W oodward—Air-Ship Propeller Problems. 5 
uppermost member of the frame truss. In these positions, the 
propellers would create currents which would not sensibly strike 
the motor frame and car, or any part of its rigging, and hence 
would not retard the ship. 
With given propellers it is seen that the horse-power required 
for a greater value of P increases more rapidly than does the 
value of P. For example, if P is made four times as great, the 
horse-power required is eight times as great. If P is multiplied 
nine times, the H must be increased 27 times. If however the face 
area of the propeller, A, increases equally with P, then the horse- 
power required to pull (or lift) will increase exactly with P. This 
appears from the equation above since 
H P 
= AOS TD nies 7 x 
p = 0.0515 J a [X] 
FP fr, 
ifs is kept constant, ps also constant. 
4. Discussion oF Formuta [VIII]. 
BF Pp 
= 975r * 550 
If the value of P given in [IX], and the value of v’ from [VI] 
be substituted in the above, it becomes 
Teeny Crk? |, 
w =| ee me |? Neo ae a [XT] 
H’ 
from which it appears that the horse power required to drive an 
air-ship increases with the cube of its velocity. If a certain 
horse-power with a certain arrangement of propellers will drive 
an air-ship 10 miles per hour, it will require 8 times as many 
horse-power to drive it 20 miles per hour.* This does not mean 
that the motor must make eight times as many revolutions per 
second, but the increased work of one revolution multiplied by 
the increased number of revolutions would involve just eight times 
as much mechanical work. 
* Tt will be seen later that a propeller fitted to a certain speed of the 
ship and to the pressure p upon the yielding air, is not properly fitted to a 
different speed and a different. backward pressure. It should also be remem- 
bered that while the value of the radius may be the same, the pitch of the 
helicoidal blades should be changed. 
