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(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. There 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 

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so far as translational motion is concerned, but they act together to give a moment tending to depress 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 airship 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 tunnel, 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- 

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