AIR-SHIP PROPELLER PROBLEMS. 
CALVIN M. Woopwarb. 
1. Wuart 1s THE Horsze-PownrR REQUIRED TO PRODUCE A GIVEN 
PuLL orn THrust By MBANS 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 Ibs. 
Since the thrust forward, or pull upon the anchorage must 
equal the backward push upon the air, we have the general 
equation 
Be Ag er aa (T] 
in which p is the average push or action in ibs. 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 Ibs. 
Aw. . 
, being 
2g 
Awv gO tae 
and its kinetic energy is 
per cu. ft.; its mass is 
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 pir square foot in the cross-section 
of the cylinder of air, produces a flow or current like the fow 
or current thru an opening between two indefinitely large tanks 
of air in one of which the atmospheric pressure is 2117 tbs. per 
sq. ft., and in the other, 2117 + p tbs. per sq. ft. 
(1) 
