’I’M  1-320  27  AIRSHIP AERODYNAMICS  (b)  W  = Total weight of dead and live loading, acting through  center of gravity,  M.  (c)  R =  Resistance of envelope and appendages, acting through cen› ter of pressure,  P.  (d)  T=  Propeller thrust, acting parallel to axis of envelope at  distance  o  below  M.  However, if the airship is riding on an even keel, the moment of  thrust and resistance is unbalanced and will tend to nose the ship up.  F or this reason airships are customarily trimmed a few degrees nose  heavy when full of gas.  b.  Suppose that some force such as a gust of air should give the  longitudinal axis a slight tilt to the horizontal.  Depending on  static condition of airship and direction of inclination, six cases which  •  ar1se. are-e - (1)  Case N o.  i.-Airship in static equilibrium, nose tilted up. In  this case, if the angle between the longitudinal axis and the direction  of motion is denoted by  (}  and the angle between the direction of motion  and the horizontal by  a,  since the airship climbs at the angle of tilt,  (}=0°  and the airship will climb at the angle,  a.  (2)  Case No.  ~.- A ir s hi p  in static equilibrium, nose tilted down.  As before,  (} = 0°  and the airship will descend at the angle,  a.  (3)  Case No.  3.-Airship statically heavy, nose tilted up.  In this  event the airship will climb at a lesser angle than the amount of tilt,  and the longitudinal axis will make the angle  a+(}  with the horizontal.  (4)  Case No.  4.-Airship statically heavy, nose tilted down.  Be› cause of the heaviness, the airship will descend at a greater angle than  the inclination, the longitudinal axis making an angle of  a-&  with the  horizontal.  (5)  Case No.  5.-Airship statically light, nose tilted up.  This case  is similar to case No. 4.  The longitudinal axis makes the angle  a - 0  with the horizontal.  (6)  Oase No.  6.-Airship statically light, nose tilted down.  H ere  the airship will descend at a lesser angle than the inclination and the  angle between the horizontal and the longitudinal axis will equal  a+  D.  41  Lu= W  R=T  (2)  Moments about M:  (a) Moment  L$_{0}$= L$_{0}$ X0=0.  (b)  Moment  W  =  W  X  0= 0.  ( o) Moment thrust-resistance couple=  T  (  o  +d).  Obviously, for static equilibrium and constant ve.locity-