44 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62 



moment about the vertical axis through the spindle, M, was mea- 

 sured on a torsion v^'we with the model inclined o, 5, 10, 15, and 25 

 degrees to right and left of the tunnel axis. Similarly the longitu- 

 dinal and lateral components of resultant wind force in the horizontal 

 plane were observed, i. e., Rx and Ry. 

 The total resultant force is then 



R=Rx^+Ry'. 



The direction of this force is at the angle 



^ = tan-i ^^ 



Rx 



measured from the axis of the tunnel. The resultant force R has 

 an arm A, the perpendicular distance from the center of buoyancy to 

 the line of action of R. Thus 



The force R is then determined in magnitude, direction, and line of 

 application, and is laid out graphically on the model drawing for each 

 angle of inclination. 



Experiments were made with the model swung on its vertical axis 

 through the center of buoyancy to obtain the yawing moments, and 

 with the model on its transverse axis to obtain the pitching moments. 



The resultant forces for angles of pitch are shown graphically on 

 the side elevation of the model, figure 11. It appears that with the 

 horizontal fins fitted, the resultant forces pass forward of the center 

 of buoyancy. The model is, therefore, unstable when moving in the 

 direction of its longitudinal axis, and if left to itself will take a 

 " drift angle " of about 20 degrees up or down. In practice this 

 pitching moment is counterbalanced by the powerful righting couple 

 due to the weight of the car suspended beneath the envelope. 



For example: If the center of gravity of the whole ship be a dis- 

 tance d below the center of buoyancy, the righting couple for a pitch 

 of 6 degrees is 



M8=lVas'm6 

 where W is the total weight. 



On the other hand, the upsetting moment on the envelope due to 

 wind forces is a function of the inclination, as shown, and the velocity 

 squared, or 



Me^KV'fie) 



where i^ is a constant. 



