Vertical Axis Wind Generators

Is there a linear relationship between rotations going into a DC generator and voltage coming out?

I'm building a small vertical axis wind turbine for a school project. I wasn't getting the voltage I needed with wind from the fan I had, so I decreased the radius to increase the rotational velocity. When I halved the radius (and doubled the RPMs), the voltage more than quadrupled. Is this an accurate relationship? Or should the relationship be linear and some other factor accounts for the increase in voltage?

Generators are usually wound to be linear over their usual operating range. When running slower than that the voltage will increase with speed but with no guarantee of linearity.

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