Bicycle Wheel Drag in Slipstream I was recently driving behind a car that had a bicycle mounted on a carrier over the rear bumper.
The bicycle wheels were not bound so they were rotating in the slip-stream of the car.
I wonder, the fact that the wheels are turning; does this theoretically increase or decrease the drag on the car?
 A: The bike's wheel has a non zero torque slowing it down from friction. Therefore, if the bike wheel is spinning, you're extracting energy from somewhere - extra fuel. In fact the bike wheel is causing far more additional drag than the negligible amount needed to spin the wheel. 
A: It will increase it. If you first consider the case of a stationary car, where the bicycle wheels are rotating; as the spokes of the wheels move they will cause a very small rotational flow field (azimuthal flow field, in cylindrical coordinates taking the direction that the car is pointing to be the z-direction). 
Now consider the case you are considering with the car moving. This small rotational flow which is perpendicular to the bulk flow over the car (acting in our z-direction) will cause a small amount of flow to be redirected (the [mass] flux vector of the flow getting an additional component due the the roation of the wheel). This minor redirection will act like additional drag as far as the bulk flow is concerned. So the rotation will act to increase the drag coefficient of the wheel.
I hope this helps.
A: It is probably too complicated to be sure, with subtle shifts in air flow easily affecting the total drag. 
However, since things (usually) tend towards their lowest energy, and the wheels tend to spin when the car is moving, I would guess that is the lowest energy state, and hence the lowest total drag, compared to clamping the brakes on the bike wheel and stopping it from spinning.
But that statement, lowest energy state, and hence the lowest total drag, is BS. Things have no tendency towards a state of lowest energy dissipation!
So: 
Drag on the car * speed = power from the car. 
power from the car = power from the spinning wheel + everything else
Increased drag on the car = power the spinning wheel generates / speed
If the wheel does not spin, it does no work.
If the wheel spins freely, it does -very little work-, because it has very little friction. So the spinning wheel adds very little more drag than the fixed one.
A: The spinning of the wheel is a cconsecuence of the assymetry in the air stream it receives.
This rotation obviously reduces the drag experienced by the car. To explain it let us consider, instead the bicycle wheel, a wheel with blades like a windmill. It is obvious that the car travels more quickly when this wheel is free to rotate.
