INTRODUCTION 



In the mass of literature on the Robinson Cup Anemometer many analytical and empirical 

 equations have been suggested to describe the performance of this instrument. None of the 

 purely analytical forms adequately consider the complicated aerodynamical processes upon 

 which the action of the anemometer depends. Indeed, the single point upon which most investi- 

 gators in the field agree is the futility of attempting any such purely theoretical treatment. The 

 need for a systematic investigation of the controlling effect of arm length, cup size and number 

 of cups was recognized by Patterson 1 and an excellent discussion of the problem from torque 

 considerations is presented by him. 



Recently large influences of a purely aerodynamic character not embraced by Patterson's 

 method have been recognized by Dryden- and Grimminger. 3 It is possible to develop a semi- 

 empirical equation whose parameters are in such a form as to enable them to be discussed accord- 

 ing to the concepts of modern aerodynamics, and it will be the endeavour of the author in this 

 monograph to present his various data in that form. 



GENERAL FORM OF THE ANEMOMETER LAW 



Empirical equations in the form of one or more terms of the power series 



V= ai +b,v+ Cl v>+ ■ ■ ■ 



(where V is the true wind velocity, v is the peripheral velocity of the cup centers and «i£id etc. 

 are constants) have been used from time to time, but the usefulness of such a form is restricted to 

 one anemometer for which the calibration curve is known. The constants cannot be related to the 

 fundamental parameters of the instrument in general. 



Lately Marvin 4 has employed an equation of hyperbolic form connecting V with N, the 

 number of cup turns per unit travel of wind, such that 



V + a 



where V is the wind velocity at which the cups just cease to rotate. Here again a satisfactory 



relation between the constants a, b and the parameters of the anemometer was not obtained. 



Marvin actually found that b depended on the length of the arms L alone for all the sizes 



of cups and arms which he considered. Now as b is the limiting value of N as V— >°o 



5280 v 

 and N=— —— (for L in feet and N in turns per mile of wind) it is evident that b, if plotted 



against L, is merelv 



£ 



j vs. L (Marvin's Fig. 9) 



The small variations of (v/F) v ^, a are obscured by this method of examination but it would 

 appear that it is a function of L alone. 



The ratio of the velocity v/V, however is nondimensional and can only be a function of L 

 alone if L occurs in a non-dimensional parameter where the other factors happen to have been 

 constants throughout the series of experimental tests. 



