TM 1-320  4o-42  AIR CORPS  be equal to produce motion in a constant turn.  From this is derived  the relation- This relation gives results widely at variance :from the results o:f actual.  tests on full-sized airships, presumably due to the assumption that the•  resultant of the hull forces is zero.  Fortunately, the total bending  moment due to a steady angle of turn is only about one-fifth as great  as that due to an equal fixed angle of pitch where unbalanced weight  and centrifugal force are of equal magnitude.  41. Forces caused  by  gusts.-a. Very little is known concerning  maximum value of forces caused by gusts.  The following statement  very excellently sums up the situation :  1  "The existence of veritable fountains of upward rushing air whose  sides at times and places are sharply separated from the surrounding  atmosphere must be taken into account in the design of airships.  The  most violent of such currents, the tornado, combines vertical velocity  with rotation, but fortunately can be seen from a great distance, and  can and must be avoided.  The thunderstorm with large fully devel› oped cumulus tops is also conspicuous and avoidable.  It  would appear  to be :folly to enter such a cloud and subject the ship to the unknown  dangers of wind, rain, hail, and lightning.  Barring •such spectacular  hazards, there remain convection currents which the ship may run into  at full speed.  There is ample evidence that upward velocities as high  as 10 feet per second may be encountered.  This vertical air velocity u,  combined with the relative horizontal speed  v  of the airship, will give  -1  the effect of a change of pitch of tan  vu.,  b.  It  remains simply for the pilot, as stated in paragraph 38e, to  reduce the speed in bumpy atmosphere, especially  if  at the same time  the airship is developing large dynamic lift, positive or negative, as  then the stresses are already large.  42. Empirical formulas for maximum aerodynamic bendin g  moment on hull and for forces on tail surfaces.-a. The follow› ing formula has been developed :for the maximum aerodynamic bend- 1  From "Airship Design" by C. P. Burgess by •permission of tbe Ronald Press.  60  2a  sin 2  ’I!= R(k2-kl)  where ’I!= angle of yaw.  a=distance from center of volume to center of pressure  of tail surfaces.  R = radius of turning circle. 