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Power of a Twelve Foot “Power” Windmill. 
| 
BY E. C. MURPHY. it 
if 
In Vol. VI, ‘No. 2, Series A, of the Kansas Universtry Quar- | 
: TERLY the writer gave the results of some windmill tests made lig 
during the summer of 1896 for the U. S. Geological Survey. The He | 
results of one of these tests, namely, that of a twelve foot power if 
Aermotor we wish to discuss more fully, especially from a mathe- is 
matical standpoint. | 
This mill is on a thirty foot steel tower. The wind wheel has Hf 
eighteen curved fans, each 44x183x73 inches, set at an angle of 
31° to the plane of wheel. The shaft is geared forward 6 to 1, so 
that the brake pulley makes six revolutions to one of wind wheel. Hie 
The method of measuring the wind velocity and the power of the 1 
mill are fully described in the article referred to above, and need 
not be repeated here. 
The curves CR, FS, and HT, Fig. 1, show the relation between i 
wind velocity and horse power for brake loads of 2 lbs., 4 lbs. and 
6 lbs. respectively on an arm of 351 inches. The curve AK is 
hi tangent to these curves and is the envelop of them. 
MATHEMATICAL RELATIONS DERIVED FROM THESE LOAD CURVES. | 
Curve AK. This curve crosses the axis. x, of wind velocity at | 
about x==5, and is seen to resemble a parabola whose axis is ver- 
tical and coincides with that of axis y (horse power). We may ei 
assume for it the form | 
| 
x?==-a--by (On) 
in which a and b are constants whose values are to be determined. 
We, see’ that) for x5, y=:0 and) for x==:15,yoan58,; hence a=25 i 
and b==34.5 and equation (1) becomes | 
x? =25-+345y (2) | 
x being wind velocity in miles per hour. eee 
If any other value of x, as 21, be substituted in (2) and the value 
of y computed it is seen to agree very closely with the ordinate of 
the curve. 
It is seen that the curve AK is tangent to the 2 lb. curve at 9 to Bi 
10; tothe 4 1b, curve at x==15, and to the 6 Ib. curve at x=2o0ito ke 
(191) KAN, UNIV. QUAR., VOL. VI, No. 4, OOT., 1897, BERLNS A. 
