If an 8 foot diameter wind turbine and a 4 foot one were rotating at the same number of revolutions per minute (RPMs), the blades tips of the 8 foot one would be moving at twice the speed through the air as for the 4 foot one. When you double the speed through the air for an air foil the drag increases by a factor of 8 while the lift increases by a factor of 4. Since the output power comes from the lift force and the drag acts to rob the mill of some of that power it then becomes advisable to design the larger mill to rotate at a slower speed to reduce the drag to lift ratio. On the other hand, you want the mill turning as fast as possible to minimize the physical size of the alternator and its expensive magnets. Since there are a lot of trade offs involved it turns out that designing the wind turbine for a tip speed ratio (TSR- ratio of the speed of the blade tip through the air to the air speed -same units) of 7, irrespective of the turbine diameter, seems to work well. So, the larger the turbine, the slower it rotates.
