Why is 3 the optimal number of blades on a wind turbine instead of say 5 or more?
Answer:
Only accounting for potential flow, a one-bladed wind turbine is the most efficient turbine design. In very simple terms, this can be explained because the turbine blade sweeps 360 degrees before encountering its wake. However, only having one blade causes many problems structurally and dynamically, so it is not very feasible on a large scale.
A two-bladed turbine is the next most efficient because each blade sweeps 180 degrees before reaching the wake of the other blade, but you get something called yaw chatter when the turbine rotates (yaws) to face the wind. The yaw chatter is a harmonically oscillating yaw rate which results in a lot of noise, vibration, and stress on the tower. The dynamics of this are complicated, but this basically happens because there are two distinct principle axes of moment of inertia in the plane swept by the turbine blades: parallel to the blades and perpendicular to the blades.
A three-bladed wind turbine has infinite principle axes in the plane swept by the blades, which makes it the most efficient turbine design without having any dynamic issues. This is why pretty much all large wind turbines these days are three bladed.
However, what I’ve just said above does not take viscous and turbulent effects into account. There is experimental evidence that for smaller scale turbines or at higher speeds, adding more blades can actually increase efficiency and other things like startup speed.