Experiments on the Start and Stop of Windmill- and Cup-Anemometers with Particular Reference to Their Over-Estimation Factors

Threeand four-bladed windmill-anemometers and cupanemometers are started from rest in the wind tunnel and are also stopped from rotation in a still air, and their responses are compared with one another. The static torque coefficients are calculated from the observation of rotational speed versus time to be used in SCHRENK's parameter. SCHRENK's overestimation factors for both anemometers are evaluated into a single chart for rectangular wind waves. For sinusoidal wind waves, graphical solution of the equation of motion is carried out, from which the over-estimation factor is computed and compared with experiment due to DEACON. The phase lag is also obtained into a chart. 1. Object of the present experiment and analysis After we have conducted a systematic investigation of the design of windmill anemometers [1], we have remarked a somewhat appreciable difference between the observed wind course with it and that with the ordinary cup-anemometer. To clarify the cause, experiments on the stop of both types are carried out in the wind tunnel and in a still air. The anemometers are started from rest in the tunnel flow and also they are stopped from rotation in a still air. From these so-S called dynamic experiments the static torque coefficients are calculated assuming some equations of motion. The analysis is further pushed on to calculate the overestimation factor. For this purpose the above-mentioned simple experiments are found to play an unexpectedly important role. 2. The start of windmill-anemometer The equation of motion of a windmill-anemometer when started by a uniform wind speed can be written in the form where 1 is the moment of inertia with respect to the axis of the anemometer, 0) the angular velocity, 1 time, c, c' and c" are constants, and (0,„ is the final angular velocity corresponding to the wind speed V. It is seen the torque of a windmill changes against the rotation ratio mR/V (R is the windmill rarlins for blade angles near 60° at 75% radius as shown in Fig. 1, (half-stalled condition, Reference 1), and the constants c, c' and c" may be written as 1 (2) c' =2c, c" == where cdo is the dimensionless torque coefficient, p the air density and V the wind speed. Equation (1) can easily be integrated and we gei-, where co, is the value of 0) at 1-0. From the second solution of (3) we see C7C" = 0. ), at t=co. If a windmill is started from rest in a wind of uniform speed of V, and is observed at each time interval, the constants c and c' (also d') can be calculated and the starting torque coefficient cdo may be obtained. In Fig. 2 are shown the experiments conducted for Speedovane with threeand four-blader windmills (their forms and dimensions are given in Reference [2]) in the 1.5-meter wind tunnel of the Meteorological Research Institute. It is observed that the four-blader is superior to the three-blader in start, and the final indication is obtained in 70% of time of that for the latter. The calculated starting torque coefficient cdo is correspondingly, about 15%, larger for the four-blader than the three-blader. The starting-torque coefficient cdo is, on the other hand, tested in the wind tunnel as shown in Fig. 3. In this test the three-blader gives larger values of cao than the four-blader by about 15-20%. This fact is somewhat questionable and the reason is not yet well explored. The moment of inertia I is 0.000324 kgms2 for the three-blader and 0.000273 kgms2 for the four-blader, but they do not come into the calculation of cao. The developed surface area A is the same for both windmill blades,