42 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62 



xA-ny angular deviation of this axis will call into play moments 

 about the axes chosen above as well as forces along those axes. The 

 forces will cause the trajectory of the center of buoyancy to be 

 deflected, and the moments will swing the ship's axis. The motion 

 is stable if the forces and moments tend to restore the original attitude 

 and state of motion. 



If we consider only the moments produced by angular deviation 

 of the ship's axis, we may say that the ship is stable if the moments 

 tend to restore the original attitude, and unstable if they tend to 

 magnify any initial deviation. 



With a model held fixed in a current of air by a spindle passing 

 through the center of buoyancy, the stability of any attitude is 

 measured by the moments about the spindle. 



An elongated ellipsoid, as can be shown by hydrodynamic theory,^ 

 has three positions of equilibrium in a wind, corresponding to the 

 directions of the three axes. Only one position, however, is stable, 

 and the body tends to place itself broadside to the wind. For torpedo- 

 shaped bodies, the stable position is intermediate between the broad- 

 side-on position and the desired bows-on position, and for any such 

 body there is a stable " drift-angle " at which the body tends to hold 

 its major axis to the wind. This angle may be between 50 and 90 

 degrees to the wind. 



A feathered arrow with weighted head is stable for a translation 

 along the direction of its shaft. In general, it is not practicable to 

 fit sufficient fin surface at the stern of a dirigible envelope to give it 

 such weather-cock stability, but it is possible to reduce the " drift- 

 angle " to 20 degrees. 



A dirigible must be steered both in a vertical and in a horizontal 

 plane and its stability of route requires both horizontal and vertical 

 fins and rudders. 



A wooden model of a dirigible hull was fitted with rudders and 

 fins in accordance with usual practice and tested in the wind tunnel 

 at 35 miles per hour. The fin and rudder area was then adjusted 

 until a satisfactory combination was obtained. 



The principal interest in the research lies in the fact that it is gen- 

 erally possible to base the designed fin and rudder area upon such 

 experimental wind tunnel tests instead of rule of thumb. 



The model was mounted in the wind on a vertical spindle passing 

 through the center of buoyancy as calculated from the plans. The 



^Lamb, Hydrodynamics, p. 121. 



