Woodward — Air-Ship Propeller Problems. 5 



uppermost member of the frame truss. In these positions, the 

 propellers would create currents which would not sensibl}^ 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 



ZI 



p== 0.0515 



4 tx] 



P H. 



li-ris kept constant, pis also constant. 



4. Discussion of Formula [VIII]. 



„,^SP'Pl 

 275r "^ 550' 



If the value of P given in [IX], and the value of v' from [VI] 

 be substituted in the above, it becomes 



H' = 



275r "^ 375 



V .'[XI] 



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 ju.st eight times 

 as much mechanical work. 



* It 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 i)ropcrly 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 

 helieoidal blades should be changed. 



