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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?

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  • $\begingroup$ I can't help but note that if one of the wheels actually touched the road, it would help if it would rotate along. I don't see how this is much different from the case where it doesn't touch the road. But I don't know for sure. $\endgroup$
    – Řídící
    Commented Sep 13, 2013 at 17:28

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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.

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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.

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  • $\begingroup$ Why the downvote? I admit, all my postulating is a bit muddled. But to say there is a simple yes or no answer to this short of actually measuring the drag is misleading. $\endgroup$
    – Bobbi Bennett
    Commented Sep 20, 2012 at 13:53
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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.

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  • $\begingroup$ By this argument, a rotating propeller would also increase drag, which is not the case, at least on an airplane. $\endgroup$
    – Bobbi Bennett
    Commented Sep 20, 2012 at 22:51
  • $\begingroup$ A propeller's blades can of course be used to create huge abounts of drag depending on the orientation of the blades. Propeller blades are constructed using aerofoil sections to produce an aerodynamic force, in a similar manner to a wing. Consequently the blades are subject to the same aerodynamics – induced drag, parasite drag, wingtip vortices, lift/drag ratios at varying aoa, pressure distribution changing with aoa etc. If you change the blade angle to zero there will be no lift componant to the force produced by the blades, but there will be drag. This is what is occuring with the wheel... $\endgroup$
    – MoonKnight
    Commented Sep 21, 2012 at 9:11
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    $\begingroup$ But the wheel spins in the slipstream of the car! That might be due to an asymmetric positioning of the wheel (like a mill-wheel dipping into a stream) or it might be due to a strange clockwise pattern in the spokes. Whatever the cause, the wheel -does not spin- when the car is not moving. There is flaw one in your model. Flaw two is the assertion that redirecting a portion of the air flow must increase drag. For instance, if I take in the outside mirror, that, too, would redirect a portion of the airflow, but it would reduce the drag. $\endgroup$
    – Bobbi Bennett
    Commented Sep 21, 2012 at 18:00
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    $\begingroup$ @Bobbi, rotating propellors do cause drag, this is why pilots of multi-engined aircraft "feather" the propellors of engines which are not working. $\endgroup$
    – RedGrittyBrick
    Commented Dec 17, 2012 at 10:58
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    $\begingroup$ @Bobbi, the rotation of the (unpowered) propellor causes additional drag. See Propellor Fundamentals "When an engine is shutdown in flight, an unfeathered propeller presents a large, flat surface face-on into the airstream. This can result in high drag on the airplane. Since the propeller is free to turn, it acts as a windmill, with the force of the air turning the propeller. The force extracted from the air causes drag on the airplane" Also see Autorotation $\endgroup$
    – RedGrittyBrick
    Commented Dec 17, 2012 at 22:52
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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.

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