FEBE0AET 19, 1909] 



SCIENCE 



285 



An interpretation of the second equation 

 reveals interesting relations. The support- 

 ing 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 500/1.52 = 222 square 

 feet, or less than one half of its present 

 size. At 80 miles per hour the area would 

 be reduced to 125 square feet, and at 100 

 miles per hour only 80 square feet of sup- 

 porting 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 one hundred 

 miles per hour, we may picture a machine 

 which has a total supporting area of 80 

 square feet, or a double surface each meas- 

 uring 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 

 weight of the motor and propellers in the 

 design of a reduced aeroplane, since in this 

 discussion the total mass is assumed con- 

 stant at 1,000 pounds. 



In the case of a bird's flight, its wing 

 surface is "reefed" as its velocity is in- 

 creased, which instinctive action serves to 

 reduce its head resistance and skin-fric- 

 tional area, and the consequent power re- 

 quired for a particular speed. 



Determination of fc for Arched Surfaces. 

 —Since arched surfaces are now commonly 

 used in aeroplane construction, and as the 

 first equation applies to plane surfaces 

 only, it is important to determine experi- 

 mentally the value of the coefficient of fig- 

 ure 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 lb. = total weight = W, 

 A = 500 sq. ft., 



y = 40 miles per hour ^60 ft. per second, 

 a ^ 7 deg. approximately. 

 Whence 



k(r = P/2AV^ sin o = 1,000/(2 X 500 X 60" X i) 

 = 0.0022 (y = ft. sec.) 

 = 0.005 (F = mi. hr.). 



Comparing this value of ka- with Lang- 

 ley's value 0.004 for a plane surface V 

 being in miles per hour, we see that the 

 lift for the arched surface is 25 per cent, 

 greater than for a plane surface of the 

 same projected plan. That is to say, this 

 arched surface is dynamically equivalent 

 to a plane surface of 25 per cent, greater 

 area than the projected plan. Such a plane 

 surface may be defined as the "equivalent 

 plane." 



Besistance and Propulsion. — The resist- 

 ance of the air to the motion of an aero- 

 plane is composed of two parts: (a) the 

 resistance due to the framing and load, 

 (&) the necessary resistance of the sustain- 

 ing surfaces, that is, the drift, or horizontal 

 component of pressure; and the unavoid- 

 able skin-friction. Disregarding the frame, 

 and considering the aeroplane as a simple 

 plane surface, we may express the resist- 

 ance by the equation 



R = Wtana + 2fA, 



in which R is the total resistance, W the 

 gross weight sustained, a the angle of flight, 

 / the friction per square unit of area of 

 the plane, A the area of the plane. The 

 first term of the second member gives the 

 drift, ihe second term the skin-friction. 

 The power required to propel the aero- 

 plane is 



