| 
| 
| 
MURPHY: RESULTS OF WINDMILL TESTS. 93 
of the energy of the wind?”—Let A. B., Fig. 2, be a strip taken 
from the outer end of one fan of a windmill; it is curved, but for 
this purpose it may be considered a plane. This strip makes an 
angle Swith the absolute direction of the wind. c¢ represents the 
1a 
amount and direction of the wind, v represents the amount and di 
rection of the velocity of the surface A. B. Then the relative ve- 
locity of the wind, that is its velocity with respect to the moving 
surface A. B. is v,, the diagonal of the parallelogram constructed 
on vorcassides. v, makes an angle 6 with the absolute direction 
of the wind. If v=o, that is, if the wheel is held so that it cannot 
revolve the angle B=8. As v increases 8 grows less and less and 
finally becomes zero in which case v,, is parallel to surface A. B. 
In this case the surface receives no pressure from the wind—this 
portion of the fan is not utilizing any of the energy of the wind. 
If v be still farther increased, B becomes negative and the wind 
pressure is on the opposite side of A. B. This portion of the fan 1s 
then doing work on the wind instead of the wind doing work on the 
fan. The effective wind area of a fan being the projection of the 
fan on a plane at right angles to the relative velocity of wind over 
it—that is to v,, it is seen that as v increases the effective area de- 
creases. The energy which the fan takes from the wind is propor- 
tional to the effective wind area. It isseen then that this reduction 
of effective wind area is the reason why the efficiency is low at high 
wind velocities. If this effective wind area could be kept constant 
by some device for changing the angle of the fans then the relation 
between wind velocity and horse power might vary nearly as athird 
degree of the wind velocity. 
