* 

c?^ 

*-  i 

z 

o    So 

6°    6"    10 
Angle  of  lnciden.ce. 

FIG.  3.    TRAVEL  OF  CENTER  OP  PRESSURE  FOR  A  SERIES  OF 
WINGS  WITH  UPTURNED  TRAILING  EDGES 

all  five  sections.  The  curves  for  the  N.  P.  L.  sections  show 
that  as  the  elevation  of  the  trailing  edge  increases,  the  centre 
of  pressure  motion  becomes  less  marked  in  its  movement 
toward  the  trailing  edge,  than  stationary,  and  finally  moves 
toward  the  leading  edge.  This  is  certainly  satisfactory  from 
the  stability  point  of  view,  but  the  questions  of  efficiency  and 
maximum  lift  have  also  to  be  considered.  The  following  are 
the  values  obtained  for  maximum  L/D  and  maximum  K, : 


Section. 

1 

2 

3 

4 


TABLE    2. 

Amount  tail 

Is  raised 

as  fraction 

of  chord. 

0.000 

0.011 

0.027 

0.057 


Maxi- 
mum 
L/D. 
16.1 
10.0 
14.3 
13.0 


Maxi- 
mum 
K, 

.0:!20 
.0294 
.0282 
.0245 


It  can  be  seen  that  as  the  rear  edge  is  turned  up  the  L/D 
and  the  maximum  K,  both  decrease  progressively. 

The  main  conclusion  of  the  British  investigators  was  that 
with  an  elevation  of  the  rear  edge  of  about  .037  of  the  chord, 
the  centre  of  pressure  can  be  kept  stationary,  but  with  a  loss  of 
12  per  cent,  of  the  maximum  L/D  and  25  per  cent,  loss  of  the 
maximum  possible  lift.  This  would  be  too  great  a  sacrifice  for 
the  sake  of  stability  and  the  designer  would  find  other  methods 
of  stabilization  such  as  the  use  of  decalage  in  biplanes  and 
negative  stabilizers  far  more  useful. 

Eiffel  has,  however,  investigated  a  section  with  a  very 
slightly  reversed  trailing  edge  (Eiffel  No.  32  Lanier-Law- 
ranee,  details  of  which  have  been  given  in  Chapter  5),  which 
is  far  more  satisfactory  and  in  wide  use.  Its  maximum  L/D 
is  about  18.2,  maximum  lift  coefficient  is  about  .0033,  and  it 
has  an  excellent  working  range.  The  centre  of  pressure 
motion  is  almost  nil  between  0  degrees  and'  10  degrees  of 
incidence,  and  such  a  wing  would  certainly  not  tend  to  dive 
a  machine,  although  it  is  not  very  good  at  stalling  angles.  Its 
shape  offers  certain  constructional  difficulties  in  the  region  of 
the  rear  spar. 

Effect  of  Thickening  the  Leading  Edge  of  a  Wing 
Contrary  to  a  somewhat  common  conception,  the  thickening 


Fio.  4.     SECTIONS  EMPLOYED  IN  INVKSTK;ATIN<;   KKKWTS  OK 
Tine  KKNIM;  I.KADI.VG  Ki/«, 

of  the  lending  edge  as  shown  in   Kig.    I  \vn<  distinctly  disac! 


vantageous,  the  decrease  in  efficiency  progressing  proportion- 
ately to  the  thickening. 

Effects  of  Thickening  Wing  Towards  the  Trailing  Edge 

Thickening  towards  the  trailing  edge  is  sometimes  advan- 
tageous from  the  point  of  view  of  structural  strength,  and 
experiments  have  been  conducted  to  see  the  loss  in  aero- 
dynamic efficiency  such  thickening  involved.  The  sections  em- 


FIG.  5.    EXPERIMENT  OF  THICKENING  THE  TRAILING  EDGK  OF 

WING 

ployed  are  shown  in  Fig.  5.  It  appears  from  these  experi- 
ments that  the  lift  coefficient  at  a  given  angle  of  incidence  is 
not  much  affected  at  angles  greater  than  7  degrees  but  that 
at  smaller  angles  of  incidence  the  lift  coefficient  is  actually 
a  little  greater  for  the  thickened  sections.  The  maximum 
Lift/Drag  steadily  diminishes  as  the  trailing  edge  is  thick- 
ened: 

TABLE    3. 


Section. 

1 

2 

3 

4 


Maximum 
L/D. 

l::.2 

.        13.4 
.        14.2 

14.6 


"  Phillips  Entry  " 

As  shown  in  Fig.  6,  the  section  R.  A.  F.  4  was  modified  into 
the  R.  A.  F.  5  to  give  the  well-known  "  Phillips  Entry."    This 


R./VF  S,  -PHILLIPS    CNTRY" 


FIG.  6.    MODIFICATION  OF  R.  A.  F.  4  WING  TO  GIVE  PHILLIPS 

ENTRY 

modification  was  found  to  have  no  effect  on  the  aerodynamic 
properties  of  the  wing,  an  important  consideration  in  view  of 
the  fact  that  numerous  attempts  have  been  made  to  utilize 
this  modification. 

Effects  of  Varying  Aspect  Ratio 

Fbppl's  and  Eiffel's  experiments  have  dealt  with  cambered 
plates;  the  N.  P.  L.  has  investigated  the  effect  of  varying 
aspect  ratios  on  a  practical  wing  section  rectangular  in  plan 


FIG.  7.    WING  SECTION'  EMPLOYED  AT  THE  N.  P.  L.  IN  INVESTI- 
GATION OK  KKKECTS  OF  VARYING  ASPECT  K.vno 

similar  to  the  Bleriot  XI  bis  which  is  shown  in  Fig.  7.  For 
a  more  or  less  accurate  understanding  of  tin-  pliei'nmena  ac- 
companying such  variation,  it  is  necessary  to  consider  pres- 
sure distribution,  but  for  design  it  is  more  important  to  bear 
in  mind  the  simple  results  of  this  investigation : 
As  aspect  ratio  increases 

(1)  The    maximum    L/D   ratio   improves,    the   corresponding 
angle  of  incidence  remaining  sensibly  the  same,  and  the 
L/D  at  other  angles  improves  also. 

(2)  the  drag  diminishes. 

(3)  the  lift  cocflicicnts  at  all  except  very  small  angles  and  the 
maximum  lift  coefficient  remain  practically  constant;  the 


AERODYNAMICAL  THEORY  AND  DATA 


43 


maximum  lift  coefficient  occurs  at  a  smaller  angle  of  in- 
cidence. 
(4)  the  angle  of  no  lift  occurs  at  smaller  positive  angles,  or 

larger  negative  angles  as  the  case  may  be. 
Although  the  Bleriot  wing  tested  by  the  N.  P.  L.  was  of 
practical  form,  it  is  not  commonly  employed  in  modern  con- 
struction. The  correction  tables  (Tables  4  and  5)  are  solely 
based  on  results  derived  from  it,  and  it  does  not  at  all  follow 
that  similar  corrections  would  apply  to  wings  of  other  form. 
In  default  of  other  experimental  work,  however,  such  correc- 
tions can  be  applied  with  probably  a  fair  degree  of  accuracy. 
The  values  for  aspect  ratio  of  6  are  taken  as  a  standard  of 
comparison,  this  being  the  aspect  ratio  used  for  so  much  ex- 
perimental work  on  wing  sections. 

TABLE    4. 

APPROXIMATE  CORRECTIONS  FOR  MAXIMUM   L/D   WITH   VARIATION  OF 
ASPECT  RATIO. 

Ratio 

of  maximum  L/D 

Aspect  to  maximum  L/D 

ratio.  at  aspect  ratio  6. 

3 .72 

4 .82 

5 .92 

6 1.00 

7 1.08 

8 1.11 

The  following  table  shows  the  ratio  of  drag  for  various  as- 
pect ratios  to  drag  for  aspect  ratio  6  as  unity : 

TABLE   5. 
APPHOXIMATE   CORRECTION   FOR   VALUES   OF   R  r  WITH   VARIATION    OF 


ASPECT  RATIO. 


Angle  of 
Incidence. 

0 

2 

4 

6 


10.. 
12.. 
14.. 
1C.. 

18.. 


3 

4 

8 

1.12 

1.05 

1.00 

1.15 

1.90 

1.02 

1.13 

1.022 

1.10 

1.11 

l.O.'il 

1.0:i 

1.22 

1.0-10 

1.01 

1.04 

1.047 

1.06 

l.SO 

l.O.-iG 

1.11 

1.14 

1.071 

1.02 

1.17 

.94 

l.OD 

.876 

1.130 

.91 

Aspect  Ratio. 
6 

1 
1 
1 
1 
1 
1 
1 
1 
1 
1 


7 
1.10 

1.00 

1.00 

.91 

.89 

.88 

.98 

.92 

.85 

1.05 


8 

1.00 

1.05 

1.00 

1.14 

.91 

.91 

.99 

.89 

1.01 

1.20 


Choice  of  Aspect  Ratio 


In  selecting  ratio  for  an  airplane  many  other  considera- 
tions enter  besides  those  of  aerodynamic  efficiency.  Thus  as 
aspect  ratio  and  the  span  of  the  wings  increase,  the  heavier 
the  structure  becomes  for  the  same  strength.  This  involves 
heavier  bracing  and  more  structural  head  resistance;  the  in- 
crease in  weight  itself  reduces  the  aerodynamic  efficiency  indi- 
rectly. Hence  if  the  aspect  ratio  were  increased  to  an  exag- 
gerated extent,  structural  difficulties  would  more  than  counter- 
balance the  gain  due  to  this  increase.  The  question  is  too  com- 
plex for  theoretical  treatment  or  for  definite  rules.  Later  in 
the  design  of  a  standard  machine,  comparative  designs  will 
be  made  for  various  values  of  aspect  ratio. 

For  preliminary  design,  the  best  method  of  fixing  aspect 
ratio  is  to  follow  standard  practice,  and  this  would  indicate: 

5  to  1  aspect  ratio  for  monoplanes  and  small  biplanes. 

6  to  1  or  7  to  1  for  large  biplanes. 

Effects  of  Raking  the  Plan  Form  of  a  Wing 

Experiments  on  the  effect  of  raking  the  plan  form  of  a  wing 
have  been  conducted  by  Eiffel  in  France  and  FSppl  in  Ger- 
many, references  to  which  are  given  at  the  end  of  this  section. 
Unfortunately,  their  investigations  were  mostly  on  circular 
wings,  were  somewhat  contradictory,  and  their  results  varied 
with  different  cambers. 

In  the  experiment  which  Eiffel  conducted  on  a  practical 
wing  section,  Coanda  Wing,  Eiffel  No.  38,  as  illustrated  in 
Fig.  8,  the  raked  wing  was  decidedly  superior  to  the  rectangu- 
lar form  into  which  it  was  cut  down.  Nor  can  this  improve- 
ment be  due  to  variation  in  aspect  ratio  which  is  negligibly 
small.  The  ratio  of  maximum  L/D  was  about  1.2  to  1. 


It  would  seem  therefore  that  experiment  is  in  agreement 
with  practice  in  imputing  certain  advantages  to  raking.  But 
in  view  of  the  variation  in  results  with  wings  of  different 


J.5^ 

_  „                                      J  x-x  . 

-»|,56|— 

.  —  ~-                 i  — 

H                                 0*20                              '' 

n 

in 

FIG.  8.     SECTIONS  EMPLOYED  IN  EIFFEL'S  EXPERIMENTS  ON 
"  RAKING  " 

camber,  it  would  be  unsafe  to  employ  a  correction  ratio  of  1.2 
in  maximum  L/D  for  the  raking  of  any  other  wing,  say  an 
R.  A.  F.  6  section,  until  there  has  been  further  investigation 
of  this  point. 

Swept  Back  Wings 

Another  variation  in  the  plan  form  of  wing  sections,  very 
largely  employed  on  German  machines  of  recent  type,  and  also 
on  one  or  two  American  machines,  is  that  of  swept  back  wings. 
Swept  back  wings  are  mainly  used  to  give  lateral  stability. 
It  has  also  been  thought  that  their  arrow-like  form  gave  them 
an  increased  aerodynamic  efficiency,  and  that  longitudinal 
stability  was  also  improved  by  their  employment.  We  are  not 
at  present  concerned  with  lateral  stability.  Aerodynamically 
a  recent  investigation  at  the  Massachusetts  Institute  of  Tech- 
nology shows  a  progressive  decrease  in  efficiency  with  in- 
creased sweep  back.  As  regards  longitudinal  stability  the  ac- 


18' 


1    — '.— f 

4- 


V-" 

FIG.  9. 


WINGS  USED  IN  EXPERIMENTS  ON  SWEPT  BACK 
WINGS 


tion  is  peculiar  and  not  at  all  so  satisfactory  as  that  of  the 
wings  with  reversed  trailing  edges. 

An  R.  A.  F.  6  wing,  originally  of  aspect  ratio  6  was  em- 
ployed and  swept  back  as  shown  in  Fig.  9.  The  results  of  the 
investigation  are  summarized  in  Table  6  : 

TABLE   6. 


Section. 

1 

2 

3 

4.  . 


Angle  of 

incidence  Maxi- 

Sweep    for  m.ixi-  mum 

back,    mum  L/D.  L/D. 

0  4°  17 

10  4°  10.5 

20  4°  16.2 

30  4"  12.8 


Ky 
for  maxi- 
mum L/D. 
.00143 
.001  :!0 
.00129 
.00120 

Angle  of 
incidence 
for  maxi- 
mum Kf. 
14° 
16° 
16° 
17° 

Maxi- 
mum 
K 
.00288 
.00276 
.00276 
.00266 

44 


AERODYNAMICAL  THEORY  AND  DATA 


Up  to  20  degrees  sweepback,  it  can  be  seen  that  the  loss  in 
efficiency  is  not  so  great,  but  the  30  degree  entails  a  loss  for 
which  good  lateral  stability  would  scarcely  compensate. 


TRAILING   EDGE 


6' 


a° 


flnylt    of  If  ci<*  eni  e 


Iff 


16' 


FIG.  10.    MOVEMENT  OP  CENTER  OF  PRESSURE  FOR  WINGS  WITH 
VARYING  DEGREES  OF  SWEEP  BACK 

The  centre  of  pressure  motion  is  illustrated  in  Fig.  10.  It 
has  the  same  peculiar  characteristic  for  each  of  the  wings. 
At  small  angles  the  centre  of  pressure  moves  backward,  thus 
producing  diving,  but  at  large  angles  the  centre  of  pressure 
moves  forward,  thus  tending  to  stall  the  machine.  Longi- 
tudinal stability  is  thus  not  secured. 

Negative  Wings  Tips  of  Swept  Back  Wings; 
Effect  on  Longitudinal  Stability 

Swept  back  wings  with  negative  wing  tips  have  been  suc- 
cessfully employed  in  German  machines;  and  in  the  Burgess- 
Dunne,  without  the  use  of  tail  surfaces.  Such  wings  certainly 
give  a  great  degree  both  of  longitudinal  and  lateral  stability, 
but  at  some  sacrifice  of  efficiency.  Experimental  results,  ex- 
cept for  complete  airplane  models,  are  not  available,  but  a 
simple  theoretical  discussion  at  this  stage  is  instructive;  this 
involves  the  application  of  the  first  principles  of  mechanics, 
yet  always  presented  considerable  difficulty.  It  also  gives  us 
the  opportunity  of  considering  the  stabilizing  influence  of  tail 
surfaces  in  an  elementary  manner. 

Consider  the  two  arrangements  of  Fig.  11,  A  and  B,  one 


"Ftfrce  on  Rwitive 
•Tail  Surface-l 


B 


! Force  on        < 
;  ta.il  5urfa.ce'  I 

r 


FIG.  11.     DIAGRAM  TO  ILLUSTRATE  VARIATION  OF  RKM-I.TANT 
FORCE  WITH  POSITIVE  AND  NKGATIVE  TAIL  SURFACES 

with  a  positive  tail  surface,  the  other  with  a  negative  tail  sur- 
face. We  will  assume  the  forces  on  the  wing  and  on  the  tail 
to  be  vertical  for  simplicity's  sake,  although  this  would  not 
actually  he  the  ease,  with  positions  of  forces  and  centre  of 


gravity  as  in  sketch.  Assume  the  force  on  the  wing  to  be  10 
times  that  on  the  tail.  Then  in  case  A  moments  about  centra 
of  gravity  are: 

(10Xl)-f-(25Xl)=35  *n  a  divmg  or  counter  clock- 
wise direction.  The  resultant  must  be  aft  of  the  centre  of 

qc 

gravity,  and  since  its  value  is  10  + 1,  it  is  —   =  3.18  feet  aft 

of  the  centre  of  gravity  between  the  two  forces  on  wing  and 
tail. 

For  ease  B  moments  about  centre  of  gravity  are: 
(10X1)— (25X1)=— 15  in  a  stalling  or  clockwise  di- 

15 

rection.    The  resultant  will  now  be  —  =  1.67  feet  forward  of 

y 

the  centre  of  gravity  and  forward  of  the  force  on  the  wing. 

A  negative  tail  can  thus  convert  a  diving  moment  into  a 
stalling  moment  at  small  angles.  At  large  angles  of  incidence 
the  negative  lifting  surface  will  become  positive  and  may  be 
used  to  convert  a  stalling  moment  into  a  diving  moment.  A 
negative  tail  surface  can  thus  be  suitably  adjusted  to  give  lon- 
gitudinal stability  at  all  angles  within  the  flight  range. 

Similarly  for  a  machine  with  swept  back  wings  and  nega- 
tive wing  tips,  as  shown  in  Fig.  12,  at  an  angle  of  1  degree 
incidence  for  a  positive  section  A-A,  the  force  has  a  counter- 


SECTION  KT  Force  on  Negative  Clement  at  B  B 

A'A\  IrVootuciog  Stalling  Moment 

JAbout  t  he  Center  of  G 


I         " 
of  Gi-o-vity  ^  B  B"" 

Force  on  Fbsitive  Element  at  A" A 
FVoiiucing  Divina  Moment  About 
the  Center  of  ph>.vity 

FIG.  12.    DIAGRAM  TO  ILLUSTRATE  STABILIZING  EFFECT  OF 
BA<  ic  WINGS  WITH  NEGATIVE  WING  TIPS 


clockwise  moment  about  the  centre  of  gravity  tending  to 
dive  the  machine.  For  a  negative  section  B-B,  the  force  has  a 
stalling  moment  about  the  centre  of  gravity  which  prevents 
diving  action.  Similarly,  at  large  angles  of  incidence  the 
positive  surfaces  of  the  wing  may  tend  to  stall  the  machine, 
while  the  negative  wing  tips  then  assume  a  positive  action 
and  counteract  the  tendency  to  stall.  Thus  if  the  wings  are 
sufficiently  swept  back  and  the  negative  surfaces  powerful, 
static  longitudinal  stability  can  be  secured. 

The  negative  surfaces  having  so  small  an  arm  compared 
with  negative  tail  surface  must  have  a  much  larger  surface 
than  the  latter.  Consequently  such  an  arrangement  must  be 
aerodynamically  inefficient.  This  may  be  compensated  for  by 
the  fact  that  no  structural  extensions  to  tail  surfaces  are  neces- 
sary in  a  machine  of  this  type. 


AERODYNAMICAL  THEORY  AND  DATA 


45 


References  for  Part  I,  Chapter  6 

EFFECT  OF  VARIATION  OF  POSITION  OF  MAXIMUM  ORDINATE 
IN  A  WING  SECTION  OF  PLANE  LOWER  SURFACE  AND 

CONSTANT  CAMBER  FOR   UPPER  SURFACE 
British  Report  1912-1913.     No.  72.     Section   (1). 


OF    WINGS    WITH   REVERSE    CURVATURE    AT   THE 

TRAILING  EDGE 
British  Report  1912-1913,  page  85. 

Supplement  to  Eiffel's  Resistance  of  Air  and  Aviation,  page  151 
"  Nouvelles    Recherches   sur   la    Resistance   de   1'Air   et   1'A 


Eiffel,   page  114. 


vlation." 


EFFECTS  OF  THICKENING  THE  LEADING  EDGE  OF  I  WING 
British  Report  1912-1913.     No.  72,  page  75. 

EFFECT  OF  PHILLIPS  ENTRY 
Loo.  Oil.,  page  70. 


page 


EFFECTS  OF  THICKENING  TOWARDS  THE  TRAILING  EDGE 
Loc.  Cit.,  page  77. 

EFFECTS   OF  VARYING  ASPECT  RATIO 

O.  Foppl,  Zeitschri/t  fur  Flugtechnik,  April  30.  1910. 

O.  Foppl,  Zeitschrift  fiir  Fluyteclmik,  August  13    1910 

British  Report  1911-1912.     No.  62,  page  74. 

Eiffel    (Hunsaker).      "The   Resistance   of   Air   and   Aviation," 
143-146. 

Eiffel.     "  Nouvelles  Recherches  sur  la  Resistance  de  1'Alr  et  i'Avia- 
tiou,"  page  138. 
EXPERIMENTS    ON   "RAKING"   THE   PLAN   FORM   OF  A    WING 

•'  Nouvelles   Recherches   sur   la   Resistance   de   1'Air   et    1'Aviation " 
Eiffel,  page  141. 

"  Mitteilungen  aus  der  Gb'ttinger  Modeiversuchsanstalt."     Sonderab- 
druck,  Zeitsclirift  Jilr  Flugtechnik.    1910,  Heft  20  ;  1911,  Heft  7,  13,  14. 
SWEPT  BACK  WINGS 

H.  E.  Rossell  and  C.  L.  Brand. 

"Wind  Tunnel  Experiments  in  Aerodynamics,"  Smithsonian  Miscel- 
laneous Collections.     Vol.  62,  No.  4. 


Chapter  VII 

Study  of  Pressure  Distribution 


For  general  purposes,  a  knowledge  of  lift,  drag  and  the 
position  of  the  vector  of  resultant  force  at  various  angles  of 
incidence  is  as  much  aerodynamical  data  as  the  designer  re- 
quires with  reference  to  a  wing  section.  But  an  investigation 
of  pressure  distribution  bears  directly  on  an  understanding 
of  the  following  important  points : 

1.  The  variation  of  stresses  in  the  covering  fabric  of  a  wing, 

due  to  the  unequal  distribution  of  pressures. 

2.  The  great  efficiency  of  a  cambered  surface  as  compared 

with  a  flat  plate. 

3.  The  analysis  of  the  forces  at  play  and  their  exact  bearing 

on  efficiency,  and  on  the  position  of  the  resultant  vector. 

4.  The  relative  importance  and  the  inter-dependence  of  the 

two  surfaces  of  a  wing. 

5.  The  effects  of  varying  aspect  ratio. 

6.  The  variation  of  lift  and  drift  with  speed  and  size  of 

model. 

It  is  evident,  therefore,  that  the  question  is  not  of  purely 
scientific  or  academic  importance.  Much  useful  work  has  been 
done  in  this  direction  by  Eiffel  and  the  N.  P.  L.,  and  a  great 
deal  still  remains  to  be  done. 

Methods  of  Obtaining  Pressure  Distribution 

The  mapping  of  pressure  distribution  is  a  lengthy  process 
requiring  numberless  readings.  It  is  fully  described  in  the 


Norma.1  Suction  Force 


tam/sonent  Fttrallel  to  MnA 


Ancle  of  IncideKcc.— 
Direction 


Component*  cf  Pressure  on  Upper  Surface . 


Drtctmrr  e/  tvjnit 

Mor/nal  Preaai/re  force,— 

IL 

"Component  PfrfrendKuUrto 
i 
Components  of  Pressure  Of  Lotvcr  Svrfo.ee. 


Fro.  1.    DIAGRAM  TO  ILLUSTRATE  How  THE  FORCES  ON  UPPER 
AXD  LOWER  SURFACES  ASSIST  EACH  OTHER. 

N.   P.  L.   reports,  and  we  shall  only  summarize  briefly  the 
methods  employe'!. 

Holes  of  '/„  inch  diameter  are  drilled  in  the  \\intr  where 
required,  normally  to  its  surface,  and  are  rl-.igged  with  plasti- 
cine, excei  t  the  one  under  observation.  The  hole  in  use  is 
connected  by  a  length  of  very  tliin  hypodermic  syringe  tubing, 
too  small  to  cause  disturbance,  with  a  three- way  cork.  A  pilot 


and  static  pressure  tube  is  placed  in  the  channel  where  the 
flow  is  undisturbed  by  the  presence  of  the  model.  The  static 
pressure  tube  is  permanently  connected  to  one  arm  of  the 
usual  manometer;  the  other  arm  can  be  connected  alternately 
by  means  of  the  three-way  cock  either  to  the  pitot  tube  or  to 
the  hole  drilled  in  the  wing  section. 

The  manometer  can  be  thus  made  to  read  either  the  velocity 
head  of  the  wind,  or  the  difference  in  pressure  between  the 
static  pressure  of  the  channel,  and  the  pressure  on  the  wing 
at  the  point  considered;  and  a  direct  comparison  between  these 
two  quantities  is  immediately  possible.  Great  care  has  to  be 
exercised  in  obtaining  values  of  pressure  distribution  which 
correspond  to  a  constant  value  of  the  wind  velocity,  and  in 
maintaining  the  same  direction  of  the  pitot  tube  relative  to 
the  wing. 

Over  the  upper  surface  of  a  wing  there  will  be  suction,  on 
the  lower  surface  pressure,  and  we  shall  indicate  the  exact 
distribution  in  this  section.  In  Fig.  1,  the  suction  force  normal 
to  the  upper  surface,  and  the  pressure  force  normal  to  the 
lower  surface,  are  represented  diagrammatically  for  the  same 
position  on  the  chord.  If  these  forces  are  resolved  along  the 
line  of  the  relative  wind  and  perpendicular  to  it,  we  see  that 
they  add  up  to  give  a  force  upwind  and  lift.  At  other  points 
along  the  chord  these  forces  may  oppose  one  another  or  inve 
a  force  downwind.  An  elaborate  method  of  graphical  in- 
tegration for  pressure  forces  has  been  devised  by  the  X.  P.  L.. 
but  their  integration  was  normal  and  perpendicular  to  the 
chord.  Such  summations,  if  taken  as  giving  lift  and  drag, 
involve  errors  except  at  very  small  angles. 

Comparison  of  Results  from  Pressure  Distribution  and 
from  Force  Experiments 

In  Chapters  2  and  3  we  have  divided  the  forces  acting 
on  a  wing  into  two  classes:  density  or  turbulence  forces, 
and  skin  friction  forces.  A  study  of  pressure  diagrams  en- 


I 


* 


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Kii;.  2.  COMPARISON  OF  KK-II.TS  FROM  PRESSURE  DISTRIBUTION 
AND  KOIII-E  EXPERIMENTS  FOR  A  R.  A.  F.  fi  \\'ING. 


46 


AERODYNAMICAL  THEORY  AND  DATA 


47 


ables  us  to  determine  the  part  which  these  forces  play  in  pro- 
ducing lift  and  drag.  In  Fig.  2,  the  results  of  a  pressure 
force  integration  are  shown  from  experiments  on  a  R.  A.  F. 
6  wing,  and  compared  with  the  usual  force  determinations. 

The  result  for  the  lift  values  coincides.  Now,  it  is  fairly 
clear  that  skin  friction  forces  would  not  impart  lift  to  a  wing. 
We  can  conclude  that  lift  is  solely  due  to  the  density  or  turbu- 
lence forces,  and,  further,  that  lift  can  be  obtained  from  the 
integration  of  the  components  of  the  pressure  forces  per- 
pendicular to  the  relative  wind. 

The  drag  curves  coincide  at  high  angles,  while  between  0 
degree  and  8  degrees  the  drag  derived  from  the  pressure  in- 
tegration is  less  than  that  obtained  from  force  experiments. 
The  difference  is  due  to  the  fact  that  the  pressure  results  give 
no  indication  of  skin  friction  forces. 

Effect  of  Variation  of  Speed  and  Scale  on  Lift 
and  Drag  Coefficients 

These  considerations  enable  us  to  deal  more  closely  with 
the  question  of  variation  in  coefficients  with  change  of  speed 
and  scale,  the  product  (IV). 

Experiments  at  the  N.  P.  L.  show  that  lift  coefficients  are 
scarcely  affected  by  such  change.  If,  as  has  been  shown,  lift 
is  due  to  pressure  forces  solely,  there  is  no  reason  why  the 
lift  should  be  affected. 

That  portion  of  the  drag  due  to  density  resistance  and  ac- 
counted for  by  the  pressure  integration  would  vary  as  AV. 
But  the  skin  friction,  not  accounted  for  by  the  pressure  ex- 
periments, varies  as  bl'^V1'".  Therefore,  with  increase  in 
speed  and  scale,  the  drag  would  not  vary  as  AV',  but  some- 
what less  rapidly,  and  Kx  would  not  be  a  constant. 

It  might  be  possible  for  any  model  wing  to  find  the  density 
component  of  the  drag  by  allowing  for  skin  friction,  step  this 


FIG.  3.    DIAGRAM  SHOWIXG  VARIATIONS  OF  LIFT/DRAG  WITH 
IV  FOR  R.  A.  F.  6. 

up  to  full  size  as  AV  and  then  to  compute  the  skin  friction 
from  the  bl '"  V1 '"  formula.  But  we  are  not  too  sure  of  this 
formula,  and  the  process  would  be  very  complicated. 

Some  experiments  at  the  X.  P.  L.  provide,  perhaps,  the 
best  guide,  although  they  have  been  carried  over  too  narrow 
a  range.  In  Fig.  3  are  given  values  L/D  for  the  R.  A.  F.  6 
section,  plotted  at  the  same  angle  of  incidence  against  log 
(IV),  the  logarithm  being  used  purely  for  convenience  in 
plotting.  If  the  designer  wishes  to  correct  to  the  full -sized 
machine,  he  must  take  the  value  IF  which  is  given  in  connec- 
tion with  the  section  he  employs  and  compare  values  of  L/D 
at  any  angle  of  incidence  with  that  corresponding  to  log 
H  =  2.75 (IT  =  560),  a  good  value  for  a  full-sized  machine. 
The  X.  P.  L.  also  gives  corrections  for  lift,  which  are  to  be 
regarded  with  doubt,  and  corrections  for  drag  coefficients. 
But  it  would  seem  safer  to  employ  only  the  L/D  corrections; 


and  even  these  should  be  only  used  for  the  designer's  personal 
benefit,  or  in  comparing  the  merits  of  two  sections,  as  in  the 
last  column  of  Fig.  9  of  Chapter  5.  Designing  without  any 
corrections  would  be  the  most  conservative  method,  and 
might  ensure  a  pleasant  surprise  for  full-size  performance. 

Distribution  of  Pressure  at  Median  Cross  Section  of 
Various  Surfaces 

With  the  ribs,  stringers,  fillers  and  good  fabrics  employed 
in  modern  wing  construction,  the  stresses  produced  in  the 
fabric  are  well  within  the  limits  of  safety,  as  we  shall  see 
later.  But  it  is  important  to  remember  that  it  is  not  the 
mean  pressure  over  a  wing  which  gives  the  maximum  stress 
in  the  fabric;  it  is  the  maximum  pressure  at  one  particular 
point.  Also  a  small  hole  at  one  point  of  the  fabric  may 


Ho 

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#H -CQefftcj*nfs  in  oovnds  ocr  &pvor*  ^0c-t-/o*r  fcof  yctond. 

FIG.  4.    DISTRIBUTION  OF  PRESSURE  FOR  MEDIAN  CROSS-SEC- 
TIONS FOR  VARIOUS  SURFACES  AT  6  DEGREES  ANGLE  t. 

cause  it  to  carry  the  added  effect  of  the  snction  at  the  upper 
surface  and  the  positive  pressure  at  the  lower  surface. 

Eiffel  in  his  earlier  experiments  consistently  investigated 
the  pressure  distribution  over  both  surfaces,  and  a  number  of 
his  diagrams  are  shown  in  Fig.  4,  while  the  maximum  effect 
of  suction  on  upper  surface  and  pressure  on  lower  face  is 
shown  in  table  in  Fig.  4,  at  the  same  angle  of  incidence  of 
6  degrees  in  each  case.  The  speed  of  the  test  was  32  feet 
per  second.  Although  these  surfaces  are  not  in  common  use, 
they  serve  as  a  qualitative  criterion  from  this  standpoint  for 
more  practical  wings. 

An  incidence  of  6  degrees  may  be  taken  as  normal  flight, 
and  at  a  speed  of  60  miles  per  hour  it  is  seen  that  pres- 
sures may  vary  from  13.4  to  8.82  pounds  per  square 
foot.  This  is,  however,  by  no  means  the  worst  loading  that 
can  occur  on  a  wing  fabric.  Under  abnormal  conditions  such 
as  flattening  out  after  a  steep  dive,  the  maximum  load  per 
square  foot  may  be  many  times  greater.  This  question  will 
be  considered  in  detail  in  dealing  with  factors  of  safety. 

Distribution  of  Pressure  Over  the  Entire  Surface  of  a 
Wing;  Lateral  Flow,  Its  Bearing  on  Aspect  Ratio 

The  most  instructive  experiments  on  the  pressure  distribu- 


AERODYNAMICAL  THEORY  AND  DATA 


tion  over  the  entire  surface  of  an  aeroplane  are  those  due  to 
Jones  and  Patterson,  at  the  N.  P.  L.  and  to  Eiffel. 

At  the  N.  P.  L.  a  single  wing  section  has  been  dealt  with 
in  this  way,  but  there  has  been  a  close  and  useful  analysis, 
which  is  a  first  step  in  the  investigation  of  phenomena  of 
lateral  flow,  and  of  the  underlying  causes  of  the  effects  of 
varying  aspect  ratio. 

A  section  resembling  the  R.  A.  F.  6,  but  with  somewhat 
greater  camber,  was  employed.  Rectangular  in  plan,  it  had 
a  series  of  observation  points  as  shown  in  Fig.  5,  on  five  sec- 


3  4- 

Profile    of  Aerofoil 

Lead  ing 


1 

!    i  • 

1 

, 

*] 

1 

i              i  ' 

Pi  JLH  of  Aerofoi 

FIG.  5.    SECTION  EMPLOYED  AT  THE  N.  P.  L.  IN  OBSERVING 
PRESSURE  DISTRIBUTION  ON 'AN  ENTIRE  WING. 

tions  parallel  to  the  median  section.  The  actual  methods  were 
similar  to  those  already  described  in  considering  pressure  dis- 
tribution over  a  median  section,  and  the  same  remark  applies 
to  the  resolution  of  components  normal  and  perpendicular  to 
the  chord  and  their  subsequent  summation.  The  centers  of 
pressure  for  each  section  were  obtained  by  taking  moments 
by  a  process  of  elementary  mechanics,  a  similar  process  is 
fully  described  in  the  Bulletin  de  I'Institut  Aerotechnique. 
Normal  forces  were  again  taken  as  a  measure  of  the  lift, 
and  forces  parellel  to  the  chord  as  a  measure  of  the  drag, 
skin  friction  being  neglected.  The  resolution  of  forces  along 
and  perpendicular  to  the  chord,  instead  of  along  and  per- 


Pressure  Distr/buioition  on  an  Aerofoil 
flrea.3  of  Ft  auras  a.re  Porp ort/ofJA  /  to  forces 
Norm  A  I  to  Chord. 


Lotver 
f~a.ce 


Lower 
f~a.cs 


\rO.  O/3O 

,  V 


f~A.ce 


0.0!  22 


Lower 
fa.  ce 


Pressure  Distribution  on  a.n  /~ero  fo// 
/~rea.s  of-f7oures  Porportiona.1  to  forces 
Par  A  I  lei  to  Chor* 

FlG.  6. 

pendicular  to  the   relative  wind,   involved  the  error  already 
mentioned,  unimportant,  however,  except  at  large  angles. 

In  Fig.  6  are  shown  the  curves  of  normal  and  parallel 
forces  at  the  five  sections  for  various  angles  of  incidence.  In 
7,  the  contributory  effects  of  each  section  of  the  wini: 
is  clearly  illustrated  by  curves  giving  lift,  L/D  and  center  of 
pressure  for  ea<-h  section.  The  following  observations  can  be 
made  from  this  data : 


(a)   As  each  section,  beginning  with  the  median,  is  consid- 
ered, the  distribution   on  the  upper  surface   from   high 


^i... 

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ooi  at 
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' 


FIG.  7.    CONTRIBUTORY  EFFECTS  ON  VARIOUS  ELEMENTS  OF  A 

WING  AT  VARIOUS  ANGLES  OF  INCIDENCE.    SECTIONS 

LOCATED  AS  IN  FIG.  5. 

suction  forward  and  low  suction  aft  alters  progressively 
until  when  the  tip  is  reached  the  highest  suction  occurs 
in  the  neighborhood  of  the  trailing  edge. 

(b)  On  the  lower  surface,  the  positive  pressures  found  over 
the  central  portion  of  the  wing  fall  off,  and  eventually 
change  sign,  so  that  near  the  tip  almost  the  whole  sec- 
tion is  under  suction. 

(c)  At   the  same  time,  the   areas   of  the   curves   of  normal 
forces  c.ii  upper  and  lower  surface  decrease  at  first  to 
about  */,  of  their   original  value,   but  subsequently   in- 
crease as  the  tip  is  readied. 

(d)  Again   as  we  move   from  the   median   section   outward, 
the   areas   of   diagrams   proportional    to    parallel   forces 
change   from   negative   values    (which   oppose   drag)    to 
appreciable  positive  values,  so  that  drag  of  the  sections 
increases  very  rapidly  in  the  neighborhood  of  the  wing 
tips.    Thus  maximum  L/D  at  A  is  24,  at  E  it  is  only  5. 

(e)  It  is  the  variations  in  pressure  distribution  as  we  move 
out  laterally  which  cause  the  center  of  pressure  of  the 
whole  wing  to  move  back. 

This  seems  to  demonstrate  clearly  that  at  the  sides  of  the 
wing  section  there  is  a  considerable  amount  of  lateral  flow, 
which  prevents  the  establishment  of  a  regime  as  efficient  as 
at  the  center,  where  the  air  does  not  escape  but  follows  the 
contour  of  the  wing. 

It  is  now  also  clear  why  increased  aspect  ratio  is  advan- 
tageous: As  aspect  ratio  is  increased,  the  inefficient  action 
of  the  exterior  sections  assumes  less  importance.  Without 
further  research  it  is,  however,  impossible  to  say  whether 
increase  in  aspect  ratio  leaves  the  aerodynamical  conditions 
at  the  median  sections  unaltered,  or  whether  it  improves  con- 
ditions everywhere  on  the  wing  except  on  the  lateral  tip. 

These  experiments  may  not  be  of  immediate  application  in 
design,  but  may  serve  to  give  a  better  conception  of  what 
may  be  expected  when  a  wing  is  varied  in  plan  form.  Be- 
sides the  effects  of  varying  ratio,  these  considerations  would 
tend  to  explain  the  effects  of  raking. 

Distribution  of  Pressure  Over  Entire  Surface  of  Wing 
and  Curves  of  Equi-Pressure 

Kill'i'l  employs  an  instructive  method  of  curves  of  equi- 
|ii-r-Mire-  over  the  entire  surface  of  the  wing,  lie  has  ob- 
tained such  curves  for  flat  plates  and  for  cambered  surfaces, 
but  has  unfortunately  not  carried  his  analysis  very  far,  and 
gives  us  nothing  beyond  a  graphical  idea  of  the  actual  dis- 
tribution of  pressures.  In  Fig.  8  we  find  curves  of  equi- 
|.nssure  and  pressures  at  various  sections  for  the  Nieuport 
which  are  somewhat  more  suggestive. 

In  tlic   Viouport   wiiiir.  the  sections,  while  preserving  their 


AERODYNAMICAL  THEORY  AND  DATA 


49 


general  character,  thin  down  as  we  move  from  the  median 
section  outward.  This  has  the  effect  of  maintaining  nearly 
tlie  same  character  of  pressure  distribution  on  all  sections. 


FT 

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2 

.  £>  O  O8S  £ 

From  these  considerations  we  can  apparently  conclude : 

(a)  That  it  is  the  upper  surface  of  a  wing  which  is  by  far 
the  most  important. 

(b)  That  hollowing  out  a  section  has  very  little  effect  either 
on  its  lifting  power  or  on  its  efficiency. 

A  somewhat  similar  conclusion  was  arrived  at  by  Bende- 


wing  Section  A/o  / 

normal  to  chord 


Wing  Secticn  Not 
Force  normal  tc  chcrd 


.0042.1. 

A 

?C 

-.^ 

/ 

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^  . 

/x 

"* 

.QO-t  7O 
C  0 
-.CO/06 

.0002/3 

-  .  C7O02/J 

> 

x 

.OOf  7O 
.00 

^ 

'/      ~     ' 

,ff- 

^ 

;^^~ 

•  

=—  i 

-< 

' 

^ 

-0 

/     ^ 

? 

r 

r"       O*      -S*       tO*.    15*     2.0'     *L5"                         O         5          f 

f^cree  a/cne  chord               ^  ,  ,         force    <*/ 

C7'      /.S"     ^<?«     ^^ 

*nc/  office 

—  -  — 

^ 

^ 

y 

"X 

Nf 

/ 

N 

~ar 

,;- 

—  ' 

-.00032 

Xx 

& 

/f/y/e  cf  /r/c/Je,ic.e    '                  jiyft  ef  /ne&MC* 

(T)  Lower 


@  Upper  Surface 


©    Total 


fill  coefficients  in  pounds f>irs4uarefp_of_  per  fn/'/e  fiovr 

FIG.  8.    DISTRIBUTION  OF  PRESSURE  ON  NIEUPORT  WING. 

The  outer  sections  have  smaller  values,  it  is  true,  but  the 
maximum  suction  on  them  is  still  not  far  from  the  leading 
edge.  This  from  considerations  of  preceding  paragraphs 
tends  to  minimize  the  aerodynamic  inefficiency  on  the  outer 
section.  A  wing  such  as  the  Nieuport  wing  might,  therefore, 
be  very  valuable,  but  further  experiments  would  be  necessary 
before  this  point  could  be  definitely  settled. 

Relative  Importance  and  Interdependence 
of  Two  Surfaces 

In  Fig.  9  are  shown  curves  due  to  the  National  Physical 
Laboratory,  which  show  the  distribution  of  pressures  along 
and  normal  to  the  chord  on  the  upper  and  lower  surfaces  of 
two  wing  sections.  The  sections  are  alike  in  their  upper 
surfaces,  but  one  of  them,  section  2,  is  hollowed  out,  while 
the  other,  section  1,  has  a  plane  under  surface. 

As  we  have  already  stated,  the  sum  of  two  forces  normal 
to  the  chord  is  scarcely  distinguishable  from  the  lift.  And 
it  can  be  readily  seen  from  these  curves  that  in  both  sections 
the  upper  surface  contributes  all  the  normal  force  at  2  de- 
grees and  nearly  three-quarters  of  it  at  12  degrees. 

Tt  can  be  deduced  from  this  that  the  lower  surface  of  a 
wing  section  provides  not  more  than  one-quarter  of  the  total 
lift.  We  notice  further  that  the  curves  for  the  upper  sur- 
faces in  both  sections  are  practically  identical. 

Section  1  has  no  components  parallel  to  the  chord;  in  sec- 
tion 2,  as  can  be  seen  from  the  curves,  the  lower  surface 
contributes  very  little  of  such  components.  Up  to  7  degrees, 
the  lower  surface  gives  an  upward  force  which  helps  to  dimin- 
ish drag ;  above  this  it  has  down  a  "  downward  "  and  detri- 
mental effect.  It  can  be  seen  here  that  the  effect  of  the  upper 
surface  is  similar  in  both  sections. 


FIG.  9.    DIAGRAMS  ILLUSTRATING  THE  INTERDEPENDENCE  AND 
'  RELATIVE  IMPORTANCE  OF  Two  SURFACES  OF  A  WING 
SECTION.    COEFFICIENTS  ARE  IN  FOOT  POUNDS 
PER  SQUARE  FOOT  PER  MILE  HOUR. 

mann  in  examining  a  heavily  cambered  almost  circular  pro- 
peller section;  the  camber  of  the  lower  surface  scarcely  af- 
fected the  value  of  the  coefficients. 

Distribution  of  Pressure;  the  Principle  of  the  Dipping 

Front  Edge.    Why  a  Wing  Section  Is  Advantageous 

as   Compared  with   a   Flat  Plate 

We  know  from  the  pressure  diagrams  that  for  any  wing 
such  as  that  in  Fig.  10,  the  pressure  at  A  is  negative,  while 


FIG.  10.    DIAGRAM  ILLUSTRATING  THE  PRINCIPLE  OF  THE 
DIPPING  FRONT  EDGE. 

that  at  B  is  positive.  This  seems  paradoxical,  since  A  would 
appear  to  be  facing  the  wind,  while  B  is  sheltered  from  it. 
Fage  gives  a  very  good  explanation  of  this  phenomenon  com- 
monly known  as  the  "Principles  of  the  Dipping  Edge." 
Photographs,  such  as  we  have  already  given  in  Chapter  3, 
show  that  the  wind  is  deflected  upward  as  it  approaches  the 
leading  edge  of  the  wing.  A,  although  it  faces  the  general 
wind  direction,  is  thus  screened  from  it,  and  becomes  a  region 
of  low  pressure;  while  on  B  the  relative  wind  impinges  di- 
rectly and  receives  a  slight  downward  deflection. 

From  somewhat  similar  considerations,  we  are  now  in  a 
position  to  explain  roughly  why  a  wing  section  is  so  much 
more  advantageous  than  a  flat  plate: 

(1)  The  suction  on  the  upper  surface  of  a  wing  toward  the 
trailing  edge  is  much  greater  than  that  for  a  flat  plate, 
explainable  by  the  principle  of  the  dipping  front  edge. 
And  a  greater  suction  implies  a  greater  lifting  power. 

(2)  From  the  pressure  distribution  curves  on  the  median  sec- 
tion, it  can  be  seen  at  once  that  the  greater  part  of  the 
force  on  the  upper  surface  is  due  to  the  suction  in  the 
region  of  the  leading  edge. 


50 


AERODYNAMICAL  THEORY  AND  DATA 


Hence  in  summing  up  components  parallel  to  the  chord, 
for  a  good  wing,  the  resultant  force  will  tend  to  be  "up- 
wind," and  tend  to  nullify  the  skin  friction,  reducing  the  total 
drag.  In  a  flat  plate  no  such  advantageous  action  will  be 
present.  A  wing  will,  therefore,  give  a  greater  lifting  power 
and  a  bigger  lift  to  drag  ratio. 


References  for  Part  I,  Chapter  7 

INVESTIGATION    OP   THE    PRESSURE    IN   A    MEDIAN    SECTION 

OVER  THE  UPPER  AND  LOWER  SURFACES 

OF   THREE   AEROFOILS 

British  Report,  1911-1012.     No.  60.     Page  62. 


INVESTIGATION   OF   THE   DISTRIBUTION   OF   PRESSURE   OVBK 

THE  ENTIRE   SURFACE   OF  AN  AEROFOIL 
British  Report,  1912-1913.     No.  73. 

EFFECT  OF  VARIATION  OP  SPEED  AND  SIZE,  LIFT  AND  DRAG 

COEFFICIENTS 
British  Report,  1912-1913.     No.  72.     Page  81. 

DISTRIBUTION  OF  PRESSURE  AT  MEDIAN  CROSS  SECTION  Of 
VARIOUS  SURFACES 

"The   Resistance   of  Air  and   Aviation,"   Eiffel    (trans.   Hunsaker), 
page  70. 

DISTRIBUTION   OF  PRESSURE 

Bulletin  de  I'lnatitut  Atrotechnlque  de  VUniversiU  de  Parit    1!U3. 
Etude  des  Surface  RU  Chariot  Electrlque. 

"Curves   of   Equl-Pressure   for   the  Nleuport   Wing,"   Eiffel    (Hun- 
saker), page  171. 

INTERDEPENDENCE  OF  THE  TWO  SURFACES  OP  A  WINO 
British  Report,  inil-1912.     No.  60.     Paev  (is. 

"  Luftschrauhen-Untersuchungen,"    F.    Bendemann.      Zeittchritt    fir 
Flugtechnik,  1911-1912. 

PRINCIPLE  OF  THE  DIPPING  FRONT  EDGE 
A.  Page.     "  The  Aeroplane,"  page  17 


Chapter  VIII 

Biplane  Combinations 


Monoplane  surfaces  are  aerodynamically  the  most  efficient. 
Biplane  combinations  of  any  kind  introduce  interference  be- 
tween the  planes,  a  diminution  of  the  suction  on  the  lower 
plane,  with  a  consequently  diminished  efficiency.  But  as  air- 
planes increase  in  size  the  difficulties  of  suitably  bracing 
monoplane  surfaces  become  very  great,  and  their  lifting  ca- 
pacity inadequate,  and  biplane  construction  must  be  resorted 
to. 

Another  important  aspect  of  biplane  construction  is  the 
possibility  of  obtaining  longitudinally  stable  arrangements  by 
staggering  or  displacing  the  wings  relative  to  one  another, 
and  by  introducing  small  angles  between  their  planes,  which 
is  known  as  decalage. 


The  effects  of  staggering  the  planes  for  convenience  of  con- 
struction or  with  a  view  to  increasing  the  range  of  view  are 
to  be  considered  within  the  province  of  practical  construction. 

Orthogonal  Biplane  Arrangements  with  Varying 
Gap  Between  Planes 

An  orthogonal  biplane,  as  shown  in  Fig.  1,  Setting  No.  1,  is 
one  in  which  the  lines  joining  the  leading  and  trailing  edges 
of  the  two  wings  are  both  at  right  angles  to  the  chord. 

Experiments  to  which  reference  is  given  at  the  end  of  this 
section  to  determine  the  aerodynamic  coefficients  of  such  com- 
binations with  varying  gap  between  planes  have  been  carried 


SETTING  N't.          I 
FORCES  ON  ORTHOGOHAL 
I  BIPLANE.  ' 

I  At,  3CMP.H StandartlAir 


\                        H    ' 

1  Ifc  DetcaLage  ,           / 

\                          ,'1 
*                          |1 
"                 \                          \ 

•ScoAf  of  Forces  V-OftS 
Scall-  of  Drawing  -p-i 

on,  Model             / 
/                      / 

\ 

f         / 

\                   1 

/                   / 

\ 

,'                   / 

\ 

/                 / 

JL    . 

T—~  A—-. 

0x^3      I 

SETTING  N?3. 

FORCES  ON  STAGGERED  BIPLANE 

MODEL 

At  30M.PJI.  StandardAir 
Stagger:  5O'/.^ 

Scale.  offorcee:V-04  Ib. 

Scale  ofDrcurinff  2'3"on- Model* 


arallel  toltnrtr  Ourrd_ 


SETTING  Hrz. 

FORCES  ON  STAGGERED  BIPLANE 

MODEL 
AtSOMfH.  Standard' Air 

Stuqger. 50?. 

Jfo  DccuLagv 

Scale  offerees  h'-04tb. 

Scale  of  Drawing.  $•  3'cn,  Mt'd*'t 


;i 


«™'  ^           r 

•  _^ 

V--r-\4          |T 

V 

SETTING  Nr 

4. 

\  \u 

FORCES  ON  STAGGERED  BIPLANE 

\      \  \\ 

MODEL 

^    H 

At  30M.P.H  StandardAir 

\   m 
\  jfl 

\      '  1  r 

Stagger  507" 
Decaiage  tZ'/z 
Scale  of  fbrceet:% 

-04lb 

Scale  cfDrnwuiy 

2'-3'<mMod<-l, 

1 

/If^l 

IMI 

\ 

*  ""*  »       ^'  !H1\  x-                    ~  —  ""—- 

fir* 


FIG.  1.    VECTOR  DIAGRAMS  FOR  DIFFERENT  BIPLANE  SETTINGS.  USING  E.  A.  F. 

51 


52 


AERODYNAMICAL  THEORY  AND  DATA 


out  solely  on  wings  of  an  antiquated  type,  and  it  is  by  no 
means  certain  that  similar  values  would  apply  exactly  to 
modern  wings.  In  default  of  further  exhaustive  experimenta- 
tion, the  N.  P.  L.  values  must  be  taken  as  a  guide,  however. 
The  results  of  the  N.  P.  L.  experiments  showed  that  for  nor- 
mal angles  of  incidence: 

(1)  Drag  per  unit  area  of  biplane  combination  was  not 
appreciably  greater  than  that  of  a  similar  monoplane  surface. 

(2)  The  lift  coefficients  as  compared  with  a  monoplane  sur- 
face decreased  considerably,  and  that  the  loss  was  the  greater 
the  smaller  the  ratio  between  gap  and  chord. 

(3)  Loss  in  value  of  lift/drag  follows: 

On  the  basis  of  these  experiments  the  following  table  can  be 
employed : 

TABLE    1. 
FOB  ANGLES  or  INCIDENCE  IN  NOIIM.M.  FLIGHT 

0.80       1.00       1.20       1.60 


tribution  of  lift  on  the  upper  and  lower  wing  of  a  biplane, 
with  ratio  gap  to  chord  1.2: 


Ratio   of  gap   to  chord 0.40 

Factor  for  K,  to  reduce  biplane  lift 
from  coefficients  of  a  monoplane 

surface    0.61 

Factor  for  Kj/Ki  to  reduce  from 
coefficients  of  a  monoplane  sur- 
face    0.75 


0.76       0.81        0.86       0.89 


0.79        0.81        0.84       0.88 


Distribution  of  Forces  Between  the  Upper  and  Lower 
Wings  of  a  Biplane 

By  an  indirect  deduction  from  Dr.  Hunsaker*s  experiments 
on  the  triplane  the  following  figures  may  be  given  for  the  dis- 


„    SETTING  N'S 


FORCES  ON  STAGGERED  BIPLANE 
MODEL 

At  30M.PH  Standard,  Air 
Stagycr:  50^. 
Decalaqe:  *4" 
Scale  ofForcea*r025U> 
Scale- of  Drawing  2~ 


_J 


SETTING  N-i*.  , 

'FORCES  OH  MODEL  BIPLANE 

\At  30MP11  StamdanLfar 
iltoDecalaae  / 

'.  Scale  of forces  'j-(j£Olb. 
I  Scale  of  Drawing  2'fXcnModtL 


Angle  of  Incidence 
0 
2 

8 
12 


TABLE    2. 
Percentage  Lift 
DpperVlng 

r,4' , 
53% 
54% 


Percentage  Lift 
Lower  Wing 
38% 

45% 
46% 
47% 
46% 


It  is  possible  that  the  upper  wing  does  not  only  carry  a 
greater  proportion  of  the  lift,  but  that  it  also  has  a  better 
L/D  ratio  and  has  a  proportionately  small  drag.  Still  the 
standard  assumption,  as  used  by  Dr.  Zahm,  among  other  emi- 
nent authorities,  that  55  per  cent  of  all  the  forces  acting  on  a 
biplane  may  be  taken  as  acting  on  the  upper  plane  is  suffi- 
ciently accurate  for  all  practical  purposes.  The  distribution 
of  forces  between  the  two  planes  is  only  useful  in  stress  cal- 
culations in  design,  where  an  error  of  a  few  per  cent  will  have 
little  or  no  importance.  In  Eiffel's  earlier  experiments  some 
interesting  data  for  pressure  distribution  on  the  upper  and 
lower  wings  of  a  biplane  are  given  which  bear  out  the  above 
values. 

Distinction  Between  Static  and  Dynamic  Stability 

It  is  important  at  this  stage  of  the  work  to  draw  a  dis- 
tinction between  static  and  dynamic  stability.  An  airplane 
with  stutic  longitudinal  stability  has  a  righting  moment 


SETTING  N'IM. 


+y— - -J 

FORCES  ON  MODEL  BIPLANE 
At  bOMP.H.  Standard  Air 
Nopecalajje 

ScjUeof Forces  •HL 

Scble  ofDramnff  2-3~imModel / 
Spout  if  both,  Win, 


1 

/ 

W'.X"                   ~*% 

L.\.  i  r  f 

/ 

-  -V-  ,-.-4 

"*    T*  -*( 

\                          ! 

/                   SETTING  N?3> 

\ 

FORCES  ON  MODEL  BIPL  ANE 

\ 

\ 

j          AtSOM.P.ll  StandanlAu- 

\ 

Zl'Dtcalage. 

\ 

!>OZ  Stayytr 

\ 

\ 

A-«A-  tfllniivinti  2'^'cn  filt'iltl 

\ 
\ 

Sail,  offerees^  02011 

\ 
\ 

Sfxtll  eflvth  )Vi«yv-/tf  ' 

\              J 

___________^^ 

«'»•  _--^5L             //i 

P           /JJ 

K 

Fin.  2.    VECTOR  DIAGRAMS  ton  DIFFERENT  BIPLANE  SETTINGS,  USING  R.  A.  F.  (i  WIN.;  SKCTION. 


AERODYNAMICAL  THEORY  AND  DATA 


53 


when  displaced  from  its  position  of  equilibrium,  which  tends 
to  bring  it  back  to  the  position  of  equilibrium.  This  righting 
moment  may  be  so  violent,  however,  that  the  airplane  may 
acquire  a  considerable  rotational  velocity  (pitching  velocity), 


-"*'  -*' -2'   0' +2  +•;•+<;•  £•  70"  7i"  w-  is'  is'  20'  22' 
Angles  of  IncicU  -'ce. 

FIG.  3.    LIFT  AND  DRAG  COEFFICIENTS. 

overshoot  its  position  of  equilibrium,  and  then,  with  the  inter- 
vention of  a  righting  moment  in  the  opposite  direction,  oscil- 
late back  and  forth.  In  fact,  the  greater  the  static  stability, 
the  more  violent  may  be  the  longitudinal  oscillations. 

In  addition,  therefore,  there  must  be  dynamic  stability  sup- 
plied by  large  tail  surfaces,  with  a  long  arm  about  the  center 
of  gravity  to  damp  out  the  oscillations  which  the  static  sta- 
bility alone  is  unable  to  subdue.  A  concise  but  authoritative 


•032C 

5 

!=i 

SS 

! 

Ky-- 

ZZ7-TT 

AV*  . 

,/ 

ft 

•0022 
W20 
<K18 

•mw 

•0014 
•OOK 

•one 
•Ma 

•OOK 

•am 

•tXXK 
C 

-IK-: 

-ff* 

M. 

P.H. 

-S(, 

IFT.-LB.-UNirS.  /, 

/ 

^ 

/ 

// 

/ 

"*•• 

/  1 

// 

t 

/ 

I 

2 

t 

1 

w 

• 

— 

/' 

z 

> 

• 

ii 

/ 

—  «-. 

-X  — 

t 
t 

• 
* 
H 

lA 

ZA 
SA 

— 

i 

_ 

z 

— 

— 

— 

%1L 

- 

r/    \ 

FIG.  4. 


Angles  or  Incidence. 
LIFT  AND  DRAG  COEFFICIENTS. 


discussion  of  dynamic  stability  has  appeared  in  AVIATION  AND 
AERONAUTICAL  ENGINEERING  (see  appended  references). 

Stable  Biplane  Arrangements 

We  have  seen  that  it  is  possible  to  secure  a  large  degree  of 
static  stability  at  the  expense  of  some  loss  in  efficiency  by  the 
employment  of  wings  with  reversed  curvature  at  the  trailing 


edge.  It  is  possible  to  insure  static  stability  also  by  the  em- 
ployment of  biplane  combinations  with  stagger  and  decalage. 
Dynamic  stability  without  preliminary  static  stability  is  im- 


•ftY.1 
•OKI 

•cat 
•fan 

•OOK 

•oas 

•nan 
•can 
n 

/jf 

•• 

77 

K. 

rar! 

r 

/ 

J 

ft 

1.P 

.a.- 

UNtr&.  * 

/// 

u 

t 

7| 

t 

3 

1 

// 

7 

! 

/ 

r 

. 

n 

// 

/ 

? 

I/ 

i 

/  , 

y/_ 

j 

>// 

tor    f 

\ 

^ 

ffi—*  —  RAf.  6  Alone 

—  4—  •         >                 f         «2 

^ 

W; 

£ 

^ 

—  tf  "••  '"          *                   « 

3 

4- 
5 

1 

-6'-4-  -24    0'+3'+«-+e-   £'    70"  73'   W 
Anglos  (f  Incidence. 

FIG.  5.    LIFT  AND  DRAG  COEFFICIENTS. 

possible,  but  if  an  airplane  is  statically  stable,  dynamic  sta- 
bility is  certainly  possible. 

Dr.  Hunsaker  investigated  a  great  number  of  biplane  ar- 
rangements at  the  Massachusetts  Institute  of  Technology,  with 


•cc:o 

1 

K  x  -  J*B.U?Z- 

I 

M.P.H.-  SQ.  FT.-  13.-  UNITS 

i  , 

•OOK 
•6X7 

•axe 

•OXu 

•OCX 
•0X2 
•0X1 

c 

I 

/ 

III 

1 

I 

// 

f 

.' 

2 

<~l 

[ 

) 

/7// 

//I// 

Qtt 

L 

t 

m 

/ 

W 

t 

A 

i 

2 

% 

2 

*- 

' 

ffe 

• 
f 

'.  ZA 

:      "A 

^J 

>, 

~ 

/ 

-f.  '" 

'-; 

^ 

1 

-4*  -2'   O'  -f  '2'-t-4'-lG'    3'   1O'   1Z'  74*   16'  TQ'  2G'  2Z' 

Angles  cf  Jbicidence. 
FIG.  6.    LIFT  AND  DRAG  COEFFICIENTS. 

varying  degrees  of  stagger  and  decalage.  and  found  that  witli 
certain  combinations: 

(1)  Static  longitudinal  stability  could  be  obtained  with  but 
little  loss  in  aerodynamic  efficiency. 

(2)  By  suitable  arrangements,  the  lift  curve  at  the  burble 
point  can  be  flattened  out  and  made  to  maintain  its  maximum 
for  a  wide  range.     This  is  particularly  valuable,  because  it 


54 


AKROUYNAMICAL  THKORY  AND  DATA 


eliminate*  the  danger  usually  attending  stalling  altitudes. 
With  a  sharp  drop  in  lift  at  the  burble  point,  the  loss  in  sus- 
tentation  beyond  a  certain  angle  may  be  so  great  that  the  ma- 
chine may  drop. 

Results  of  Experiments  on  Biplanes  with 
Stagger  and  De'calage 

In  Table  3  are  given  the  summarized  results  for  a  series  of 
tests  on  such  combinations.  In  Figs.  1  and  2  are  shown  the 
corresponding  combinations  with  the  vector  diagrams ;  in  Figs. 
3,  4,  5  and  6  are  shown  Ky  and  Kx  curves,  and  in  Fig.  7  are 
plotted  these  Kv  against  K*  curves  for  all  the  settings. 

To  judge  of  the  stability  of  any  combination  it  is  necessary 
to  assume  a  number  of  positions  for  the  center  of  gravity, 
to  assume  a  normal  flying  angle  of  incidence,  and  to  see 
whether  displacement  from  the  normal  flying  position  is  fol- 
lowed by  the  correct  righting  moment  about  the  center  of 
gravity.  If,  for  instance,  the  center  of  gravity  for  the  setting 
No.  4  of  Fig.  1  is  placed  as  shown,  between  the  vectors  for  4 
degrees  and  6  degrees  incidence,  with  normal  flying  angle  5 
degrees,  there  will  be  statical  stability.  If  the  airplane  dives 
to  2  degrees,  the  resultant  force  will  have  a  clockwise  mo- 
ment about  the  center  of  gravity  and  will  tend  to  right  the 
machine.  If  the  airplane  stalls  to  8  degrees,  the  resultant 
force  will  have  a  counter-clockwise  moment  and  will  again 
tend  to  restore  the  biplane  to  its  normal  position. 

In  Table  3  the  various  settings  are  classified  as  stable  and 
unstable,  and  it  forms  a  very  useful  exercise  to  examine  each 
•ombination  from  this  point  of  view.  The  comparative  values 
aerodynamically  and  the  lift  at  the  burble  point  are  Drought 
out  clearly  by  Table  3  and  by  the  Kv  and  Kx  curves. 

Even  with  these  extensive  tests  it  is  impossible  to  draw- 
definite  conclusions  as  to  the  selection  of  any  particular  type, 


and  the  results  should  be  regarded  as  more  qualitative  than 
quantitive.  The  qualitative  results  would  prevent  any  fan- 
tastic combination  being  employed. 

Some  of  the  main  conclusions  may  be  summarized  as  fol- 
lows: 

(1)  Stagger  alone  improves  the  aerodynamical  qualities  of 
a  biplane,  and  flattens  out  the  burble  point,  moves  the  vectors 
of  force  forward,  but  does  not  increase  the  stability  to  any 
appreciable  extent. 

(2)  Cutting  down  the  lower  wing  of  a  biplane  does  not  im- 
prove the  stability,  but  it  lessens  interference,  improves  the 
aerodynamic  efficiency,  and  flattens  out  the  burble  point. 

(3)  Increasing  decalage   combined  with  stagger   produces 
progressive  stability,  but  at  the  expense  of  aerodynamic  cfli- 
ciency. 

(4)  Among  the  most  promising  arrangements  seem  to  be: 
No.  4.    Decalage  2%  degrees,  stagger  50  per  cent.   The 

stability  is  gained  at  the  expense  of  but  4  per  cent  of  the 
maximum  lift/drag  ratio,  while  a  gain  is  obtained  in  all 
other  properties. 

No.  3A.  Decalage  2.1  degrees,  stagger  50  per  cent, 
lower  chord  83  per  cent  of  the  upper  chord.  Here  the 
stability  is  also  attained  at  a  loss  of  but  4  per  cent  on 
maximum  lift/drag  ratio,  while  the  lift  curve  remains  at 
its  maximum  over  a  range  of  12  degrees. 

Comparison  of  Aerodynamic  Losses  Imnlvrd  in  Obtain- 
ing Stability  by  Reversed  Curvature  \\  iiiys  and 
by  Stagger — Decalage  Combinations 

For  reverse  curvature  wings  giving  static  longitudinal  sta- 
bility the  maximum  lift  is  17  per  cent  less  and  the  maximum 
lift/drag  ratio  is  about  14  per  cent  less  than  for  a  simple 
orthogonal  biplane,  as  seen  from  the  last  column  of  Table  3. 


TABLE  3. 
CHIEF  PABTICOT.ABB  FOB  STABLE  BH-UNB  ABRANOIIIENT* 


Rang* 

K,/K. 

Kf/K, 

of  Hat 

Typ« 

Gap 

Stagger 

Tpper 
Chord 

Lower 
Chord 

Deralage 

1  :'•  ,-r-  .  - 

MMT. 
K,/K, 

Max. 
K, 

w  here 
A'.   - 
0.0005 

where 
K,   - 
0.0018 

Hurl.  If. 
Point  in 

I    )'    ,-M    .    s 

Remarks  on  Stability  with  reference  to  FipB.  1  and  2 

Monoplane  

C 

1.16 

1.18 

0  90 

1.24 

2° 

Unstable. 

Biplane  No.  1... 

c 

0. 

C 

C 

0.0 

1.00 

1.00 

1.00 

1  00 

2° 

Unstable. 

Biplane  No.  2.  .  . 

C 

O.SOC 

c 

C 

0.0 

1.00 

1.06 

1.00 

1.02 

2° 

nt  forces  from  2Vi°  to  li                      <  t  near  a 

single  point.     If  thiw  point  lie-  the  center  of  gravity 

tin!.-  wilt  be  no  pit.  hint-  moment  throughout  this 

range.     1"-                                     of  ri  vine  angles  from 

1^4°  to  •_'!"                         lilirmni  IK  M 

Biplane  No.  3... 

C 

.  ioc 

c 

C 

1.0 

0.95 

1.03 

1.00 

1.01 

6° 

The  force  vector*  for  ;uu'!es  from  0°  to  10°  intersect 

' 

neur  .1  point.      If   the  center  of  uijiviu    be  nt  this 

point    the   e<iuilil>rn:ru    is   ueutT:tl   from   0(    to    111°. 

Miil.lc  from  in1  to  18°  and  uMtable  f  rotn  0°  to  -.r>°. 

If  center  of  i_*r:t\it\  l>t  i                                  i  t  ho  in- 

tersection of  the  \-                        LIU!  the  low 

the  e.niinl.Mi  in   is  Mul.le  for  all  the  range  from 

-2°  to   +18°. 

Biplane  No.  4... 

C        O.SOC 

c 

fj 

2.5 

0.95 

1.03 

1.00 

1.02 

4° 

n!n  of  irra\  ity  locntci!  nn.VM  here  in  the  lower 
-2C'  :inil  —  5° 

the   entire    nil.^e   ol    pifehinK   angle    —6°   to    -T-200. 

\  cr\    rond   :iT[:iiiK<-inrnt. 

c 

' 

c 

C 

4.0 

0.87 

1.04 

0  DO 

0  99 

4° 

Kxreraivc  nubility.     Mncliim  s  MiitnMr  for  amateur*. 

Biplane  No.  1A. 

c 

0. 

0.83C 

0.0 

1.04 

1.04 

0  90 

1  05 

4« 

..iinidly  nriMnble. 

Biplane  No.  2A. 

c 

' 

C 

0.83C 

0  0 

1  04 

1  04 

0  93 

1  08 

12" 

I'll"! 

Biplane  No.  3A. 

c 

.,   ,.  - 

C          'i  HC          -'   1          I'  '-"<          1.03 

0.96 

1.05 

12° 

Longitudinal    Mi.bilit>     for    nny    center    of    gravity 
•  1    within    tl  >                         n^lc   formed   bv    the 

, 

-,  for  -2°  and   -5°.    This  will  be  the  raw 

(or  n                      olane. 

ture  Winn.  . 

c 

0. 

C          « 

0.0 

o  -.. 

0.83 

1.21 

2« 

longitudinally  stable. 

C  <•  chord  length  (upper). 

K.JK,  and  other  aerodynamic  roeffirienu  referred  to  th«  othoffoul  itantUrd  bipUike  M  unity. 


AERODYNAMICAL  THEORY  AND  DATA 


55 


With  a  stagger  decalage  combination  there  is  an  actual  in- 
crease in  the  maximum  lift,  while  the  L/D  loss  is  only  4  per 
cent.  The  constructional  difficulties  in  the  region  of  the  rear 
spar  are  also  avoided.  On  the  other  hand,  stagger  involves 


the  biplane  drag  was  greater  than  that  of  the  monoplane, 
while  at  high  angles  the  biplane  gave  the  better  qualities.  The 
later  Massachusetts  Institute  of  Technology  experiments  gave 
diametrically  opposite  indications.  Since  these  experiments 


* 

IS 
14 
13 
12 
1t 

to 

, 

*- 

^X 

!+ 

f^^ 

*^l          *  H.A.F.6ALONE 
UNSTABLE 

/ 

\ 

*% 

H—  C—  ** 

f 

v~ 

^ 

> 

•o~~- 

^ 

Tl 

: 

E                                   SETTING  NT/. 

UNSTABLE 

\                                  SETTING  «2 
\                                   UNSTABLE 

\                                   SETTING  K3. 
\                                     NEUTRAL 

\                                  SETTING  N'4. 
\                                   STABLE 
m^ml 

\                                   SETTING  N^S 
\                   ?         "    VEKY  STABLE 

r 

M 

^ 

s 

\ 

\# 

aJ— 

S 

^g-\ 

^T- 

w 



T  —  . 

^ 

^ 

^. 

^ 

s 

Is 

1      / 

/ 

X; 

^ 

\s 

V 

\ 

\ 

// 

| 

s 

f 

^^^ 

V 

K 

\ 
\ 

\ 

-c- 

s 

4 

1 

(/ 

V 

s 

/ 

i- 

AERODYNAMIC  LABORATORY 
MASS.  INSTITUTE  TECHr 
BIPLANE  ARRANGEMENTS      - 
Span  ofallMo&els:  18  Inches 
Sap  of.  all  Models:  SInches 
Wmd  Velocity:  30  Miles  per  Hoar 
Density  of  Air:  0-07608Lbsper  OMcR 
IOTE:-Resistance.  of  Struts  and 
Supports  has  beervSubtracteA 
WingSection,  ofaliModels:JRA.F.{ 

\ 

1 

/ 

/I 

\ 

\ 

A 

/ 
t 
1 
1 

f 

it\ 

^ 

vt> 

\ 

2 

\       , 

1 

1 

i 

^ 

2 

I 

u 

j 

SETTING  Nil*. 

~    UNSTABLE 

i 

/ 

"S 

[i 

*•!&€+ 

\    \                                  SCTTINGN7&I. 
V      \     \                            "    UNSTABLE 

._L^§~i—  1. 

j_                r>-«JC« 

*--.  v    V" 

z*      \     \                                 SETTING  MM*. 
\      \                                    STABLE 

2 
1 
O 

I 

ft 
i 

/ 

$ 

/ 

L,, 

-OOOff   •««»    -«W    -«7t0    -COW 

Lift  Coefficient- 


»/«     -COW    OBZ7    -«!ZZ 

-Pounds  per  Scf  Ft-  MPM 

FIG.  7.    LIFT  COEFFICIENTS  PLOTTED  AGAINST  DRAG  FOR  VARIOUS  SETTINGS. 


increased  length  and  resistance  of  wing  struts  and  increased 
stresses  in  the  drift  bracing  of  the  wings. 

The  relative  merits  of  the  two  systems  can  only  be  decided 
upon  by  a  practical  comparative  experience  of  the  two  types. 
In  the  authors'  opinion,  the  stagger-decalage  system  is  more 
likely  to  give  good  results  than  the  reversed  curvature  wing 
system  for  ordinary  machines.  For  very  high  speed  machines, 
flying  at  a  small  angle  of  incidence,  however,  the  reversed 
curvature  biplane  offers  20  per  cent  less  resistance  than  the 
orthogonal  biplane  with  R.  A.  F.  6  wing  section.  In  such  ma- 
chines, where  a  low  maximum  Kv  coefficient  and  high  landing 
speeds  are  permissible,  the  reversed  curvature  wing  might  be 
very  advantageous  from  the  point  of  view  of  high  maximum 
speeds. 

Aerodynamic  Comparison  Between  the  Monoplane 
and  the  Biplane 

In  Table  1  are  given  the  correcting  factors  from  monoplane 
values  for  biplanes  with  varying  gap/chord  ratios  from  the 
N.  P.  L.  experiments.  These  will,  although  based  on  a  wing 
section  of  an  antiquated  type,  as  already  mentioned,  be  quite 
correct  enough  for  angles  of  normal  flight,  4,  6  or  8  degrees 
incidence.  But  for  very  low  angles  of  incidence  and  for  very 
high  angles  of  incidence  there  is  a  discrepancy  between  the 
results  obtained  by  the  British  investigators  and  by  Dr.  Ilun- 
saker.  The  former  concluded  that  at  low  angles  of  incidence 


were  conducted  at  a  later  date,  and  were  carried  out  with 
R.  A.  F.  6  wing  sections,  they  are  probably  worthy  of  more 
credence.  The  following  table  has  been  deduced  from  the 
curves  of  Fig.  7,  where  Kv  is  plotted  against  K  x  : 

TABLE    4. 

LIFT/DRAG  RATIO  AND  K,  FOR  ORTHOGONAL  BIPLANE,  R.  A.  F.  6  WING 
SECTION,  GAP/CHORD  RATIO  1,  GIVEN  AS  PERCENTAGE  OF  MONO- 
PLANE VALUES  FOB  THE  SAME  A'y 


K? 

0.11004 
O.H006 
0.0008 
0.0012 
0.0(11  (} 
0.0o:>0 
0.00^4 


KS 

110 

10T 

09 

85 

85 

75 

73 


K, 

90 

93 

101 

115 

115 

125 

127 


To  consider  L/D  and  Kx  for  the  same  values  of  ~KV  for  mon- 
oplane and  biplane  is  really  a  much  fairer  comparison  than 
to  consider  L/D  and  Kx  for  the  same  angles  of  incidence. 
It  really  matters  very  little  what  the  angles  of  incidence  for 
biplane  and  monoplane  are,  provided  we  have  the  same  Kv 
and  the  same  sustaining  power  at  the  same  speed. 

From  Table  4  one  would  conclude  that  the  biplane  has  a 
very  distinct  advantage  for  a  high-speed  scout.  Apparently 
at  a  high  speed,  and  hence  a  low  lift  coefficient,  the  biplane 
resistance  is  10  per  cent  less  than  the  monoplane  resistance. 
This  is  an  appreciable  saving.  For  a  machine  which  must  fly 
slowly,  and  consequently  with  a  high  lift  coefficient,  the  bi- 
plane resistance  is  from  15  to  25  per  cent  greater  than  the 
monoplane  resistance. 


5(j  AERO  DYNAMICAL  THEORY  AND  DATA 


References  for  Part  I,  Chapter  8  ^"jan.^aSS'i^T;..                 by  J"  C"  Hunsakcr-  in 

"  Dynamic  stnMllt.v  of  Aeroplanes,"  by  J.  C.  Hunsaker,  In  AVIATION 

"  Chapter  on  Aeronautics,"  by  J.  C.  Hunsaker,  In  The  Neic  Mechanical  AND  AERONAUTICAL  ENGINEEUIM;.  Aug.   1,   1910. 

Enpineeri'  Handbook.  "Determination  of  the  Effect  on  the  Lift  and  Drift  of  a  Variation  in 

"  The  De«lgn  of  Aeroplane*,"  by  A.  W.  Judge,  page  42.  the  Spacing  In  a  Biplane."     British  Report,  1911-2,  No.  60. 

„               _._  .                                .  "  Determination  of  the  Effects  of  Staggering  the  Wings  of  a  Biplane." 

"The  Resistance  of  Air  and  Aviation,     by  G.  Eiffel   (translated  by  J.  British  Beport,  1911-2,  No.  60. 

C.  Hunmker).  ..  Application  of  Experimental  Results  to  Practical  Problems  In  Aero- 

"  La  Reslstencc  de  1'Alr  ct  1'Avlatlon,"  by  G.  Eiffel,  1914.     Chapter  5.  plane  Design."     British  Report,  1911-2,  No.  60. 


Chapter  IX 

Triplane  Combinations  —  Uses^of  Negative  Tail 

Surfaces 


In  an  article  on  "  The  Aerodynamical  Properties  of  the  Tri- 
plane," by  J.  C.  Hunsaker  and  T.  H.  Huff,  published  in  the 
November  1,  1916,  issue  of  AVIATION  AND  AERONAUTICAL  EN- 
GINEERING, the  reader  will  find  a  complete  treatment  of  the 
aerodynamic  properties  of  the  triplane,  with  a  complete  record 
of  the  experimental  results  obtained  at  the  Massachusetts  In- 
stitute of  Technology.  It  remains  for  us  only  to  summarize 
the  main  results,  and  to  review  recent  constructional  applica- 
tions of  the  triplane  principle. 

The  main  conclusions  from  these  experiments  are: 

(I.)  At  the  stalling  angles  such  as  16  degrees  the  triplane 
and  biplane  give  nearly  the  same  maximum  lift;  the  triplane 
has  a  materially  lower  resistance  at  this  angle,  giving  a  much 
better  performance  at  slow  speed.  Thus  the  L/D  ratio  at 
16  degrees  is  4.5  for  the  monoplane,  5.6  for  the  biplane,  and 
6.5  for  the  triplane. 

(II.)  At  angles  below  12  degrees  the  drag  coefficient  is 
not  greatly  different  in  the  three  cases,  but  the  lift  for  the 
triplane  is  considerably  reduced;  it  is  inferior  to  that  of 
the  biplane  which  again  is  inferior  to  that  of  the  monoplane. 

(III.)  The  best  L/D  for  the  triplane  combination  is  only 
12.8  as  compared  with  13.8  for  the  biplane,  and  17  for  the 
monoplane. 

(IV.)  The  center  of  pressure  motion  is  almost  identical 
with  that  of  the  biplane.  We  have  seen  previously  that  the 
center  of  pressure  motion  for  the  biplane  is  nearly  that  of  the 
monoplane.  This  demonstrates  that  the  commonly  made  as- 
sumption of  monoplane  center  of  pressure  motion  for  a  wing 
of  a  biplane  also  holds  for  the  triplane.  This  is  an  important 
fact  in  view  of  the  methods  employed  in  stress  diagrams. 

The  experimental  results  for  Kr  and  L/D  for  the  triplane 
as  compared  with  the  monoplane  and  biplane  are  summarized 
in  Table  1 : 

TABLE  1 

TABLE  SUMMAUIZING  COMPARATIVE  VALUES  OK  K     AND  L/D  FOR  MONO- 
PLANE, BIPLANE  AND  TKIPLANE. 


» 

0. 

,  —  MONO 
Actual 

Ky 

000486 

PLANE.  —  N 

Per- 
centage. 

100 
100 
100 
100 
100 
100 

L/D 
100 
100 
100 
100 
100 
100 

,  BIPLANE.  v  ,  TRIPLANE.  , 
Actual     Percent,  of    Actual  Percent,  of 
/Cj,      Monoplane.        K  y    Monoplane. 

.000432          88.8          .000404          83.0 
.000864          83.8          .000776          75.4 
.00123            85.4          .00109            75.7 
.00186            85.2          .00169            77.4 
.00244            87.6          .00226            81.2 
.00273            98.5          .00267            96.4 

L/D             L/D            L/D            L/D 
6.3              73.2              6.1              70.8 
12.2              74.7            11.4              69.8 
13.8              82.0            12.8              76.1 
11.3              81.9            11.1              80.4 
9.5              95.0              8.9              89.0 
5.6            124.0              6.5            145.0 

2  

.  .  .     00103 

4  

...     00145 

8  

.  .  .     00218 

12 

00278 

16. 

00277 

0 

L/D 
8  6 

2  

16  3 

4  

16.8 

8  
12 

.  .  .    13.8 
100 

16.. 

4.5 

Interference  in  Triplanea 

Dr.  Hunsaker's  paper  also  deals  fully  with  interference  in 
triplanes.     It  is  important  in   the  structural   design   of  the 


wing  girder  to  know  what  portion  of  the  lift  and  drag  to 
attribute  to  each  wing.  The  comparitive  efficiency  of  each 
wing  is  also  important  from  the  point  of  view  of  overhang. 
It  appears  from  Table  2  that  the  upper  wing  is  very  much 
the  most  effective  of  the  three  and  the  middle  wing  the 
least  effective.  The  very  poor  lift  of  the  middle  wing  is 
caused  by  the  interference  with  the  free  flow  of  air  due  to 
the  presence  of  the  upper  and  lower  wings. 

One  interesting  point  brought  out  by  Dr.  Hunsaker  toward 
the  end  of  his  paper  was  the  fact  that  when  the  effects  of 
the  upper  and  lower  wings  were  combined,  results  identical 
with  that  of  a  simple  biplane  combination  were  obtained.  This 
would  tend  to  show  that  the  interference  in  the  case  of  a 
triplane  is  similar  to  interference  in  the  case  of  a  biplane. 
The  upper  wing  of  a  triplane  would"  seem  to  be  influenced 
by  the  middle  wing  in  the  same  way  that  the  upper  wing  of 
a  biplane  is  influenced  by  the  lower  wing  of  a  biplane.  Again 
the  lower  wing  of  a  triplane  would  seem  to  be  influenced  by 
the  middle  wing  in  the  same  way  that  the  lower  wing  of  a 
biplane  is  influenced  by  the  upper  wing.  These  are  im- 
portant considerations  to  be  kept  in  mind  when  modifications 
of  the  triplane  are  attempted  such  as  stagger,  overhang, 
decalage,  etc. 

TABLE   2 

TABLE  OF  VALUES  FOR  LIFT  AND  L/D  FOR  EACH  WING  OF  A  TRIPLANE 

COMBINATION  AS  RATIOS  TO  LIFT  AND  L/D  OF  MIDDLE  WING. 

Angle  of          Lift  Lift  Lift  L/D  L/D  L/D 

Incidence.      Upper.      Middle.      Lower.  Upper.       Middle.       Lower. 

0 2.68  1.0  1.82  3.63  1.0  2.30 

2 2.14  1.0  1.76  3.18  1.0  2.13 

4 1.91  1.0  1.64  2.59  1.0  1.69 

8 1.56  1.0  1.36  1.49  1.0  1.37 

12 1.56  1.0  1.31  1.30  1.0  1.34 

16 1.49  1.0  1.20  1.22  1.0  1.17 

Some  Considerations  for  Triplanes 

There  are  two  types  of  airplanes,  quite  dissimilar,  for 
which  triplanes  have  been  employed  in  this  country,  the  huge 
Curtiss  flying  boats,  and  the  recent  Curtiss  speed  scout.  It 
is  interesting  to  consider  what  the  possible  advantages  of  the 
triplane  are  at  these  two  extremes  of  design. 

In  the  heavy  types,  particularly  in  seaplanes,  the  increased 
size  must  be  developed  without  increase  in  landing  speed. 
To  insure  about  the  same  landing  speed,  the  loading  must 
remain  at  a  figure  of  about  5  pounds  per  square  foot.  And 
for  an  aeroplane  of  four  times  the  ordinary  weight  the 
wing  area  must  be  increased  in  like  proportion.  Monoplane 
construction  is  obviously  impractical  for  such  great  areas 
of  wings,  and  even  with  the  biplane  there  is  an  enormous 
wing  span.  Such  a  span  introduces  great  difficulties  from  the 
stress  point  of  view  and  from  the  point  of  view  of  housing  and 
handling.  The  employment  of  a  triplane  enables  the  span  to 
be  kept  within  reasonable  dimensions  and  also  permits  the 
employment  of  larger  nspect  ratios. 


57 


AERODYNAMICAL  THEORY  AND  DATA 


At  high  angles  the  lift  of  a  triplane  is  only  1.1  per  cent 
less  than  that  of  a  biplane  of  the  same  area.  At  16  degrees 
the  L/D  ratio  of  a  triplane  is  16  per  cent  better  than  that 
of  a  biplane.  At  stalling  attitudes,  the  triplane  has  therefore 
very  decided  advantages,  giving  a  greater  reserve  power  at 
low  speeds  in  alighting.  At  4  degrees  incidence  for  best  L/D 
the  triplane  does  not  show  up  so  well,  and  requires  an  increase 
in  power  of  about  6  per  cent.  It  would  seem  as  if  the  6  per 
cent  increase  in  power  can  be  compensated  for  by  the  pos- 
sibility of  a  less  heavy  type  of  construction  with  decreased 
span.  Also  there  is  the  possibility  of  employing  much  greater 
aspect  ratios  than  in  biplane  work,  and  this  may  compensate 
to  some  extent  for  the  losses  due  to  extra  interference. 

Triplanes  for  Fast  Speed  Scouts 

From  the  photographs  issued  by  the  Curtiss  Company,  it 
seems  clear  that  the  original  machine  (see  AVIATION  August 
15,  1916)  was  transformed  (see  AVIATION  October  15,  1916) 
by  placing  the  triplane  wing  structure  on  the  same  body  struc- 
ture as  for  the  biplane.  With  approximately  the  same  wing 
area  divided  between  these  planes  the  aspect  ratio  was  in- 
creased very  considerably,  without  exaggerating  the  span,  giv- 
ing some  aerodynamical  advantage.  The  extremely  narrow 
blade  like  wing  permitted  the  single  plane  bracing  system  to 
be  used  with  much  greater  security.  The  employment  of  a 
single  plane  bracing  system  cuts  down  resistance  very  con- 
siderably, and  if  this  bracing  system  is  only  possible  with 
triplane  narrow  blade  construction,  then  triplane  construction 
would  be  a  very  sound  tendency  in  the  design  of  small  fast 
machines. 

Use  of  Negative  Tail  Surfaces 

In  Chapter  6  we  saw  the  possibility  of  using  a  negative  tail 
surface  so  as  to  give  static  longitudinal  stability,  and  in  the 
problem  which  follows  a  definite  case  will  be  taken  as  an  illus- 
tration of  this  possibility.  In  other  methods  of  attaining 
stability  such  as  employment  of  the  reversed  curvature  wing 
or  of  stagger-decalage  combinations,  dynamic  stability  might 
not  follow  the  static  stability  unless  tail  surfaces  were  em- 
ployed. In  such  cases  the  tail  surfaces  would  probably  have 
to  be  placed  at  zero  angle  to  the  wings,  or  even  at  a  small 
positive  angle.  It  is  for  this  reason  that  the  stable  biplane 
arrangements,  apparently  so  advantageous,  are  not  more  fre- 
quently used  in  practice. 

Effect  of  Influence  of  the  Wash  of  the  Wings  on 
Stabilizer  Surface 

Eiffel  in  his  later  experiments  conducted  some  tests  on 
tandem  wings.  One  important  result  of  these  tests  was  to 
prove  that  an  airplane  built  with  tandem  wings  would  be 


Fio.  1.     DIAGRAM  FROM  EIFFEL  TO  SHOW  DKVIATION  07 
STREAM-LINES  BY  "  DOWN-WASH  "  OF  WINGS. 

aerodynamically  disadvantageous.  Another  loult  was  that 
the  down  wash  of  the  trout  wing  would  cliiinye  the  flow 
relative  to  the  rear  wing  so  that  the  angle  of  incidence  of  the 


latter  would  be  smaller  than  that  of  the  former.  The  al- 
lowances made  for  the  change  in  the  angle  of  incidence  were 
arrived  at  indirectly  by  measuring  lift  and  drag  on  the  sec- 
ond wing  while  in  the  presence  of  the  first,  and  are  not  en- 
tirely reliable.  Fig.  1  represents  Eiffel's  conclusions  diagram- 
atically  for  a  specific  case. 

The  relative  wind  for  the  front  wing  is  horizontal;  the 
chord  of  the  front  wing  is  at  10  degrees  to  the  horizontal, 
the  chord  of  the  rear  wing  is  at  4  degrees  to  the  horizontal, 
with  a  decalage  of  6  degrees.  Owing  to  the  downwash  of 
the  front  wing  the  stream  lines  at  the  rear  wing  now  make 
a  negative  angle  of  7  degrees  with  the  horizontal,  and  the 
rear  wing  is  actually  at  a  negative  angle  of  3  degrees  to  the 
stream. 

Owing  to  the  fact  that  the  tail  surfaces  of  a  machine  are 
so  much  further  away  from  the  wings,  the  deviation  will 
be  less  perceptible  and  the  following  practical  formula  gives 
satisfactory  results: 

If  t  =  angle  of  incidence  of  the  wings, 

Deviation  of  stream  =   (J/£  »  -)-  1) 

To  take  a  concrete  case,  if  the  wings  are  at  8  degrees 
incidence,  and  the  stabilizer  is  placed  at  a  negative  angle  of 
2  degrees  to  the  chord,  then  its  incidence  will  be 
(8  —  2)     —    (i/2  i  +  1)   = 
(8—2)     —     (8/2  -f  1)    =  1 

This  deviation  has  an  important  bearing  in  the  design  of 
stabilizing  surfaces  on  the  angle  of  setting  between  the  chord 
of  the  wing  and  the  line  of  the  stabilizing  plane. 

Problem  on  the  Design  of  Tail  Surfaces  to  Give 
Longitudinal  Static  Stability 

The  requirements  of  static  longitudinal  stability  may  be 
briefly  stated  as  follows : 

(1)  The  machine  must  be  in   stable  equilibrium   at  some 
angle  of  incidence,  generally  the  angle  of  normal  flight,  say  6 
degrees  for  purposes  of  illustration. 

(2)  If  the  angle  of  incidence  of  the  aeroplane  is  from  any 
cause  less  than  6  degrees,  there  should  be  a  positive  restoring 


^TQ£wt-*~m*K^  K/8  I      | 


Fio.  2.    DIAGRAM  ILLUSTRATING  STABILIZER  PROBLEM. 

moment  or  stalling  moment;  if  for  any  reason,  greater  than  6 
degrees,  there  should  be  a  negative  or  diving  moment. 

(3)  Within  a  t'ew  degrees  of  the  position  of  equilibrium  the 
ri^hiiujr  moments  should  be  comparatively  small  so  as  to  give 
iVxibility  of  control. 

(4)  As  the  displacement  from  the  position  of  equilibrium 
increases  the  righting  moments  should  increase  also. 

(5)  The  righting  moments  should   never  be  excessive  and 
should  never  exceed   '  :1  of  the  possible  moment  which  can  be 
exercised  by  the  elevator. 

These  results  can  be  readily  obtained  by  the  use  of  a  suit- 
able negative  tail.  \Vc  shall  now  take  a  concrete  case  of  an 
unstable  orthogonal  biplane  with  a  total  wing  area  of  432 
square  feet;  wing  section  R.  A.  F.  6;  the  center  of  gravity  of 


AERODYNAMICAL  THEORY  AND  DATA 


59 


TABLE   3. 
TABLE    ILLUSTRATING   COMPUTATIONS  IN  STABILUEB  DESIGN 


S 

o 

sH. 

L 

S 

2 

ij 

0 

£« 

1 

I 

C 

1.2 

s« 

•S   H 

• 

d"0 

**  a 

J3 

•gs 

•g.5 

•"a 

E-3 

1     * 

3 

•§  " 

•§~ 

as 

B  a 

1 

•s 

1.9 

1.2 

Ed 

•aj 

JD 

3-9 

•<  t 

1 

a  a) 
a.9 

* 

fa 

II 

la8? 

8.9  « 

«1 

5.9 

Jj" 

1.9 

Moment 
drag  in  1 

K 

S3 

§J 
.11 

t-i  E 

1- 
11 
$*" 

|1M 

J 

fl  . 

°l 

3.9 

Moment 
stabilizer 

Resultani 
about  c.g 

0 

.000493 

.000075 

110. 

392 

2560 

2 

-1.2 

+784 

-3020 

-2236 

-3 

-.00051 

16 

-309 

+4950 

2614 

2 

.000882 

.000072 

82.5 

212 

2560 

2 

-   .6 

+424 

-1500 

-1076 

-2 

-.00035 

16 

-119 

+  1910 

834 

4 

.00121 

.000093 

70. 

197 

2560 

2 

-   .30 

+394 

-  750 

-  356 

-1 

-.00018 

16 

-44.1 

+  704 

348 

e 

.00155 

.000130 

62. 

216 

2560 

2 

-    .24 

+432 

-  600 

-   168 

0 

0 

16 

0 

0 

-  168 

8 

.00187 

.000166 

56.6 

230 

2560 

2 

-   .12 

+460 

-  300 

+  160 

1 

+  .00018 

16 

+28.7 

-  459 

-  299 

13 

.00242 

.000255 

49.8 

275 

2560 

2 

0 

+550 

0 

+  550 

3 

+  .00051 

16 

+65 

-1040 

-  490 

the  machine,  as  shown  in  Fig.  2.  The  loading  is  such  that 
the  machine  has  an  angle  of  incidence  of  about  4  degrees  at 
a  speed  of  70  miles  per  hour.  The  gap  chord  ratio  is  1.0.  The 
tail  surfaces,  stabilizer  and  elevator  are  taken  together,  are 
placed  at  a  distance  of  16  feet  from  the  center  of  gravity.  It 
is  required  to  design  a  stabilizer  to  meet  the  above  require- 
ments. 

We  will  assume  that: 

(a)  The  design  of  the  stabilizing  surface  is  carried  out  prior 
to  wind  tunnel  tests. 

(b)  The  center  of  pressure  motion  for  each  wing  of  the  com- 
bination is  precisely  similar  to  that  of  the  wing  acting  alone, 
so  that  L  and  D  forces  on  each  wing  may  be  taken  as  acting  at 
precisely  the  same  point  they  would  on  a  monoplane  wing ;  this 
assumption  is  justified  by  results  of  both  the  biplane  and  tri- 
plane  experiments. 

(c)  The  resultant  force  on  the  tail  surfaces  may  be  taken 
as  approximately  perpendicular  to  the  moment  arm  and  as 
being  equivalent  to  the  lift.    This  is  not  far  from  true  for  an- 
gles wilhin  normal  llight  and  simplifies  our  calculations  enor- 
mously.   The  stabilizer  surface  is  taken  as  being  equivalent  to 
a  flat  plate. 

(d)  The  displacement  of  the  vertical  through  the  center  of 
gravity  for  varying  angles  of  incidence  is  neglected. 

The  machine  selected  for  this  problem  is  shown  in  Fig.  2 
with  the  position  of  the  center  of  gravity  as  indicated.  It  has 
a  wing  area  of  432  square  feet.  The  normal  angle  of  flight 
being  4  degrees,  it  must  weigh  from  elementary  considerations 
(introducing  .85  as  correcting  factor  for  lfy  due  to  biplane 
effect). 

W  =  KyAT  =  .0014  X  -85  X  432  X  702  =  2560  pounds 

Taking  moments  about  the  center  of  gravity  the  general 
equation  for  the  pitching  moment  at  any  angle  is 

M  =  2La  —  DC  +  DC'  —  167?  (1) 

Where  a  is  the  distance  between  the  vertical  center  of  grav- 
ity line  and  the  parallel  line  of  lift  on  each  wing  (the  wings 
assumed  to  carry  equal  loads),  C  and  Cl  are  the  distances  from 
the  horizontal  axis  through  the  center  of  gravity  to  the  point 
of  application  of  the  drag  forces.  The  distance  of  16  feet  is 
assumed  as  the  distance  from  the  center  of  gravity  to  the  point 
of  application  of  the  resultant  force  R  acting  on  the  stabilizer 
as  defined  previously. 

Since,  Fig.  2,  the  distance  C  =  4  feet ;  6rl  =  2  feet ;  the  quan- 
tity (6  —  b)  =2  and  the  equation  can  be  simplified  to  the 
following  form : 

2(La  —  D  —  8B)=M  (2) 

The  lift  arm  a  varies  of  course  with  the  center  of  pressure 
motion. 

Unfortunately  no  set  method  of  design  exists  for  this  par- 


ticular problem.  Area  of  stabilizer  and  the  angle  of  setting  to 
the  wing  chord  have  to  be  assumed  more  or  less  arbitrarily 
until  the  right  combination  is  found,  although  each  designer 
will  probably  find  a  short  cut  method.  In  two  instances  after 
a  number  of  tentative  combinations,  the  following  values  were 
found  to  specify  our  conditions  fairly  well. 

Stabilizer,  aspect  ratio  3,  area  50  square  feet,  angle  of  set- 
ting to  wing  chord  2  degrees.  The  K7  coefficients  for  the  sta- 
bilizer treated  as  a  flat  plate  can  be  taken  from  the  curves 
given  in  Chapter  4. 


•5000 


-«M 


^000 


yaao 
zyx 

ZOOO 


1500 

1000 

JOO 

0 

-500 

-{0«l 

-BOO 
-tax 


* 


MC* 
S 


WINGS 


EN'  T3     ON    MACH 


Or  WING 

TO  WINO 


FIG.  3.    LONGITUDINAL  PITCHING  MOMENTS  ON  MACHINE. 

A  careful  distinction  has  to  be  made  between  the  apparent 
angle  of  incidence  of  the  stabilizer  to  the  relative  wind  and 
the  real  angle,  taking  account  of  the  deviation  of  the  stream 
in  accordance  with  the  formula  given.  Thus  if  the  wings  are 
at  an  incidence  of  6  degrees  to  the  wind,  and  the  stabilizer  is 
at  —  2  degrees  to  the  wing  chord,  the  real  angle  of  incidence 
becomes 

(6  —  2)—  (1/2-6  +  1)  =  0  degrees 

The  computations  for  the  setting  finally  selected  are  shown 
in  the  Table  3.  The  curves  of  moments  due  to  the  wings,  the 
moments  due  to  the  stabilizer,  and  the  resultant  moment  are 
shown  in  Fig.  3.  The  conventional  method  of  regarding  mo- 


BO 


AERODYNAMICAL  THEORY  AND  DATA 


meiits  tending  to  stall  the  machine  as  positive,  and  moments 
tending  to  dive  the  machine  as  negative  is  adhered  to. 

It  is  seen  from  the  curves  of  Fig.  3  that  the  solution  is  only 
fairly  good.  Equilibrium  is  secured  at  6  degrees.  Approxi- 
mately on  either  side  of  the  equilibrium  position,  the  correct 
moments  are  obtained.  If  the  machine  goes  below  6  degrees 
the  resultant  moment  tends  to  stall  it  bock  to  6  degrees.  If 
the  machine  goes  above  6  degrees  the  resultant  moment  tends 
to  dive  it  back  to  6  degrees;  that  is  satisfactory  so  far.  But 
the  resultant  moment  curve  is  far  too  steep  about  the  position 
of  equilibrium  and  the  machine  is  sometimes  too  stable  to  be 


under  perfect  control.    The  problem  is  left  in  tlii>  t'orui,  how- 
ever, because  an  improvement  of  the  solution  would  be  an  ex- 
n'llciit  exercise  for  a  student.    The  variations  possible  are  in 
I     Length  of  stabilizer  arm. 
II    Area  of  stabilizer. 

Ill    Angle  of  setting  of  stabilizer. 

It  must  also  be  pointed  out  that  the  approximations  em- 
ployed, and  the  factors  neglected,  such  as  the  effect  of  the  body 
and  other  structural  parts,  are  so  numerous  that  in  construct- 
iiii;  ;m  actual  machine  a  wind  tunnel  test  would  be  finally 
necessarv. 


Chapter  X 

Resistance  of  Various  Airplane  Parts 


N.P.L.  Body  5 


B.F.  36 


One  of  the  most  difficult  problems  in  aeronautical  design  is  40  pounds.  A  blunt,  square  form  of  body  such  as  is  often 
the  prediction  of  the  total  resistance  of  the  machine.  The  seen  in  American  practice  may  increase  resistance  even  more, 
wind  tunnel  test  is  a  good  check,  but  it  is  most  important  to 
assign  resistance  values  to  various  parts  and  to  tabulate  them 
prior  even  to  the  construction  of  the  model.  In  this  chapter 
have  been  collected  as  far  as  possible  all  the  data  available 
for  bodies,  radiators,  fittings,  wheels,  cables  and  wires  and 
certain  other  miscellaneous  objects. 

Airplane  Bodies  from  the  Aerodynamical  Point  of  View 

If  airplane  bodies  were  designed  from  a  purely  aerodynam- 
ical point  of  view,  they  would  follow  dirigible  practice  and 
be  of  streamline  form.  There  are,  however,  a  number  of 
structural  requirements  which  have  to  be  met,  which  preclude 
the  employment  of  such  forms.  The  body  must  enclose  the 
power  plant  and  the  personnel,  the  length  must  be  long  enough 
to  place  the  rudders  well  clear  of  the  wash  of  the  planes,  the 
shape  of  the  body  must  conform  to  structural  requirements 
such  as  the  use  of  four  longitudinal  girders,  or  a  triangular 
form  which  has  been  found  to  be  advantageous  in  steel  con- 
struction. 

No  wind  tunnel  tests  on  bodies  alone  can  determine  exactly 
their  resistance  on  an  airplane,  because  the  question  is  com- 
plicated by  the  position  and  form  of  the  motor,  and  the  dis- 
position of  the  tail  surfaces.  The  propeller  in  a  tractor  ma- 
chine also  introduces  three  possible  variations  in  drag  coeffi- 
cients: (1)  when  the  propeller  is  pulling  and  there  is  a  slip 
stream  of  velocity  greater  than  the  airplane  velocity,  (2)  the 
resistance  on  a  glide  when  the  engine  is  shut  down,  but  the 
propeller  is  revolving  as  an  air  motor;  (3)  when  the  propeller 
is  not  revolving  at  all.  the  engine  being  held. 

Tractor  Bodies 

In  Table  1  is  given  a  comparative  table  of  resistance  co- 
efficients for  area  in  normal  presentation  of  a  number  of  air- 
plane bodies,  and  in  Fig.  1  are  shown  sketches  of  the  same 
bodies.  Exact  comparisons  are  impossible  because  some  of 
the  bodies  are  made  for  two  men  and  others  for  one.  Still 
qualitative  conclusions  can  be  drawn.  The  N.  P.  L.  Model  5, 
more  symmetrical  than  the  B.  E.  3,  shows  a  distinct  improve- 
ment over  the  latter  which  is  somewhat  discounted  by  the  fact 
that  the  B.  E.  3  carries  two  men  unshielded.  The  B.  F.  36, 
an  almost  perfect  dirigible  form,  is  markedly  better  than 
either  of  these  two  bodies. 

The  resistance  of  the  body  in  an  airplane  is  apparently  a 
small  quantity,  but  the  figures  given  below  do  not  represent 
the  resistance  of  a  body  in  full  flight  where  it  is  increased  by 
40  per  cent,  the  propeller  slip  stream  increasing  the  relative 
speed  of  the  air  by  some  25  per  cent.  Also,  it  must  be  re- 
membered that  with  a  best  glide  of  1  in  8,  a  5-pound  increase 
in  resistance  is  practically  equivalent  to  an  added  weight  of 

61 


Deperdussin 
FIG.  1.     TRACTOR  BODIES. 

and  better  aerodynamical  design   of  bodies  seems  a  feature 
worth  considering. 

TABLE   1. 


Designation. 


COMPARATIVE  TABLE  FOB  TRACTOR  BODIES. 

Coefficient  of  resist- 
ance, K  where  R  — 
KA7*  (A  =  area 

in  normal  presenta- 
tion in  square  feet    

7  =  miles  per  hour ;  maximum 
B  =  drag  in  Ibs.)         depth. 


Length 


British  B.  E.  3  (with  2  men)  .  .    .000720  7.35 

N.  P.  L.  Model  5 000420  (approx.)5.50 

British  B.  P.  36  (dirigible  form)   .000258  5.75 

Deperdussin     (enclosing    rotary 

motor)     001215  5.6 


TABLE   2. 
COMPARATIVE  TABLE  FOR  PUSHER  BODIES. 


Resistance 

for  a  body 

of  8  square 

feet  normal 

presentation 

at  a  speed 

of  60m.  p.  h. 

20.7 
12.0 

7.4 

35.1 


Designation. 


Coefficient  of  resistance 
K  where  R  =  KA.V* 
(A  ~  maximum  area 
in  normal  presenta- 
tion in  square  feet ; 
V  =  miles  per  hour  ; 
R  =  drag  in  lbs.1 


X.  P.  L.  Model  Body  3  (fairly 
symmetrical  section) 000271 

Farman  3  (body  in  form  of  a 

boat,  two  men  unshielded)..  .OOOS45 


Pusher  Bodies 


Length. 

3 

3.2 


Resistance 

for  a  body 

of  8  square 

feet  normal 

presentation, 
at  a  speed 

of  60  m.  p.  h. 


7.8 
24.4 


A    pusher    body    such    as    the    Farman    3,    illustrated    in 
Fig.  2,  gives  a  not  much  larger  resistance  than  the  tractor 


62 


AERODYNAMICAL  THEORY  AND  DATA 


bodies,  bat  when  the  head  resistance  of  the  uncovered  oat- 
riggers  is  taken  into  account,  it   will   probably  HP  found  that 


Farman  8 
Fin.  2.     A  PUSHER  BODY. 

pusher  arrangements  offer  considerably  more  resistance  than 
tractor  bodies. 

Radiator  Resistance 

The  only  values  available  for  this  are  the  results  of  some 
tests  at  the  Massachusetts  Institute  of  Technology.  These 
were  carried  out  on  portions  of  a  radiator  of  the  honeycomb 
type  having  sixteen  %-inch  cells  to  each  square  inch  of  the 
surface  normal  to  the  wind.  The  tests  were  repeated  on  two 
sizes  of  radiator  section,  one  0.25  square  feet  and  the  other 
OJ.11  square  feet,  and  at  various  wind  speeds.  No  important 
variation  in  the  resistance  coefficient  was  apparent  and  the 
average  coefficient  may  be  used  for  practical  calculations. 
This  has  a  value  Kx  =  .000814  pounds  per  square  foot  of  pro- 
jected area  per  foot  per  second  or  .00173  pounds  per  square 
foot  of  projected  area  per  mile  per  hour. 

Resistance  of  Fittings 

Fittings  are  so  variable  in  design  that  it  is  impossible  to 
give  definite  figures  to  meet  every  type  of  wing  strut  fitting. 
Tests  were  conducted  at  the  Massachusetts  Institute  of  Tech- 
nology on  the  fittings  of  which  dimension  drawings  are  given 
in  Fig.  3;  the  coefficients  of  resistance  are  R  —  .00030  \ 
B  =  .00040  1"  for  the  two  types  which  at  60  miles  an  hour 


ranol.     R  -  .OOOrin  v:. 


Inn.  r  rand  with  Wins  Illinji'. 


BfcB 

R  =  .00040  V1. 


.1.    FITTINGS  EMPI/JYKI.  IN  TESTS  FOR  HEAD  RESISTANCE 
AT  MASSAI  i M -SETTS  INSTITKTK  OK  TECHNOLOGY 

CIAIIK  HTRIT  FITTJNON.  Id-«l'.|aii<-1.  ln<  Imlcii  fitting,  five  turntmrk].^ 
and  nuU  but  not  dotti  il  portions  UK  Imllrntnl  mi  drnuliiKi.  ItnUtann* 
In  pound!:  Velocity  In  mil"*  J»T  h»ur 

gives  1.07  and  l.H  pound-;  respectively.     Such  figures  will  he 
•t  least  apprrmninlcK 


\irplaiir    \\  lirrU 


For  a  standard  airplane  wheel  of  about  26  X  4  inenes  in 
size,  the  drag  found  by  the  X.  P.  L.  is  about  1.7  pounds  at  tiO 
miles  per  hour.  This  again  is  sufficiently  accurate  for  prac- 
tical purposes.  Eiffel  has  experimented  with  a  number  of 
wheels  and  shown  that  no  great  variation  need  be  expected 
from  the  above  value.  An  important  result  from  the  French 
experiments  was  the  fact  that  an  uncovered  wheel  had  a  re- 
sistance of  50  per  cent  more  than  a  covered  wheel  of  similar 
dimensions.  This  justifies  the  standard  practice  of  covering 
the  wheel  in. 

Resistance  of  Wires  ami    Methods  of  Plotting 

A  certain  complication  is  necessary  in  the  methods  of  plot- 
ting the  results  for  the  resistance  of  cables  ami  wires.  As 
we  have  seen  from  the  diagram  of  Kig.  1!'.  in  Chapter  '.'•,  of 
the  Course,  the  resistance  of  a  wire  or  any  cylindrical  body 
is  partly  due  to  turbulence,  partly  due  to  skin  friction.  It 
cannot  therefore  be  represented  by  such  a  simple  expression  as 
R  =  KAV*  as  for  a  wing,  but  by  an  expression  involving 

v 
Kevnolds'  number,  R  =  KA\"~  f  (  -  ),  or  if  we  replace  th« 

DV 
area  of  a  wire  by  LD  where  I)  =  diameter  and  L  is  length 

v 
in  feet,  then  E  —  KLD  T"  /  (  -    -  ).    Since  v,  th.-  coefficient 

DV 

of  kinematic  viscosity  is  constant  for  air,  we  can  simplify  this 
expression  by  writing: 

R    =   KLD    V-  F(VD). 

We  do  not  know  what  the  function  F(V'D)  is  exactly,  nor 
how  it  varies  with  size  and  scale  except  from  experimental  re- 
sults, and  comparisons  of  resistance  varxing  as  l.l>  I"  can 
only  be  made  between  two  cables  if  VI)  \<  a  constant.  If  K 
is  taken  as  a  function  of  VD,  then  E  may  be  written  R  — 
KLD  P  but  then  A'  must  be  plotted  against  \T>  in  analyzing 
experimental  results.  This  is  the  only  rational  and  scientific 
method. 

An  empirical  method,  however,  is  sometimes  employed  with 
fair  accuracy  of  plotting  the  resistance  of  a  wire  whose  length 
is  equal  to  its  diameter  against  T5  Tf.  This  has  the  advantaire 
that  the  graph  approximates  very  closely  to  a  straight  line, 
the  slope  of  which  is  equal  to  K,  thus  giving  an  easy  means  of 
determining  a  mean  value  of  A". 

Resistance   of  Stationary    Smooth   Win-- 

The  most  accurate  researches  have  been  carried  out  nl   the 

X.   1'.  L.  and  their  results  are  shown  in   Kig.   I  plotted  against 

B 

V'D.     In  the  expression  A"  .  /.'  is  in  pounds,  /.  in 

r.  in" 

feet,  1)  in  feet,  and  1"  in  miles  per  hour.  Hut  in  the 
values  of  \  '!>,  V  is  in  feet  per  second,  and  l>  in  feet,  so  as  to 
give  the  correct  scale  and  speed   relationships  which  must   he 
in  the  same  units. 

The  accuracy  of  the  curve  at  its  |owi-i  portion  is  doubtful. 
-nice  (he  (low  is  apparently  jiisl  changing  its  nature  at  that 
point,  and  successive  observations  under  the  same  conditions 
may  i_'ive  quite  different  results.  On  modern  machines  of 
fairly  high  speed,  however,  the  value's  of  \"D  nearly  always 
•  I  II.  .'i5  and  consequently,  do  not  he  on  (his  section  of  the 
curve'. 

Similar  tests  were  made  by  Mr.  Tlmrston  and  M.  KifTel,  and 
the  values  obtained  by  the  Conner  are  plotted  in  the  same 
fiinire.  ThnrslonV  experiment*,  however,  were  very  nnn-h 


AERODYNAMICAL  THEORY  AND  DATA 


63 


earlier,  and  Eiffel's  covered  a  less  range  and  were  performed 


VD        IM 


;c.  or 

SMOOTH  WIRES 
OMITS:  LBS.  FT. 
MILES 


o  .3  10  i.sr  £o  e.5  3a 

FIG.  4.    RESISTANCE  OF  SMOOTH  WIRES  PER  FOOT  RUN. 

with  less  sensitive  apparatus,  so  it  is  advisable  to  use  the 
N.P.L.  results. 

Resistance  of  Vibrating  Wires 

When  the  question  of  resistance  first  began  to  arouse  in- 
terest, it  was  popularly  supposed  that  a  vibrating  wire  had 
jnuch  greater  resistance  than  a  stationary  one.  This,  however, 
is  not  the  case.  Research  on  this  point  at  the  N.P.L.  failed 
to  disclose  any  difference  whatever,  although  the  balance 
would  have  shown  deviations  as  small  as  3  per  cent,  even  for 
the  extremely  small  forces  under  consideration.  Mr.  Thurs- 
ton,  on  the  other  hand,  concluded  that  vibration  at  the  rate 
of  15  per  second  increased  the  resistance  by  about  5  per  cent 
for  small  wires  and  by  a  somewhat  smaller  percentage  for 
those  of  larger  diameter.  In  any  case,  the  effect  is  unim- 
portant. 

Resistance  of  Stranded  Wires 

The  air  resistance  of  stranded  wires  was  also  investigated 
at  the  N.P.L.,  and  was  found  to  be  about  20  per  cent  greater 


r 


FIG.  5. 


RESISTANCE  OP  WIRES  IN   TANDEM  AS  A  RATIO  OF 
THE  RESISTANCE  OF  A  SINGLE  WIRE. 


than  that  for  a  smooth  wire  of  the  some  diameter.  This  is 
only  approximate,  as  the  coefficient  depends  on  the  number 
of  strands,  type  of  lay,  etc.  It  is  also  impossible  to  plot  the 
values  of  K  against  VD  for  wire  rope,  as  the  VD  law  holds 
good  only  for  objects  which  possess  strict  geometrical  simi- 
larity, a  thing  which  stranded  wires  of  different  sizes  never  do. 

Resistance  of  Wires  Placed  Behind  One  Another 

The  manner  in  which  resistance  is  affected  by  the  close  juxta- 
position of  two  wires,  one  behind  the  other,  is  a  point  of  great 
interest.  Here,  too,  it  is  at  present  necessary  to  rely  on  Mr. 
Thurston,  although  we  hope  to  be  able  soon  to  present  the 
results  of  some  more  extensive  and  accurate  tests  on  this 
matter. 

Fig.  5  gives,  in  terms  of  the  resistance  of  a  single  bar,  the 
resistance  of  two  bars  or  wires  separated  by  various  dis- 
tances. It  will  be  seen  that  two  wires  placed  one  behind 
the  other  and  spaced  from  5  to  9  diameters  apart,  as  is  usual 
in  double-wiring  a  biplane  cellule,  have  from  60  per  cent  to  75 
per  cent  more  resistance  than  a  single  wire.  The  force  is, 

K  for  LIMITS 

pounds  per  V  D  in 

OBJECT  square  foot  foot  second  ATTITUDE 

per  mile  units 
hour  units 

phere 0.000445        V  D  >  32        »• 


Hemispherical  Shell  0.003840        V  D  >  11 


Hemispherical  Shell  0.008100        V  D  >  22 


Circular  Disk 0.002820        V  D  >  22 


Cone  Closed  Base.  .[.0. 001300 


Cone  Closed  Base..  0.000850 


Cone  Hemispherical 
End..  .   0.000406 


Cone  Hemispherical 

End..  .  0.000222 


FIG.  6.    RESISTANCE  OF  MISCELLANEOUS  OBJECTS 
(AFTER  EIFFEL) 

however,  materially  less  than  for  the  two  wires  placed  side 
by  side. 

Resistance  of  Inclined  Wires 

Eiffel  has  experimented  on  the  resistance  of  inclined  wires. 
As  would  be  expected  the  resistance  of  a  wire  progressively 
decreases  as  its  angle  with  the  wind  diminishes.  Table  3  gives 
correcting  values. 

TABLE  3. 

Ratio  of  resistance  to  that  of  a 

Angle  of  a  wire  to  the  wind.  wire  at  90  degrees  to  the  wind. 

90  degrees.  1.00 

75  degrees.  0.92 

60  degrees.  0.70 

45  degrees.  0.46 

30  degrees.  0.20 


AERODYNAMICAL    THEORY     A  IS  D    DATA 


Suggestions  for  Stream-lining  Wires 

It  has  been  suggested  from  time  to  time  that  wire  resist- 
ance should  be  decreased  by  "stream-lining"  or  adding  a 
triangular  portion  in  back  of  the  wire.  From  experiments 
by  Ogilvie,  however,  it  appears  that  a  section  made  up  of  a 
semi-circle  and  a  triangle  has  a  decidedly  high  resistance,  and 
the  gain  from  such  a  procedure  would  be  small. 

Wires  placed  behind  one  another  have  also  been  covered  in. 
The  British  Royal  Aircraft  Factory  produces  a  very  heavy 
R.A.F.  wire  in  use  on  big  machines  which  is  stream-line  in 
form.  But  the  direction  in  which  progress  manifests  itself 
at  present  is  in  the  elimination  of  wires  by  certain  modern 
trussing  such  as  used  in  the  recent  Curtiss  biplane. 

Resistance  of  Miscellaneous  Objects 

The  resistance  of  certain  miscellaneous  objects  as  deduced 
by  Eiffel  may  sometimes  be  useful.  The  values  for  such 
objects  within  certain  limits  are  illustrated  in  Fig.  6. 


References  for  Part  I,  Chapter  10 

AIRPLANE  BODIEH 

British  Ucport  1911-1012,  page  52. 

British  Report  1012-1913,  page  lie,. 

"  La  Resistance  de  1'Alr  et  r  Aviation,"  Eiffel,  1914,  page  250. 

AIRPLAXE  WUEE1*.- 


Britlsh  Report  I'.H-  l!'i::.  I«'K"  T-- 

"La  Resistance  de  1'Alr  ••<  1'Avlatlon,"  Eiffel,  page  250. 

\\1I1K  AND  CABLES 

"  Aerodynamic  Resistance  of  Struts,  Bars  and  Wires,"  by  A.  P. 
Thurston,  Aeronautical  Journal,  April  and  July,   1912. 

British  Report  1010-1911. 

"  La  Resistance  de  1'Alr  et  1'Avlatlon,"  Eiffel,  page  97. 
"New  Mechanical  Engineers'  Handbook,"  Section  on  Aeronautics, 
by  J.  C.  Hunsaker. 


Chapter  XI 

Resistance  and  Comparative  Merits  of 

Airplane  Struts 


Considerations  of  Comparative  Merit  of  Strut  Sections 

It  is  naturally  desirable  that  some  single  expression  be 
found  which  will  give  the  general  efficiency  and  theoretical 
desirability  of  any  strut  section  under  consideration.  This 
was  first  done  by  the  staff  of  the  National  Physical  Labora- 
tory, who  devised  what  they  called  the  "  equivalent  weight,"  ami 

we  have  here  employed 
an  adaptation  of  this 
quantity  under  the  name 
of  the  "  merit  factor." 
In  deriving  this,  we 
start  with  the  basic-  as- 
sumptions that  the 
speed  of  the  machine  is 
60  miles  per  hour,  the 
gliding  angle  1  in  7, 
and  the  average  width 
of  the  struts  about  1 
inch  (the  exact  breadth 
assumed  depending  on 
the  form  and  strength 
of  the  section). 

Then,     since     gliding 

W 
angle  =  ^- ,     every      / 

pounds  of  strut 
\vright  will  give  rise  to  1  pound  of  resistance,  in  addition  to 
the  aerodynamic  resistance  of  the  struts.f  We  can,  therefore, 

W 
write  T  =  — 1-  R,  where  T  =  thrust  due  to  the  struts,  and 

It  is  their  aerodynamic  resistance.  Simplifying,  we  have 
G  =  W  +  7R,  but,  since  this  expression  has  a  maximum  value 
for  the  least  efficient  strut,  the  reciprocal  is  here  employed, 

14300 
and  multiplied  by  the  constant  14300,  giving  C  =  =   jp   i   7^ 

The  best  strut  under  the  conditions  above  specified  is  then 
the  one  showing  the  highest  value  for  C.  The  reason  for 
choosing  this  particular  value  for  the  multiplier  is  that  it 
makes  C  =  100  for  the  best  strut  of  the  first  and  largest  series 
which  we  shall  consider. 

If  the  speed  of  the  machine  for  which  the  struts  are  being 
selected  is  greater  than  60  miles  an  hour,  the  resistance  be- 
comes of  greater  importance  as  compared  with  the  weight, 
and  the  merit  factors  for  those  sections  which,  although  heavy, 
offer  very  low  resistances  are  relatively  improved.  If  the  glid- 
ing angle  is  flatter  than  1  in  7,  a  similar  effect  ensues. 

On  the  other  hand,  if  it  becomes  necessary  to  use  struts 
having  a  diameter  of  more  than  1  inch  or  thereabouts,  the  ad- 


OGILVIE'S  SECTIONS 


vantage  inclines  toward  the  sections  which  have  the  greatest 
strength  for  their  weight,  and  the  relative  importance  of  re- 
sistance is  diminished,  since,  in  similar  sections,  weight  varies 
as  the  square  of  the  breadth  and  resistance  only  as  the  first 
power.  These  effects  are,  however,  of  slight  importance,  and 
would  not  be  likely  to  change  the  merit  factors  enough  to  have 
serious  influence  on  the  choice  of  a  section  in  any  given  case. 

The  question  of  strength  will  be  taken  up  more  fully  in 
another  section  of  the  course.  It  will  suffice  to  say  here  that 
the  strengths  of  two  struts  have  been  considered  to  be  equal 
when  their  moments  of  inertia  about  their  longitudinal  axes 
are  equal. 

Strut  Sections  Developed  by  Ogilvie 

We  may  now  proceed  to  the  examination  of  definite  data  for 
a  number  of  series  of  struts,  tested  at  various  times  and  places. 
The  following  figures  are  the  result  of  experiments  performed 
at  the  N.  P.  L.  at  the  suggestion  of  Alec  Ogilvie,  the  sections 
being  illustrated  in  Fig.  1. 

/  =  moment  of  inertia  for  the  section  in  question  about  its 
longitudinal  axis  (inches*  for  a  strut  1  inch  wide). 

R  =  resistance  in  pounds  of  100  feet  of  strut  1  inch  wide  at 
60  miles  per  hour. 

W  =  weight  in  pounds  of  100  feet  of  spruce  strut  1  inch 
wide. 

b  =  width  of  strut  whose  strength  will  be  equal  to  that  of  a 
strut  of  section  a,  and  1  inch  wide. 

W  =  weight  of  100  feet  of  spruce  strut  of  width  b. 

CM  =  merit  factor  at  60  miles  per  hour. 


No. 


W 


W 


a 

.167 

104.4 

41.6 

1.00 

41.8 

19 

b 

.049 

81.9 

16.4 

1.36 

30.3 

18 

c 

.090 

59.2 

30.4 

1.17 

41.6 

27 

d 

.124 

36.9 

34.8 

1.08 

40.6 

45 

e 

.074 

63.0 

33.4 

1.23 

50.6 

24 

1 

.134 

28.6 

37.7 

1.06 

42.4 

56 

0 

.094 

54.9 

30.0 

1.15 

39.7 

30 

h 

.119 

12.8 

39.7 

1.09 

47.1 

99 

i 

427 

12.8 

41.0 

1.07 

47.0 

100 

; 

.119 

13.5 

39.7 

1.09 

47.1 

96 

i 

.111 

13.5 

38.0 

1.11 

46.8 

94 

I 

.106 

29.9 

36.4 

1.12 

45.6 

51 

m 

.106 

45.9 

36.6 

1.12 

45.9 

35 

n 

.171 

14.2 

51.9 

0.99 

509 

97 

o 

.146 

13.5 

47.0 

1.03 

49.9 

97 

p 

.128 

18.7 

44.1 

1.07 

50.5 

75 

q 

.245 

15.1 

71.0 

0.91 

58.9 

93 

r 

.227 

16.4 

67.2 

0.93 

58.1 

87 

s 

.194 

13.5 

62.0 

0.96 

57.2 

97 

t 

.209 

13.5 

66.1 

0.95 

59.7 

95 

.115 

24.6 

42.5 

1.10 

51.4 

59 

t  Relationships   between   weight   and   resistance   on   a   glide   will   be 
fully  considered  in  Section  12. 


Many  very  interesting  conclusions  can  be  drawn  from  this 
table.  In  the  first  place,  it  is  evidently  of  the  utmost  im- 
portance to  avoid  rapid  changes  in  curvature.  Several  sec- 
tions, notably,  e  and  I,  although  they  appear  to  have  a  very 
smooth  outline,  oppose  a  large  resistance  simply  because  the 
transition  from  the  entrance  to  the  run  is  so  abrupt  that  the 
air-flow  cannot  follow  its  contour,  and  violent  eddy-making 
ensues. 


8fi 


AERODYNAMICAL  THEORY  AND  DATA 


The  good  performance  of  several  sections  so  formed  indi- 
cates that  it  may  be  wise  actually  to  run  the  sides  of  the  strut 
parallel  for  some  little  distance,  as  illustrated  by  q  and  t. 
This  is  counteracted,  however,  by  the  fact  that  skin-friction 
increases  in  proportion  to  the  "  wetted  surface  "  of  the  strut. 
It  is  for  this  reason  that  the  very  longest  sections  did  not  give 
such  low  resistances  as  those  of  more  moderate  form.  This 
matter  of  the  ratio  of  length  of  section  to  width  will  be  dis- 
cussed more  fully  somewhat  later,  in  connection  with  another 
series  of  tests. 

It  will  be  seen,  too,  that  the  resistance  is  little  affected  by 
the  chopping  off  of  a  portion  of  the  tail  in  such  a  manner  as 
to  leave  it  straight  across.  Examples  of  this  are  furnished 
by  n,  (  and  i.  This  is  due  to  the  fact  that  it  has  not  been  pos- 
sible in  any  strut  yet  designed  to  totally  eliminate  the  region 
of  deadwater  behind  the  strut.  As  will  be  evident  from  any 
section  of  air-flow  about  a  fair-shaped  section,  the  lines  of 
flow  always  leave  the  contour  of  the  strut  some  distance  short 
of  the  extreme  rear.  Since  no  changes  made  in  the  contour 
within  this  region  will  have  any  decided  effect  on  the  re- 
sistance, it  avails  nothing  to  go  to  the  trouble  and  expense 
involved  in  the  attempt  to  construct  a  wooden  strut  running 
out  to  a  sharp  point  at  the  back. 

Another  Series  of  Struts  Tested  at  the  N.  P.  L. 

At  about  this  same  time  another  series  of  struts  was  tested 
at  the  same  laboratory,  the  sections  being  those  actually  em- 


Dt  Haulllant 


Beta 


B.F.34 


c 


Baby 

FIG.  2.   STRUT  SECTIONS 
TESTED  AT  N.  P.  L. 


G> 


PIG.  3.    N.  P.  L. 
STRUTS 


ployed  in  machines  then  existing.  The  outlines  of  the  sections 
tested  are  shown  in  Fig.  2,  and  the  characteristics  are  given 
below. 


Blerlot    A 070 

Bleriot    B 107 

Fmrma  n 074 

De  Harilland.  .052 

Baby    110 

B.F.  34 279 

B.F.  35 238 

188 


K 

51.0 
52.7 
49.3 
54.9 
17.0 
i: -..r. 
13.5 
14.8 


34.9 
25.2 
20.5 
41.6 
93.2 

si!   7 

61.7 


b 
1.24 

1.11: 
1.22 
1  .:;•» 
1.11 

0   -v 

0.92 
0.97 


40.0 
43.8 

36.8 

r,i.:. 

n.9 

70.0 
58.0 


Om 
80 

31 

26 

7K 

90 


of  the  symbols  being  the  same  as  in  the  tables  already  given, 
except  that  n  =  the  ratio  of  the  length  to  width  of  section. 


n 
2. 
2.5 
3. 
3.5 
4. 
4.5 
5. 


.094 
.117 
.141 
.104 

.iss 
.211 
.235 


R 

24.8 
13.7 
13.4 
11.4 
11.2 
11.7 
12.1 


W 

32.0 
40.0 
48.1 
50.1 
04.1 
72.1 
80.1 


b 

1.15 
1.0!) 
1.04 
1.00 
0.97 
O.94 
0.92 


W 

42.3 

47.5 

52.1 

M.1 

)i'J.'J 

67.8 

73.7 


59 
94 

9(i 

in:, 

LOS 

99 
94 


Tims  it  is  apparent  that  the  best  of  these  sections  are  inatc- 
rinlly  superior  to  the  best  of  the  sections  tested  by  Ogilvie. 
both  in  resistance  and  in  merit  factor.  In  Fig.  4  resistance  of 


RESISTANCE 

OP 
R.A.K  STRUTS 


FIG.  4. 


UESISTAVCE  AND  FACTORS  OP  MEKIT  FOR  R.  A. 
STRUTS 


100  feet  of  strut  at  60  miles  per  hour,  and  merit  factor  at  60 
miles  per  hour,  are  plotted  against  ratio  of  length  to  width. 
As  this  ratio  diminishes,  the  air-flow  about  the  strut  takes  on 
a  very  uncertain  character,  and  the  values  when  n  is  less  than 
2  are  rather  doubtful.  Such  extremely  short  sections  as  this 
are  also  undesirable  from  the  standpoint  of  lateral  stability. 
as  will  be  shown  in  another  section  of  the  Course.  On  the 
other  hand,  n  may  be  considerably  pi-eater  than  the  absolute 
optimum  value  without  any  great  disadvantage,  so  it  will  be 
well  in  general  to  employ  a  ratio  of  four,  or  even  a  slightly 
higher  figure.  The  photographs  of  Mow  aliout  strut  sections. 
reproduced  in  Fig.  ~>.  show  clearly  why  such  a  procedure  c-.-m 
be  safely  adopted. 


It  will  be  seen  that  these  figures  simply  supplement  and 
confirm  the  conclusions  already  deduced  from  the  more  exten- 
sive and  systematic  investigations  directed  by  Mr.  Ogilvie. 

Te»U  on  Struts,  Length  to  Width   Varied 

As  a  result  of  these  and  other  tests.  »  series  of  struts  em- 
bodying the  best  features  of  those  already  tried,  and  varying 
only  in  the  ratio  of  length  of  section  to  width,  was  made  and 
tested  at  the  National  Physical  laboratory.  Three  rep  re 
live  members  of  tin-  series  are  shown  in  Fig.  .'!.  The  table 
below  gives  the  characteristics  of  these  struts,  the  meaning 


Two  Kiffcl  Struts 

Two  struts  of  somewhat  the  same  section  as  those  just  di- 
eiisscd  have  recently  l.een  I,  '-led  by  Kifl'el.  and  show  remark- 
ably low  resistances.  Their  outlines  arc  uivcn  in  Fiir.  (i.  For 
Xo.  1,  having  n  equal  to  :!.L'.'I,  If  equals  !i.7  pounds,  while  for 
No.  2.  with  a  somewhat  sharper  entry,  »i  is  L'.lKi  and  R  is  only 
8.7  pounds.  I'arl  of  this  improvement  oxer  the  best  of  the 
Knglish  tests,  hoxvexei.  i-  undoubtedly  due  to  the  higher  wind 
speed  which  is  secured  in  Kiffel's  laboratory,  the  resistance 
coefficient  having  a  tendency  to  rise  as  the  speed  of  test  i^. 
decreased. 


AERODYNAMICAL  THEORY  AND  DATA 


67 


Effect  of  Length  of  Struts 

We  now  turn  our  attention  to  the  effect  of  the  length  of 
the  strut.  While  this  point  is  less  important  than  was  gen- 
erally supposed  a  few  years  ago,  and  while  its  effects  are 
largely  determined  by  the  nature  of  the  surfaces  in  which  the 
strut  terminates,  the  experimental  results  bearing  on  the  mat- 
ter should  nevertheless  be  studied.  For  this  data  we  are 
indebted  to  Mr.  Thurston,  who  has  described  his  results  in 
the  series  of  articles  already  cited.  As  the  result  of  a  great 


nel  would  be  exceedingly  difficult  to  devise.  The  matter  might 
well  be  investigated  in  an  outdoor,  full-scale  plant  such  as 
that  at  St.  Cyr. 

Resistance  of  Inclined  Struts 

The  only  point  which  remains  to  be  studied  is  the  resistance 
of  struts  which  are  not  normal  to  the  line  of  flight.  Some 
much  more  recent  tests  by  Mr.  Thurston  have  covered  this 
point,  and  show  very  surprising  results.  Struts  of  square, 
rectangular,  circular,  and  stream-line  section  were  tested  at 
angles  from  0  to  90  degrees,  and  the  effects  of  the  ends  of  the 
strut  offering  a  direct  resistance  when  inclined  were  overcome 
by  the  use  of  the  method  of  differences:  that  is,  tests  were 
made  first  on  a  strut  34  inches  long,  and  then  on  one  16 
inches  long,  the  difference  of  the  figures  obtained  being  equal 
to  the  resistance  of  an  18-inch  section  of  an  infinite  strut. 

The  ratio  of  the  resistance  of  a  strut  inclined  at  various 


BETA 


FIG.  5. 


DE  HAVILLAND 
ILLUSTRATING  FLOW  AROUND  STRUTS 


many  experiments  on  manifold  different  types  of  strut,  he 
came  to  the  conclusion  that  resistance  for  a  strut  with  free 
ends  could  best  be  expressed  by  the  formula  B  =  KltV1- 
.0073fF2,  where  R  is  the  resistance  in  pounds,  I  and  *,  re- 
spectively, the  length  and  thickness  of  the  strut  in  feet,  K  a 
constant,  and  V  the  speed  in  miles  per  hour. 

It  is  evident  from  this  equation  that,  even  with  the  lowest 
values  of  K  yet  obtained,  the  effects  of  length  will  be  prac- 


Fio.  6.    Two  EIFFEL  STRUTS 

tically  negligible  when  the  length  is  more  than  50  times  the 
thickness,  as  it  generally  is.  Since,  in  addition,  the  case  of  a 
strut  with  free  ends  is  one  which  never  occurs  in  practise, 
resistance  may  be  considered  as  independent  of  length-thick- 
ness ratio  for  all  the  purposes  of  design. 

The  form  of  air-flow  about  the  wing  may  have  very  decided 
effects  on  the  resistance  of  interplane  struts,  but  we  have  no 
means  of  knowing  how  great  these  aro.  and  experiments  cover- 
ing this  point  and  susceptible  of  performance  in  a  wind  tun- 


INCMMATIOM  Of  BAH  TO  WIMO 

FIG.  7.    DATA  FOR  INCLINED  STRUTS 

angles  to  the  resistance  of  a  normal  strut  of  like  section  and 
equal  projected  length  is  plotted  in  Fig.  7.  It  will  be  seen 
that  the  resistance  at  30  degrees  to  the  wind  is  less  than  one- 
third  of  that  at  90  degrees,  and  this  large  difference  is  by  no 
means  accounted  for  by  the  difference  in  length  of  section 
parallel  to  the  wind.  When  a  circular  strut  is  placed  at  an 
angle  of  30  degrees  to  the  wind,  the  section  parallel  thereto 
is  an  ellipse  having  a  length  of  twice  its  width,  and  the  resist- 
ance of  an  elliptical  strut  such  as  this,  when  placed  normal. 
is  only  36  per  cent  less  than  that  for  a  circular  section. 
About  45  per  cent  of  the  reduction  due  to  inclination  thus 
remains  unaccounted  for. 

Since,  however,  the  curve  of  reduction  is  substantially  a 
sine  curve,  and  is  therefore  very  flat  at  the  ends,  there  is 
very  little  advantage  to  be  gained  from  inclining  a  stream- 
line strut  unless  it  is  inclined  at  least  30  degrees  to  the  nor- 
mal. This  reduced  resistance  should,  however,  be  kept  in 
mind  as  a  point  in  favor  of  the  staggered  biplane.  Eiffel 
also  made  a  few  tests  on  struts  inclined  30  degrees  from  the 
normal,  the  results  cheeking  very  well  with  Mr.  Thurston's. 

The  Effect  of  Changing  the  DV  Product  for  Struts 

As  was  shown  in  Chapter  10,  the  resistance  coefficient  is 
not  an  absolute  constant,  but  is  a  function  of  VI),  when- 
V  Is  the  speed  and  I)  the  diameter  of  the  strut.  The  coeffi- 
cient tends  to  decrease  as  VI)  increases,  but  the  change  for 
values  of  I'D  (in  foot/second  units)  above  6  is  extremely  small, 
as  Eiffel  lias  demonstrated.  The  tests  made  at  thp  National 
Physical  Laboratory  have  been  made  with  a  value  of  VD 
equal  to  only  2.5.  whereas,  in  an  actual  machine,  this  quantity 
would  never  be  likely  to  fall  below  5,  and  is  generally  from 
7  to  10. 


i  is                         AERODYNAMICAL  THEORY  AND  DATA 

We  can  therefore  deduce  from  Kitlel's  experiments  that  it  References  for  Part  I.  Chapter  11 
is  safe  to  reduce  the  values  for  resistance  here  given  (for  the 

N.  P.  L.  tests)  by  about  25  per  cent  in  applying  them  to  a  "  strut*."  FHoht.  June  is.  1012. 

design.    This  indicates  that,  as  was  hinted  above,  the  superior-  -Aerodynamic   RMMUM   of   struts.   Bare,   and   wires."   by   A.   v. 

ity  of  Eiffel's  strut  sections  is  more  apparent  than  real,  and  Thurston ;  Aeronautical  Journal,  April  and  July,  191::. 

that   the  best  sections  yet  available  are  the  N.   P.   L.   sections  Technical   Reports  of  the  British  Advisory  Committee  on  Aeronautics. 

having  fineness  ratios  of  from  3.5  to  4.5.     The  correction  1911-12.  1912-13. 

given    here   should    be    applied    only    to   Struts   of    fairly    good  "The  Resistance  of  Inclined  Struts  In  a  Uniform  Air  Curri'iit,"  by  A. 

section,  as  the  value  of  VD  has  much  less  effect  on  those  sec-  i^1"1""0"  "Dd  "'  Tonnsteln'  Aeron<""lcal  •""•"•«'•  Janu"5'- 

tions  for  which  the  resistance  is  relativelv  IUL-II.  and  in  which 

"  Nouvelles  Recbercues  sur  In  Resistance  de  1'Alr  et  1'Avlatlon."  by  G. 

there  is  more  effect  due  to  turbulence  than  to  skin  friction.  Eiffel.     (1914  edition.) 


Chapter  XII 

Resistance  and  Performance 


Nomenclature 

It  may  be  useful  to  restate  the  symbols  which  we  employ 
in  considering  performance  curves,  ascent  and  descent. 

IT"  =  weight  of  the  machine; 

A  =  area  of  the  wings. 

i  =  angle  of  incidence  of  the  wings. 

L  =  lift. 

Ku  =  lift  coefficient. 

D  =  drag  of  wings. 

K.,  =  drag  coefficient. 

11  =  resultant  of  lift  and  drag  on  the  wings. 

P  =  parasite  or  structural  resistance  of  a  machine. 

Dt  =  total  resistance  or  drag  =  T)  -\-  P. 

Rt  =  total  resultant  air  force  on  a  machine. 
//      =  -propeller  thrust. 

6  =  angle  of  flight  path  with  the  horizontal. 

Structural  and  Wing  Resistance  for  the  British  B.E.2 

In  Chapter  4,  a  problem  was  worked  out  on  the  sustentation 
and  resistance  of  wing  surfaces,  which  in  spite  of  some  rough 


50  00 

MILES  PER  HOUR 

FIG.  1.    PERFORMANCE  CURVES  FOR  THE  B.E.2 


assumptions,  illustrated  the  main  performance  curves  and  cal- 
culations employed.  In  Fig.  1  are  shown  curves  for  the  Brit- 
ish B.  E.  2.  It  is  not  a  particularly  modern  machine,  but  has 
been  worked  out  so  thoroughly  that  it  deserves  particularly 
careful  study. 

The  body  or  parasite  resistance  which  includes  the  resis- 
tance of  the  wing  bracing,  chassis,  etc..  as  well  as  the  resistance 
of  the  body  proper,  is  taken  as  varying  as  T'"2  and  allowance 
has  been  made  for  propeller  slip  stream  velocity.  The  body 
resistance  is  seen  to  play  an  unimportant  part  at  low  speeds. 
But  at  about  53  miles  per  hour  it  becomes  greater  than  the 
plane  or  wing  resistance,  and  at  high  speeds  it.  is  almost  twice 


as  great  as  the  wing  resistance.  This  emphasizes  the  imppr- 
tance  of  minimizing  the  resistance  for  a  high-speed  machine. 
However  good  a  wing  section  itself  may  be,  high  structural 
resistance  will  make  high  speeds  impossible. 

The  plane  resistance  curve  has  a  minimum  value  at  about 
65  miles  per  hour  and  increases  on  either  side  of  this  speed. 
It  is  interesting  to  follow  out  how  this  increase  in  resist- 
ance on  either  side  occurs.  At  high  speeds,  the  angles  of 
incidence  and  the  drift  coefficients  are  small  but  the  speeds 
are  very  great,  and  the  increase  in  wing  resistance  is  obvious. 
At  small  speeds  on  the  other  hand  the  airplane  is  flying  at 
large  angles  of  incidence  to  give  the  necessary  sustentation  and 
the  drift  coefficients  are  large.  The  shape  of  the  total  re- 
sistance curve  follows  from  the  summation  of  the  two. 

Theoretical  Laws  for    Minimum   Thrust  and 
Minimum  Horsepower 

From  a  theoretical  treatment  of  the  question,  the  following 
interesting  law  has  been  derived : 

Minimum  thrust  is  required  to  overcome  the  resistance  of  an 
airplane  when  Hie  parasite  resistance  is  equal  to  the  drag  of 
the  wings. 

For  a  proof  of  this  law,  reference  to  Chasseriaud  and 
Espitallier  is  appended.  In  the  case  we  have  selected,  illus- 
trated in  Fig.  1,  the  structural  air  resistance  and  the  wing 
drag  are  equal  at  a  speed  of  53  miles  an  hour,  while  the 
minimum  resistance  is  at  49  miles  per  hour.  The  law  does  not 
seem  to  be  borne  out  by  practice,  though  it  may  be  occasion- 
ally useful  as  a  rough  check. 

The  minimum  horsepower  required  generally  occurs  at  a 
low  speed,  but  not  at  the  minimum  speed;  and  its  position 
will  vary  for  every  machine.  Another  theoretically  deduced 
law  states  that: 

Minimum  horsepower  is  required  irln'ii  Hie  machine  is  mov- 
ing at  a  speed  at  which  the  wing  resistance  is  three  times  the 
body  resistance. 
"•  This  law  is  often  highly  inaccurate,  but  may  be  useful. 

Effective  or  Propeller  Horsepower  Available  Curve 

Typical  curves  for  these  are  also  illustrated  in  Fig.  1,  and 
are  of  the  greatest  interest  to  the  designer.  In  establishing 
such  curves  it  is  generally  assumed  that  the  engine  is  running 
at  the  rated  revolutions  per  minute  and  that  in  designing  the 
propeller  the  efficiency  for  this  revolution  per  minute  at  every 
airplane  speed  is  known.  Thus  assuming  an  engine  which 
delivers  140  horsepower  at  an  ail-plane  speed  of  80  miles  an 
hour,  the  propeller  having  an  efficiency  of  75  per  cent  at  this 
speed,  the  available  horsepower  will  be 
140  X  75 


100 


=  105  horsepower. 


69 


70 


AERODYNAMICAL  THEORY  AND  DATA 


Since  the  power  of  a  propeller  is  given  by  the  product  of 
us  thrust  into  the  speed  and  the  speed  of  the  propeller  is  the 
speed  of  the  airplane,  it  follows  that  when  the  propeller  is 
delivering  sufficient  power,  it  is  also  delivering  sufficient 
thrust.  Hence  propeller  horsepower  available  is  sufficient  for 
all  practical  consideration,  and  propeller  thrust  curves  need 
not  be  included  in  a  performance  chart. 

Minimum   and    Maximum   Speed;    Maximum    Excess 
Power;  Best  Climb;  Descent 

The  maximum  and  minimum  speeds  of  an  airplane  are  gen- 
erally given  by  the  two  points  of  intersection  of  the  propeller 
horsepower  available  and  the  total  horsepower  required.  If 
the  machine  is  highly- powered,  and  the  propeller  efficient,  the 
two  curves  may  not  intersect  at  the  speed  at  which  the  lift 
becomes  insufficient,  and  the  airplane  would  climb  at  stalling 
angle,  unless  the  engine  is  considerably  throttled  down.  The 
climb  decreases  the  angle  of  incidence,  and  checks  stalling. 
It  is  thus  a  decided  advantage  to  have  excess  available  power 
at  high  angles. 

It  is  a  simple  matter  to  deduce  the  speed  of  climb  from  the 
excess  power.  This  is  absorbed  in  raising  the  machine. 


Ex 


power 


Total  weight  X  climb  per  second 

551) 


The  maximum  excess  power  does  not  occur  at  the  lowest 
speed.  To  find  it,  we  must  measure  the  maximum  ordinate 
between  the  available  propeller  horsepower  and  the  total  re- 
quired horsepower.  In  Fig.  1  this  is  to  be  found  at  48  miles 
per  hour.  The  excess  is  21  horsepower  and  the  weight  of  the 
machine  is  1650  pounds. 


Climb  = 


21  X  550 


=  7  feet  per  second  or  420  feet  per  min- 


ute.  This  is,  however,  only  the  initial  rate  of  climb.  As  the 
machine  rises,  the  density  of  the  air,  the  power  of  the  engine, 
and  the  climb  gradually  diminish. 

In  practice,  the  pilot  need  not  know  the  change  of  in- 
cidence that  he  produces  to  climb,  although  for  a  given  ma- 
chine it  is  an  easy  matter  to  calculate  the  correct  angle  from 
the  performance  curves.  In  Dr.  Hunsaker's  words,  "  a  care- 
ful man  moves  his  elevator  slowly  until  he  has  placed  him- 
self on  the  desired  trajectory."  Part  of  the  art  of  aviation  is 
to  do  this  without  exceeding  safe  limits,  for  obviously  there  is 
a  limit  to  the  rate  of  climb  the  engine  can  handle.  If  the 
machine  is  put  on  a  climb  too  steep  for  the  power  of  the  ma- 
chine, the  speed  is  suddenly  lost,  the  controls  become  ineffec- 
tive, and  the  machine  has  stalled. 

In  descent,  very  analogous  considerations  obtain.  The 
pilot  decreases  his  angle  of  incidence  to  a  negative  value.  At 
this  angle  the  speed  required  for  sustentation  is  beyond  that 
of  the  maximum,  and  the  propeller  horsepower  is  insufficient. 
If  D  =  deficiency  in  horsepower, 

n        Total  weight  X  velocity  of  descent. 
Mt 

The  machine  descends  and  gains  the  required  speed  under  tin- 
action  of  gravity. 

The  Two  Regions  of  Control.     Control  by    I  limiilin- 

Consider  the  performance  curves  of  the  same  machine,  the 
Hnti-h  I'..K.'_'  shown  in  Fig.  1.  Suppose  the  machine  to  be 
flown  iit  in  degrees  at  the  point  J/  with  the  engine  throttled. 
so  that  there  is  equilibrium,  and  the  power  curve  is  as  shown. 
26  horsepower.  The  pilot  wishing  t<>  rise  will  naturally  in 
crease  his  angle  of  incidence  to  say  12  degrees.  He  will  thru 
require  30  horsepower  while  the  throttled  engine  will  deliver 


even  less  than  the  2(j  horsepower  through  the  propeller.  In- 
stead of  rising  the  machine  will  fall. 

Suppose  now  that  flying  at  the  same  point  and  under  the 
same  conditions  he  wishes  to  descend,  and  decreases  his  angle 
to  8  degrees.  He  will  now  have  an  excess  of  power  of  3 
horsepower  as  can  be  seen  from  the  curves  and  will  ascend 
instead  of  descend.  There  is  therefore  a  region  of  reverse 
controls,  known  to  French  authors  as  the  regime  lent. 

At  the  point  M  .  when  the  pilot  wishes  to  rise  and  in- 
creases his  angle  of  incidence,  he  does  indeed  obtain  excess 
power  and  rises.  Here  the  controls  are  normal  and  the  region 
is  known  as  regime  rapide.  For  an  inexperienced  pilot  the 
regime  lent  is  dangerous.  Even  if  he  knows  the  angle  of  in- 
cidence at  which  he  is  working,  he  is  likely  to  get  into  diffi- 
culties. 

With  a  flexible  engine,  an  expert  pilot  can  operate  an  air- 
plane in  the  slow  speed  region  by  manipulation  of  the  throttle 


40  M  60  TO  SO  90  100 

MILES  PEU  HOUR 

Fiu.  2.    VARYING  SPEED  RANGE  WITH  ENGINE  THROTTLED 

alone.  In  Fig.  2  the  propeller  horsepower  available  is  shown 
with  the  engine  throttled  down  to  various  speeds  for  a  design 
taken  i'rom  Dr.  Hunsaker's  pamphlet,  to  which  reference  is 
appended.  For  each  speed  of  the  engine  there  is  a  different 
maximum  and  minimum  speed  of  the  airplane,  and  a  different 
speed  range.  If  the  airplane  is  living  at  the  minimum  speed 
in  the  regime  lent  region  at  a  certain  revolution  per  minute, 
the  pilot  can  by  unthrottling  his  engine  pass  to  a  larger  speed 
!.-iii'_re,  obtain  excess  power  and  climb  without  changing  his 
forward  speed  or  angle  of  incidence.  When  an  engine  is 
throttled  the  danger  of  reversed  controls  is  still  greater,  lie- 
cause  the  speed  range  becomes  so  very  small.  Kven  the  best 
of  pilots  may  mistake  his  position  on  the  curve. 

In  French  airplane  contests,  a  premium  has  been  placed  on 
low  speeds,  and  the  regime  lent  with  throttling  has  been 
largely  and  successfully  used.  Such  operation  does  not  seem 
advisable  for  ordinary  flying. 

Variations  in  PropHIrr  Horsepower  (lunr- 

We  will  now  consider  the  possible  variations  in  performance 
by  changing  the  design  of  the  propeller  from  a  high  speed  to 
a  climbing  propeller.  In  Fig.  3  the  B.E.2  is  again  illustrated. 
The  power  required  curve  remains  the  same.  By  suitable 
design  the  propeller  ellicicncy  curve  can  be  changed  so  as  to 
give  maximum  etlicieney  at  varying  speeds.  The  design  of  a 
suitable  propeller  cannot  unfortunately  be  detailed  here. 

For  the  propeller  with  Kllieicncy  Curve  1,  the  maximum 
ellieiency  is  at  high  speed,  and  the  Horsepower  Available 
Curve  1  shows  that  such  a  propeller  will  give  a  high  maxi- 


AERODYNAMICAL  THEORY  AND  DATA 


71 


mum  speed.     It  is  a  high  speed  propeller  when  applied  to 
this  particular  airplane. 

For  the  propeller  with  Efficiency  Curve  2,  the  maximum 
efficiency  occurs  at  a  lower  speed.     Such  a  propeller  will  give 


100* 


70 

MILES  PER  HOUR 

FIG.  3.    VARIATION  OF  PERFORMANCE  WITH  CHANGE  IN  PRO- 
PELLER DESIGN 

a  smaller  maximum  speed,  as  can  be  seen  from  Horsepower 
Available  Curve  2,  but  a  greater  excess  power.  It  will  be  a 
climbing  propeller.  There  are  many  such  variations  pos- 
sible for  any  machine. 

Angle  of  Glide 

The  best  L/D  for  a  wing  section  may  be  in  the  neighbor- 
hood of  14  or  15.  But  the  parasite  resistance  of  a  machine, 
i.  e.,  the  resistance  of  the  body,  wing  bracing,  etc.,  increases  the 
drag  to  such  an  extent  that  the  L/Dt  of  the  whole  machine 
may  be  reduced  to  7  or  8.  It  is  this  value  of  L/Dt  which  de- 
termines the  angle  of  glide  of  a  machine. 

In  Fig.  4  is  shown  a  machine  which  is  gliding  with  the 
engine  shut  down  so  that  the  propeller  exerts  no  thrust,  i  be- 
ing the  angle  of  incidence,  and  0,  the  angle  which  the  machine 
makes  with  the  horizontal  line,  being  the  angle  of  glide.  Re- 


solving forces  perpendicular  to  and  along  the  line  of  motion, 
the  equations  of  equilibrium  for  steady  glide  are: 

L  (1) 

=  Dt  =  D  +  P         (2) 
The  angle  of  glide  is  therefore  given  by  the  equation 


tan 


=-      (3) 
L 


and  has  its  maximum  value  when  Dt  is  a  maximum. 

The  minimum  angle  of  glide  is  also  termed  the  "  best  " 
angle  of  glide.     At  a  given   height  above  the  ground,   the 


WSinff=  D+P 

FIG.  4.    FORCES  ON  AN  AIRPLANE  IN  A  GLIDE 

forward  displacement  of  the  machine  before  landing  varies  as 
cos  6  and  will  be  a  maximum  for  the  smallest  value  of  6.  The 
pilot  has  at  this  angle  the  greatest  radius  of  action  when  de- 
scending from  a  height  with  his  engine  shut  off. 

The  angle  of  glide  for  any  machine  at  any  speed  can  be  at 
once  obtained  from  the  total  resistance  curve  for  Dt  and  the 
weight  of  the  machine,  assuming  L  =  W  which  makes  a  com- 
paratively small  error.  In  Fig.  1,  the  angle  of  glide  is  shown 
for  all  speeds  of  the  machine  in  question. 


References  for  Part  I,  Chapter  12 

Barnwell's  "  Aeroplane  Design." 

"  Aeroplane  Design,"  by  J.  C.  Hunsaker,  United  States  Naval  In- 
stitute Proceedings,  November-December,  1914. 
Itrttish  Uep.)rt.  1912-1013.     No.  SB. 
Chasseriaud   et   Espltalller,    "  Conrs   d'Aviatlon." 


Chapter  XIII 

Resistance  Computations — Preliminary  Wing 

Selections 


Example  of  Estimate  for  Parasite  Resistance 
for  a  British  Machine 

The  B.E.2,  mentioned  in  Chapter  1:2,  will  serve  as  an  ex- 
ample of  the  estimate  of  the  total  parasite  resistance  of  a 
machine.  The  estimate  was  arrived  at  by  the  Royal  Aircraft 
Factory  after  the  most  careful  tests,  both  at  the  N.  P.  L. 
laboratory  and  in  full  flight,  and  is  given  in  Table  1. 

TABLE   1. 

B.E.2;  WEIGHT.  1650  POUNDS;  372  SQUARE  FEET  BIPLANE  ScKrACE,  70  HORSE- 
POWER ENGINE. 

Estimated  parasite  resistance  at  60  miles  per  hour. 


Value  in  pound.* 
per  ««uar«  foot  of             Resistance 
Part.                             Whence  obtained.         projected  area.             in  pound*. 
Strut* 
8.6'0"X1«"  N.P.L.Teet  .     4.2 
4.  4'0"  X  IJi"...                        "                                                             1  * 

6,  3'0"  X  1M"  

*» 

1  6 

Wings 
2.  2O"  cable. 

7.2 
29  5 

70,  12G.H.T.  wire  

M 

5  6 

Estimated 

3  0 

Rudder  and  elevators  

38.1 
20 

Body  with  passenger  and  pilot. 
Axle  

N.P.L.  Teet  

40.0 
2  0 

Main  skids  and  axle  mounting 
Rear  skid... 

1.0 

5 

Wheels  

N  P  L.  Test 

3  5 

Wing,   skids,    wiring,    plates, 
•ten.  silencers,  etc.  .  . 

Estimated    . 

.   10.0 

59.0 

Szpoted  to  a  tlip  stream  of  IS  feet  per  second,  for  an  airplane  speed  of  SO  miles  per 
hour.  i.  e.,  SS  feet  per  second. 

Bodv 40. 

4.  4'0"  strata 1.4 


2/3  of  3'0"  strut*. 

50"  cable 

30'H.TwJre 

Rudder  and  clerator . . 

Rear  skid 

Fittings 


.8 
6.7 
2.4 
2.0 

.5 
2.0 

55^8 
91.5 


In  slip  stream  resistance  increased  to 

Increase 35.7 

Total 140.0 

One  of  the  most  interesting  features  of  this  resistance  esti- 
mate is  the  allowance  for  slip  stream.  The  parts  of  the  air- 
plane included  in  the  slip  stream  are,  of  course,  taken  within 
the  area  swept  out  by  the  propeller.  The  speed  of  the  machine 
is  60  miles  per  hour,  i.e.,  88  feet  per  second,  and  the  slip 
stream  is  25  feet  per  second,  i.e.,  28.4  per  cent,  increasing  the 
resistance  of  the  parts  involved  by  some  i>5  per  • 

I    \.llllple-     ill      I'.IIM-itl-     l!r-i-t;UHT     I  )\-\  T\  Illlt  i<  III 
ill    •"rhiMil     M.leliine- 

Tahle  J  furni-he-  useful  estimates  of  parasite  resistance 
distribution  tor  a  number  ol  -tandard  school  machines.  The 
-lip  stream  velocity  ha«  been  taken  as  15  per  cent  of  (lie  air- 
plane speed,  givintr  an  im-na-e  in  re.«i» lance  of  .TJ  per  Cent 
for  the  parts  exposed  to  it. 


Uiscrejmncies  in  these  values  arise  from  a  number  • 
The  Martin  has  interplane  ailerons,  and  the  other  machines 
have  wing  flaps.  The  Curtiss  has  a  water-cooled  motor  with 
radiator  in  front.  The  machine  designed  at  M.  I.  T.  has  a 
radiator  above  the  upper  wing.  The  Curtiss  has  a  two-wheeled 
landing  gear,  while  the  Martin  has  a  third  wheel  in  front. 

TABLE  2. 
Percentage  of  Parasite  Resistance. 


Zgi 

j 

S 

Z: 

i 

.  3 

*• 

IP 

ii 

i 

C 

^  « 

C     T. 

c 

llli 

"t 

i.  C 

5 

• 

!< 

u  C 

j:  — 

5 
$ 

o 

-  c 

-^-  j= 

• 

fo  ** 

M  fi 

M 

H™ 

2   * 

™ 

S'l  a. 

=  ' 

M 
C 

-  5 

d  / 

'|  £  ? 

^  i 

1      ifel 

ll 

yg 

£'£ 

E| 

§1 

tfc 

N 

£3 

Curtis  90  h.p.. 
two  place,  1893 
Ibs.  tractor 39.5% 

Martin,  1800  lb»., 

70  h.p.  Renault. .  28.8% 


P-. 


10.5%     17.5%     28.5%      4.0% 
18.7%      14.1%      14.7%     22.7%     P 


.Q3SW 
.042V" 


126lb». 
151  Ibs. 


90  h.p.  biplane, 
1850  Ibs.,  tractor, 
designedatM.I.T.  36.0%  15.1% 


.'•'•  :).5%    P-.OMV*  ll.Ml.i. 


Two  tractor  machines,  carefully  designed  by  students  at  the 
Massachusetts  Institute  of  Technology,  gave  the  following 
figures : 

Paras:-  Allnuint: 


Tractor  Biplane 
Reconnaissance. 

Tractor  Biplane 
Reconnaissance , 


WVicht 
in  Ibs. 

2300 


iirionl.        In 
Engine.        I'inm.p.h.       for  t*lip  stream. 


2885 


120  h.p. 
125  h.p. 


P-.040  V 
P-.04.S.-,  I' 


.011  V« 


Resistance 
at 

00  m.p.h. 

158  ll.s. 


Parasite  Resistance  Coefficient  for  a  Stnrtevant  Seaplane 

For  a  Sturtevant  seaplane,  weighing  2650  pounds,  with  a 
140  horsepower  engine,  and  where  para-iie  iv.-isiance.  01 
count  of  the  floats,  is  higher  than  for  a  land  machine  of  the 
same  weight,  the  structural  n-i-tance  i|  e.-timated  as  being 
given  by  the  formula  P=  .()".:;_' I  .  and  10  per  cent  increase 
on  all  the  parasite  resistance  is  allowed  for.  hrin<_rin<r  up  the 
Value  to  7'  •  .0.")7fiT/;.  or  212  pounds  approximately,  at  tin 
null  -  per  hour. 

Mlowanrc  for  Slip   Stream 


The  i|ue-iimi  ni  -]i|i  •,11-rani  \elm-itv  i<  mn-  of 
plexily,  ami.  in  the  present  stair  ol  knowledge,  it  docs  not 
-•.•in  advisable  to  enter  into  very  eomplinitcd  calcuhilions 
when  working  out  perfuniianee  eiirves.  The  estimated  liirure- 
triven  tor  the  various  American  ma<-hine~  ^enu  to  he  very  well 
liorne  out  by  tests  in  tile  field.  The  Hrilish  allowance  for  slip 


-•1 


AERODYNAMICAL  THEORY  AND  DATA 


73 


stream  increase  was  28.4  per  cent,  and  the  one  given  by 
American  practice  is  15  per  cent.  It  would  be  safe  to  say  that 
if  for  the  parts  of  the  machine,  within  the  area  swept  out  by 
the  propeller,  the  speed  is  increased  by  some  20  per  cent,  and 
resistance  of  those  parts  increased  by  some  44  per  cent,  a 
sufficiently  accurate  estimate  will  be  made. 

The  other  method  adopted  of  increasing  the  total  structural 
resistance  by  some  10  per  cent  to  allow  for  slip  resistance, 
though  not  so  rational,  has  the  advantage  of  being  simpler, 
and  is  still  in  accordance  with  tests  in  the  field.  For  a  mono- 
plane, where  the  parts  exposed  to  the  slip  stream  bear  a  larger 
ratio  to  the  rest  of  the  machine,  an  increase  of  15  per  cent  on 
the  total  structural  resistance  is  probably  advisable. 

Preliminary  Estimates  for  Parasite  Resistance 

In  making  preliminary  estimates  for  a  machine,  a  really 
difficult  point  is  the  allowance  to  be  made  for  parasite  re- 
sistance. Some  authorities  allow  for  the  parasite  resistance 
by  finding  the  resistance  of  the  body  and  multiplying  it  by 
four  for  a  biplane  and  by  three  for  a  monoplane.  Such  rules 
can  only  be  roughly  correct,  and  it  is  best  to  refer  to  data  for 
standard  machines  and  select  parasite  resistance  coefficients 
of  a  machine  of  similar  type  and  weight.  The  figures  given 
in  this  section  will  be  sufficiently  accurate  for  a  preliminary 
design. 

Preliminary   Selection   of  Wing  Section   and  Area 

A  great  many  ingenious  methods  have  been  devised  for  the 
selection  of  correct  wing  sections  and  areas  for  the  preliminary 


design  of  a  machine  whose  engine-power  and  specification  are 
given.  Eiffel,  among  others,  has  developed  a  very  complete 
system.  It  seems  best,  however,  to  employ  the  simplest  and 
most  straightforward  trial  and  error  methods,  based  on  the 
following  rules : 

(1)  From   a   consideration   of   standard   practice,   select   the 
loading  per  horsepower  and  hence  weight  of  the  machine. 

(2)  From  a  consideration  of  standard  practice,  select  the  ap- 
proximate loading  per  square  foot. 

(3)  From  some  such  considerations  as  those  given  in  Chapter 
IV  select  two  or  three  wings  which  are  likely  to  give  the 
qualities  desired. 

(4)  Assume   a   parasite   resistance   coefficient   which   from   a 
standard  practice  is  likely  to  apply  to  a  machine  of  the 
type  and  weight  in  question. 

(5)  Draw  up  a  number  of  performance  curves  varying: 

(a)  Wing  sections 

(b)  Area  for  each  wing  section 

(c)  Assumed  propeller  efficiency  curves. 

Some  data  on  standard  practice  will  be  given  in  the  Second 
Part  of  the  book,  and  the  above  rules  will  be  applied  to  the 
design  of  a  standard  machine. 


References  for  Part  I,  Chapter  13 


Barnwell's   "  Aeroplane  Design." 
British   Report,  1912-1913.      No.   86. 


Part  II 
Airplane  Design 


Chapter  I 


Classification  of  Main  Data  for  Modern  Airplanes 

Unarmed  Land  Reconnaissance  Machines 

Land  Training  Machines 


The  Army  Classification 

Constructors  in  America  have  hitherto  mainly  developed 
one  type  of  airplane,  the  tractor  biplane  reconnaissance  ma- 
chine. But  with  the  rapid  development  of  military  aeronau- 
tics, airplanes  are  evolving  into  distinct  classes,  just  as  the 
component  vessels  of  a  fleet.  The  memorandum  on  "  Military 
Airplanes,"  prepared  by  the  office  of  the  Aviation  Section  of 
the  Signal  Corps,  offers  the  most  authoritative  classification, 
and  one  which  constructors  must  of  necessity  follow  very 
closely.  It  suggests  six  distinct  types,  which  we  shall  study 
as  closely  as  possible,  within  the  limits  of  data  held  confidential 
by  manufacturers.  (I)  Land  Reconnaissance  Machine,  used 
when  there  are  no  enemy  airplanes;  (II)  Land  Primary 
School  Machine;  (III)  Land  Advanced  School  Machine;  (IV) 
Land  Gun  Carrying  Machine,  (V)  All-round  Twin-engined, 
Land  or  Water,  (VI)  Land  Pursuit  Type. 

Unarmed  Land  Reconnaissance  Machine 

For  tliis  machine,  the  memorandum  gives  the  following 
figures : 


and  the  empirical  rules  to  be  derived  from  it  are  invaluable 
in  the  preliminary  stages  of  a  design,  and  enable  the  designer 
to  avoid  misleading  rough  estimates  of  weights  and  dimen- 
sions. 

TABLE  2. 

MAIN    DATA    FOR    TWO-SEATER    TRACTOR    BIPLANES    op    THE    UNAH.MKU 

RECONNAISSANCE  TYPE  OVER  2,500  POUNDS  IN  WEIGHT.    RECENT 

EXAMPLES  op  CONSTRUCTION. 


TAnr.K  i. 


Unarmed  Land 
Reconnaissance 

Machine. 

130 

Tractor 


Horsepower   

Puslipr  or  trac'tor 

Number  of  men 

Military  load,  pounds 475 

Fuel  load,  pounds 450 

Miles  radius  of  action,  full  power 41 ." 

Climb  In  10  nn'imtes.  feet 3,400 

High  speed,  miles  per  hour 82 

Low  speed,   miles  per  hour 4ti 

Factor  of  safety 7 

Percentage  made  in  war 2 

(Gross  load  is  well  over  2,500  pounds  for  this  type.) 

The  memorandum  deals  very  unfavorably  with  this  type  of 
machine,  which  forms,  as  we  have  said,  an  important  part  of 
American  construction.  It  is  said  to  be  a  false  development, 
suitable  only  for  use  against  an  enemy  who  has  no  airplanes. 
Possibly  useful  for  long-range  reconnaissance,  it  will  be  out- 
matched in  warfare  by  the  armed  "  pursuit "  type  and  the 
large  armed  twin-engine  machine.  For  short  ranges  the  pur- 
suit type  will  surpass  it,  for  long  ranges  the  larger  machine 
may  be  not  quite  so  rapid,  but  will  have  a  greater  radius  of 
action.  A  careful  study  of  these  views  would  lead  one  to 
believe  them  correct  and  in  accordance  with  developments 
abroad. 

Analysis    of    Main    Data    for    Representative    Unarmed 
Reconnaissance  Biplanes  More  Than  2500 

Pounds  Gross  Weight 

This  group  is  composed  of  excellent,  controllable  machines 

In  Table  2  are  given  the  main  dimensions  and  perform-      very  similar  in  character.     It  is  therefore  possible  to  drnw 
ances  of  a  number  of  representative  machines.     Such  analysis      some  fairly  definite  conclusions. 

77 


Machine     Standard 

Curtiss  Wright-  Sturtevant     Wright-) 

H-3 

R-4     Martin  V          S           Martin  R  j 

Engine    Hall-Scott 

Curtiss  Hispano-  Sturtevant  Hall-Scott  1 

A-5 

Suiza                                A5a      J 

Horsepower    135 

200             150             140             150 

Number  of  cylinders.          6 

8886 

Revolutions  per  min..  1,250 

1,400           1,450           2,000           1,375 

Gasoline    tank    capac-       68 

100               ...               ...                 70  ) 

ity    gallons 

gallons                                          gallons  ) 

Endurance  in  hours..         6 
Maximum  speed,  miles 

5.42apiir.  6                 4.5              4.84 

per  hour  84 

90               ...                 86                Sfi 

Minimum  speed,  miles 

per    hour  40 

4S               ...                 42                47 

Climb  in   10  minutes, 

feet     3,400 

4,000               .  .  .           3,500           3,500 

Propeller  diameter(two 
blades)     9' 

8'  4"                                S'  f." 

Weight  loaded,  pounds  2,700 

3,245           2,310           2,550           2,880 

Weight  bare,   pounds.  1,900 

2,225           1,725           1,850           1,905 

Useful    load,    pounds.      800 

1,020              90f>              700              ns:« 

Percent  useful  load..        29.6 

31.4             34.2             27.4             34.2 

Weight  per  horsepow- 

er in  pounds  20.0 

16.21           16.86           18.2             19.1 

Weight  per  square  foot 

wing  area  in  pounds.         5.08 

6.42             5.86            4.64             6.25 

Overall    length  27'  0" 

29'  0"         27'  2"         27'  0"         26'  8" 

Mean  span  of  wing/ 

length    1.41 

1.49             1.37             1.65             1.64 

Wing    section  R.  A.  F.  6 

R.  A.  F.  6  Vought  4     R.  A.  F.  6    .  .  . 

Upper    span  407  1' 

48'4VS"     39'  S%"      49'  6"      50'  8" 

Upper    chord  6'  6' 

'            6'  3"           5'  9"            6'  3"         5'  6" 

Upper   aspect   ratio..          6.2 

7.7">             0.95             7.95             9,25 

Lower   span  40'  1" 

38'  5(4"       39'  81/-"      39'  6"     36'  10" 

Lower  chord  6'  6" 

6'  3"            5'  9"            6'  3"          5'  6" 

Lower   aspect   ratio..          6.2 

6  15             0.95             6.32             6.6 

Gap    6'  6" 

6'  2"            5'  7"            6'  3"          6'  0" 

Gap,    lower    chord....         1.00 

0.9S             0.98             1.00             1.09 

Total    area   of   wings. 

including     ailerons, 

in  square  feet  532 

505              430              540              458 

Area     of     rudder     in 

square  feet  10 

16.5            12.37appr.  15                 8.7 

Area    of    vertical    fln 

in  square  feet.  ...          5 

7                  5  appr.      .  .  .                  7.3 

Area    of    elevator    in 

square   feet  23 

27.5           ...                24              ... 

Area   of   stabilizer   in 

square   feet  32 

40.5            51.2  (ele-  28              53.21 

vator  and  sta-    (elevator  and  V 

bilizer)                 stabilizer)       1 

Ailerons  upper  wing.        31 

33.S             32.3             39                48 

Ailerons   lower  wing.        31 

20.5             32.3             3fi 

Type  of  fuselage  Rectan- 

Rectan-     Rectan-      Trian-           ...    \ 

gular 

anlar          gular          aular                      ) 

Dihedral    3° 

3°            "     1°  15'         2°                 1" 

Stagger    10° 

5°  appr.      1  ft.        None       20.4%  ) 

chord  length  ( 

Sweephack    10° 

Xone          None         None        None 

Average  \'  allies  for  Machines  Over  2500 
Pounds  in  Weight 


78 


AIRPLANE    DESIGN 


(a)  Average  gross  weight,  2737  pounds. 

(b)  Average  wing  area,  493  square  feet. 

(c)  Average  horsepower,  155.    The  latter  figure  is  consider- 
ably increased  by  the  inclusion  of  the  Curtiss  R-4  with  its  200 
horsepower  engine.    There  is  a  tendency  to  give  higher  power 
to  this  class,  with  correspondingly  better  performances. 

(d)  Average  endurance,  5.65  hours.    This  figure  is  probably 
a  very  fair  value  of  the  endurance  possible  if  good  climb  is  to 
be  maintained.     It  should  be  noted  that  it  would  be  possible 
to  take  up  much  more  fuel,  and  not  decrease  the  speed ;  in  fact, 
to  increase  it  slightly.     At  the  same  time,  minimum  speed 
would  be  increased. 

(c)  Average  weight  per  horsepower,  18.1  pounds.  The 
Curtiss  lowers  this  average  value,  and  is  an  indication  of  what 
will  follow  when  lighter  new  engines,  such  as  the  new  Thomas 
and  Sturtevant,  enter  into  construction. 

(f)  Average   weight   per  square  foot  of  wing  area,   5.65 
pounds. 

(g)  Average  maximum  speed,  86.50  miles  per  hour. 
Average  minimum  speed,  45.75  miles  per  hour. 
Average  climb  in  10  minutes,  3666  feet. 

The  number  of  machines  considered  is  too  small  for  curves 
to  be  plotted,  but  it  is  interesting  to  see  how  in  diminishing 
the  weight  per  horsepower  from  24.2  pounds  to  16.21  pounds 
the  maximum  speed  increases  from  84  to  90  miles  per  hour, 
while  the  low  Sturtevant  wing  loading  gives  a  landing  speed 
of  42  miles  per  hour  as  compared  with  the  Curtiss  of  50  miles 

per  hour. 

mean  span 

(h)  Average  of  ratios  of — -  =1.51. 

overall  length 

This  is  an  important  point  to  be  considered  in  the  design 
of  a  machine.  As  we  shall  see  later  in  considering  longi- 
tudinal stability,  it  is  quite  possible  to  secure  adequate  static 
stability  by  using  a  short  body  with  a  large  tail  surface  placed 
at  a  negative  angle.  But  an  excessively  short  body,  although 
it  means  saving  in  weight,,  may  fail  to  give  dynamic  stability, 
due  to  lack  of  damping.  At  this  stage  of  the  science,  we  can 
only  fix  on  a  length  for  the  body  by  taking  average  values  such 
as  the  above. 

(i)  Average  aspect  ratio  upper  wing,  7.60. 
Average  aspect  ratio  lower  wing,  6.76. 

There  seems  in  the  light  of  these  figures  no  reason  why  an 
aspect  ratio  of  7.5  for  the  upper  span,  and  7.0  for  the  lower 
should  not  be  successfully  employed. 

(j)  Gap/chord  ratio  is  practically  1.00  in  every  case. 
Without  undue  conservatism,  it  would  appear  that  for  ma- 
chines of  this  size,  the  increased  structural  weight  of  a  larger 
gap/chord  ratio  is  prohibitive,  whereas  in  smaller  machines 
with  smaller  chord,  much  greater  values  might  be  employed 
to  advantage. 

The  dimensions  of  control  and  stabilizing  surfaces  present 
an  exceedingly  complex  problem,  so  many  factors  brinj;  in- 
volved. They  will  be  carefully  studied  in  our  design,  but  in 
the  preliminary  stages  some  of  the  following  empirical  rela- 
tionships may  be  useful : 

(k)  Aileron  or  wing  flap  area:  The  dimensions  of  these 
will  depend  on  the  area  of  the  wings  whose  rolling  moment 
it  may  be  necessary  to  overcome,  on  tlie  weight  and  lateral 
radius  of  gyration  of  the  machine  and  on  the  span  of  the 
wings  which  gives  the  moment  arm  of  the  ailerons.  These 
factors  are  too  complex,  however,  and  at  present  the  following 
fonnula  offers  a  fairly  satislactnry  standard  of  comparison: 

'i,  -}-S,a,)  =  CA,  where  A  —  area  nf  wings,  S,  and  S,  = 
spans  of  upper  and  lower  wings,  o,  and  a,  =  aileron  areas  on 
upper  and  lower  wings.  ('  =  a  constant.  Where  ('  is  large 
there  is  powerful  lateral  cmtrol,  where  ('  is  small  there  i- 


weak  lateral  control, 
are  as  follows : 


The  values  for  the  above  live  machines 


Standard 
H  :s 
4.65 


Curtiss 
R-4 
4.50 


Wright-Martin 
5.95 


Sturtevaut 

S 
6.50 


Wright-Martin 
It 


Too  powerful  lateral  controls  present  difficulties  in  handling 
just  as  too  weak  controls.  The  average  value  of  C  =  5.38 
might  be  at  least  some  guide. 

(1)  For  the  horizontal  elevator  and  stabilizer,  the  following 
very  rough  formula  is  sometimes  employed  in  preliminary 
work,  based  on  ideas  similar  to  those  enunciated  in  the  pre- 
vious paragraph: 

QL 

d  =  *TJ,  where  d  =  some  constant,  Q  =  area  of  elevator  and 
.1C 

stabilizer,  L  =  overall   length,  A  =  area  of  wings  and  C  = 
mean  chord. 

The  following  constants  hold  for  our  five  well  controlled 
machines : 


Standard 

ri-3 

.429 


Curtiss 
R-4 
.625 


Wright-Martin 
.607 


Sturtevant 

S 
.416 


\Vriclit-Mnriin 

i: 
.661 


These  constants  are  fairly  close  together,  with  an  average 
value  of  .507.  A  big  value  of  d  means  powerful  control. 
Without  further  analysis,  it  is  seen  from  Table  1  that  the 
stabilizer  is  made  between  20  to  50  per  cent  larger  than  the 
elevator. 

(m)   Similarly  for  vertical  surfaces,  if  /  =-r^»  where  f  = 

A& 

constant,  V  —  vertical  area  of  rudder  and  fin,  L  =  length, 
A  =  area  of  wings  and  s  =  mean  span  of  wings,  we  find 


standard 
H-3 
.019 


Curtiss 
H-4 
.031 


Wright-Martin 
V 


sturtcvaiit 

S 

.01.-, 
Average  value,  .023. 


Wright-Martin 
.082 


We  shall  discuss  the  problem  of  vertical  fin  and  rudder  area 
more  closely  later. 

Primary   ami   Advanced  Training   Airplanes 

In  the  training  of  military  pilots  similar  methods  are  now 
employed  in  the  majority  of  schools,  and  there  are  two  distinct 
stages,  "  primary  "  and  "  advanced  "  training. 

On  the  primary  machine,  the  aviator  obtains  his  first  certifi- 
c.-ite.  and  the  requirements  of  this  type  tend  toward  a  steady, 
slow  type  of  machine,  in  which  it  is  easy  to  acquire  confidence. 
The  advanced  training  machine  is  scarcely  distinguishable 
from  the  land  reconnaissance  machine,  although  it  is  somewhat 
slower.  In  the  memorandum  on  Military  Airplanes,  the  fol- 
lowing suggestions  arc  made  for  these  two  types,  which  are 
of  obvious  and  permanent  utility. 

TAl'.u:  :;. 

Land  Adviitu  .  <1  S,-lnr>l,  may 
l/iinil  Primary  School,  can    possibly  be  used  for 


also  he  used  for  tielii 
artillery  flre  control 

Horsepower    M» 

I'u-li.  r   or  tractor Trie  tor 

Number  of  riH'ii '2 

Military  loail,  pnun.ls :IT". 

Fuel  load,   pounds 150 

Miles  radius  (f  netinn.  full  power..    l:i.~> 

Climb,  foet  in  in  minutes 2.000 

llitfli  speed,  miles  per  hour Ort 

l/ow  speed,   miles  per  hour 37 

r    (if    safety T.'i 

Pcrcentace  mnde   In   war 2.1 


mountain  and  forest 
tactical  recomiai 

100 
Tra<  tor 

•-• 

40(1 

240 

:too 

8,000 

Tl 

43 

7.5 
M 


In  dcsignm-:  training  machines,  tin-  constructor  has  the  ad- 
\. -intake  of  complete  specifications  issued  by  the  Signal  Corps 
I  Aeronautical  Specifications.  Nos.  1001  and  1002).  These 
specifications  are  readily  obtainable,  but  some  of  the  main 
points  are  set  forth  here,  as  they  will  he  applicable  to  our 
design  of  a  standard  machine,  and  must  lie  constantly  kept  in 
mind  by  the  designer. 


AIRPLANE    DESIGN 


MODERN  AMERICAN  TWO-PLACE  TRACTORS 

These    Photographs    Show    Representative    Two-Seater    Tractor    Biplanes    of    the    Unarmed 
Reconnaissance    Type,    Weighing    Over    2,500    Pounds 


THK  WRIGHT-MARTIN.  MODEL  R.  TRACTOR 


STURTEVANT  S  TRACTOR 


MODEL   V.    WRIGHT-MARTIN   TRACTOR 


THE  STANDARD.  MODEL  H-S.  TRACTOR 


THE  CURTISS  R-4  MILITARY  TRACTOR 


80 


AIRPLANE    DESIGN 


IMPORTANT  POINTS  IN  SPECIFICATIONS  NOS.  1001  AND 
1002  FOR  MILITARY  TRAINING  AIRPLANES 


I 


Advanced 


Primary 
1.  Tractor  biplane,  useful  load 

(a)  Pilot  nud  passenger. 
330  pounds. 
Three  hours 

(b)  Gasolene,    oil    an  •; 
water. 

1>.  Curtiss  eight-cylinder,  OX-2,  90  horsepower  at  1400  revo- 
lutions per  minute,  or  an  approved  American  made  engine  be- 
tween 70  and  90  horsepower,  for  the  primary,  and  between  00 
and  110  horsepower  for  the  advanced. 


(a)  Pilot  mid  passenger. 
330  pounds. 

Four  hours 

(b)  Gasolene,    oil    and 
water. 


."..   Minimum  speed,  37  miles 

I>er  hour. 

Maximum  speed,  not  less 
than  66  miles  per  hour. 


Minimum  speed,  43  miles  per 

hour. 
Maximum  speed,  not  less  than 

75  miles  per  hour. 

4.  Fully  loaded   machine  must  attain  an  altitude   of  10.000 
feet  in  1 

Two  hours.  To  minutes. 

5.  Climb  in  10  minutes  shall  be  not  less  than 

2600  feet.  |  3000  feet. 

6.  Celerity  of  response  to  control,  the  proper  degree  of  sym- 
metric and  assymmetric  stability  (static  and  dynamic)  ;  steadi- 
ness in  disturbed  air,  etc.     Satisfactory  inanoeuvering  on  the 
ground. 

7.  Both  the  dual  Curtiss  (shoulder  or  chest  yoke)  and  dual 
Deperdussln  types  of  control  ready  for  installation  in  cockpits. 

8.  Factors  of  safety. 

(a)  Main  plane  structure.    Conditions  assumed  : 

(1)  Load  as  above. 

(2)  Angle  of  incidence  of  mean  chord  of  main  planes  : 
that  of  maximum  lift  coefficient. 

(3)  Air  speed  :   that  normally  corresponding  to  the 
above  load,  and  angle  of  incidence  for  the  net 
effective  surface  area. 

Factor  of  safety  not  less  than  7.5. 
(It)   Body  and  tail  structure. 

(1)  Air  speed,  100  miles  per  hour. 

(2)  Angle  of  incidence  of  fixed  horizontal   tail   sur- 
face,  minus   0   degrees;   elevator  surface   minus 
20  degrees. 

Factor  of  safety  not  less  than  2.5. 

9.  A  complete  outfit  of  instruments,  tools,  pressure  gauges. 
etc.,  is  specified. 


Lauding  gear  of  two-wheel 
type.  Wheels,  26  x  4  inch 
tires,  and  6  x  I1/!)  inch  hubs. 


10.  Three-wheel    type    land- 
ing gear,  the  third  wheel  be- 
ing 20  x  4  inches,  just  in  rear 
of   the   plane  of   rotation   of 
the    propeller;    normally    not 
touching  the  ground,   but  de- 
signed  to    touch    the   ground 
when  the  mean  chord  of  the 
main     planes     is     horizontal. 
Mil  in    wheels,    26    x    4    inch 
tires,  and  6x1%  Inch  hubs. 
with  spokes. 

11.  Hody  shall  be  of  one  part,  not  the  jointed  tail  type.    All 
nirnbuckles  in   the  body   wiring  to  be  readily  accessible.     In 
ihr  •-i'le  wiring  they  should  be  near  the  upper  longerons.     The 
wini:  spar  fittings  on  the  body  to  which  the  lower  planes  are 
attached    shall    be    tied    together    across    through    Hie    body    by 
M'-el  tubing.     The  interior  of  the  body  shall  bo  so  constructed 
n-  in   permit    thorough   inspection  of  :iil   wiring,   control    lend-.. 
.•tc.     As  far  as  praelieable  .-ill   leads  shall   be  direct. 

]•_'.  The  design  and  monnliiiL'  of  the  tail  skid  and  vertical 
rudder  sbiill  be  such  us  to  prevent  injury  to  Hie  verlicjil  rudder 
in  case  of  failure  of  the  tall  skid. 

I."?.  The  number  of  different  sixes  of  tiirnbuckles  shall  be  n- 
di|ee,|  to  the  minimum.  Pulleys,  pins,  bolls,  ninibin-kles.  Bt< 


drilled  for  safety  ing.     Safety  wire  shall  be  of  No.  is  gage  cop 
per  wire. 

14.  Satisfactory  fields  of  vision. 

15.  Seats  in  tandem,  padded  cockpits,  safety  belts. 

16.  Housing  around  power  plant  readily  detachable.     Con- 
venient access  to  all  parts  of  the  engine  which  may  require  ad- 
justment or  inspection. 

17.  Radiator  proof  against  vibration. 

IS.  Gravity  feed  throughout  preferred.  A  positive  and  reli- 
able system  of  pumping  may  be  used;  in  which  case  a  gravity 
feed  tank  holding  at  least  forty  minutes  supply  to  be  embodied. 

19.  Upper  plane  to  extend  beyond  the  lower  plane  laterally 
by  an  amount  approximately  equal  to  the  chord.     Lateral  con- 
trol to  be  by  means  of  trailing  edge  flaps  on  the  upper  plane 
only. 

20.  Stranded  steel  cable  shall  be  used  for  all  tension  mem- 
bers which  are  readily  accessible  for  adjustment  and  for  all 
control   leads.     Structural  tension  members  shall   be  of  hard 
cable,  and  control  leads  shall  be  used  for  terminals  of  hard, 
single-strand  wire.    No  spliced  terminals  in  hard  cable  will  be 
accepted.     All   cables  which   are  members  of  the  wing  struc- 
ture and  normally  under  tensile  load  in  flight  shall  be  in  du- 
plicate and  made  independent  between  fittings.     Satisfactory 
provision   for  convenient  and  thorough   inspection  of  control 
cables  and  pulleys  and  vital  structural  members.     In  the  in- 
ternal   wing  bracing,    the  compression    members   carrying  the 
drag  of  the  wings  shall   be  separate  wooden   struts  and   not 
wing  ribs.     Rib  webs  shall  be  reinforced  between  lightening 
holes  to  strengthen  them  in  longitudinal  shear. 

The  above  specification  not  only  provides  an  excellent  guide 
for  the  design  of  the  school  machine,  but  is  also  a  guide  to  the 
.  performance  which  may  be  expected  of  this  type.  A  machine 
might  be  perfectly  acceptable,  however,  even  if  it  did  not 
adhere  rigidly  to  the  above  specification,  provided  its  main 
requirements  were  successfully  carried  out.  Particularly  is 
this  true  as  regards  the  engine  power. 

Data  for  a  Typical  School  Machine  Less  Than 
2000  Pounds  in  Weight 

The  Curtiss  JN4-B,  for  which  full  data  is  supplied  by  the 
manufacturer  is  a  good  example  of  this  type,  and  in  default 
of  a  classification  such  as  that  of  Table  '_'.  should  prove  a  reli- 
able guide  in  preliminary  design. 

CURTISS    .IN    1  i: 

Engine,  Curtiss  OX;  horsepower.  '.MI;  cylinders.  S;  revolu- 
tions per  minutes,  1400;  weight  per  rated  horsepower.  4.02 
pounds:  bore  and  stroke,  4x5  inches;  fuel  consumption  per 
hour,  '.)  gallons;  fuel  tank  capacity,  20  gallons;  oil  capacity,  4 
gallons;  fuel  consumption  per  brake  horsepower  per  hour.  0.60 
pounds:  oil  consumption  per  brake  horsepower  per  hour.  0.030 
pounds. 

Maximum  speed,  75  miles  per  hour:  minimum  speed.  4.'!  miles 
per  hour;  climbing  speed,  3000  feet  in  10  minutes. 

Net  weight,  machine,  empty,  1320  pounds:  gross  weight  of 
machine  and  useful  load  (fuel  for  4.16  hours),  1905  pounds; 
distributed  us  follows:  225  pounds  fuel.  30  pounds  oil.  1(15 
pounds  pilot.  165  pounds  passenger.  Total.  5*5  pounds.  Per- 
centage  useful  load,  30.7  per  cent. 

Total  support  ing  surface.  :;:.i;.7  square  feet  :  loading  per  brake 
horsepower.  21.16  pounds:  loading  per  square  foot  of  support- 
ing surface.  ."..".  pounds. 

Win-  section.  Eiffel.  ::ii:  upper  span.  I.",  feet  7%  inches; 
upper  chord.  4  feel  II'...  indies:  lower  span.  33  feet  11% 
inches:  lower  chord.  I  feet  11 'j  inches;  gap.  5  feet  2  3-16 
inches:  o\crall  length  of  machine.  'J7  feet  3  inches;  overall 
height.  '.»  feet  lo'..  inches;  ratio  of  mean  span  to  overall 
lenu'ih.  l.t::. 

liihcdral.  2'L-  degrees;  swcepback.  .(I  degrees;  stagger,  12  5-16 
inches. 

Control  surfaces.— Ailerons   (upper  wingl.  35.2s  square  led 


AIRPLANE     DESIGN 


81 


Constant  in  formula  (S,  a,  +  S.  a.)  =  CA.  C  =  4.3.    Horizon-      developed  in  our  design  in  subsequent  sections,  and  drawings 
tal  stabilizer  28.7  square  feet ;  elevator  22.0  square  feet.    Con-      of  one  or  two  representative  machines  will  precede  this  design. 

In  the  ensuing  chapter,  we  shall  study  the  pursuit  type,  the 
Twin  Engine  Machine,  and  the  armed  reconnaissance  type. 


QL 


stant  in  formula,  d=^-d  =  .766.  Rudder  12.00  square 
feet;  Vertical  fin  3.80  square  feet.  Constant  in  formula, 
/=  -|g-,  /  =  .029. 


References  for  Part  II,  Chapter  1 


Photographs  and  Drawings 

Considerations   of  space   do  not  permit   inclusions   of  draw-  "Memorandum  on  Military  Airplanes,"  Prepared"  in  the  office  of  tbe 

f  ,v                            mi                                           u   i  Officer  in  Charge  of  the  Aviation  Section.  Signal  Corns.  U.  S    A      AVIA- 

mgs  ot  these  types,     ihe  accompanying  photographs  are  rep-  TION  AND  AERONAUTICAL  ENGINEERING,  September  lo    1910 

resentative.    Details  of  construction  and  drawings  will  be  fully  6.Jo^er0naUtiCR'"  by  J'  '  '  I1IinHttker-  in  the  *«*««<«"  Engineer  Han,,- 


83 


AIRPLANE    DESIGN 


EXAMPLES  OF  PURSUIT  TYPE  AIRPLANES 


GERMAN  AI.HATHOSS  OK  UMIi 


Tin:  Cri;Ti«  TIMIM.  \\ :i 


Photo.   Irum  I'mlrrtrimtl  ami  I'mli  nr<,<«l 


\   N'iKi  IMIKT  FrHsriT  MAI  HINK 


EXAMPLES  OF  GERMAN  ARMED  BIPLANES 


Aw  L.  V.  0.  OP  1916 


AN  AVIATIK  GUN-CARRIEK 


Chapter  II 

Land  Pursuit  Machine 

Land  Gun  Carrying  Machine 

Twin  Engined  All  'Round  Machine 


The  High  Speed  Scout  or  Land  Pursuit  Type 

The  high  speed  scout  or  pursuit  type  has  in  the  present  war 
assumed  a  very  great  importance.  In  the  War  Department 
memorandum  on  "  Military  Airplanes,"  its  functions  are  well 
defined : 

"  By  virtue  of  its  tremendous  speed  and  climbing  ability,  it 
can  dodge  and  outmaneuver  its  larger  enemy,  maintaining 
an  effective  fire  with  its  machine  gun,  at  the  same  time  pre- 
senting a  small  and  bewildering  target.  This  is  an  ideal  ma- 
chine for  tactical  reconnaissance.  It  can  even  drop  a  few 
bombs  where  they  will  do  most  good." 

The  United  States  Army  memorandum  gives  the  following 
figures  pertaining  to  this  type: 

TABLE  1. 
LAND  PURSUIT  TYPE. 

Horsepower 110 

Type    '. Tractor 

Number  of  men 1 

Military  load,  pounds 200 

Fuel  load,  pounds 1  f>i  i 

Miles,  radius  of  action,  full  power 

Climb,  feot  in  10  minutes 

High  speed,  miles  per  hour 

Low  speed,  miles  per  hour 

Factor  of  safety 

Percentage  demand  in  war 


Sir, 
3000 
116 
43 

7.5 
21.0 

Very  few  machines  of  this  type  have  been  built  in  America. 
Abroad  such  machines  have  been  used  in  great  numbers,  but 
little  information  is  available  for  recent  French  and  English 
types,  such  as  the  Nieuport,  Morane,  Vickers,  Bristol,  Sop- 
with,  etc.,  with  light  rotary  engines  of  between  80  and  130 
horsepower.  Lately  very  light  and  more  powerful  150  horse- 
power V-type  Hispano-Suiza  engines  have  been  employed  in 
great  numbers. 

We  may  say  that  an  average  of  120  horsepower  is  used  in 
this  type,  that  it  is  a  single  seater  machine,  almost  always  a 
biplane  with  the  smallest  possible  wing  spread,  a  tractor  with 
a  light  machine  gun  firing  either  through  the  propeller  or 
above  the  wings. 

English  opinion  based  on  experience  in  the  war  supports 
an  inherently  stable  machine  which  the  pilot  can  leave  uncon- 
trolled for  a  short  period  while  engaged  in  combat  or  other 
functions.  To  obtain  inherent  stability  in  this  type  is  a  diffi- 
cult problem.  The  high  loading  per  square  foot  of  area  is  not 
conducive  to ,  stability,  and  the  employment  of  correct  fin 
areas  and  dihedrals  is  still  a  problem.  The  high  loading  also 
introduces  difficulties  from  the  point  of  view  of  stresses  in 
the  wing  structure.  Nothing  lower  than  7  pounds  per  square 
foot  of  wing  area  seems  possible. 

With  the  production  in  the  United  States  of  such  engines 
as  the  General  Vehicle  Company's  Gnome  and  the  Hispano- 
Suiza,  there  is  to  be  expected  a  very  rapid  increase  in  the 


number  of  American  speed  scouts.  These  light  and  powerful 
engines  will  enable  the  weight  per  horsepower  to  be  diminished 
and  the  speed  and  climb  to  be  increased  until  European  prac- 
tice is  equaled. 

Data  for  Pursuit  Type,  100  Horsepower  Engine 

In  Table  2  some  data  has  been  collected  bearing  upon  some 
ol:  these  types.  Little  detailed  information  is  available,  but 
these  figures  and  illustrations  should  be  sufficient  to  give  a 
general  idea  of  present  development. 

TABLE  2. 
DATA  FOR  HIOH-SPEED  PURSUIT  MACHINKS. 


Model  

Nieuport 

S.P.A.D. 

Bleriot 

Curt  IMS 

150  h.p. 

150  h.p. 

triplane 

Kn^ine  

80  h.p. 

Hispano- 

Hispano- 

OXX-2 

Le  Rhone 

Suiza 

Suiza 

100    h.p. 

Xuinber  of  men  

1 

1 

1 

Endurance  at  full  speed  (hours. 

2'A  to  3 

214  to  3 

Maximum  speed   (miles  per 

hour)  

125 

125 

120 

Minimum  speed   (miles  per 

hour)   .   . 

56 

Climb  in  10  minutes  (feet)  .... 
Climb  to  3,200  feet  (minutes) 
Climb  to  6,400  feet  (minutes) 

6,000-7,000 

9,200 
3 
6 

9,200 
3 
6 

10,000 

(  'limb  to  9,600  feet  (minutes) 

10)4 

W% 

Total  weight  (pounds)  

1,218 

Useful  load  

460 

460 

I'ounds  per  horsepower.  .  .  . 

12.18 

Area  wings  (square  feet)..  .  . 

185 

185 

143 

Wing    loading    (pounds    per 

square  foot)  .  .    . 

8.5 

Wing  area  per  brake  horse- 

power (square  feeO  

1.23 

1.23 

1.43 

Span  top  plane  

24'  6" 

25'  20" 

all  three  planes 

Chord  top  plane  

:f  11" 

2'0" 

Aspect  'Ratio  top  pi-mo  

6.15 

all  three  planes 
125 

Span  bottom  plane'  

23'  0" 

all  three  planes 

Chord  bottom  plane  

2'  4" 

Aspect  ratio  bottom  plane.  .  . 

9.9 

Data  for  More  Powerful  Pursuit  Types 

So  rapid  is  the  deye'ppment  of  the  foreign  military  air- 
planes that  it  would  seem  as  if  the  speed  scout  fitted  with  a 
rotary  engine  of  about  100  horsepower,  is  now  being  displaced 
by  a  more  powerful  type. 

It  is  interesting  to  note  that  in  the  S.  P.  A.  D.  and  Bleriot 
type*  the  climb  does  not  apparently  fall  off  with  altitude, 
showing  probably  that  the  difficulties  of  maintaining  the 
power  of  the  engine  at  high  altitudes  have  been  successfully 
met. 

Trend  of  Design  in  the  Pursuit  Type 

Among  the  salient  features  of  this  type  is  the  very  small 
weight  per  horsepower,  12  pounds  or  thereabouts,  as  compared 


M 


AIRPLANE    DESIGN 


with  tin-  18  or  20  of  the  large  reconnaissance  type.  There  is 
a  tendency  t<>  employ  large  aspect  ratios— the  small  weight 
per  horsepower  and  small  wing  surface  permitting  the  chord 
r.,  he  cut  down  considerably.  Thus  we  find  in  the  Nieuport 
aspect  ratios  of  6.15  and  9.9;  in  the  Curtiss  triplane  12.5  on 
nil  the  planes.  In  the  triplane  the  extraordinary  aspect  ratio 
•  •I1  1  •_'..">  is  rendered  possible  by  the  distribution  of  the  carry- 
ing Mirface  among  three  planes  instead  of  two.  Stream-lining 
to  the  very  limit  is  another  feature. 

Hitherto  (ierman  constructors  do  not  appear  to  have  sought 
the  reduction  of  head  resistance  to  any  great  extent,  but  the 
new  AII.Mli-o--  shows  a  beautiful  body,  struts  reduced  to  a 
minimum,  and  the  stream-lining  carried  to  the  extent  of  a 
hemispherical  nose-pieee  over  the  propeller  boss.  In  the  Nieu- 
|iort  scout  the  Y  strut  system  "jives  both  lightness  of  construc- 
tion ami  aerodynamic  efficiency.  The  wonderful  improvement 
of  the  Curtiss  triplane  with  no  larger  power,  as  compared  with 
its  predecessor,  the  "  Baby"  scout,  is  due  in  part  to  the  large 
aspect  ratio  which  counterbalances  the  inefficiency  of  the  tri- 
pliine.  lint  more  to  the  clever  K  strut  construction  with  the  two 
tubular  struts  stream-lined  in,  and  the  stream-lined  chassis 
construction.  Such  valuable  yet  simple  ideas  in  the  design  of 
this  type  are  well  worth  attention. 

German  practice  in  every  respect  seems  to  be  following 
I'Yench  practice  very  closely  tor  this  type.  Recent  information 
at  hand  shows  that  the  small  biplane,  such  as  the  Albatross 
just  mentioned  and  the  new  Fokker  biplane  are  being  built  in 
great  numbers.  The  Fokker  biplane  has  apparently  super- 
seded the  monoplane. 

Guns  on  the  Pursuit  Type 

However  stable  a  machine  may  be,  and  even  if  it  is  equipped 
with  a  stabilizer  or  automatic  pilot,  it  seems  impossible  that 
a  pilot  should  at  the  same  time  be  a  gunner  capable  of  firing 
in  all  directions.  The  light  machine  guns  which  are  employed, 
are  probably  fired  straight  ahead  towards  the  enemy  machine 
which  the  pilot  is  approaching.  They  may  be 

(1)  fired  thromjh  the  propeller,  which  is  suitably  protected 

for  rtrlleetinji  stray  bullets. 

CM  tired  through  the  propeller  with  a  suitable  synchroniz- 
ing mechanism  as  on  the  Fokker  (see  appended  refer 
once i . 

C'.p  placed  al.ove  (lie  wing  within  reach  of  the  pilot  as  on 
the  \ieii|Mirl. 

Land  Gun  Carrying  Machines 

l-'..r  the  land  gun-carrying  type  of  airplane  the  War  De- 
partmeni  memorandum  specifies: 


TABL 

i 

Number  or   ni'-n 

Military   liu.il.    |i" 

Km  I   l< .. 

Th  n.   full   • 

I.IT  liour 

Kn-tor  of  Mnfr-ty 

I  In  war.  . 


180 

Tractor 


BOO 

1-j:. 


77 


I   . 


ntured  with  regard  to  the  menu. 

randum.  it  is  on  tli-  :•">  implicit  faith  in  the  all  round 

Iwin-ciiL'ined   machine,  and   iieiMc.-t    ..I    the   importance   of  the 
Riin-carryin";  machine  of  thi-  type.     Most  of  our  information 
as  tn  tin-  t\pi-  c..iiie-   from  the  splendid  description-  of  cap 
lured   (termini    machines   in   /.'.!»' r»/<//i'/' .      The   Hermans   have 
.•led    in    providing   this    t\pc    with    one   or   two    marhine 


guns,  with  a  good  range  of  fire  and  arrangements  for  throw- 
ing bombs,  and  yet  with  excellent  performance. 

TABLE  4. 

DATA  FOR  GERMAN  TWO-SEATER  GCM-CAHRTINI;   MVHIM 
(From  L' Atraphilt). 


Rumpler  1916 

Aviatik   1'Mi. 

1916 

'.:  •  -  .     I7ii 

Mrrrpili';*  165- 

horsepower 

horsepower 

170     hors«i> 

Maximum  speed  on  ground. 

92 

93 

•  :. 

Minimum  speed  on  ground. 

49.5 

Speed     at      1,000     meters, 

84 

87 

Speed     at     2,000     meters. 

85 

82 

81 

at     3,000     meters, 

81.5 

u 

dim!.,  in  feet  per  minute..  . 

3,200  in  10 
6.400  in  16 
9,600  in  '.".I 

1,600  io     r 

:!,i;iHiin    •..-.. 

6,400  in  '2  1  '  -j 
9,600  i 

3.201! 

Maximum      altitude      fully 
loaded,  feet  

14,800 

11,200 

10,000 

Endurance,     fully     loaded, 

hours  

4 

4M 

4H 

2,780 

1340 

!  MO 

1,830 

1,860 

HO 

980 

980 

Percentage  useful  load  

:>!.•_", 

34.4% 

34 

580 

:,.-,ii 

-,  -..  i 

Loading    per    brake    horse- 
power, pounds  

16.8 

lli.7 

Loading  per  square  foot  of 

7.35 

6.6 

7.1 

25.2 

Total  wine  area,  square  feet 

378 

39.2 

40.68 

1 

Chord    feet 

5.4 

6.1 

35.4 

35.4 

36.4 

5.4 

6.1 

Gap    feet            

G.H 

27.8 

22 

.SIM!  ili/cr-iicii,  square  feet. 

35.4 

35.2 

—  1.36° 

—  1° 

>r  area,  square  feet 

18.2 

I 

..1    fin,    square 

4> 

7.25 

i 

DiliKlr.il   (if  willyy  

2' 

•  :'  wings  to  l» 

&• 

4.5' 

Ala 

-      •  • 

None 

Pilot 

t    i    r    i    n 
t  h  i  •  • 

-   LMT       i 

rear  ^ 
<lr..|i|.in«  '!' 

In  i, 
ttir.  •-• 
in      1 

hin 

all  <ir 

culnr  i 

for 
Her,           UK 

In  Table  4  some  useful  data  has  been  collected,  and  photo- 
graphs of  (he  Aviatik  and  L.  V.  (!.  shown  herewith,  are  good 
examples  of  this  type.  lieeent  development  in  America  has 
sho«n  the  necessity  of  slandardi/.cd  te.-ts  al  \ai'i..us  altitude- 
nnd  it  is  interestinc  to  note  that  Inures  are  Ki\,-,\  for  spe.  d 


AIRPLANE    DESIGN 


85 


the  ground  and  at  various  standard  altitudes;  while  maximum 
altitude,  or  "  plafond,"  as  the  French  term  it,  is  also  specified. 

These  German  machines,  as  regards  climb,  are  on  a  par 
with  the  American  unarmed  reconnaissance  machines.  They 
appear  to  be  much  superior  in  maximum  speed.  Their  per- 
centage of  useful  load  is  greater.  By  careful  construction  and 
probably  with  a  lower  factor  of  safety,  they  actually  have  a 
lower  loading  per  brake-horsepower,  even  when  carrying  two 
machine  guns,  the  ammunition  required,  and  bombs  and  bomb- 
ing devices.  This  indicates  how  much  room  there  still  is  for 
improvement  in  American  machines  as  regards  weight  saving. 

They  are  short  machines,  with  large  stabilizing  planes,  but 
comparatively  small  control  surfaces.  The  wings  are  very 


FIG.  1.    AVIATIK  WING  SECTION 

heavily  cambered,  as  shown  in  Fig.  1,  yet  look  as  if  they  were 
efficient,  and  deserve  careful  study.  They  appear  to  be  an 
improvement  on  the  wing  sections  commonly  employed.  The 
wings  also  appear  to  be  set  at  large  angles  to  the  body,  so  that 
the  propeller  axis  is  coincident  with  the  line  of  flight  at  nor- 
mal angle  of  incidence,  and  at  a  small  angle  to  the  line  of 
flight  in  climb. 

Their  design  is  characterized  by  a  robust  lightness  due  to 
careful  utilization  of  material  throughout,  and  probably  a  uni- 
form factor  of  safety. 

The  Mercedes  engine  so  largely  employed  on  German  air- 
planes has  the  reputation  of  being  extremely  reliable  and  effi- 
cient, but  is  considerably  heavier  per  brake-horsepower  than 
American  engines  of  about  the  same  power,  an  important 
fact  to  be  considered  when  the  American  designer  sets  out  to 
equal  the  German  machine. 

Twiii-Engined  Machines 

The  memorandum  prepared  in  the  office  of  the  officer  in 
cliarge  of  the  Aviation  Section,  Signal  Corps,  U.  S.  A.,  gives 
very  interesting  data  on  twin-engined  seaplanes,  reproduced 
in  Table  5  herewith.  It  lays  strong  stress  on  the  advantages 
of  this  type,  partly  on  the  ground  that  a  thoroughly  developed 
engine  of  over  200  horsepower  had  not  yet  been  constructed; 
but  since  that  time  progress  has  been  made  and  the  300  horse- 
power engine  is  becoming  a  practical  possibility.  Stress  is 
laid  on  the  versatility  of  the  twin-engined  machine.  In  a  land 
twin-engined  machine,  with  the  engines  supported  on  the 
wings,  and  a  central  body,  it  is  suggested  that  the  pilot  with 
his  controls  could  be  placed  in  the  rear  cockpit  in  rear  of  the 
propellers ;  the  observer  with  his  machine  gun,  in  the  forward 
cockpit  forward  of  the  propellers ;  and  the  bombs  and  gasoline 
between  the  pilot  and  observer,  near  the  center  of  gravity  of 
the  complete  system.  With  such  an  arrangement,  the  observer 
would  have  an  ideal  field  for  observation  and  for  gun  fire; 
with  a  stabilizer  the  pilot  could  fight  the  machine  to  the  rear, 
and  the  machine  would  be  an  excellent  fighting  airplane  as  well 
as  a  bomber.  By  decreasing  the  bomb  weight,  the  radius  could 
be  increased  to  a  very  long  range.  A  third  man  could  be  in- 
stalled in  between  the  front  and  rear  cockpits  by  making  slight 
alterations  in  the  construction  of  the  body.  If  the  third  man 
had  charge  of  the  controls,  there  would  be  an  even  better  fight- 
ing machine.  If  neither  bombs  nor  a  third  man  were  carried, 
the  landing  wheels  could  be  replaced  by  two  or  three  pontoons, 
giving  a  military  seaplane. 


TABLE  5. 

Horsepower   260 

Type   Pusher  or  tractor 

Number  of  men 2 

Military  load,  pounds n50  to  1100 

Fuel  load,   pounds 600  to  1150 

Miles  radius  of  action,  full  power 450  to  600 

Climb,  feet  in  10  minutes 3400 

High  speed,  miles  per  bour 90 

F»\v  speed,  miles  per  hour 47 

Factor  of  safety 7.0 

Percentage  made  in  war 4 

A  further  evident  advantage  of  this  type  is  that  it  could  be 
flown  with  one  engine  out  of  commission.  The  propeller 
would  not  be  required  to  take  the  great  power  of  a  300  horse- 
power engine.  Although  the  support  of  the  engine  on  the 
wing  presents  considerable  difficulties,  yet  this  arrangement 
might  react  favorably  on  the  weight  of  the  wing  structure 
by  distributing  the  load,  and  therefore  giving  less  bending 
moment  to  the  inner  wing  panels. 

If  a  single  engine  of  250  or  300  horsepower  were  used,  the 
same  military  and  useful  loads  would  be  available.  With  a 
single  body  the  parasite  resistance  would  probably  be  dimin- 
ished. But  the  difficulties  of  constructing  such  a  machine  for 
fighting  as  well  as  bombing  purposes  would  be  very  consid- 
erable. With  the  engine  in  front,  it  might  be  possible  for  the 
pilot  to  sit  in  the  forward  cockpit  and  shoot  through  the  pro- 
peller, while  in  the  rear  the  observer  could  operate  a  machine 
gun  in  all  directions.  If  bombs  and  bombing  apparatus  were 
included  in  the  single  body,  there  would  be  an  extremely  diffi- 
cult construction  problem.  If  the  high-powered  machine  were 
made  a  pusher,  the  rear  occupant  would  be  under  difficulties 
as  a  machine-gun  operator.  The  other  possible  alternative 
would  be  to  place  the  observer  in  a  cockpit  forward  of  the 
propeller — which  would  revolve  round  the  body — the  engine 
behind  the  propeller,  then  the  pilot  in  the  rear  seat.  None  of 
these  arrangements  seem  to  have  the  straight  forwardness  and 
simplicity  of  the  twin  engined  type. 

It  would  seem,  therefore,  that  in  spite  of  the  development 
of  a  reliable  300  horsepower  engine,  the  twin-engined  machine 
would  have  much  to  recommend  it. 

The  following  points  may  be  disadvantages  of  the  twin- 
engined  machine,  or  merely  problems  which  careful  design  can 
overcome : 

(1)  There  are  difficulties  in  preliminary  design.  In  the 
school  machines,  the  armed  and  unarmed  reconnaissance  types, 
and  in  the  speed  scout,  we  have  data  to  draw  upon  from  which 
loading  per  square  foot  of  wing  area,  loading  per  brake-horse- 
power, useful  load,  etc.,  can  be  at  once  fixed  within  certain 
limits.  Here  we  have  an  entirely  new  problem.  Theoretical 
considerations  show  that  with  increased  span,  the  bending 
moment  and  other  stress  producing  forces  for  geometrically 
similar  machines  vary  as  the  cube  of  the  span.  The  resistance 
of  bracing  wires  would  vary  as  the  square  of  tlie  span.  The 
section  modulus  of  the  wing  spars  would  vary  as  the  span 
cubed,  but  their  area,  resisting  direct  tension  or  compression 
would  only  vary  as  the  square  of  the  span.  Similar  considera- 
tions would  follow  for  other  strength  members.  Even  if  we 
allow  the  structural  weight  advantage  of  engines  on  the  winsis 
MS  previously  mentioned,  the  conservative  designer  would  still 
I'xptrt  weights  to  go  against  him.  If  the  twin  seaplane  that 
he  is  designing  follows  the  same  outlines  of  construction  that 
In-  hiis  been  accustomed  to  in  a  single-engined  type,  he  should 
allow  for  a  slightly  heavier  loading  per  horsepower  and  a 
slightly  smaller  loading  per  square  foot  of  wing  area,  i.  e.,  a 
larger  wing  area  than  he  would,  in  the  light  of  past  experience, 
expect  to  employ.  Such  a  conservative  outlook — well  founded 
in  the  author's  opinion,  particularly  for  experimental  machines 
— would  lead  again  to  less  favorable  estimates  of  performance, 
and  avoid  the  ridiculously  optimistic  estimates  for  these  large 
machines  in  the  recent  bids.  It  is  interesting,  in  the  light  of 
these  remarks,  to  study  the  performances  submitted  in  these 


X,, 


AIRPLANE    DESIGN 


lii«U  for  seaplanes.  (AVIATION  AMI  AEKU.NAUTICAX,  ENGINEKK- 
i\t..  December  1.  1916.)  The  Curtiss  Company,  with  its  past 
1-Mx-rienee  in  the  building  of  twin-engined  machines  (Twin 
JN),  specified  n  climb  of  2.000  feet  and  a  speed  of  65  mil» 
per  hour,  although  probably  equipped  with  two  200  horsepower 
engines.  The  Wright-Martin  Corporation  was  so  conservative 
as  to  specify  no  performance.  A  great  many  optimistic  bids 
were  submitted.  The  average  climb  sent  in  appears  to  be 
3,580  feet,  the  average  maximum  speed  77  miles  i>er  hour.  One 
would  be  inclined  to  think  that  with  present  American  methods 
of  construction,  a  climb  of  2,800  feet,  and  a  maximum  speed  of 
about  6S  mile*  IMT  hour  would  be  as  much  as  could  possibly 
be  expected. 

(2)  Control  surfaces  ;md  stability  furnish  interesting  prob- 
lems.   The  effect  of  placing  the  engines  out  on  the  winsrs  is  to 
increase  the  moment  of  inertia  in  roll,  and  it  is  very  difficult 
to  say  what  effect  this  will  have  on  inherent  lateral  stability. 
It  is  certain  that  the  aileron  area  required  will  be  somewhat 
greater  than  that  in  a  machine  where  the  engine  is  at  the  cen- 
ter of  gravity  and  that   the  machine  will  be  slow  to  respond 
to  lateral  controls.    The  moment  of  inertia  in  yaws  will  simi- 
larly be  increased  so  that  rudder  and  vertical  fin  surfaces  may- 
have  to  be  larger  proportionately  than  on  the  usual  machine. 
These  are  points  requiring  the  most  careful  attention  in  design 

(3)  Another  problem  in  connection  with  the  twin-engined 
machine  is  that  of  propeller  slip  from  the  two  screws,  both 
turning  inwards.     This  symmetrical  arrangement  is  prescribed 
by  the  Army  specifications  as  avoiding  torque  and  gyroscopic 
effects.     The  down   stream  from   the  propellers  impinging  on 
the  stabilizer  is  said  to  increase  the  safety  from  the  point  of 
view  of  longitudinal  balance,  giving  tail  heaviness  with  power. 


and  nose  heaviness  without  power.    The  exact  effects  are,  how- 
ever, still  open  to  experimentation. 

Space  forbids  a  discussion  of  numerous  other  points  which 
this  type  presents.  The  appended  references  will  give  the 
reader  some  information.  The  German  twin-hydro  reproduced 
iii  AVIATION  AND  AERONAUTICAL  ENGINEERING.  September  lf>. 
1916,  is  of  particularly  neat  construction,  the  specification 
No.  1002  is  almost  a  text-book  on  design,  and  the  S.  A.  E.  pa- 
per on  twin-engined  machines  read  by  Lieut.  Col.  V.  K.  (lark. 
U.  S.  A.,  touches  on  a  greater  number  of  points  than  we  are 
in  a  position  to  deal  with.  Anyone  setting  out  to  construct 
such  a  type  would  do  well  to  devote  considerable  time  to  wind 
tunnel  experimentation,  computation  of  moments  of  inertia. 
etc. 


References  for  Part  II,  Chapter  2 

"OUlf-CARRYlXG    TWO-SEATER    MACHINES." 

•  Itumpler,"  L'AfropMle,  Dcccuilier.  t!U6. 

". \\ialik."   L'AfropMle,  October,    liilii 

"  L.  V.  O.,"  L'Afrophilr.   Nnveml  .  r.    ]:>:>; 

"  Other  German  liaehii"1*."  /."  \nophile,  March.  I'.HI. 

PROPELLER  AND  MACHINE  QUX  SYNCHRO  M/.l  \  f/ 
UACUIKES. 

"  Fokker  Firing  Mechanism."  L'Afrophilf.  .linn-,  I'.ni, 

"  Twin-Kngined  Machines." 

L'AfropMle,  July,  lalO   (abstract  in  AVIATION  AM*  .Si.i!<>~  .  > 

ENGIKKEBINO,  Sept.  15,  I'.H-: 
"Some  Problems   in   Airplane  Construction "    (S.   A.    K.    llullrtin, 

December,  1916). 

"Army  Aeronautical  Specification  No.  1002." 
"The  Development  of  the  Milii.-irv  Aeroplane,"  by   !'.  W.  I-anches- 

ti-r.  Knyineerina.  March  ::.  191G. 


Chapter  III 

Estimates  of  Weight  Distribution 


of   flip    Siihiprt  Details  tor  upper  wings: 

Front  spar,  total  span  18'  5%"  ;  18'  8%"  length 25.0  Ib. 

Hear  spar,  total  span  18'  9%"  ;   19'  0     length 23.5  " 

Hardly  any  branch  of  practical  airplane  design  offers  such  Compression  posts  or  solid  ribs  (7) . 16.2  " 

Lightened  ribs  and  straps  (10  long,  7  short),  total 18.4  " 

difficulties  as  the  estimate  of  weights.     A  manufacturer  who  Entering  edge,  4  pieces 8.0  " 

,  .                                                „   ,         .   ,  ,  Trailing  edge,  4  pieces 3.9  " 

has  built  a  number  of  machines  and  has  kept  careful  weight  Edge  pieces  and  cross  battens 5.5  ' 

schedules  has  valuable  data  in  his  possession,  but  is,  as  a  rule,  Wire°BcSiip's  and  'turnbuckie's.'.'. ll's  " 

chary  of  making  such  data  public.    Even  an  experienced  manu-  Donpen'anddvSrnishnd  .tape  and  taeks.  ^  'tap'°g; :              !  "I  » 

fWtilvor     hnwpTTPT-     rnnv   \\o   nt    a    Incc    wVlon    VmilHintr    art    anti-rolv  Flaps     Uncovered,     total .     20.0    " 

er,  However,  may  C                                       ling  an  entirely  Flap  ninges  and'hlnge  flttlngs>  complete 1.1  •• 

new  type,  particularly  if  the  new  type  is  of  a  very  different  Om?ccoSntisdBforOpe  and  varnlsb ' '                                   '  2oo  '"' 
size  from  that  to  which  he  has  been  accustomed. 

Theoretical  considerations  apply  only  to  a  limited  extent. 

n        •   •      ,  j,                                                         ,     ,  ,                    .         ..       . . .  Kody   wing  section .    16.5  Ih. 

Empirical  formulas  have  ')een  suggested  by  several  authorities, 

but  are  only  partly  satisfactory.    The  authors'  thanks  are  due  Details  for  lower  wings : 

to  manufacturers  and  others  for  such  data  as  they  have  per-  Front  gpari  total  span  18,  5%,, .  18,  s%,,  len^n                  25-OUj. 

mission  to  publish.  ^gSt^^  £f^£j  (189,'.0.   .lengt": '.               \  Hi  '•'• 

Lightened  ribs  and  straps  (7  short,  9  long) 19.5 

Weight  Shedules  for  a  Machine  of  the  Unarmed  Tractor  Trailing  edge,'  4  pieces! '.'. '. '.  \\ .'.'..]'.'.'.'.'.'.'. '.'.'.'.'.'. '.'.'.'.'.'.     3.9 

m             ,m          ci             \    HT           rni  Edge  pieces  and  cross  battens,  hinge,  block  braces,  etc.  .          5.5  " 

Reconnaissance    lype   (iwo  beater)   More    Lhan  Fittings    ...... 1.3  " 

.-\re\i\   TI           i      •       wr    •    i  Wire,  clips  and  turnbuckles 11.8  " 

2.->(>(j  bounds    111    Weight  Linen,  undoped,  and  tape  and  tacks  for  taping 15.9  '• 

Dope  and  varnish 6.3  " 

Flaps  uncovered,  total 20.0  " 

Full  weight  data  can  be  published  for  one  of  the  tive  ma-  F'ap  binges  and  hinge  flttngs,  complete 1.1  '• 

Flap  yokes  and  yoke  fittings 3.8  " 

chines  which  have  been  examined  in  Part  2,   Section  1 — the  Flap  coverings,  dope  and  varnish 1.2  '• 

oi,       ,      -.    TT  „       „,,          ,     ,    .      ,,        ...             ,  .        .  Unaccounted  for    2."i.:;  " 

Standard  H-3.  Ihe  schedule  for  this  machine  is  very  com- 
plete, and  is  almost  exactly  in  the  form  specified  by  the  Avia- 
tion Section  of  the  Signal  Corps. 

Weight 
Weight  Area  per  sq.  ft. 

TABLE  '•  Upper   wings    178.0  Ib.         262  sq.  ft.         .680  Ib. 

Standard  H-3,  Hall-Scott  A-5,   135  h.p.     Maximum  speed  S4  m.p.h.  Body  section 

Minimum  speed  46  m.p.h.     Climb  3400  ft.     Total  wing  area,  532  sq.  ft.  Lower   wings    190.0  262  .720 

Weight  loaded,  2651.9  Ib.  (6  hours).     Weight  bare,  1908  Ib.  Tota,   wing   w(;.ght g^^ 

Body  structure  :  Percentage  of  total  weight,  14.52%. 

Details : 

Longeron,  forward  upper  right 9.0  Ib. 

Longeron,   rear  upper  right                                                     .  .      9.0  Interplane  struts,  fittings,  and  wiring:                                            107.6  Ib. 

LoSIcron'   re™  uppTleft          '                                              "90  Weight  per  square  foot  of  wiDS  arwl 203  ' 

Longeron|  forward  lower  right!  ...!.!!....!!..! 9.0  Percentage  of  total  weight,  4.06%. 

Longeron,  rear  lower  right 9.0 

;  r'e^owerTf't . ^ * ! ! ! ! ! ! ! ! ! ! '  I '.  "i ! ! !! ! ! ! ! !     S3  •'•»»  ^rfaces  :                                                                                        Weigh, 

PPo°sSttS'    t0tal"                                                                    l!i  Vertical    fin    complete,    covered    We'8ht             ^         ^  ^ "' 

Horiontal    nostV'to't'a'l' '                                                                    135  and  varnished    3.0  Ib.            5  sq.  ft.          .600  Ib. 

Fneine  beds    (two)         19  0  Vertical   rudder    9.0  "          10  ••  "           .900  " 

Enfinl  bldf  s'upportin-g  poVts : : : ! : ! ! : ! : : : : ••:. :::::::::::  Jlo  E^^to^'20111211  ta" : :        '  iii  ••     5? « "• 

Engine  plates,  total 19.0  Elevators    ^l.o 

Kadiator  supports    27.5  „  .   . 

Fittings,  total    27.5  Total 53-3  "'• 

Kivets,  bolts,  nuts,  screws,  total 7.1  Percentage  of  total,  2.0%. 

Wire  and  cable,  total  with  terminal  clips  and  thimbles,  etc.  21.1 

Turnbuckles    10.0 

Floor  of  cockpits 18.0  Control  system  : 

Tail   skids    6.0 

Body   cover   strips 7.0  Combined  Curtiss  and  Dep.  control,  with I   o«  9  u 

Front  and  rear  seats  and  supports 31.5  Control  operators  in  rear  cockpit  only / 

Cowling  and  body  cover 59.5  Control  wires,  wiring  and  switches 4.4  " 

Total 302.0  Ib.  Total 30.6  Ib. 

I'ercentacr  of  total  weight,  11  f,  Percentage  of  total  weight,  1.15%. 


Chassis : 
Details : 

Wheels  and  tires,  2  at  26"  x  5" 57.0  Ib. 

Axles    (1)    22.0 

Struts   (2)    25.0 

Axle   braces    8.5 

Axle  mounting  and  guides 12.0 

Rubber  shock   absorber 2.5 

Fittings    7.5 

Wiring  and   turnbuckles 2.5 

Fairing    1.5 

Total 138.5  Ib. 

Percentage  of  total  weight,  5.23%. 


Gasoline  and  oil : 

Gasoline  for  6  hours 396.00  Ib. 

Oil  for  6  hours 33.5     •• 


Total 429.50  Ib. 

Percentage  of  total,  16.2%. 


Tanks : 


Tanks  and  connections  and  supports   (68  gallons  fuel) . 
Percentage  of  total,  2.95%. 


78.5  Ib. 


87 


88 


AIRPLANE    DESIGN 


Engine  group : 

Kadlator,  complete*  and  con- 
nections without  watrr..  40.0  Ib. 

Engine,  complete  without 
propeller,  radiator  or  any 
water,  any  oil,  long  ex- 
haust tube  or  self-starter.558.5  " 

Water  for  radiator  piping 
and  jackets  (30  Ih.  car- 
ried in  raillntnr  alone) . . .  911.8  " 

Propeller  complete  and  bolts  27.5  " 

Long  exhaust  pipe 13.0  " 


Weight    of    radiator 

per  hp .".  1     Ib. 

Engine    weight    per 

up     4.15     " 


Water     weight     per 

hp     095  " 

Propeller  weight  per 

hp    2IC-    " 


Total 738.8  Ib. 

r.-rrcntago  of  total  weight.  27  , 

I'.i  -~cnger  and  equipment  : 

IMlot    

Passenger    


Total 

Percentage  of  total,  1  - 


1  r,.-..i>  Ih. 
H-..VO  •• 


330.0  Ib. 


Equipment : 

Instruments  iMid  Instrument  liuard.  nnd  accessories  com- 
piled for  rear  cockpit 22.7  Ib. 


Same  for  front  cockpit. 

Side  pockets,  both  sides 

Cnmsfiaft   oiler    

Speaking   tutio    

Pyrene  and  brackets  complete, 
Oil  pressure  line  and  sight  oil. 
Tool  kit  and  case  complete. . . . 


9.2 
3.0 
4.1 

2.8 

c-,.7 
1.8 

7.:: 


Total 

Percentage  of  total  weight,  2.20%. 


OS.G  Ib. 


Summary  of  Weight  Distribution  for  Standard  H-3 


(irnup  Weight 

lv  assembly  and  equipment 370.5  Ib. 

Chassis    138.5 

Wing  group    384.5 

Interplane   bracing    107.6 

Tail   surfaces    53.3 

Control  system   30.6 

Gasoline  and  oil 429.5 

Casollne  taaks  and  piping 78.5 

Knsine  group 738.8 

Passengers  and  equipment 330.0 


Percentage  of 

1'scful  Load 

18.60% 

6Jtt 

14.: 

4.i» 

s.ou 

1  1  :/  : 
10.20% 

2.9.1% 
27.70% 
12.50% 


Totals 2651.9  Ib.  100.00% 

The  Standard  figures  are  fairly  representative  for  this  type 
of  niaohim-. 

Percentage  Table  for  Machines  About  2500  Pounds 

In  Table  2  are  given  figures  compiled  by  Dr.  J.  C.  Hunsaker 
for  a  number  of  typical  machines.  The  percentage  values  seem 
to  hold  very  closely  for  machines  of  the  large  tractor  type. 


TABLE  2 
Useful  load  : 

Personnel  and  equipment 

Gasoline  and  oil,  6  hours 

Engine  weight : 

Tanks  and  pipes 

Engine  and  accessories, 

Radiator  (empty)   

Cooling  water 

Propeller  and  bub 

Structural  weights : 

Body    

Landing  carriage  

Directive  surface*  . 


Wing  bracing 


useful  load.  .     .  . 
•  nginc  weight    .    . 
structural  weight 


Per  cent 
13.1 
19.8 


3.3 
17.9 
2.2 
1.7 
1.0 


8.2 

ij 

4.1 

lft.8 

4.M 

82  :> 
M.1 
41.0 

100 


Weight  Distribution  for  a  Typical  School  Machine 

Figures  can  be  published  for  the  Curtiss  JN-4.  Data  was 
given  in  Section  1  for  the  JN-4B,  but  the  difference  between 
the  two  types  is  very  slight. 


CurtlM  JN-4.  OX  90  hp  engine.  Maximum  speed  75  inph.  Mini- 
mum speed  43  mph.  Climbing  speed  :t<>OO  ft.  In  10  min.  Total  wing 
area.  Including  wing  flaps,  367.0  iq.  ft.  Weight  lond-l.  l!i"i!.35  Ib. 


Weight  bare,  12M.:, 


4.4  hours  fuel. 


Part : 

:  v  assembly 

Tall  skid  with  rubber  ela»tlc  cor.l   .::  ft  i  . 
Cushions    


Welglit 

linn  ciOlb. 

2  7.-.   " 

3.50  " 


Total 


of  total  load.  15.60%. 


290.25  Ib. 


Chassis  : 
Details  : 

Landing  gear  braces  with  fittings  .................. 

Axle    ...................................... 

2  Aluminum  hearings  for  sbock  absorbers  and  straps. 
2  Itubbcr  shock  absorbers  (elastic  cord  37  ft.)  ........ 

2  Wheels  26"  x  3"  tire  and  IV,"  hub  ............... 

Total  chassis  group  ........................... 

Percentage  of  total  weight,  4.03%. 
Wiug  group: 


.    28.5  Ib. 

1.V7.-,  " 
•J.( ii i  •' 
.-...-,n  " 

•J7.0II   •• 

7f,.7."  Hi. 


Part  Weight 
Upper  wings  without  flaps  or 

fittings    ................  120.00  Ib. 

Upper  center  section  without 

fittings    .................  13.00  " 

Lower  wings  without  fittings.  112.00  " 

2  wing  flaps  with  fittings  ----  2  I  .:.« 

Total  for  wing  group.  .  .   269.50  Ib. 
Percentage  of  total  weight,  14.1 

Wing  bracing  and  fittings  : 

1'etails  : 


Area 
172.2  sq.  ft. 


152.2 
40.8 


Weight  PIT 

SM.    fl 

Slll'i 

.772  Hi. 


.7.".n 


Upper  wing  fittings,  8  strut  fittings,  4  fittings  to  center 

section    .........................................  lii..-,ii  Hi. 

Lower  wins  fittings.  8  strut  fittings,  4  fittings  to  body.  .  .      '.i.."i"i  " 
2  Win;;  skids  ..................     ........     ......                   2  - 

4  (Inter  section  struts  (length  of  staggered  struts  =  lil"  •.  i:;..".n  •• 

4  Intermediate  se<  ti.ni  struts  ......................  IT..  MI  •• 

4   Drift  wires  i  .....  ise  from  upper  anil  lower  planes  ......      3.OO  " 

Klylng  landing  and  outer  strut  wires   (not  in.  -111(11111: 

..........................  21  mi  •• 

4  Aileron  wires  with   littings  ..........  .........  .Vim  •• 

4   Short  uprights  for  bracing  overhang  .....  l.im  " 

Center  section  struts  ..................  I  ."in  " 

Center  section  brace  wire  ............... 


Total 

Percentage  of  total  load,  -4 

Tall  surfaces  : 

Weight 
Vertical  tall  fin  and  fittings.  14.00  Ib. 

Kudder  and  fittings 10.00  " 

Fixed  liori/oiitnl  tall  with 

hinge  lit  tines  only 14.00  " 

2  Elevator  Maps  with  wires 

and  pnMs    14.50  " 


111.2.-,  Hi. 


'-'.."l    Sl|.    ft. 

10.2  "  " 

22.7    "    " 
17.r.    "    - 


\V, 

per  sq.  ft. 

ii  112  III. 
1.09   " 

n.r,2  - 
0.88  " 


Total 52.50  Ib. 

•Mtage  of  total,  2 

Control  system  : 

Steering    post.     nnMer    wheels    with     rudder    wires 

littings    

4   Elevator   wires 


Total 

Percentage  of  total  weigh t. 

Gasoline  and  oil : 

4.4  hours 

Percentage  of  total  load,  i 

Tanks : 


me  tank  with  capneit>   of  ."."  gall.. 
Percentage  of  total  weight,  1 


Weight 

2V  1  Hi. 


Engine  group  : 

Propeller  nnd  hub  .......     :;4.75  Ib. 

;ie     nnd      accessories 

(including     2     hot     air 

stoves.   :;.,ri  HI.,  top  of 

enu-inc    Tilates    and    side 

plate.   20.1.-,   ib.)  ......   ::ii::.7r,  " 

Radiator    ..............      ri.V7.-.   " 

Water    ................      39.00  " 

1     Water     pl|B-     and     fit- 

tings    ...............        :i.OO  " 

Total  ..............    496.25  Ib. 

IVr,  enlace  of  total  weight.  2i;.Hf;. 

Passengers  : 

I'ilot      ................ 


t   per  hp 


Wright  per  lip. 
Weight  per  hp. 
Weight  per  hp. 


12.25  Ib. 


1.V7.-I  Ib. 


C.-.2  Hi. 


WciuM  of 

tank  per 
galli>n 


::M;  |l>. 


.  .  .    4.0.-.H    - 

.  .  .    u.i;2n    " 

.    0.4:!0    " 


ir.f,  ib. 
in:,  •• 


Totnl  ....................... 

Percentage  of  total  weight,  lti.95%. 


Ih 


Summary  of  Weight  Distribution  for  J!ST-4-B 


.-igbt 

.25  Ib. 


assembly   and   equipment  .....  200. 

ill     .........................  070.7.-. 

Wings    ..........................  2'-.'.i.:.i> 

Inl.-rplane    bracing.  n'.i  I  2". 

urfaces    ...................  052.50 

I'onlrol    system    .................  015.75 

in-    and    oil  ..................  252.00 

liasi.line   tnnk   and    piping  ..........  028.10 

Kiiglne    i:  "up    ....................  (:ii;.'J-i 

Passengers    ......................  .",21  nn 


IVrcclltace  nf 
total 
16.50% 
i  0 

14  1 
al  Q 

II2.7I-.  " 

Illl    - 

i :;  20  " 
in  r,:t  " 

in  - 
n.'.ir,  •• 


1902.r.5lb. 


ion  mi'; 


AIRPLANE    DESIGN 


89 


Empirical  Formulae  and  Values  for  Weight  Estimates 

Some  empirical  formulae  and  values  are  given  here.  Such 
empirical  formulas  can  never  be  entirely  trustworthy,  since  so 
much  depends  on  the  type  of  machine  to  be  constructed,  the 
type  of  construction  to  be  employed  for  any  particular  part 
of  the  machine,  and  the  factor  of  safety  desired.  Much 
greater  reliance  is  to  be  placed  on  direct  comparisons  from 
actual  machines  and  on  actual  computations  from  drawings. 
Still,  they  may  serve  a  useful  purpose  in  the  preliminary 
stages  of  design,  when  a  rapid  estimate  is  needed. 

(1)  Body 

Bare  rectangular  wooden  longeron  body,  with  fabric  cover- 
ing for  small  monoplane  and  biplane  scouts  about  1200  Ib. 
total  weight,  70  Ib.  is  a  good  average  figure.  For  large  biplanes 
about  2500  Ib.  total  weight,  150  Ib.  is  a  liberal  allowance. 

(2)  Seating 

About  10-12  Ib.  per  person  is  sufficient. 

(3)  Single  control  system  30  Ib. 
Double  control  system  50  Ib. 

(4)  Landing  Gear 

A  landing  gear  of  about  V16  the  loaded  weight  of  the  machine 
can  be  easily  designed. 

(5)  Tail  skid 

Is  roughly  V,0th  the  weight  of  the  landing  gear. 

(6)  Main  plane  weights  (surface  alone) 

A  fair  average  figure  is  0.75  Ib.  per  square  foot  of  wing 
area,  although  wing  weights  will  vary  with  size  of  machine, 
section  employed,  aspect  ratio,  strut  spacing  and  numerous 
other  features  in  design. 

(7)  Weiyltt  of  control  surface 

Control  surfaces  with  fittings  and  hinges  may,  with  careful 
design,  not  exceed  0.5  or  0.6  Ib.  per  square  foot. 
.(8)   Tanks 

About  0.75  Ib.  to  1.00  Ib.  per  gallon. 

(9)  Engine  weights,  fuel  consumption 

Full  values  for  these  are  available  and  will  be  given  in  a 
subsequent  section. 

(10)  Engine  mounting 

One-eighth  of  the  engine  weight  for  a  rotary  type  and  one- 
twelfth  the  engine  weight  for  a  fixed  type  engine. 

(11)  Propellers 

A  good  rule  is  weight  =  2.5 Vhp. 

(12)  Radiators 

For  radiators,  manufacturers'  figures  will  be  given  later,  and 
empirical  formulas  are  not  necessary. 

(13)  Passengers 

Some  10  Ib.  should  be  added  for  aviation  dress. 

(14)  Miscellaneous 

An  allowance  of  10  Ib.  is  sufficient  for  instruments,  such  as 
compass,  altimeters,  etc.    Fire  extinguisher,  8  Ib.    Tool  kit,  5 
Ib.    First-aid  kit,  5  Ib. 
(15) 

In  a  subsequent  section  we  shall  deal  with  weights  of  such 
parts  of  the  machine  as  cables,  wires,  turn-buckles,  fabrics, 
dopes,  wheels,  etc.,  etc. 

Some  General  Considerations  on  Distribution  of 
Weight  and  Useful  Load 

F.  W.  Lanchester  has  approached  the  question  of  weight 
distribution  for  various  sizes  of  machines  in  a  very  interesting 
article.  The  subject  offers  many  difficulties,  and  the  following 
notes,  mainly  based  on  Mr.  Lanchester's  article,  are  merely  an 
introduction. 

When  estimating  the  structural  weight  of  a  new  machine 


from  data  available  on  one  constructed,  certain  theoretical  con- 
siderations are  available. 

Simple  and  reasonable  assumptions  in  dealing  with  the  main 
planes  are  that  the  wing  section  remains  geometrically  similar, 
and  the  velocity  constant.  On  such  a  basis  from  ordinary  con- 
siderations of  aerodynamics,  the  span  must  vary  as  the  square 
root  of  the  gross  weight,  and  conversely  the  loading  on  the 
wing  will  vary  as  the  square  of  the  span.  The  direct  forces 
of  tension  and  compression  on  the  spars  will  vary  directly  as 
the  loading  and  square  of  the  span,  but  the  cross-sectional 


500   7000   1500  2000  2500  3000  3500  4000  4500  5000  5500  3000 

Pounds 
FIG.  1. 


areas  of  the  spars  will  also  vary  as  the  square  of  the  span ; 
geometrically  similar  wings  will,  therefore,  be  equally  strong 
as  regards  direct  forces.  The  bending  moments  will  vary  as 
the  gross  weight  or  loading  multiplied  by  the  span,  i.e.  as  the 
cube  of  the  span.  But  the  resisting  moment  of  the  spars  will 
vary  as  the  section  modulus  or  cube  of  the  linear  dimensions; 
geometrically  similar  wings  will,  therefore,  be  equally  strong 
as  regards  bending  moments.  It  follows  that  with  constant 
velocities  geometrically  similar  wings  will  be  equally  strong 
for  both  direct  and  bending  stresses.  From  the  weight  of 
aerofoil  point  of  view,  the  position  is  unfavorable,  since  the 
weight  will  vary  as  the  cube  of  the  linear  dimensions  or  cube 
of  the  span. 

It  follows  that  the  weight  of  the  wings  will  vary  as  W*/* 
where  W  is  the  gross  weight. 

In  the  interplane  bracing,  the  wires,  which  only  take  direct 
stresses,  will  be  equally  strong  when  geometric  similarity  is 
maintained.  For  the  struts  just  as  for  the  spars,  the  same 
will  apply.  Therefore,  the  interplane  bracing  will  also  vary 
as  W3/1. 

For  the  body  it  is  possible  to  make  the  somewhat  more 
favorable  assumption  that  its  weight  is  directly  proportional 
to  the  gross  weight.  With  increase  in  span,  it  is  by  no  means 
necessary  to  increase  the  arm  of  the  tail  surfaces  proportion- 
ately, while  the  resisting  moment  of  a  body  cross-section  varies 
as  the  depth  squared  and  the  breadth.  Current  practice  also 
seems  to  bear  out  the  above  assumption.  It  might  even  prove 
to  be  true  that  on  large  machines  a  slight  saving  on  weight  of 
body  would  be  possible. 

The  shock  of  landing  to  be  taken  up  by  the  chassis  depends, 
for  the  same  landing  speed,  on  the  gross  weight. 

If  a  chassis  for  a  large  machine  were  geometrically  similar 
to  that  of  a  smaller  machine,  it  would  probably  show  greater 
strength  in  the  struts,  and  equal  strength  in  the  shock  absorber. 
The  question  is  very  complex.  Mr.  Lanchester  insists  on  the 
analogy  of  the  greater  relative  diameter  of  the  legs  of  such  a 
large  animal  as  an  elephant  as  compared  with  the  legs  of  a 
flamingo.  But  with  very  big  landing  gear  so  much  becomes 


AIRPLANE    DESIGN 


possible  in  the  way  of  shock  absorption  that  keeping  the  weight 
of  the  chassis  a  constant  proportion  of  the  gross  weight  seems 
feasible. 

For  -the    power   installation,   no   general    discussion    seems 


1000        1200        1400 

POUNDS 
Fir..  2. 


its  ordinatcs  represent  il»  u'ro>-  wciL-iii.  juM  MS  the  abscissae 
for  the  same  point  represent  the  gross  weight.  In  accordance 
with  the  above  considerations,  the  total  structural  weight  i- 
taken  as  a  constant  proportion  of  the  gross  weight,  namely. 
25  per  cent.  The  power  installation  weight  is  taken  a.-  25  pel- 
cent,  as  previously  mentioned.  The  weight  of  aerofoil  curve. 
\arying  as  W'/',  is  obtained  i'roui  present-day  English  prac- 
tice in  biplane  construction,  with  a  factor  of  safety  of  6 — 
somewhat  lower  than  American  practice.  The  military  load  is 
kept  at  500  Ib.  in  one  case,  at  150  Ib.  in  the  other,  and  the 
remainder  is  allotted  to  the  supply  of  petrol. 

The  above  remarks,  the  distribution  of  weights,  and  these 
two  curves  arc  open  to  criticism.  However,  they  are  the  con- 
clusions of  a  most  eminent  authority,  and  may  serve  as  a  use- 
ful guide  in  the  preliminary  design  oi  a  machine,  particularly 
as  regards  possible  endurance,  which  can  at  once  be  derived 
from  the  petrol  capacity.  They  also  give  an  idea  of  the  lim- 
itations of  the  airplane.  Thus  the  curves  of  Fig.  1  show  the 
lowest  possible  weight  level,  with  a  big  load  of  500  Ib.,  and  if 
extended  to  greater  gross  weights  would  show  where,  witli  in- 
creased size,  the  petrol  capacity  begins  to  diminish.  Fit:.  - 
would  be  particularly  useful  in  considering  the  |"issihilit: 
a  speed  scout  with  a  single  passenger. 


possible,  and  Mr.  Lanchester  has  assumed  this  to  be  25  per 
cent  of  the  gross  weight  in  the  graphs  of  Fig.  1  and  Fig.  2. 

The  construction  of  these  is  easily  followed.    The  bounding 
line  of  these  curves  is  drawn  at  45r  to  the  Case  line,  so  that 


References,  for  Part  11.  Chapter  ,'i 

The  Development  of  tbe  Military  Aeroplane."  l>v  K    \v     ].:in 
Miirdi  ::.  " 


Chapter  IV 

Engine  and  Radiator  Data 


General  Requirements   of   Aeronautical   Engines 

The  main  requirements  of  an  airplane  engine  are  light 
weight,  low  fuel  and  oil  consumption,  reliability,  accessibility, 
and  a  form  suitable  for  installation  in  an  airplane.  The 
general  form,  apart  from  its  weight,  is  important  because  of 
the  question  of  mounting  in  the  body,  and  the  problem  of 
engine  cooling  and  body  stream-lining.  Selecting  an  engine 
for  an  airplane  means  unfortunately  buying  the  engine  most 
nearly  suitable  which  is  purchasable  at  the  moment,  and 
the  choice  is  none  too  great.  Nevertheless  it  is  part  of  a 
designer's  training  to  consider  the  comparative  merits  of 
every  engine  available,  mainly  with  reference  to  the  above 
points. 

As  regards  reliability,  no  rules  can  be  laid  down.  Satis- 
factory tests  in  Government  or  college  laboratories  are  good 
guides.  The  reputation  which  an  engine  has  earned  among 
pilots  under  the  more  trying  conditions  of  actual  flying  is 
even  more  important.  Accessibility  depends  not  only  on 
the  design  of  the  engine  itself,  but  on  its  careful  mounting 
in  the  body.  Fuel  and  oil  consumption,  weight  and  suitability 
of  form  are  best  studied  by  the  compilation  of  such  a  table 
as  Table  1.  Such  a  table  will  require  constant  revision. 

In  considering  weights  of  two  engines  of  like  power  but  of 
different  type,  such  as  a  stationary  air-cooled  and  a  water- 
cooled  engine,  or  a  rotary  air-cooled  engine  and  a  stationary 
water-cooled  engine,  radiator  and  cooling  water  should  not 
be  neglected.  In  dealing  with  rotary  engines,  fuel  and  oil 
consumption  tend  to  make  comparisons  with  stationary  engines 
less  favorable  to  the  former  type  than  is  at  first  apparent. 
Particularly  is  this  the  case  when  a  flight  of  more  than  2\» 
or  3  hours  duration  is  contemplated.  The  extra  weight  ol 
gasoline  and  oil  to  be  carried  for  the  rotary  may  actually  make 
it  the  heavier  engine  at  the  beginning  of  a  fairly  long  flight. 

The  form  of  an  engine,  from  the  points  of  view  of  mount- 
ing and  projected  area,  are  best  studied  from  drawings 
appearing  in  technical  magazines  and  makers'  catalogs.  The 
dimensions  given  in  the  table  serve  as  a  preliminary  guide  in 
narrowing  down  selection. 

For  a  general  study  of  the  subject  of  aeronautical  engines 
reference  is  appended  to  one  or  two  excellent  books — in 
which,  however,  no  information  as  to  recent  developments  is 
available. 

The  question  of  revolutions  per  minute  apart  from  the 
question  of  power  and  efficiency  in  the  engine  itself  has  an 
important  bearing  on  propeller  design.  Wooden  propellers 
of  large  diameter  seem  to  reach  their  maximum  permissible 
safe  speed  at  about  1300  r.p.m.  Beyond  this  figure,  it  is 
hard  to  keep  stresses  down.  Questions  of  direct  drive  and 
geared-down  drives  must  be  considered  from  this  point  of 
view. 


Acknowledgment  is  made  to  Lieutenant  H.  C.  Child,  and 
to  Mr.  Lee  S.  Wallace  for  valuable  data. 

Weights  for  Radiators  and  Cooling  Water 

The  following  are  good  preliminary  figures  for  design  in 
accordance  with  general  data: 

Bare  radiator 55  Ib.  per  blip. 

Water  in  radiator 13  Ib.  per  bhp. 

The  Ajax  radiator  employed  in  conjunction  with  a  130-hp. 
Hall-Scott  engine  weighs  45  Ib.  bare  and  carries  30  Ib.  of 
water.  On  a  school  Curtiss  of  the  JN  type  with  n  90  hp. 
Curtiss  engine,  the  figures  for  a  Rome-Turney  radiator  are 

Weight  of  empty  radiator 58%  Ib. 

Weight  of  water  contents   24%  Ib. 

Thickness  of  core   2%  in. 

Active  front  area   400  sq.  in. 

Total  radiating  surface   15,360  sq.  in. 

For  the  Livingston  Radiator,  the  following  information  is 
available: 

"For  a  120  h.p.  engine,  from  16,000  to  18,000  sq.  in.  of 
radiator  surface  is  required.  Each  square  inch  of  projected 
area  of  4  in.  section  contains  50  sq.  in.  of  cooling  surface. 
A  5  in.  section  contains  60  sq.  in.,  and  a  3  in.  section  contains 
40  sq.  in.  Therefore,  a  radiator  for  a  125  h.p.  engine  will  have 
between  320  sq.  in.  (2.2  sq.  ft.)  and  360  sq.  in.  (2.5  sq.  ft.) 
projected  area  of  4  in.  section.  A  radiator  for  such  an  engine 
contains  approximately  4  gallons  of  water.  Of  this,  1  gallon 
is  contained  in  the  cells,  the  other  3  gallons  in  the  headers. 
The  headers  should  be  of  such  proportions  that  the  lower  has 
about  two-thirds  the  capacity  of  the  upper." 

Practical  Rules  for  Cooling  Surface  for  Radiator 
of  Honeycomb  Type 

From  Dr.  Hunsaker's  experiments  at  the  Massachu- 
setts Institute  of  Technology,  and  certain  theoretical  con- 
siderations, a  surface  of  .83  sq.  ft.  per  bhp.  has  been  found 
necessary  for  the  honeycomb  type.  C.  Sage  recommends 
1.08  sq.  ft.  per  bhp.  for  an  airplane  of  an  average  speed 
of  60  m.p.h.,  and  presumably  a  minimum  speed  of  45  m.p.h. 
An  allowance  of  1  sq.  ft.  per  bhp.  seems  very  fair  for 
machines  of  medium  speed.  In  fast  machines  of  the  pursuit 
type,  it  would  be  possible  to  go  considerably  below  this  figure; 
even  if  a  fast  machine  makes  a  prolonged  climb,  it  will  never 
do  so  at  its  slowest  speed.  Dr.  Hunsaker  has  shown  that  an 
empirical  formula  may  be  established  of  this  type: 

C  X  blip. 

—?- 

where  a  =  area  of  cooling  surface,  C  is  some  constant  and  V 
is  the  speed  in  miles  per  hour.     A  designer,  who  has  satis- 


91 


92 


DATA   FOR   AMI 


Subject 


Maker 
and 
Model 

No.  Cylinders. 

1 

0j 

H 

T3 

1 

SB 

CH 

rt 

R.P.M.  of  Propeller. 

£J 

_c 

4 

Pu 

a 

a 
1 

o 

_i 
^C 

u 
•? 
fc 

m 

I 

0 

.6 
** 

'1 

a 

E° 

"1 

_  - 

1.8 

>* 

f  a 

Weight  Cooling  Water  in 
Radiator  and  Engine,  Ib. 

•o 

V 

"E 

a  • 

OC 

II 

Weight  Cooling  Water 
in  Radiator,  Ib. 

•o 

• 
"3. 

L 

0~" 

si 
tm 

^ 

^ 

1 

( 
1 
*, 
1 
'J 

\ 
\ 
9 

Aeromarine 

6 

Vert. 

85 

1400 

1150 

.7 

.069 

440 

37.5 

31 

8.12 

Aeromarine  D-12 

12 

V. 

160 

1400 

750 

• 

Aeromarine 

8 

V. 

100 

410 

• 

Atwocxl  C-12 

12 

V. 

150 

2500 

1250 

.64 

.V.I2 

63 

13.25 

Christofferson 

6 

Vert. 

113 

1450 

1450 

.665 

.0266 

510 

67.5 

8.7 

4i 

ii 

8 

V. 

160 

2500 

630 

65 

85 

15 

17 

Curtiss-Ox  2 

8 

V. 

90 

1400 

1400 

375 

58>i 

24^ 

"     -OXX  2 

8 

V. 

100 

1400 

1400 

.59 

.035 

423 

44 

76 

12.26 

1 

"    -VX 

8 

V. 

160 

1400 

1400 

.575 

.0328 

04.-> 

62 

86 

16 

7 

"    -VX  3 

8 

V. 

200 

.73 

.031 

667 

70 

94 

Iti 

6 

"    -V-4 

12 

V. 

250 

.612 

1125 

100 

120 

2rl 

Duesenberg 

4 

Vert. 

140 

2100 

455 

7.21 

ii 

12 

V. 

250 

1800 

425 

15.5 

Genl.  Ordnance  Co. 

8 

V. 

230 

1800 

867 

Genl.  Vehicle  Gnome 

9 

Roty. 

100 

1200 

.72 

272 

Gyro  K 

7 

Roty. 

90 

1250 

.VI.-, 

.  100 

^!L> 

"     L 

9 

Roty. 

100 

1200 

Oil 

.180 

285 

Hall-Scott  A-7 

4 

Vert. 

80-90 

1370 

1370 

.47 

.037 

410 

34* 

40 

A-5 

6 

Vert. 

125 

1300 

1300 

.507 

Ol'S 

592 

52* 

45 

30 

4 

A-5at 

6 

Vert. 

162 

1325 

14.  7J 

•4t 

562 

IH-pano-Suiza 

8 

V. 

154 

1500 

455 

48.3 

10 

Knox 

12 

V. 

300 

1800 

1425 

19.4 

7 

Packard 

12 

V. 

225 

2100 

800 

Rausenberger  C-12 

12 

V. 

150 

1300 

570 

Sturtevant  5 

8 

V. 

140 

2000 

.54 

IMS 

600 

70 

60 

40 

5 

5-A 

8 

V. 

lio 

2000 

1200 

514 

66 

54 

10 

• 

tt 

12 

V. 

276 

2000 

9 

Thomas  8 

8 

V. 

i:<r> 

2000 

1200 

59 

.053 

572 

so 

LOO 

16.3 

6 

"      88 

8 

V. 

160 

2000 

.59 

485 

Wisconsin 

6 

Vert. 

110 

1380 

1380 

.550 

027 

637 

38* 

50 

26 

ii 

12 

V. 

260 

1200 

1200 

liO'J 

.029 

1000 

142 

18.1 

t 

Wright 

6 

Vert. 

60 

1400 

.-,!.-, 

39 

6.28 

*  Kngine  only. 

t  Figures  obtained  from  test  run. 

t  Gallons  per  hour. 


RICAN    ENGINES 


ication 


"o 

CD 

"a, 
B 

It 

o  tT 

s= 

la 

0>    O 

s£ 

Weight  of  Example  of 
Mounting,  Ib. 

"S 

CD 

"E 

S 

$ 

w  . 

«4-(  -^ 

o~ 

•w  h/D 

|l 

^j   O 

5^U 

m 

<D 

J3 

O 

_C 

^g 

£ 
1 

GQ 

5 
1 

a 

| 
1 

QQ 

Piston  Displacement, 
cu.  in. 

.0 

1 

J 

1 
1 

O 

_g 

^a 

M 

43 

73 

^ 

1 
| 

O 

,c 
.a 

^ 

f 

3 

1 

O 

60 

a 
1 
|d 

=  1 

wi 

0   g 

2;« 

S 

§  . 

f.3 
3J 

£§ 

2^ 

-  a 
*S 

II 

Athwartship  distance 
between  Brackets. 

Athwartship  distance 
between  Bolt  Holes. 

Maker 
and 
Model 

29.  8 

28.2 

5.5 

4A 

5% 

449 

58 

30 

36?4 

Aeromarine 

67 

24 

30 

3 

Aeromarine  D-12 

Aeromarine 

58 

55 

40.9 

3% 

4Ji 

519.5 

48 

27 

26 

Atwood  C-12 

!6.5 

34 

6.5 

4% 

6 

Christofferson 

40 

41 

17.5 

•• 

4 

5 

502 

50 

30 

27 

3 

9 

12% 

Curtiss-Ox  2 

!2.5 

23.2 

10.6 

4M 

5 

567.5 

50 

30 

29 

3 

9 

12% 

"     -OXX  2 

64 

45 

12.2 

5 

7 

1100 

67  */8 

35 

34 

5 

9 

14 

16 

••   -vx 

64 

14.7 

12.2 

5 

7 

"     -VX  3 

95 

60.1 

19.6 

5 

7 

84^ 

34^ 

40 

"     -V-4 

29.5 

4.8 

4% 

7 

496 

43% 

15J^ 

37% 

4 

13% 

13% 

14M 

Duesenberg 

49.2 

18 

4% 

7 

1488 

68 

31M 

39% 

4 

15% 

14 

15^ 

tt 

4% 

6H 

920 

Genl.  Ordnance  Co. 

4.33 

6M 

920 

Genl.  Vehicle  Gnome 

23.2 

22.7 

12.4 

4^ 

6 

Gyro  K. 

27.6 

24.4 

13.2 

4K 

6 

859 

24.7 

37^ 

371A 

'•     L 

37 

28.9 

4.5 

5 

7 

550 

57 

18^ 

39^ 

4 

16M 

14 

16 

Hall-Scott  A-7 

42.5 

39.6 

6.8 

5 

7 

825 

63  ?s 

18H 

41^ 

3 

35^ 

14 

16 

A-5 

A-5af 

17 

13.5 

28.3 

4% 

5 

672 

52^ 

32H 

35M 

12^ 

14% 

Hispano-Suiza 

56.8 

21 

4% 

7 

1555 

"   " 

Knox 

4 

6 

905 

62^ 

23  A 

41  J^ 

3 

16M 

18M 

Packard 

4% 

6 

900 

42 

24 

Rausenberger  C-12 

40 

30 

30 

4 

5J--2 

522 

59A 

23 

29^ 

3 

14A 

13% 

Sturt.evant  5 

4 

5J^ 

522 

59  A 

34 

34^ 

3 

14A 

5-A 

24 

4 

5K 

49.8 

40.1 

13.6 

4 

5^ 

552.9 

60 

28 

37% 

3 

ISA 

13^' 

Thomas  8 

3 

13A 

l:!:i-, 

88 

42 

5 

5K 

765.7 

17M 

24 

«A 

4 

14H 

13M 

16^ 

\\  iscuiism 

54.2 

10.8 

5 

6J^ 

1532 

76^ 

wys 

37  A 

4 

14?i 

15H 

IS', 

" 

19 

25.9 

6.4 

4% 

4^ 

Wright 

AIRPLANE    DESIGN 


factory  data  on  a  machine  of  a  certain  speed,  cau  employ 
this  rule  for  machines  of  a  different  speed. 

Position  and  Resistance  of  a  Radiator 

Tests  at  the  Massachusetts  Institute  of  Technology  show 
that  the  resistance  of  a  radiator  may  be  represented  by  the 

equation 

R  =  KTAV'- 

where  R  =  resistance  in  pounds 

A  =  area  of  radiator  face  in  square  feet 
F  =  speed  in  miles  per  hour. 

and  Kf=  .00175 

While  these  tests  were  conducted  on  very  small  sections,  the 
results  are  safely  applicable  to  full-size  radiators. 

Figures  on  the  resistance  of  a  given  section  of  radiator  in 
a  current  of  air  do  not  by  any  means  settle  the  problem  of 
the  best  position  for  the  radiator.  Manufacturers  have 
placed  radiators  in  various  positions,  claiming  minimum  re- 
sistance for  each  position.  If  a  radiator  is  placed  behind  the 
propeller  where  the  slip  stream  increases  the  velocity  by 
some  25  per  cent,  the  cooling  surface  may  be  decreased  by 
25  per  cent  with  a  consequent  reduction  of  resistance  pro- 
ducing area,  but  since  the  resistance  varies  as  the  square  of 
the  velocity,  there  is  finally  an  increase  of  25  per  cent.  These 
or  similar  considerations  have  led  designers  to  place  radiators 
underneath  the  wings.  But  it  is  forgotten  that  when  a  radiator 
is  placed  underneath  the  wings,  it  is  no  longer  a  shelter  for 
the  body.  There  is  also  the  question  of  extra  length  of  piping. 
For  radiators  placed  at  the  sides,  Dr.  Hunsaker's  opinion  is 
that  a  more  generous  allowance  is  necessary.  Dr.  Zahm's  skin 
friction  formula  is  of  the  form  E  =  0.0000158 1*"  Vlfe  b. 
as  we  saw  in  Part  1,  Section  3,  AVIATION  AND  AERONAUTICAL 
as  we  saw  in  Part  1,  Chapter  3,  where  I  is  the  length  of  sur- 
face parallel  to  the  wind.  Owing  to  the  greater  length  of 
side  radiators  in  the  direction  of  motion,  they  are  therefore 
probably  less  effective. 

The  authors'  opinion  is  that  the  best  and  most  natural  posi- 
tion of  the  radiator  is  behind  the  propeller,  but  the  question 
is  hardly  capable  of  a  decision  so  far. 

Practical  Construction  of  Radiators 

C.  Sage,  engineer  of  the  Rome-Turney  Radiator  Company, 
has  submitted  the  following  authoritative  views: 

"  As  to  the  construction  of  radiators,  we  may  say  that  the 
simpler  the  outline  the  more  durable  will  be  the  radiator — and 
the  cheaper.  The  cooling  section  of  honeycomb  radiators 
ought  to  have  outlines  composed  entirely  of  straight  lines — 


curves  in  the  honeycomb  are  expensive  and  are  weak  points 
for  the  reason  that  all  honeycomb  cooling  sections  are  at  the 
start  made  of  rectangular  blocks  and  then  sawed  to  shape  on 
a  band  saw  like  a  board.  The  sawed-off  waterways  have  then 
to  be  patched  up  again  with  solder  and  their  ends  are  naturally 
not  as  strong  as  before.  Then  this  section  has  to  be  fitted  to 
the  case  and  the  more  curves  there  are  the  more  difficult 
and  costly  the  fitting  will  be.  Concerning  the  case  of  the 
radiator  the  same  principle  holds  good — the  simpler  the  design 
the  better  and  cheaper  the  product.  All  curved  surfaces  are 
costly  if  they  have  to  be  produced  by  hand  work  and  pressed 
eases  must  be  made  in  large  quantities  in  order  to  pay  for  the 
necessary  punches  and  dies  and  it  takes  a  long  time  until 
production  can  be  started  on  them. 

"  As  for  water  connections  between  engine  to  radiator  and 
pump  to  radiator,  it  is  very  important  that  they  be  large 
enough  to  convey  the  large  bulk  of  water  with  the  least  possible 
pressure.  If  the  connections  are  too  small  a  considerable 
vacuum  will  be  set  up  in  the  suction  line  from  the  radiator  to 
the  pump  and  consequently  air  will  be  drawn  into  this  line 
at  all  leaky  points,  prominent  among  these  being  the  stu fling 
box  and  the  grease  cups  of  the  pump.  This  air  will  be  mixed 
with  the  water  forming  a  milky  liquid  like  charged  water, 
increasing  its  volume,  and  consequently  a  considerable  loss 
through  the  vent  pipe  will  take  place. 

"  As  to  support  of  a  radiator,  the  most  satisfactory  method 
is  the  use  of  a  cradle  or  cross  piece  at  the  front  of  the  body, 
in  the  case  of  a  tractor,  on  which  the  radiator  is  placed  and 
fastened  by  studs  in  the  bottom  tank.  In  the  case  of  pushers, 
many  different  suspension  methods  are  used,  none  of  which 
can  be  called  standard,  and  the  same  is  true  for  side  radiators." 

An  excellent  point  made  by  the  manufacturers  of  the  Ajax 
radiator  is  the  reinforcement  of  the  fins  rear  and  front  by 
soldering  on  1/16  in.  wires.  Dividing  a  radiator  into  two 
parts  by  a  small  %  in.  deep  water  tank  to  permit  settling  of 
the  water,  is  another  good  point  in  this  type. 

As  a  general  rule,  the  sub-division  of  a  radiator  into  a 
number  of  sections  is  advantageous.  In  the  present  ill-defined 
position  of  radiator  design,  it  is  an  advantage  to  be  able  to 
increase  or  diminish  the  radiator  surface  of  a  given  machine. 


References  for  Part  II,  Chapter  4 

••  Surface  Cooling  and  Skin  Friction."  by  F.  W.  Lancbester.  British 
Iteporta,  No.  94,  1912-1913. 

"  Notes  on  Radiator  Design,"  by  J.  C.  Hunsaker,  Aerial  Age,  May  29. 
1916. 

"  Aeronautical  Engines."  by  Francis  J.  Kean,  1916. 

"  Aero  Engines."  by  G.  A.  Burls. 

"  Entwerfen  von  leichten  Benzlnmotoren."  by  0.  Winkler. 

"  Report  on  Aeronautical  Engines."  by  Charles  E.  Locke.  First  An- 
nual Report  of  the  National  Advisory  Committee  for  Aeronautics. 


Chapter  V 

Materials  in  Airplane  Construction 


Within  the  limits  of  one  chapter  it  is  impossible  to  treat 
adequately  all  the  data  on  materials  required  for  airplane 
construction.  The  data  included  here  will  be  sufficient  for  the 
purpose  of  our  design,  however,  and  a  number  of  refer- 
ences are  appended.  For  practical  work,  the  designer  must 
procure  all  necessary  handbooks,  make  tests  of  his  own  special 
fittings,  and  generally  collect  his  own  data. 

Special  Utility  of  Wood  in  Airplane  Construction 

It  is  the  remarkable  strength  for  its  weight  which  makes 
wood  so  useful  in  airplane  construction.  If  we  compare  spruce, 
weight  per  cubic  foot  26  lb.,  tensile  strength  9000  lb.,  with 
mild  steel  weighing  490  lb.  per  cubic  foot  with  a  tensile 

strength  of  60,000  lb.,  the  spruce  will  be-^     ^X^-  =  2.9 

oO,000        26 

times  as  strong  for  the  same  weight. 

The  selection,  mechanical  properties  and  correct  structural 
employment  of  timber  are,  however,  inexhaustible  subjects, 
and  the  following  notes  are  the  barest  summary  of  the  factors 
the  designer  must  have  in  mind. 

Weight  of  Wood 

The  weight  of  wood  varies  greatly  for  the  same  species  and 
for  portions  of  the  same  tree.  Sapwood  is  heavier  than  heart- 
wood,  summerwood  than  springwood.  Green  timber  naturally 
weighs  more  than  dry  timber,  due  to  the  presence  of  sap  and 
moisture.  The  ultimate  wood  fiber  of  all  species  has  a  specific 
gravity  of  1.6,  so  that  no  wood  would  float  in  water  were  it 
not  for  the  buoyancy  of  the  air  present  in  the  cells  and  walls. 

TABLE  1 
Specific  Gravity  and  Weights  of  Woods 


Dry  woods  Wt.  per  cu.  ft.  lb. 

Ash,  American  white 38. 

Balsa 6.5 

Boxwood 60. 

Cherry 42. 

Chestnut 41. 

Cork 15. 

Elm 35. 

Ebony 76.1 

Hemlock 25. 

Hickory 53. 

Lignum-vitjB 83 . 

Mahogany,  Spanish ....                                .  53 . 

Mahogany,   Honduras 35. 

Maple. . .' - 49. 

Oak,  live 59.3 

Oak,  white 48. 

Oak,  red 40. 

Pine,  white 25. 

Pine,  yellow 34.3 

Pine,  southern 45 . 

Sycamore 37. 

Spruce 25. 

Walnut 38. 


Specific  gravity 
.610 
.104 
.960 
.672 
.660 
.250 
.560 
1.220 
.400 
.850 
1.330 
.850 
.560 
.790 

950 

770 
.640 
•400 
.550 
.720 
.590 
.400 
.610 


The  weight  of  wood  is  experimentally  determined  by  sub- 
jecting thin  discs  to  an  oven  temperature  of  100°  Cent,  until 
they  cease  to  lose  weight  by  evaporation  of  moisture.  But 
even  with  this  provision,  the  results  will  be  extre-nely  variable, 


and  the  value  usually  assigned  to  a  given  species  is  simply  the 
average  of  a  large  number  of  tests.  Table  1,  taken  from  a 
Bulletin  of  the  Forestry  Division,  United  States  Department 
of  Agriculture,  will  give  values  sufficiently  accurate  for  design. 
Weight  is  a  good  indication  of  the  strength  of  wood,  pro- 
vided the  amount  of  moisture  contained  is  known.  As  a  gen- 
eral rule,  we  may  say  that  a  comparison  of  two  woods,  each 
containing  the  same  percentage  of  moisture,  will  show  the 
heavier  to  be  the  stronger;  in  fact,  the  strength  will  be  very 
nearly  proportional  to  the  weight. 

Factors  in  the  Mechanical  Properties  of  Woods 

The  strength  properties  of  wood  depend  on  (1)  correct 
identification  of  species  and  variety;  (2)  age  and  rate  of 
growth;  (3)  position  of  test  specimens  in  the  tree;  (4)  mois- 
ture content;  (5)  relative  freedom  from  defects,  such  as 
knots,  etc. 

Tensile  Strength 

Tensile  tests  are  difficult  because  tests  cannot  be  devised  that 
do  not  involve  either  shear  along  the  grain  or  compression 
across  the  grain.  It  is  for  the  same  reasons  that  wood  may 
be  unsuitable  in  tension,  though  it  is  apparently  strong  under 
such  a  stress. 

Failure  in  tension  along  the  grain  involves  principally  the 
resistance  offered  by  the  wood  elements  to  being  torn  apart 
transversely  or  obliquely.  The  strands  of  wood  elements  are 
practically  never  pulled  apart  by  failure  of  the  union  between 
adjacent  strands  or  fibers. 

Cross  grain  is  prejudicial  to  tensile  strength  and  rays,  ow- 
ing to  their  transverse  position  with  respect  to  a  load  applied 
along  the  grain,  and  small  resistance  to  tension  in  a  direction 
normal  to  the  direction  of  their  fibers  greatly  weaken  the 
timber.  Knots  weaken  wood  subjected  to  longitudinal  tension. 

Conipressive  Strength 

Individual  fibers  act  as  so  many  hollow  columns  bound 
firmly  together,  and  failure  involves  either  buckling  or  bend- 
ing of  the  individual  fibers  or  bundles  of  elements  which 
finally  come  to  act  almost  independently. 

Conipressive  strength  depends  on  a  number  of  factors:  (1) 
density;  (2)  strength  of  union  between  individual  fibers  as 
affected  by  moisture  content;  (3)  stiffness  of  wood  fibers 
(again  largely  a  matter  of  moisture  content) ;  (4)  continuity 
of  the  course  of  longitudinal  strands  in  a  direction  parallel 
to  axis  of  the  piece.  Woods  in  which  separate  elements  are 
closely  interlaced  and  bound  together  will  be  stronger  than 
woods  of  opposite  character. 

The  strongest  woods  in  compression  with  the  grain  are, 
roughly,  in  the  following  classes : 


95 


!X5 


AIRPLANE    DESIGN 


(1)  The  dense  and  tough  hickory,  birch,  hard  maple,  etc.; 
(2)  oak,  elm,  ash;  (3)  spruce,  pine  and  fir. 

Crushing  Across  the  Grain 

Crushing  strength  across  the  grain  is  dependent  practically 
entirely  upon  the  density  of  the  wood.  Crushing  strength 
across  the  grain  is,  therefore,  least  for  the  lightest,  most  porous 
woods,  and  greatest  for  heaviest  and  densest  woods. 

Compressive  strength  across  the  grain  is  to  compressive 
strength  along  the  grain  as  13  to  14  per  cent  for  white  pine, 
cedar,  cypress  and  spruce,  15  to  16  per  cent  for  the  various 
grades  of  hard  pine,  18  to  26  per  cent  for  elms,  21  to  26  per 
rent  for  ash,  22  to  26  per  cent  for  oaks,  23  to  31  per  cent  for 
hirkuries. 

Strength  in  Bending 

In  considering  the  strength  of  a  wooden  beam  in  bending, 
several  difficulties  occur.  Longitudinal  shear  is  very  important. 
A  wing  spar  may  be  amply  strong  in  bending,  and  yet  if 
highly  channeled  out  fail  by  longitudinal  shear.  The  tensile 
fiber  strength  of  wood  is  much  ia  excess  of  the  compressive 
stress,  but  even  if  the  compressive  fiber  stress  of  wood  is  em- 
ployed in  the  formula  /  = — — ,  it  is  no  true  criterion.  If  this 

formula  is  employed  for  strength  computations  in  bending,  it 
is  assumed  that  the  material  is  still  behaving  elastically  up  to 
actual  failure,  and  therefore  that  the  fiber  stress  is  still  di- 
rectly proportional  to  the  distance  of  the  fiber  from  the  neutral 
axis.  As  a  matter  of  fact,  the  elastic  limit  of  the  material 
may  have  long  been  passed  when  the  breaking  load  is  reached, 
the  neutral  axis  may  have  shifted,  and  the  extreme  fiber  may 
be  no  longer  proportional  to  the  bending.  Therefore,  in  stress 
calculations  for  wing  spars,  these  considerations  should  be 
applied,  making  use  of  the  modulus  of  rupture — for  which 
values  are  given  in  Table  2 — deduced  from  actual  bending 
tests,  which  are  far  more  trustworthy  guides. 

Knots 

Knots  originate  in  the  timber  cut  from  the  stem  or  branches 
of  a  tree  because  of  the  encasement  of  a  limb,  either  living  or 
dead,  by  the  successive  animal  layers  of  wood.  Most  limbs 
originate  at  the  pith  of  the  stem,  and  the  knots  found  deep 
in  a  log  are  therefore  small,  increasing  in  size  toward  the  bark. 
So  long  as  the  limb  is  growing,  its  layers  of  wood  are  a  con- 
tinuation of  those  of  the  stem.  But  a  majority  of  the  limbs 
die  after  a  time,  and  if  a  portion  of  a  dead  limb  is  subse- 
quently encased  by  the  growing  stem,  there  will  be  no  intimate 
connection  between  the  new  stem  wood  and  the  dead  wood  of 
the  limb,  and  a  board  so  cut  as  to  intercept  this  portion  of  the 
log  will  contain  a  loose  knot.  A  board  cut  from  the  log  at 
such  a  depth  that  the  limb  is  intercepted  at  a  point  where  it 
was  encased  while  still  living  will  contain  a  sound  knot,  unless 
the  knot  has  rotted,  become  badly  checked,  or  contains  a  large 
pith  cavity. 

A  sound  knot  is  usually  harder  than  the  surrounding  wood, 
and  in  coniferous  woods  is  apt  to  be  very  resinous.  On  this 
account  it  may  constitute  a  defect  because  of  its  non-retentiv- 
ity  of  paint  or  varnish.  Otherwise  it  constitutes  a  defect  only 
on  account  of  the  disturbance  to  the  grain  and  difliculty  caused 
in  working,  or  in  the  event  of  its  occurrence  on  the  under  side 
of  a  timber  used  as  a  beam,  a  weak  point  exists,  owing  to  its 
small  resistance  to  tensile  stress.  A  knot  constitutes  an  im- 


pediment to  the  splitting  of  timber,  since  the  fibers  of  the  stem 
wood  above  a  limb  bend  aside  and  pass  around  the  limb,  while 
the  fibers  below  run  continuously  into  the  limb.  Thus  it  often 
happens  that  a  cleft  started  above  a  limb  will  never  run  into 
a  knot,  but  one  started  below-  is  very  apt  to  do  so. 

The  Effect  of  Moisture  on  Strength  of  Wood 

Loss  of  moisture  does  not  affect  the  strength  of  wood  in 
any  way,  until  the  total  moisture  content  has  been  reduced 
below  the  critical  percentage,  which  represents  the  fiber-sat- 
uration period.  Beyond  this  point,  progressive  loss  of  mois- 
ture affects  the  strength  very  considerably.  Thus  the  strength 
of  green  wood  is  only  50  to  60  per  cent  of  normal  air-dry 
conditions  (12  per  cent  moisture),  while  the  strength  of  kiln- 
dry  wood  exceeds  the  strength  of  air-dry  woods  by  some  50 
to  70  per  cent. 

Time  Factor  in  Tests  of  Timber 

Timber  differs  from  most  other  materials  in  that  small 
variations  in  the  rate  of  application  of  load  have  a  more 
pronounced  effect  upon  the  strength  and  stiffness  shown  by 
a  specimen  under  test.  If  a  timber-compression  block  or 
beam  is  loaded  rapidly,  it  will  appear  to  have  a  higher  elastic 
limit  and  ultimate  strength,  and  will  also  appear  to  be  stiffer, 
than  it  will  if  loaded  less  rapidly.  This  is  due  to  the  fact 
that  the  deformation  lags  far  behind  the  load,  and  if  any 
load  is  permitted  to  remain  upon  a  specimen  for  a  time  the 
deformation  increases,  the  amount  of  increase  becoming  greater 
for  heavier  loads.  Actual  failure  appears  to  be  consequent 
upon  the  attainment  of  a  certain  limiting  amount  of  deforma- 
tion or  strain,  rather  than  a  limiting  load  or  stress. 

Difficulties  of  Wood  Construction  in  Airplanes 

The  comparative  values  of  Table  2  demand  the  most  care- 
ful study.  A  certain  type  of  timber  may  be  most  suitable 
for  the  direct  stress  to  which  it  is  subjected,  yet  fail  completely 
under  certain  indirect  stresses,  either  inherent  in  the  construc- 
tion or  due  to  faulty  design.  For  example,  at  the  hinging 
of  a  wing  spar  to  the  body,  if  the  bolts  are  not  correctly 
placed,  they  may  shear  out  the  wood.  These  points  will  be 
considered  in  detail  in  the  design,  but  enough  has  been  said 
to  show  the  value  of  studying  not  only  the  direct  stresses  on 
a  piece  of  timber  in  a  machine,  but  also  the  indirect  stresses 
producing  crushing  across  the  grain,  shear,  etc. 

Strength  Values  for  Timber 

In  no  material  are  such  conflicting  values  given  by  various 
authorities  as  for  timber.  The  size  of  the  specimen  under  test, 
the  dryness,  the  method  of  applying  the  load,  and  its  previous 
history,  all  tend  to  introduce  discrepancies.  Until  the  Bureau 
of  Standards,  or  some  other  testing  laboratory,  lias  gone  thor- 
oughly into  the  question,  all  the  values  employed  by  airplane 
constructors  will  be  open  to  suspicion.  Table  2  is  a  summary 
of  information  taken  from  various  sources.  This  table  is  not 
unimpeachable,  but  it  approximates  closely  values  used  in 
current  practice.  In  airplane  design,  fiber  stress  is  still  taken 
as  a  criterion,  without  due  consideration  of  the  modulus  of 
rupture. 

Acknowledgement  is  due  Prof.  W.  H.  Keith  for  collabora- 
tion on  brief  notes  on  timber. 


AIRPLANE    DESIGN 


97 


TABLE  2 


x 

ifeX 

'a! 

ss 

a 

- 

1 

1 

j?sf 

•ffl 
3 

II 

£ 

1 

i 

a1 

i-Ii 

a 
£ 

fa-- 

3 
i 

| 

! 

i 

£ 
1 

|| 

u 

a 

• 

£—  5j 

t£ 
°l 

3 

01 

i 

3*3  -^ 

c?  ^ 

a>  ^  m 

3.S 

OTJ.^ 

•i 

i-i 

'55  e 

s.s 

g-3    OT 

SJ  <• 

1-3 

S 

hfi 

Is 

H  no 

61 

6  II 

M§J 

Si 

Ash  

12,000 

1,600 

9,000 

1  300 

1,500 

56  5 

15,660 

11,000 

1,600 

1,200 

60-70 

Beech  

11,000 

1,600 

8,600 

1,200 

10,000 

Birch 

15000 

1  800 

3  500 

1,050 

11,700 

Cedar 

10800 

700 

5700 

7,400 

Elm 

10000 

7000 

8,800 

Hickory.  .  . 

15,000 

2,200 

11,000 

944 

1,500 

15,000 

Mahogany. 

16,000 

8,200 

11,000 

Maple  

11,150 

1,500 

7,150 

606 

1,130 

12,000 

Oak 

15  000 

2000 

7000 

1,215 

1,139 

10,600 

Pine.yellow 

13,000 

1,100 

5,400 

342 

640 

310 

•4,760 

Pine,  white 

10,000 

1,100 

5,000 

314 

640 

304 

5,000 

Spruce  

9,000 

600 

6,500 

400 

500 

272 

9,200 

Wires  and  Cables 

The  following  terms  are  in  common  use:  (1)  "  Solid  wire 
stay  "  or  "  aviation  wire  "  of  one  wire  of  suitable  diameter ; 
(2)  "  strand  stay,"  consisting  of  either  7  or  14  wires  stranded 
together  and  known  to  the  trade  as  "aviation  strand";  (3) 
"  cord  "  or  "  rope  stay,"  consisting  of  7  strands  twisted  to- 
gether, forming  a  rope,  the  strands  being  either  7  wires  or  19 
wires;  (4)  "flexible  cord,"  composed  of  six  strands  of  seven 
wires,  with  a  center  of  either  cotton  or  wire,  as  ordered.  The 
cord  with  the  cotton  center  is  considerably  more  pliable  than 
that  with  the  wire  center. 

Vanadium  steels  and  other  special  steels  have  uot  as  yet 
become  established  as  desirable  wire  steels,  and  carefully  made 
high-grade  carbon  steel  is  at  present  most  largely  employed  in 
the  manufacture  of  wires  and  cables. 

Properties  of  Metals 


Strength   and  Weights  for  Wire   and  Cables 
TABLE   3 


Diameter 
of  cord, 
Inches 
1/16 
5/69 
3/32 
7/64 
1/8 
5/32 
3/16 
7/32 
1/4 
5/16 


ROEBLING  SOLID  WIRE 

Breaking  strength 

of  cord, 

Pounds 

400 

480 

780 

830 

1,150 

2,200 

2,750 

4,000 

5,000 

7,900 


Approximate  weight 
per  100  ft., 
Pounds 
.73 
.83 
1.30 
1.50 
2.20 
4.20 
5.30 
7.43 
4.50 
15.00 


ROEBLING'S   19   WIRE   GALVANIZED — AVIATOR  WIRE   STRAND 


1/32  (7  wire) 
1/16 
5/64 
3/32 
7/64 
1/18 
5/32 
3/16 
7/32 
1/4 
9/32 
5/16 
11/32 
3/8 

AMERICAN    STEEL    AND    WIRE 


1/32  (7  wires) 

1/16 

3/32 

1/8 

5/32 


185 

500 

780 

1,100 

1,600 

2,000 

2,800 

4,200 

5,600 

7,000 

8,000 

9,800 

12,500 

14,400 

Co.    GALVANIZED 
STRAND 

125 

500 
1,100 
2,000 
3,000 


0.30 

0.78 

1.21 

1.75 

2.60 

2.88 

4.44 

6.47 

9.50 
12.00 
14.56 
17.71 
22.53 
26.45 

(19   WIRE)    AIRPLANE 


.23 
.89 

1.70 

3.3 

5.1 


ROEBLING'S  7  BY  19  HEAVILY  TINNED — AVIATOR  CORD 


1/8 
5/32 
3/16 
7/32 
1/4 
9/32 
5/16 
11/32 
3/8 


2,000 
2,800 
4,200 
5,600 
7,000 
8,000 
9,800 
12,500 
14,400 


2.88 

4.44 

6.47 

9.50 

12.00 

14.56 

17.71 

22.53 

26.45 


ROEBLING  EXTRA  FLEXIBLE  AVIATOR  CORD,  6x7  COTTON  CENTER 


5/16 

1/4 

7/32 

3/16 

5/32 

1/8 

7/64 

3/32 

5.64 

1/16 


9,200 

5,800 

4,600 

3,200 

2,600 

1,350 

970 

920 

550 

485 


16.70 

10.50 

8.30 

5.80 

4.67 

2.45 

1.75 

1.45 

.93 

.81 


AMERICAN  STEEL  AND  WIRE  Co.  GALVANIZED  OR  TURNED  FLEXIBLE  CORD 


3/16  (19  x  7) 

5/12  (19  x  7) 

1/8  (19x3) 

3/32  (12  x  3) 


2,600 

1,800 

1,150 

725 


5.52 
3.85 
2.45 
1.55 


The  figures  given  above  have  been  revised,  and  the  following 


Only  the  briefest  outline  can  be  given  of  the  metals  that  are 
commonly  employed  in  airplane  construction.     To  enter  into 
any  adequate  discussion  of  this  branch  of  the  work  would 
require  a  book  in  itself.    The  constructor  must  keep  constantly 
before  him  some  standard  book  on  this  subject  and  at  the  same 
time  resort  to  strength  of  material  and  part  tests  whenever 
new  combinations  are  to  be  employed  in  his  design. 
The  following  table  of  weight  and  melting  points  for  various 
metals  may  be  of  service  : 

ROEBLING  TINNED  AIRCRAFT  WIRE 

American                                                                    Minimum 
gauge                                                                       breaking                              Weight 
(B&S)                             Diameter,                         strength,                              Ib.  per 
Number                                  in.                                     Ib.                                   100ft. 
8                                   .128                               3000                               4.40 
9                                      .114                                  2500                                  3.50 
10                                   .102                               2000                               2.77 
11                                   .091                                1620                               2.20 
12                                   .081                                1300                                1.744 
13                                   .072                                1040                               1.383 
14                                   .064                                 830                                1.097 
15                                   .057                                 660                                  .870 
16                                     .051                                    540                                    .690 
17                                     .045                                    425                                     .547 

18 

.040 

340                                    .434 

Weight  per 

Weight  per 

Specific 

Melting  point 

19 

.036 

280                                     .344 

Metal. 

cu.  in. 

cu.  ft. 

Gravity 

Fahr.  °. 

20 

.032 

225                                    .273 

Aluminum                . 

096 

166 

2.66" 

1,215 

21 

.028 

175                                  .216 

Antimony             .... 

.242 

418 

6.70 

786 

Bismuth  

.350 

607 

9.74 

516 

ROEBLING 

19-WiRE  GALVANIZED 

AIRCRAFT  STRAND 

Brass    ca^t 

.292 

504 

8.10 

1,635 

Bra^s    rolled  

.303 

524 

8.40 

Diameter 

Breaking 

Approximate 

Bronze,  gunrnetal... 

.  .      .305 

529 

8.50 

1,866 

of  strand, 

strength  of 

weight, 

Copper    cast        .... 

.314 

542 

8.70 

1,980 

in. 

strand,  Ib. 

Ib.  per  100  ft. 

Copper    cold 

321 

555 

8.90 

5/16 

12,500 

20.65 

Duralumin               .  .  . 

.103 

178 

2.85 

(approx.)  1,300 

1/4 

8,000 

13.50 

Gold    24  carat 

694 

1,204 

19  26 

1,950 

7/32 

6,100 

10  00 

Iron    cast                 .  . 

260 

450 

7.21 

2,012 

3/16 

4,600 

7.70 

Iron,  wrought  

..      .278 

480 

7.70 

2,912 

5/32 

3,200 

5.50 

Lead    cast 

410 

710 

11.38 

621 

1/8 

2,100 

3.50 

Mercury  60"  Fahr.. 

...      .489 

846 

13.58 

7/64 

1,600 

2.60 

Monel  metal  

..      .320 

553 

8.85 

2,486 

3/32 

1,100 

1.75 

Platinum               .  .  . 

.779 

1,342 

21.50 

3,236 

5/64 

780 

1.21 

Silver  

.378 

655 

10.50 

1,762 

1/16 

500 

.78 

Steel    rolled 

.283 

490 

7.85 

2,552 

1/32  7  wire 

185 

.30 

Tin    cast  

.266 

459 

7.35 

450 

Zinc.  cast... 

.248 

429 

6.88 

786 

98 


AIRPLANE    DESIGN 


ROEBLINO  6x7  (COTTON  CENTER)  GALVANIZED  AIRCRAFT  COKD 


Diameter 
of  cord. 

Breaking 
strength  of 

Approximate 
weight, 

in. 

cord,  Ib. 

Ib.  per  100  ft. 

5/16 

7,900 

15.00 

1/4 

5.000 

9.50 

7/32 

4.0()0 

7.43 

3/18 

2,750 

5.30 

5/32 

2,200 

4.20 

1/8 

1,150 

2.20 

7/64 

830 

1.50 

3/32 

780 

1.30 

5/64 

480 

.83 

1/16 

400 

.73 

ROEBLINO 

7x7  (Wine  CENTER)  GALVANIIED  AIRCRAFT 

CORD 

Diameter 

of  cord, 

Breaking 
strength  of 

Approximate 
weight, 

in. 

cord,  Ib. 

Ib.  per  100  ft 

5/16 

9,200 

16.70 

1/4 

.-,.NK> 

10.50 

7/32 

•1,600 

8.30 

3/16 

3,200 

5.80 

5/32 

2.0011 

4.67 

1/8 

1.350 

2.45 

7/64 

970 

1.75 

3/32 

920 

1.45 

3/64 

550 

.93 

1/16 

485 

.81 

ROEBLINO  7x19  TINNED  AIRCRAFT  CORD 

Diameter 

Breaking 

Approximate 

of  cord, 
in. 

strength  of 
cord,  Ib. 

weight, 
Ib.  per  100  ft. 

3/8 

14,400 

26.45 

11/32 

12,500 

22.53 

5/16 

9,800 

17.71 

9/32 

8.000 

14.56 

1/4 

7,000 

12.00 

7/32 

5,600 

9.50 

3/16 

4,200 

6.47 

5/32 

2,800 

4.44 

1/8 

2,000 

2.88 

Wire,  Strand  or  Cord 

Roebling's  report  does  not  settle  the  question  as  to  which  is  a 
correct  selection.  A  comparative  table  shows  the  progressive 
decrease  in  strength. 


Material. 
Wire 
Strand 
7  by  19  cord 


Diameter. 
3/16 
3/16 
3/16 


Strength  of  material. 
5,500 
4,600 
4,200 


Strength  of  stay 
5,100 
4,100 
3,500 


A  stranded  or  cord  stay  has  about  20  per  cent  more  aero- 
dynamical resistance  than  a  solid  wire  of  about  the  same 
diameter.  There  appears  to  be  a  slight  advantage  in  favor  of 
solid  wire  as  regards  strength  of  stay.  On  the  other  hand,  the 
strand  stay  is  one  and  a  third  times  more  elastic,  the  cord  one 
and  three-quarter  times  more  elastic  than  the  solid  wire.  In 
American  practice  all  three  types  of  stays  appear.  No  doubt 
the  use  of  strand  or  cord  is  justified  by  the  extra  elastic  stretch 
and  flexibility. 

Exact  data  on  the  fatigue  values  of  the  three  materials  is 
not  available,  but  it  is  well  known  that  strand  or  cord  will 
stand  up  much  better  to  vibration  than  a  wire.  Also  in  a 
continuous  beam  structure  such  as  that  of  a  wing,  there  may 
be  deflections  of  unknown  magnitude,  in  which  case  the  more 
elastic  cable  will  be  somewhat  safer.  On  the  other  hand  an 
exposed  cable  is  liable  to  damage.  A  single  small  wire  of  one 
strand  may  be  damaged  and  lead  to  the  eventual  destruction 
of  the  whole  cable.  In  the  covered  in  body  a  cable  is  not  likely 
to  be  damaged.  The  problem  is  by  no  means  settled  yet,  and 
only  comparative  experience  in  actual  flight  and  further  experi- 
mentation can  give  a  definite  solution. 

Tnrnbuckles 

The  breaking  strength  of  turnbuckles  made  of  precisely  the 
same  material  will  vary  enormously  with  every  type  of  con- 
struction, and  the  makers'  catalog  or  data  sheet  has  to  be  con- 
sulted for  every  special  case.  In  Figs.  1  and  2  are  shown  two 
representative  types,  the  Curtiss  and  the  National,  Burgess, 
Meyer,  Binet  types.  The  weights  and  strength  values  are 
I'iiirly  representative  of  what  can  be  obtained  from  this  impor- 


tant brand  of  airplane  material.  In  Table  4  are  given  results 
of  tests  on  some  specimens  of  the  Standard  Screw  Co.  of 
Pennsylvania : 

TABLE    4 
STANDARD  SCREW  Co.  TURNBUCKLES 

Manufacturer  Mean  break-     Mean  break-  Initial  shank           Weight  in  Ib 

number.  ing  load.       ing  load  from  test,  area  per  s<*.  in.  Long,barrel  male 

326  2,150  2,432  .01864                      .122 

327  2,850  3,490  .0260                        .167 

328  3,500  4,605  .0350                         .232 

329  5,000  6,545  .0515                         .275 

330  840  9,530  .0794  .411 

Mean  tensile  strength  of  shank,  128.610  Ib.  per  s<<.  in.  Material — shank,  3>£  per 
cent,  nickel  steel,  heat  treated;  barrel,  robin  bronze.  Turnbuckles  are  madejin 
short  and  long  male  and  female  ends. 


Strength  of  Steel — Pounds  per  Sq.  Inch 


0.05  %C  for  rivets... 
0.10%  C  boiler  plate. 
0.25%  C  structural.  . 
040%  C  rails  . 

Tension 
Ultimate 
yield  point. 
.    45,000    22,000 
.    55.000   30.000 
.    65,000    34,000 
70  000    45  000 

Compression 
Ultimate 
yield  point. 
70,000     40,000 
95,000     65.000 
110,000     85,000 
120000     90000 

Shearing 
Ultimate 
vield  point. 
45,000     22,000 
50,000     28,000 
55,000     32,000 
60000     35000 

0.90%  C  machinery. 
1.00  to  2.00%  tool... 

.    90,000    70,000* 
.  150,000      none 

140,000    110,000* 
200,000      none 

70,000    «45,000 
120,000        none 

•When  well  annealed. 


Modulus  of  elasticity. 


Direct 

Shearing 

0.05%  C... 

.  .  .  .  26,000,000 

13,000,000 

0.10%  C  

.  .  .  .  28,000,000 

13,500,000 

0.25%  C  

30,000,000 

14,000,000 

0.40%  C  

30,000,000 

14,000,000 

0.90%C  

32,000,000 

14,500,000 

When  well  annealed. 

1.00  to  2.00%  C  

.  .  .  .  35,000,000 

16,000,000 

When  hardened. 

Modulus  of  Kupture 

For  flat  plates  

1.0     (t.  s.) 

For  squares  

1.2     (t.  s.) 

For  high  rectangles  

1.5     (t.  s.) 

For  rounds  and  diamonds.  .  .  . 

1.8     (t.  s.) 

Strength  of  Steel  Castings  —  Well  Annealed  — 


SMALL  CASTINGS 


Shearing 
ld 


Tension  Compression 

Ultimate  yield  point  Ultimate  yield  point  Ultimate  yield  point 

60,000     30,000  80,000      45,000  45,000     25,000  * 

Modulus  of  elasticity  (direct)  .......  ..............................  29,000,000 

Modulus  of  elasticity  (shearing)  ...................................   13,000,000 

Modulus  of  rupture  in  same  ratios  as  above. 

LAKGE  CASTINGS 

Tension  Compression  Shearing 

Ultimate  yield  point  Ultimate  yield  point  Ultimate  yield  point 

40,000     20,000  70,000     40,000  40,000     20,000 

Modulus  of  elasticity  (direct)  .....................................  28,000,000 

Modulus  of  elasticity  (shearing).  ..................................  13,000,000 

Modulus  of  rupture  in  same  ratios  as  above. 

Steel  Castings  with  Vanadium  show  about  20  per  cent  increase  over  the  above 
values. 


Special  Steel  Alloys — Pounds  per  Square  Inch 


Tensile  strength. 

Manganese Up  to       140,000 

Nickel HO.mn 

Chrome  Vanadium 200,000 

Chrome  Nickel 140,000 

Tungsten 170,000 

Chrome  Tungsten 185,000 


up  to 


Yield  point 

90,000 

90,000 
175,000 
100,000 
150,000 
160,000 


Strength  of   Copper,  Aluminum   and   Various   Alloys 
Pounds  per  Square  Inch 


CAST 

Tension  ...........................................    22.000 

Compression  .......................................    45,000 

Shearing  ..........................................    18,000 

Modulus  of  elasticity  (direct)  .....................................   12,000,000 

Modulus  of  elasticity  (shearing)  ...................................     8,000,000 

Modulus  of  rupture  (rectangular  sections)  ..........................          35,000 

COLD    ROLLED   OR   HAMMKKKD    PI.ATKS 

Tension  ...........................................  32,000 

Compression  .......................................   60,000 

Shearing  ...........................................  28,000 

COLD  DRAWN   \ViKK 

Tension  ....................................  50,000  to  60,000 

Shearing  ...................................  40,000 

Modulus  of  elasticity  of  cold  worked  cupper  17,000,000.     Copper  has  no  well 
defimd  >  ield  point. 


AIRPLANE    DESIGN 


99 


L 


Cur- 

Th'ds 

tiss 

No. 

A 

H 

C 

L) 

E 

F 

G 

H 

I 

j 

K 

L 

M 

N 

0 

P 

Q 

R 

S 

T 

u 

V 

\v 

X 

Per 

Br'k'g 

Cable 

Weight 

No. 

Inch 

Stress 

M  iQ- 

Spec 

ial 

7?4 

4 

X 

K 

X 

A 

H 

.320 

A 

% 

% 

14 

A 

H 

H 

A 

1A 

A 

H 

X 

H 

A 

IX 

IX 

24 

8846 

^able 

3 

326 

8 

4 

A 

A 

% 

ft 

A 

.159 

X 

.203 

H 

% 

M 

.110 

A 

A 

ft 

A 

1A 

A 

,".. 

,:!,, 

IX 

lij 

30 

2183 

h 

4 

327 

7H 

4 

M 

H 

15 

H 

A 

.187 

A 

.234 

A 

tt 

X 

H 

A 

M 

H 

A 

K 

X 

ft 

M 

IX 

LM 

28 

3037 

%  in. 
Cable 

5 

328 

T:,: 

4 

H 

H 

H 

A 

% 

.215 

A 

.265 

A 

H 

A 

H 

A 

K 

H 

M 

H 

H 

'4 

k 

i  A 

1« 

26 

3993 

A 

6 

329 

~\':, 

4 

H 

'A 

H 

tt 

A 

.258 

A 

A 

% 

K 

% 

H 

A 

A 

H 

A 

K 

A 

A 

A 

14 

i,s« 

24 

5750 

A 

10GA 

326-S 

'•'•I':. 

2 

A 

A 

X 

ft 

A 

.159 

X 

.203 

X 

H 

34 

.110 

A 

A 

ft 

A 

J4 

A 

A 

A 

A 

H 

30 

2183 

Wire 

8GA 

327-S 

4A 

2H 

H 

H 

H 

J5 

A 

.187 

A 

.234 

A 

H 

X 

.110 

H 

M 

H 

A 

H 

Yt 

A 

K 

A 

H 

28 

3037 

Wire 

Material: — Mang.  Bronze  and  55-Ton  Steel 

FlO.    1. CUHTISS  TURNBUCKLES. 


i  ! 

30 

L 


-L-- 


! 


SPECIMEN 

L 

H 

d, 

d, 

da 

di 

d, 

1 

Weight  Ibs. 

Estimated  Load. 
Pounds 

Remarks 

2  35 

1  30 

28 

23 

11 

15 

20 

45 

039 

1250 

National  No    327 

2  50 

2  50 

40 

32 

19 

23 

35 

60 

161 

2200 

National  No.  328    

5.00 

2.75 

48 

37 

20 

27 

.40 

.65 

.''29 

2800 

Yield  in  barrel. 

National  No    328           

5  00 

2  80 

46 

38 

22 

27 

40 

70 

.242 

2200 

National  No    329 

6  00 

3  25 

54 

44 

23 

31 

47 

85 

361 

4000 

A    J    Meyer  No.  3  

2.35 

1.30 

.28 

.21 

.11 

.15 

.19 

.45 

.037 

1200 

Yield  in  barrel. 

Above  average. 

A  J   Meyer  No  4 

3  00 

1  75 

32 

20 

14 

18 

28 

45 

0682 

1500 

A  J   Meyer  No.  6.          

4  50 

2.5ID 

42 

32 

19 

23 

35 

.55 

.161 

2200 

Yield  in  barrel. 

6  00 

20 

.172 

"SOU 

4.80 

2.70 

.62 

.51 

.30 

.33 

.57 

.80 

.506 

7000 

Yield  in  barrel. 

Estimated  load  based  upon  average  strength  at  yield  point  of  barrel  41,000  Ib.  per  sq.  in.     Average  tensile  strength  barrel,  69,033  Ib.  per  s<j.  in.      Average 
tensile  strength  of  shank  130,000  Ib.  per  sq.  in. 

FIG.  2: — MEYER.  NATIONAL.  BURGESS  AND  BINET  TURXBUCKLES. 


100 


AIRPLANE    DESIGN 


CAST  AI.UMI.NCH 

Tension 14,000 

Compression 25,000 

Shearing 10,000 


COLD  WOBKED  ALUMINUM  PLATE  AND  WIRE 

Tension.. .  24,000  (Plate) 

Tension 40,000  (Wire) 

Modulus  of  elasticity  (direct) 8,000,000 

Aluminum  has  no  well  defined  yield  point. 


DUEALUMIN 

Tension.  33,000;  Compression,  68,000;  Modulus  elasticity,  10,000,000. 
High  brass Tension  35,000 


Low  brass 

Composition 

Bronze 

Phosphor  bronze. . . . 

Tobin  bronze 

Tobin  bronze 

Delta  metal 

Manganese  bronze. . . 


28.000 
30,000 

30,000  to  75,000  varying  with  composition. 
40,000  to  130,000,  varying  with  form. 
80,000,  yield  point  50,000  hot  rolled. 
100,000,  vield  point,  70,000  cold  rolled. 
45,000  Cast.     Tension,  70,000  cold  rolled. 
70,000  Ibs./sg.  in. 
Compression,  120,000  Ibs./sq.  in. 

Monel  metal  (hot  rolled) Tension  (ultimate)  88,150  Ibs./sq.  in. 

(yield.  58,000  Ibs./sq.  in. 
elongation  in  2  inch,  38  per  cent. 

The  steel  at  present  in  common  use  among  manufacturers 
is  the  mild  sheet  steel  generally  designated  as  cold  rolled  steel 
(C.R.S.).  Whether  its  easy  working  qualities  or  its  cheap- 
ness and  easy  supply  has  brought  about  this  poor  choice,  is 
hard  to  judge.  It  is  a  relief  to  find  that  the  constructors  and 
the  Government  are  endeavoring  to  do  away  with  this  most 
unreliable  and  inefficient  of  materials.  Instances  have  only 
too  often  been  brought  to  our  attention  when  upon  the  com- 
pletion of  some  small  stamped  fitting,  the  apparently  solid 
metal  is  found  to  be  of  two  distinct  layers  of  thinner  metal 
held  together  only  at  a  few  points.  It  is  not  well,  however, 
to  jump  too  quickly  to  the  other  extreme  and  attempt  to  use 
the  very  high  strength  alloys — requiring  expert  working  and 
heat  treatment.  Companies  to-day  are,  with  a  few  exceptions, 
not  in  a  position  to  undertake  this  added  responsibility  and 
the  forcing  of  such  delicate  work  upon  inexperienced  hands 
would  be  as  dangerous  as  the  present  methods. 

The  following  table  outlines  the  general  influence  of  chemical 
composition  of  the  physical  properties  of  steel: 


i 

E 

i 

J-          c 

8 

0 

S£ 

01 

£      1 

w 

H 
C 

a      g 

SCO 

r-    ^ 

£•»! 

s 

V               o 

1 

1 

g     I  . 

11 

S"l 

.0 

B          'S 

8 

•D 

9 

3     -2-3 

.2« 

SS  » 

T3 

g          % 
H          K 

Q 

i 

a 

£    11 

ll 

6»« 

fi-S? 

^ 

(1)         + 

• 

(2) 

+       (12) 

I 

Phosphorus  .  . 

(13)       .  .  . 

(3) 

0 

(4)        — 

— 

0 

.1.                 

_L_ 

(5) 

0 

(6) 

0 

(7) 

(8) 

0 

Vanadium.  .  . 

+                  + 

(9) 

+ 

4_ 

Chromium..  . 

+                  + 

_l_ 

•L 

,1. 

4- 

4-          4- 

Nickel  

i             i 

(9) 

1 

t 

-f. 

0 

00) 

_l_ 

(11) 

_L 

The  above  table,  while  very  comprehensive,  should  not  be 
considered  as  final. 

The  matter  of  weldability  of  the  chrome  vanadium  and 
nickel  steel  is  indefinite,  very  reliable  information  showing 
that  3a/4  per  cent,  nickel  steels  give  better  welds  than  the  chro- 
mium steel. 

The  S.A.E.  Specification  No.  3130  for  a  low  carbon  chrome- 
nickel  steel,  or  Specification  No.  2330  for  3l/2  nickel  steel 
would  seem  to  meet  the  requirements  of  the  manufacturers  as 
well  as  the  Army  Specifications  of  the  S.A.K.  No.  6130 


chrome-vanadium,   eliminating   at   the   same   time,   the   great 
danger  of  segregation  due  to  faulty  heat-treatment. 

Heat  treatment  and  its  influence  cannot  be  gone  into;  it 
requires  very  careful  study  and  infinite  care  in  application. 

Strength  and  Weight  of  Mild  Steel  Rivets  and  Pins 

Diameter,  inches.  Strength  in  Pounds 

"d."  Single  Shear.  Double  Shear.            Crushing  +  (. 

1/8  1,000  1,600  1,200 

3/16  1,600  3,000  1,800 

1/4  2,750  4,500  2,400 

5/16  3,900  7,000  2,800 

3/8  5,000  9,800  3,600 

1/2  9.000  17,800  4,800 

3/4  20,000  40,000  7,200 

1  35,500  71,000  9,600 

The  above  values  are  based  upon  a  shearing  strength  in 
pounds  per  square  inch  fs  =  45,000  and  a  crushing  strength, 
fc  =  96,000. 

Ps  =  ff—~  for  single  shear. 

pc  =  fcdxt,  for  crushing,  where  t,  the  thickness  of  the  plate 
or  other  piece  held  by  the  rivet  or  pin. 

The  values  for  crushing  have  been  worked  out  for  a  plate 
1  inch  thick,  therefore  the  crushing  strength  for  various  thick- 
nesses of  plate  may  be  computed  by  multiplying  the  above 
values  by  "  t  "  in  inches. 

If  the  crushing  strength  of  the  rivet  is  greater  than  its 
shearing  strength  the  design  should  be  based  upon  the 
smaller  result. 

In  case  the  bolt  is  subjected  to  a  load  other  than  tension, 
the  strength  should  be  based  upon  the  corresponding  form  of 
loading.  When  bolts  and  pins  are  used  in  turnbuckle  fittings 
and  wire  connections  they  arc  usually  subjected  to  a  form 
of  bending  and  should  be  calculated  as  a  beam  round  cross 
section  loaded  at  the  center. 

/  =  — ,  where  /  =  modulus  of  rupture,  M  =  bending  mo- 
ment due  to  load  generally  considered  concentrated  at  the 
center,  Y  =  distance  from  neutral  axis  to  most  strained  fiber, 
in  this  case  */2  D ;  I  =  moment  of  inertia  of  cross  section. 

In  figuring  bolts  that  pierce  wooded  members  the  failure  of 
the  wood  should  be  considered  first,  since  in  this  type  of  con- 
nection rupture  is  most  often  caused  by  the  fastening  pulling 
out  or  loosening  due  to  the  wood  crushing  in  front  of  the 
P  =  fc  X  L  X  D.  Where  P  =  crushing  load,  /c  =  crushing 
strength  of  wood,  L  =  length  of  bolt  in  wood,  D  =  normal 
bolt  diameter. 

United  States  Standard  Bolts  and  Nuts 


X 

*~ 

*o  - 

j 

><  c 

S 

V)    W 

5  — 

o 

o  ii 

1 

|.s 

i 

I? 

S 

If 

S  . 

"g 

.  a 

1 

.213" 

41 

T) 

a  c 
^  a 

.S-°a 
WB1" 

.2  * 

i 

"°  a 

C-- 

™   S 

g 

b 

.   Ol     - 
C.  G  « 

dc 

h 

§5 

1* 

^^ 

i 

H 

«  M 

<8c 

§8.S 

1/4 

0.185 

0.049 

0.027 

20 

1/4 

0.578 

0.707 

5/16 

0.240 

0.077 

0.045 

18 

19/32 

0.686 

0.840 

3/8 

0.294 

0.110 

0.068 

16 

11/16 

0.794 

0.972 

7/16 

0.345 

0.150 

0.093 

14 

25/32 

0.902 

1  .  105 

1/2 

0.400 

0.196 

0.126 

13 

7/8 

1.010 

1.237 

9/16 

0.454 

0.249 

0.161 

12 

31/32 

1.119 

1.371 

5/8 

0.507 

0.307 

0.202 

11 

1-  1/16 

1.227 

1  503 

3/4 

0.620 

0.442 

0.302 

10 

1-  1/4 

1.443 

1.768 

7/8 

0.731 

0.601 

0.420 

9 

1-  7/16 

1.661 

2.033 

1 

0.837 

0.785 

0.550 

8 

1-  5/8 

1.876 

2.298 

1-1/8 

0.940 

0.994 

0.694 

7 

1-13/16 

2.093 

2.564 

1-1/4 

1.065 

1.227 

0,891 

7 

o 

2.310 

2.828 

1-3/8 

1.160 

1.485 

1.057 

6 

2-  3/16 

2.527 

3.094 

1-1/2 

1.284 

1.767 

1.295 

6 

2-  3/8 

2.743 

3.358 

1-5/8 

1.383 

2.074 

1.515 

5-1/2 

2-  9/16 

2.959 

3.624 

1-3/4 

1.431 

2.405 

1.746 

5 

2-  3/4 

3.176 

3.889 

1-7/8 

1.616 

2.761 

2.051 

5 

2-15/16 

3.393 

4.156 

NOTE:  —  Depth  of 

nut     = 

nominal 

diameter. 

Depth  of 

head    •- 

one-half 

short  diam. 

of  hex.  and 

su.  nuts. 

AIRPLANE     DESIGN 


101 


The  strength  of  United  States  standard  bolts  may  be  based 
upon  the  formula  P  =  A  X  ft-  Where  P  =  the  strength  of 
the  bolt,  ft  =  tensile  fiber  stress  per  square  inch  =  65,000, 
A  =  effective  area  at  root  of  thread.  Solving  for  D  the  nom- 


inal diameter  Z>  =  1.24  -»  — 


.088. 


Quality 


Width 


TABLE  6. 

Approximate  breaking  strength 
per  inch. 


A24  .  .  . 

inches. 
36 

Warp 
72  Ib 
90.5 
108.5 
114.7 
112 
129.4 

Weft. 
78  Ib 
101.9 
94.6 
103.6 
115.6 
123.4 

Weight  per 
4.00  o 
4.00    ' 
4.00   ' 
4.00   ' 
4.12   ' 
3.75   ' 

an.  yd. 

,. 

A29   . 

36 

A31  

36 

A33 

36 

*A37. 

36 

*A40... 

.     36 

*British  Government  Standard  qualities. 


Airplane  Fabrics 

The  general  requirements  and  tests  for  airplane  fabrics  are 
well  summarized  by  the  following  table: 

(1)  Fabric  should  present  reasonably  great  resistance  to  flame. 

(2)  It  should  be  proof  against  the  action  of  salt  water,  moist  air,  extreme  dryness 

quick  changes  of  temperature. 

(3)  It  should  not  stretch  in  any  direction. 

(4)  It  should  have  a  tensile  strength  of  at  least  75  !b.  per  inch  width  in  any, 

direction. 

(5)  The  tendency  to  tear  and  split  because  of  tacks,  bullets,  etc.,  should  be 

almost  nil. 

(6)  The  weight  should  be  taken  in  an  atmosphere  of  65  per  cent  relative  hu- 

midity at  70°  Fahr. 

(7)  The  weight,  yarn  number  and  tensile  strength  of  the  fabric  should  be  ob- 

tained when  it  is  in  a  bone  dry  condition,  i.  e.  after  it  has  been  subjected  to 

a  temperature  of  221V  Fahr.  for  two  hours. 
Identity  and  average  length  of  fibers  should  be  ascertained. 
Determination  should  be  made  of  the  percentage  moisture  "regain"  under 

the  available  range  of  temperature  and  humidity. 
A  shrinkage  determination  should  be  made. 


(8) 
(9) 

(10) 


Some  Representative  Specifications,  Strength  and 
Weight  Figures 

In  Table  4  are  given  some  representative  specifications  which 
represent  the  average  values  of  current  practice. 


TABLE  5. 


Specifications 
Curtiss  No  66 

Weight 
per 
square 
yard 
ounces 
4 

Threads      Threads 
per              .per 
inch             inch 
warp            weft 

96               100 

92                95 
94               100 

95                99 
275  threads  per  sq.  in. 

Strength 
per  inch 
width 
(warp) 

91 

92 

75 

87 

Strength 
per  inch 
width 
weft 
(Ib.) 
102 

95 
85 
(minimum) 
108 

96 

Oct.  26,  1916 
R.  A.  F.  No.  17-C.... 
U.  S.  Army  No.  1002  . 

McBratney  tests  

4 
.3.75-4.4 

4 

Clarence  Whitman 
(cotton)... 

4 

Messrs.  Lamb,  Finlay  and  Co.  have  kindly  communicated 
the  average  values  of  tests  extending  over  a  number  of  ship- 
ments, in  accordance  with  British  Government  specifications: 

"Three  pieces  are  cut  from  the  length  and  three  pieces  from  the  width  of  the 
goods.  These  samples  must  be  long  enough  to  leave  6  in.  clear  between  the  grips 
and  sufficiently  wide  to  leave  the  test  pieces  2  in.  wide  after  trimming.  The  test 
pieces  are  soaked  in  water  for  two  hours.  They  are  then  taken  out  and  the  excess 
water  ia  removed  and  the  goods  put  in  an  Avery  machine,  the  load  being  applied  at 
the  rate  of  50  Ib.  per  inch  width  per  minute." 

This  method  of  testing,  while  apparently  arbitrary,  is  con- 
venient and  avoids  errors  due  to  humidity  changes,  and  is 
preferable  to  a  test  on  dry  material. 

In  the  National  Advisory  Report  the  following  figures  are 
given  for  fabrics  of  difrYient  weights: 


I 

Weight  in  ozs. 
per  sq.  vd. 
3.67 

Strength 
Warp          Filler 
65.0            54.4 
69.5            49.2 
80.7            79.0 
86.9            74.0 
90.2            82.7 
82.9           100.1 
95.0            60.0 
90.4           102.5 

II 

3.78 

III 

3.87 

IV                       

4.04 

V                

4.09 

VI 

4.48 

VII 

4.60 

VIII. 

....4.86 

Wing  Dope  and  Varnish 

The  following  notes  on  dope  and  varnish  may  be  of  interest 
to  the  manufacturer: 

Dope  alone  on  Irish  linen  surfaces  has  proven  very  satis- 
factory. Four  to  five  coats,  allowing  about  one-half  hour  for 
drying  between  each  coat  are  ample  protection  for  the  most 
severe  conditions.  Very  rigorous  tests  on  samples  exposed 
to  the  weather  during  the  month  of  February  resulted  in  no 
ill  effects,  the  cloth  remaining  tight,  glossy  and  without  spots, 
cracks  or  tears.  The  weight  of  the  covering  is  increased  about 
.66  oz.  per  square  yard  per  coat,  with  an  application  of  ap- 
proximately one  gallon  to  ten  square  yards. 

Varnish  finish  is  recommended  in  many  cases  as  more 
permanent  and,  being  less  effected  by  salt  water,  has  some  ad- 
vantages on  water  machines.  When  repairing  is  to  be  done 
it  is  first  necessary  to  remove  the  varnish  before  the  patch  is 
applied  with  dope,  as  a  glue,  causing  some  inconvenience. 

Doped  surfaces  have  about  8  per  cent  to  10  per  cent  more 
strength  and  more  resistance  to  tearing.  It  is  necessary  to 
redope  all  surfaces  every  three  to  five  months. 

Cotton  and  silk  fabrics  have  a  tendency  to  rot  when  covered 
with  dope  or  varnish  and  such  surfaces  are  not  recommended. 


References,  Part  II,  Chapter  5 


AIRPLANE  FABRICS 

"First  Annual  Report  of  the  National  Advisory  Committee  on  Aeronautics." 
"Balloon  and  Aeroplane  Fabrics,"  by  Willis  A.  Gibbons  and  Omar  H.  Smith. 
"Circular  No.  41."  Bureau  of  Standards. 

TIMBER 

Judge's  "Aeroplane  Design." 

"Material  of  Construction,"  Adelbert  P.  Mills. 

"Mechanical  Engineers'  Handbook,"  Lionel  S.  Marks. 

"Lanza's  Applied  Mechanics." 

"The  Mechanical  Properties  of  Wood,"  by  Samuel  J.  Record  (containing  numerous 
references.) 

"Reports  of  Tests  on  the  Strength  of  Structural  Material,"  Made  at  the  Watertown 
Arsenal,  Mass. 

Publications  of  the  U.  S.  Forest  Sertice  on  "The  Mechanical  Properties  of  Wood 
and  Timber  Testing." 

METALS 
"Materials  of  Construction,"  Prof.  Upton,  of  Cornell  University. 

WIRES  AND  CABLES 

First  Annual  Report  of  the  National  Advisory  Committee  on  Aeronautics,  Avia- 
tion Wires  and  Cables." 

(This  also  contains  much  valuable  information  on  fastenings.) 

TURNBUCKLES 
Arthur  Orr,  AVAITION  AND  AERONAUTICAL  ENGINEERIEG,  December  1,  1915. 


Chapter  VI 

Worst  Dynamic  Loads;  Factors  of  Safety 


One  of  the  most  difficult  problems  in  aeronautics  is  the 
estimate  of  the  worst  loads  likely  to  come  on  under  unusual 
circumstances,  on  which  alone  correct  allowances  for  factors 
of  safety  can  be  based.  In  speaking  of  factors  of  safety,  a 
distinction  must  be  made  between  the  load  factor  of  safety  and 
the  gross  factor  of  safety.  Thus,  if  the  load  factor  of  safety 


levotot- 


FlG.l 

for  a  certain  part  of  the  machine  is  four,  the  material 
employed  may  be  so  untrustworthy  that  an  allowance  for  it, 
of  say  one  and  a  half,  may  have  to  be  made,  bringing  up  the 
gross  factor  of  safety  to  six.  It  is  the  gross  factor  of  safety 
which  is  commonly  spoken  of  as  the  factor  of  safety. 


Conditions  Under  Which  Heavy  Loads  Come 

Heavy  loads  come  on  an  airplane  under  so  many  conditions, 
that  the  following  classification  is  probably  incomplete.  It  is, 
however,  all  that  is  possible  in  the  present  stage  of  the  art. 

(A)  In  the  air: 

(1)  in  flattening  out  of  a  steep  dive 

(2)  in  heavy  banking 

(3)  in  looping 

(4)  in  sudden  gusts. 

(B)  On  the  ground: 
(1)     on  landing 

We   shall   consider   these   conditions   one   by   one   as   far   as 
possible. 

The  wing  structure  will  meet  with  the  greatest  loads  in  the 
air.  On  landing,  the  wing  structure  has  to  meet  only  the  shock 
resulting  from  the  decceleration  of  its  own  weight  which  may 
be  some  12-15  per  cent  of  the  weight  of  the  machine,  while  in 
the  air,  it  has  to  support  the  whole  weight  of  the  airplane  and 
under  certain  conditions  five  or  six  times  the  whole  weight. 
It  is  in  the  air,  therefore,  that  the  wings  meet  the  worst  condi- 
tions. The  body  may  carry  severe  stresses  in  the  air  when 
powerful  forces  come  into  play  on  the  rudder  and  elevator, 
but  it  may  also  be  powerfully  stressed  on  landing.  For 
chassis  design,  it  is  only  landing  and  taxi-ing  stresses  that  need 
be  considered. 

(1)  Flattening  Out  After  a  Steep  Dive 

The  exact  mathematical  computation  of  stresses  in  such  a 
case  is  not  yet  possible;  it  is,  however,  interesting  to  see  how 
such  stresses  arise,  and  how  they  are  limited. 

In  order  to  have  a  concrete  case,  we  will  consider  the  Clark 
model  tested  at  the  Massachusetts  Institute  of  Technology,  and 
described  in  Hunsaker's  "  Dynamical  Stability."  This  had  the 
following  estimated  characteristics: 

Wing  area  including  ailerons 404  sq.  ft. 

Span    4O.2  ft.  mean 

Area,    stabilizer 10  1   sq.   ft. 

Area,    elevators 10.0  sq.   ft. 

Area,  rudder "J. .';.")  sq.   ft. 

Length,  body £4,5  ft. 

Weight  (tanks  half  full) 1000  II). 

(5.2   ft.   in   roll 
Kadii  of  gyration •{  4.05   ft.   In   pitch 

U).!>75  ft.   in  yaw 

lirake  horse-power 110 

Maximum   speed N7   in.p.h. 

-Minimum   speed 35   m  p.li. 

Best  glide 1  in  9 

For  a  tail  setting  of  — 5  deg.  to  the  wings,  the  model 
(l/26th  full  size)  had  the  following  forces  acting  on  it  at  a 
speed  of  30  m.p.h.,  which  we  shall  use  without  correction  for 
Iranst'erring  to  the  full  size  machine: 

Lift  on  model  at  Drift  on  model  at 

Angle  30  m.p.h.  :;o  ni.p.h. 

— 1  —.ll.->  +.12S 

— 2  +.112  +.M8 

—1  -f.240  +.104 

0  +.::oo  +.lol 

+1  +.41KI  +.102 

+2  +.025  +.105 

+4  +.872  +.115 

+8  +1.305  +.1.13 

+12  4-1.BA8  +.213 

+  10  4-1,640  +.:t70 

+  18  4-1.680  +.498 


102 


AIRPLANE    DESIGN 


103 


In  the  U.  S.  Army  Specifications  1002  (reprinted  in  AVIA- 
TION AND  AERONAUTICAL  ENGINEERING  of  November  1,  1916), 
one  of  the  stipulations  for  airworthiness  is  that  the  pilot  may 
be  required  to  dive  at  an  angle  of  50  deg.  to  the  horizontal, 
to  maintain  such  a  dive  for  one  or  two  seconds,  and  then  to 
pull  out  reasonably  quickly.  We  will  assume  that  the  dive  is 
continued  for  even  a  longer  period  so  that  the  limiting 
velocity  is  reached,  and  then  try  to  see  what  will  happen  on 
flattening  out  sharply. 

The  propeller  thrust  on  the  dive  may  be  neglected  whether 
the  engine  is  cut  off  or  not,  the  slip  being  so  enormous  as  to 
reduce  it  to  a  negligible  quantity. 

Considering  the  sketch  of  Fig.  1,  the  equations  of  motion 
evidently  are 

D  =  W  sin  6 
L  =  W  cos  6 

The  most  straightforward  way  of  finding  at  what  incidence 
to  the  flight  path  the  machine  is  under  steady  limiting  condi- 
tions, is  one  of  trial  and  error.  After  one  or  two  trials,  we 
find  that  the  angle  of  incidence,  2%  deg.  will  satisfy  condi- 
tions. 

The  drag  on  the  model  at  this  angle  is  0.111  lb.,  and  the  lift 
0.094  lb.  at  30  m.p.h.  The  two  equations  are  very  nearly 
satisfied.  Thus  converting  to  full  size  conditions: 

(1)  TF  sin  50  deg.-=  (1600)  (0.7660)  =  0.1235  = 

0  111  X  26" 

-~ 7'and  F=  =  14,850,  V  =  122  m.p.h. 

(2)  TF    cos    50    deg.  =  (1660)     (0.06428)  =  1030    while 
0.094  X26* 


302 


•  X  0.14850  =  Lift  =  1040  lb. 


the  difference  of  10  lb.  in  the  lift  being  negligible. 

If,  at  this  point,  the  pilot  throws  his  elevator  hard  up,  he 
will  increase  his  angle  of  incidence  rapidly,  and  move  his  path 
more  and  more  to  the  horizontal.  .  The  rapidity  with  which  he 
can  come  out  of  the  dive  depends  on  the  force  which  he  can 
bring  to  bear  on  the  elevator,  and  is  resisted  by  the  inertia  of 
the  machine,  and  the  damping  against  angular  rotation.  There 
is  reason  to  believe  that  during  this  process  he  loses  very  little 
speed.  The  equations  of  motion  during  this  process  are  some- 
what complicated  and  cannot  be  solved  directly.  But  if  we 
assume  that  for  a  machine  of  this  type,  the  pilot  can  change 
his  angle  of  incidence  to  say  8  deg.  without  losing  speed,  the 
lift  on  the  model  at  this  speed  being  1.305,  the  lift  on  the 
machine  becomes 

-X26'X1222  =  14,400   lb. 


or  a  load  of  nine  times  the  weight  of  the  machine.  It  is 
commonly  accepted  that  the  actual  load  is  not  quite  so  great, 
being  between  5  and  6.  The  pilot  could  not  easily  wreck  a 
machine  with  moderately  strong  controls,  and  weights  dis- 
tributed far  from  the  center  of  gravity  giving  a  large  moment 
of  inertia.  But  with  a  light  machine,  with  weights  close  to  the 
center  of  gravity  and  a  powerful  elevator,  a  reckless  recovery 
would  be  highly  dangerous. 

It  should  be  pointed  out  that  the  uncertainty  as  to  the  exact 
movements  a  machine  goes  through  on  flattening  out,  makes 
the  question  of  the  angles  of  incidence  at  which  loads  on  front 
and  rear  spars  should  be  distributed  and  computed  a  very  con- 
troversial one.  The  latest  U.  S.  Army  specifications  call  for  a 
stress  diagram  at  15  deg.,  which  throws  the  greater  load  on 
the  front  spar.  If,  as  is  quite  possible,  a  machine  flattening 
out  after  a  steep  dive  does  not  reach  such  a  high  angle  of 
incidence,  but  arrives  at  some  intermediate  angle  such  as  the 
8  deg.  mentioned  above,  then  it  would  be  fairer  to  draw  a 


stress  diagram  at  this  angle  of  incidence,  with  a  more  equal 
distribution  between  the  two  spars. 

(2)   Loading  in  Heavy  Banking 

The  loading  on  a  steep  bank  is  dependent  on  the  speed, 
radius  of  turn,  and  angle  of  bank. 

In  the  sketch,  Fig.  2,  the  machine  is  moving  out  of  the  plane 
of  the  paper  and  turning  at  an  angle  of  bank  6.  The  three 
forces  acting  in  the  vertical  plane  of  the  machine  are  the  lift, 
the  weight  and  the  centrifugal  force,  which  may  be  assumed 
as  acting  at  the  center  of  gravity  of  the  machine.  Resolving  L 
along  the  lines  of  these  two  forces,  we  have  as  equations  of 
equilibrium 

TF  F2 

L  sin  6  =  KT  AV*  sin  6  =—  -^~ 

g  K 

L  cos  6  =  K*  AV  cos  6  =  TF 

where  F  =  speed  in  feet  per  second,  and  R  =  radius  in  feet. 
From  these  equations,  one  important  fact  appears,  that  on  a 


FIG.  2 


steep  bank  where  cos  6  is  small,  the  lift  of  normal  flight  is 
insufficient,  and  that  before  banking  a  pilot  must  increase  his 
power  and  speed,  otherwise  his  machine  may  drop  on  the 
bank. 

The  load  on  the  machine  in  banking  will  increase  with  the 
centrifugal  force  to  be  overcome  in  addition  to  the  weight,  and 
is,  therefore,  greatest  when  the  velocity  has  increased  beyond 
the  maximum  in  normal  flight  and  when  the  radius  of  turn  is 
very  small. 

For  the  Clark  model  previously  considered,  we  will  assume 
that  the  machine  has  attained  a  speed  of  120  m.p.h.  or  176 
ft.  per  second,  after  a  dive  and  that  the  pilot  goes  into  a  sharp 
turn  of  400  feet  radius. 

From  the  equations  of  equilibrium  we  have 
W  F| 

g  JR_  _     V^  _      30.500 
gE 


tan  6  = 


=  2.37 


TF          gE       32.2  X  400 

6  =  67  deg.  and  sec  6  =  2.559,  which  is  certainly  a  fairly 
steep  angle  of  bank.  Since  L  cos  6,  L  =  sec  TF  =  2.559  TF. 

It  is  possible  to  consider  a  case  where  the  velocity  would  be 
still  greater  than  the  120  miles  per  hour,  and  the  radius  still 
smaller,  in  which  case  the  loading  might  still  be  heavier.  It 
does  not  seem  probable,  however,  that  the  worst  possible 
loading  on  a  bank  would  exceed  3  or  4  TF. 

The  angle  of  incidence  on  a  bank  interests  us  again  from 
the  point  of  center  of  pressure  and  distribution  of  pressure 


104 


AIRPLANE    DESIGN 


between  the  two  spars.     Considering  the  Clark  model  of  the 
previous  paragraph,  IF  =  1600  and  L  =  2.559  TT  =  4100  = 
K,  X  464  X1201 
from  which  K,  =  *  =  0.000615 


4,400 

and  the  angle  of  incidence  is  not  much  above  0  deg.  for  the 
Clark  machine  on  such  a  bank. 

(3)  Loading  in  Looping 

In  looping  similar  methods  would  be  employed  as  in  con- 
sidering flattening  out  after  a  dive.  The  probable  maximum 
loading  is  estimated  to  be  4. 

(4)  Stresses  Due  to  Gusts 

Another  cause  of  violent  stresses  is  in  the  action  of  sudden 
gusts  on  a  machine,  where  the  inertia  tends  to  maintain  the 
same  speed  for  a  different  angle  of  incidence,  or  the  same 
incidence  for  a  different  speed. 

The  machine  may  encounter: 

(a)  a  head-on  gust 

(b)  a  following  gust 

(c)  an  up-gust 

(d)  a  down-gust. 

Granted  a  sufficiently  violent  gust,  there  is  no  possible  limit 
to  the  stresses  which  may  come  on  a  machine  in  such  cases, 
and  a  hurricane  might  wreck  a  machine  for  whatever  factor 
of  safety  it  was  designed.  It  is  necessary  to  investigate,  how- 
ever, whether  the  gusts,  as  we  may  expect  to  occur  in  ordinary 
practice  from  our  metereological  data,  are  well  within  safe 
limits. 

(a)     Head-on  Gusts 

Imagine  the  Clark  machine  to  be  moving  at  59  m.p.h.  at 
an  angle  of  incidence  2  deg.  against  a  head-on  wind  of  20 
m.p.h.  so  that  its  absolute  velocity  relative  to  the  earth  is 
39  m.p.h.  If  the  head-on  wind  increases  to  30  m.p.h.,  the 
absolute  velocity  relative  to  the  earth  will  still  remain  at  39 
miles  for  a  second  or  two.  During  this  period,  the  velocity 
to  the  air  will  increase  to  69  miles  per  hour,  with  the  angle 
of  incidence  unchanged.  The  lift  on  the  machine  will,  there- 

69* 
fore,  be  momentarily  increased  in  the  ratio  of     -rrj  *=  1.36. 


Elevator 


(c)  Up-gusts;  (d)  Down-gusts 

Without  going  into  numerical  examples,  we  can  see  easily 
from  Fig.  3,  the  effect  of  an  up-gust  in  increasing  the  load. 
The  up-gust  both  increases  the  velocity  of  the  relative  wind  and 
its  angle  of  incidence,  with  a  corre- 
sponding increase  in  lift,  except  at 
very  high  angles  where  a  reverse  effect 
is  possible.  For  a  down-gust  the  con- 
verse would  hold  true. 

With  normal  l:ying  weather,  the  ef- 
fect of  gust  should  never  increase  the 
load  to  more  than  two  or  three  times 
the  weight  of  the  machine. 

Limiting  Velocity  for  a  Sheer 
Vertical  Dive 

A  sheer  vertical  dive  is  unlikely  to 
occur  and  is  not  required  for  stress 
calculations  in  practice,  but  it  is  inter- 
esting to  note  the  extreme  limiting 
velocity  in  such  a  case.  A  sheer  ver- 
tical dive  is  only  possible  if  the  ma- 
chine is  at  the  angle  to  the  vertical 
which  gives  no  lift,  and  the  elevator  is 
set  only  at  such  an  angle  that  the 
moment  of  the  total  drag  about  the 
center  of  gravity  is  neutralized. 

For  the  machine  in  question  the 
angle  of  no  lift  is  — 3  deg. 

The  drag  on  the  model  at  this  angle 
is  0.118  Ib.  To  find  the  limiting  veloc- 
ity, we  can  write 

0.118  =  26' 


FIG.  4 


W  =  1600  =  - 


30' 


from  which  V  =  134  m.p.h.,  which  is  not  so  very  much  greater 
than  the  limiting  speed  on  the  50  deg.  drive. 

Worst  Loads  on  Landing 

The  computation  of  such  loads  is  connected  with  chassis 
design,  and  we  shall  deal  more  fully  with  it  later.  Some  calcu- 
lations taken  from  "  Notes  on  Aeroplane  Shock  Absorbers  of 
Rubber"  are  an  interesting  introduction  to  the  subject: 

An  airplane  weighing  W  pounds  striking  the  ground  at  I"  feet  per  second  on  a 
glide  of  1  in  7  has  kinetic  energy  to  be  absorbed  by  the  landing  gear  of  —  ( "7  ) 
If  the  machine  comes  to  rest  after  a  motion  of  z  feet,  the  work  done  by  gravity  on 
it  is  Wx,  and  the  tot  al  stored  in  the  shock  absorber  is  W  li  +  o~  (y  )  *  }  •     Tne 
average  force  in  the  springs  is  half  the  maximum  /•',  given  by  the  equality: 


FIG.  3 


There  will  be  au  acceleration  upwards  and  an  increased  load 
on  the  machine  =  1.36  W. 

(b)  Following  Gusts 

If  the  machine  were  traveling  in  a  following  wind,  which 
suddenly  diminished,  a  similar  action  would  ensue,  since  the 
relative  velocity  to  the  air  would  here  also  increase. 

If,  on  the  other  hand,  in  the  case  considered  above  the  head- 
on  gust  suddenly  diminished  to  10  miles  an  hour,  the  relative 
velocity  to  the  air  would  be  decreased  to  4!)  miles  per  hour,  and 

49s 
Ihc-  lift  w.nild  he  diminished  in  the  ratio  of   cgT  =  0.6!)  and  the 

lift  on  the  wings  would,  in  this  case,  be  actually  less  than  in 
norniiil  tli'_rht.  MI  that  the  machine  would  drop. 

It  i-  al-n  clear  from  (lie  above  tlint  the  gust  effects  are  nn»t 
important,  when  the  speed  of  the  machine  is  lowest. 


If    we    take    ordinary    conditions    as 

2.77 


'66    ft.    per    sec.      (45    m.  p.    b.) 

(2  77\ 
2  +  — ; —  1,  from  which  we  get  the  following  table  for  use  in  design: 


i 

1  in. 

2  " 

3  " 

4 


8 
10 

ia 


F 

:t.-».o  W 

19.0  W 

13.0  W 

10.. -i  W 

8.6  W 

7.r.  If 

ii.1  H 

5.:i  w 

4  X  li- 


lt appears  that  the  load  on  the  landing  gear  is  nearly  14 
times  the  weight  of  the  airplane,  if  a  motion  of  only  5  in.  is 
allowed.  This  requires  an  excessive  factor  of  safety  and  makes 
a  very  heavy  construction.  Of  course,  no  allowance  has  been 
made  for  the  collapse  of  pneumatic  tires  which  may  add  2  in. 
to  the  motion  of  the  recoil  mechanism. 


AIRPLANE    DESIGN  l()o 

P-irt    TT     Chanter   f\  Volume  (Oldenbury.  Mime-hen). 

rart   11,   Chapter   t  untish  Report  Xo.  96.  (not  yet  published) 

••  Dynamical   Stability  of  Airplanes."   J.   C.   Hunsaker,   Smithsonian, 
"  The  Flying  Machine  from  an  Engineering  Standpoint,"  F.  W.  Lan-       Vol.  62,  No.  5. 

Chester.  "  Notes  on  Airplane   Shock  Absorbers  of  Rubber,"   J.   C.   Hunsaker, 

"  Mechanische    Grundlagen    des    Flugzeugbaues,"    A.    Baumann.    2nd        AVIATION  AND  AERONAUTICAL  ENGINEERING,  Sept.  1,  1916. 


Chapter  VII 

Preliminary  Design  of  Secondary 
Training  Machine 


Preliminary   Weight   Estimates 

Every  designer  will  approach  the  design  of  a  new  machine 
in  a  different  manner,  and  no  definite  rules  can  be  laid  down. 
In  the  design  of  a  standard  secondary  training  machine,  we 
have  the  advantage  of  following  well-known  lines,  with  such 
excellent  examples  of  machines  tried  out  in  practice  as,  for 
example,  the  Curtiss  JN.  Following  such  practice  we  can  make 
very  close  estimates  of  possible  weights  and  performances,  and 
easily  determine  possible  wing  and  control  surfaces.  A  new 
and  difficult  type,  such  as  a  military  twin-hydro,  would  require 
long  preliminary  study. 

Recalling  Army  Specification  No.  1001 — detailed  in  Part  '2, 
Chapter  1 — we  have  to  meet  the  following  requirements : 

Pilot  and  passenger,  330  Ibs. 

Gasoline  and  oil  for  4  hours'  flight 

Kneinc  between  00  and  110  h.p. 

Maximum  speed,  75  ui.p.h. 

Minimum  speed,  43  m.p.h. 

Climbing  speed.  3000  ft.  in  10  min. 

Two  wheel  landing  gear 

From  the  engine  data  of  Chapter  5  we  could  select  a  number 
of  suitable  engines.  We  shall  select  the  Curtiss  90  h.p.  OX. 
It  is  with  this  engine  that  a  student  has  designed  a  similar 
machine,  the  salient  features  of  which  we  shall  embody  in  the 
post-graduate  course  at  the  Massachusetts  Institute  of 
Technology. 

Practice  shows  that  the  above  performances  can  be  achieved 
with  a  weight  of  about  1850  lb.,  i.e.,  20.4  Ib.  per  horsepower, 
and  we  shall  make  this  our  preliminary  estimate.  This  figure 
is  slightly  less  than  that  of  the  JN-4,  but  is  probably  very  near 
to  the  JN-4B. 

The  first  step  is  to  set  down  all  weights  of  which  we  can  be 
fairly  certain,  and  on  which  no  improvement  is  possible,  thus: 

lb. 

A  B     Pilot  and  passenger  in  aviation  dress 330 

C     Engine  and  accessories 360 

D     Radiator     50 

K     Water  )n  engine  and  radiator  and  piping 40 

F     Propeller  and   hub 35 

G     Gasoline  tank  of  40  gallons  capacity '•'•" 

II     Gasoline  and  oil  for  4  hours'  flight 220 

I  J     2  Instrument  boards,  with  a  set  of  barograph,  tachometer. 

nlr-speed  Indicator  and  clock  on  each 40 

K  L     2  Dep  controls 25 

1130 

This  leaves  us  with  some  720  lb.  available  for  the  purely 
structural  parts  of  the  machine :  chassis,  complete  body  assem- 
bly, wings,  interplane  bracing,  and  tail  surfaces.  On  the  Cur- 
tiss JN-4  (Part  2,  Chapter  3)  we  have  the  following  per- 
centages for  these  groups : 

Chauls     4.03%  equivalent  In  our  machine  to     74.5  lb. 

Wings    14.13%  "         " 201.0" 

Inu-rplane    bracing •(  :iv;  "         "     "         "         "      91.5  •• 

Tall   surface* 2.70%  "         "     "         "         "      61.0  " 

Body    assembly 15.55% 

equivalent  to  286.0  lb., 
from  which  must  be  de- 
ducted 40  lb.  for  ItiKrru 
in'  ni  boards  and  Instru- 
ments, leaving 240.0  " 


724.0 


Since  we  are  following  standard  practice  very  closely  we 
can  take  the  above  figures  to  hold  fairly  well  for  various  parts 
of  the  machine. 

Choice  of  Wing  and  Area 

For  a  machine  of  this  type  it  is  not  necessary  to  have  a 
wing  of  extreme  characteristics.  It  is  more  practical  to  select 
a  good  all-round  wing,  with  fair  structural  characteristics, 
than  to  choose  a  wing  with  high  efficiency  at  low  speeds,  but 
a  low  lift  coefficient  at  maximum  angles,  and  the  R.A.F.6  can 
be  adopted  without  much  chance  of  mishap. 

In  a  machine  of  the  pursuit  type,  it  would  be  worth  while 
trying  a  number  of  different  wing  areas,  but  in  a  training 
machine  it  is,  in  the  first  place,  essential  to  secure  the  necessary 
landing  speed,  and  then  to  attain  as  high  a  speed  and  climb 
as  possible  with  careful  design.  It  only  remains  for  us  to  find 
the  maximum  Kv  of  the  R.A.F.6  and  the  necessary  correcting 
factor  for  biplane  effects. 

There  is,  first  of  all,  the  question  of  stagger  to  be  consid- 
ered. The  increased  efficiency  due  to  staggering  is  offset  by 
questions  of  weight  and  head  resistance,  while  the  increase  in 
efficiency  is  not  so  very  important.  Stagger  is,  therefore, 
mainly  determined  by  considerations  of  the  view  obtainable 
by  pilot  or  passenger.  On  this  particular  machine  we  shall 
employ  a  very  slight  stagger  of  about  5  per  cent,  giving  a  good 
overhead  view  for  the  pilot. 

Overhang  is  likely  to  improve  efficiency,  but  no  aerodynam- 
ical data  is  available.  It  must  be  remembered  that  a  large 
overhang,  together  with  the  aileron  loads,  imposes  a  very 
serious  load  on  the  rear  spar  of  the  wing.  If  any  unsupported 
overhang  is  employed,  it  should  be  less  in  length  than  the  gap. 
We  should,  in  the  present  state  of  the  art,  make  no  improve- 
ment in  the  K,,.  correction  for  biplanes  on  account  of  overhang. 

We  must  also  settle  on  gap/chord  ratio.  We  have  seen  in 
our  aerodynamical  work  the  improvement  consequent  on  great 
gap/chord  ratio.  But  to  offset  this,  we  have  the  question  of 
increased  weight  and  resistance  of  struts  and  wires.  For  tri- 
planes  with  their  blade-like  wings,  a  very  high  gap/chord  ratio 
is,  no  doubt,  permissible,  but  for  biplanes  the  permissible  lim- 
its are  0.9  to  1.2.  We  shall  assume  a  value  of  1.0  as  a  good 
conservative  figure. 

Under  these  circumstances,  we  need  only  correct  our  maxi- 
mum Ky  as  for  an  orthogonal  biplane  with  gap/chord  ratio 
of  1.  The  correcting  figure  for  this  as  given  in  Part  1,  Chap- 
ter 8  is  0.81,  but  Dr.  Jlunsaker's  experiments  have  shown  that 
at  maximum  lift  a  better  factor  of  0.86  may  be  employed. 

Since  at  high  angles  the  tail  surfaces  will  also  be  providing 
some  lift,  we  may  safely  use  this  figure.  Any  obstruction  be- 
tween  the  wings,  such  as  the  body,  will  diminish  the  Kv,  and 
in  a  twin-engined  machine  this  effect  would  become  quite  seri- 


IMI, 


AIRPLANE    DESIGN 


107 


ous,  but  it  need  not  be  considered  for  a  single-engine  type. 
Constructors,  in  fact,  using  a  correcting  factor  of  0.81  or  0.82 
and  neglecting  the  lifting  effect  of  the  tail  surfaces  have  found 
their  landing  speeds  surprisingly  low. 

The  maximum  Ky  for  the  R.A.F.6  is  0.00310.  Extending  the 
equation  W  =  KVAV  to  include  the  correcting  factor  of  0.86, 
we  have  when  F  =  43  m.p.h. 

1850  =(0.0031)  (0.86)4  (43)' 
1850 

'  =  376 


=  (0.0031)  (0.86)43 
clnde  the  ailerons. 


ft"  which  »  taken  to  in~ 


lateral  stability.  For  longitudinal  stability  to  place  the  sta- 
bilizer at  3  deg.  to  the  wings  is  a  good  setting  prior  to  a  wind 
tunnel  test. 

Position  of  Center  of  Gravity 

In  order  to  fix  the  position  of  the  center  of  gravity,  a  vector 
diagram  for  the  whole  machine  is  necessary.  But  to  draw  a 
vector  diagram,  a  wind  tunnel  model  test  is  necessary,  and  in 
the  model  we  have  already  fixed  the  positions  of  the  various 
parts  of  the  machine.  To  draw  a  probable  vector  diagram 


Fio.  1 


The  questions  of  aspect  ratio  is  again  only  partially  de- 
pendent on  efficiency,  and  a  large  aspect  ratio  introduces 
structural  difficulties  and  tends  to  lateral  instability.  We  shall 
assume  an  aspect  ratio  of  7  to  1  on  both  planes.  If  the  planes 
are  slightly  raked,  the  aspect  ratio  will  be  7  for  the  mid-line 
of  the  wings. 

If  x  =  chord  in  feet,  Ix  =  span,  and  we  have  14x2  =  376 
and  chord  =  o  ft.  2  in.  and  span  =  36  ft.  5  in. 

We  shall  now  fix  purely  on  empirical  grounds  the  length  of 
the  machine  and  the  size  of  the  control  and  fixed  surfaces. 

The  designer  is  always  tempted  to  shorten  the  length  of  the 
machine  and  to  rely  on  a  large  stabilizer  placed  at  a  big  nega- 
tive angle,  to  secure  static  longitudinal  stability.  But  in  dynam- 
ical stability,  it  cannot  be  too  strongly  emphasized  that  damp- 
ing is  also  essential,  and  damping  improves  rapidly  with  the 
length  of  the  stabilizing  arm.  Too  short  a  length  would  give 
rapid,  undamped  oscillations.  The  overall  length  of  the  Cur- 
tiss  JN-4,  27  ft.  3  in.,  is  the  outcome  of  several  years'  practical 
experience,  and  is  probably  a  most  suitable  figure. 

By  empirical  rules,  such  as  outlined  in  Part  2,  Chapter  I, 
the  control  surfaces  may  be  fixed  approximately  at 

Ailerons   35     sq.  ft. 

Horizontal    stabilizer. ...    28     sq.  ft.  (atau  angle  of  3  deg.  to  the  wings) 

Elevator    22.0  sq.  ft. 

Rudder 12.0sq.  ft, 

Vertical  fln 4     sq.  f  t. 

The  question  of  lateral  stability  is  one  which  still  requires 
much  investigation.  Purely  on  empirical  grounds,  we  can  say 
that  with  no  sweepback,  but  a  fin  of  the  above  size  with  a 
dihedral  between  the  wings  of  2  deg.  will  secure  a  moderate 


without  a  model  test  is  a  most  difficult  matter.  We  have  ex- 
periments to  show  the  vectors  for  an  orthogonal  biplane  alone, 
but  with  every  different  tail  setting,  body,  shape  and  landing 
gear,  we  have  a  different  vector  diagram. 

The  best  that  can  be  done  in  preliminary  design  is,  therefore, 
to  make  as  shrewd  a  guess  as  possible,  and  to  draw  compari- 


FIG.  2 

sons  from  as  many  model  tests  as  possible.  We  have  fortu- 
nately at  our  disposal  the  results  of  the  tests  on  the  Curtiss 
JN-2,  which  is  almost  identical  with  the  design  we  are  fol- 
lowing. The  vector  diagram  of  this  machine  is  shown  in 
Fig.  2.  Eiffel  36  wings  are  used,  but  in  general  arrangement 


108 


AIRPLANE    DESIGN 


the  machine  is  almost  identical  with  ours.  In  Fig.  1  is  shown 
a  side  view  of  this  machine,  with  the  vector  diagram  of  a  wind 
tunnel  test. 

The  center  of  gravity  is  indicated  in  the  sketch,  and  lies  on 
the  4  deg.  vector.  Such  an  arrangement  will  give  an  adequate 
amount  of  longitudinal  static  stability.  The  propeller  thrust 
passes  through  the  center  of  gravity  and  does  not,  therefore, 
affect  the  stability  in  normal  flight.  Let  us  suppose  that  4 
deg.  is  the  normal  angle  in  flight,  as  it  very  probably  would 
be.  Then  if  the  machine  dives  to  2  deg.,  the  2  deg.  vector 
passing  in  front  of  the  center  of  gravity  will  tend  to  pitch  the 
airplane  back  to  4  deg.  If  the  machine  goes  to  a  higher  angle, 
say  8  deg.,  the  vector  will  be  behind  the  center  of  gravity  and 
will  give  a  counter  clockwise  moment  about  the  center  of  grav- 
ity tending  to  restore  it  to  4  deg.  again. 

The  next  step  is  to  see  whether  we  can  balance  our  machine 
about  this  point  both  in  a  vertical  and  in  a  horizontal  plane. 
Before  drawing  up  our  three  general  arrangement  views,  we 
must  go  into  a  number  of  points  connected  with  chassis  de- 
sign, but  we  can  use  the  side  view  of  Fig.  1  with  slight  modi- 
fications for  our  balancing  up. 

We  shall  employ  the  usual  method  for  finding  the  center  of 
gravity  of  a  system  consisting  of  a  number  of  small  bodies. 
That  is,  we  choose  a  plane  somewhere  in  the  system  as  an  axis 
and  take  moments  about  it,  finally  dividing  the  sum  of  the 
moments  by  the  total  weight  of  the  members  to  find  the  equiva- 
lent moment  arm,  or  distance  of  the  center  of  gravity  from  the 
axial  plane.  In  this  case  we  shall  take  the  axis  at  the  rear 
propeller  flange,  that  being  the  usual  practice. 

The  following  table  illustrates  the  method  in  detail.  The 
designations  refer  to  Fig.  1,  where  the  positions  of  the  centers 
of  gravity  of  the  various  elements  are  indicated. 


Designation 
A 
B 
C 
D 
E 
P 
G 
B 
I 
J 
K 
L 
M 
N 
O 
P 
Q 


\ 

Name  of  Element 
Pilot     

height, 
Ib. 
165 
165 
360 
50 
40 
35 
30 
220 
20 
20 
12 
12 
74.5 
2G1 
91.5 
51 
246 

J  )ist.  from  Moment  about 
propeller       propeller 
flange           flange 
(ft.)           (ft.  Ibs.) 
10.57             1745 
6.67              1100 
2.59                932 
0.77                   39 
2.36  •                94 
—0.17                —6 
6.44                 193 
6.44              1417 
9.46                 189 
5.90                118 
10.57                 127 
6.67                   80 
4.59                342 
6.32              1649 
6.32                 578 
24.75              1262 
9.11              2241 

Hadiator  

Water   

Propeller   

Rear  Instrument  board..  .  . 
Forward  Instrument  board 

Wings   

Tall   

Body    

Totals 1853 


12,100 


Dividing  the  moment  by  the  total  weight  of  the  machine,  we 
see  that  the  center  of  gravity  of  the  machine  is  6.53  ft.  back 
of  the  moment  axis.  This  brings  it  to  a  position  virtually 
coincident  with  the  tanks,  and  about  one-third  of  the  chord 
from  the  leading  edges  of  the  wings,  which  is  virtually  the 
position  chosen  from  the  vector  diagram.  If  the  center  of 
gravity  does  not  come  to  the  desired  position  at  the  first  trial, 
it  may  be  forced  to  do  so  by  manipulation  of  the  weights, 
shifting  the  engines,  pilot,  etc.,  slightly  forward  or  backward, 
as  the  need  may  be. 

A  similar  method,  with  moments  taken  about  the  ground 
line,  is  used  to  give  the  vertical  position  of  the  center  of  grav- 
ity. The  actual  work  for  this  computation  is  omitted  in  order 
to  avoid  confusing  the  figure. 


References  for  Part  II,  Chapter  7 

Barnwell's  "Airplane  Design." 

"  Experimental   Analysis   of   Inherent    Longitudinal    Stability   for   a 
Typical  Biplane." 

National  Advisory  Report,  1915. 


Chapter  VIII 

General  Principles  of  Chassis  Design 


The  design  of  landing  gears  is  among  the  most  complex  of 
the  problems  which  confront  the  aeronautical  engineer,  due 
to  the  many  conflicting  factors  which  must  be  taken  into 
consideration  and.  so  far  as  possible,  reconciled. 

General  Proportions 

The  height  of  the  chassis  is  dictated  by  the  necessity  of 
providing  ground  clearance  for  the  propeller  and  by  the 


allowing  a  total  displacement  of  five  or  six  inches,  the  pro- 
peller clearance  with  the  machine  stationary  should  be  not 
less  than  twelve  inches,  thereby  insuring  a  minimum  clearance 
of  six  inches  when  the  shock  absorber  has  its  maximum 
displacement. 

Under  some  circumstances,  the  governing  condition  may  be 
the  angle  of  incidence  to  which  it  is  desired  to  pitch  the 
machine.  The  greatest  possible  angle  should,  in  general, 
be  at  least  as  great  as  that  which  corresponds  to  the  burble 


FIG.  1. 


angle  of  attack  which  is  desired  in  starting  and  in  pulling  up 
after  touching  the  ground.  The  track  must  be  sufficient  to 
insure  against  overturning  when  making  a  landing  on  rough 
ground,  yet  not  so  great  that  the  striking  of  a  soft  spot  by 
one  wheel  will  give  rise  to  an  excessive  moment  tending  to 
spin  the  machine  around.  The  fore-and-aft  location  of  the 
wheels  is  determined  by  the  requirements  of  longitudinal 
stability  on  landing.  The  structure  must  be  strong  enough 
'to  withstand  side  thrusts  and  twisting  moments  due  to  alight- 
ing on  one  wheel,  as  well  as  the  large  direct  dynamic  stresses 
which  are  set  up  when  an  airplane  lands  without  sufficient 
flattening  out  of  the  angle  of  descent.  Lastly,  the  means  of 
shock  absorption  must  be  of  such  quality  and  number  that 
they  will  permit  of  high  speed  along  the  ground  and  of  heavy 
landings  without  breakage  of  the  shock  absorption  means 
itself  and  without  danger  of  the  "  bottoming  "  of  the  axle  in 
its  guides.  The  play  of  the  absorbers  should  also  be  large 
enough  so  that  the  dynamic  landing  and  taxying  loads  pre- 
viously alluded  to  will  not  reach  excessive  values.  Each  of 
these  conditions  will  now  be  taken  up  in  turn,  and  discussed 
in  detail. 

Chassis  Height 

Ordinarily,  the  most  important  factor  here  is  the  protec- 
tion of  the  propeller.     With  a  conventional  shock  absorber. 


point,  and  it  may  be  advisable,  if  a  very  short  run  after 
landing  is  required  and  brakes  are  not  desired,  to  make  it 
somewhat  larger  than  this.  The  following  example  will  illus- 
trate the  use  of  this  condition : 

A  two-seat  tractor  biplane  is  26  feet  long,  and  the  hori- 
zontal distance  between  the  axle  and  the  point  of  contact  of 
the  tail  skid  is  20  feet.  In  normal  flight,  when  the  line  of 
thrust  is  horizontal,  the  wings  are  set  at  an  angle  of  incidence 
of  4  deg.,  and  the  point  of  contact  of  the  tail  skid  is  2  ft. 
vertically  below  the  line  of  thrust.  It  is  desired  to  find  the 
least  distance  of  the  lower  rim  of  the  tire  below  the  thrust 
line  which  will  permit  the  assumption  of  an  angle  of  18  deg. 
Since  the  wings  are  at  an  angle  of  4  deg.  in  normal  flight, 
the  maximum  angle  between  the  thrust  line  and  the  ground 
must  be  18  deg. — 4  deg.,  or  14  deg.  Tan  14  deg.  =  .249,  and 
the  difference  in  heights  of  the  wheels  and  tail  skid  is  therefore 
20  X -249,  or  4.98  ft.  It  is  then  evident  that  the  required 
height  is  4.98  -(-  2,  or  virtually  7  ft,  a  much  greater  height 
than  would  be  necessitated  by  propeller  clearance  alone.  If 
such  large  angles  must  be  attained  it  is  worth  while  to  sacri- 
fice something  from  the  perfect  symmetry  of  the  body  by 
putting  most  of  the  longitudinal  curvature  on  the  lower 
surface  of  the  body,  thereby  bringing  the  tail  skid  more 
nearly  into  the  line  of  thrust  and  decreasing  the  height,  and 
consequently  the  weight  and  resistance,  of  the  body,  to  an 


1(19 


110 


AIRPLANE    DESIGN 


extent  which  more  than  compensates  for  any  loss  of  aero- 
dynamic efficiency  of  the  body. 

The  tread,  or  track,  is,  on  airplanes  of  conventional  size, 
from  5  to  7  ft.,  except  on  slow  pusher  biplanes  with  long 
skids,  where  it  may  reach  values  as  high  as  13  ft. 

Location  of  Chassis  with  Respect  to   C.   C. 

In  Fig.  1  are  shown  the  forces  which  come  into  play  while 
the  machine  is  running  along  the  ground.  It  is  evident  that, 
if  we  assume  the  thrust  line  to  pass  through  the  c.  g.,  and 
the  machine  to  be  in  equilibrium  with  the  elevator  either  in 
neutral  or  diving  position,  so  that  the  resultant  air  pressure 
with  the  body  horizontal  passes  through  or  slightly  behind  the 
c.  g.,  the  moment  P  X  a>  due  to  the  upward  reaction  of  the 
ground,  must  be  at  least  equal  to  the  moment  R  X  &>  due  to 
the  tractive  resistance.  We  then  have,  since  we  may  write 


E  =  fP,  P  X  a  =   >vP  X  b,  or  ^  —  tan  6  =  f,  where 

Y  is  the  coefficient  of  tractive  resistance.  If  we  assume 
Y  =  1/10,  which  is  perhaps  a  fair  value  for  a  vehicle  with 
large  and  flabby  pneumatic  tires  running  over  smooth  grass, 
we  have  8  =  5  deg.  44  min.  Since,  however,  it  is  necessary 
to  allow  for  soft  ground,  where  the  coefficient  of  tractive 
resistance  will  be  much  increased,  as  well  as  for  ruts  and 
changes  of  slope,  which  introduce  a  backward  component  in 
P  itself,  it  is  obvious  that  6  will  have  to  be  considerably  larger 
than  the  value  given  above.  Lieut.  Col.  B.  Q.  Jones,  U.  S.  A., 
states  that  the  best  practise  indicates  a  value  of  13  deg.  10 
min.  for  0. 

Stresses   and   Structural   Considerations 

An  unequal  distribution  of  stress  between  the  wheels,  due 
to  landing  on  one  wheel  before  the  other  or  to  a  difference  in 
ground  conditions  between  the  two  tracks,  produces  a  moment 
tending  to  twist  the  axle  about  a  vertical  axis.  This  moment 
is  carried  to  the  struts  or  skids  by  means  of  axle  guides  or 
radius  rods,  and  thence  to  the  body.  A  landing  on  one  wheel 
generally  involves  a  sideways  motion,  and  the  resulting  side- 
ways blow  is  usually  carried  by  the  cross-wires,  although 
some  landing  gears,  particularly  on  speed  scouts,  have  in- 
clined struts  which,  acting  either  in  tension  or  compression. 


take  the  place  of  the  wires  in  this  respect.  In  order  to 
resist  side  blows,  too,  a  special  wheel  construction  is  neces- 
sary, as  an  ordinary  wire  wheel,  such  as  is  used  on  motor- 
cycles, will  be  completely  wrecked  by  a  relatively  small  side 
blow  against  the  rim.  It  may  be  laid  down  as  a  rule  that  the 
length  of  hub  should  be  at  least  twice  the  diametei  of  the 
tire,  and  three  times  is  preferable.  The  obliquity  ol  the 
spokes  is  thus  greatly  increased. 

Direct  dynamic  loads  in  landing  have  already  been  dis- 
cussed in  this  course  (see  Part  II,  Chapter  6). 

Shock  Absorbers 

Rubber  and  steel  springs  are  the  only  substances  which 
have  been  widely  used  as  shock  absorbers.  Of  these,  rubber 
has  proved  by  far  the  more  satisfactory,  due  to  its  easy 
fabrication  and  replacement,  its  greater  energy-storing  capac- 
ity (500  to  1,000  ft.  Ibs.  per  lb.,  as  against  10  to  20  ft.  Ibs. 
per  lb.  for  steel),  and,  most  of  all,  the  fact  that  it  actually 
absorbs  and  dissipates  the  energy,  instead  of  merely  storing 
it  and  giving  it  out  again.  If  steel  springs  are  used,  some 
auxiliary  device  must  be  employed  to  dissipate  the  energy  in 
the  form  of  heat.  In  the  case  of  leaf  springs,  this  is  done 
in  a  fairly  satisfactory  degree  by  friction  between  the  leaves, 
and  such  springs  have  been  used  on  light  machines  built  for 
smooth  fields,  but  they  do  not  afford  sufficient  give  for  heavy 
work.  Where  helical  springs  are  used,  as  on  many  large 
pusher  biplanes  with  four-wheeled  landing  gears,  they  are 
usually  in  combination  with  a  hydraulic  or  pneumatic  shock 
absorber.  As  an  illustrative  problem,  we  shall  give  the 
complete  calculation  of  a  rubber  shock  absorber  for  a  two- 
seator  tractor  biplane  weighing  2000  Ibs..  having  a  gliding 
angle  of  1  in  7,  and  a  speed  range  of  from  45  to  90  miles 
an  hour.  We  shall  start  with  the  assumption  that  the  heaviest 
landing  shock  which  needs  to  be  provided  against  is  that  due 
to  landing  at  45  m.p.h.  on  a  slope  of  1  in  6  without  any 
attempt  at  flattening  out. 

The  shock  absorbers  will  be  made  up  of  rubber  rings  '2  in. 
in  diameter,  and  2  in  X  T5ff  i'1-  in  section.  We  shall  use  a 
two-wheeled  landing  gear,  so  that  each  wheel  will  have  an 
initial  load  of  1000  Ibs.  The  initial  stretch  will  then  be 

'     .    E,  the  modulus  of  elasticity,  may  be  taken  equal 
*  X  -A-  X  n 

to  300  Ibs.  per  sq.  in.  for  rubber  of  good  quality.  A,  the 
total  cross-section  area  of  one  ring,  is  2  X  2  X  T\H  or  I1/^ 
sq.  in.  I,  the  length,  may  be  taken  equal  to  one-half  the 

perimeter  of  the  rings,  or  Z=  — ^ — =  3.14  ins.     »?  is  the  num- 

2 

number  of  rings  employed. 


We  then  have  the  initial  stretch  =  S  =  • 


1000X3.14 


300  X  IVi  X  a 

o  •)(!  -|  rj  r-y  i  • 

— ,  and  s,  the  deflection  under  any  load,  =  — rr; — ,  /•'  IMMIII; 

the  total  load. 

On  landing  on  a  slope  of  1  in  6  at  a  speed  of  66  ft.  per  see., 
the  vertical  speed  is  11  ft.  per  sec.,  and  the  kinetic  energy  is 

( 11 )  *  X  W 

- — -^-± — ,  or  1.8817  ft.  Ibs.     The  potential  energy  possessed 

II" s  / 

on  touching  the  ground  is— ^-,  making  a  total  of  W  {  1.88  + 

—  I,  or  17  I  .04  +  —  I  on  each  wheel. 

The   enei'uy    absorbed   bv   the   shock    absorber   is  —  V  —  = 
II  W 
. ,.9  -   •    Equating  this  to  the  energy  possesed  by  the  machine, 

3§'=  "(«  +  £}    * 


shall  assume   a   deflection   of 


AIRPLANE    DESIGN 


111 


,r,  402.7  (.94  +  5/24) 

0  in.     Then  n  =  -         v         '      '  —   =  18.54.     We  shall  use 


00 


18  rings  and  recalculate.     Then         „  =  .94  -|-  -j-,  and  18  s 
=  378  +  16.78  s.    s  =  5.05  in. 


„ 


C  AC 


The  stress  in  the  rubber  is  ^^  X  300  =  482  Ib.  per  sq.  in., 

as  against  a  breaking  strength  of  800  Ibs.  per  sq.  in.,  and  the 

(s  \ 
1.88  +  -[I, )         4000  x  2  30 


load  on  the  chassis 


s_ 
12 


.42 


21,900  Ibs.     At  the   instant   of  greatest   displacement,   then. 


FIG.  3.     ARRANGEMENTS  OF  RUBBER  CORD  AND  RINGS  USED  ON 
VARIOUS  FRENCH  MONOPLANES. 

every  part  of  the  machine  has   on   it  a  downward   load   of 
eleven  times  its  own  weight. 

We  have  so  far  assumed  the  most  unfavorable  condition 
with  respect  to  the  tires:  that  is,  that  they  do  not  deflect  at 
all.  We  shall  now  work  the  same  problem  on  the  assump- 
tion of  the  most  favorable  conditions  reasonably  to  be  ex- 
pected, that  26  X  4  tires  are  used,  and  that  they  are  pumped 
to  such  pressure  that  they  collapse  2  in.  under  the  same 
force  which  causes  the  shock  absorbers  to  yield  5  in.  The 
effect  of  this  is  equivalent  to  increasing  the  length  of  the 

shock  absorbers  by  40  per  cent.   We  then  have  F  =— — —  ,  and 

s  now  equals  7  in.,  and  n  is  there- 


isl=  w  (M  +>: 

563.8  (.94+-^) 


49 


=  14.28.     Only  14  rings  will  be  needed 


under  this  assumption. 

Actually,  a  2500-lb.  airplane  usually  employs  about  12  rings 
on  each  bridge,  and  is  therefore  unable  to  sustain  conditions 
as  severe  as  those  which  we  have  assumed.  In  order  to  provide 
the  desired  shock  absorption  capacity,  machines  of  the  size 
which  we  are  considering  use  26  X  4  or  26  X  5  wheels.  These 
wheels  weigh,  complete  with  tire,  from  17  to  25  Ibs.  each, 
and  the  manufacturers  recommend  that  they  be  pumped  to 
60  Ib.  pressure. 

In  place  of  rubber  rings,  as  specified  above,  rubber  cord 
woven  from  manv  strands  mav  be  used.  Some  recent  tests 


on  %  in.  cord,  made  up  of  180  strands  ^  in.  square,  showed 
a  modulus  of  elasticity  of  434  Ib.  per  sq.  in.  The  breaking 
load  was  not  determined.  During  these  tests,  it  was  discov- 
ered that  of  the  "  permanent  "  set  which  rubber  cord  takes 
after  being  stretched,  40  per  cent  of  its  original  length  almost 


FIG.  4 


entirely  disappears  after  17  hours  of  rest,  the  rubber  regaining 
;ill  its  original  pi'operties. 

Types  of  Chassis 

We  may,  in  general,  divide  chassis  into  three  classes:  self- 
contained  chassis  with  wheels  alone,  chassis  with  two  principal 
wheels  and  a  tail  skid,  and  chassis  built  up  around  one  or  two 
long  skids  as  a  basis.  There  are  also  numerous  compromise 
designs,  which  it  is  difficult  to  assign  to  any  one  class.  Nearly 
all  the  land  machines  now  built  in  the  United  States  come 
into  the  second  of  these  classes,  although  all  three  types  had 
some  vogue  here  at  one  time. 

Chassis  with  wheels  alone  were  first  used  by  Curtiss.     Due 


FIG.  5 


to  their  complexity  and  considerable  weight  and  resistance, 
they  are  now  seldom  employed  except  on  heavy  machines,  par- 
ticularly pusher  biplanes  designed  for  gun-carrying,  where 
they  are  generally  combined  with  helical  steel  springs  and 
hydraulic  shock  absorbers.  Such  a  chassis  may  have  either 
three  or  four  wheels,  four  being  the  more  common.  The  fore- 
and-aft  distance  between  the  two  pairs  of  wheels  must  be  con- 
siderable, in  order  to  insure  against  the  machines  falling  over 
on  its  tail  as  it  is  brought  to  rest. 

Chassis  with  two  principal  wheels  and  a  tail  skid,  either  with 
or  without  one  or  two  subsidiary,  and  usually  unsprung,  wheels 
in  front,  are  nearly  universally  employed  on  machines  of  me- 
dium and  light  weight,  except  on  the  very  slow  and  lightly- 
loaded  pusher  biplanes.  The  framework  of  such  a  landing 
•rear  is  reduced  to  its  lowest  terms,  consisting,  in  its  conven- 
tional form,  merely  of  two  Vs,  closed  at  the  top  by  the  lower 
body  longerons,  and  separated  at  the  top  by  a  distance  equal 


112 


AIRPLANE    DESIGN 


to  the  width  of  the  body,  and  at  their  lower  vertices  by  a  little 
less  than  the  track  of  the  wheels.  The  bottoms  of  the  Vs  are 
connected  by  a  strut.  The  two  wheels  are  mounted  just  outside 
the  Vs,  either  on  a  single  axle  or  on  separate  axles  hinged  at 
the  center,  usually  the  former.  The  present  practice  is  to  in- 
cline the  axle  guides  HO  that  the  wheels  travel  backward  some- 
what as  they  rise  in  the  guide  slots,  but  this  causes  excessive 
wear  on  the  front  of  the  slots,  and  experiments  at  the  Signal 
Corps  school  indicate  that  no  harmful  results  follow  the  elim- 
ination of  the  backward  slope.  Fig.  2  gives  a  diagrammatic 
view  of  a  typical  chassis  of  this  class. 

On  speed  scouts,  where  the  reduction  of  resistance  is  of  the 


FIG.  6.    SOPWITH  CHASSIS,  SHOWING  COMBINATION  OF  Two 
WHEELS  WITH  SHORT  SKIDS 

utmost  importance,  the  chassis  is  sometimes  so  built  that  it 
forms  a  unit  with  the  wings.  This  makes  possible  the  elimina- 
tion of  all  wiring  from  the  chassis,  and  in  a  few  cases  from 
the  wing  panel  as  well.  Fig.  4  represents  a  machine  so  braced. 
Chassis  based  on  long  skids  are  used  on  Farman.  Caudron. 
and  Wright  biplanes.  They  generally  embody  four  compara- 
tively small  and  light  wheels  arranged  in  a  straight  line,  one 
pair  of  wheels,  about  18  inches  apart,  being  attached  to  each 
skid.  Each  pair  of  wheels  has  its  own  axle,  and  radius  rods 
are  used  to  prevent  the  axle  twisting  with  respect  to  the  skid. 
Rubber  shock  absorbers  are  used.  In  some  cases  the  skids 
are  carried  up  in  front  to  a  forward  elevator,  as  in  the  Maurice 
Farman,  or  in  the  rear  to  the  tail,  as  in  the  Caudron.  Such 
a  chassis  is  illustrated  in  Fig.  5. 

.Among  the  hybrid  types,  involving  some  of  the  features  of 
all  three  classes,  one  of  the  most  interesting  is  the  old  Nieuport. 
In  this  there  were  2  pairs  of  struts,  each  pair  forming  a  V 
with  the  vertex  downward.  At  the  bottom  of  these  was 
mounted  a  comparatively  short  skid.  Below  the  skid  a  leaf 
spring,  of  semi-elliptic  form,  was  clamped,  and  the  wheels 
were  at  the  extremities  of  this  spring.  The  rear  of  the  skid 
acted  as  a  tail  skid,  and,  in  addition,  made  a  very  effective 
brake,  as  it  was  close  to  the  c.  g.,  and  consequently  carried  a 
considerable  portion  of  the  weight. 

Brakes  and  Braking 

All  the  devices  which  have  been  brought  forward  for  check- 
ing the  speed  of  airplanes  after  touching  the  ground  fall  natu- 
rally into  one  of  two  divisions:  depending  either  on  air  re- 


sistance or  ground  resistance.  The  best  example  of  a  brake 
depending  on  air  resistance  is  the  airplane  itself.  We  have 
already  mentioned  the  desirability  of  being  able  to  depress 
the  tail  to  such  a  degree  as  to  secure  a  very  large  angle  of 
incidence,  not  only  so  that  we  may  land  at  low  speed,  but  also 
so  that  the  drag  may  be  increased,  and  thus  aid  in  checking 
the  speed  after  landing. 

It  has  often  been  proposed  that  air  brakes,  consisting  of  sur- 
faces normally  lying  parallel  to  the  line  of  flight,  but  capable 
of  being  pulled  around  approximately  normal  to  that  line, 
should  be  provided.  If  two  such  surfaces,  one  on  either  side 
of  the  body  and  at  a  considerable  distance  from  the  longi- 
tudinal axis,  are  furnished,  one  at  a  time  may  be  pulled  out 
lo  act  as  a  drag  and  assist  in  turning  the  machine  in  a  small 
circle  while  taxi-ing,  or  both  may  be  used  at  once  as  a  brake. 
The  trouble  with  all  air  brakes  is  that  they  rapidly  lose  their 
effectiveness  as  the  airplane  begins  to  slow  up.  They  have, 
on  (he  other  hand,  the  advantage  that  their  force  is  exerted 
well  above  the  c.  g.,  so  that  there  is  no  tendency  to  stand  the 
machine  on  its  nose. 

Brakes  depending  either  directly  or  indirectly  on  friction, 
with  the  ground  for  their  retarding  power,  may  be  subdivided 
into  wheel  brakes  and  sprag  or  claw  brakes.  Wheel  brakes, 
although  they  can  be  made  very  powerful,  are  hardly  ever 
used,  due  to  their  danger,  which  lies  in  the  difficulty  in  releas- 
ing them  quickly,  and  in  the  fact  that  they  have  no  tendency 
to  release  themselves  automatically  as  the  machine  starts  to 
pitch  over  on  its  nose. 

Claw  brakes  are  more  used  than  any  other  type.  Thev  :ire 
usually  attached  to  the  strut,  which  lies  just  below  the  axle 
in  a  V-type  landing  gear,  and  are  hinged  to  that  strut.  The 
claw  on  the  end  can  be  brought  to  bear  against  the  ground 
by  a  lever  within  reach  of  the  pilot.  The  advantage  of  such 
a  brake  is  that,  being  in  back  of  the  forward  point  of  suspen- 
sion, the  claw  tends  to  release  itself  as  the  machine  starts  to 
dive,  pivoting  about  the  point  of  contact  of  the  wheels  with 
the  ground.  From  this  point  of  view,  the  brake  should  be 
as  far  back  as  possible,  but  the  available  retarding  force  is 
greater  and  the  construction  is  simpler  when  it  is  kept  near 
the  chassis  proper.  The  tail  skid  itself  acts  as  a  very  ellicient 
claw  brake  if  it  is  so  arranged  as  to  carry  a  considerable  por- 
tion of  the  load.  If  extra  quick  stops  are  desired  from  a 
machine,  whatever  type  of  brake  is  used,  the  wheels  should  be 
placed  farther  forward  of  the  c.  g.  than  usual,  thus  permit- 
ting a  larger  moment  to  be  applied  at  the  ground  level  without 
upsetting  the  machine,  making  it  easier  to  get  the  tail  skid 
down  in  contact  with  the  ground  immediately  after  landing, 
and  throwing  a  larger  portion  of  the  weight  on  the  tail  skid 
or  sprag  brake,  if  one  is  used. 

It  is  of  interest  to  determine  the  retarding  force  required  to 
bring  a  machine  to  rest  in  a  given  distance.  If,  for  exam- 
ple, we  wish  to  land  a  2oOO-lb.  machine  at  45  m.p.h.  and  bring 
it  to  rest  in  200  ft.  after  touching  the  ground,  we  have 

s  =  — ,  or  a  =        '    =  7.20  ft.  per  see.  where  a  is  the  nec- 
2a  GOO 

essary  deceleration.  F,  the  average  retarding  force,  = — 

9 

50.")  II).,  a  force  whieji  might  easily  be  secured  without  the  u><- 
of  any  brake  save  that  afforded  by  the  wings  themselves. 

NOTE — The  vector  diagram  for  the  JN-2,  to  which- reference 
was  made  in  discussing  the  design  of  a  secondary  training 
airplane  in  the  last  installment  of  the  course,  is  reproduced 

herewith.     The  weights  are  omitted  in  order  not  to  confuse  the 
diagram,  but  the  position  of  the  c.  g.  is   that    indicated   pre 
vioiislv. 


AIRPLANE    DESIGN 


113 


References  for  Part  II,  Chapter  8 

('!.  de  Havilland  in  flight,  March  9,   1912. 
F.  W.  Lanchester  in  Engineering,  May  22.  1914. 

"  The   Flying  Machine   from  an   Engineering  Standpoint,"   by   F.    W. 
Lanchester ;   p.   80. 

"  Itelativo     Positions    of     Propeller    Axis,     Center    of    Gravity    and 


Wheels,"  by  Capt.  B.  Q.  Jones ;  AVIATION  AND  AERONAUTICAL 
ENGINEERING,  Nov.  1,  191G. 

"  L'Essor  et  1'Atterissage,"  by  Maurice  Percheron. 

"  La  Construction  des  Organes  de  Contact  avec  le  Sol,"  by  P.  James  ; 
Revue  Generate  de  I'Aeronautique,  Jan.,  1914. 

"  Notes  on  Aeroplane  Shock  Absorbers  of  Rubber,"  by  J  C  Hun- 
saker ;  AVIATION  AND  AERONAUTICAL  ENGINEERING,  Sept.  1,  1916. 


Chapter  IX 

Type  Sketches  of  Secondary  Training  Machine 
General  Principles  of  Body  Design 


In  Fig.  1  are  shown  three  views  of  a  secondary  training 
machine,  very  similar  to  the  JN-2,  and  in  accordance  with  our 
figures  of  Chapter  7. 

A  few  modifications  have  been  made  in  the  process  of  draw- 
ing up  the  machine  from  the  figures  given  in  Chapter  7.  The 
figures  there  were  derived  from  empirical  formulas,  but  in  the 
present  stage  of  the  art  it  cannot  be  too  strongly  insisted  that 
no  empirical  formulas  hold  with  absolute  rigidity,  and  that 
"  eyeability  "  is  almost  as  important — except  in  the  case  of 
the  stabilizer  and  elevator,  on  which  more  data  is  available. 
Thus  the  rudder  lias  been  reduced  in  area  from  12  to  10  sq. 
ft.,  and  the  vertical  fin  from  4  to  3.5  sq.  ft. 

The  stabilizer  and  elevator  have  been  left  unchanged.  In 
drawing  the  plan  view  of  the  machine,  modifications  were  also 
found  necessary  in  the  ailerons.  The  original  scheme  was  to 
place  the  ailerons  on  the  top  plane  only.  But  in  order  to 
secure  the  necessary  area  it  was  necessary,  with  the  spar  posi- 
tion selected,  to  make  the  ailerons  very  long  and  bring  them 
in  comparatively  close  to  the  body  (with  an  overhang  on  the 
top  plane  this  difficulty  would  not  have  occurred),  and  ailerons 
brought  in  close  to  the  body  have  an  insufficient  leverage  for 
part  of  their  surface.  The  better  plan  seemed  to  be,  there- 
fore, to  place  the  ailerons  on  both  surfaces.  Their  area  was 
also  slightly  increased,  from  38  to  42  sq.  ft.  total  area. 

It  must  be  insisted  upon  again  that  this  machine  is  not  a 
perfect  specimen  of  its  type.  For  instance,  had  an  overhang 
been  employed  as  on  the  JN-4,  the  aileron  area  of  35  sq.  ft., 
with  its  greater  lever  arm,  would  have  been  amply  sufficient. 
Also  the  outer  strut  would  have  been  almost  at  the  mid  point 
of  the  aileron,  thus  permitting  the  use  of  a  single  aileron  post ; 
whereas  in  the  present  case  we  are  obliged  to  use  two  aileron 
posts. 

Another  poor  point  is  that  the  tail  skid  abuts  directly  on 
the  rudder  post.  The  control  surfaces  should  never  be  so 
placed  as  to  sustain  injury  by  an  abrupt  landing,  as  might 
be  the  case  in  this  arrangement. 

A  drag  wire  is  shown  carried  from  the  top  of  the  inner 
strut  to  the  engine.  This  helps  to  keep  the  body  from  twisting 
under  the  effect  of  gyroscopic  forces  on  the  engine,  and  also 
to  relieve  the  drag  bracing.  Nevertheless,  in  computing  the 
drag  bracing  the  effects  of  such  a  wire  are  totally  neglected. 

General  Requirements  in  Body  Design 

These  may  be  very  briefly  summarized : 
(1)  Stream-Line  Form 

The  power  plant  and  personnel  must  be  enclosed  in  a  form 
approximately  stream-lined.  The  general  shape  of  the  bodi- 
es largely  determined  by  the  size  and  shape  of  the  engine 
selected.  For  the  vertical  six-cylinder  engine  the  body  may 


be  narrow  and  deep.  For  a  V  cylinder  engine,  a  wider  but 
shallower  body  is  advisable,  and  with  a  rotary  engine  a  body 
of  very  large  maximum  diameter.  But  consistent  with  struc- 
tural and  other  considerations,  a  body  should  be  selected  which 
gives  minimum  aerodynamic  resistance.  The  best  form  of 
body  would,  of  course,  be  symmetrical  about  an  axis.  Some 
data  for  the  resistance  of  airplane  bodies  has  been  given  in 
the  first  part  of  the  Course,  but  there  is  no  doubt  that  con- 
siderable improvement  is  possible  in  this  direction,  possibly 
by  employment  of  monocoque  construction.  Where  a  four 
girder  body  is  used,  and  attempts  are  made  to  secure  stream- 
line form,  the  designer  must  guard  against  excess  weight. 

(2)   Fin   Area   of  Body 

A  flat  bottomed  body  may  be  very  helpful  in  securing  longi- 
tudinal dynamic  stability.  A  body  with  flat  sides  has  to  be 
handled  carefully.  It  is  equivalent  to  a  long  fin,  with  most 
of  the  fin  area  aft  of  the  center  of  gravity,  and  this  tends  to 
head  a  machine  into  the  wind — an  advantage  if  the  effect  is 
not  excessive.  Such  fin  area  is,  however,  best  secured  by  the 
use  of  a  vertical  fixed  fin.  With  a  large  flat  sided  body,  it  is 
as  well  to  investigate  yawing  moments  in  the  wind  tunnel. 
One  of  the  reasons  why  totally  enclosed  bodies  have  not  come 
into  use  is  that  with  their  large  fin  areas,  they  have  a  tendency 
to  spinning. 

(3)  Length  of  Body 

Apart  from  the  necessary  length  of  body  to  give  sufficient 
arm  to  the  tail  surfaces,  it  is  important  that  the  tail  surfaces 
should  be  far  enough  away  from  the  wing  so  that  the  wash 
of  the  wings  should  not  affect  them  too  much. 

(4)  Provision  for  Pilot  and  Passenger 

The  necessary  requirements  are  obvious.  To  protect  the  face 
of  the  passenger,  a  transparent  lip  is  generally  fitted  on  the 
front  edge  to  deflect  the  air  upwards.  The  back  of  the  pilot's 
head  may  be  stream-lined  with  a  suitable  projection.  Specifi- 
cation 1002  gives  standard  arrangements  for  pilot's  and  pas- 
senger's seats. 

(5)   Engine  Installation 

Should  be  readily  accessible  and  cowling  easily  removable. 
(6)   Gasoline  Tanks 

Should  be  near  the  center  of  gravity  of  the  whole  machine, 
so  as  to  disturb  balance  as  liltle  as  possible  as  fuel  is  con- 
sumed. Where  it  is  impossible  to  place  the  fuel  supply 
directly  over  the  center  of  gravity,  the  gasoline  and  oil  may 
be  made  to  balance  one  another  approximately. 

(7)   Engine  Foundation 

Must  be-  rugged  to  prevent  loosening  up  of  the  bolts  by 
vibration,  transmission  of  the  torque  of  the  engine  to  the  body, 


114 


AIRPLANE     DESIGN 


115 


FIG.  1 


AIRPLANE    DESIGN 


and  breaking  loose  in  a  bad  landing.  Nevertheless,  the 
foundation  should  be  flexible  enough  so  that  slight  engine 
vibration  is  easily  taken  up.  The  following  example  will  illus- 
trate the  forces  on  the  foundation  bolts  due  to  engine  torque: 

Six  cylinder  120  h.p.  1200  r.p.m.  Torque  =  ^  °  ^S^.°  =  525, 

JrcX  £v 

then  if  /•'  is  force  on  either  side,  2F  X  -575  =  525.  where  .575 
is  half  the  distance  between  engine  bed  bolts,  and  the  force  on 
either  side  is  457  Ib. 

(8)   Engine  Must  Be  Secured  Against  Weaving 

When  the  airplane  pitches,  there  is  a  tendennj  owing  to 
gyroscopic  action  of  the  propeller,  for  the  engine  to  "  weave  " 
either  to  right  or  left.  Diagonal  members  in  the  plane  of  the 
engine  bearers  as  well  as  wires  are  often  used.  The  ideal 
engine  foundation  would  seem  to  be  of  pyramidal  form. 

(9)   Strength   of   Body 

The  body  must  be  strong  enough  to  withstand  (a)  air  loads 
due  to  tail  surfaces,  (b)  dynamic  loads  in  the  air,  (c)  loads 
on  landing. 

These  are  but  a  few  of  the  requirements  in  body  design. 
Numberless  points  arise  in  detail  work,  in  which  experience 
and  care,  and  not  general  roles,  are  necessary. 

Formulas  for  Spruce  Compression  Members 

The  most  reliable  data  on  spruce  struts  —  the  material  in 
which  we  are  most  interested  —  is  given  in  Dr.  Hunsaker's 
note  to  which  reference  is  appended.  Experiments  were  car- 
ried out  on  Maine  white  spruce,  West  Virginia  white  spruce, 
and  Oregon  red  spruce.  Values  varied  so  much  for  each 
specimen  that  it  would  be  unsafe  to  use  them  definitely  for 
wood  of  varied  origin,  of  varied  position  in  the  log,  and  de- 
gree of  seasoning,  and  in  actual  construction  tests  on  speci- 
mens are  always  necessary. 

In  these  experiments,  the  modulus  of  elasticity  found  by 
observing  deflection  under  loading  was  found  to  be  1,825,000 
pounds  per  square  inch.  Two  formulas  for  crippling  stress, 
defined  as  the  crippling  load  divided  by  the  area  of  cross  sec- 
tion in  square  inches,  were  deduced. 

8.72  E 


(1)    For  long  struts,      L     >70,    •-  = 
K  A. 


2   where  7>  = 


crippling  load  A  =  area  in  square  inches  L  =  length  in  inches 
K  -=  least  radius  of  gyration  in  inches  E  =  modulus  of  elas- 
ticity in  pounds  per  square  inch.  (Some  designers  employ 


using  n  value 


WJ 

the  ordinary  Euler's  formula.      —     = 

A 

of  £  =  1,600,000.) 

(2)  For  short  struts,  ^  <  70,  —  =  6500  —  46.5  — .     ( Some 
**-  A  K 

designers    employ    a     modification     of    Rankine's    formula: 
where  fe  =  8,000  Ibs.  for  spruce,  E  = 


1.HOO.OOO.  4>  = 


-— 

It    C, 


By  careful  selection  of  spruce  the  crippling  loads  given  by 
the  above  formulas  can  be  easily  secured.  It  was  formerly 
customary  to  use  a  material  factor  of  safety  of  2  for  the  wing 
struts,  and  IVz  for  body  struts. 

There  arises  a  further  difficulty  in  connection  with  the  above 
formulas,  in  determining  whether  a  strut  is  fixed  or  hinged  at 
the  ends.  It  is  usually  assumed  that 


(1)  wiug  struts  with  pin  joint  fastcuiugs  are  hinged  at  either  cml 

(2)  wing   struts   with   socket   fastenings   of   usual    type  are   consid- 
ered as  being  fixed  at  one  end.  and  round  at  the  other. 

(3)  body   longitudinals,   continuous  over  Joints,   are   taken   as   flxeil 
at  cuds. 

(4)  body  horizontal  and  upright  struts  arc  taken  as  fixed  at  one  end 
and  hinged  at  the  other. 

For  a  strut  fixed  at  one  end,  and  hinged  at  the  other,  the 

L 

equivalent  length  becomes      -=,  for  a  strut  fixed  at  both  ends. 

v - 

the  equivalent  length  becomes   — .    Thus  the  above  formulas  lie- 
come: 

p        8.7-J  /•:         P  r. 

£.  =  6500  —  46.5  ^ 

A'. 


(1)    Ends  hinged   —  =        L    2 


(2)    One  end  fixed       = 
one  hinged 


(|) 


2 


=  6500 


(3)   Both  ends         -=     , ""  .  ~  . 
fixed  1  (I) 


""'  '' 


Z-6BOO-       2K 


Body  .Stress  Diagrams 

Body  stress  diagrams  are  still  on  a  somewhat  unsatisfactory 
basis,  and  a  number  of  different  methods  are  adopted.  Al- 
though the  longerons  of  a  body  are  continuous,  and  the  cross 
bracing  members  more  or  less  fixed,  stress  diagrams  are  always 
drawn  as  if  it  were  entirely  a  pin-jointed  structure.  Subse- 
quently, compression  members  are  treated  as  either  wholly  or 
partly  fixed  at  the  ends.  This  is  inconsistent  but  probably  all 
that  can  be  done,  without  very  lengthy  refinements. 

Factors  of  safety  have  been  specified  in  a  number  of  way*, 
of  which  we  have  noted  some  already. 

Army  Specifications  1000,  1001  and  1002 

Air  speed,  100  miles  an  hour.  Angles  of  incidence  of  fixed 
horizontal  tail  surface,  minus  6  deg. ;  elevator  surface,  minus 
20  deg.  Factor  of  safety  not  less  than  2.5.  This  is  based  on 
the  forces  met  with  when  the  machine  is  violently  righted 
after  a  rapid  dive.  It  takes  care  solely  of  the  air  loads  due  to 
tail  surfaces.  When  in  the  air  the  body  is  supported  at  the 
hinges  of  the  wings,  and  the  air  loads  are  not  transmitted  to 
the  part  of  the  body  forward  of  the  hinge  pins.  It  can  be 
seen  that  this  is  by  no  means  an  ideal  specification.  It  has 
also  been  criticized  on  the  ground  that  no  pilot  can,  under 
ordinary  conditions,  exert  sufficient  force  to  move  the  elevator 
to  such  a  position. 

Army  Specification  1003 

Body  forward  of  the  cockpit  shall  be  designed  for  a  factor 
of  safety  of  ten  (10)  over  static  loading  conditions  with  the 
propeller  axis  horizontal.  Body  in  the  rear  of  cockpit  shall  be 
designed  to  fail  under  loads  not  less  than  those  imposed  under 
the  following  conditions : 

(a)  Dynamic  loading  of  ">  as  the  result  of  quick  turns  in 
[Hilling  out  of  a  dive;  (b)  superposed  on  the  above  dynamic 
loading  shall  be  the  load  which  it  is  possible  to  impose  upon 
the  elevators,  computed  by  the  following  formulas :  L  = 
.(»»."). I  I"3  where  A  is  the  total  area  of  the  stabilizing  sur- 
faces, i.e.  elevators  and  fixed  horizontal  surface,  and  I  is 
the  horizontal  high  speed  of  the  airplane.  The  units  are  kilo- 
grams. s<|u:uv  meters,  kilometers  per  hour;  (<•)  superposed  on 
this  loading  shall  be  the  force  in  the  control  cables  producing 
compression  in  the  longerons. 


AIRPLANE    DESIGN 


117 


This  specification  is  sounder  than  the  previous  one.  It  im- 
poses the  air  load  on  the  rear  part  of  the  body,  which  is  as  it 
should  be,  and  provides  a  sufficient  dynamic  loading  for  the 
forward  part  of  the  machine. 

Another  Suggested  Method 

In  the  author's  opinion,  the  stress  diagrams  should  be  even 
more  complete.  They  should  include  calculations  (a)  carried 
through  on  the  air  loads,  (b)  calculations  carried  through  on 
the  landing  loads,  specifying  some  landing  speed,  a  gliding 
angle,  and  travel  of  shock  absorber. 

A  Detailed  Example  of  Stress  Diagram 

In  Fig.  2,  is  shown  the  skeleton  framework  of  a  JN-2  body, 
which  fits  in  with  our  design  of  a  standard  airplane  body. 


Pio.  2 


lu  accordance  with  the  preceding  paragraph,  we  should  draw 
two  diagrams  for  it: 

(1)   With  the  body  and  tail  surfaces  in  position  shown  in 
Fig.  2,  horizontal  tail  surface  at  minus  6  deg.,  elevator  sur- 


Kl 

<L 


face  at  minus  20  deg.  The  air  loads  on  these  surfaces  can  be 
computed  as  follows:  Lacking  precise  experimental  data,  we 
may  assume  that  in  the  worst  possible  case,  the  pressure  on 
the  tail  =  .00264  V  area  of  stabilizer  and  elevator  =  50  sq. 
ft.  V ,  the  highest  speed  attainable  during  a  dive,  may  be 
taken  as  100  m.p.h.  F,  the  tail  load,  then  equals  .0026  X  50  X 
(100)2  =  1300  Ib. 

With  these  air  loads  computed,  a  stress  diagram  can  be 
easily  drawn  as  for  a  simple  cantilever  with  supports  at  the 
rear  body  hinges.  As  an  article  in  AVIATION  and  AERO- 
NAUTICAL ENGINEERING  for  March  1,  1917,  shows,  the  stresses 
obtained  in  this  way  are  in  certain  members  smaller,  in  other 
members  larger,  than  those  obtained  from  the  landing  diagram. 

(2)  The  stress  diagram  on  the  assumption  of  the  landing 
shock  leaves  room  for  much  discussion.  The  difficulty  arises 
primarily  from  the  fact  that  it  is  difficult  to  say  what  the  worst 
landing  conditions  before  breaking  are  for  which  a  machine 
should  be  designed.  Also  it  is  extremely  difficult  to  include 
all  the  forces  in  play,  which  may  include  (a)  lift  on  the  wings, 
(b)  drag  on  wings  and  body,  (c)  lift  and  drag  on  the  tail 
surfaces,  (d)  the  reaction  perpendicular  to  the  ground,  (e) 
tractive  resistance  on  the  wheels. 

Further  difficulties  arise  from  the  fact  that  the  center  of 
the  wheels  does  not  lie  under  the  center  of  gravity  of  the 
whole  machine,  so  that  if  a  dynamic  load  is  applied  vertically 
at  the  wheels,  the  weight  applied  at  the  center  of  gravity  gives 
a  turning  moment  which  must  be  balanced  in  some  way  or 
another.  Two  methods  are  suggested  which  seem  fairly 
reasonable,  and  provide  a  rational  method  of  computation. 
In  the  first  method,  it  is  assumed  that  the  machine  is  gliding 
on  a  path  of  say  1  in  7,  and  hits  the  ground  nose  heavy.  In 


\  '  L  ' 


FIG.  4 


118 


AIRPLANE    DESIGN 


such  a  case  as  can  be  seen  from  Fig.  3  the  reaction  of  the 
ground  may  be  assumed  to  pass  through  the  center  of  gravity 
of  the  machine,  and  a  balance  of  forces  is  obtained.  The 


FIG.  3 


dynamic  load  in  such  a  case  may  be  obtained  on  lines  indi- 
cated in  a  previous  section  on  chassis  design. 

In  the  second  method,  the  pilot  is  assumed  to  flatten  out 
from  the  glide,  and  then  turn  up  to  a  big  angle  and  pancake 
down,  with  the  wheels  and  skid  striking  the  ground  simul- 
taneously. In  such  a  case,  it  is  very  difficult  to  compute  the 
dynamic  load,  but  a  balanced  system  of  forces  is  readily  ob- 
tained, distributing  the  load  between  the  wheels  and  the  skids 
as  shown  in  Fig.  4.  The  dynamic  load  factor  there  is  taken 


as  8.  In  Table  1  are  tabulated  the  stresses  in  various  mem- 
bers. In  the  ensuing  sections,  dimensions  will  be  allotted  to 
such  members. 

TABLE  I 

BODY  STRESSED 


av 
bx 
ci 
ca' 
cc' 
ce' 

c< 
ci 

ck' 


PR 
ra 

tu 


gr 
at 
uv 
wx 

y» 
at)' 


0 

460  T. 
490  C. 
1680  C. 

aoro  c. 

2070  C. 
1990  C. 
1910  C. 
1770  C. 
1540  C. 
1170  C. 


560  C. 

330  C. 
3900  C. 
1410  C. 

470  C. 
0 


570  T. 
1200  T. 
3400  T. 
1910  T. 

590  T. 

100  T. 


Pl- 
ot 
mu 
Iw 


hd' 
fi 

* 


Longerons 


490  C. 
1250  C. 

260  C. 
1200  T. 
1600  T. 
2000  T. 
1920  T. 
1780  T. 
1550  T. 
1180  T. 


b'c' 
d'e' 
fV 
h'i' 
i'k' 


StrutsO 


70  C. 

90  C. 
140  C. 
210  C. 
:  10  C. 
9  .  C. 


c'd' 
e'f 


c 


Wires 


120  T. 
210  T. 
300  T. 
480  T. 
1470  T. 


References  for  Part  II,  Chapter  9 

"Notes  sur  la  Construction  des  Aeroplanes,"  by  P.  James;  Recite  Gentrale  dt 
I'Aeronn'i'itj'.'f  Mili'-i-r,  \faroh,   19M. 

"Sprure  Aeroplane  struts  under  Compression,"  by  J.  C.  Hunsaker;   Aerial      Ag 
August  13,  1910. 


Chapter  X 

Computation  of  Strength  Members  and  General 

Layout  of  Body 


In  designing  tension  members  for  the  body,  no  feature  is 
of  greater  importance  than  the  choice  of  terminal  fastenings 
which  will  permit  the  development  of  as  large  a  percentage 
as  possible  of  the  true  strength  of  the  wire  or  other  tension 
member. 

The  main  points  to  be  considered  in  dealing  with  terminal 
connections  are : 

(1)  The  efficiency,  as  mentioned  above. 

(2)  Quickness  and  ease  of  manufacture. 

(3)  The  possibility  of  easy  and  efficient  repair  or  replace- 
ment in  the  field. 

(4)  Reliability,  i.e.,  the  difference  in  efficiency  between  the 


FIGS.   1-15.     TERMINAL   FITTINGS   FOR   SOLID   WIRE,   TESTED   BY 
JOHN  A.  ROERI.ING'S  SONS  Co. 


best  and  poorest  terminals  of  a  series  all  made  up  in  the  same 
way  should  be  as  small  as  possible. 

(5)  The  possibilities  of  defects  due  to  the  use  of  acid  and 
solder,  overheating,  imperfect  bends,  flattening  of  wire  on 
bends,  or  unskillful  handling  of  the  material  in  the  field.  This 
requirement  is  obviously  closely  allied  to  that  of  reliability. 

Extended  tests  on  terminal  connections  of  all  types  have 
been  made  by  John  A.  Roebling's  Sons  Co.  A  summary  of  the 
most  important  results  is  given  herewith,  and  reference  to  the 
original  report  is  appended. 

The  first  series  of  tests  related  to  hard-drawn  aviator  wire. 
The  form  of  terminal  which  was  most  common  up  to  a  few 
years  ago,  consisting  of  a  ferrule  made  from  a  coil  of  wire, 
through  which  the  wire  is  passed  and  then  doubled  back  on 
itself  (Figs.  2  and  3),  gave  very  poor  and  uneven  results,  the 
efficiency  varying  from  60  to  75  per  cent,  with  an  average  of 


65  per  cent.  These  efficiencies  were  improved  by  about  5  per 
cent  when  the  free  end  of  the  wire,  instead  of  being  doubled 
back  outside  the  ferrule,  was  wound  three  times  around  the 
standing  portion  of  the  stay. 

The  next  type  of  terminal  tested  was  similar  to  the  last,  but 
was  dipped  in  solder  after  being  made  up  (Fig.  1).  The  fer- 
rule for  such  a  connection  may  be  made  of  a  coil  of  wire,  as 
previously,  or  of  a  strip  of  thin  sheet  metal,  wrapped  around 
both  portions  of  the  wire.  The  efficiencies  obtained  ran  from 
60  to  90  per  cent,  with  an  average  of  80  per  cent.  These  values 
are  surprisingly  low,  and  indicate  probable  damage  of  the  wire 
by  overheating  in  the  process  of  soldering,  as  a  connection 
such  as  this,  absolutely  preventing  any  slippage  of  the  wire 
through  the  ferrule,  should  always  show  100  per  cent  efficiency 
if  properly  made  up.  Tests  on  similar  terminal  fittings  at  the 
Massachusetts  Institute  of  Technology  have  nearly  always  de- 
veloped the  full  strength  of  the  wire,  the  stay  breaking  near 
the  center  on  every  test.  The  soldered  joints  have,  however, 
the  disadvantage  that  they  cannot  readily  be  replaced  in  the 
field,  and  they  are  peculiarly  susceptible  to  poor  workmanship, 
the  effects  of  which  cannot  be  determined  in  any  way  until  the 
break  actually  comes. 

In  the  Roebling  tests,  the  best  results  were  secured  by  the 
use  of  tapered  ferrules,  winding  a  coil  of  wire  into  the  form 
of  a  slightly  flattened  cone  instead  of  a  flattened  cylinder,  in 
conjunction  with  wedges  designed  to  increase  the  friction  be- 
tween the  stay  and  the  ferrule  as  the  pull  increased.  Such 


FIG.   16. 


SERVED  AND  UN  SERVED  SPLICED  JOINTS  AND  TYPICAL 
FRACTURE  IN  AVIATOR  CORD. 


wedges  may  be  separate  members,  fitted  between  the  eye  and 
the  ferrule,  in  which  case  the  wire  is  looped  completely  around 
to  make  a  double  eye,  or  they  may  be  embodied  as  a  part  of 
the  thimble,  which  is  interposed  between  the  fittings  and  the 
eye  to  prevent  any  change  in  shape  or  size  of  the  eye  under 
strain.  No  solder  whatever  is  used  (Figs.  13-15).  The  effi- 


119 


120 


AIRPLANE    DESIGN 


,-iencies  obtained  with  such  terminals  were  very  uniform,  rang- 
ing only  t'rnin  i>-  to  96  j>er  cent,  with  an  average  of  94  per 
cent.  Such  a  terminal,  although  necessarily  somewhat  complex, 
has  marked  advantages.  It  can  readily  be  made  up  in  the 


may  ail\  antageously  be  used  ( Fig.  1!) ) .  They  give  100  per  rent 
ellieiency.  or  very  nearly;  they  require  no  high  degree  of  skill  to 
apply,  and  the  fitting  is  neat  and  simple  in  appearance.  The 
common  type  consists  of  a  conical  shell,  the  hole  in  the  small  end 
being  just  large  enough  to  admit  the  strand.  The  strand  is 
passed  through  this  hole  for  a  short  distance,  unravelled,  and 
the  ends  spread  out  as  much  as  possible.  The  conical  shell 
is  then  poured  full  of  solder,  and  the  ends  of  the  component 
wires  cut  off  flush  with  the  large  end  of  the  shell.  The  only 
danger  in  the  use  of  such  a  fitting  arises  from  the  liability  to 
deterioration  of  the  solder. 

As  we  mentioned  in  the  preceding  chapter  of  the  course,  the 
stress  diagram  which  was  then  drawn  does  not  form  a  complete 


l-'n:.  17.     SERVED  AND  UNSERVED  SPLICED  JOINTS  AND  TYPICAL 
FRACTURE  IN  AVIATOR  STRAND. 


field,  and  there  are  unlikely  to  be  hidden  defects,  any  slipshod 
workmanship  being  instantly  apparent  on  inspection. 

The  British  standard,  which  has  recently  been  adopted  by 
the  Society  of  Automotive  Engineers,  calls  for  the  use  of  the 
plain  wire  coil  ferrule  with  solder.  A  device  which  has  been 
considerably  used  in  England,  although 
not  yet  employed  in  this  country,  is 
the  streamline  wire  with  swaged  and 
threaded  ends,  thus  doing  away  with  the 
necessity  for  turnbuckles.  Such  wires 
are  very  expensive  and  difficult  to  make, 
but  have  decided  advantages  in  prac- 
tice. They  are  unlikely  to  come  into 
use  except  for  fighting  machines,  where 
cost  is  of  no  importance. 


Cable  Terminals 

Both  strand  and  cord  can  be  spliced 
with  excellent  results  if  the  work  is 
done  by  an  expert  rigger.  Roebling's. 
tests  indicated  an  efficiency  of  from  80 
to  85  per  cent  for  aviator  cord  with 
spliced  and  served  terminals  (Fig.  16), 
and  from  90  to  100  per  cent,  the  highest 
values  corresponding  to  the  smallest 
wire  sizes,  for  19-wire  aviator  strand 
(Fig.  17).  The  break  always  occurred 
at  the  last  tuck  in  the  splice,  which 
would  suggest  the  advisability  of  taper- 
ing the  splice  to  a  greater  extent. 

For  Held  connections,  fittings  similar 
to  those  recommended  for  solid  wire. 
consisting  of  a  thimble  embodying  a 
wedge  and  a  ferrule  of  soft  wire  (  Fig. 
18),  gave  excellent  results,  showing  an 
efficiency  of  90  per  cent. 

The  status  of  solder  is  the  same  a-  in 
llie  case  of  solid  wire.  100  per  cent  cffi- 
eiencie-  c.in  lie  secured  by  the  use  of 
thimble,  ferrule,  and  solder  with  either 
-tiand  or  cord,  but  there  is  the  same 

risk  of  injury  to  the  material  through  improper  manipulation. 
In  connection  with  tin-  larger  diameters  of  strand, 


I'n,    l*.      UKSOL- 

1 1  I    i:  1 .  1 1     F  I  E  I.  II 

TERMINAL      FOR 
AVIATOR   STRAND. 


FIG.    19.     SOCKET    TERMINALS    FOH    AVIATOR    STRAND. 

basis  for  the  choice  of  members,  but  should  lie  supplemented 
by  various  other  diagrams  corresponding  to  different  condi- 
tions of  loading.  We  shall,  therefore,  confine  ourselves  to  fig- 
uring, for  purposes  of  illustration,  a  few  of  those  members 
which  are  most  heavily  stressed  under  the  conditions  which 
we  have  already  considered. 

Since  a  dynamic  load  factor  of  8  has  already  been  allowed 
tor,  we  shall  use  a  factor  of  safety  above  this  of  only  one  and 
a  half.  This  is  equivalent  to  an  overall  factor  of  safely,  rela- 
tive to  tbe  static  load,  of  t \vel\e,  a  value  which  is  fairly  rep- 
resentative of  modern  practice  in  the  design  of  bodies  for 
training  machines.  The  latest  specification  issued  by  the 
(iovernment  calls  for  an  overall  factor  of  ten,  but  tins  relates 
to  pnr.Miit  machines,  which  are  to  be  flown  by  skilled  pilots 
oni\.  and  in  which  the  factor  of  safety  is  purposely  kept 
low  in  order  to  make  possible  a  belter  performance,  and  hence 
a  higher  decree  of  military  safety.  In  tbe  case  of  those  por- 
tions of  the  longerons  which  are  curved  to  a  considerable  extent 


AIRPLANE    DESIGN 


121 


Steel  Mr* 


I < 

GALVANIZED  NON- FLEXIBLE  CABLE  ENDS 

^'  [ 

••-•A  -••"P--~S  erring  •  ^.-^o/dered  under  serving 


S  fan  ijard  Thimbl f 


'--ShcllaKfd  Harness   ™'wo'  0,28'WIREK  LARGO 


OlOlwiRE 


,- 
p     Splice!  j  -----  1 

FIGS.  20,  21,  22.     S.  A.  E.  STANDARD  TEBMINALS  FOR  SOLID  WIRE,    STRAND,  AND  CORD. 


0.080  WIRE 


FIG.  23.     LAYOUT  OF  BODY  FOR  STANDARD  TRAINING  MACHINE. 


between  struts,  th  •  factors  of  safety  should  lie1  considerably  in- 
creased, as  a  strut  which  has  even  the  slightest  sign  of  initial 
curvature  will  support  much  less  load  than  one  which  is  per- 
fectly straight. 

The  members  I'm-  which  we  shall  compute  the  required  size 
include  a  longeron  section,  a  strut,  and  a  wire,  and  they  are 
marked  with  numbers  on  the  layout  drawing.  We  shall  con- 
sider all  compression  members  as  perfectly  square,  although 
channeling  is  commonly  employed,  especially  in  struts  and  the 
rear  portions  of  the  longerons. 

(1)  The  length  of  the  section  is  40  in.  We  shall  try,  as  a 
lirst  assumption,  a  section  l1/^  in.  square.  The  crippling  load 


i  hen   17.44  X  1,825,000  Xl 
4U 


>  or  4,050  Ib.     This  corre- 
- 

sounds  t<»  a  factor  of  safety  of  9  nr-.y  or  1.95,  above  the  dynamic 

_,.u  i  i  * 

loading.  We  shall,  therefore,  use  this  section.  It  is  well  to 
have  the  factor  in  the  longerons  slightly  greater  than  in  the 
struts.  since  their  end  conditions  approach  less  closely  to  fixa- 
tion. 

(2)  The  length  of  the  strut  is  31  in.,  and  the  com- 
pressive  load  is  3,900  Ibs.  Here,  again,  a  section  IVi  in. 
square  will  be  tentatively  chosen.  The  crippling  load  equals 


(I1/. 

17.44  X  1,825,000  X -371 


safety  is  then  1.72. 


X  12' 


or    (i,740 


The    factor    of 


(3)  The  tensile  load  is  3,400  Ibs.  We  shall  select  for  this 
stay  10-wire  strand  &  in.  in  diameter.  The  breaking  load  of 
such  strand  is  6,100  Ib.,  and  the  factor  of  safety,  allowing  for 
90  per  cent  efficiency  of  the  terminal  connections,  is  1.61. 

The  struts  which  carry  the  weight  of  the  engine  should  be 
materially  heavier  than  would  be  indicated  by  considerations 
of  dead  loading  alone,  since  they  are  constantly  submitted  to 
a  live,  vibrative  load,  and,  in  addition,  are  subjected  to  bending 
forces  because  of  the  gyroscopic  action  hi  diving.  These  forces 
are  calculable,  but  such  an  analysis  is  beyond  the  scope  of  this 
pa  |  er. 

In  Fig.  23  is  shown  the  layout  of  the  body.  The  only  points 
at  which  channeled  struts  are  used  are  the  forward  panels, 
which  have  the  duty  of  transmitting  the  propeller  thrust  to  the 
longerons,  and  thence  to  the  wings.  The  other  struts  are  made 
octagonal  by  chambering  off  the  corners  slightly.  The 
longerons  are  channeled  everywhere  in  back  of  the  forward 
chassis  strut,  except  that  they  are  left  solid  for  a  few  inches 
adjacent  to  every  strut. 


References  for  Part  II,  Chapter  10 

First  Annual  Hcport  of  the  National  Advisory  Committee  on  Aero- 
nautlos,  Report  No.  2;  Government  Printing  Office,' 1916. 


Chapter  XI 

Wing  Structure  Analysis  for  Biplanes 


There  are  many  difficulties  in  the  analysis  of  a  biplane  struc- 
ture: the  distribution  of  loading  between  upper  and  lower 
planes;  the  resolution  of  loading  in  the  planes  of  the  lift  truss 
and  the  internal  bracing;  the  resolution  of  loading  to  give 
bending  moments  on  the  spars,  and  the  alternative  methods 
which  may  be  employed  in  drawing  up  the  stress  diagrams. 
But  in  the  following  notes  is  developed  a  system  which  is  now 
generally  employed,  and  which  although  it  is  not  rigidly  exact, 
gives  sufficiently  accurate  results  for  practical  needs,  and  as  a 
system  of  comparison  for  machines  which  have  been  successful 
in  flight. 

Distribution  Between  Planes 

The  information  available  regarding  distribution   of  loads 


FIG.  1 


between  planes  is  scanty  and  contradictory.     In  practice  it  is 
sufficient  to  follow  this  equation : 

(1)  W  =  (Avx)-£j  -\-Aix,  where  W  =  gross  loading  of  the 
machine,  Au  =  area  of  upper  wing,  AI  =  area  of  lower  wing, 

x  =  gross  loading  per  square  foot  on  lower  wing,  -p-x  =  gross 

y 

loading  per  square  foot  on  upper  wing. 

Unless  the  biplane  truss  falls  away  very  much  indeed  from 
the  conventional  form,  this  will  be  a  fair  approximation. 

Spacing  of  Wing  Spars — Limiting  Angles  of  Incidence 

As  the  angle  of  incidence  of  a  wing  changes  its  center  of 
pressure  moves,  and  accordingly  varying  loads  are  placed  on 
the  rear  and  front  spars  (the  center  of  pressure  motion  in  a 
biplane  is  assumed  to  be  identical  with  that  of  a  monoplane). 
The  spar  spacing  lias  to  be  so  arranged  that  too  great  a  pro- 
portion of  the  load  is  not  thrown  on  either  of  the  spars  within 
the  range  of  the  usual  angle  of,  flight.  This  would  be  the  case 
were  the  spars  too  close  together  or  placed  so  that  one  of  them 
would  be  quite  close  to  one  center  of  pressure.  At  the  same 
time,  the  spars  must  not  be  placed  too  near  either  the  front 
or  the  rear  edge,  so  that  there  is  always  sufficient  depth  of 
spar.  Thus  in  t  he  machine  the  design  of  which  we  are  carrying 
through,  the  spars  are  placed  as  shown  in  Fig.  1,  about  10  per 
cent  from  leading  edge  and  about  30  per  cent  from  trailing 
edge,  where  the  centers  of  pressure  at  0  deg.  and  at  16  deg. 
are  indicated.  The  loading  is  in  this  case 

Front  spar  Hear  spar 

At    0°     29.8%  70.2% 

At   16°    06.6%  33.3% 


0  deg.  and  16  deg.  are  taken  in  our  design  as  the  limiting 
angles  of  incidence,  although  very  possibly  the  machine  might 
fly  both  at  some  negative  angle,  and  at  some  angle  above  16 
deg. 

Running  Loads 

Applying  equation  (1)  where  W  =  1793  Ib.  and  Au  =  188 
sq.  ft.,  A  i  =  175  sq.  ft.  for  our  machine,  we  find  that  the  gross 
loading  per  square  foot  on  the  upper  wing  is  5.4  Ib./sq.  ft.  and 
on  the  lower  wing  it  is  4.43  Ib./sq.  foot.  In  the  same  manner 
the  total  gross  weight  supported  by  the  upper  wing  is 
1020  Ib.  and  the  total  gross  weight  supported  by  the  lower 
wing  is  773  Ib. 

For  simplicity,  the  running  load  is  assumed  to  be  uniform 
from  tip  to  tip  of  the  wings,  and  hence  the  gross  running  lifts 
are  for  a  span  of  36  ft.  6  in.,  28.0  Ib./foot  on  upper  wing  and 
22.8  Ib./foot  on  lower  wing. 

It  is  from  the  gross  running  lifts  per  foot  that  we  obtain 
the  running  drifts  per  foot  run,  by  dividing  by  the  L/D  ratio. 

Thus  we  have 

Lower  wing 
running  drift 
in  Ib.  /ft.  run 


At     0° 
At    10° 


L/D 

7.2 

6.92 


Upper  wing 
running  drift 
in  Ib.  /ft.  run 

3.90 

4.05 


3. IS 
3.30 


Next  it  is  necessary  to  determine  the  net  running  lift.  To 
do  this  it  is  necessary  to  make  assumptions  for  the  weight  of 
the  wings  and  the  weight  of  the  interplane  bracing. 

Thus  for  the  upper  wing,  assuming  a  weight  of  .73  Ib./sq. 

ft.,  and  half  the  weight  of  the  interplane  bracing  of  91.5  Ib. 

to  be  carried  by  it,  we  have  a  net  lift  of  1020  — 137  —  45.7  = 

837.3  Ib.  or  22.9  Ib./ft.  run,  and  for  the  lower  wing  773  — 128 

-  45.7  =  599.3  Ib.  or  17.7  Ib./ft.  run. 

We  can  now  tabulate  our  results  in  such  form  that  they  can 
be  used  in  resolving  forces  in  planes  of  lift  trussing  and  of 
the  wings. 

Percentage   front  spar   _'.!> 
At  0°  Percentage  rear    spar  till. 2 


Upper  wing 

Gross  loading  per  foot  run.  .  28  Ib. 
Drift  per  ft.  run  front  spar.  1.16  Ib. 
Drift  per  ft.  run  rear  spar.  .  2.74  Ib. 
Net  lift  per  ft.  run  front  spar  6.85  Ib. 
Net  lift  per  ft.  run  rear  spar  16.05  Ib. 

At  10° 
Upper  wing 

Drift  per  ft.  run  front  spar.  .  2.7O 
Drift  per  ft.  run  rear  spar.  .  1.35 
Net  lift  per  ft.  run  front  spar  in. 20 
Net  lift  per  ft.  run  rear  spur  7.65 


Lower  wing 

22. 8       Hi. 

.95    Ib. 

2.23    Ib. 

5.27    Ib. 

12.43    Ib. 

Percentage  front  spar  ii(i.(> 
Percentage  rear    spur  :;."...". 

Ixwer  wing 

2.17 

1.09 

11.80 

5.90 


Resolution  of  Forces  in  Planes  of  Wing  Trussing  and 
of  Wings,  and  in  Plane  of  Spar  Web 

In  Figs.  2  and  3  are  shown  the  resolutions  of  forces  at  0  deg. 
and  16  deg.  respectively.  It  will  be  noticed  that  the  resultant 
force  in  the  plane  of  the  lift  truss  is  decomposed  in  plane  of 
the  spar  web.  It  is  this  component  in  the  plane  of  spar  web 


122 


AIRPLANE    DESIGN 


123 


RESOLUTION   OF' FORCES  IN  PLANES  OF  LIFT  TRUSS  &  WINGS 
NET  LIFT  is  ALSO  COMPONENT  IN  PLANC  or  SPAR 


RESOLUTION  or  FORCES  IN  PLANES  or  LIFT  TRUSS  t  Wwcs  AT  /6" 


NET  Lirr    I6.0S  ' 


TOTAL  Fo«c«  m  PLANE 
or  Wine    56" 


TOTAL  Fence  IN  PLANE 
^       OF  Wine    1, 9* 


Fence   11 

OF 

LIFT  TRUSS 
5.34* 


O/MC  .95 


FIG.  2 


Z.S3 


TOTAL  FOHCS  IN  PLANE    or 
*,~o    4.4S" 


which  is  subsequently  used  to  draw  the  bending  moment  dia- 
unnns  for  the  spurs.  This  is  u  slightly  arbitrary  procedure. 
It  would  be  more  accurate  to  take  the  force  in  the  plane  of  the 
lift  truss  as  producing  bending,  but  there  would  then  he  the 
<-i>iii|>liciitiiiii  of  computing  moments  of  inertia  about  an  axis 
not  perpendicular  to  the  web. 

From  these  resolutions  it  is  now  possible  to  tabulate  figures 
which  can  be  employed  in  the  lift  truss  stress  diagram,  the 
drift  bracing  stress  diagram,  etc. 


At  0° 


L'ppor  wing. 
Front   spar.  Hoar   spar. 

Force   In   plane   of   lift    truss  run- 
ning  foot. 

7  Ib.  16.3  Ib. 

Force   in   plane  of  wiag/nmnlng 

foot. 

2.4  Ib.  5.6  Ib. 

Force  in   plane  of  spar  web/run- 
ning  foot. 
6.85  Ib.  16.05  Ib. 


Lower    \\  IML 
Front   spar.  Hear   spar. 

Force  in   piano  of  lift    truss/run- 
ning foot 

5.34  Ib.  12.67  Ib. 

Force    in    plane    of    wing/running 

foot 

1.9  Ib.  4.45  Ib. 

Force   in    piano   of   spar   wob/run- 

nliiK    foot 
5.27   Ib.  12.43  Ib. 


Upper  wing. 

Front  spar.  Hoar  spar. 

Force   in   plane   of  lift    truss/run- 
ning  foot. 

15.5  Ib.  7.8  Ib. 

Foive    in    plane   of   wing/rumiiug 

foot. 

1.18  Ib.  0.48  Ib. 

Force  in   plane  of  spar   web/run- 
ning foot. 
15.2   Ib.  7.75  Ib. 


At  16° 

Lower  wing. 

Front   spar.  Hoar   spar. 

Force   in   plane  of  lift   truss/run- 
ning   foot 

12.1  Ib.  6.0  Ib. 

Force   in   plane   of   wing/running 

foot. 

0.90  Ib.  0.40  Ib.    - 

Force  in    plane   of   spar   wob/run- 

ning   foot. 
11.9  Ib.  5.9  Ib. 


Figs.  2  and  3  indicate  some  peculiar  results.  Thus  at  0  deg., 
part  of  the  net  lift  is  resolved  into  the  plane  of  the  wing, 
greatly  increasing  the.  demands  on  the  internal  wing  bracing. 
Were  the  stagger  of  the  biplane  more  pronounced,  this  effect 
would  be  still  greater,  and  that  is  one  of  the  disadvantages  of 
excessive  stagger.  But  at  16  deg.,  in  this  particular  case,  the 
component  of  the  net  lift  along  the  plane  of  the  wing  relieves 
the  internal  wing  bracing. 


LIFT- 


TOTAL  foflc/r  IN 
PLANE,  of  LIFT 
TRUSS  IS.  ^ 


COMPONENT    IN 
PLANS   of 


TOTAL.   Fence   IN 
PLANE  of  LIFT 
THUSS     7.6* 
DP/IS  2.7* 

1  ,FT    7.65 


TOTAL  Fo/tcf  IN 

PLANE  OF  WINS 

//a* 


TOTAL  Foncf 
IN  PLANE   OF 
WING     .-fa* 


COMPONENT 
PLANS   of 
11.9* 


TOTAL 

of 
LIFT  Ttrvss     6 


TOTAL 

N  PLANE   of 
.9or 


COMPOHCNT 

IN  PLANE  or 
SPAR  WEB    77 


DRAG      1. 35 


COMPONENT  IN 
PLANE  or  SPAR 
wee  f.S* 

DPAS    /.OS* 


TOTAL  Fopce    IN 
PLANE   or  WING 

.40' 

Kin.  3 


Different  Methods  Employed  in  Stress 
Diagrams  for  Lift  Truss 

Two  distinct  methods  have  been  adopted  in  getting  out 
stress  diagrams  for  the  lift  truss. 

(1)  The  trussing  is  treated  as  if  pin  jointed  throughout  by 
the  ordinary  bridge  truss  method,  and  the  bending  moments 
for  the  spars  found  as  if  they  were  freely  supported  at  the 
ends,  with  uniformly  distributed  loads. 

(2)  The  spars  are  treated  as  if  continuous,  so  that  bending 
moments  in  them  and  reactions  at  their  supports  are  found 
by  theorem  of  three  moments.    Then  the  reactions  having  been 
found,  the  stress  diagram  is  drawn  with  such  reactions  as  a 
basis. 

The  first  method  has  the  advantage  of  simplicity  and  of  giv- 
ing a  very  large  factor  of  safety.  The  second  method  is  much 
more  difficult,  but  probably  is  nearer  the  mark,  and  we  shall 
employ  it  accordingly. 


Bending  Moment  Diagrams:   Theorem  of  Three 
Moments 

Any  good  text  book  on  applied  mechanics  treats  fully  of 
the  theorem  of  three  moments,  so  that  the  following  notes  will 
be  of  the  briefest : 

In  Fig.  4  is  shown  a  beam  loaded  with  unequal  distributed 
loads  over  the  two  spans.  At  the  three  supports,  0,  1,  2 
M0,  Ma  M2  are  corresponding  bending  moments;  Ba  Ba  R,  are 
corresponding  reactions;  S  +„,  £-„;  S  +0,  S-l;  S  +,,  S  — 
are  shears  on  either  side  of  the  supports. 


124 


AIRPLANE    DESIGN 


Jf  the  beam  is  continuous  over  tlie  three  supports  and  has 


1 

i 

1 

i 

J 

1 
J) 

1 

o 

Z 

5 

b                                     O 

t                             —  o 

**-  1 

R 

5n 

t  o 

FIG.  4 

I  lie  same  cross-section  throughout,  the  bending  moments  at  the 
supports  and  the  loads  are.connected  by  the  following  formula: 


All  difficulties  in  working  the  theory  of  three  moments  are 
due  to  mistakes  in  the  conventional  signs. 


TfrNS 


NEGATIVE 

&ENDING- 
MoMfcNT 


Fio.  5 


The  convention  for  bending  moments  is  shown  in  Fig.  5. 
From  this  follows  the  rule: 

Forces  lo  left  of  a  point  must  tend  to  turn  a  beam  clockwise 
'tbout  that  point  in  order  to  give  a  positive  bending  moment 
fit  that  point  —  anti-clockwise  to  give  a  negative  bending  mo- 
ment. 

Forces  to  the  right  of  a  point  must  turn  the  beam  anti-clock- 
wise about  that  point  in  order  to  give  a  positive  bending 
moment  at  that  point  —  clockwise  to  give  a  negative  bending 
moment. 

If  these  rules  are  observed, 
the  effect  of  the  fixing  moments 
is  also  automatically  deter- 
mined. Thus  if  a  fixing  mo- 
ment  is  found  to  be  negative  at 

a  support,  and  the  above  rules  are  followed,  its  effect  will  be 
negative  on  either  side  of  that  support. 

The  convention  for  shear  is  shown  in  Fig.  6.     If  forces  to 

BENDING  noMENT.S  SHEflR  DlflGPflMS  FO)?  REflR  UPPER   SPflf?    flT     O° 

_  LonpmG       1fc.05*  PE(?  FOOT  Pun    .   W  ENS,  MI  Pw.r._ 


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the  left  of  a  point  tend  to  shear  the  beam  upward,  the  shear  at 
this  point  is  positive.  As  a  result  of  this  arbitrary  rule,  when 
finding  the  shear  by  means  of  bending  moments,  the  sign  as 
found  must  be  reversed  if  the  origin  chosen  is  to  the  left  of 
the  line  of  action  of  the  shearing  force. 

Observance  of  this  rule  is  not  so  important  as  the  observance 
of  the  rule  for  bending  moments.  Tt  is  generally  easier  to  see 
what  happ ons  physically. 


Working  Out  of  Bending  Moment  and  Shear  Diagrams 
for  Upper  Rear  at  0  Deg. 

The  principles  of  the  preceding  paragraph  will  be  best 
illustrated  by  working  out  the  above  case  fully.  In  Fig.  7  is 
shown  the  disposition  of  the  wing.  With  a  total  span  of  36 
ft.  6  in.  and  an  engine  panel  of  2  ft.  6  in.,  we  allow  an  over- 
hang of  2  ft.  6  in.,  7  ft.  9  in.  for  outer  span  between  struts. 
and  a  smaller  inner  span  of  6  ft.  9  in.,  which  seems  a  reason- 
able spacing.  The  loading  in  plane  of  spar  web  as  previously 
found  is  16.05  Ib./ft.  run.  .  For  simplicity's  sake,  we  neglect 
the  engine  panel. 

To  get  bending  moments  at  supports  : 

(a)  M,  =  0,  since  wing  is  hinged  at  engine  panel; 

(b)Jfi=1606X(2.5)'    =50.21b,.ft.. 

(c)   to  find  Mn  we  write 

MA  +  2(1,  +  L)M.  +  MJ,  =    -  %!!../,  —  %!«•/: 
and  by  substituting  in  this  equation, 

M0  =  03.7  Ibs.-ft. 
To  get  shears  at  supports: 

(a)  S_,  =  2.5  X  16.05  =  40.1  Ibs. 

(b)  Taking  moments  about  support  0  we  have 


therefore  S  +,  =    —56.7  Ibs. 
(c)   Taking  moments  about  support  2  we  have 


therefore  (reversing  signs), 

S_0  =  68.0  Ibs. 
(d)   Taking  moments  about  support  1  we  have 


therefore  S+,,  =  —  68.3  Ibs. 

(e)   Taking  moments  about  support  0  we  have 

^"i  "7          "I      *J 1^1    ~~  «*ni 


therefore  (reversing  signs) 

6'_,  =  40.4  Ibs. 

To  find  the  total  reactions  (the  absolute  sum  of  tlie  shears)., 
we  have 

£_,-  +  *>'+«  =  K..  =  96.8  Ibs. 
tf_.  +  -V  =  «."  =  136.3  Ibs. 
S_t  =  It,  =  40.4  Ibs. 

After  having  found  the  bending  moments,  shears,  and  re- 
actions at  the  supports,  it  is  very  easy  to  draw  the  entire  bend- 
ing moment  diagram  by  finding  points  of  zero  shear  and 
maximum  bending  moment. 

Thus  in  the  outer  span,  if  x  is  the  distance  to  the  light 
of  support  2  of  the  point  of  zero  shear,  S+!  =  a •«•..  and  .c  = 
56.7 


16.05 


=  3.53  ft. 


The  bending  moment  at  this  point  is  (taking  forces  to  the 
left) 


+ 


,x  =   -  49.8  Ibs.-ft. 


Similarly  in  the  inner  span,  if  x  =  distance  to  the  righl  of 
support  0  of  the  point  of  zero  shear, 

and  x  =  4.26  ft. 

The  bending  moment  at  this  point  is   (taking  forces  to  the 
left) 

,.,         wx'. 

M  „  =  -p-1  +S+  .r  =  —  ol.3 


References  for  Part  II,  Chapter  11 

"Wins  Data  and  Analysis  for  a  Staggered  Biplano,"  by  Dr.  A.  F. 
Kahm,  Franklin  Institute,  December  1914. 

British  Ueport  1912-l!tl.",.  .No.  s:s.  A  pivlimiiiary  note  on  methods 
<>f  calculation  whicli  may  he  employed  in  the  determination  of  the 
sinssrs  in  the  spars  of  airplane  wings  l;y  Itairsimv  niul  MacLachlan. 


Chapter  XII 

Wing  Structure  Analysis  for  Biplanes 


Reactions  in  Plane  of  Lift  Truss  Due  to 
Upper  Rear  Spar  at  0  Degree 

At  tlic  conclusion  of  the  previous  chapter,  we  drew  the  bend- 
ing  moment  diagram  for  the  upper  rear  spar  as  a  continuous 
beam,  and  found  the  appropriate  reactions.  But  since  the 
bending  moment  diagram  was  drawn  for  that  component  of 
the  force  in  the  plane  of  the  lift  truss  which  was  in  the  plane 
of  the  spar  web,  allowance  has  to  be  made  for  it  on  "reverting 
in  the  lift  truss.  The  running  loads  were  in  the  ration  of  16.3 
tn  10.05.  Hence  rca'-limis  arc 

10.3 


R,=  96.8  X 
K0  =  136.3  X 
fl,  =  34.0  X 


16.05 
16.3 

16.05 
16.3 

10.05 


=    98.311). 


=  138.4  Ib. 


=    41.011). 


Reactions  in  Plane  of  Lift  Truss  Due  to 
Lower  Rear  Spar  at  0  Degree 

Since  the  spacing  of  the  supporting  points  on  the  lower 
wing  is  identical  with  that  of  the  upper  wing,  and  the  slight 
overhang  is  the  same,  the  bending  moment  diagram  and  the 
shears  and  reactions  will  be  in  direct  ratio  to  the  loads.  The 
ratio  of  loads  on  upper  plane  to  lower  plane  is  14  to  11.5. 
1  ICMCC  reactions  are 


/•'.     =    98.3 


=    75.4  Ib. 


«„  =  138.4  X         r  =  107.5  Ib. 
10.3 


/.',  =    41.0 


~ 


=:    31.4  Ib. 


Stress   Diagram  for  Rear  Lift  Truss  at  0  Degree 

We  are  now  in  a  position  to  draw  the  stress  diagram  for 
the  lift  truss  as  shown  in  Fig.  1.  The  only  other  loud  to  be 
added  is  20.3  Ib.,  which  is  allowance  for  half  the  air  force  din- 
to  the  engine  panel  acting  on  the  rear  spar. 

In  drawing  this  stress  diagram,  the  strut  K  L  is  assumed  as 
taking  no  tensile  load,  and  the  lift  load  at  F  G  is  transmitted 
by  the  cross  wire  L  M  to  the  body. 

Stress  Diagram  for   Internal  Upper  Wing 
Bracing  at  0  Degree 

In  Fig.  2  is  drawn  the  stress  diagram  for  the  internal  brac- 
ing of  the  upper  wing  at  0  deg.  incidence. 

The  spars  have  so  much  less  resisting  moment  in  the  plane 
of  the  wing  that  it  is  perfectly  justifiable  to  treat  the  inter- 


plane  wing  bracing  as  a  pin-jointed  structure  and  neglect  all 
consideration  of  bending  moments. 

The  running  loads  per  foot  run  are  taken  from  the  preced- 


FIG.  1     STRESS  DIAGRAM  OK  REAR  LIFT  TRUSS  AT  0  DEG. 
INCIDENCE 

ing  sections,  with  the  addition  of  J/2  Ib.  drift  at  each  external 
bracing  point. 

Computations  for  Dimensions  of  Rear  Upper  Spar 

Having  drawn  the  bending  moment  diagram,  the  lift  truss 
stress  diagram  and  the  internal  wing  bracing  stress  diagram, 


FOR  EXTERNAL  DRIFT   AT  EACH  EXTERNAL  CONNECTION 


FIG.  2    STRESS  DIAGRAM  OF  UPPER  WING  INTERNAL  DRAG 
BRACING  AT  0  DEG.  INCIDENCE 

all  at  0  deg.  incidence,  we  are  in  position  to  determine  the 
dimensions  of  the  rear  upper  spar.     Since  the  worst  loads 


125 


AIRPLANE    DESIGN 


come  on  the  rear  spar  at  this  angle  of  incidence,  it  is  not  neces- 
sary to  recompute  it  at  16  deg.  also. 

The  worst  loads  it  has  to  meet  occur  in  the  inner  span,  3 
feet  from  the  wing  hinge: 

Compression  from  the  lift  diagram  of  675  Ib. 

Compression  from  the  drag  diagram  of  330  Ib. 

Bending  moment  of  44  ft.  Ib. 

It  is  first  of  all  necessary  to  fix  the  effective  deptli  of  spar 
for  the  wing  section  employed,  namely,  the  R.A.F.6.  The  spar 
is  placed  at  30  per  cent  from  the  rear  edge,  where  the  thickness 
of  the  wing  is  .054  of  the  chord.  For  a  62-in.  chord,  this  gives 
a  thickness  of  3.34  in.,  or  3  21/64  in.  very  nearly. 

From  this  must  be  deducted  the  thickness  of  the  two  rib 
caps  or  flanges.  The  construction  and  dimensioning  of 'ribs  is 
a  matter  of  some  uncertainty  and  controversy,  and  will  be 
dealt  with  fully  in  a  later  article. 


moment  that  a  thickness  of 
rib  flanges,  so  that  the 
effective  depth  of  the 
flanges  will  be  re- 
duced tx)  3  5/64  in. 
The  actual  drawing 
up  of  the  beams  is 
largely  a  matter  of 
trial  and  error.  That 
is  to  say,  an  appar- 
ently suitable  section 
has  to  be  drawn  in  its 
area,  and  moments  of 
inertia,  etc.,  have  to 
be  computed  together 
with  the  factor  of 
safety  consequent 
thereon. 


in. 


We  will  assume 
will  be  sufficient 


for 
for 


the 
the 


NLUTRRL 


FIG.  3 


—    1.75 

REAR  UPPER  SECTION 


After  ;i  number  of  trials,  the  spar  section  of  Fig.  3  is  found 
to  be  satisfactory. 

The  upper  surface  of  the  spar  follows  the  outline  of  the 
R.A.F.6  wing  section  at  this  point,  but  in  making  computations 
the  slight  slope  may  be  neglected. 

To  compute  the  moment  of  inertia,  the  quickest  way  is  to 
compute  for  the  solid  section  and  deduct  the  moment  of  inertia 
of  the  material  channeled  out.  The  moment  of  inertia  of  a 

rectangle  being  given  by  the  formula  -rj 


1.75  X  3.083        1.125  X  1.7:' 


=  4.27  —  (1.46  =  3.81 


12  12 

A  =  1.75  X (3.08)— 1.125  X  1-7  =  5.39  —  1.91  =  3.48 
The  stress  in  the  outermost  fibers  will  now  be  given  by  the 
formula 

P        My 
/  =  —  -     —f—  where  P  =  direct  load,  y  =  distance  of  outer 

A.  I 

fibers  from  the  neutral  axis  and  /  =  stress.     Since  P  =  1120 
Ib.,  M  =  93.7  ft,  Ib.  =  1125  inch.  Ib.  and  maximum  /  =; 
1125X1-54 


3.48 


3.81 


=  777  Ib. 


Allowing  a  maximum  fiber  stress  for  spruce  of  6500  Ib.,  we 
get  a  factor  of  safety  of  8.35,  which  is  in  excess  of  the  7.5 
specified  by  the  Army. 


Similar  computations  can  be  carried  out  for  the  upper 
front  spar  at  16  deg. — since  the  biggest  'oad  is  carried  at  this 
angle. 

It  must  be  pointed  out,  however,  that  although  the  formula 

/  =—  -(--^-y-is  largely  used,  and  is,  therefore,  perfectly  sound 
A.  i 

on  a  comparative  basis,  the  factor  of  safety  given  by  it  is  not 
exactly  true.  Tests  on  breaking  beams  by  bending  show  great 
variations  from  the  above  formula,  depending  largely  on  sec- 
tions employed,  but  special  values  for  moduli  of  rupture  by 
bending  are  not  available. 

For  the  lower  wing,  if  the  same  chord  is  employed  as  in  the 
upper  wing,  and  the  spars  have  the  same  dimensions,  no  com- 
putations need  be  made,  since  the  loads  on  the  lower  wing 
will  always  be  considerably  less.  Whether  with  the  same 
chord  the  lower  spars  should  be  smaller  than  the  upper  ones 
is  a  matter  to  be  determined  largely  from  the  manufacturing 
point  of  view. 

A  Complete  Example  of  Wing  Analysis  Arrangement 

In  Fig.  4  is  shown  the  complete  analysis  for  the  wing 
structure  of  a  Curtiss  biplane.  The  methods  employed  in  get- 
ting out  this  analysis  are  substantially  the  same  as  indicated 
above,  and  the  method  of  presentation  is  an  excellent  model. 

Computations  for  Shear  in  Spars 

Wood  is  so  much  weaker  in  shear  than  in  either  tension  or 
compression,  that  it  is  somewhat  surprising  that  designers  do 
not  make  computation  for  shear  in  the  spar  web — although 
spars  are  always  made  solid  for  2  in.  or  3  in.  on  either  side  of 
a  supporting  point,  to  allow  for  the  maximum  shear  occurring 
at  such  points. 

The  maximum  longitudinal  shear  for  a  beam  which  is  sub- 
jected to  vertical  shear  occurs  at  the  neutral  axis,  and  its  value 
is  determined  by  the  formula 

F    . 


where  /''  =  vertical  shear  at  the  point  due  to  external  loads, 
I  =  moment  of  inertia  of  whole  section,  b  =  breadth  of  web  at 
neutral  axis,  .4,  =  area  of  section  above  neutral  axis,  y  =  dis- 
tance of  ccntroid  of  this  area  from  the  neutral  axis. 

Thus  consider  the  same  upper  rear  spar  6  inches  from 
support  0.  The  shear  at  this  point,  as  given  by  the  shear 
force  diagram  of  Fig.  7  of  the  preceding  chapter,  is  60  11). 
Considering  the  section  of  spar  shown  in  Fig.  3: 

/  =  3.81  in.4 
Al  =  1.76  in/ 
b  =  0.625  in. 
,/  =  093  in. 

«=  3^V625  X  1-76  =  0.93  =  41.2  II, 

Allowing  shearing  value  of  spruce  to  be  400  Ib./sq.  inch,  we 
have  a  factor  of  safety  of  9.7,  which  is  amply  sufficient.  But 
cases  might  occur  where  the  shear  near  supports  is  very  large, 
and  resistance  to  shear  being  largely  due  to  the  web,  it  is  al- 
ways advisable  to  make  such  computations. 


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Ft     POINTS    OF  GREATEST     STffESS 
PRUTS    SEE    DRIFT    PUGRAMS. 

NET  RwNNir.ii    LIFT  AND   ORIPr COMPONENTS 
IN   FIANEC     or   WIN*    TRUSSING 


SROSS  LIFT  Awo  D»irr 


LirrLo»D»  »NB  »Tt»ts»t*iNPL*Mt  or  »i»«   STRUTS  IMCLUOIX 

OPBCNDrN*  MOMENT  AND   WEIGHT   OF    STRUTS  AND  STAYS 


POUNDS 


3000 
ESOo 
loo  o 
15  e  « 
i«e  o 

50" 

O 

500 

i  o  0  e 

ISO  O 

Zoo  e 
tsoo 


*  4-tlHEOIUI. 


ON  FRONT,  TOP  AND  LOWCBSPAKS 
OF   IBCAM  WEB. 


t  DRIFT  C.IZ4 
Pen  TNC.H 


j         n      n 


17  i  is        in         11       j 

PUAN   OF    UPPER    SPARS 


;OMPUTEP     VALUES 


Appendix 


Notes  of  Aerial  Propellers 

By  H.  Bolas 

Presented  by  Mervyn  O'Gorman,  Superintendent  of  the  Royal  Aircraft  Factory 
Reports  and  Memoranda,  No.  65.     March,  1912 


The  object  dl'  the  present  notes  is  to  give  an  account  of  a 
met  IKK!  which  has  been  employed  in  propeller  design  at  the 
lioyal  Aivcrai't  Factory,  with  some  particulars  as  to  the  theo- 
retical assumptions  on  which  it  is  based.  In  principle  the 
met  hud  is  essentially  the  same  as  that  which  has  been  described 
by  M.  Dr/ewiecki,*  and  is  commonly  referred  to  as  the  con- 
stant incidence  method. 

Ciiiixtinit  Influence  Method. — In  this  method  the  propeller 
blade  is  regarded  as  an  aerofoil,  each  element  of  which  makes 
a  constant  angle  with  its  path  in  space.  In  other  words,  the 
lihnle  is  treated  exactly  as  though  it  were  an  airplane,  except 
that  the  path  of  the  blade  is  a  helix  instead  of  a  straight  line. 

The  path  in  space  of  any  point  of  a  propeller  moving  for- 
ward with  constant  velocity  is  a  helix,  the  advance  of  the  screw 
per  revolution  being  called  the  pitch.  If  the  angle  of  the 
Made  at  any  point  corresponds  with  that  of  the  effective  helix, 
the  only  resistance  to  motion  is  head  resistance  and  skin  fric- 
tion, and  no  thrust  is  obtained.  If,  however,  any  element  is 
gel  at  some  angle  of  incidence  to  the  effective  helix  it  becomes 
an  aerofoil  possessing  lift  and  drift,  and  a  propeller  so  de- 
signed will  give  a  definite  thrust. 

In  this  method,  then,  the  angles  of  the  effective  helix  are  first 
calculated  for  various  fixed  points  of  the  blade  for  a  given 
velocity  of  advance  and  a  given  propeller  speed.  Each  of  these 
angles  is  then  augmented  by  the  angle  of  attack. 

Value  of  Angle  of  Attack. — The  value  of  the  angle  of  attack 
to  be  used  depends  chiefly  on  the  form  of  blade  profile  adopted. 


FIG.  1 

Consider  Fig.  1,  which  is  intended  to  represent  a  section  of  an 
aerofoil,  or  of  a  propeller  blade,  in  motion.  D  =  drift  or  re- 
\jstance  to  motion;  L  =  lift  (not  to  be  confused  with  thrust  of 
element  )  ;  B  =  angle  of  attack;  G  =  gliding  angle,  or  ratio 
1>  I.  nearly.  As  the  angle  of  attack  U  is  varied  the  ratio  II  I. 
will  also  vary,  and  for  some  particular  value  of  B  this  ratio 
will  be  a  minimum.  It  is  this  value  of  H  which,  on  this  method, 
is  employed,  so  far  as  possible,  in  practice.  As  already  stated, 
this  best  value  depends  on  the  form  of  blade  profile;  it  is 
usually  found  to  be  in  the  neighborhood  of  4°  f  for  good 


*  See  Abstracts  No.  4r>.  Report  for  1909-10.  Theorie  Generate  dee 
Propvlsewi  IleHcoiclnuj-  ct  Mi-tlnnlc  dc  Caicul  dc  ces  prouuUcurs  pour 
I' Air.  Paris,  F.  Louis  Vivien.  I'.m'.i. 


forms.  It  is  well  to  note,  however,  that  in  some  cases  it  is 
impossible  to  use  this  best  value,  as  the  width  of  blade  required 
may  be  too  great.  In  such  a  case  a  compromise  must  be  made 
and  the  angle  of  attack  increased.  This  only  happens,  how- 
ever, when  the  primary  conditions  are  bad. 

Efficiency   of  Eli-mcnlal   XtripA    and   Curve   of   Efficiencies 

I 


FlG.   2 

(see  Fig.  '2). — Let  -1  denote  the  angle  the  effective  helix  makes 
with  the  line  at  right  angles  to  the  axis,  B  the  angle  of  attack. 
Also  as  above,  let  D/L  =  K  =  tan  G.    Then  the  efficiency  E  of- 
the  element  is  readily  shown  to  be  given  by 
,,  _        tan  A 

~  tan  (.4  -\-G) 

and  for  variation  of  G,  K  is  a  maximum  when  G  is  a  minimum. 

From  this  a  curve  of  efficiencies  for  different  values  of  the 

angle  A  can  be  plotted  (Fig.  3).    The  curve  in  Fig.  3  has  been 


7CC 


•~40- 

§ 

20- 

Radius       JL 

Scale  of  Effect   Pitch  A/e 

4  . 

. 

0                  .2 

.4                     .6                     .8                     7.0       7.7 

Scn/e   .>/  ^;;s//e   ^ 

60°     43°     30' 

78'                         72°                     9°                 8' 

FIG.  3 

drawn  for  G  =  4°  35'.    In  propeller  diagrams  it  is  more  con- 
venient to  employ  r/pe  as  abscissa  instead  of  the  angle  ,-i 

i  Si'c  Notes  added  June,  1912,  p.  136. 

j  Di-iiiH-il  as  the  ptliciency  of  a  strip  of  blade  at  radius  r  and  of 
width  dr  this  strip  being  supposed  not  isolated  from  thc>  neighboring 
elements. 


12!) 


NOTES   ON    AERIAL    PROPELLERS 


when?  /i  is  the  clTi-ctive  pilch,  I  he  relation  between  them  being 

r/pt  =  — .  volA. 
alt 

One  other  point  may  !«•  inentioiieil — tile  <|Ueslion  of  variation 
til'  efficiency  a-  we  I  ravel  out  along  tile  Made.  It  will  be  >cen 
from  the  cun-e,  that  as  we  inerea.-e  r  ji,  the  elliciency  increases 
very  rapidly  at  first,  and  reaches  a  maximum  at  the  point  where 
r/pt  =  0.17  (or  A  =  about  43°).  From  the  formula  given 
ab.i\e  for  K  it  is  readily  shown  that  /•.'  heeomes  a  maximum 
when-  -I  =45°  —  (G/2).  Thus  in  the  particular  case  given. 
G  =  4°  35,'  and  the  angle  for  max.  efliciency  =  42°  43'.  As 
r/pe  increases  still  further,  it  will  lie  noticed  that,  the  efficiency 
decreases  and  continues  to  do  so.  Hence,  beyond  a  certain 
radius  on  the  blade  the  elements  get  less  and  less  efficient 
towards  the  tip.  This  is  an  unfortunate  point  in  the  design 
of  actual  propellers. 

1'riifirlli'r  I Hiii/ nuns.  Supposing  the  velocity  of  advance, 
the  revs,  per  minute  of  the  propeller,  and  the  horse-power  of 
the  engine  are  known,  we  can  now  proceed  to  set  out  our 


1.0 


I.I 


FIG.  4 


2'8" 


3-4" 


4'0"  4'3" 


diagrams.  The  scales  of  these  are  in  the  first  place  immaterial. 
(flee  Fig.  4.)  It  will  be  best  to  explain  first  the  meaning  of 
the  various  curves,  and  afterwards  to  devote  some  attention 
to  the  ideals  to  lie  aimed  at  and  the  determination  of  scale. 

'  'irre  1. — This  is  termed  the  Linear  Gradimi  Ciiri-e,  and  its 
ordinates  are  everywhere  proportional  to  the  blade  widths, 
these  l>eing  supposed  to  be  developed  on  to  the  plane  of  the 
paper. 

Curve  2.  Pressure  per  sq.  ft.  curre. — The  pressure  upon  the 
blade  per  unit  area  of  surface  at  any  point  depends  principally 
upon  (i)  the  form  of  section,  (ii)  the  angle  of  attack,  (iii) 
the  velocity  of  that  particular  point  relative  to  the  air.  Let 
C  be  a  constant  depending  upon  the  form  of  section.  Let  B 
as  before  be  the  angle  of  attack,  and  I',  the  velocity  of  a 
particular  element  relative  to  the  air.  Then  we  may  write  with 
sufficient  truth — 

I 're-sure  per  >«,.  ft.        I  It  I      , 
and  since  i    and  II  are  constants  along  the  blade  we  can  write 

I 're-sure  per  sq.  ft.  a   1     . 
Now  if  K  be  the  axial  velocity  of  translation 

Vt'=  V/sin-.\. 
But  V  also  in  constant  along  the  blade.    We  may  therefore  put 

Vt'  a  1/sinM, 

and  it  is  now  only  necessary  to  plot  a  curve,  the  ordinates  of 
which  are  proportional  In  1  -in  I,  in  order  to  obtain  the  pres- 
sure per  sq.  ft.  diagram.  The  scale  i-  for  the  present  imma- 
terial. 

<  iirf  .','.  I.fiiil  i,rii>iinii  (  itrve. — Consider  any  value  of  r/p, 
represented  by  0-r.     Then  at   lhi>  point   the  width  of  blade  is 
icprc-cnicd    by     Hi.      Kvidcntlv    then    the   quantity    f.ri/ 
will   He  a  measure  .,1    the  load   |>er   tool    run   on   the  blade,  and 


if  we  perform  this  operation  for  a  number  ol  points  at  dif- 
ferent  radii  we  can  draw  a  curve,  the  ordinates  of  which  will 
represent  the  loading  per  foot  run.  (,'urve  :i  (  Fig.  4l  has  been 
obtained  in  this  way. 

Cun-f  I.  Thrust  (irinliii<i  Caret'.  -The  thrust  grading  curve 
is  such  that  the  ordinate  at  any  point  repre-ents  the  thrust  per 
unit  length  (per  foot  I  of  blade,  and  is  obtained  from  the  load 
grading  curve  in  the  following  manner. 

Consider  the  sketch  shown  in  Fig.  ~>,  which  represent*  .1  MC 


Fi.i.  5 

tion  of  the  blade  at  any  radius.  The  line  KO,  which  rcpu- 
sents  the  pressure  per  unit  length  upon  the  element,  makes 
with  the  axis  (or  direction  of  thrust)  an  angle  (A  -\  i.  . 
where  as  before  A  is  the  angle  the  effective  helix  makes  with 
OM,  and  (i  is  the  gliding  angle.  Both  A  and  (1  are  known  for 
any  point  of  the  blade.  Now  we  have: — 

Thrust  per  foot  run  =  load  per  foot   run  X  ('os  ( -1  -\-  (!1. 

The  ordinates  of  the  thrust  grading  curve  are  thus  obtained 
from  those  of  the  load  grading  curve  by  multiplying  by  eot 

(.1  +  '•'• 

Curve  :'>.  Efficiency  Curve. — The  values  of  the  angle  .1  and 
gliding  angle  G  being  known,  the  efficiency  at  any  point  is 
given  by 

tan  .1 

tan  (A  +  G) 
and   an   efficiency   curve  can   be   plotted   a>   described   earlier. 

It  should  be  explained  that  the  order  in  which  we  set  out 
the  diagrams  will  depend  upon  our  initial  data.  For  instance, 
if  we  are  given  the  shape  of  the  thrust  grading  diagram,  we 
may  first  lay  down  the  load  grading  diagram,  then  the  pressure 
per  si|uaie  foot  curve,  and  finally,  from  the  pivviou-  two,  the 
•  linear  grading  curve,  vi/...  the  plan  form  of  the  blade.  On 
the  other  hand,  if  we  start  with  the  plan  form  curve,  we  may. 


FIG.  6 

by  rcvcr-ing  the  above  process,  finally  ain\e  at  the  thrust 
grading  curve.  In  practice  the  latter  method  is  always  adopled 
for  reason-  which  we  are  now  in  a  position  to  explain. 

lilnil  ('tin-,'-.      1 1    we  a— lime   as  an    ideal   condition   that    the 
velocity    in    the  slip   -liea'ii    i-   e\  cry  where   parallel    lo   the   axis 


NOTES    ON    AERIAL    PROPELLERS 


131 


and  uniform,  then  the  momentum  per  second  imparted,  and 
hence  I  he  thrust  at  any  radius,  will  be  proportional  to  that 
radius.  In  other  words,  the  ideal  thrust  grading  diagram  is  a 
straight  line  passing  through  the  origin,  as  shown  in  Fig.  G — 
M  I)B.  In  practice,  however,  such  a  form  of  diagram  would 
be  undesirable,  even  if  attainable,  and  some  compromise  as  that 
sketched  in  Fig.  6 — AEB — would  have  to  be  adopted.  Accord- 
ing to  Mr.  Lanchester,  the  best  practical  shape  of  thrust  grad- 
ing curve  is  that  shown  in  the  next  figure,  in  which  "  con- 


jugate "  '    points  on   the  diagram   have  ei|iial  efficiencies   (Fi". 
7). 

If,  however,  we  started  out  with  a  diagram  of  this  type,  and 
from  it  constructed  a  linear  grading  curve,  our  final  plan  form 
would  take  the  shape  shown  in  Fig.  8.  Such  a  Wade  could 


Linear   Orat//,, 


FIG.  8 

never  be  employed  in  practice,  since  under  existing  conditions 
we  should  require  an  immense  blade  width  and  a  very  large 
diameter  in  order  to  obtain  the  needed  thrust.  It  is  useful, 
however,  inasmuch  as  we  know  the  direction  in  which  to  work 
when  given  good  conditions  at  the  start. 

When  designing  then,  as  I  have  already  stated,  we  invariably 
begin  with  our  plan  form,  and  finish  up  by  obtaining  a  thrust 
grading  diagram,  which  will  usually  differ  considerably  in 
shape  from  the  ideal  diagram  first  described. 

The  propeller  curves  being  laid  down,  it  only  remains  now  to 
give  them  their  proper  scales  in  order  that  we  may  satisfy  the 
initial  requirements. 

Determination  of  Scales. — Since  the  ordinates  of  the  thrust 
finding  diagram  are  measures  of  the  thrust  per  foot  run  along 
tua  blade,  and  the  abscissae  represent  the  radii  in  feet  (pt-  the 
effective  pitch  being  constant),  it  will  be  evident  that  the  area 
of  the  thrust  grading  diagram  represents  to  some  scale  the  total 
thrust  on  the  blade. 

T 

Now  thrust    per  blade  I  =  — , 

.\ci.  of   blades 

»  here  T  is  the  total  thrust  of  the  propeller. 

Let  p  =  horizontal  scale  (known),  viz.,  1  inch  on  diagram 
=  f>  ft.  of  radius. 

Let  q  =  vertical  square  (required),  viz.,  1  inch  on  diagram 
=  </  Ibs.  per  ft. 

Then  jiq  X  area  of  diagram  in  square  inches  =  Thrust  per 
blade. 

Hence 

Thrust   per  blade 
area  of  diagram  .  p' 

In  this  equation  the  horizontal  scale  p  is  known,  the  area  of 
the  diagram  may  easily  be  computed  by  means  of  a  planimcter, 

•Conjugate  points  are  dcfliuMl  as  the  points  in  which  a  straight 
line  through  tho  origin  cuts  the  thrust  grading  diagram. 


and  it  is  then  only  necessary  to  tind  t,  the  thrust   per  blade,  in 
order  to  determine  completely  the  vertical  scale. 

Before  t  can  be  calculated,  however,  the  total  efficiency  of 
the  propeller  must  be  found  (see  Fig.  9).  To  do  this  we  divide 
up  our  thrust  grading  diagram  into  a  number  of  parts  and 


FIG.  9 

then  compute  the  area  of  each.  The  mean  efficiency  of  each 
part  is  now  read  off  on  the  efficiency  curve,  then  divided  into 
its  corresponding  area,  and  all  the  quotients  so  obtained  are 
summed  up.  The  sum  arrived  at  in  this  way,  divided  into  the 
area  of  the  thrust  grading  diagram,  will  give  the  total  efficiency 
of  the  blade. 

Computation   of   Thrust. — Let  H  =  H.P.   of   engine,  Et  = 
total  efficiency  of  propeller,  V  =  velocity  of  advance  in  ft.  per 
SIM-.,  7'  =  thrust  of  propeller. 
Then  rr/550  =  11.  F 

We  then   have 

Thrust  per  blade  =  7'/No.  of  blades. 

The  thrust  per  blade  having  been  thus  ascertained,  the 
vertical  scale  of  the  thrust  grading  diagram  is  calculated  as 
before  explained,  from 

Thrust  per  blade 

q  =  —  . 

area  of  diagram  X  P 

Thus  in  a  given  case  H  =  58,  E  =  .67,  T"  =  73  ft./sec. 
Therefore 

T  =  58  X  07  X  550  =  .,,,._,  ^ 

No.  of  blades  =  4. 

Therefore,  thrust  per  blade  =  73  Ibs. 

Further,  area  of  thrust  grading  diagram  =  40  sq.  ins. 

p  =  0.381  ft, 
Therefore 


Load  (iratlhiy  Curve. —  Since  this  was  obtained  by  dividing 
the  ordinates  of  the  thrust  grading  curve  by  cos  (A-\-G), 
wliich  is  itself  a  mere  ratio  (and  has  therefore  no  dimensions), 
the  scales,  both  thrust  and  load  grading  curves,  will  evidently 
be  identical. 

Pressure  per  sq.  ft.  Curve. — The  determination  of  the  in- 
tensity of  pressure  on  the  blade  at  any  point  is  of  course  a 
matter  for  experiment,  and  the  data  at  present  available  are 
somewhat  scanty.  In  an  account  of  the  recent  experiments  of 
M.  Eiffel,  however,  a  curve  will  be  found  which  gives  the  lift 
and  drift  for  a  particular  form  of  section,  and  this  form  of 
section  is  the  one  we  have  adopted.  A  rough*  reproduction  of 
M.  Eiffel's  curve  is  shown  in  Fig.  10.  some  explantion  of  which 
is  perhaps  necessary. 

The  angles  of  incidence  (viz.,  angles  of  chord  UV)  are 
marked  along  the  curve  itself.  Consider  the  point  where  the 


*  NOTE.    -This  curve  is  to  be  taken  .-is  diagrammatic  only. 


132 


NOTKS    (IN     \KKI\I.    I'KOI'I  I  I  I  li- 


angle  is  4J  (I'\  and  lot  the  ordinal <•  then-  be  denoted  by  A"v 
and  the  abscissa  by  A".r.  Then  wo  have  for  this  particular 
angle  of  attack 

I.it't   per  unit   area  of  surface  •  K'II  \  (velocity)'. 
Drift  "  =  K'x  X 

Further,  if  the  point  /'  l>e  joine<l  to  (>.  the  alible  /'")    i-  the 


» 


0.005      0.004       0.003 


0.00. 


0.001 
K'  x 


0.05 


0.04 


0.03 


0.02 


0.01 


0.00 


t—1- 


Form  of  Sec'/nn 

h'Ki.  10 


•rlidinj;  an^le  of  the  aerofoil,  since 
ratio  ot  drift  to  lift  of  the  plane, 
that    the    best    an^le    of    incidence 
tangent   from  n  to  the  curve,  since 
drill    lift,  and  what  is  more,  it  will 
for  this  particular  section  is  4°. 
planalion   we  can   now   proceed   to 
choose  some  point  on  the  blade,  -ay 
0.9. 

Then  a>  before  explainol. 


the  tangent   oi'  I'O  )     is  the 
It  will  therefore  be  evident 
\s   obtained   by    drawing   a 
this  gives  the  least   value  of 
be  seen  that  the  best  angle 
With   this   preliminary  cx- 
the  scale  of  our  diagram: 
the  point    A"  wh-T-  r 


eol.-l  =  -  •-;  whence  .1  =  10°  ^, 
/'• 

and  sin  A  =  0.17*1'. 

Hut    we   have   prc\  ioiisU    -how n    that 

Ab-olnte  velocity  of  point        Velocity  of  advance   sin  .1. 

I'Jii  ft.   per  sec. 

Now    from    KilTel'.-    curve,    lor    aiiL'le    of    attack         1   .    A',r 
H.iMiori'    in,  English  iin 

Therefore,  lift  in  Ibs.  |>er  sq.  ft.  —  A',,   (velocity  in  ft.  per 

=  .( 5  U'JOi 


_;!-li  iii.il-i 
\<.  . 

"l«l<-il   .Inn-. 


KlITi- 


In    :..• 
|>     ! 


:i  -    im 


,  we  have  from  the  pressure  per  s<|.  ft.  curve 


=  88  Ibs.  per  sq.   ft. 
Therefore  1"  =  25.7  Ibs.  per  sq.  ft., 

thus  fixing  the  scale  of  our  pressure  per  sq.  ft.  eur\c. 

It  will  be  noticed  in  the  above  that  I  have  taken  actual  lift* 
on  blade  instead  of  total  pressure,  vi/...  \/  ( A'//'  -f-  A'.r").  I'', 
but  the  difference  is  usually  so  small  as  to  be  negligible. 

Liin'iir  (Inidiiifi  1'iin-i-.      Again  consider  the  point    \  of  this. 
where  r/p,  —  .9 
We  have 

Ordinate  of  blade  f   ^    f    pn-sure   per 
in  feet  at  point     \          '    sq.  ft.  in  Ibs. 
Ma  le. 

Ordina.e  ot    blade  in   fl.  a.   point  =     'Oa(1  **T.  " 

preesnre  per  s<).  ft. 
\  M  X  4.79   = 

'  X  25.7 
=  7".33 


„. 
per  it.  run 


V   -  1".7  =  (!'.4  of  Made  width. 
1"  .    ll'.L'.'l.-)  Of  Made  wi  Illi 
We  lliive  :llso 

Max.  blade  width  •=  0'..'>f>7        (i".H.  say  7"  wide. 

The  scale  tit  the  lirear  eradiuy  rune  belli*:  known,  we  are 
now  in  :i  posi'ion  In  set  out  our  propeller,.,  -moo  (lie  blade 
angles  at  the  \arions  radii  have  lieen  previously  deterinined. 

.\nmber  of  lilades. — At  the  present  lime,  the  majority  of 
propellers  in  use  are  of  wood,  and  hence  two  or  four  lilades 
are  employed,  three  blade*  lieiny  excluded  for  eiiiislnictional 
reasons. 

It  is  difficult  at  present,  until  further  experimental  data  are 
available,  to  decide  as  to  the  relative,  merit-  of  two-  and  four- 
bhided  pro]iellers.  The  four-bhided.  propeller  is  possibly  better 
ae:-odynamically  and  from  the  point  of  view  of  balance,  but 
the  two-bladed  propcll'T  involves  much  |(.Ss  work  in  cons' ruc- 
tion and  is  stronger  at  the  buss. 


Kl(i.     11 

////.  erence,  or  the  disturbinj;  actio'i  which 

any  one  blade  e\ert>  upon  the  air  dealt  with  by  any  olhev.  i>  a 
matter  abotii  which  little  is  yet  known.  The  following  siiir- 
L;c-tion  is  put  forward  merely  as  afl'ordini;  a  rou.irh  yuidc  in 
design. 

Kc\(i'iini:  |i>  comparison  with  the  airplane.  IIIO\I.IL;  in  a 
continuous  -' rai^lit  line,  we  may  look  upon  the  blade-  of  a 
propeller  a.-  -upcrpo.-ed  aerofoils  which  travel  in  a  helical 
path.  Assume  that  the-  thickness  of  air  -iralum  affected  by 
the  blade  is  a  constant  proportion  of  the  blade  width  at  any 
point.  Then  we  may  write  (Kin.  Ill 


NOTES    ON    AERIAL    PROPELLERS 


133 


EO  =  PO  cos  A  =  ^  cos  A. 
n 

(n  =  No.  of  blades). 
Let  blade  width  at   point  =  b,  and   put,   according  to   above 

SO 

assumption,  —  j^-   =  m. 


Then  l>  must  lie  less  than 


m  X  '•' 


cos  .A. 


If  we  now  plot  a  curve  where  abscissa  represent   radii,  or 
/•  /i, .  and  whose  ordinates  are  the  calculated  values  o; 


m  X  ' 

cos  A,  we  shall  arrive  at  what  we  call  the  limit  curve,  and  the 
linear  curve  should  at  all  points  lie  within  this  if  there  is  to  be 
no  interference.  Such  a  curve  has  been  plotted  for  the  case 
ni  l  he  propeller  already  mentioned,  and  is  shown  in  Fig.  12. 


15- 


- 

^^ 

Eforfej 

Limit 

Curve 

\ 

.  —  •  —  • 
(  :-  ear 

Grading 

-C«rve 

^ 

I.-                 ,  _,"            ji'0"             f-u"             3 

4"             4'U"f>'ldnis 

FIG.  12 


N//VJ////;/  of  Blade.  —  Having  now  indicated 
l  he  method  of  fixing  the  sizes  of  a  propeller  in  order  to  satisfy 
•riven  mechanical  and  aerodynamical  conditions,  it  would  ap- 
pear desirable  to  devote  a  little  attention  to  the  actual  con- 
structional design.  The  following  remarks  are  made  with 
ivt'ei-enre  io  ilie  usual  type  of  wood  propeller,  though  the  man- 
ner ol  procedure  is  quite  general  whatever  the  material 
iidopte:!.  The  process  is  essentially  one  of 
trial  and  error.  The  extreme  radius  of  the 
Made  beiiij;'  known,  a  number  of  sections  are 
decided  upon,  say  (j  or  8  inches  apart,  and 
the  blade  angles  at  these  points  computed. 
The  linear  grading  curve  will  now  provide  us 
with  the  necessary  blade  widths,  anil  it  is  only 
I'r-sary  to  set  these  down  at  their  proper 
projection  in  order  to  determine  the  true  plan 
form.  The  di  -intuition  of  the  width,  however, 
about  a  line  lluough  the  centre  of  the  blade 
root  has  yet  to  lie  discussed.  It  is  usual  in 
deMun  so  to  shape  the  blade  that  twisting  ac- 
tion is  either  greatly  minimized,  or  eliminated 
altogether,  and  for  this  reason  a  symmetrical 
plan  form  is  undesirable.  Fig.  13  will  explain 
this  point. 

A  number  of  preliminary  liial  blade.'  sec- 
tions must  now  be  sketched  out,  and  previous 
examples  ol  similar  design  will  act  as  a  good 
guide  as  to  the  thicknesses  required.  The  next 
point  is  to  estimate  the  strength  of  the  blade, 
and  the  stresses  to  which  this  is  subjected  must 
be  divided  into  (1)  Centrifugal,  (2)  Bending. 
These  are  to  be  treated  separately  and  then 
added  together. 

(1)  Cent  :•/  f>ii/nl  Stresses.  —  It  has  been 
found  convenient  lo  write  out  the  calculations  in  column  form 
as  follows  : 


13 


c 

c 

8 

g 

I 

I 

section. 

>f  clt-iw 

1 

section 

"o 
"3 

i 

"S 

§ 

•2 

II 

|J 

E 
en 

<M 

. 

« 

0 

-~ 

- 

0 

x  -? 

'E  - 

01 

~  " 

. 

s 

t 

A 

1 

r- 

•*~T 

1 

^  7 

E 

B 

[c 

v  c 

"  - 

7. 

z 

< 

Z-. 

*  = 

O  o 

O  o 

O  e 

lb».  sq. 

feet. 

sq.cm. 

cm. 

sq.  c-m. 

cu.cm. 

Ibs. 

Ibs. 

if,, 

inch. 

1 

A 

1.0 

44 

20.3 

44 

893 

1.1 

635 

424S 

620 

2 

B 

1.67 

44 

20.3 

40.5 

822 

1.01 

970 

3610 

530 

3 

C 

2.33 

37 

20.3 

31.5 

640 

0.79 

1060 

2640 

460 

4 

D 

3.00 

26 

20.3 

21 

426 

0.52 

895 

1580 

390 

5 

E 

3.67 

16 

20.3 

11 

223 

0.28 

590 

685 

275 

6 

K 

4  .  1  1'.", 

6 

7.6 

4 

31 

0.04 

95 

95 

102 

3.74      4245 


NOTE. — In  CDrupJtin;  weignt  of  eleaunts,  cm,  (cm)?,  and  (cm)3  were  em- 
ployed. This  is  m^rsly  a  matter  of  convenienc3,  the  weights  being  obtained  in 
In.  nnd  streams  calculated  in  Ibs.  per  square  inch. 

Bending  Stresses. —  (See  Figs.  14,  15,  16.-) 

In  order  to  determine  the  bending  stress,  a  bending  moment 


FIG.  14 


Load  Grading  Diagram 


FIG.  15 


3  4 

FIG.  16 


diagram  for  the  blade  is  first  drawn,  and  it  will   usually  be 
found  good  enough  to  assume  all  the  loading  uniplannr.     Ta:; 
ing  each  of  the  elements  A,  B,  C,  D,  E  and  F,  estimate  the  lo  id 
on  each  from  the  load  grading  diagram  thus : 


~ 

-  '"  •; 

=  0 

i 

D 

""•c 

I 

.£ 

i 
« 

c  "-^ 

It-1 

~  - 
7.2 

1  •-- 

.-;  = 
"t 

=  '-_ 

i 

».  J 

* 

D 

<-  ^  i" 

t  l_ 

'"c-— 

'~  i 

n 

!*  ; 

Y. 

^ 

E 
- 

jl  r. 

u 

i  ~ 

^r 

|| 

=  ,~ 

^  ~ 
Z-- 

if 

1 

A 

1.40 

2.56 

0  275 

12  5 

4  5 

12 

1150 

2 

B 

4  .  34 

7  '!") 

0.45 

ao.s 

99 

1«X> 

S 

C 

8.06 

14.75 

L'T  L1 

313 

4 

D 

11.78 

21  55 

0.79 

36.0 

604 

1080 

." 

I 

11.78 

•J.\  55 

0  <»7 

44.3 

783 

1000 

— 

F 

•2  ill 

5  38 

1.07 

48.8 

48.8 

220 

T  t:.l  40.  .'i 

7;;  7t 

2031 

— 

m 


NOTES    ON    AERIAL    PROPELLERS 


bending  moments  MI  each  of  the  sections  1,  2,  3,  4,  5  im<l 


Btnd/ng   Moment  L  B.  Inohia 
2031 — 


FIG.  17 


6  are  now  known,  and  the  moduli  of  the  sections  are  to  be 
computed  either  graphically  or  by  dividing  up  into  parts  and 
estimating  for  each  part. 


Then 


Bending  moment  on  section 


=  Stress  due  to  bending. 


Modulus  of  section 
The  sum  of  centrifugal  and  bending  stresses  at  each  section 
will  then  be  the  maximum  skin  stress  to  which  the  section  is 
subjected.     (See  table.) 


Section 

. 

2 

3 

4 

5 

Centrifugal  strcso.  llw.  s<|.  inch.  . 
Bending  strew.  the.  sq.  inch  

620 
1150 

530 
1000 

460 
1050 

390 
1080 

275 

1000 

Total  stress   . 

1770 

1330 

1510 

1470 

IL'7.-, 

Materials  and  Stresses.— Walnut,  Honduras,  mahogany  and 
spruce  are  the  best  materials  for  a  wood  propeller,  and  wal- 
nut, though  the  heaviest,  is  probably  the  best  of  the  three,  since 
mahogany  is  more  inclined  to  warp,  and  spruce  is  rather  weak 
in  tension.  The  ultimate  tensile  strength  of  walnut  and  ma- 
hogany is  about  4  tons  per  sq.  in.  (though,  of  course,  it  varies 
considerably),  so  that  a  working  load  of  2,000  Ib.  pur  sq.  in. 
may  be  considered  fairly  safe.  As  a  matter  of  fact,  in  order 
to  insure  good  jointing  and  provide  the  required  stiffness  when 
in  action,  the  best  working  figures  are  found  to  be  l,(iOO  to 
1,800  Ib.  per  sq.  in.  for  walnut  and  mahogany,  and  800  Ib.  per 
sq.  in.  for  spruce.  These  figures  arc  for  the  root  where  the 
materials  are  most  highly  stressed. 

Having  strengthened  up  the  sections  satisfactorily,  the  next 
process  is  to  arrange  the  lamination  and  "fair  up"  the  eon- 
tours.  For  glueing  purposes  the  thickness  of  the  laminas 
should  be  in  the  neighborhood  of  1  inch  (except  in  very  small 
propellers).  It  will  usually  be  found  on  setting  out  the  con- 
tours that  it  is  impossible  to  draw  a  fair  eurve  through  the 
series  of  point*  obtained  primarily-  -the  blade  sect mns  must  he 


revised  until  tliis  can  be  done.  Probably  the  best  method  is 
first  to  draw  a  smooth  curve  to  lie  evenly  between  the  contour 
points  and  then  reset  out  the  sections  to  suit. 

Before  leaving  the  discussion  of  blade  strength,  it  may  be 
advisable  to  say  a  word  or  two  as  to  the  conditions  governing 
the  employment  of  thick  and  thin  blades.  In  the  case  of  a  very 
fast  running  propeller  in  which  the  thrust  is  comparatively 
small,  the  stress  produced  by  centrifugal  action  alone  is  a  large 
proportion  of  the  total,  and  no  advantage  is  gained  by  unduly 
thickening  up  the  sections.  This  will  be  evident  where  we  con- 
sider that  an  increase  in  sectional  area  means  a  proportional 
increase  in  weight,  and  therefore  in  centrifugal  force,  the 
centrifugal  stress  remaining  constant.  On  the  other  hand,  a 
slow-moving  propeller  with  a  big  thrust  requires  the  reverse 
treatment.  A  large  proportion  of  the  total  stress  is  now  due 
to  bending  action,  while  the  centrifugal  stress  is  of  minor  im- 
portance. Hence  a  fairly  thick  blade  section  now  becomes 
advantageous. 


NOTES  ADDED  JUNE,  1912. — More  recent  experiments  have 
afforded  us  the  following  additional  data: 

Eiffel's  Experiments  show — (1)  that  for  different  shapes  of 
section  the  best  angle  of  attack  remains  constant.  (In  the  par- 
ticular case  given  it  was  5°.)  This  would  indicate  the  inad- 
visability  of  employing  a  variable  angle  of  attack,  unless  it  be 
found  that  very  high  velocity  has  a  big  effect. 

(2)  That  the  best  gliding  angle  varies  a  little.      For  the 
effective  portion  of  the  blade  this  variation  is  not  great.     The 
mean  value  was  6°. 

(3)  That  the  lift  constant  varies  somewhat   (as  one  would 
expect)  for  the  different  sections. 

The  yatintidl  Phj/sical  Laboratory  Experiments  are  valuable 
so  far  as  ordinary  aerofoil  experiments  can  be  applied  to 
propeller  design  (and  these  are  practically  all  we  have  to  go 
upon  at  present).  They  indicate  the  advantage  of  employing 
a  thin  section.  Strength  considerations,  however,  forbid  this  in 
the  case  of  wood,  and  we  are  thus  led  to  the  serious  considera- 
tion of  metal  construction. 

Effect  of  Plan  Form  ii/mn  Kflici<-m->i. — Purely  mathematical 
treatment  has  led  to  the  conclusion  that  very  little  is  to  be  ex- 
pected in  the  direction  of  effect  of  plan  form  upon  efficiency. 
The  two  cases  which  have  been  treated  are — 

(a)  Triangular  developed  plan  form  with  apex  at  blade  tip. 

(b)  Triangular  developed  plan  form  with  base  as  tip. 

The  integration  is  cumbersome  and  is  not  given  here.  It  was 
found  that  the  total  efficiency  of  the  propeller  could  be  repre- 
sented very  approximately  by  the  expression 


1 


where 


1  -f-  A'  tan  (i  cot  0 

K  =  a  constant  depending  upon  plan  form. 

ti  =  gliding  angle  of  section  adopted. 

8  =  angle  of  effective  helix  at  tip  of  blade. 


an  I  cot   0  = 


Kit 


where       l>  =-  diameter,  and  //,        cfl'ectivc  pitch. 

K  was  found  to  be  about  0.6  in  case  (a)  and  0.8  in  case  (b). 

Thus  as  a  first  approximation  for  the  efficiency  of  a  propel- 
ler we  may   use   the   formula 

1 


1  -(-  0.7  tan  (1  cot  0 

The  results  given   by  this  will   be  found   to  agree,  very  well 
with  those  obtained  from  the  diagrams. 


Addenda 


Summary  of  Procedure  in  Design 

Data  initially  required: — 

Horse  Power  and  r.p.m.  of  engine. 
Estimated  speed  of  aeroplane  or  dirigible. 
Number  of  blades  required. 

1.  Fix  diameter  of  propeller.     This  should  usually  be  as 
large  as  the  general  design  will  allow.     It  is  here  assumed 
that  the  propeller  is  direct  driven  from  the  engine.    If  geared 
down,  the  speed  of  rotation  will  first  have  to  be  decided  upon. 
Experience  is  the  only  guide  as  to  what  this  can  conveniently 
be  for  the  weight  at  our  disposal. 

2.  Calculate  effective  pitch  (pe)  and  angles  of  effective  helix 
(A)    at  suitably  chosen  radii.     Tabulate  these  and  augment 
each  by  angle  of  attack  (say  4  degrees). 

3.  Decide  upon  the  general  developed  plan  form  of  blade. 
Here  again  experience  will  help  us.     A  blade  which  tapers 
towards  the  tip  has  greater  efficiency  and  has  its  material  better 
distributed  to  withstand  stresses  than  one  with  full  tip.     Plot 
linear  grading  curve. 

4.  Plot  pressure  (Ibs.  per  sq.  ft.)  curve,  remembering  that 
this  is  proportional  to  l/sin2^  (Scale  at  first  quite  immaterial). 

5.  Lay  out  load  grading  curve  by  multiplying  ordinates  of 
(3)  and  (4). 

6.  Lay  out  thrust  grading  curve.     This  is  obtained  by  multi- 
plying ordinates  of  (5)   by  cos   (A  -(-  G)   where  G  =  gliding 
angle  for  particular  section  to  be  adopted. 

7.  Calculate  values  of  tan  A/tim.  (A  -\-  G)  for  various  radii 
and  plot  efficiency  curve. 

8.  Compute  total  efficiency  of  blade  from  above  curve  and 
Ilirust  grading  diagram. 

t).  Calculate  total  thrust  and  then  thrust  per  blade,  knowing 
horsepower  of  engine,  total  efficiency,  and  velocity  of  advance. 


10.  Obtain  scales  of  diagrams  and  thus  true  blade  widths  at 
various  radii. 

11.  Plot  "  limit "  curve  for  blade  width  to  ensure  no  inter- 
ference. 

12.  Lay  out  preliminary  blade  sections  at  correct  angles  and 
subsequently  projected  plan  form  of  blade,  having  regard  to 


Flat  Working  Space 


FIG.  18 


elimination  of  "  twist."     A  good  form  of  section  is  shown  in 
Fig.  18. 

13.  Investigate  strength  of  various  sections,    finding    first 
centrifugal,  and  then  bending  stresses,  afterwards  summing 
to  obtain  total.     Do  not  exceed  stress  at  root  of  about  1,800 
Ibs.  per  sq.  in.  in  case  of  walnut  or  mahogany,  "and  800  Ibs. 
per  sq.  in.  for  spruce. 

14.  Set  down   blade  laminations  and   plot  contours.     The 
thickness  of  laminations  should  be  about  %"  to  1"  in  ordinary 
propellers  (say  about  8  to  9  ft.  diameter)   and  the  contours 
should  be  smooth  continuous  curves.     Adjust  sections  judici- 
ously until  correct. 

15.  Design  boss  and  run  blade  root  into  boss  by  suitable 
curves.     It  is  advisable  also  to  lay  out  a  blade  section  quite 
close  to  the  boss.     In  this  part  of  the  blade  the  chosen  form 
of  section  will  usually  have  to  be  departed  from,  but  this  is 
not  a  serious  matter.     The  angles  of  such  sections,  however, 
should  not  be  less  than  the  corresponding  effective  helix  angles. 


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-  '    •       '  *         ~  I"  '  -  •-  •   '  i     I  U  /' "  •*       '".      ";'"•",  ',-'  ••  i  ;  "I-  f. 

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