TM 1-320
.
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 air ship 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 revolut ion, the pressure distribnt .ion
has the following charactertist ics : ·
( 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 dis
tributions. 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 verti
cal plane, the following chara_cteristics are observed:
(1) Positive pressure on the nose lies almost entirely in a zone be
neath the axis.
(2) Plane of transition, BO, figure 17, is oblique with regard to the . . aX;J.S.
AffiSHIP AERODYNAMICS
TM 1-320
{3) Areas of redu ced pressure are not symmetrical. Their maxi
mum 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 positio n of its various parts unaltered in any
contingency.
b. Conditi ons necessary for specific stability are the invariahility
of-
(1) Shap e of envelope whethe r airs hip is in motion or not.
(2) Relative positions of envelope and cars and surfa ces.
c. Methods used to maint ain envelope shape are discussed in sec
tion I. Invariabili ty of suspension of the car from the envelope is in
sured by a rectangular system of suspensions braced by diagonal cables
------- ...
-
.
FIGURE 17 .- Pressure distribution on nlrsbip hull (longitudin a l axis Inclined to dir ectio n
of motion).
lengthwise and crosswise. These cables prevent any very app reciable
motion of the car in regard to the envelope in case of oscillations of
the airship in vertical longitudinal plane or in tran sverse plane . As
. will be shown later specific stability is absolutely essential to static
sta bility of airships .
d. W'hen invariability of suspensions has been assured, the position
· of the center of gravity of the airsh ip 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 oppo se the lifting power of
the gas. The position of the center of grav ity is natura lly not invari
able since the live load of the airship is varia ble. Usually for 'non
rigid airships the center of grayity, M , falls above the car and either
slightly above or slightly below the bottom of the envelop e (see
fig. 18).
24. Center of buoyancy. - The center of gravity of the ascen
sional 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 vert ical line passing through the center
of gravity, M, and for an envelope which has the form of a sym
metrical 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 longi
tudina lly, 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 descrip-
FiouRE 18.- Posltlons of · f h · d b cente rs 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) Horiz ontal 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 symmetrica l about
the axis of rota tion, 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
Advi sory Committee for Aeronautics, the system of r:otation outlined
in figur e 19 will be unif orm througho ut this manual.
a. Obviously any angu lar deviation whatsoever of the airship will
be found to be either pit.ch, yaw, or roll, or a combination of these
AIRSHIP AERODYNAMICS
TM 1-320
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 stabi lity is accomplished by two means, static and
dynamic.
(1) Strictl y speaking, the only real statical stability is that which
exists when the engines are stopped . Under this condition an air-
Normt~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 0 ~ I ~ 0 . ........... . ....
..9l..8
~
-;s s:l
~
t:l
Designa tion '"'» 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
Y- -z RolL __
LateraL __ ________ y y Pitching __ M z X Pitch __ I NormaL _________ z
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
requir ement 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 . W ere it not for these surfaces air
ships would become unmanageable at very slow speeds.
c. Stability may be classified fur ther . An airship in steady flight
has three types of stability, pitch or longitudinal, yaw or directional,
and roll about the longi tudina l axis. While these stabilities are all
corr elated in the case of an airplane, this is not the case with an air
ship, the three types of stability being independent of each other.
,.
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 followi ng discussion will be based upon the assumptions
for each situation that-
(1) Ascensional force remains constant.
(2) Tota l weight remain s constant.
(3) Speed remain s 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 traje ctory .while its longi
tudinal 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.
AIRSHIP AERODYNAMICS
'I'M 1-320
(b) W = Total weight of dead and live loading, acting throug h
center of gravity, M.
(c) R = Resistance of envelope and append ages, acting through cen
ter of pressure, P.
(d) T= Propeller thrust, acting parallel to axis of envelope at
distan ce o below M.
(2) Moments about M:
(a) Moment L 0 = L 0 X0 =0.
(b) Moment W = W X 0= 0.
( o) Moment thru st-resistan ce couple= T ( o +d).
Obviou sly, for stati c equilibrium and const ant ve.locity-
Lu= W
R=T
However, if the airship is ridin g on an even keel, the moment of
thrust and resista nce is unbalanced and will tend to nose the ship up.
F or this reason airs hips are customa rily 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. Depend ing on
static condition of airship and dire ction of inclinatio n, six cases which
•
ar1se. are-e -
(1) Case N o. i.-Air ship in static equili brium, nose tilted up. In
this case, if the angl e between the longit udin al axis and the direct ion
of motion is denoted by (} and the angle between the direction of motion
and the horizonta l by a, since the airship climbs at the angle of tilt ,
(}=0° and the airship will clim b at the angle, a.
(2) Case No. ~.-Airship in static equilibriu m, nose tilted down.
As before, (} = 0° and the airship will descend at the angle, a .
(3) Case No. 3.-Air ship 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. Be
cause of the heavines s, the airship will descend at a greater angle than
the inclinatio n, the longitu din al axis making an angle of a-& with the
horizontal.
(5) Case No. 5.-Air ship statically light, nose tilted up. This case
is similar to case No. 4. The longitudina l axis makes the angle a - 0
with the horizon tal.
(6) Oase No. 6.-Airship statica lly ligh t, nose tilted down. H ere
the airship will descend at a lesser angle t han the inclin ation and the
angle between the horizontal and the longitudinal axis will equal a+ D.
TM 1-320
27 AIR CORPS
c. Figur e 21 shows case No. 3. Figures showing the other cases
would be quite similar. Referring to figur e 21, the following forces,
lever arms, and moment s, all general to cases Nos. 1 to 6, inclusive, are
noted:
(1) Forces:
(a) L 9 = 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= H orizontal component of dynamic force on hull.
(/ ) F a= Resultant force on tail surfaces.
(g) L8 = Li£t of tail surfaces.
(h.) R a= Drag of tail surfaces.
( i) T =Thrust of propellers.
(j) t = Hori zontal componen t 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 equal s 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 . T heir difference, since the nose
force is slight ly t he greater, is calle d dynamic lift of hull. However,
both forces cause rotation in the same dire ction, and their moment
is refe rred to as dynamic upsetting moment, Me. I t will be evaluated
late r.
NOTE.-Tbe force beneath the tail has been omitted from the figure in order
to avoid confusion in the dra wing, the entire upsetting moment being treated
as though it were caused by the increased pressure under the nose.
AIRSHIP AERODYNAMICS
Tltl 1-320
(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. Ther e 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 depr ess 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 atti
tude, but acts always in such a manner as to oppose existing motion
and bring the airshi p 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 tunne l, but the mathe
matical 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 illustrated-
M. + Wh sin (a+O) >Me+ T(c +h).