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08 



AIR-SHIP PROPELLER PROBLEMS. 



Calvin M. Woodward. 



1. What is the Horse-Power Required to Produce a Given 

 Pull or Thrust by Means of One or More Air-Ship 

 Propellers, When the Frame is Anchored? 



The net horse-power of the motor is measured by the kinetic 

 energy imparted to the air acted upon by the propeller. I as- 

 sume that an absolute velocity of v feet per second is given to a 

 cylindrical stream of air, originally still, and that the cross-sec- 

 tion of the stream (or streams if there be more than one propeller) 

 is the same as the area of the propeller circle (or circles). Call 

 this area A sq. ft., and let the given or required pull or thrust 

 be P lbs. 



Since the thrust forward, or pull upon the anchorage must 

 equal the backward push upon the air, we have the general 

 equation 



P = Ap [I] 



in which p is the average push or action in lbs. per sq. ft., upon 

 the cylinder of air. 



Hence the volume of air acted upon and set in motion every 

 second is Av; its weight is Awv, in which w is the weight in lbs. 



per cu. ft.; its mass is ,and its kinetic energy is-^r— , being 



g ^9 



the mass into half the square of its velocity. 



Now V is determined by p in accordance with the laws for the 

 flow of gases; but since p is small compared with ordinary at- 

 mospheric pressure, all changes in density and temperature may 

 be neglected, and the flow of air may be assumed to follow closely 

 the laws for the flow of liquids. 



The pressure of p pounds per square foot in the cross-section 

 of the cylinder of air, produces a flow or current like the flow 

 or current thru an opening between two indeflnitely large tanks 

 of air in one of which the atmospheric pressure is 2117 lbs. per 

 sq. ft., and in the other, 2117 + p lbs. per sq. ft. 



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