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You cannot not take drag into account since drag is what makes this thing rotating. For determining the wind speed you need to solve equations of motion which come from analysis of drag forces on the cups: bigger when wind blows on the inside of the cup, smaller when on the outside. More detailed info is here: https://www.eas.ualberta.ca/jdwilson/EAS327/eas327wind.html (ctlr+f cup anemometer) yet it is only for simplified case with two-arm anemometer, however still shows the correct way of reasoning.