46 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62 



For longitudinal stability, the following inequality must be satis- 

 fied : 



M,>Me 



Wa sin e>KV~f (6). 



For given incidence, f(d) and sin 6 are constant, and hence the 

 righting moment due to weights is constant. The upsetting moment 

 of the wind increases as the square of the velocity. At some critical 

 velocity the upsetting moment may preponderate and the ship become 

 unmanageable. 



This is the critical velocity first pointed out by Colonel Renard, 

 which led to serious difficulties in the early dirigibles. 



For a given design, it is possible from wind tunnel tests to deter- 

 mine this critical velocity, and by suitable additions to the horizontal 

 fin area or lowering of the car to insure that in operation the critical 

 velocity can never be reached. 



The tests as described above were repeated for angles of yaw. In 

 the first series, a single vertical fin of 5.6 square inches area was 

 fitted as shown in figure 11. The resultant forces are drawn on 

 figure 12. The model is very unstable, and tends to swing to the right 

 or left of its course until the axis makes an angle of about 40 degrees 

 to the wind. The fin area is obviously insufficient. It will be noticed 

 that the resultant force for 5 degrees yaw passes outside the model. 

 This is no doubt due to the arbitrary mechanical definition of resultant 

 force. The resultant force as drawn merely represents that force 

 which, acting along the line shown, will have the same moment about 

 the center of buoyancy as the complicated distribution of pressure 

 about the model. This experimentally observed moment might as 

 well be represented by a couple.'' 



To improve the stability of steering, a larger vertical fin and a 

 vertical rudder were next fitted and the test repeated. The rudder 

 was fixed in the plane of the fin. The resultant forces are shown on 

 the lower part of figure 12. It appears that the drift angle has been 

 reduced from 40 to 20 degrees, but that the ship is still unstable. It 

 is not practicable to fit more fin surface, and the remaining instability 

 must be met with the rudder. 



The rudder was then set at i6| degrees to the keel line and the test 

 repeated. The resultant forces shown on figure 12 are seen to lie 



^ This position of the resultant force at small angles was predicted by Sir 

 George Greenhill, and later verified experimentally by L. Bairstow, Tech. 

 Report of the Advisory Committee for Aeronautics, p. 35, London, 1910-11. 



