For a basic explanation:

The two primary purposes and affect of feathers and vanes upon a shaft are to, as efficiently and as quickly as possible, "stabilize" the shaft when shot and "control" in flight.

As the arrow leaves the string, the feathers/vanes serve to straighten out the bending actions of the shaft (stabilize) and to guide and control the shaft in flight. The "control" aspect applies to the fact that a "fixed" blade broadhead will control and affect the flight and accuracy of the shaft if the feathers/vanes lose control. The size of the feathers/vanes become more critical with heavy setups (arrows) and as the speed of the shaft slows.

Therefore, for "fixed" blade broadheads, especially shot off the high-energy and fast compounds that are out there today, I personally would not use anything less than a 5" feather/vane.