TECHNICAL MANUAL } 

No. 1-820 

*TM 1-320 

WAR DEPARTMENT, 

W ASHlNGTON, Pebr·um·y 11, 1941. 

AIRSHIP AERODYNAMICS 

Prepared under direction of 

Chief of the Air Corps 

SroriON I. General. Paragraph 

Definition of aerodynamics__________________ 1 

Purpose and scope________ _____ __ ______ _____ 2 

Importance -------------------------------- 3 

Glossary of terms____ _____ _____________ ____ 4 

Types of airships--------------------------- 5 

Aerodynamic forces_______________ __________ 6 

ll. Resistance. Fluid resi&ance___________________ _________ 7 

Shape coefficients_______ ____________________ 8 

Coefficient of skin friction_ __________________ 9 

Resistance of streamlined body-------------- 10 

Prismatic coefficient------------------------ 11 

Index of form efficiency_______ _____________ 12 

lllustrative resistance problem_______________ 13 

Scale effect-------------------------------- 14 

Resistance of completely rigged airship______ 15 

Deceleration test --------------------------- 16 

III. Power requirements. 

Power required to overcome airship resistance_ 17 

Results of various speed trials_______________ 18 

Burgess formula for horsepower------------- 19 

Speed developed by given horsepower________ 20 

Summary-----------------------""'----------- 21 

IV. Stability. 

Variation of pressure distribution on airship 

hull------------------------------------- 22 

Specific stability and center of gravity of airshiP------------------------------------- 23 

Center of buoyancy________________________ 24 

Description of major axis of airship__________ 25 

Types of stability___________________ _______ 26 

Forces and moments acting on airship________ 9/l 

Damping moment-------------------------- 28 

Longitudinal stabilitY---------------------- 29 

Directional stability________________________ 30 

Lateral stability---------------------------- 31 

SummarY---------------------------------- 32 

*Thia manual supersedes or:a ll'lG-290, November 16, 1929. 

285746°--41 1 
TM: 1-320 

1-2 

SECTION 

AIR CORPS 

V. Control. Paragraph 

<Jenera! types______________________________ 33 

Directional________________________________ 34 

Altitude----------------------------------- 35 

Re 36 verse ___________________________________ _ 

Application of dynamic control to operation of . h' airs Ips _____ __________________________ __ _ 

VI. Aerodynamic stress. 

Assumption as to conditior1 of maximum stress_ 

Transverse forces acting on airship flying at 

constant angle of pitch __________________ _ 

Transverse forces acting on airship in steady 

37 

38 

39 

turn_____________________________________ 40 

Forces caused by gusts______________________ 41 

Empirical formulas for maximum aerodynamic 

bending moment on hull and for forces on 

tail surfaces-----·------------------------ 42 

Method of calculating shear and ben_ding moment on hulL ___ . _________________ ;________ 43 

Conclusion____________ _____________________ 44 

SE<:mON I 

<JENERAL 

Paragraph 

Definition of aerodynamics-- ------ --- --- --- -- ------ ------------------ 1 

Purpose and scope------------ ----------- ---·----------------------------- 2 

Importance-- --------------~--------------- ------- ---- ---- ------ ----- 3 

Glossary of terms--------------------- --------- --------------------- ---- 4 

Types of airships_·---------------------- ------------- ------------------- 5 

Aerodynamic forces-------------------------------- ----- --------------- - 6 . 

1. Definition of aerodynamics.-Aerodynamics is that branch 

of dynamics which treats of the motion of air and other gaseous 

fluids, and of the forces on solids in motion relative to such fluids. 

2. Purpose and scope.- This manual is designed as a text for the· 

instruction of airship student pilots and as a reference text for th~ 

rated pilot. Accordingly the subject has been so approached as to · 

give the knowledge of aerodynamics essential to the operation of airships. Intricate formulas involving higher mathematics, although 

valuable to the designer, are of secondary importance to the pilot. 

Such formulas therefore have been omitted and the entire subject so 

treated as to bring. out basic principles and their application to lighter 

than air aircraft operation. 

2 
AffiSHIP AERODYNAMICS 

TM 1-320 

3-4 

3. Importance.-Airships are controlled in two ways, stati<-ally 

a.nd dynamically. The former method is discussed in TM 1-325 and 

will be mentioned but incidentally in this manual. Because of the 

existence of static means of control, the study of aerodynamics may" 

appear of minor importance to the operation of airships. This is 

untrue. Stability and control are constantly effected by a combination of static and dynamic forces. To insure safety of the airship 

and to preclude possibility of exposing it to dangerous conditiOJ:!.S, the 

pilot must be aware of existing dynamic forces and their effects on 

the airship itself and on its flight path. F requently airships, due tJ 

unavoidable causes such as leakage of gas or accumulation of moisture, have become statically uncontrollable but have been sayed by the 

intelligent application of dynamic means of control. 

4. Glossary of t erm s.-During recent years many t erms have 

been introduced into the English language covering various aspects of 

aeronautical science. Report No. 240, National Advisory Committee for Aeronautics, defines the meaning of the most common of these 

expressions, from which most of the following definitions have been 

abstracted : 

.A.erodynamics.-Branch of dynamics which treats of the motion of 

air and other gaseous fluids and of the forces acting on solids in 

motion relative to such fluids . 

.A.eronautics.-Science and art pertaining to the flight of aircr aft . 

.A.ero3tat.-Generic term for aircraft whose support·is chiefly due to 

buoyancy derived from . aerostatic forces. The immersed body 

consists of one or more bags, cells, or other containers filled with 

a gas which is lighter than air. 

Airfoil.-Any surface designed to be projected through the air in 

order to produce a useful dynamic reaction. 

Airfoil section (or profile) .- Cross section of an airfoil made by a 

plane parallel to a specified reference plane. A line perpendicular 

to this plane is called the axis of the airfoil. 

Air scoop.-Projecting scoop which uses the wind or slipstream to 

maintain air pressure in the interior of the ball<:met of an aerostat. 

Airship.-Aerostat provided with a propelling . system and with 

means of controlling the direction of motion. When its power 

plant is not operating it acts like a free balloon. 

Nonrigid.-Airship whose form is maintained by the internal 

pressure in the gas bags and ballonets (fig. 1) . 

Rigid.-Airship whose form is maintained by a rigid structure 

(fig. 3). 
TM 1-320 

4 AIR CORPS 

Se1nirigid.- Airship whose form is maintained by means of a 

rigid or jointed keel in conjunction with internal pressure in 

the gas containers and ballonets (fig. 2). 

The term "airship" is sometimes incorrectly applied to 

heavier than air aircraft either in full or as "ship." This is a 

slang use of the word and should be avoided. 

Air speed'.-Speed of an aircraft relative to the air. Its symbol 

is V. 

Angle, critical.-Angle of attack at which the flow about an airfoil 

changes abruptly with corresponding abrupt changes in lift and 

drag. 

Angle, elevator.-Angular displacement of elevator from neutral 

position. It is positive when trailing edge of the elevator is below 

neutral position. 

Angle of attack.-Acute angle bet-.veen the. chord of an airfoil and 

its direction of motion relative to the air. (This definition may 

be extended to other bodies than airfoils.) Its symbol is a. 

Angle of pitch.-Acute angle between two planes defined as follows: 

One plane includes lateral axis of the aircraft and direction of 

the relative wind; the other plane includes lateral axis and longitudinal axis. (In normal flight the angle of pitch is the angle 

between longitudinal axis and direction of relative wind.) This 

angle is denoted by 0 and is positive when nose of the aircraft has 

• 

nsen. 

Angle of roll, or angle of bank.- Acute angle through which aircraft 

must be rotated about its longitudinal axis in order to bring its 

lateral axis into a horizontal plane. This angle is denoted by 

<I> and is positive when the left wing is higher than the right. 

Angle of yaw.-Acute angle between direction of relative wind and 

plane of symmetry of an aircraft. This angle is denoted by 'II 

and is positive when the aircraft has turned to the right. 

Angle, propeller blad'e.-Actual angle between chord of propeller 

section and plane perpendicular to axis of rotation of propeller. 

Usually caUed "blade angle." 

Angle, rudder.-Acute angle between rudder and plane of symmetry 

of the aircraft. It is positive when trailing edge has moved to 

the left with reference to normal position of pilot. 

Angle, zero lift;.-Angle of attack of an airfoil when its lift is zero. 

Aspect ratio of propeller blade.-Half the ratio of propeller diameter 

to maximum blade width. 

Awes of aircraft.-Three fixed lines of reference, usually centroidal 

and mutually perpendicular. The longitudinal axis in the plane 
AIRSHIP AERODYNAMICS 

TM 1-320 

4 

of symmetry, usually parallel to axis of the propeller, is called 

the longitudinal axis; the axis perpendicular to this in the plane 

of symmetry is called the normal axis; and the third axis perpendicular to the other two is called the lateral axis. In mathematical discussions, the first of these axes, drawn from front to 

rear, is called the X axis; the second, drawn upward, the Z axis; 

and the third, running from right to left, the Y axis. 

Ballast.-Any substance, usually sand or water, carried in a balloon 

or airship and intended to be thrown out, if necessary, for the purpose of reducing load carried and thus altering aerostatic relations. 

Ballonet.- Compartment of variable volume constructed of fabric 

or partitioned otf within the interior of a balloon or airship. It is 

usually partially inflated with air under control of valves from a 

blower or from an air scoop. By blowing in or letting out air, 

it serves to compensate for changes of volume in gas contained in 

the envelope and to maintain gas pressure, thus preventing deformation or structural failure. By means of two or niore ballonets, 

often used in nonrigid airships, the trim can also be controlled. 

The ballonet should not be confused with gas cell. 

Blade back.-Si<le of propeller blade which corresponds to upper 

surface of an airfoil. 

Blade face.-Surface of propeller blade which corresponds to lower 

surface of an airfoil. Sometimes called "thrust face" or "driving 

face." 

Blade width ratio.-Ratio of developed width of propeller blade at 

any point to circumference of ·a circle whose radius is the distance 

of that point from the propeller axis. 

Bow stiffener.-Rigid member attached to bow of nonrigid or semirigid envelope to reinforce it against pressure caused by motion 

of the airship. Sometimes called "nose stiffener" or "nose batten." 

Buoyancy.-Upward air force on aerostat which is derived from 

aerostatic conditions. It is equal to weight of air displaced. 

Buoyancy, center of (aerostat).-Center of gravity of volume of 

contained gas. 

Oamber.-Rise in curve of an airfoil section from its chord, usually 

expressed as ratio of departure of the curve from the chord to the 

length of the chord. "Upper camber" refers to the upper surface 

of an airfoil and "lower camber" to the lower surface; "mean 

camber" is the mean of these two. 

Capacity.-Volume of the gas-containing portion of an aerostat. 

Oar.- That portion of an airship intended to carry power unit or units, 

6 
TM 1-320 

4 AIR CORPS 

personnel, cargo, or equipment. It may be suspended from the buoyant portion or it may be built close up against it. It is not to be 

applied to parts of the keel of a rigid or semirigid airship which 

have been fitted for the purposes mentioned. 

Oeiling, static.-Altitude in standard atmosphere at which an aerostat 

is in static equilibrium a.fter removal of all dischargeable weights. 

Oenter of presswre coetflaient.- Ratio of distance of center of pressure 

from leading edge to chord length. 

Oenter of pressure of cd1•foil section.-Point in chord of airfoil section, prolonged if necessary, which is at the intersection of the 

chord and the line of action of the resultant air force. Abbreviation 

is C. P. 

Ohord (of airfoil section) .-Line of straightedge brought into contact with lower surface of the section at two points; in the case of 

an airfoil having double convex camber, the straight line joining 

the leading and trailing edges. (These edges may be defined for this 

purpose as the two points in the section w~ich are farthest apart.) 

The line joining leading and trailing edges should be used also in 

those cases in which lower surface is convex except for a short flat 

portion. The method used for determining the chord should always 

be explicitly stated for those sections concerning which ambiguity 

seems likely to arise. 

Ohord length.-Length of projection of airfoil section on its chord. 

Its symbol is c. 

Oont1•ols.-General term applied to means provided to enable the pilot 

to control speed, direction of flight, altitude, and power of aircraft. 

D1•ag.-Component parallel to relative wind of total air force on 

aircraft or airfoil. Its symbol is D. 

Dynamic (or impact) pressure.-Product 1;2pV 2 , where p is density 

and V is relative speed of the air. It is the quantity measured by 

most air speed instruments. Its symbol is q. 

:Elervator.-Movable auxiliary airfoil, function of which is to impress 

pitching moment on the aircraft. The elevator is usually hinged to 

the stabilizer. 

Envelope.-Outer covering of aerostat, usually of fabric. It may or 

may not be also the gas container. It may be divided by diaphragms into separate gas compartments or cells, and it may also 

contain internal air cells or ballonets. 

Flight path.-Path of center of gravity of aircraft with reference to 

the earth. 

H orsepower of engine, ma.:vim-wm.-Maximum horsepower engine can 

develop. 

6 
AIRSHIP AERODYNAMICS 

I 

TM 1-320 

4 

Horsepowe'l' of engine, rated.-Average horsepower developed by an 

engine of a given type in passing the standard 50-hour endurance 

test. 

Hull (airship) .-Main structure of a rigid airship consisting of a 

covered elongated framework which incloses gas cells and supports 

cars and equipment. May also be applied to complete buoyant unit 

of any aerostat. In this latter sense sometimes called "gas bag." 

lndraft (inflow) .-Flow of air from in front of propeJler into blades. 

Keel (airship) .-Assembly of members at bottom of hull of semirigid or rigid airship which provides special strength to resist hogging and sagging and also serves to distribute effect of concentrated. 

loads along the hull. It may be a simple Gall's chain as in some 

semirigids, or a very extensive structure inclosing the corridor as 

in most rigids. 

Leading edge.-Foremost edge of airfoil or propeller blade. Also 

called "entering edge." 

Lift.-That component of total air force on aircraft or airfoil which 

is perpendicular to relative wind and in plane of symmetry. It 

must be specified whether this applies to complete aircraft or to 

parts thereof. In the case of an airship this is often called 

"dynamic lift." Its symbol is L. 

Lift, gross (airship) .-Lift obtained from volume of buoyant gas 

equal to nominal gas capacity of the a;ircraft. Obtained by multiplying nominal gas capacity by lift per unit volume of gas used for 

inflation. 

Lift, static ( aerostat) .-Resultant upward force on an aerostat at 

rest obtained by multiplying actual volume of the air displaced by 

density of the air and subtracting weight of contained gas. (The 

volume of the air displaced multiplied by the difference of density 

of the air u.nd the contained gas.) 

Load: 

Dead.-Structure, power plant, and fixed equipment of an air· 

craft. Included in this fixed equipment are water in radiator 

and cooling system, all essential instruments and furnishings, 

fixed electric wiring for lighting, heating, etc. In the case of 

the aerostat the amount of ballast which must be carried to 

assist in making a safe landing must also be included. 

Full.-Weight empty plus useful load. Also called "gross 

weight." 

Pay.-Tha.t part of useful load from which revenue is derived. 

namely, passengers and freight. 

7 
TM 1-320 

4 AIR CORPS 

U seful.-Crew and passengers, oil and fuel, ballast other than 

emergency, ordnance, and portable equipment. 

Nose heavy.-Condition of an airship which when at rest in still air 

trims with its axis inclined down by the bow. The term "bow 

heavy" is preferred to "nose heavy" in describing airships. 

Oscillation, stable.-Oscillation whose amplitude does not increase. 

Oscillation, ~tnstable .-Oscillation whose amplitude incres.ses continuously until an attitude is reached from which there is no 

tendency to return toward the original attitude, the motion becom-. 

ing a steady divergence. 

P erformance CM'I'CUJteristics (airship) .-In general: 

Maximum speed at various altitudes. 

Maximum altitude attainable with definite weight relations and 

ballonet volume (if fitted). 

Endurance at full and half power. 

Static ceiling. 

Dynamic lift under specified conditions. 

Pitch of propeller: 

Etfective.-Distance which aircraft advances along its flight 

path for one revolution of propeller. Its symbol is pa. 

Geomet,rical.-Distance which an element of a propeller would 

advance in one revolution if it were moving along a helix of 

slope equal to its blade angle. 

Mean geometrical.- Mean of the geometrical pitches of the several elements. Its symbol is p0 • 

Standard.-Geometrical pitch taken at two-thirds of thE' radius. 

Also called "nominal pitch." Its symbol is Ps· 

Ze1'0 th?'U8t.-Distance which propeller would have to advance 

in one revolution in order that there might be no thrust. Also 

called "experimental mean pitch." Its symbol is pv. 

Zero torque.-Distance which propeller would have to advance in 

one revolution in order that the torque might be zero. Its 

symbol is Pa· 

Pitch mtio.-Ratio of the pitch (geometrical unless otherwise stated) 

to the diameter pj D. 

Pitch speed.-Product of mean geometrical pitch by number of revolutions of propeller in unit time, that is, the speed aircraft would 

make if there were no slip. 

Propeller area, proje~ted.-Total area in the plane perpendicular to: 

propeller shaft swept by propeller, except portion covered by the 

boss and that swept by root of the blade. This portion is usually 

taken as extending 0.2 of maximum radius from axis of the shaft. 

8 
AIRSHIP AERODYNAMICS 

'rM 1-320 

4 

Prope'!Ze1t blade area.- Area of the blade face, exclusive of the boss 

and the root, that is, of a portion which is usually taken as extending 0.2 of maximum radius from axis of the shaft. · 

Propeller-caml;er ratio.-Ratio of maximum thickness of proj)eller 

section to its chord. 

Propeller efficien<n.J.-Ratio of thrust power to power input of propeller. Its symbol is 'YJ· 

Propeller, pusher.-Propeller mounted to rear of engine or propeller 

shaft. (It is usually behind the wing cell or nacelle.) 

Pr9peller rake.-Mean angle which the line joining the centroids of 

the sections of propeller blade makes with a plane perpendicular tO 

the axis. 

Propeller section.-Cross section of propeller blade made at any point 

by a plane parallel to axis of rotation of propeller and tangent at 

· the centroid of the section to an arc drawn with the axis of rotation 

as its center. 

Propeller th1'U8t.--Component parallel to propeller axis of the total 

air force on the propeller. Its symbolisT. 

Propeller torque.-Moment applied to propeller by engine shaft. Its. 

symbol is Q. 

Race rotation.-Rotation produced by action of propeller of stream of 

air passing through or influenced by propeller. 

Vl Reynold~ number.-Name given the fraction P-;lli whichp= density of the air. 

V =relative velocity of the air. 

l= linear dimension of the body. 

,u.=coefficient of viscosity of the fluid. 

Revolutions, ma.a:imum.-Number of revolutions per minute cone. 

sponding to maximum horsepower. 

Revolution.s, normal.- Highest number of revolutions per minute that 

may be maintained for long periods. 

Righting rM11&ent (or restoring moment).-Moment which tends to 

restore aircraft to its previous attitude after any small rotational 

displacement. 

Rudde1'.-Movable auxiliary airfoil function of which is to impress 

a yawing moment on aircraft in normal flight. It is usually located 

at rear of aircraft. 

Skiln frictiO'n.~Tangential component of fluid force at point on 

surface. 

285746"-41.-----
TM 1-320 

4 AIR CORPS 

. . . 

Slip.-Diiference between mean geometrical pitch and effective pitch. 

Slip maY' be expressed as a percentage of the mean geometrical pitch' 

or as a linear dimension. · 

SliiJ junction.- Ratio of speed of advance through undisturbed a:ir 

to the product of propeller diameter by number of revolutions in 

unit time,_ that is, Jv· Slip function is the primary factor controlling propeller performance. It is 1r times ratio of forward speed 

to tip speed of propeller. 

Slipstream.- Stream of air driven astern by propeller. (The indraft 

~- is sometimes included also.) · 

Speed, grouou.l.-Hor~zontal c•mponent of velocity of aircraft relative to the earth. 

Stability.-That property of a body which causes it, when disturbed · 

from a condition of equilibrium or steady motion, to develop .forces 

or moments which tend to restore the body to its original condition . 

.Automatic.-Stability dependent upon movable control surfaces 

automatically operated by mechanical means. 

Directional.-Stability with reference to rotations about the normal axis, that is, an airship possesses directional stability in 

its simplest form if a restoring moment comes into action 

when it is given a small angle of yaw. Owing to symmetry, 

directional stability is closely associated with lateral stability. 

Inherent.-Stability of an aircraft due solely to disposition and 

arrangement of its fixed parts, that is, that property which 

causes it when disturbed to return to its normal attitude of 

flight without use of controls or interposition of any mechanical devices. 

Lateral.-Stability with reference to disturbances involving 

rolling, yawing, or side slipping, that is, disturbances in which 

position of the plane o£ symmetry of the aircraft is affected. 

Longitudinal.- Stability with reference to disturbances in the 

plane of symmetry, that is, disturbances involving pitching 

.and variation of longitudinal and normal velocities. 

Static.-Stability of such a cha-racter that, if the airship is displaced slightly £rom its normal attitude by rotation about an 

axis through its center of gravity (as may be done in wind 

tunnel experiments), moments come into play which tend to 

return the airship toward its original attitude. 

Streamline.-Path of a small portion of a fluid relative to a solid 

body with respect to which the fluid is moving. The term is coin10 
· AIRSHIP AERODYN AMICS 

TM 1-320 

4-5 

monly used only of such flows as are not eddying, but the distinction should be made clear . by the context. 

Streamline flow.-Steady flow past a solid body, that is, a flow in 

which the direction at every point is independent of time. 

Strea;mlirw form.-Solid body which produces approximately streamline flow. 

Surface, control.-Movable airfoil designed to be rotated or otherwise moved by the pilot in order to change attitude of airplane 

or airship. 

Tait group (or tail unit).-Stabilizing and control surfaces at rear 

end of aircraft, including stabilizer, fin, rudder, and elevator. 

(Also called "empennage.") 

Tau heavy (airship) .-Condition in which in normal flight the after 

end of an airship tends to sink and which requires correction 

by means of the horizontal controls. In this condition an airship 

is said to "trim by the stern.'' It may be due to either aerodynamic or static conditions, or to both. 

Thrust, static.-Thrust developed hy propeller when rotating at a 

fixed point. 

Tractor propeller.-Propeller mounted on forward end of engine or 

propeller shaft. (It is usually forward of fuselage or wing 

nacelle.) 

Trailing edge.-Rearmost edge of airfoil or propeller blade. 

5. Types of airships.-a. Airships are divided into three general 

classes in accordance with their method of construction. These 

three classes are 

(1) Nonrigid. 

(2) Semirigid. 

{3) Rigid. 

b. The names describe means by which shape of the envelope is 

maintained. In the nonrigid, gas in the envelope is kept under sufficient pressure to keep the hull shape by this means alone. In the 

semirigid a central keel is provided which carries the loading and 

is itself swung by suspensions from the top of the envelope. Due 

to its rigidity, the keel assists the internal pressure in maintaining 

f;hape of the envelope. In rigid construction a metal structure is 

provided to maintain shape of the hull. Usually the gas is at atmospheric pressure, although in some cases a slight superpressure is 

maintained. 

c. All types .have control and power plant cars and control surfaces. 

11 
TM 1-320 

0-6 AIR CORPS 

(1) In small nonrigids cars are usually open and contain power 

plants as well as altitude and direction controls. Such cars a.re 

usually suspended by cables attached to the envelope. In semirigid 

and rigid construction cars are in contact with the keel which carries 

their load. Power plant cars are sepn.rate from the control car. 

FIGUHE 1.-U. !:i. Army uuurigi<.l 1'(;-7. 

. 

(2) Control surfaces on nearly all airships consist of fixed ve~tical and horizontal surfaces, ~tttached to which are elevators and 

rudder. On nonrigids and some semirigids these surfaces are attached to the envelope by rigging. On Italian type semirigids and 

on all rigids control surfaces are supported by metal framework. 

d. Figures 1, 2, 3, and 4 depict types of airships, showing general 

streamlined shape of the hull and arrangement of cars and surfaces. 

6. Aerodynamic forces.-Aerodynamic forces may be divided 

into two classes, those parallel and those normal to the path. 

a. The former, or drag forces, retard the flight of the airship and 

must be overcome by the power plants acting through the thrust of 

the propellers. Power requirements in their turn affect fuel consumption and limit perfo~·mance of the airship. Hence a thorough 

knowledge of resistance and power requirements ·is essential to 

intelligent operation of airships. 

12 
AIRSHI P AERODYN AM ICS 

• 

• 

13 

TM 1-320 

6 

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• t:l 

0 

0 

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oS 

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t:l 

0 

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CIS 

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"' en 

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'"' 0 

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Cl 

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f/2 

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TM 1-320 

6-7 AIR CORPS 

b. The second class of aerodynamic :forces, sometimes called transverse :forces, is the result of use of control surfaces or of gusts encountered by the airship. Calculation of the effects of these :forces 

is, as mentioned before, often a matter of more interest to the designer 

than to the operator, but an understanding of the principles involved 

' 

• 

FIGUIII:l 3.- U. S. Army ;semirigid RS- 1. 

' 

is necessary because it is through these forces that control and 

stability are effected. 

SECTION II 

RESISTANCE 

Paragraph 

Fluid resistance-------------------------------------------------------- 7 

Shape coefficients------------------------------------------------------- 8 

Coefficient of skin friction_____________________________________________ 9 

Resistance of streamlined bodY------------------------------------------- 10 

Prismatic coefficient ---------------------------------------------------- 11 

Index of form etfi.ciency ------------------ ------------------------------ 12 

Illustrative resistance problem------------------------------------------- 13 

Scale effect------------------------------------------------------------ 14 

Resi!;)tance of completely rigged n i rshiP----------- --------------------- 15 

Doceleration tesL------------------------------------------------------ 16 

7. Fluid resistance.-a. Before attempting the study of resistance 

the student should be familiar wjth the composition and nature of 

14 
AIRSHIP AERODYNAMICS 

TM 1-320 

7 

the atmosphere, with density and specific gravity calculations, and 

with the action of gravitational forces. These matters are discussed 

in TM 1-325. 

b. Whenever a solid object moves through a fluid it encounters a 

resistance to its motion. This resistance may be considered from two 

points of view. 

(1) Momentum theory.-(a) By Newton's first law, a body at rest 

or in motion will remain at rest or continue to travel at constant 

• 

• 

' 

FIGURE 4.-U. S. Nnvy rigid Los .d.t~geles. 

velocity unless some force is exerted to change its condition. To 

enable the solid to maintain its motion relative to the fluid, the 

molecules of the fluid must be deflected to make room for t he passage 

of the solid. So to deflect the fluid or air a force must be applied. 

I n the case of the airship this f orce is that furnished by the propeller 

thrust. 

(b) It can be proved mathematically that if air were incompr essible 

and nonviscous, that is, incapable of offering r esistance to shear between the particles, the thrust of air particles opposing the motion 

of the solid would exactly equal the thrust of the air assisting the 

motion. H ence there would be no resistance to the motion. However, in th& atmosphere this ideal condition does not exist and the 

resistance is proportional to the total kinetic energy of the deflected 

particles of air. 

15 
TM 1-320 

7-8 AIR CORPS 

(2) Pressure-differenoe theory.-Figure 5 shows the motion of the 

particles of an air stream passing a flat plate held at right angles 

to the flow. The air is deflected from its course some distance in front 

of the plate and has a complex eddying motion in rear o.f it. In front 

of the plate the air is under an increased pressure, while behind the 

plate there is an area of reduced pressure. The drag can be considered as due to the difference between the pressures in front of and 

behind the plate. 

8. Shape coefficients.-a. The two systems in common use for ex-. pressing air resistance are the engineering and the absolute. 

(1) Under the engineering system the formula isRv=K a:AV2 . 

where Rv=air resistance due to pressure difference. 

A = cross sectional area normal to the air stream in 

square feet. 

V =velocity of motion in miles per hour. 

K IJ)=an empirically determined constant depending on the 

shape of the solid and the mass density of the air. 

In lighter than air practice the letter "K," minus subscript, is used to 

denote K IJ) when the mass density of the air is standard (0.00237 

pound per cubic foot, which is the ·value when the pressure is 29.92 

inches and the temperature is 60° F.). 

(2} The absolute system, adopted by the National Advisory Committee for Aeronautics, uses the formula: 

. u2 

Ro= K DAP2 

where p= mass density of the air. 

v= velocity of motion in feet per second. 

Kv=an empirical shape coefficient. 

2 

';' .is the dynamic pressure per unit of area or the velocity head of 

the air stream. This formula has more definite physical interpretation than the engineering formula from both the momentum and 

pressure-difference theories. Before studying aerodynamic data, the 

system which is being used should always be determined. 

b. Some of the first practical tests made to determine the effect of 

shape upon the resistance offered the motion of solids through 

the air were .conducted by Eiffel. Since then studies have been 

conducted by various investigators until at present the store of information on this subject is quite elaborate. Figures 5 to 15 give 

the action of the air on various shapes together with the values of K. 

16 
AIRSHIP AERODYNAMICS 

TM 1-320 

8 

. (1) Flat plate.-Figure 5, as described in paragraph 7b (2), shows 

a flat plate held normal to the air stream. Eiffel demonstrated that 

the circular disk gives about 5 percent less resistance than the square 

flat plate. Rectangles have slightly higher values of K than the 

square plate · of the same area, the airflow around the edges of the 

X= .00328 

___ .... 

. -

_ _ .... ·-: ... 

-··-' -

FIOURI!l 5.-Air stream fiowing by a fiat plate. 

---. -

- .. . ... ·-~

-~ .. -- ...... ~ .. -· . 

cc 

X= .00328 27 

·-

-· .. 

F IGURFJ 6.-Air stream tlow!ng by an inclined plate. 

rectangle being somewhat more restricted than that in the case of 

the square. 

(2) Flat plate, inclined.- Figure 6 illustrates the case of the flat 

plate inclined to the air stream. Eiffel's constants for different 

angles of incidence are as follows: 

Angle of incidence 

J• 

50 

10° 

15° . 

20° 

K 

0.00010 

0.00059 

L).00124 

0.00193 

0.00265 

(3) Oonoave h.emisph.ere.- Expe1'iments have shown that the resistance of a hemisphere with the concave side facing the-direction 

of motion is greater than that of a flat disk of the same exposed 

17 

285746"--41 8 
TM 1-320 

8 AIR CORPS 

cross section. K for a concave hemisphere is about 0.00389 (see 

fig. 7). 

( 4) Oonvero hemisphere.-For a hemisphere with the convex side 

facing the direction of motion or pointing against the wind the 

X= . 00389 

: 

-

Jl'louam 7 .-Air stream tlowing by a concave hemisphere. 

x = .oooea 

FIGURE ~.-Air stream flowing by a convex hemisphere. 

X= .0008 

: 

: 

FIGURE 9.-Air stream flowing by a sphere. 

resistance is much less than for the concave hemisphere shown in 

figure 7. The resistance of the convex hemisphere is much less than 

t.hat of a flat plat of the same cross section or exposed area. Th~ 

coefficient of resistance is found to be about 0.00082 (see fig. 8}. 

18 
AIRSHIP AERODYNAMICS 

TM 1-320 

8 

(5) Sphe-1-e.-The air flow around a sphere (which more closely approaches a streamline form) . is shown diagrammatically in figure 9. 

It will be observed that the spreading out of the lines of flow before 

reaching the sphere is less marked than for the flat plate in figure 5. 

The coefficient of resistance of a sphere va.ries somewhat with the speed, 

R.= 1.00 fat- flat -pla.te 

R.= .83 where L:o. = t 

R= .77 where L: 0=3:1 

FIGOREl 10.-Cyllnders. 

but for ordinary velocities its value is about 0.008. The sphere is the 

simplest geometrical form and is the most efficient shape for maximum 

volume per unit weight but has a greater resistance than the more 

perfect streamline form (see fig. 9). 

( 6) Oylinder ( longitudiMl aaJis horizontal).- The resistance of such 

cylinders decreases wl.th length until the fineness ratio is approxiX= ·?0123 fort= .5 

,. 

,. , ... 

li'IGOR!l 11.-Alr stream flowing by a cylinder (arts normal to air t'low). 

mately 4 to 1, after which it increases. The increase is due to the effect 

of slcin friction which will be discussed later. The relative resistance 

of cylinders as compared to that of a flat plate of the same cross section is as shown in figure 10. Where the fineness ratio is 4 to 1, 

K = 0.00205. 

19 
TM 1-320 

8 AIR CORPS 

(7) OyUnderr (vertical).-When a cylinder of given cross-sectional 

area is placed with its axis of revolution at right angles to the direction 

of motion the resistance depends upon the fineness ratio of the cylinder. 

When the length and diameter of the cylinder are the same the coefficient of resistance is only slightly greater than for a sphere of the same 

L K = . 0006 for D = 4 

--

FIGURE 12.-Air stream flowi ng by a cylinder (hemispherical ends) . 

. 

cross-sectional area. When the length-diameter ratio is increased to 

4 to 1 the coefficient of resistance is approximately doubled, or 

K =0.0018, and if the length-diameter ratio is reduced to one-half (or 

0.5/ 1) the coefficient of resistance is increased 27 percent, or K =0.00123 

(see fig. 11). . 

(8) Cylinder with hemispherical ends.-It is possible to reduce 

greatly the resistance of a cylinder by capping the ends with hemiWIRJ:S CABLES 

X: . 0026 K: . 0013 

~ 

K =. 0015 X = • 0029 

• ~ 

FIGURE 13. 

spheres. The resistance is reduced to 20 percent of that of a cylinder 

with flat ends. The value of K for a cylinder with hemispherical ends 

·and a fineness ratio of 4 is approximately 0.0006 (see fig 12). 

(9) Wires and cables.- Wires and cables may be considered as cylinders of very long length. E xperiments show that the resistance of wire 

or stranded cable when placed normal to direction of motion is very 

nearly equal to the resistance of a flat plate of the same projected area. 

The gain by the circular form of the wire is counterbalanced by its very 

20 
AffiSHIP AERODYNAMICS 

TM 1-320 

8 

great length. The resistance of a long, narrow object perpendicular to 

direction of motion is greater than that of a more symmetrical form. 

The experimentally determined value of the coefficient of resistance is 

0.0029 for stranded cables and 0.0026 for smooth wires. K is almost inN.PL. "I 

N.P! .. 12 

. Fimnessl!t:dto 4j/!. K=.ooo4 

N.PL 11'..3 

' 

/'inmes.s ~crlto 41% K:.OOQ38 

NP.J.. ..-4 ~-r-:- ·- ·- ~ 

' "/ / 

~ / 

l'lnen~ss Raho 2/1 1<Q.ooo8:J 

FIGURE 14.-Struts. 

dependent of the diameter for all sizes of 

wire and cable. Stranded wire or cable ha~ 

a resistance about 14 percent greater than 

solid wire. 

(a) The above discussion relates only to 

wires and cables perpendicular to the wind 

direction or direction of motion. . When a 

wire or cable is inclined to the perpendicular 

its resistance is very much decreased as the 

air flows around it in more uniform streamlines or in a more gradual curved path. An 

inclination of about 30° from the vertical 

reduces the resistance 20 percent and an inclination of· 45° reduces the resistance 50 

percent. 

(b) When two wires or cables are close 

together and placed one just behind. the other 

there is a reduction in resistance due to 

shielding of the second wire by the first. If 

they are placed very close together their 

combined resistance is considerably less than 

the resistance of one wire .alone, as the two 

wires have the effect of an increased fineness 

ratio. If they are spaced more than 3ljz diameters their combined resistance becomes 

greater than a single wire but is still less 

than the resistance of the two wires tested 

separately. This shows that if two wires or 

cables are close together (within 5 diameters 

of each other) it is very advisable to put a filler block in between 

them, thus preventing the air from flowing in between them and . 

giving them the advantage of a single member of high fineness-ratio. 

If the two wires are streamlined in this way their combined resistance 

can be kept down to about 50 percent of the resistance of a single 

wire until their fineness ratio becomes greater than seven. The high 

value of the resistance caused by wires and cables immediately suggests reduction of wires and cables to the minimum by means of 

refinements in design and arrangement. - . 

21 
TM 1-320 

8 AIR CORPS 

. 

(10) Struts of strecmWirw form.-It is fou~d in practice that the 

best fineness ratio for struts is 4 to 1. Inclining the strut to the vertical 

does not have the effect of reducing the resistance for streamline forms, 

but for blunter shapes (shorter than the true streamline) inclination 

reduces the resistance considerably. A group of strut sections are 

shown in figure 14 and the value of K for each shape is shown. It can 

be seen that the effect of yawing is to increase greatly the resistanoo by 

placing the strut sidewise or at a different angle to the air stream. 

(11) AirshVp cars.-All cars are built to take advantage of streamline form. This is especially true of the inclosed models for which an 

average value of K is 0.001. However, there is a wide variance in the 

shape of airship cars and a corresponding variance in the value of K. 

K=.OOl (average value) 

FIGURE 15.-Air stream fiowing by airship~ 

For each different shape a new value of K must be determined by wind 

tunnel test. 

c. The following problem illustrates use of the resistance formula: 

( 1) Problem.-(a) What is resistance of a fiat. plate 1 foot square 

placed at right angles to direction of motion when moving at a velocity 

of 30 miles per hour in air of standard density? 

(b) What is resistance at 60 miles per hour~ 

(2) Sol!ution. 

(a) Rv= KAV2=0.00328X 1 X900=2.95 pounds. 

(b) Rv = KA V 2 = 0.00328 X 1 X 3600= 11.81 pounds. 

This problem illustrates rapidity with which resistance increases 

with increasing velocity. 

d. Based on resistance of a fiat disk, the following shapes have the 

relative resistance shown below : 

Percent 

Square plate--------------------- -------- ----- ------------ 104.5 

Cylinder, horizontal--- ---------------------------------- 65. 5 

Sphere--------------------------------------------------- 25.4 

Cylinder, capped ends------------- ---- - - ------------------ 21.0 

Airship model --------- - - ·- -·- ---------------------- 3. 0 

22 
AIRSHIP AERODYNAMICS 

TM 1-320 

9-10 

9. Coeftioient of skin friction.-a. In the case of a flat plate at 

right angles to the air stream the resistance is almost entirely due to 

the pressure difference in front of and behind the _plate. This is not 

however the case with most solids. In general, resistance may be 

divided into two parts: 

( 1) Pressure difference. 

( 2) Skin friction. 

b. When a solid passes through the air it carries along with it a very 

thin layer of air, the exterior surface of which forms a plane of air 

cleavage. The resistance of the air particles to shear on this plane is 

called skin friction. 

c. The value of the skin friction on an airship hull, as determined 

empirically by Zahm and others, is given by the formula: 

R ,=0.0035pS0 •

98 vue 

where S is the total surface area. A somewhat more convenient formula is--

R r= 0.00309pS vu5 

10. Resistance of streamlined body.-a. As mentioned before, 

the total resistance is composed of resistanc:A-e-

(1) Caused by pressure difference. 

(2) Due to skin friction. 

The pressure-difference resistance is least for a very long and slender 

form. In fact, the greater the fineness ratio, the less will be the pressure-difference resistance. An increase in fineness ratio, however, leads 

to an increase in surface area and so to an increase in skin friction. It 

is necessary therefore to compromise on a moderate fineness ratio, as 

a very long and slender form would have so high a skin friction as to 

more than counterbalance the gain by reduction of the pressuredifference resistance. A fl_neness ratio of 4 to 1 is very good for a small 

nonrigid, but for large rigids it has been found advisable to increase 

this ratio to 6 or 7 to 1. Recently an airship had been designed whose 

hull has a much smaller fineness ratio than the conventional designs. 

This airship has a capacity of 200,000 cubic feet and a fineness ratio of 

2.82, noticeably shorter than any ships recently constructed. A model 

of this ship was tested in the wind tunnel of the Washington Navy 

Yard and was found to have the lowest resistance coefficient -of any 

model ever tested there. 

b. Since the volume varies as the cube of a linear dimension, while 

the cross-sectional area and surface area both vary only as the square, 

23 
TM 1-3'20 

10-11 AIR CORPS 

the resistance is proportional to the two-thirds power of the volume. 

TMs leads to a more convenient expression for the resistance of airship 

hulls as follows : 

R = 0 DP (volume) •;s v~.se 

where OD is called the P randtl shape coefficient after the eminent authority, Professor Prandtl. Values of 0 D for various speeds are given 

in table I. 

c. The offsets for different types of airships are given in table II. 

A study of the shapes given therein in connection with the Prandtl 

coefficients will bring out the relative efficiency of the different streamlines. 

d. Certain general rules of design developed by experience and test 

may be summarized as follows: 

( 1) The best form is one of continuous curvature with radius of curvature constantly increasing toward rear portion. 

(2) The shape of extreme rear portion of the hull does not seriously 

affect the resistance. 

( 3) The introduction of a cylindrical midsection causes an additional resistance equal to the skin friction on the increased surface 

area of the hull. 

(4) The major diameter should lie between 33 and 40 percent of total 

length from the bow. 

11. Prismatic coefficient.- The ratio of the volume of any hull 

form to that of the circumscribing cylinder is called the prismatic 

coefficient, Qv. 

Volume 

Qv= Maximum cross-sectional area X length 

VOl= Q.t.A.L 

The prismatic coefficients for different shapes are given in table I . . 

24 
~ 

00 

---. --·- -1 --

"' -t 

.... 

C) 

Name of model I x.en th. Dlame· , I ter. /) 

0 

I 

.... 

.... 

l - ·- -. -- I 

} 

N a.vy B (Goodrich)---·_. 3. 5 

Navy 0 ---------------2. 9 

Navy E--------------- 4. 1 

E. P- _ .. __ ____ --- __ - _- 3. 0 

I. E _______ ----- -- - ---- 2. 9 

Goodyear 4 2 _______ __ 3. 1 

Goodyear- L ______ __ __ 3. 4 

Goodyear- 2 ___ ___ - - ---- 3. 8 

Goodyear- 3 ____ .. ___ _ . _ 3. 6 

Goodyear- 4 ____ -·- ··-- __ 3. 1 ~ Astra-Torres __ . . _____ .. _ 3. 1 

Ol Parseval P. L ________ __ 3. 9 

Parseval P. !!_ ____ ___ _ _ 3. 2 

Parseval P. IlL _____ __ _ 3. 2 

Parseval S. S. T ___ ___ __ 5. 6 

Pony Blimp AA ______ __ 1. 9 

UB-FC _________ _____ 4. 9 

UB- 2 ___________ ___ __ 4. 4 

C class cylindric midships 

1-1 diameter __ ________ __ 3. 1, 

Yz diameter ____ ------ __ 3. 2 

1 diameter _____ __ ____ __ 3. 5 

2 cliamet3r ___________ __ 4. 2 

3 diameter ____________ _ 4. 8 

4 diameter_ ____________ 5. 5 

Feet 

0. 6967 

. 6417 

• 6417 

. 6417 

. 6417 

• 6870 

• 6660 

• 6350 

• 6150 

. 6870 

. 6914 

. 6417 

• 6417 

• 6417 

1. 1330 

• 58"V " ~ 1. 0591 

ll. 1638 

- 6417 . 6417 

. 6417 . 6417 

. 6417 . 6417 

TABLE I.- Airship model characteristics and data 

Area Prandtl sha8~ coefficient, Fine- Dis- Prismaxi· ness tance Dis- matic 

mum ratio, maxi- tance coeffi· Surface. Volume, s cross- Vol. FR mum CG cient, 

sectional L diameter from Q=- VtJI. 

area 20 40 60 15 from nose 

A m.p.h. m. p.h. m.p.h. nose 

AXL 

-· -- --- --·····- - - Sq.ft. Sq.ft. Ou.ft. P.d. L P.ct. L 

5. 800 0. 381 0. 8304 0. 0168 o. 0 154 0.0148 5. 060 37. 80 ------ 0. 6176 

4. 750 . 323 . 6259 • 0159 . 0144 . 0136 4. 620 30. 00 46.37 . 6562 

5. 007 . 323 6690 . 0168 . 0146 . 0142 4. 870 36. 25 48. 64 . 6621 

4. 597 . 323 . 5890 . 0166 . 0147 . 0138 4. 820 41. 59 43. 92 . 6891 

4. 597 . 323 • 5955 . 0175 . 0155 . 0144 4. 650 38. 18 44. 25 . 6169 

5. 470 . 371 . 7840 • 0162 . 0144 . 0134 4. 640 28. 76 - . .. --- . 6624 

5. 600 . 348 . 7360 ------ ------ . 0141 5. 130 34. 15 --·· - - - . 6184 

6. 000 . 317 . 7520 ------ ------ . 0141 6. 030 36. 14 ------ . 6194 

5. 900 . 297 . 7760 ------ ------ . 0140 5. 970 36. 36 --~·--- . 7119 

5. 470 . 371 . 7840 ------ ------ . 01 53 4. 640 28. 76 ------ . 6624 

5. 190 . 309 . 6583 . 0190 . 0159 . 0147 4. 580 33. 80 49. 08 . 6590 

5. 465 . 323 . 7240 . 0185 . 0174 . 0165 6. 140 38. 75 43. 19 . 5679 . 

4. 528 . 323 . 5891 . 0181 . 0170 . 0164 4. 990 38. 90 44. 46 . 5677 

4. 750 . S23 . 6331 . 0179 . 0169 . 0161 4. 699 47. 33 45. 85 . 6095 

14.720 1. 008 3. 4550 . 0174 . 0173 . 0170 4. 960 45. 00 45. 88 . 6090 

2. 760 . 267 . 3196 . 0205 . 0254 . 0277 3. 410 42. 50 46. 00 . 6003 

12. 9584 . 8810 2. 8603 . 0321 . 0223 . 0219 4. 663 - -· ~ -- -- ·-·-... . 65U 6 

12. 224C 1. 063::: 2. 9201 . 0205 • 0 189 . 0192 3. 823 - - ....... ----.. ·-- . 61145 

. 

5. 073 . Z~3 . 6777 . 0154 . 0140 . 013Z 4. 85::: -··-·· .. ... ··-·-- -- 6749 

5. 398 . 323 . 7297 . 0153 . 0141 . 0135 5. 100 • . 6909 ------ --·---- 6. 043 . 323 . 8330 . 0164 . 0146 . 0136 5. 570 ------ ------ . 7184 

7. 337 . 323 1. 0404 . 0175 . 0150 . 0136 6. 600 ------ ------ . 76 11 

8. 627 . 323 1. 2471 . 0173 . 0156 . 0148 7. 590 ------ ------ . 7925 

9. 922 . 323 1. 4548 . 0175 . 01.'>7 . 0146 8. 590 ------ ------ . 8167 

5 diameter _________ ____ 6. 1 . 641711.218 • 323 1. 6625 • 0164 • 0154 • 0148 9. 602 ------ ------ • 8358 

Index ofform efficiency; Q Hr=-· CD . ----- ·- . 

20 40 60 

m.p.h. m. p. h. m. p. h, 

36. 76 40. 10 41. 7~ 

41 27 45. 57 48. 25 

- - - --- ------ ------ 35. 49 40. 08 42. 70 

35. 25 39. 80 42. 84 

40. 89 45. 37 49. 43 

------ ------ ---. ... ------ ------ -----·· ------ ------ -----· ------ -- --- ~ --~-

- 34. 68 41. 45 44. 83 

30. 70 32. 64 34. 42 

31. 36 33. 39 34. 62 

34. 05 36. 06 37. 86 

35. 00 35. 23 35. 82 

29. 28 23. 63 21 67 

~~- -··---- ------ - -··--- ---· -- ·-----""' 

43. 82 48. 21 51. 13 

45. 16 49. 00 51. 18 

43. 80 49. 21 52. 82 

43. 49 50. 74 55. 96 

45. 81 50. 80 53. 55 

46. 67 52. 02 55. 94 

50. 96 54. 27 56. 47 

'! 

l:rl 

~ 

~ 

~ > 

>-<1 

~ 

Q 

~ ~-'t-4 

..... ~ 

t.:l 

0 
TABLE I.-Airship model characteristics and data-Continued 

. 

Area Prandtl shape coefficient Fin&- Dis- . Prismaxi- ness tanoo Dis- matic 

mum CD ratio, maxi- tan co coom- Lenzth· Diame- Surface, Volume, Name of model cross- FR mum CG cient, ter, D 8 sectional Vol. L diameter from Q Vol. 

area 20 10 60 ~-D · from nose -A-L 

A m. p. b. m. p. b. m. p. b. nose 

- - - . -·· ·- - - EUiptical series (British) 

Feet Feet Sq. ft. Sq. ft. Cu. ft. P.ct.L P.ct. L 

E ---------------- --- 2. 371 0. 3906 ------- 0. 120 0. 1658 0. 0132 0. 0135 ------ 6. 070 33. 19 ------ 0 5835 

E 2- --- --------------- 1. 743 . 3910 ------- . 120 . 1261 . 0138 . 0128 ------ 4. 460 33. 86 ------ . 6024 

E 3------------------- 1. 568 • 3920 ------- . 121 . 1112 . 0147 . 0120 ------ 4. 000 34. 19 ----- - . 5876 E4 _____________ ___ ___ 1. 384 • 3923 ------- . 121 . 0972 . 0167 . 0139 ------ 3. 500 35. 18 ------ . 5810 

~ E 5------------------- 1. 178 • 3929 ------- . 121 . 0826 

' . 0184 . 0147 ------ 3. 000 33. 43 ------ . 5786 

Parabolic series (British) 

p } ____________ ____ ___ 1. 594 . 3900 ------- P2 . 120 . 0970 . 0168 . 0137 ------ 4. 090 49. 39 ------ . 5094 ______________ ____ _ 1. 598 . 3903 ------- - 120 . 1000 . 0169 . 0176 ------ 4. 070 32. 06 ------ . 5265 Pa ________ __ _______ __ 1. 173 . 3867 ------- . 117 . 0729 . 0226 . 0173 ------ 3. 830 50. 35 ------ . 5293 

P4------------------- 1. 217 . 3870 ------- . 118 • 0714 . 02-15 . 0193 ------ 3. 140 35. 05 ------ . 4989 

- --···- -------------------------- -··- - ---- ---------------

.. 

Index of form efficiency 

H,- Q -

CD 

20 40 eo 

m.p.h. m. p.h. m. p. 11. 

- -

44. 20 43. 22 ------ 43. 65 47. 06 ------ 40. 00 45. 55 ------ 34. 79 41. 80 ------ 31. 45 39. 36 ------

30. 32 37. 18 ------ 31. 15 30. 00 ------ 23. 42 30. 60 ------ 23. 20 25. 85 ------ ···---------- ------ --- ----

~ ... I-' 

... J., 

~ 0 

0 

~ al 

t-:) 

0 
T ABLE Il.- Ojfsets of various streamline forms, United States models 

Navy B (Goodrich) NavyO NavyF E. P. Parseval P . I Parse val P. II Parse val P. III 

-- - - - - - - -.... - --- -

Distance Dlam- Distance Dlam- Distance Diam- Distance Diam- Distance Diam- Distance Diam- Distance D!am- from eter from eter from etor from eter from etcr from et.cr from eter nose nose nose nose noso nose nose 

--- -- - - - - ---- ·- - - -- - Pa. L. Pet. D. Pet. L. Pet. D. Pet. L. Pet. D. Pet. L. Pet. D. Pet. L. Pet. D. Pet. L. Pet. D. Pet. L. Pet. D. 

2. 36 24. 16 2. 81 32. 47 1. 23 23. 12 0. ];3 24. 88 1. 25 27. 37 1. 25 27. 27 1. 25 21. 56 

4. 73 41. 27 5. 62 55. 06 2. 45 35. 06 2. 59 34. 60 2. 50 37. 92 2. 50 37. 92 2. 50 32. 99 

7. 09 55. 14 8. 43 69. 61 3. 68 43. 90 5. 19 48. 44 5. 00 51. 95 5. 00 51. 95 5. 00 47. 79 

9. 45 65. 27 11. 24 79. 22 4. 91 50. 61 10. 37 66. 10 10. 00 71. 17 10. 00 71. 17 10. 00 66. 23 

11. 81 75. 36 16. 86 91. 17 7. 36 62. 73 15. 56 78. 12 14. 99 83. 38 15. 00 83. 36 15. 00 78. 70 

14. 18 81. 94 22. 48 97. 40 9. 81 72. 08 20. 75 86. 66 19. 98 91. 17 20. 00 91. 17 20. 00 88. 05 

18. 90 90. 31 28. 11 100. 00 12. 26 78. 57 25. 94 92. 73 24. 98 96. 10 25. 00 96. 10 25. ~8 94. 03 

23. 63 94; 98 33. 73 100. 00 14. 71 84. 93 31. 12 96. 75 29. 98 98. 96 30. 00 98. 96 30. 0 97. 40 

28. 35 98. 09 42. 16 98. 18 19. 62 93. 51 36. 31 99. 40 34. 97 100. 00 35. 00 100. 00 35. 00 99. 22 

33. 09 99. 64 50. 59 94. 29 24. 54 98. 05 41. 50 100. 00 39. 96 99. 48 40. 00 99. 48 40. 00 100. 00 

~ 37. 82 100. 00 59. 02 88. 83 29. 45 99. 61 48. 81 98. 44 44. 96 98. 18 45. 00 98. 18 45. 00 100. 00 47. 25 98. 44 fr7. 45 81. 56 34. 35 100. 00 56. 12 93. 77 49. 96 94. 81 50. 00 94. 81 50. 00 98. 06 

56. 70 93. 06 75. 89 71. 69 39. 27 99. 74 63. 43 86. 23 54. 96 89. 87 55. 00 89. 87 55. 00 95. 86 

66. 15 83. 25 84. 32 59. 48 44. 17 98. 96 70. 74 75. 32 59. 96 83. 90 60. 00 83. 90 60. 00 91. 69 

70. 88 76. 91 89. 94 48. 57 49. 07 97. 53 78. 05 60. 52 64. 95 76. 36 65. 00 76. 36 65. 00 85. 97 

75. 60 69. 38 92. 75 41. 56 53. 98 95. 15 85. 36 44. 16 69. 95 67. 53 70. 00 67. 53 70. 00 78. 96 

80. 33 61. 00 95. 56 31. 95 58. 78 62. 34 92. 68 23. 90 74. 94 57. 66 75. 00 57. 66 75. 00 70. 91 

85. 05 51. 44 98. 37 18. 96 63. 69 88. 31 100. 00 - 0 79. 94 47. 01 80. 00 47. 01 80. 00 59. 74 

89. 78 39. 35 100. 00 .0 68. 69 83. 25 --- ---- ---- -- 84. 93 35. 84 85. 00 35. 84 85. 00 47. 27 

92. 14 31. 94 ------- ------ 73. 60 77. 27 ------- ------ 89. 92 24. 16 90. 00 24. 16 90. 00 23. 25 

94. 50 23. 44 ------ - ------ 78. 51 70. 26 ------- ------ 91. 92 12. 21 95. 00 12. 21 95. 00 17. 14 

96. 86 14. 00 --- ---- --- --- 83. 41 62. 38 ------- ------· 100. 00 . 0 100. 00 .0 100. 00 .0 

98. 14 8. 97 ------- ------ 88. 32 52. 47 ------- ------ -----·-- ------ ------- ------ - ----- ------ 100. 00 . 0 -- ---- ------ 93. 22 40. 52 ------- ------------- ------ ------ - - - ---- ------ --- ---

------ ------ ------- ------ 94. 45 36. 75 ------------- ------- ------ ------- ------ ------ ---- -- ------ ------ ------- - - - - - - 95. 68 33. 12 - - - - -- - ------ ------- - ----- ------- ------ ------ ------ ------ ------ ------- ------ 96. 91 28. 31 ------- ------ -- ----- ------ - - - ---- ------ ------ ---- -- ------ ------ ------- ------ 98. 13 22. 47 ------- ------ ------- ------ ------- ------ ------ - - - ---

------------ ------- ------ 99. 36 12. 26 ------- ------ ---- --- ------ ------- ------ ------ ------ 100. 00 .0 . ------ ------ ------- ------ ------ - ------ ------- ------ ------- ----- .. ------ ------

a. s. T. 

Distance Dlam- from eter nose 

- Pet. L. Pet. D. 

1. 24 21. 41 

2. 51 32. 98 

4. 99 47. 83 

9. 99 66. 07 

14. 98 78. 89 

19. 97 88. 07 

24. 97 94. 04 

29. 96 97. 32 

34. 97 99. 11 

39. 98 99. 80 

44. 99 100. 00 

50. 00 98. 75 

54. 99 95. 87 

59. 97 91. 75 

64. 96 86. 24 

69. 94 79. 14 

74. 93 70. 34 

79. 91 59. 76 

84. 89 47. 39 

89. 87 32. 99 

94. 86 10. 83 

100. 00 . 0 

------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ -- ----

Pony blimp A.A. 

Distance Dlam· from eter nose 

Pet. L. Pet. D. 

2. 09 20. 58 

4. 19 33. 49 

8. 38 54. 65 

12. 57 67. 71 

16. 75 77. 50 

20. 94 84. 60 

25. 13 89. 99 

29. 32 94. 18 

33. 51 97. 23 

37. 70 99. 01 

41. 88 100. 00 

46. 07 99. 43 

50. 26 98. 08 

54. 45 95. 88 

58. 64 93. 47 

62. 83 89. 64 

67. 02 84. 81 

71. 20 78. 42 

75. 40 71. 04 

79. 58 63. 52 

83. 76 54. 65 

87. 96 45. 78 

92. 14 35. 49 

96. 34 22. 21 

100. 00 . 0 

- - ---- ------ ------ ------ ------ ------ ------ ------ - ----- ------

~ H 

.!"d 

i 

t:j 

~ 

z 

> 

~ 

~ {/l 

~ ... I-£ 

... ~ 

~ 
TM 1-320 

12-14 AIR CORPS 

12. Index of form e:fficiency.- In general, in design it is desired 

to get the greatest volume from the. least surface area as this reduc~ 

weight and diffusion. Fortunately, good streamlined shapes usually 

have high prismatic coefficients, but of course some shapes are r.nore 

efficient in this regard than others. In studying relative efficiency 

of shapes, both the resistance coefficients and the prismatic coefficients 

must be considered. The ratio of the latter to the former is called 

the index of form efficiency, H t· · 

H,=& 

13. Dlustrative resistance problem.-a. Proolem .. -Given an 

airship whose hull has a length of 200 feet and a major diameter of 

43.5 feet 'vith the hull offsets those of the C type airship envelope. 

( 1) w·hat is total volume of envelope~ 

(2) "What is hull resistance at 60 miles per hour in standard atmosphere~ 

b. Solution. 

,(1) Vol=Q.vAL 

From Table I, Qv is 0.6562. 

7rd2 3.1416 A=4= 4 (43.5)2= 1,485 square feet. 

Hence Vol=0.6562X1,485X200=195,000 cubie feet. 

(2) R=0Dp(vol)2/3vl.86 

22 60 MP H=60X15=88 feet per second. 

GD from T able 1=0.0136 at 60 M PH 

R=0.0136 X0.00237X (195,000)213X881·86 

R=455 pounds. 

14. Scale effect.-a. One great reason why so much difficulty is 

encountered in determining prior to construction the resistance o£ the 

completed hull lies in the fact that the resistance of the model cannot 

be multiplied by the ratio of the linear dimensions of the model and 

the completed hull to determine the resistance of the latter. The 

discrepancy between the calculated resistance and the actual resistance 

of the full-sized airship is attributed to scale effect. Often errors 

in calculation due to :faulty data or bad theories are so explained away 

by those responsible :for the mistakes. There are several reasons however, why, even with proper data and theory discrepancies will·exist 

between calculated and actual resistance. 

28 
AIRSHIP AERODYNAMICS 

TM 1-320 

14-15 

b. The theory of dimensions shows that the coefficients of resistance. 

1'L 

vary directly as -;-· where 

v=velocity in feet per second. 

L=some convenient linear dimension of the body such as the 

diameter in the case of a cylinder. 

v= kinematic viscosity coefficient of the fluid. 

a. v, the kinematic viscosity coefficient, is defined as the ratio between the absolute viscosity coefficient and the atmospheric mass 

density. Hence- -

v=~' where v 1s the absolute viscosity coefficient of the air and is a 

constant. 

vL 

d. -;' called the Reynolds number after Professor Reynolds, 

depends on three variable quantities, p, v, and L : To predict fullscale performance from the model tests, allowance must be made for 

the fact that the L in the full-sized airship is very different from the 

L in the model, and consequently the co-efficient of resistance will be 

different. 

e. To overcome the effect of this difference a wind tunnel has been 

built at Langley Field in which p may be sufficiently increased to 

make the product pL for the model equal that of the full-sized small 

nonrigid airship, thus eliminating scale effect. 

15. Resistance of completely rigged airship.-a. There are· 

very little data available showing the relative resistance of the various 

parts combining to produce the total r esistance of a completely rigged 

airship due to the difficulty in obtaining dynamic similarity between 

the model tested and the full-scale airship. 

b. Total resistance of airships may be subdivided approximately as 

follows for-

(1) Large nonrigids with closed cars: Percent 

(a) ~nvelope_____ ____ ____ __ ___ ___ ____ ______ ___ _ 45 

(b) Surfaces--------------------------------------- 20 

(c) Rigging and suspension cables__ __ ________ _______ 15 

(d) Cars__________________ ___ ___ _______________ ____ 15 

(e) Accessories ------------------------------------- 5 

(2) Small nonrigids with open cars : 

(a) ~nvelope ____ --------_ ----·· _______ -·------- _____ . 35 

(b) Surfaces--------------------------------------· 25 

(c) Rigging and cables __ __ __________ _________ ____ ___ 20 

(d) Cars------------------------------------------ _ 15 

(e) Accessories------------ ... _ ------------------- 5 

29 
TM 1-320 

16-16 Am CORPS 

(3) Semirigids: Percent 

(a) ~ve e- ------------ ------------- ------ --- -- ~ 53 (b) Surfaces _______ _____ ____________________ ___ ____ 20 

(c) Jtiggjng- -- -- -----~-------- ---- -- ---- -------- -- 7 

(d) Cars __________ _____ -----------------__ --------- 13 

(e) Accessories------------------------------------- 7 

( 4) Large rig ids : 

(a) IIull _________________________ __ ___ _____________ 60 

(b) Surfaces_______________ _____ ________ _____ ____ __ 15 

(c) Cars and suspensions---------------------------- 2q 

(d) Miscellaneous rigging and accessories____________ 5 

16. Deceleration test.-a. Tests are 1nade frequently on fullsized airships to determine actual risistance of the airship at various 

speeds. In these tests the airship is brought to a certain velocity 

and then the motors are idled, the velocity being recorded against 

time as the airship decelerates. 

b. The general theory is that the resistance, or force causing deceleration, is given by the equation : 

R= Mv a, where 

ex.= (deceleration in f eet per second) z. 

Mv= the virtual mass of Lhe ship. 

The virtual mass of an airship is the mass of airship and contents 

plus the mass of air which is carried along with it. This latter is 

computed by the Munk formula : 

AMo=P1, where r is the radius of largest cross section. 

c. Observing velocity at end of each second gives the rate of 

change of velocity, or deceleration, for each second and by interpolation for each air speed. Actually formulas are employed which in- . 

volve calculus and are beyond the scope of this manual. 

d. These deceleration .tests are quite valuable as a check against 

the resistance formulas developed in this section. They are however 

often complicated by poor instruments or faulty observation, rendering it difficult to place a proper value on results so obtained. For 

the present more confidence is to be placed on the resistance formulas 

and the power requirement formulas which will be developed in the 

next section. 

30 
AIRSHIP AERODYNAMICS 

SECI'ION III 

POWER REQUIREMENTS 

TM 1-320 

17 

Paragraph 

Power required to overcome airship resistance____________________________ 17 

Results of various speed trials-------------------------'----------------- 18 

Burgess' formula for horsepower---·------------------------------------- 19 

Speed devel~ped by given horsepower____________________________________ 20 

Summary----------------------------------- ______________ --·------------ 2l 

17. Power required to overcome airship resistance.-a. To 

maintain uniform velocity in flight, resistance of the airship must be 

overcome by thrust of the propellers. The work done by the propellers equals the product of the resistance times the distance through 

which the airship moves. · 

b. The unit of work in the English system is the foot-pound, or the 

quantity of work performed by 1-pound force acting through a distance of 1 foot. Hence work done in propelling the airship in footpounds equals resistance in pounds times air distance traveled by 

the airship. 

a. Power is defined as the rate of doing work, 1 horsepower equaling 

550 foot-pounds per second. Therefore the power utilized to overcome hull resistance must equal resistance multiplied by velocity in 

feet per second divided by 550. 

d. The resistance is given by the equation (see sec. II): 

R= CD p (vol) 213ut.86 

Then the horsepower required to overcome this resistance is given by 

the formula: 

Cn p (vol) 213if·86 

H. P.= 550 

e. Problem and solution-(1) Problem.-What horsepower will be 

required to drive an airship of 195,000-cubic-foot capacity at 60 miles 

per hour ( 88 feet per second) in atmosphere of standard density~ 

The envelope shape coefficient is 0,0136. The propeller efficiency, E, 

is 60 percent. The envelope resistance, F, is 40 percent of the total 

resistance of the airship. 

(2) Solution.-The horsepower necessary to overcome hull resistance is given byCn p (vol) 213if·86 

H. P = 550 

_ (0.0136 X 0.00237 X 3376.4 X 359000) 

550 

=71.1 horsepower. 

31 
T.M 1-320 

17-18 Am CORPS 

Since hull resistance is but 40 percent of total, the horsepower to overcome total resistance 

Since propeller efficiency is 60 _percentTotal horsepower required= (71.1)(o.40~o. 60) =296 horsepower. 

f. As illustrated in the problem in d above, the following is a convenient formula for the horsepower required when the percentage of 

resistance due to the hull and the propeller efficiency are known. 

g. A commoner method of determining the horsepower requirements 

is to determine a shape coefficient by wind tunnel test of the completely 

rigged model. In this case the body in question is not as perfect 

a streamlined shape as the hull itself so the resistance varies more 

nearly as the square of the velocity. Then the horsepower required 

becomess--

0 D p(vol) 213v

8 

H. P.= 550E 

where 0' D is the shape coefficient of the model. 

( 1) Problem.-What horsepower wil~ be required to drive an airship of 195,000-cubic-foot capacity at 60 miles per hour (88 feet per 

second) when the atmospheric density is standard, the coefficient of 

resistance 0' D of the completely rigged ship is 0.0165, and the propeller 

installation efficiency is 60 percend 

(2) Sol1JJtion. 

H P = 0' D p(vol) 213

v

8 

. . 550 E 

0.0165 X0.00237X 195000213 888 

~----~~5s=o~x~o~.=6o~-----

= 275 horsepower, nppro:-dmately. 

18. Results of various speed trials.-a. The following data 

were obtained by progressive speed trials made on the United States 

Navy C class nonrigid airship of 180,000-cubic-foot capacity: 

22 
• 

AIRSHIP AERODYNAMICS 

R- pounds 

V in 

foot- R. P M. B. H. P . E ' 

seconds • Total Hull 

66. 6 1, 100 109 60 540 334 

73. 3 1,200 143 60 643 394 

80. 1 1, 300 183 60 754 457 

87. 7 1,400 231 60 875 517 

Appendages 

206 

249 

297 

358 

TM 1-320 

18-19 

C'D 

0.020 

. 019 

. 019 

. 018 

The value 0' D is the corrected coefficient of resistance, but its accuracy is somewhat uncertain, also the proportions o£ hull resistance 

appear high. The value o£ 0' D obtained from the wind tunnel test 

was ·o.027. The proportional value of the appendages or parasiw 

resistance was computed from the wind tunnel data. 

b. The follow·ing data were obtained from deceleration tests of 

German rigid airships: 

Num- Maxi- Prober of mum porName Cubic feet D L B. H. P. tional C' D en- veloc- effigmes ity • ctency 

Foot- . Feet Feet seconds 

J-'Z 10 706,000 45. 9 460 3 62. 4 450 67 0. 107 

L 33 2,140,000 78. 3 645 6 92. 5 1, 440 49 . 039 

L 36 2,140,000 78. 3 645 6 92. 5 1, 440 62 . 045 

L 43 2,140,000 78. 3 645 5 88. 9 1, 200 56 . 047 

L 44 2,140, 000 78. 3 645 5 94. 0 1, 200 56 . 031 

L 46 2, 140,000 78. 3 645 5 95. 5 1, 200 58 . 031 

L 57 2, 640,000 78. 3 745 5 94. 8 1, 200 69 . 034 

L59 2, 640,000 78. 3 745 5 94. 6 1,200 66 . 038 

L 70 2,400,000 78. 3 694 7 113. 5 2,000 65 . 031 

19. Burgess formula for horsepower.-a. A very h andy formula for determining the horsepower required to drive an airship 

of any given volume and speed is furnished by the National Advisory 

Committee for Ae1·onautics Report No. 194, as follows: 

v3p_(vol)2

'

3 

H. P.= Op 

~8 
TM 1-320 

19-20 AIR CORPS 

where Op is a constant which can be taken from the compilation 

below: 

NO"nrigid airships . 

50,000 to 200,000 cubic feet--------------- ------------- Op=20,000 

200,000 to 300,000 cubic feet_ ________ .. . -·------------ Op=21,000 

300,000 to 400,0J:> cuui<: feeL--------·-·----------------- Op= 22,000 

R igid airships 

1,000,000 to 2,000,000 cubic feeL _______________________ Op=30,000 

2,000,000 to 3,000,000 cubic feeL- ---------------------- Cp=32,000 

3,000,000 to 4,000,000 cubic feeL _______________________ Cp=33,000 

4,000,000 to 6,000,()()() cubic f eet_ _______________________ Cp= 34,000 

6,000,000 to 10,000,000 cubic f eeL____________ -------- Cp=35,000 

b. Solving the problem given in paragraph 17g (1) by the Burgess 

formula gives-

• 

P ( vol )213 va 

H. P.= Cp 

- (0.00237) (195,000) 11'

3 (88)8 

20,000 

= 273 horsepower. 

20. Speed developed by g iven horsepower.-a. By transposing the horsepower formulas the following formulas are obtained for 

the speed developed by a given horsepower : 

2

.sn /H. P. X550XEX F (H. P.X550 XEXF\0

'

36 

v=-y CvXPX (vol)2ta = CvXP X (vol)2/3- ) from paragraph 17}. 

3 /H. P. X550X E 

= -y 0 , X P X ( vol )2'3 from paragraph 17 g. 

3fH.P. X 01)f h 9 

= V P ( vol)213 rom paragrap 1 a. 

b. Problem and. solution.-(1) Problem.-An airship of 195,000-

cubic-foot capacity has a power installation of two motors developing 

150 horsepower each, or a total of 300 horsepower. The atmospheric 

density is standard. What speed should be obtained at full powed 

(2) S olution.- Using Burgess' formula. 

3 /H. P. X 01) 

v=-y p(vol)21a 

3 I 300 X 20000 

- v o.oo237 x (195ooo)2

'

3 

=90.8 feet per second = 6L9 miles per hour. 

34 
.. 

AIRSHIP AERODYNAMICS 

c. Problem UJrU1 solution. 

TM 1-320 

2Q-21 

(1) Problem.-An airship of 195,000-cubic-foot capacity is to be 

equipped with two .engines developing a total of 300 horsepower. 

What speed can be expected using the following data~ 

(a) Standard atmospheric density. 

(b) Shape coefficient, 0 n is 0.0136. 

(e) Propeller efficiency, E, is 60 percent. 

(d) Envelope resistance is 40 percent of total resistance of completely rigged airship. 

(2) Solution.-Using Prandtl coefficient. 

( 

300X550X0.60X0.40 ) 0

·

86 

V= 0.0136X0.00237X3,376.4 

=88.4 feet per second=60.3 miles per hour. 

d. Experience has shown the lower figure, as determined by Prandtl 

coefficients, to be more generally correct than the higher figure as 

determined by the Burgess formula. . 

21. Summary.-a. From study of the formulas it appears that 

the speed of an airship is proportional to the cube root of the horsepower, or vice versa the horsepower varies directly as the cube of 

the speed. Since power plant weights vary directly as the horsepower, the weight of the power plant varies also as the cube of the 

speed. A point is readily reached therefore beyond which it is not 

economical to increase the speed due to the excessive weight"s involved. 

b. In still air the higher the speed the less economical the fuel 

consumption and the shorter the radius of action. This is not true 

when the airship is traveling against adverse winds. The study of 

just which air speed is the most economical will not be discussed in 

this manual as it properly belongs to the subject of navigation. 

8EariON IV 

STABILITY 

Paragraph 

Variation of pressur-e distribution on airship bull________________________ 22 

Specific stability and center of gravity of airshiP-------------- -------- ---- 23 

Center of buoyanCY- -------------------- - --------- --------------------- 24 

Description of major axis of airshiP- ------------ ----------------- ------ 25 

Types of stability---------------- --------- - ---------·--- ------------- 26 

Forces and moments acting on airshiP----------------------------------- 27 

Damping moment------------------------- ------ ---------------------- 28 

Longitudinal stabi I i ty ---------------- --- ----------- --------------------- 29 

Directional stabilitY----------------------- ------------ - -------------- 30 

Lateral stability---------------------- - - - ---- -------------------------- 31 

S1JmJuarr-----·-----·-------------..... . ····- ----------------... -·fl"'---·-·- ~ 

35 
TM 1-320 

22 . AIR CORPS 

. 

22! Variation of pressure distribution on airship hull.--a. 

In section II resistance of an airship was shown to be parfly caused 

by increased n<?Se pressure. Throughout the discussion the airship 

was considered to be flying on an even keel and in a straight line .. 

All forces were parallel to the direction of flight. Before entering· 

the subject of stability proper it will be necessary to show variation 

in pressure distribution on the hull when the airship is not flying as 

considered in section II, or, in other words, when transverse aero- . 

dynamic forces are present on the hull. 

b. Figure 16 shows a typical pressure distribution on an airship hull 

when the airship is in horizontal flight in a straight line and on an even 

keel. This pressure distribution will be true whenever the line join~ 

ing the tip of the nose with the tip of the tail (longitudinal axis) is 

- + 

+ 

Direefion o! mofiDfl 

FIGURE 16.-Pressure distribution on airship hull (longitudinal arls pa rat:el to direction 

· of motion). 

pa.rallel with the direction of motion. Because an airship can be con~ . 

sidered as a symmetrical solid of revolution, the pressure distribnt.ion 

has the following charactertistics: · 

( 1) Distribution depicted is uniform for any plane passed through ~ 

the longitudinal axis. 

(2) Varying reduced pressure exists from a section just in rear of 

the nose to a section just forward of the tail. 

{3) Both nose and tail have positive pressure, but that on the tail 

is too small to be of much assistance to forward motion. 

c. Figure 17 shows the distributions in pressure for an 18° angle 

of attack to the relative air. Other angles of attack have similar distributions. The distribution shown holds equally true whether the 

deviation of the axis from the direction of motion is in a horizontal 

or a vertical plane. When, for instance, the inclination is in the vertical plane, the following chara_cteristics are observed: 

(1) Positive pressure on the nose lies almost entirely in a zone beneath the axis. 

(2) Plane of transition, BO, figure 17, is oblique with regard to the . . aX;J.S. 

36 
AffiSHIP AERODYNAMICS 

TM 1-320 

22-24 

{3) Areas of reduced pressure are not symmetrical. Their maximum values occur beneath the stern and above the bow. 

23. Specific stability and center of gravity of airship.-a. 

By specific stability is meant the property of the airship itself to 

maintain the relative position of its various parts unaltered in any 

contingency. 

b. Conditions necessary for specific stability are the invariahility 

of-

(1) Shape of envelope whether airship is in motion or not. 

(2) Relative positions of envelope and cars and surfaces. 

c. Methods used to maintain envelope shape are discussed in section I. Invariability of suspension of the car from the envelope is insured by a rectangular system of suspensions braced by diagonal cables 

------- ... 

-

. FIGURE 17 .- Pressure distribution on nlrsbip hull (longitudina l axis Inclined to direction 

of motion). 

lengthwise and crosswise. These cables prevent any very appreciable 

motion of the car in regard to the envelope in case of oscillations of 

the airship in vertical longitudinal plane or in transverse plane. As 

. will be shown later specific stability is absolutely essential to static 

stability of airships. 

d. W'hen invariability of suspensions has been assured, the position 

· of the center of gravity of the airship may be determined. The center 

of gravity is the point at which may be aE:3umed to be applied the total 

resultant of the various weights which oppose the lifting power of 

the gas. The position of the center of gravity is naturally not invariable since the live load of the airship is variable. Usually for 'nonrigid airships the center of grayity, M , falls above the car and either 

slightly above or slightly below the bottom of the envelope (see 

fig. 18). 

24. Center of buoyancy.- The center of gravity of the ascensional force of the gas contained in the envelope is called the center 

of buoyancy. For an envelope which is not moving this point should 
TM 1-320 

24-26 AIR CORPS 

obviously be located on the vertical line passing through the center 

of gravity, M, and for an envelope which has the form of a symmetrical solid of rotation and which is full of gas, it should be located 

on the axis of the envelope itself. 

a. However, when one or the other of the conditions mentioned is not 

fulfilled, that is, when the envelope is not a solid of rotation (as is 

the case with the Italian semirigid) , or when it is not full . of gas, or 

when with the airship partially filled with gas the axis is deviated in 

the vertical plane from the position of rest, the center of gravity, G, 

is not located on the axis in question, since this is supposed to be a 

straight line connecting the extreme end of the prow with the extreme 

end of the stern (see fig. 18) . 

b. That dissymmetry may cause this phenomenon is quite obvious. 

Moreover, if the airship is not full, even if the envelope is symmetrical 

the point G will be located above the axis. Lastly, if in addition to 

not being full the envelope is inclined longitudinally, movement of the gas toward the 

high end will cause the point G to move in the 

same direction. 

l c. Without entering into a minute descripFiouRE 18.- Posltlons of · f h · d b 

centers of gravity and tlon 0 t e vanous arrangements resorte to y 

buoyancy in nonrigid air· different constructors in order to lessen as far 

ship. as possible movement of the gas in the gas bag, 

assume, before going any further, that for an envelope with-

(1) Horizontal axis, the point G is on the axis when the envelope is 

full, and moves along a line through M perpendicular to the axis 

as the amount of gas in the envelope decreases. 

(2) Oblique axis, the point G moves a moderate distance away from 

the above vertical, or at least it moves in such a way that the distance 

is a definite function of the angle of inclination of the envelope on 

the horizon. 

25. Description of major axis of airship.-a. The airship hull, 

as previously stated, is a solid of rotation and hence symmetrical about 

the axis of rotation, X' X in figure 19. Actually, due to the loading 

of a nonrigid, the shape of a cross section of the hull is more nearly 

elliptical with the major axis of the ellipse vertical, but the distortion 

is slight enough to be disregarded. 

b. To conform to the system of nomenclature used by the National 

Advisory Committee for Aeronautics, the system of r:otation outlined 

in figure 19 will be uniform throughout this manual. 

a. Obviously any angular deviation whatsoever of the airship will 

be found to be either pit.ch, yaw, or roll, or a combination of these 

38 
AIRSHIP AERODYNAMICS 

TM 1-320 

25-26 

motions. With this fact in mind the types of stability now will be 

considered. 

26. Types of stability.-a. Stability is defined as the tendency 

to return to a position of equilibrium after a small deviation from that 

position. 

b. In airships stability is accomplished by two means, static and 

dynamic. 

(1) Strictly speaking, the only real statical stability is that which 

exists when the engines are stopped. Under this condition an airNormt~l or verlh;;a/ Axis 

/ 

/ 

\ 

\ 

osifive Oirecf"itms oF 1'9xe.s and /lnfJ~ 

(Forces ond.moment-.5 .s wn hit drrow.s) 

' 

Axis 3' Moment about axis Angle . ~ I 

I ~ 

0 ~ . 0 ........... . .... 

..9l..8 ~ 

Q 

-;s s:l ~ t:l 

Designation '"'» 0 0 a!UJ .... .,... 

- B ~ ..... Q) ~ 0 g, 0 > ~ 

.a ~ .0 .... 

~ bO . s ..... a .... ..... ,.. rJl 

~ tl.l 

£ & Q) >. Q) 

~ 00 ~ 

LongitudinaL __ ___ X X Rolling ___ L 1 Y- -z RolL __ LateraL __ _______ _ y y Pitching __ M z X Pitch __ NormaL _________ I z I z Yawing __ N x--Y Yaw ___ 

' 

Velocities 

I ,.-... 

8.·~ 

s~ Obi) 

~~ ....... 0 

~ 0 ,.. ..... .a ala! 

~ Q)~ 

~ Q . bO ..... Q) 

00 H ~=: · ~ 

4> u p 

e v q 

'1' w r 

FJGtJRE 19.-Cbart showing axes of airship and conventional symbols related thereto. 

39 

-
TM 1-320 

2~27 AIR CORPS 

ship is statically stable if it tends to return toward initial condition 

of steady motion whenever slightly disturbed from that motion. This 

requirement is not dependent upon the plane in which deviation from 

steady motion occurs, and, as will be shown later, an airship is 

statically unstable in yaw. 

(2) Dynamic stability is the stability effected by action of the air 

~tream upon controlled surfaces. Were it not for these surfaces airships would become unmanageable at very slow speeds. 

c. Stability may be classified further. An airship in steady flight 

has three types of stability, pitch or longitudinal, yaw or directional, 

and roll about the longitudinal axis. While these stabilities are all 

correlated in the case of an airplane, this is not the case with an airship, the three types of stability being independent of each other. 

,. 

w 

Airs/lip l'rtll'~h/1~ hDri'zonl"t~l!y in Sl"t~flc 

~9uiliiJri11m. Lon~ifudintJ! t~xis coinicidenr 

with direction o/ mot-ion 

FIGURE 20.- Forces on airship in horizontal flight. 

d. The following discussion will be based upon the assumptions 

for each situation that-

(1) Ascensional force remains constant. 

(2) Total weight remains constant. 

(3) Speed remains the same. 

(4) Form of airship remains unchanged. 

(5) Center of gravity and center of buoyancy remain fixed. 

(6) Controls remain in neutral. 

27 .. Forces and moments acting on airship.-a. Suppose an 

airship flies along a horizontal right-line trajectory .while its longitudinal axis makes an angle of oo with the flight path, then the 

airship will be acted on by the following forces and moments (see 

fig. 20). 

(1) Forces: 

(a) L0=Lift of inflating gas acting through center of buoyancy, G. 

40 
AIRSHIP AERODYNAMICS 

'I'M 1-320 

27 

(b) W = Total weight of dead and live loading, acting through 

center of gravity, M. 

(c) R = Resistance of envelope and appendages, acting through center of pressure, P. 

(d) T= Propeller thrust, acting parallel to axis of envelope at 

distance o below M. 

(2) Moments about M: 

(a) Moment L 0= L 0 X0=0. 

(b) Moment W = W X 0= 0. 

( o) Moment thrust-resistance couple= T ( o +d). 

Obviously, for static equilibrium and constant ve.locityLu= W 

R=T 

However, if the airship is riding on an even keel, the moment of 

thrust and resistance is unbalanced and will tend to nose the ship up. 

F or this r eason airships are customarily trimmed a few degrees nose 

heavy when full of gas. 

b. Suppose that some force such as a gust of air should give the 

longitudinal axis a slight tilt to the horizontal. Depending on 

static condition of airship and direction of inclination, six cases which 

• ar1se. are-e -

(1) Case No. i.-Airship in static equilibrium, nose tilted up. In 

this case, if the angle between the longitudinal axis and the direction 

of motion is denoted by (} and the angle between the direction of motion 

and the horizontal by a, since the airship climbs at the angle of tilt, 

(}=0° and the airship will climb at the angle, a. 

(2) Case No. ~.- ir hip in static equilibrium, nose tilted down. 

As before, (}= 0° and the airship will descend at the angle, a . 

(3) Case No. 3.-Airship statically heavy, nose tilted up. In this 

event the airship will climb at a lesser angle than the amount of tilt, 

and the longitudinal axis will make the angle a+(} with the horizontal. 

(4) Case No. 4.-Airship statically heavy, nose tilted down. Because of the heaviness, the airship will descend at a greater angle than 

the inclination, the longitudinal axis making an angle of a-& with the 

horizontal. 

(5) Case No. 5.-Airship statically light, nose tilted up. This case 

is similar to case No. 4. The longitudinal axis makes the angle a - 0 

with the horizontal. 

(6) Oase No. 6.-Airship statically light, nose tilted down. H ere 

the airship will descend at a lesser angle than the inclination and the 

angle between the horizontal and the longitudinal axis will equal a+ D. 

41 
TM 1-320 

27 AIR CORPS 

c. Figure 21 shows case No. 3. Figures showing the other cases 

would be quite similar. Referring to figure 21, the following forces, 

lever arms, and moments, all general to cases Nos. 1 to 6, inclusive, are 

noted: 

(1) Forces: 

(a) L9 = Lifting force of gas. 

(b) W = Total weight. 

(c) Fe=Resultant air force on hull. 

(d) Le= Vertical component of dynamic force on hull. 

(e) Re=Horizontal component of dynamic force on hull. 

(/ ) F a=Resultant force on tail surfaces. 

(g) L8 = Li£t of tail surfaces. 

(h.) Ra=Drag of tail surfaces. 

( i) T =Thrust of propellers. 

(j) t = Horizontal component of propeller thrust. 

(k) Lt=Vertical component of propeller thrust. 

(2) Lever mms about G.-Lever arm of-

(a) W =k sin (a±8). 

(b) L9= o. 

(c) T = (c+h). 

(d) F8=a (assuming F, perpendicular to the surfaces). 

(e) L 8=a cos (a ±8). 

{f) Rs=a sin (a± 8). 

(g) Fe varies with the position of P, which in turn depends on 

the angle 8. 

(h) L e=b COS (a±8). 

(3) Moments about G.-Moment of-

(a) Weight. Defined as static righting moment. It is present 

irrespective of speed and at all times equals W h sin (a± 8). 

(b) P ropeller thrust, T ( c +h). 

(c) F6 • D ue to increased pressure below the hull, Fe tends to rotate 

entire airship in a positive direction about M. This is assisted by 

reduced pressure beneath the tail (see fig. 17). The force below nose 

and tail are opposite in direction. Their difference, since the nose 

force is slightly the greater, is called dynamic lift of hull. However, 

both forces cause rotation in the same direction, and their moment 

is referred to as dynamic upsetting moment, Me. It will be evaluated 

later. 

NOTE.-Tbe force beneath the tail has been omitted from the figure in order 

to avoid confusion in the drawing, the entire upsetting moment being treated 

as though it were caused by the increased pressure under the nose. 

42 
AIRSHIP AERODYNAMICS 

Tltl 1-320 

27-29 

(d) Tail surfaces, Ms. This opposes the dynamic up tting 

moment. Ms=Ls a cos (a±O+ Rs a sin (a±O). 

28. Damping moment.-a. There is one moment which has not 

been discussed. If the airship, oscillating as it travels along its path, 

is considered as having two motions, one of translation as a whole 

and one of rotation about the center of gravity, superposed on each 

other, it is clear that during that portion of the angular oscillation 

in which the nose is rising, every part of the airship forward of the 

center of gravity is m~:>Ving upward, while all parts to the rear of that 

point, including the tail surfaces, are moving downward. 

b. There will then be an upward pressure of the air against the 

rear part of the airship and a downward pressure on the forward part. 

The upward and downward forces approximately cancel each other 

Ship lxvlvy-No.se elevt~tw/ L; F"e Le 

FlGUU 21.- Forces on airsb1p in inclined fligbt (case No. 3). 

so far as translational motion is concerned, but they act together to 

give a moment tending to depress the nose and so to resist the motion 

existing. If the rotation were such that the nose was descending, a 

moment tending to raise the nose would appear. This is called the 

damping moment as it is entirely independent of position and attitude, but acts always in such a manner as to oppose existing motion 

and bring the airship to steady fli~ht. Oscillations of the airship 

are damped exactly as oscillations of a pendulum are damped if the 

bob is light and has a large vane attached to it. Damping moments 

may be determined experimentally in a wind tunnel, but the mathematical theory when these moments are quantitatively taken into 

account is extremely complex and will not be discussed here. 

29. Longitudinal stability.- a. For longitudinal stability, the 

sum of the restoring moments must exceed the upsetting moments. 

In the case illustratedM. + Wh sin (a+O) >Me+ T(c+h). 

43 
'l'M 1-320 

29 AIR CORPS 

However, this r elation does not hold in each case . . For instance, the 

static couple, W·h sin (ex± 0), works against the thrust couple when _ 

the airship is in a climbing attitude and with it when the airship is in 

a descending one. The dynamic moment of £he hull, on the other 

hand, assists the righting moment in case Nos. 4 and 5, but opposes it 

in case Nos. 3 and 6. Case Nos. 1 and 2 ar e unimportant as will be 

shown later. Obviously case Nos. 3 and 6 are the ones which must be 

considered when designing for stability. 

b. The static righting moment is nearly a right-line function of 

the angle, 0. So for practical purposes is the upsetting moment. 

But whereas the righting moment is independent of the velocity, the. 

upsetting moment varies as the square of the speed. Obviously as 

the speed increases a velocity will be reached where the upsetting 

moment just equals the righting moment. This is called the critical . 

speed. 

c. For an airship without control surfaces, neglecting for the moment 

propeller thrust and resistance, the critical speed would be reached 

whenM e= Wh sin (a± B). 

By the formula of Doctor M:unk: 

M .= Vol)~ k2-kt) sin 28 

where k2 and k1 are constants to correct for the fact that masses of 

air are carried along with the hull in both transverse and longitudinal 

motion. Tables of values of k2 and k1 are given in National Advisory 

Committee for Aeronautics Report No. 184. From the M:unk equation it appears that 111 c varies directly as sin 20 and as the square of the 

speed. Combining the constant factors in the formula into one 

constant, Me: 

M t=Me sin 28v2. 

H ence the relation for critical speed without fins becomesMe sin 28Ve2= Wh sin (a±8) 

Wh sin (a±8) 

Vc=-= M e sin 28 

where Vc=critical speed. 

This would give a very low. critical speed. For an Italian military 

airship of the M type the critical speed without fins is 29 miles 

per hour. 

d. I ntroducing the tail surfaces gives a much higher value of the 

critical speed. From the relations given in a above for case No.3, the 

44 
AIRSHIP AERODYNAMICS 

TM 1-320 

29 

equation of stability at the critical speed, omitting the thrust-resistance 

couple, iss--

F$a+ Wh sin (a- 8)=Me. 

S,ince the force on an inclined plate is approximately a right-line 

function of the angle of inclination, 

Fs= 0.(Jvc2 

where 01 is a constant combining the surface coefficient and the fin 

a,rea. As before-e -

Hence 

M e sin '28v/= 0 18ve2a+ W h sin (a+B) 

v _ / Wh sin (a+ O) . 

e - -y M e sin 28- 018a 

e. For a condition of static equilibrium, as stated in paragraph 27b, 

the flight path theoretically coincides with the longitudinal axis. 

Hence 8 becomes zero and Vo becomes infinite. This agrees with the 

theoretical facts since with no angle of attack to the air stream the 

transverse dynamic forces become zero for all speeds and the static 

righting moment would restore quickly the airship to the horizontal 

position. Actually, however, this can never be practically true, since 

inertia of the airship retards change in direction of motion from the 

horizontal path and prevents the airship immediately adopting a line 

of flight coincident with its longitudinal axis. 

f. In the preceding discussion the controls have been considered to 

be held in neutral. Actually by varying his elevator angle, the pilot 

may increase materially the effect of the control surfaces. This further increases the speed which the airship may travel without loss of 

control. If the airship is not longitudinally stable, or if in other 

words it is being operated above its critical speed, the pilot must correct deviations from the chosen path as soon as they appear, , while 

on a stable airship these deviations would be capable of self-correction 

if left manually uncorrected. 

g: The statical righting moment varies as the fourth power of a 

linear dimension of the airship, the ascensional force F being proportional to the volume and so to the cube of a linear dimension. All 

aerodynamic moments, on the other hand, both on the hull proper and 

on the tail surfaces, vary as the cube of a linear dimension. The critical speed is therefore proportional, for geometrically similar airships, to 

~fa or to the square root of a linear dimension. A large airship can 

therefore be stabilized with tail surfaces proportionally smaller than 

4o 
TM 1....:.:320 

29-Sl AIR CORPS 

those necessary on a small one traveling at the same speed. An unstable airship requires closer attention from the pilot than does one 

which is stable, but it is not necessarily either difficult or dangerous 

·to operate and has the advantage of being more easily maneuverable 

than the more stable types. 

30. Directional stability.-a. Directional stability is maintained 

in part by use of vertical fixed fins and rudder. When the rudder 

is set in neutral it acts as additional fin surface, but the total fin surface is never large. enough to provide complete directional stability 

Since there is no statical restoring moment to overcome a horizontal 

deviation from the flight path, maintenance of directional stability 

devolves upon the pilot who must correct any deviations as soon as 

they appear. Otherwise a deviation once started will tend to in-

. crease until the airship is traveling in a circle of so small a radius 

that the d~mping moment balances the turning moment due to pressure on the nose. This is quite different from the condition of longitudinal stability where the elevator can be left locked in any particular 

position and the airship will return to its original attitude if atmospheric disturbances have momentarily changed that attitude. 

b. As soon as there is any deviation from the straight line of flight 

the a.ir strikes on the side of the envelope and sets up a moment tending to turn the airship farther from its original course. This moment 

corresponds exactly to the upsetting moment, Me, which opposes longitudinal stability. There is then an unbalanced moment which tends 

to give the airship an angular acceleration and so to turn her more 

and more rapidly. At the same time the lateral force on the envelope, 

which corresponds to the dynamic lift, is increasing and .furnishes the 

necessary centripetal force to keep the airship traveling in a circular 

path. It is quite true that a force resisting this circling is exerted by 

the vertical surfaces, but, as mentione.d above, the vertical fin surfaces 

are never large enough to provide full stability, and the rudder must 

be used to assist them. Use of the rudder will be more fully discussed 

in sec6on V. 

31. Lateral stability.-a. Stability in roll, which is a very difficult problem in airplanes, is taken care of almost automatically in airships; since the same statical restoring moment acts with regard to roll 

as with regard to pitch and there is no dynamic upsetting moment to 

oppose it. The only rolling motions are those due to side gusts against 

the car and bag and those due to centrifugal force when turning. The· 

moments of these forces are overcome immediately by the large restoring moment due to the low position of the center of gravity. Roll46 
AffiSHlP AERQ.DYN AMI CS 

TM 1-320 

31-33 

ing may be very uncomfortable because of the short and snappy period, 

but there is never any danger of its reaching an excessive value. 

b. The static stability of an airship wit~ regard to both roll and 

pitch may be increased by lowering the car, but this gives equilibrium 

only at the sacrifice of ease of control and efficiency, since lowering the 

thrust line increases the thrust moment and lowering the car increases 

length of suspensions and hence parasite resistance. 

32. Summary.-a. Airship stability may be summarized as 

follows: 

(1) Airships are very stable about their lateral axis. In this nr 

gard the designer has no trouble whatsoever. 

(2) Airships must be designed carefully to give longitudinal stability. This problem is however of more interest to the designer than 

to the pilot. 

(3) Airships are statically unstable in yaw, necessitating the closest 

attention on the part of the direction pilot to counteract circling by 

means of the rudder. 

b. No concrete problems have been given in this section as the application of fundamentals covered therein will be shown in section V. 

SECTION v 

CONTROL 

Paragraph 

General types---------------------------------------------------------- 33 

Directional - ----------····-------- ------- --- ·- --- - - - ----------- - --...----- - - 34 

AJtitude--------------------------------------------------------------- 35 

Reverse---------------------------------------------------------------- 36 

Application of dynamic contr ol to operation of airshiPS-------------------- 37 

33. General types.-a. Control of airships may be subdivided 

into two classes, directional and altitude. On nearly all airplanas 

these two types of control are so interrelated as to necessitate their 

both being performed by one pilot. In airships this is not the case, 

and on all but the smallest airships two pilots are utilized, one for 

direction, one for altitude. . 

b. For efficient performance the two pilots should be familiar with 

each other's style of flying and constantly alert to render each other 

assistance. For instance, to obtain the proper additional superheat 

to effect a landing (see TM 1- 325), the altitude pilot may desire a 

longer approach than usual. The direction pilot should so arrange 

the course as to meet needs of the situation. Instances of the value of 

coordination are too numerous to mention, but fortunately capable 

pilots have little difficulty in achieving desired results. 

47 
TM 1-320 

34 AIR CORPS 

34. Directional.-a. As stated in paragraph 33, the direction pilot 

is charged with control of the course of the airship in a horizontal 

plane. On cross-country .flights his problem resolves itself into that 

of holding the course required by the mission of the airship. Once 

the course is set, the airship will hold its own course unless acted on 

by some exterior forces such as gusts. These must be overcome by 

prompt application of the rudder in the opposing direction. When 

flying in very gusty air it is impossible tD prevent yawing, but a good 

pilot can keep the magnitude of the oscillations from exceeding a few 

degrees. Then since the gusts strike about equally from both sides 

the mean course of the airship will be the one desired. 

b. It is essential that the pilot have a clear conception of the reaction to rudder control of the airship in a turn. When it is desired to 

turn to the right, for example, the rudder is put over to the right,. 

The instantaneous effect of this rotation is to produce a force to the 

left acting on the right side of the rudder. This force to the left has 

a dual effect. In the first place, it gives the moment about the center 

of gravity tending to turn the nose to the right. I n the second place, 

it moves the entire airship to the left. As the airship moves to the 

left and as its nose turns to the right, both motions combine to cause 

the air to strike on the left of the envelope and so to turn the nose 

still farther to the right. After this has proceeded for an interval, 

the pressure on the left-hand side of the nos? becomes equal to that on 

the right-hand side of the rudder and the total resultant pressure is 

therefore zero, but since one force is applied to the front and the other 

to the rear, there is a resultant turning moment tending to continue 

the twisting to the right. As the motion proceeds still farther, the 

force on the left-hand side of the envelope becomes greater than the 

force on the right-hand side of the rudder and there is a centripetal 

force to the right so that the airship starts to move to the right. If 

the rudder is left in hard or even if it is turned to neutral, this turning to the right will continue, and in order to check the circling it is 

necessary to put the rudder over to the left of the envelope. 

o. The turning radius is governed by the damping moment on the 

envelope and is greater for an airship of large fineness ratio than for 

one where this ratio is small. It should be one of the first concerns of 

the pilot whenever he assumes control of a new type of airship to 

familiarize himself with its turning radius. Otherwise he might 

very conceivably endeavor to execute a turning maneuver where the 

space limitatio~ was insufficient. 

d. Referring again to the turn described in b above, it appears, 

curiously enough, that the first effect on putting the rudder over to 

48. 
. 

AIRSHIP AERODYNAMICS 

TM 1-320 

34 

the right is to shift the airship slightly to the left so that if the airship were being flown along close to the right side of a wall or other 

obstruction, it would not be safe to put the rudder over sharply to the 

right in order to turn to the right and get away from the obstruction, as the immediate effect of such an action would be to drive the 

airship into the wall. The approximate path of the airship when 

the rudder is put over to the right, together with several successive 

positions of the axis of the airship, are indicated in figure 22. 

e. It occasionally happens, especially when flying through foggy 

atmosphere, that an obstacle will suddenly loom up in front of the 

r; I 

I 

I 

I 

1Ye 

I 

I 

I 

'Yr 

rrr \ 

(I) 

'(Yr '('Y,. 

FIGURE 22.- rlction of airs hip In a turn. F IGURE 23.-Actlon of alrsblp in a ,·oiding nn obstacle. 

airship. To miss the obstacle t he pilot must first put over the rudder 

to deflect the nose of the airship and then completely reverse the 

rudder. In this case the action is as shown in figure 23. 

f. There is one other situatioll in which the direction pilot must 

exercise caution. As the airship turns under action of the rudder, 

centrifugal force acting on the center of gravity will swing the car 

to the outside. This action will so tilt the hu1l that the rudder will 

become in part an elevator. .Air striking on the inside of the rudder will depress the nose of the ship. This depression can be stopped 

by prompt application of the elevator controls by the altitude pilot. 

However in some cases, especially when near the ground with a heavy 

airship, the altitude pilot may be unable to. use the elevators without 

endangering the tail of the airship. Hence the 'direction pilot must . 

49 
TJ4 1-320 

84-86 AIR CORPS 

be very careful to turn a heavy airship slowly when at low altitudes. 

On the other hand, he can very materially assist the altitude pilot 

in holding a light airship down by making abrupt turns. 

35. Altitude.-a. Methods.-(l) Altitude control of airships is 

effected by two means, static and dynamic. Tha former method is 

discussed in TM 1-325. 

{2) Static means of control must always be augmented by dynamic means. Even though an airship takes off in perfect equilibrium it will not remain so. Changes occur in the static lift due 

to changes in meteorological conditions and loading is being varied 

constantly by consumption of fuel. To balance inequalities between 

loading and lift, dynamic means must be used. 

b. Trim of airship.-(1) In the study of stability, to simplify the 

discussion the subject of trim of the airship was omitted. A thorough know ledge of trim is however essential to intelligent control of 

the airship. 

(2) Under action of the static righting moment, the center of 

gravity of the airship will lie directly below the center of buoyancy. 

If the line joinil!-g these two points is at right angles to the longitudinal axis, this axis is horizontal, and the airship is said to be 

trimmed in neutral. If, on the other hand, due to the manner of 

loading or to location of the air i.n the ballonets of a pressure airship, 

the longitudinal axis is inclined to the horizontal when the center of 

gravity is directly below the center of buoyancy, the airship is said 

to be trimmed nose heavy or tail heavy, as the case may be. The 

application of trim to dynamic control of airships is discussed in 

paragraph 37. 

c. Olimbing fJifiA.l descending.-(l) Change in altitude is accomplished dynamically by use of elevators in conjunction with thrust of 

propellers. To simplify the following discussion the airship is 

assumed to be flying with neutral trim and in static equilibrium. If 

it is desired to climb, the altitude pilot raises the elevators which causes 

an action in the vertical plane similar to that described in paragraph 

34 for turning in a horizontal plane. However, in this case, the elevators must be held in the raised position to prevent the static righting 

moment bringing the longitudinal axis back to the horizontal. 

(2) It should be especially noted that when the elevator is raised 

the tail of the airship actually descends. For this reason extreme 

caution should be used in use of the elevator when the airship is near 

the ground. 

36. Reverse.-a. There is one curious paradox in control of airships at very low speeds. It the speed falls below a certain definite 

lSO 
. 

AIRSHIP AERODYNAMICS 

TM 1-320 

36 

value known as the "reversing speed," control becomes reversed and 

pulling up the elevators causes the airship to descend, although it turns 

the nose upward. The reason for this is that at low speeds (for most 

types about 15 miles per hour) the air forces are entirely unimportant 

in comparison with the static restoring moment due to the weight 

when the airship is inclined. Then if the elevators are pulled up, the 

momentary effect is to turn the nose upward, but the axis will incline 

only at a very small angle before the static restoring moment becomes 

equal to the moment due to the force on the elevators, and the inclination will then cease to increase. If this angle of inclination is held to 

a small enough value, the dynamic force on the nose will be less than 

the downward force on the elevators. There will then be an excess of 

downward force and the airship will be thrust downward as a whole. 

This reversing speed offers a reason for not making the static stability 

excessive, since reversing speed increases as the center of gravity is 

lowered and the resulting difficulty in control becomes more serious 

where the static stability is large. 

b. The phenomenon of reverse control is especially apparent if the 

airship is trimmed quite nose heavy. Then any attempt on the part of 

the pilot to lift the nose at slow speeds is resisted by the static moment. 

The decrease in the dynamic thrust downward on the nose will be less 

than the gain in the down ward force on the elevator and the airship as 

a whole will descend. 

c. The particular situation just described is one of the most serious 

into which the airship can be brought. It is of most frequent occurrence when a nose heavy airship is being brought to a landing and due 

to loss· of superheat becomes statically heavy. The airship will descend 

as a result of this heaviness and, if the speed is below reversing speed, 

application of the elevators at that speed will simply cause more rapid 

descent. 

d. The only recourse of the pilot in this situation, unless his airship 

is equipped with reversing propellers, is to throw ballast or materially 

increase his speed beyond the reversing limit as he raises the elevators. 

·when the airship is quite near the ground there may not be sufficient 

altitude to execute the latter maneuver without striking the ground 

with the tail. If his airship is equipped with reversing propellers, 

the pilot can cause the airship to ascend while the nose is down by 

merely reversing the direction of propeller rotation. 

e. There is one other situation in which reverse control occurs. The 

maximum dynamic lift on the hull occurs at an angle of attack of 10° 

or 11° for most. types of airships. If an airship is flying with this 

angle of attack and the elevators are raised so as to increase the angle 

51 
TM 1-320 

36-37 AIR CORPS 

of attack beyond that giving the ma-ximum lift, the dynamic lift nat .. 

urally decreases. At the same time the downward thrust on the elevators is increased. The gain in the upward component of the propeller 

thrust at reversing speed or below will not compensate for the loss 

in lift just described and the airship will be under the action of a 

greater resultant downward force than at the start. 

f. The opposite effect to that described in c above occurs when an 

airship is trimmed tail heavy and the elevator is depressed. In this 

case the whole airship will rise. 

g. It might appear that reverse control would be a source of great 

annoyance to the pilot. This is not the case when the phenomenon is 

Ls 

FIGURE 24.-Fl!gbt at constant altitude (airship statically heray, trimmed tail heavy, 

·elevators neutral). 

properly understood. I n fact, many maneuvers are executed by intelligent use of reverse control, for example, heavy take-off. This is 

described in paragraph 37. 

37. Application of dynamic control to operation of airships.-a. The three major maneuvers in airship operation which 

are assisted by dynamic control are-

(1) Flight at constant altitude. 

(2) Take-off. 

(3) anding~ 

These operations are fully covered in TM 1-310 and are discussed but 

briefly here to bring out the aerodynamic principles involved therein. 

b. As soon as the take-off is completed and the obstacles in the immediate foreground cleared, the pilot climbs to the altitude at which he 

desires to cruise. He then trims the airship so that with the controls 

in neutral the algebraic sum of the vertical forces is zero. Since the 

airship is almost never in static equilibrium, one of two situations will 

prevail, static heaviness or lightness. 

52 
AIRSHIP AERODYNAMICS 

TM 1-320 

37 

(1) Figure 24 shows the case in which the airship is statica:Jly·heavy 

and trimmed nose light. In this case the equation of vertical forces 

to give constant altitude flight with neutral controls becomesW =£ 0+ Le+ Lt+ ~ 

The pilot may be called upon to fly a heavy airship on account of various reasons such as--

(a) Collection of moisture if rain is encountered. 

(b) Leakage in envelope. 

(c) Loss of superheat. 

(d) Heavy take-off. 

Most airships can carry about 10 percent. of their gross lift dynamically 

at the surface of the earth. Since the dynamic lift varies as the air 

·density, it decreases with nltitude. Table III shows results of some experiments on an Italian M type airship at- full speed : 

TABLE III.- Lijt of Italian M type at full speed 

[In pounds] 

Altitude, 3,000 feet Altitude, 10,000 feet Altitude, 16,500 feet 

Angle of I I <I) I I I I !XI 1:1 0 1:1 0 ~ 1:1 0 inclination in .... Q)Q) !').~ 1:1 .... Q)Q) '"'fl) .... Q)Q) .... fl) 

radiants ..... 

~ ..... o. ~ :=l o. .... ~ .... 0.~-o ~ -~ ..... o. .._.a> ..... ;..::: ..... o. 

oo ..... oo ._Cil .... ..... - o- 0 - Q3 0~ 0 - 0~ 0 ..... 0 . <IS Q) . Q) .5 s Q3 .... -+"> <!:0. .... -+"> .... 0. .... -+"> +>o. .... 0 - ~ 0 .... .... .... 0 - ..... ~ ·- ...... E-< H H H E-. H ·- H ·- H ·- E-. H ·- H ·- ..:I 

0.03- - ---- - - - 1, 224 330 60 834 I, 012 269 48 695 839 218 40 481 

0.06 __ ___ ____ 1, 855 612 125 1, 118 1, 542 495 101 946 1, 287 400 82 805 

0.09_- ------- 2, 290 810 200 1, 2801, 914 657 163 1,095 1, 608 530 130 948 

0.12 ___ __ ____ 2,497 913 290 1, 294'2, 101 742 235 1, 124 1, 778 599 189 99 0 

(2) Figure 25 shows the case in which the airship is fl.yin~ statically 

light at constant altitude with controls in neutral. In this case 'the 

equation of the vertical forces becomesL0= W + L e + Lt + L8 

(3) In the unusual case in which the airship is in perfect static 

equilibrium, it will be necessary to trim the airship about 2° nose 

heavy to overc6me the upturning moment of the propeller thrust. So 

trimmed the airship will fly on an even keel at cruising speed. The 

motorized observation ba1loon, having only one ballonet, cannot be 

trimmed for an individual flight. An approximate 2° nose heavy 

53 
Tl4 1-320 

87 AIR CORPS 

trim is given this type of airship during initial inflation by proper 

adjustment of car suspension rigging. 

c. It is customary to take off large semirigids and rigids statically 

light, but nonrigids are taken off as much as 6 or 7 percent heavy. 

(1) The light take.-off may be made with the airship in any trim 

from tail heavy to a few degrees nose heavy. In the latter case the 

airship should be free-ballooned to a safe altitude before the motors 

are opened. The light take-off presents little difficulty. 

(2) For the take-off when the airship is in static equilibrium the 

trim should be neutral or a few degrees tail heavy, preferably the latter. In this case the car party of the maneuvering crew gives the airship a toss upward, the men on the nose of the car throwing their end 

up first, then the men to the rear throwing up their end. This gives 

• 

FIGURl'l 25.- Flight at constant alt itude (airsbip statically Hght, trimmed nose heavy, 

elevators ne\ltral). 

t.he airship an initial angle of attack to the air stream. When clear 

of the party the pilot opens his motc·rs and raises his elevators slightly. 

The thrust of the propellers assisted by the slight force on the elevators will further raise the nose of the airship and it . will climb 

rapidly. 

(3) For the heavy take-off the ajrship must be carefully trimmed 

tail heavy. The amount of the trim varies with degree of heaviness, 

type of airship, and wind velocity. If there is a good wind blowing it 

gives the airship an initial air speed to assist the ascent. Experience 

has shown that an airship of the TO type with a trim of 9° tail heavy 

will take off 700 pounds heavy in still air. For this degree of heaviness the car party should be augmented to at least 20 men and 4 men 

should be assigned to lift on the tail surface. At the proper signal 

the car is thrown up, nose first as before. The elevators should be 

depressed about 10° and as the pilot opens his motors he will find it 

necessary to depress the elevators fully to keep the tail from striking 

the ground. Action of the airship in rising is a pure case of reverse 

control. The air from the slipstream of the propellers strikes the 

54 
AIRSHIP AERODYNAMICS 

TM 1-320 

87 

elevators and gives the tail a positive lift. At the same time the trim 

of the airship will keep its nose elevated so that there will be the 

familiar dynamic lift on the hull surface and the vertical component 

of the propeller thrust to assist the ascent. In this cas:e-e -

Lu+Le+L t+Ls> W 

d. The most diffic•lit maneuver which confronts the pilot is the 

landing. This operation may b~ divided into three parts, as· follows: 

(1) Weigh-off. 

(2) Approach. 

(3) Arrival at the landing party. 

e. Weigh-off is made at a safe altitude (1,000 feet for large airships, 

250 to 500 feet for smaller ones). For this maneuver controls are 

~~~W<tl9h oil horo 

_,.• NJ • ......,.-JtOO 

~------------- 2Mi------------------~ 

FIGURE 26.-Approach of an a.irship to a landing. 

placed in neutral and air speed reduced to as low a speed as possible. 

The airship will quickly assume an attitude determined by the trim, 

which can be read from the inclinometer. At the same time the pilot 

can notice whether the airship is rising or descending statically. It is 

useless to bring the airship to an even keel to eliminate dynamic lift 

caused by unavoidable residual speed incident to idling propellers, as 

this would, in reality create a dynamic thrust on the tail surfaces. 

As a result of the knowledge of condition of the airship derived from 

weigh-off and after due consideration of existing meteorological conditions, the pilot is ready to make the approach. 

f. The principal object of the approach is to determine in advance 

of the arrival at the party the behavior of the airship at landing speed. 

Figure 26 gives a graphical picture of the approach. 

(1) From the altitude of weigh-off the airship is brought quickly 

to the altitude of approach. This varies from 150 feet for a nonrigid 

to 500 feet for a large rigid, depending in some measure on gustiness 

of the atmosphere. During the descent the pilot arranges the trim 

he estimates to be necessary to make the landing. On arrival at the 

55 
TM 1-320 

87-38 AIR CORPS 

approach altitude the speed of the airship is reduced to 15 miles per 

hour plus the wind velocity. This is an excellent approach speed. 

(2) The pilot now wishes to check behavior of the airship at this 

speed. Controls are placed in neutral and if the trim is correct the 

airship will maintain constant altitude in a manner described in b 

above. If it does not, it is necessary to adjust further the trim to 

effect that result. The principle is exactly the same whether the air. 

ship is statically light or heavy. During remainde~ of the approach 

·controls are useu to overcome gusts or changes in static conditions, 

care being taken to observe principles of reverse control should the 

speed fall below reversing speed or should the airship be placed in 

danger by loss of static lift. 

g. When the airship arrives within 50 to.200 yards of the landing 

party it is brought to landing height. This depends on type of airship and length of handling guys used. Large nonrigids usually land 

about 60 feet off the ground, rigids at a much higher altitude, while 

the motorized observation balloon must be landed at an altitude of 

25 feet or less. In this conn.ection it should be borne in mind that the 

lower a statically h~avy landing can be made the smaller the drop 

after aerodynamic control ceases. In that case,· also, care should be 

t aken to level the airship by use of elevators as it falls into the hands 

of the party, as otherwise the tail would be injured. 

h. The landing described above is the usual type of landing. The 

description is not at all complete since it omits nearly all the static 

principles involved. The other types of landings, such as turn landings, will not be discussed, since the dynamic principles involved 

therein are similar to those already explained. 

SECTION VI 

AERODYNAMIC STRESS 

Paragraph 

Assumption as to condition of maximum stress------------------- --- -- - 38 

Transverse forces acting on airship flying at constant angle of pitch______ 39 

Transverse forces acting on airship in steady turn_____________________ 40 

Forces caused by gusts--------- ---- - ------- --------------------------- 41 

Empirical formulas for maximum aerodynamic bending moment on hull 

and for forces on tail surfaces---------- - ------ --------- - ------------- 42 

Method of calculating shear and bending moment on hnll_________________ 4g 

Conclusion____________________________________________________________ 44 

38. Assumption as to condition of maximum stress.-a. For 

airships designed prior to the World War the air speeds were quite 

slow. The aerodynamic forces acting on these airships were conse56 
AIRSHIP AERODYNAMICS 

TM 1-320 

38 

quently insufficient to give shear or bending moments large enough to 

endanger an airship designed to care for the static loading. At present the speed of airships has been so materially increased that aerodynamic forces, which vary as the square of the speed, must be considered. While it is not the function of this manual to teach design 

of airships, a general know ledge of results of these forces and moments 

is sufficiently important to the pilot to warrant inclusion herein a 

simplified discussion thereof. 

b. As previously stated, the longitudinal aerodynamic forces are 

usually not a source of danger to the airship. The single exception 

to this statement occurs in the case of the pressure airship flying at 

maximum or nearly maximum speed. At this time the nose pressure 

· may attain such magnitude that it 'may very conceivably exceed the 

pressure for which the airship was designed, in which event the nose 

will cave in. Since it is the internal pressure of the gas which resists 

such caving action, it should be the duty of the pilot to increase his 

internal pressure to the maximum allowable pressure when flying at 

velocities approximating maximum design speed. 

o. The most important aerodynamic stresses are those caused by 

transverse forces. In order to design for such stresses, it becomes 

necessary to make assumptions concerning conditions which give greatest transverse forces. It was early believed that the worst condition 

occurred at the instant of si,multaneous application of full rudder and 

elevator control. This assumption would appear reasonable in view 

of the fact that momentarily inertia of the airship will arrest any 

tendency toward rotation, but as soon as an angular velocity is attained, rotation of the tail reduces the forces on the surfaces. However, this argument omits one important consideration. It frequently 

occurs that at the moment of application of the controls, the airship 

may be under the acti~n of forces giving it yaw or pitch in a direction 

opposite to that desired. In this case while initial yaw or pitch is 

being overcome, the hull will be subjected to a twisting action caused 

by two opposing moments. Theoretical treatment of stresses so caused 

is quite complicated and many designers simply arbitrarily double 

the forces which arise when full rudder and elevator are applied simultaneously. 

d. During the design of the RS-1 airship various conditions of 

static loading, with a load factor of 4, were investigated. Stresses 

found in the keel members under static loading conditions were combined with stresses found under the following conditions of aerodynamic loading to determine maxi~um stress in any member: In 

·arriving at !ow load factors applied to aerodynamic loading condi57 
TM 1-320 

88-89 AIR CORPS 

tions, the effect of the envelope in relieving the keel by resisting a 

portion of the shear and bending was neglected. It was found that 

this was very conservative as subsequent tests on water-filled models 

and full-scale tests on the RS-1 airship indicate that the keel resists 

approximately 50 percent of total bending due to static loads. However, in flight tests it was found that the keel resists only 10 percent 

of the bending moment due to external air loads in pitch. ·In order 

to l!>e conservative however in future designs of semirigid airships the 

design should be based on the assumption that the proportion of the 

total loads on the airship due to external air loads in pitch in flight 

resisted by the keel is half that found in the case of static weights 

and that a load factor of 2.0 be used. 

(1) Horizontal flight at 55 miles per hour with a load factor of 4.0. 

(2) Horizontal flight at 70 miles per hour with a load factor of 3.0. 

(3) Pitch up or down at an angle of 3° 19' at 55 miles per hour 

with a load factor of 3.0. 

( 4) Yaw at 55 miles per hour with load factor of 3.0. 

(5) Turning, 1,500 feet radius at 55 miles per hour with load factor 

of 2.0. 

(6) Mooring by the nose with pitch up, pitch down, and yaw of 4° 

0', in a gale of 70 miles per hour with a load factor of 2.0. 

e. From the foregoing discussion it is evident that the pilot should 

be cognizant of maximum angles of pitch and yaw for which his aircraft was designed. Then when atmospheric conditions render it 

impossible to keep the. airship within design limits he should reduce 

his air speed to effect a reduction of the aerodynamic forces. 

f. To simplify the discussion transverse forces will be considered 

under three classes : 

(1) Transverse forces at fixed angle of pitch. 

(2) Transverse forces in steady turn. 

(3) Forces caused by ·gusts. 

39. Transverse forces acting on airship :flying at constant 

angle of pitch.-a. 'When an airship is flying at a constant positive 

angle of pitch it is acted on by the following dynamic transverse forces: 

(1) Component normal to longitudinal axis of dynamic force on 

tail surfaces. 

(2) Component normal to longitudinal axis of dynamic force on 

hull. 

Since rotation is considered about the center of buoyancy it is necessary to divide the latter force into two parts. This is essential because 

the normal force on the forebody is directed upward, whereas the 

normal ·foroo on the afterbody is directed downward. It has been 
'AIRSHIP AERODYNAMICS 

TM 1-320 

39=40 

. shown by a member of the · National Advisory Committee for Aeronautics that the algebraic sum of the forces on the fore and after 

bodies is theoretically zero, which would indicate that the dynamic 

lift on the hull was zero, and that the total lift obtained dynamic~lly 

by the airship, exclusive of the vertical component of the propeller 

thrust, was that furnis!1ed by the surfaces. This is not in strict agreement with the actual facts, since the down thrust on the afterbody is 

-less than the theoretical down thrust. However, the fact remains that, 

since the pitch remains constant, the sum of the moments about the 

, center of buoyancy must equal zero. 

· b. The turning moment of the aerodynamic forces on the hull 

theoretically equals the formula : 

(Vol)iv2 (k2 -kl) sin 20 

where O=angle of pitch. 

k2 and k1 =constants correcting for additional masses of air carried 

longitudinally and transversely. Values of k1 and k 2 are given in 

National Advisory Committee for Aeronautics Report No. 184. 

o. If it is granted that the dynamic force on the tail equals the total 

resultant static transverse force, its moment must equal the formula 

given ~n b above. . HenceFa= (Vol)~v (kz-k ) sin 20 

where F = component of force on tail surface normal to longitudinal axis. 

a= distance from center of buoyancy to center of pressure 

of tail surface. 

'The above formula will give an approximation of dynamic lift of the 

airship. . 

d. Practically, F need not be as large as indicated aboye due to the 

discrepancy betwen actual and theoretical values of the down thrust 

on the afterbody. The point of application of F is slightly forward 

of the center of the area of the tail surfaces. 

e. For method of calct1lation of shear bending moments due to 

dynamic forces see paragraph 43. 

40. Transverse forces acting on airship in steady turn.-The 

theory in this case is quite similar to that described in paragraph 39. 

· Assuming, as before, that the algebraic sum of the forces on the for& 

.. :, and after portions of the airship hull equals zero, the other two forces 

:>acting on the airship (the force on the fins and centrifugal force) must. · ... . ~ 

59 
TM 1-320 

4o-42 AIR CORPS 

be equal to produce motion in a constant turn. From this is derived 

the relation2a 

sin 2 'I!= R(k2-kl) 

where 'I!= angle of yaw. 

a=distance from center of volume to center of pressure 

of tail surfaces. 

R= radius of turning circle. 

This relation gives results widely at variance :from the results o:f actual. 

tests on full-sized airships, presumably due to the assumption that the· 

resultant of the hull forces is zero. Fortunately, the total bending 

moment due to a steady angle of turn is only about one-fifth as great 

as that due to an equal fixed angle of pitch where unbalanced weight 

and centrifugal force are of equal magnitude. 

41. Forces caused by gusts.-a. Very little is known concerning 

maximum value of forces caused by gusts. The following statement 

very excellently sums up the situation : 

1 "The existence of veritable fountains of upward rushing air whose 

sides at times and places are sharply separated from the surrounding 

atmosphere must be taken into account in the design of airships. The 

most violent of such currents, the tornado, combines vertical velocity 

with rotation, but fortunately can be seen from a great distance, and 

can and must be avoided. The thunderstorm with large fully developed cumulus tops is also conspicuous and avoidable. It would appear 

to be :folly to enter such a cloud and subject the ship to the unknown 

dangers of wind, rain, hail, and lightning. Barring ·such spectacular 

hazards, there remain convection currents which the ship may run into 

at full speed. There is ample evidence that upward velocities as high 

as 10 feet per second may be encountered. This vertical air velocity u, 

combined with the relative horizontal speed v of the airship, will give 

-1 

the effect of a change of pitch of tan vu., 

b. It remains simply for the pilot, as stated in paragraph 38e, to 

reduce the speed in bumpy atmosphere, especially if at the same time 

the airship is developing large dynamic lift, positive or negative, as 

then the stresses are already large. 

42. Empirical formulas for maximum aerodynamic bendin g 

moment on hull and for forces on tail surfaces.-a. The following formula has been developed :for the maximum aerodynamic bend1 From "Airship Design" by C. P. Burgess by ·permission of tbe Ronald Press. 

60 
AIRSHIP AERODYNAMICS 

TM 1-320 

42-48 

ing moment to be expected from such bumpy weather as would be encountered in mountainous country: 

Mb=0.005 ,W (vol) 213L 

where Mb= the maximum bending moment in foot-pounds. 

L = the length of the airship in feet. 

Use of this formula enables the pilot to calculate rapidly maximum 

stresses to which his velocity in bumpy air may be subjecting his 

airship. 

b. Where surfaces are designed in approximate accordance with the 

formula A = 0.13 ( vol) 213 , the total transverse force on either vertical 

or horizontal surfaces may be computed quickly by the relation: 

F = 0.026 (vol) 218 p v 2

• 

In above formulas 

A=total area of either surface. 

F = total force on either surface. 

43. Method of calculating shear and bending moment on 

hull.-a. The designer and also the pilot in determining shear and 

bending moments on the airship must consider both static and dynamic loads. Both must be computed independently and then added 

together algebraically. It often happens that dynamic loads serve 

to reduce stresses due to static loading, but naturally the dangerous 

case occurs when stresses are arithmetically additive. 

b. The method to be described applies more particularly to rigid 

airships, but the principle can be applied to a nonrigid. In the latter 

case, the load instead of being distributed throughout the length of 

the hull is swung from the envelope by suspension cables which by 

their tensions control very largely distribution of loading on the 

envelope. 

c. For calculation of stresses, the hull is considered as a beam loaded 

with the weights acting downward, lift of gas cells acting upward and 

aerodynamic forces acting in any longitudinal plane whatsoever. All 

loads. are considered as concentrated at the frames rather than as 

uniformly distributed. The calculations may be divided into steps, 

as follows: 

( 1) Calculation of static load. 

(2) Calculation of shear due to static loading. 

(3) Calculation of bending moment due to static loading. 

( 4) Calculation of load, shear, and bending moments due to aerodynamic forces. 

( 5) Algebraic summation of effects of static and dynamic loading. 

61 
TM 1-320 

48 AIR CORPS 

d. The initial step in the computation is determination of .distribution of weights. This is taken from the detailed weight t~tement, 

weights therefrom being distributed to the proper frames. Lift of 

the gas in each cell is computed next and distributed as concentrated 

forces on the frames. The static loads on the hull are the differences 

between weight and buoyancy at each frame, lift being considered 

9 

1000 

so 

- .Jo 

/.. 

tq 000 

{Plane conftnl1in? C.G al1d C.8. 

90 po 80 

I 

20 

/0 000 

00 

/() 

00 

&olf4ncr <~ncl 1000 Loadi~ ,., 

0 LBS. 

2 000 

I""'!•,__---Overall len9rh oF /lir.ship----~ 

t 1 I Loads'" 1.85. j 2000 2000 • 

~----~------~~-----~.r-----~------~. 1000 /000 /000 1000 

I 1+1000 

I 

- 1000 

I 

...__ ____ __,,_,QOQ 

fjft1. IN 

LB. Meter.s 

F tcu•n: :.!7.-Loads, shear, a1111 bending moments caused by static loading. 

positive and loads negative. When the airship is in static equilibrium, 

the algebraic sum of the loads must equal zero. Figure 27 illustrates 

the computation of loads at each frame of an airship 50 meters long, 

having four frames spaced 10 meters apart. The method shown is 

applied to the largest airships. 

e. Commencing at either end of the airship, the shear at any frame 

equals the algebraic sum of loads up to that frame. This system 

gives a constant shear between frames, changing at each frame QY 

62 
AmSHIP AERODYNAMICS 

TM 1-320 

48 

the amount of load at that frame. The shear in figure 27 was computed in this manner. 

(1) For instance, the load at station 0 is -1,000 pounds. Then 

the shear between stations 0 and 10 equals -1,000 pounds. At station 

10 the load is + 2,000 pounds. Hence the shear between stations 10 

and 20 is -1,000 pounds + 2,000 pounds, or + 1,000 pounds. 

(2) For an airship in static equilibrium, when centers of buoyancy 

and gravity are vertically disposed, areas under the shear curve must 

add algebraically to zero. This should be checked before proceeding 

to computation of bending moments. 

f. For calculation of bending moments, all loads between ends of 

the airship and any frame are considered as supported by cantilever 

action from that frame. In the case illustrated by figure 27 starting 

at station 0, the bending moment for-

(1) Station 0= 0. 

(2) Station 10= - 1,000X 10= -10,000 meter-pounds. 

(3) Station 20= ( -l,OOOX20) + (2,000X 10) =0. 

g. An easier method of computing bE ding moments is to sum up 

the areas under the shear curve. Thus in figure 27, for station 20, 

the bending moment= 10,000- 10,000= 0. For an airship in static 

equilibrium, when the center of gravity is vertically below the center 

of buoyancy, the bend-ing moment c_urve returns to zero at both ends 

of the airship, since the summations of positive and negative areas 

under the shear curve are numerically equal. 

h. Table IV, extracted from "Airship Design," by C. P. Burgess, 

of the Bureau of Aeronautics, United States Navy, shows loads, shear, 

and bending moments on the ZR- 1, computed in accordance with 

the method described therein. 

i. In computing aerodynamic loads, shear, and bending moments, a 

method. somewhat similar to that described above is employed. 

(1) Upturning dynamic forces on the hull are computed, using the 

Munk formula. This formula is omitted here as it involves mathematical computation beyond the scope of this manual. The forces 

so determined are distributed to the frames as concentrated loads. 

(2) Excess static weight or buoyancy is then distributed to the 

frames in proportion to the cross-sectional area at the frames, unless 

known eccentric loading shows this distribution to be greatly in error. 

(3) Dynamic force on surfaces is then distributed to proper frames. 

This force, as shown in paragraph 39c, is given by the relationF= (Vol) v2

[a(kz- k1) sin 28 

63 
TM 1-320 

43 AIR CORPS 

TABLE IV.-Loads, shear, and bending moments in U. S. S. ZR-1 

when the gross lift is 136,631,. pounds 

[This table reproduced from Airship Design, by C. P. Burgess, by permission of 

the Ronald Press] 

Station Gross Fixed Dispos- Total Load Shear 

Bending 

able moment meters lift weight weight weight m. 

Pounds Pounds Pounds Pounds Pounds Pounds Pounds 

o ___ ______ 307 2, 618 0 2, 618 - 2, 311 10 ______ ___ - 2, 311 1,453 1,877 0 1, 877 - 424 -23, 110 20 _________ - 2, 735 2,812 1, 902 0 1, 902 910 - 50,460 . 30 ___ ____ __ - 1, 825 4, 496 1, 991 2, 276 4, 267 229 -68,710 40 _________ - 1, 596 5, 789 2,328 2,200 4, 528 1, 261 -84, 670 50 _________ - 335 7, 128 2,389 5, 182 7, 571 - 443 - 88, 020 60 _________ - 778 8, 218 5,858 1, 512 7, 370 848 -95,800 70 _______ __ 70 8, 985 2, 708 2,378 5, 086 3, 899 - 95, 100 80 _____ ____ 3, 969 9, 402 3, 091 5, 656 8, 747 655 -55, 410 4, 624 90--------- 9,510 9,483 6, 100 15,583 - 6, 073 - 9, 170 100 _____ ____ - 1, 449 9,540 3, 224 6, 055 9, 279 261 -24 660 

uo __ . ______ - 1, 188 ' 9, 584 3,069 5, 704 8, 773 811 -36, 540 120 __ _____ __ -377 9, 560 8, 183 5, 016 13, 199 - 3, 639 -40, 310 130 ___ ______ - 4, 016 9, 536 3, 096 1, 790 4,886 4, 650 -80,470 140 ___ ____ __ 634 9,417 3, 064 5, .562 8, 626 791 -74, 130 150 ___ _____ _ 1,425 9, 003 2, 712 5, 406 8, 118 885 - 59, 880 

}6() _________ 2, 310 8, 169 8,057 2, 259 10, 316 ~. 147 -36, 780 170 _________ 160 6, 778 3, 076 2, 653 . 5, 729 1, 049 -35, 150 180 ___ __ ____ 1, 212 4, 467 3, 212 1, 227 4, 439 28 -23,030 1, 240 188- ---- ---- 2, 222 1, 520 0 1, 520 702 - 13, 110 1, 942 194.75 __ ____ 258 1, 100 1, 100 2, 200 - 1, 942 0 

136, 634 74, 558 62. 076 136, 634 0000 . 

I I 

( 4) The load on each frame, shearing forces, and bending moments 

are then computed and tabulated as explained in d, e, f, g, and h 

above. A table so prepared, extracted from Airship Design, is given 

below. 

64 
AIRSHI P AERODYNAMICS 

TM 1-320 

43 

TABLE V .-Aerodynamic forces, shear, and bending moments in U. S. 

S. ZR- 1 at 85 foot/seconds and 5° 42' pitch 

Turning Unbal- I I Bending ' anced I I moment Station meters forces ' L Load Shear static I ' . on hull I I 10 

weights 1 pounds I 

- 1 Pounds , Pounds 

o ________________ _ -820 -57 - 877 0 ~---- ---- . -------- 10 _____ ____________ - 1,032 - 179 0 2, 3oo 1 l. 089 - 877 -8, 770 20 __ __ ____ ___ ______ -1, 200 - 334 I 2, 300 ! 766 212 -6,650 

ao _____ ____________ -1, 228 -500 3. 754 2.026 978 3, 130 

40 _____ ____ __ __ ____ - 1, 180 - 665 I 0 4. 937 30 092 3, 004 33, 170 50 _____ ____ ___ __ ___ ' -985 ..:.... 816 I 2, 300 499 6. 096 I 94, 130 60 _____ ________ ____ - 755 - 933 - 1. 688 I 

-------- 6, 595 160, 080 I 70 _________ ____ ____ - 494 - 1, 020 ---- ---- - 1, 514 4, 907 209, 1~0 80 _______ __ ___ ___ __ - 151 - 1,067 -------- -1. 218 3. 393 243,080 

90----------------- - 55 - 1, 077 -------- - 1. 132 2, 175 264,830 100 _____ ____ ______ __ 0 - 1, 077 -------- -1.077 1, 043 275, 260 110 _____ _____ _______ 0 - 1,077 -------- - 1, 077 - 34 274, 920 120 ________________ _ 0 - 1, 077 -------- -1.077 - 1. 111 263,810 130 ____________ _____ 41 - 1, 077 -------- -1. 036 - 2, 188 241, 930 140 _____ ___ ___ ____ __ 151 - 1, 067 -------- - 916 - 3, 224 209, 0690 150 _____ __ _____ ___ __ 494 -1, 030 -------- -536 - 4, 140 168, 290 -L60 _____ _______ ___ __ 851 - 933 -------- - 82 - 4, 676 121, 530 

170- - - -- -- --- -- -- - . - 1,346 - 783 -------- 563 - 4, 758 73, 950 180 _________ ________ 1,891 -563 -------- 1, 328 - 4, 195 32, 000 188 ____________ _____ 1, 780 - 250 --------, 1, 530 - 2, 867 9,020 

194.75 __ , ---0 -------- 1. 346 - 9 . 1. 337 -1. 337 0 --------, 

-15,591 15. 591 000 I 

I 

j. To determine total shear or bending m<?ment at any frame, it is 

necessary to add results obtained from static loading to those computed 

from aerodynamic forces. 
TM 1-320 

43-44 AIR CORPS 

( 1) To obtain total shearing force between stations 30 and, 40: 

Pounds· 

Shear due to aerodynamic forces from table V = 3, 004 

Shear due to static loading from table IV =-1, 596 

Total shearing force = 1, 408 

(2) To obtain total shearing force between stations 80 to 90: 

Shear due to static loading 

Shear due to aerodynamic forces 

Total shearing force 

(3) To obtain total bending moment at station 130: 

Pounds 

- 4 624 ' 2,175 

6,799 

Meter pounds 

Bending moment due to static loading from table IV = - 80, 470 

Bending moment due to aerodynamic forces from table V = 241, 930 

Total bending moment = · 161, 460 

44. Conclusion.-While static means of sustentation and control 

are available to lighter than air aircraft, the intelligent pilot should 

constantly bear in rriind the effects of aerodynamic forces on his airship. He must understand the relation of velocity to resistance, power 

requirements, and fuel consumption. He must be cognizant of the 

characteristics of his propellers and be able to make utmost use of 

variable pitch should his propellers be·capable of adjustment in that 

regard. He should comprehend the theory of airship stability and 

be alert to augment that stability by use of his controls. It is essen-· 

tial that he at all times appreciate effect of dynamic forces on his flight 

path in regard to both direction and altitude, and be able to assist his 

static control by dynamic means whenever necessary. F inally, he 

· must be aware of the stresses to which his airship is being subjected 

and, knowing maximum performance for which his aircraft was designed, so vary the velocity as to preclude possibility of exces.S 

structural stresses. 

[A. G. 062.11 (9- 11-40) .] 

BY ORDER OF THE SECRETARY OF wAR: 

OFFICIAL: 

E. S. ADAMS, 

Major General, 

The Adjutant General. 

DISTRIBOTION : 

G. C. MARSHALL, 

Ohief of Staff. 

D 1 ( 3) ; B 1 ( 2) ; IR 1 ( 5) -; IBn 1 ( 10). 

66 

II.!. GOVERNMENT PRINTING OFFICE: 1$41 

For sale by the Superintendent of Documents,. W.ashington, D. C. · · - .. . - Price, 15 cents