content_image/553840.jpg content_image/553842.jpg content_image/553843.jpg
equation of stability at the critical speed, omitting the thrust-resistance couple, iss-- 

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S,ince the force on an inclined plate is approximately a right-line function of the angle of inclination, 

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where 01 is a constant combining the surface coefficient and the fin a,rea. As before-e - 

Hence 

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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 

