

the Robinson Cup- Anemometer. 67 



Wind's Driving- Action. 



§ 4. To get a preliminary general idea of the driving action 

 of the wind, let us suppose each Robinson cup replaced by a 

 thin plank, infinitely long in the vertical direction and of 

 horizontal breadth b, the planes of the planks intersecting — 

 if we imagine them continued inwards — in the axis of rotation, 

 and suppose each plank attached to a horizontal arm of 

 negligible section. Let each arm and plank be rotated with 

 negligible velocity round the vertical axis, while a horizontal 

 wind blows with uniform velocity v. Let a denote the incli- 

 nation of the wind to the normal to the plank ; then, treating 

 the air as a perfect liquid, we have, by Lord Rayleigh's 

 formula*, for the driving-force per unit length of plank, 



F __ i rpY 2 b cos a, ^ 



4 + 7T cos a ' ' 



where p is the air's density. F acts normally to the plank at 

 a distance 



z = 3&sin«/{4(4 + 7rcosa)} . . . . . (2) 



from the central vertical line of the plank, on the side on 

 which the direction of the wind makes an acute angle with 

 the surface. There is thus a couple about the axis of rotation 

 whose value per unit length of plank is 



TrpV^cos* 



4 + 7TCOS« V n ' 



where I is the distance of the central line of the plank from 

 the axis of rotation. The angle «, and thus z, is to be taken as 

 positive when the direction of the incident wind makes an acute 

 angle with the horizontal line drawn from the plank's centre 

 outwards along the surface from the axis of rotation. There 

 is a continual variation in the magnitude of the resultant 

 force and couple, and the centre of pressure moves from one 

 side to the other of the central line every half revolution. 

 The distance between the extreme positions of the centre of 

 pressure is no less than 36/8. The wind-pressure, it will be 

 noticed, aids the motion in one half-revolution and opposes it 

 in the other. 



Suppose, next, the plank and arm to rotate round uniformly, 

 the velocity v at the central line of the plank being com- 

 parable with though less than V. The direction of v is 

 perpendicular of course to the arm. Let us first find the 



* See Basset's ' Treatise on Hydrodynamics/ vol. i. art. 138. 



F2 



