ATMOSPHERIC FRICTION. 
271 
These equations show that for high speeds both R and H , 
that is, both the mileage cost and propulsive power, in¬ 
crease with the velocity. In the limit the mileage cost 
varies as v 1>85 , while the power varies as v Q ’ 85 . By giving 
concrete, practical values to W, ?, and A, it is easy to show 
that both the resistance and power of a soaring plane have 
minimum values at some small angle, say between one and 
ten degrees. An example will illustrate this. 
Let it be required to find the power necessary to propel a 
soaring plane one foot square weighing one pound. The 
soaring angle, «, is given in terms of the velocity by the 
equation (c) by making k ? = 0.004, A being one square foot, 
W one pound, and v being miles an hour. The resistance 
may then be computed from the formula 
R = tan a + 2 /, 
f being the coefficient of friction, as given by table IV. The 
power and pounds carried per horse-power are obtained by 
obvious means. The computations for such a plane are 
given in table VI. 
Table VI. 
Computed Power and Speed for a Soaring Plane; Area, One Square Foot; 
Weight, One Pound. 
Soaring 
speed. 
Soaring 
angle. 
Com] 
Drift. 
puted resist 
Friction. 
ance. 
Total. 
Tow-line 
power. 
Tow-line 
horse load. 
Mi. hr. 
Deg. 
Lb. 
Lb. 
Lb. 
Ft. lb. sec. 
Lbs. 
30 
8.25 
0.145 
0.0170 
0.162 
7.13 
77.1 
35 
5.94 
0.104 
0.0226 
0.1266 
6.51 
84.3 
40 
4.52 
0.790 
0.0289 
0.1079 
6.32 
86.7 
45 
3.55 
0.0621 
0.0360 
0.0981 
6.39 
86.1 
50 
2.88 
0.0500 
0.0439 
0.0939 
6.89 
80.2 
60 
2.03 
0.0354 
0.0614 
0.0962 
8.50 
64.7 
70 
1.47 
0.0257 
0.0814 
0.1071 
11.00 
50.0 
80 
1.12 
0.0195 
0.1045 
0.1240 
14.56 
35.8 
90 
0.88 
0.0154 
0.1300 
0.1454 
19.17 
28.7 
100 
0.71 
0.0124 
0.1584 
0.1708 
25.00 
22.0 
39—Bull. Phil. Soc., Wash., Vol. 14. 
