MILITARY AERONAUTICS SQUIER. 137 



Pkinciple of Reefing in Aviation. 



An interpretation of (2) reveals interesting relations. The sup- 

 porting area varies inversely as the square of the velocity. For 

 example, in the Wright aeroplane, the supporting area at 40 miles 

 per hour is 500 square feet, while if the speed is increased to 60 miles 



per hour this area need be only y-^ = 222 square feet, or less than 



one-half of its present size. At 80 miles per hour the area v^ould be 

 reduced to 125 square feet, and at 100 miles per hour only 80 square 

 feet of supporting area is required. These relations are conveniently 

 exhibited graphically. 



It thus appears that if the angle of flight be kept constant in the 

 Wright aeroplane, while the speed is increased to 100 miles per hour, 

 we may picture a machine which has a total supporting area of 80 

 square feet, or a double surface, each measuring about 2^ by 16 feet or 

 4 by 10 feet if preferred. Furthermore, the discarded mass of the 

 420 square feet of the original supporting surface may be added to the 

 Aveight of the motor and propellers in the design of a reduced aero- 

 plane, since in this discussion the total mass is assumed constant at 

 1,000 pounds. 



In the case of a bird's flight, its wing surface is " reefed " as its 

 velocity is increased, which instinctive action serves to reduce its head 

 resistance and skin-frictional area, and the consequent power required 

 for a particular speed. 



Determination of k for arched surfaces. — Since arched surfaces are 

 now commonly used in aeroplane construction, and as the above 

 equation (1) applies to plane surfaces only, it is important to deter- 

 mine experimentalh' the value of the coefficient of figure k, for each 

 type of arched surface employed, especially as k is shown in some 

 cases to vary with the angle of flight a; i. e., the inclination of the 

 chord of the surface to the line of translation. 



Assuming a constant, however, we may compare the lift of any 

 particular arched surface with a plane surface of the same projected 

 plan and angle of flight. 



To illustrate, in the case of the Wright aeroplane, let us assume 

 P = 1,000 pounds = total weight = W. 

 A = 500 square feet. 



Y ;= 40 miles per hour = 60 feet per second. 

 a =7°, approximately. 



^, ^ P 1,000 



Whence ka — 



2AV2 sin « 2 X 500 X 60= X 

 = 0.0022 (V ^ foot-seconds) 

 = 0.005 (V = miles per hour). 



