Tltl  1-320  27-29  AIRSHIP AERODYNAMICS  (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  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- Ship lxvlvy-No.se  elevt~tw/  L;  F"e  Le  FlGUU 21.- Forces on airsb1p in inclined fligbt (case No. 3).  M.+ Wh  sin  (a+O) >Me+ T(c+h).  43 