TECHNI CAL MANUAL }
No. 1-820
*TM 1-320
WAR DEPARTMENT ,
W ASHlNGTON, Pebr·um·y 11, 1941.
AIRSHIP AERODYNAMICS
Prepar ed under direction of
Chief of the Air Corps
SroriON I. General. Paragraph
Definition of aerodynamic s__________________ 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
Resista nce of streamlined body------ --- ----- 10
Prismatic coefficient----------- ---- --------- 11
Index of form efficiency____________________ 12
lllust rative resistance problem_______________ 13
Scale effect-------- ----- ------- --- ---- - ---- 14
Resistance of completely rigged airship ______ 15
Deceleration test -------- - ------ ------- ----- 16
III. P ower requirements.
Power require d to overcome airship resistance_ 17
Results of vari ous speed t rials_______________ 18
Burgess form ula 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 grav ity of air-
shiP----- ------------------ ---- ------ - --- 23
Center of buoyancy________________________ 24
Descrip tion of major axis of airship__________ 25
T ypes of stab ility_ _________________________ 26
Forces and moment s acting on airship________ 9/l
Dampi ng moment----- --- ------------------ 28
Longi tudina l stabilitY--------- ------- ------ 29
Directiona l stability_________ _______________ 30
Latera l sta bility- ------- --------- --- --- --- -- 31
SummarY--------- -- ---- - ------ ------------ 32
*Thia m anual supersedes or:a ll'lG-290 , November 16, 1929.
285746°--41 1
TM: 1-320
SECTION
AIR CORPS
V. Control. Paragraph
<Jenera! types______________________________ 33
Directional__ ______________________________ 34
Altitude-------- -------------------- - ------ 35
Re 36 verse ___________________________________ _
Applica tion of dynamic control to operation of
. h' airs Ips _________________________________ _
VI. Aerodynam ic 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
turn_____________________________________ 40
Force s caused by gusts______________________ 41
Empirical formulas for max imum aerodynamic
bending moment on hull and for forces on
tail surfaces----- ·------------------------ 42
Method of calculating shear and ben_ding mo-
ment 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.-Aer odynamics 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·
instru ction of airship student pilots and as a reference text for th~
rated pilot. A ccordingly the subject has been so approached as to ·
give the knowledge of aerodynamics essential to the operation of air
ships . 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.
AffiSHIP AERODYNAMICS
TM 1-320
3. Importance.-Ai rships are controlled in two ways, stati<-ally
a.nd dynami cally. The former method is discussed in TM 1-325 and
will be mentioned but incidentally in this manual. Because of the
existence of stat ic means of control, the study of aerodynamics may"
appear of minor importance to the operation of airships . This is
untrue . Stabili ty and contr ol are constantly effected by a combina
tion of static and dynamic forces. To insure safet y of the airshi p
and to preclude possibility of exposing it to dang erous conditiOJ:!.S, the
pilot must be aware of existing dynamic for ces 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 mois
ture, 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 terms have
been introduced into the English language covering vari ous aspects of
aeronau tical science. Report No. 240, Nationa l Advi sory Commit
tee for Aeronautics, defines the meaning of the most common of these
expressions, from which most of the following definitions have been
abstr acted :
.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.-Ge neric term for aircraft whose support ·is chiefly due to
buoyancy derived from . aerostatic forces. The immer sed 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 perpendic ular
to this plane is called the axis of the airfoil.
Air scoop.-Projecting scoop which uses the wind or slipst ream 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 contro lling the dire ction of motion. W hen its power
plant is not operating it acts like a free balloon.
Nonrigid .-Air ship whose form is maintained by the inte rnal
pressure in the gas bags and ballonets (fig. 1) .
Rigid.-Airsh ip 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 conjun ction with internal pressure in
the gas containers and ballonets (fig. 2).
The term "airship" is sometimes incorrectly appli ed 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.-An gle 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 neutr al
position. It is positive when trailing edge of the elevator is below
neutra l 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.
Angl e of pitch .-Acute angle between two planes defined as follows:
One plane includes lateral axis of the aircraft and direct ion of
the relat ive wind; the other plane includes lateral axis and longi
tudinal 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 aircra ft
must be rotated about its longitudinal axis in order to bring its
lateral axis into a horizontal plane. This angl e is denoted by
<I> and is positive when the left wing is higher than the right.
Angle of yaw.-Acute angle between dire ction of relati ve wind and
plane of symmetr y 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 perpendi cular to axis of rotation of propeller.
Usually caUed "blade angle."
Angle, rudder.-Ac ute 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 rati o of propeller blade.- Half the ratio of propeller diameter
to maximum blade width .
Awes of aircraft.- Three fixed lines of refer ence, usually centroidal
and mutually perpendicular. The longitudinal axis in the plane
AIRSHIP AERODYNAMICS
TM 1-320
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 perpen
dicular to the other two is called the lateral axis. In mathe
matical 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 pur
pose of redu cing load carried and thus altering aerostatic rela
tions.
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 mainta in gas pressure, thus preventing defor
mati on or structura l 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 circumferen ce 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 semi
rigid envelope to reinforce it against pressure caused by motion
of the airship. Sometimes called "nose stiffener" or "nose batten."
Buoyancy.-Upw ard 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 airfoi l 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,
TM 1-320
4 AIR CORPS
personnel, cargo, or equipment. It may be suspended from the buoy
ant 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.-A ltitude in stand ard 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 sec
tion, 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 airfoi l section) .-Line of straightedge brought into con
tact 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
pur pose 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 pro jection of airfoil section on its chord.
Its symbol is c.
Oont1•ols.-General term appli ed to means provided to enable the pilot
to control speed, direction of flight, altitud e, and power of aircraft .
D1•ag.-C omponent parallel to relative wind of tota l 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 instrum ents. Its symbol is q.
:Elervator.-Movable auxiliary airfoil, function of which is to impr ess
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 dia
phragms into separa te gas compartment s or cells, and it may also
contain internal air cells or ballonets.
F light 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.
AIRSHIP AERODYNAMICS
TM 1-320
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 consist ing of a
covered elongated framewor k w hich incloses gas cells and supports
cars and equipment. May also be applied to complete buoyant unit
of any aerostat. In this latter sense sometim es called "gas bag."
lndraft (inflow) .-Flow of air from in front of propeJler into blades.
K eel (airship) .-Assembly of members at bottom of hull of semi
rigid or rigid airship which provides special strength to resist hog
ging and sagging and also serves to distribute effect of concent rated .
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 .-Foremo st edge of airfoil or propeller blade. Also
called "entering edge."
Lift.-That component of tot al air force on aircraft or airfoil which
is perpendicular to relative wind and in plane of symmetry. It
must be specified whethe r this applies to complete aircra ft or to
parts thereof. In the case of an airship this is often called
"dynamic lift." Its symbol is L.
Lift , gross (air ship) .-Lift obtaine d f rom volume of buoyant gas
equal to nominal gas capacity of the a;ircraft. Obtained by multi
plying nominal gas capacity by lift per unit volume of gas used for
inflation.
Lift, static ( aerostat) .-Re sultant 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 differen ce 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 furni shings,
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.-W eight empty plus useful load. Also called "gross
weight."
Pay.-Tha.t part of useful load from which reven ue is derived.
namely, passengers and freight.
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 .-Osc illation whose amplitude incres.ses con
tinuously until an attitude is reached from which there is no
tendency to return toward the origina l attitude, the motion becom- .
ing a steady divergence.
P erform ance CM'I'CUJteristics (air ship) .-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.-Distan ce which an element of a propeller would
advance in one revolution if it were moving along a helix of
slope equal to its blade ang le.
Mean geometrical.- Mean of the geometrical pitche s of the sev
eral elements. I ts symbol is p0 •
Standa rd.-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. I ts
symbol is Pa·
Pitch mtio .-Ratio of the pitch (geometrical unless otherwi se stated)
to the diam eter pj D.
Pitch speed.- Product of mean geometrical pitch by number of revo
lution s of propelle r in unit time, that is, the speed aircraft would
make if there were no slip.
Propeller area, proje~ted.-Total area in the plane perpendicu lar to:
propeller shaf t 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.