274 
ZAHM. 
foot. It seems, therefore, most important to the science of 
flight to determine accurately the lift and drift of arched 
surfaces for various speeds and angles of advance. 
The frictional resistance of arched surfaces can be deter¬ 
mined by the method previously employed for wedges. 
Thus, resolving the friction on any element, ds, of the sur¬ 
face into components at right angles and parallel to the 
course and integrating the latter component over the sur¬ 
face, we have 
R = zfj- d ° d £ = 2fx ’ 
in which / is the average unit friction and x the length of 
surface fore and aft, the width being unity. Hence the 
frictional resistance of a plane or arched surface, soaring at 
small angles on a horizontal course, equals the horizontal 
projection of the surface multiplied by the average unit 
friction, as given by table IV; that is, 
R — 2 f S, 
in which f is the average friction and S is the projected 
surface. 
The reader may like a practical application of the above 
formula. Take, for example, the Wright brothers’ gliding 
machine of 1902. Its surface measures 5 feet fore and aft, 
spreads 320 square feet, and meets a total resistance of 30 
pounds when soaring 18 miles an hour. By table IV the 
average friction is 0.00302 pounds per square foot. Hence 
by the last formula 
R = 2 X 0.00302 X 320 1.9 lbs. 
The friction, therefore, seems to be only about six per cent, 
of the total resistance. 
For spindle-shaped hulls, or surfaces of revolution, the skin 
resistance is computed in a similar way. Thus resolving the 
