'l'M 1-320
29 AIR CORPS
However, this relat ion 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 righ ting momen t in case Nos. 4 and 5, but o pposes it
in case Nos. 3 a nd 6. Case Nos. 1 and 2 are 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 i s nearly a right-line function of
the angle, 0. So for practical purposes is the upsetting moment.
But wherea s the righting moment is indepen dent of the velocity, the .
upsetting moment varies as the square of the speed. Obviously as
the speed inc reases a velocity will be reached where the upsetting
momen t just equal s the right ing moment. Thi s is called the critica l .
speed.
c. For an airship without cont rol surfaces, neglecting for the moment
propeller thrust and resistance, the critical speed would be reached
when-
M e= Wh sin (a± B).
By the formul a of Doctor M:unk:
M .= ( Vol)~v2 (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. Tabl es of values of k2 and k1 are given in National Advi sory
Committe e for Aeronauti cs Report No. 184. From the M:unk equa
tion it appears that 111 c varie s directly as sin 20 and as the square of the
speed. Combining the constant factors in the formula into one
constan t, Me:
M t= Me sin 28v2.
H ence the relation for critica l speed without fins becomes
Me sin 28Ve2= Wh sin (a±8)
Wh sin (a± 8)
Vc=-= M e sin 28
where Vc=critic al speed.
This would give a very low . critica l speed. For an Italian military
airship of the M type the critical speed without fins is 29 miles
per hou r.
d. I ntroducing the tail surfa ces gives a much higher valu e of the
critical speed. From the relations given in a above for case No.3, the
AIRSHIP AERODYNAMICS
TM 1-320
equation of stability at the criti cal speed, omitting the thrust-resistance
couple, iss--
F$a+ Wh sin (a- 8)=Me.
S,ince the force on an inclined plate is approxim ately 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 theore tica lly coincides with the longit udinal axis.
Hence 8 becomes zero and Vo becomes infinite . T his agrees with the
theoretical facts since with no angle of attack to the air stream the
transverse dynami c for ces become zero for all speeds and the static
righting moment would restore quickly the airship to the horizontal
position . A ctua lly, however, this can never be practically true , since
inertia of the airship ret ards chang e in direction of motion from the
hor izontal path and prevents the airship immediately adopting a line
of flight coincident with its longitud inal axis.
f. In the preceding discussion the controls have been considered to
be held in neutral. Actua lly by varying his elevator angle, the pilot
may increase materiall y the effect of the control surfaces. This fur
ther increases the speed which the airs hip may travel without loss of
control. If the airship is not longitudinally stable, or if in other
words it is being operated above its critica l speed, the pilot must cor
rect deviations from the chosen path as soon as they appear, , while
on a stable airshi p these deviatio ns would be capable of self-correction
if left manually uncorrec ted.
g: The statical righting moment varies as the fourth power of a
linear dimension of the airship, the ascensional forc e F being propor
tional to the volume and so to the cube of a linear dimension. All
aerodynami c moments, on the other hand, both on the hull proper and
on the tail surfaces, vary as the cube of a linear dimension. The crit i
cal speed is therefore prop ortional, for geometrically similar airships, to
~fa or to the square root of a linear dimen sion. A large airship can
therefore be stabilized with tail surfaces propor tionally smaller than
4o
TM 1....:.:320
29-Sl AIR CORPS
those necessary on a small one traveling at the same speed. An un
stable 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 sur
face 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 pres
sure on the nose. This is quite different from the condition of longitu
dinal stability where the elevator can be left locked in any particular
position and the airship will return to its original attitude if atmos
pheric 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 tend
ing to turn the airship farth er from its original course. This moment
corresponds exactly to the upsetting moment, Me, which opposes lon
gitudinal 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 diffi
cult problem in airplanes, is taken care of almost automatically in air
ships; 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 re
storing moment due to the low position of the center of gravity. Roll-
AffiSHlP AERQ.DYN AMI CS
TM 1-320
ing may be very uncomfortabl e 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 airshi p 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
thru st line increases the thrus t moment and lowering the car incr eases
length of suspensions and hence parasite resistance.
32. Summary.- a. Airship stabil ity may be summarized as
follows :
(1) Airship s 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 longitu dinal sta
bility. This problem is however of more intere st 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 thi s section as the appli
cation of fundam entals covered therein will be shown in section V.
SECTION v
CONTROL
Paragraph
General types-------- ------- -------- -------- --- ------------- ----------- 33
Directional - --------- -····--- ---- - ------ - --- ·- --- - - - ------ ----- - --...---- - - - 34
AJtitude--- ----- - -------- - ------------------- - - --------- ------ - ---- - --- 35
Reverse---- ------- -------------------- ----- ---- ------------------- ----- 36
Application of dynamic cont r ol to operation of airshiPS---------- ---- ------ 37
33. General types. -a. Control of airship s may be subdivided
into two classes, directional and altitude. On nearly all airplanas
these two types of control are so inter related 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 pilot s 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 constant ly 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 situatio n. Instances of the value of
coordination are too numerous to mention, but fortunately capable
pilots have little difficulty in achieving desired results.
TM 1-320
34 AIR CORPS
34. Dire ctional. -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 s uch as gusts. These must be overcome by
prompt applica tion 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 f ew
degrees. Then since the gusts strik e 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 reac
tion to rudd er control of the airship in a turn . When it is desired to
turn to the right, for example, the rudd er 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 rudd er. 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 farthe r 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 resultan t pressure is
therefore zero, but since one force is applied to the front and the other
to the rear, ther e is a r esultant turning moment tending to continu e
the twistin g to the right . As t he motion proceeds still farther, the
force on the left-hand side of the envelope becomes greate r than the
force on the righ t-h and 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 neutra l, this turn
ing to the right will continue, and in order to check the circling it is
necessary to put the rudd er over to the left of the envelope.
o. The turning radi us 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 rad ius. 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,
curiou sly enough, that the first effect on putting the rudd er over to
48.
.
AIRSHIP AERODYNAMICS
TM 1-320
the right is to shift the airship slightl y to the left so that if the air-
ship 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 obstruc
tion, 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, togethe r with several successive
position s of the axis of the airship , are indicat ed in figure 22.
e. It occasionally happ ens, especially when flying through foggy
atmosphere, that an obstacle will suddenly loom up in fro nt of the
r; I
1Ye
'Yr rrr \
(I)
'(Yr '(' Y,.
FIGURE 22.- rlction of ai rs hi p In a tu rn. F IGURE 23.-Actlon of alrsbl p in a ,·oid-
ing nn obst acle.
airship. To miss the obstacle the pilot must first put over the rudde r
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 gra vity will swing the car
to the outside. This action w ill so tilt the hu1l tha t the rudder will
become in part an elevator. .Air striki ng o n t he inside of the rud
der will depress the nose of the ship. This depression can be stopped
by prompt application of the elevator control s by the altit ude 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 . H ence the 'direction pilot must .
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 dy
namic means. Even though an airship takes off in perfect equi
librium it will not remain so. Changes occur in the static lift due
to changes in meteorologi cal 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 thor
ough know ledge of trim is however essential to intelligent control of
the airship.
(2) Under action of the stat ic 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 longitu
dinal 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 airsh ip 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 accom
plished dynamically by use of elevators in conjunction with thrust of
propell ers. 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 vertica l plane similar to that described in paragraph
34 for turning in a horizontal plane. However, in this case, the ele
vators must be held in the raised position to prevent the static righting
moment bringing the longi tudin al axis back to the horiz ontal.
(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 air
ships at very low speeds. It the speed falls below a certain definite
lSO
.
AIRSHIP AERODYNAMICS
TM 1-320
value known as the "reversing speed," control becomes reversed and
pull ing up the elevators causes the airshi p 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 elevator s, and the inclina
tion will then cease to increas e. 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 rever se 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 occur
rence when a nose heavy airship is being brought to a landing and due
to loss· of superheat becomes stati cally 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 situatio n in which revers e 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