’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 righting moment in case Nos. 4 and 5, but opposes it  in case Nos. 3 and 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 is nearly a right-line function of  the angle,  0.  So for practical purposes is the upsetting moment.  But whereas the righting moment is independent of the velocity, the.  upsetting moment varies as the square of the speed.  Obviously as  the speed increases a velocity will be reached where the upsetting  moment just equals the righting moment.  This is called the critical .  speed.  c.  For an airship without control surfaces, neglecting for the moment  propeller thrust and resistance, the critical speed would  be  reached  when- By the formula of Doctor M:unk:  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.  Tables of values of  k2  and k1 are given in National Advisory  Committee for Aeronautics Report No. 184.  From the M:unk equa› tion it appears that  111 c  varies directly as sin 20 and as the square of the  speed.  Combining the constant factors in the formula into one  constant,  Me:  H ence the relation for critical speed without fins becomes› where Vc=critical speed.  This would give a very low. critical speed.  For an Italian military  airship of the M type the critical speed without fins is 29 miles  per hour.  d.  I ntroducing the tail surfaces gives a much higher value of the  critical speed.  From the relations given in  a  above for case No.3, the  44  Me  sin  28Ve $^{2}$=  Wh  sin  (a–8)  Wh  sin  (a– 8)  Vc=-=  M e  sin 28  M t=Me  sin  28v2.  M .=  ( Vol)~ v 2 ( k2-kt)  sin 28  M e= Wh  sin  (a– B). 