On a Theory of the Cup-Anemomnter

[摘要] It is well known that the factor of the cup-anemometer varies with the wind velocity. It increases with decreasing wind velocity.Why the anemometer factor varies with the wind velocity? How the angular velocity of rotation of the anemometer depends on the true wind velocity? These are the subjects of the present memoir.Let us suppose that the couple of forces due to the winds which compel to rotate the anemometer is composed of two components due to viscosity and inertia of air. Their intensities are proportional to the velocity of wind and its square respectively. In the same way we can suppose two terms of the first and second powers of the speed of the anemometer rotation. In this case however we have to take the friction between the rotating part and the fixed one of the instrument into account, in addition to the resistance of air.Hence for stationary state of rotation of the anemometer we can assume the relation between the true velocity of winds V and the speed of rotation of the cup u as follows: aρV2+bV=cρu2+du where ρ is the density of air and a, b, c, d are constants.In practice of the ordinary observation of wind speed by the cup-anemometer, it is assumed that v=kuwhere is the scale value of the wind speed, and k is the ordinary anemometer factor. Then we haveIf we express the wind velocity which satisfies the last equation with V', we obtainIf we put k' for the variable anemometer factor, then it is clear thatThese equations show the relations between the true wind velocity or the variable anemometer factor and the scale value of wind velocity of the anemometer.As an example, let us take the experimental data for the 9-inch cup-anemometer in the Observer's Handbook of the Meteorological Office, London. Then we get the following numerical values for the constants of the anemometer:- α=0.7277, β=2.9193, m=0.3543. and accordingly for the true wind velocity and the variable anemometer factor we obtainThe calculated values of them by these formulae show fair coincidence with the observed ones in the Handbook.

[学科分类] 大气科学