AIRSHIP AERODYNAMICS
'rM 1-320
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 extend-
ing 0.2 of maximum radiu s 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 pro
peller. 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 perp endicular 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 rotatio n
as its center.
Propeller th1'U8t.--Componen t parallel to propeller axis of the total
air force on the propeller . I ts symboli sT.
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.
Reynold~ number.-N ame given the fraction P-;lli which-
p= 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. I t 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 throu gh undisturb ed a:ir
to the product of propeller diameter by number of revolutions in
unit time, _ that is, Jv· Slip function is the primary factor con
trolli ng propeller performance. It is 1r times ratio of forwa rd speed
to tip speed of prop eller.
Sli pstream.- Stream of air driven astern by propeller. (The indraft
~- is sometimes included also.) ·
Speed, grouou.l .-Hor~zontal c•mponent of velocity of aircraft rela
tive 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 condi
tion .
.Automatic.-Stability dependent upon movable control surfaces
automatically operated by mechanical means.
Directional.-Stability with reference to rotations about the nor
mal 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 aircra ft due solely to disposition and
arra ngement 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 mechani
cal devices.
Lateral.-Stability with reference to disturbances involving
rolling, yawing, or side slipping, that is, distu rbances 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 dis
placed slightly £rom its norm al attitud e by rotati on 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 coin-
· AIRSHIP AERODYN AMICS
TM 1-320
monly used only of such flows as are not eddying, but the dis
tinction should be made clear . by the context.
Streamline flow.-Ste ady 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 produ ces appr oximately stream
line flow.
Surface, control.- Movable airfoil designed to be rota ted or other
wise moved by the pilot in order to change attit ude of airplane
or airship.
Tait group (or tail unit).-Stabilizing and control surfaces at rear
end of aircraft, includin g stabilizer, fin, rudder, and elevator.
(Also called "empennage.")
Tau heavy (air ship) .-Condition in which in normal flight the after
end of an airship tends to sink and which require s 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 aerody
namic or static conditions, or to both.
Thrust, static.-Thru st developed hy propeller when rotatin g at a
fixed point .
Tracto r propeller .-Propeller mount ed 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 genera l
classes in accordan ce 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
maintain ed. In the nonrigid, gas in the envelope is kept under suffi
cient 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 structu re is
provided to maintain shape of the hull. Usually the gas is at at
mospheric pressure, although in some cases a slight superp ressure is
maintained.
c. All types .have control and power plant cars and control sur
faces.
TM 1-320
0-6 AIR CORPS
(1) In small nonri gids cars are usually open and contain power
plant s as well as altitude and direction controls. Such cars a.re
usually suspended by cables attached to the envelope. In semirigid
and rigid constr uction cars are in contact with the keel which car ries
their load. Power plant cars are sepn.rate from the control car.
FIGUHE 1.-U. !:i. Army uuurigi<.l 1'(;-7.
.
(2) Control surfac es on nearly all airships consist of fixed ve~ti-
cal and horizontal surfa ces, ~tttached to which are elevato rs and
rud der. On nonrigids and some semirigids these surfaces are at
tached to the envelope by rigging. On I talian type semirigids and
on all rigid s control surfaces are support ed by metal framework.
d. Figur es 1, 2, 3, and 4 depict types of airships , showin g genera l
streamlined shape of the hull and arrang ement 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, reta rd the flight of the airs hip and
must be overcome by the power plant s acting through the thru st of
the propell er s. Power requirements in their turn affect fuel con
sumption and limit perfo~·mance of the airship. Hence a thorough
knowledge of resistance and power requirements ·is essential to
intelligent operation of airships.
AIRSH I P AERODYN AM I CS
•
•
TM 1-320
•
'i' ::.>
• t:l
--oS J:>
t:l
-...
CIS
> ...
"' en
'0
"' .. ·-...
'"' 0
'0
·-1>0
·-...
>.
!3 :..
< .
f/2
• :::;,
I • ('I
Ci:l
;;)
<:>
-c..
TM 1-320
6-7 AIR CORPS
b. The second class of aerodynamic :forces, sometimes called trans
verse :forces, is the result of use of control surfaces or of gusts en
countered 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 R S- 1.
'
is necessary because it is through these forces that control and
stability are effected.
S ECTION II
RESISTANCE
Paragrap h
Fluid resistan ce--- - - --- --- ----- - - ------- --- --------- - --- - ------ - --- ---- 7
Shape coefficients- ----------- -------- ------- ----------------- -------- - -- 8
Coefficient of skin fricti on_____________________________________________ 9
Resistance of streamlined bodY--- - - ----- ---------- ---------- ---------- --- 10
Prismatic coefficient ---- --- ---- ------- --- ------- - - --- --- ------- ----- --- - 11
Index of form etfi.ciency -------- --------- - - ----- ------------ - ----- ------ 12
Illu strative resistance problem------- ----- - - ---- --- ----- - - -------- ------- 13
Scale effect- - -------- - --- ---- ---- ------- -------- ------------ ---- - --- --- 14
Resi!;)tance of completely rigged n i rshiP------ ---- - -- --- ------------- - -- 15
Doceleration tesL- ------ ------- ----------- ---- ------ ---- ------ ---- - --- - 16
7. Fluid resistance. -a. B efore attempting the study of resistance
the student should be fami liar wjth the composition and nature of
AIRSHIP AERODYNAMICS
TM 1-320
the atmosphere, with density and specific gravity calculations, and
with the action of gravitat ional forces. These matters are discussed
in TM 1-325 .
b. Whenever a solid object moves through a fluid it encounters a
resistance to its mot ion. This resista nce may be considere d 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 trave l at consta nt
•
•
'
FIGURE 4.-U. S. Nnvy rigid Los .d.t~geles.
velocity unless some force is exerted to change its condit ion. To
enable the solid to maintain its motio n r elative 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 furn ished by the propeller
thru st.
(b) It can be proved mathematically that if air were incomp ressible
and nonvi scous, tha t is, incapable of offering resistance to shear be
tween the parti cles, the thru st of air partic les oppo sing the motion
of the solid would exact ly equal the thrust of the air assisting the
motion. H ence there would be no resistance to the motion. How
ever, in th& atmo sphere this ideal condition does not exist and the
resistance is proportional to the tota l kinetic energy of the deflected
particle s of air.
TM 1-320
7-8 AIR CORPS
(2) Pressure-diff erenoe theory.-Figure 5 shows the motion of the
part icles of an air stream passing a flat plat e 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 con
sidered as due to the difference between the pressures in front of and
behind the plat e.
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 is-
R v= K a:AV2 .
where Rv=ai r resistance due to pressur e difference.
A = cross sectional area norm al to the air strea m in
square feet.
V =velocity of motion in miles per hour.
K IJ)=an empirically determine d 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 standa rd (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 Com
mittee for Aeronauti cs, uses the formula:
. u2
Ro= K DAP2
where p = mass density of the air.
v= velocity of motion in feet per second.
K v=an empirical shape coefficient.
';' .is the dynam ic pressure per unit of area or the velocity head of
the air stream. This formula has more definite physical interpreta
tion than the engineering formula from both the momentum and
pressure-differe nce theorie s. Before studying aerodynamic dat a, the
system which is being used should always be determined.
b. Some of the first prac tical 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 variou s investigators until at present the store of in
formation on this subject is quite e laborate . Figure s 5 to 15 give
the action of the air on variou s sha pes together with the values of K.
AIRSHIP AERODYNAMICS
TM 1-320
. (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 percen t less resistance than the square
flat plate. Rectangle s have slightly high er value s of K than the
square plate · of the same area, the airfl ow 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. E iffel's constants for different
angles of incidenc e are as follows:
Angle of incidence
J •
10°
15° .
20°
0.00010
0.00059
L).00124
0.00193
0.00265
(3) Oonoave h.emisph.ere.- Expe1'iments have shown that the re
sistan ce of a hemisphere with the concave s ide facing the -dire ction
of motion is greater than that of a flat disk of the same exposed
285746 "--41 8