TM 1-320  29  AIRSHIP AERODYNAMICS  S,ince the force on an inclined plate is approximately a right-line  function of the angle of inclination,  where 01 is a constant combining the surface coefficient and the  fin  a,rea.  As before-e - Hence  F$a+  Wh  sin  (a-8)=Me.  equation  of  stability at the critical speed, omitting the thrust-resistance  couple, iss-- Fs= 0.(Jvc 2  M e  sin  ’28v/= 0 1 8ve $^{2}$a+ 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. T his 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 fur› ther 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 cor› rect 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 propor› tional 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 criti› cal 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 