196 KANSAS UNIVERSITY QUARTERLY. 
Aiea eto i 
tween the ratio for value of a, Pa being the normal pressure 
90 
on a plane making an angle a with the direction of motion of the 
wind, P,, being the pressure when a=90%. The curve AE is one 
given by Prof. Langley fora 12x12 in. plane, AF another by Prof. 
Langley for a 30x4-8 in. plane (ratio 6.2) the longer edge being :at 
right angles to direction of wind. The curves for sin®a and 
V sina are also shown. 
The fans of our wind mill have a mean width of 134%” and a 
length of 44 ins. The ratio of length to méan width is 3.1.’ The 
‘ ; } Pa 
fans are slightly curved. We do not know the value of -—-- for the 
90 
fans of this mill but these values lie somewhere between the values 
given by the curves AE and AF and they cannot differ much from 
those of \ sina. 
It is easily seen from the curves sin®o.and’V sina that any 
formula for the power of a wind mill based on the assumption that 
the normal pressure varies as sin®a is very much in error. The 
formula then for the normal pressure on an inclined surface like 
the fan of a wind mill when not moving is from equation (18) 
PO OOLOGAV Siac: (19) 
Pls Dee DemSGi tt, AVIS cQuitt, Cim ttn Det.secands 
PRESSURE ON MOVING FAN OF WIND MILL. 
In the formula (1g) the surface A is stationary and the wind is 
striking it with a velocity c. The fans of a wind mill are moving 
in a plane at right angles to the direction of the wind, Let v be 
the volocity of a strip of a fan at a distance R from the axis of wind 
wheel. 
In Fig. 3*, AB is this strip making an angle @ with the direction 
of the wind. Completing the parallelogram on v and c\we have v, 
the relative velocity, or velocity of wind with respect to moving 
fan. v, makes an angle a with the direction of the wind. 
The normal pressure on this strip would be that due to v, if the 
strip did not move away from the wind, but the strip being in 
clined to v, is moving away from it, and the velocity producing 
pressure is v, minus the amount that the surface moves away from 
P 
v, in the direction of v,. 
1 
a 
= — 
————— 
q 
