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My uncle and my aunt had a discussion over dinner about whether a car with a wind turbine could be used to make the vehicle more efficient. She thought it could, and he said it violated entropy. So I was dragged into the physics debate (kicking and screaming, of course), and I immediately tried to qualify under what circumstances the wind turbine would be useful. This method chaffs with my uncle, since it seems obvious it can't work.

But I'd argue it's not obvious. Before going on: I'm darn near certain that any turbine that impedes airflow will lower the efficiency of the vehicle. But what about a system that alters the aerodynamic profile of the vehicle such that the overall airflow is improved? Then you'd have something to exploit (effectively ruining the airflow improvement, but now with an input of mildly useful power). Clearly, streamlining the vehicle would provide similar and better results (since the improvements at not lossy from power conversion), but how over-engineered a solution can we devise that generates power? (read: not passive improvement)

I'd propose that the key is in exploiting the p*dV work done by the car on the environment by ramming aside air. A good portion of the air diffuses/bounces out, but the streamlines seem to exist, and there is a speed differential that could be exploited between the layers. The mechanism is tricky - since the greatest differentials are merely microns off the aerodynamic surface. It's possible entire inches are useful, but the need is to alter the velocity field so that the 'at rest' air is even closer to the surface. Only the differential's shape is adjusted to be closer to the car, no other change should occur.

I'm still undecided if this is a plane-on-a-conveyor-belt situation, though. If it is, it really is a waste of time. If note, it becomes rather interesting, but still prolly not economical. Feel like you've an idea?

Edit: The idea boils down to a mechanical manipulation of drag/air-bouyancy - instead of merely improving drag or whatever, make it better and then ruin the gains by introducing a mechanical component that converts the gains into useful power (at a loss, of course). This should be a bit more interesting, since in this restatement we've removed the useless violators of CoE and 2nd Law.

Yes, it is reaching around your head to scratch your nose, but I'm interested in mechanisms that can be implemented.


Final Edit: I got around to seeing what kind of magnitude this work would produce, and the result is that the work that can be had from this method is very small. The PdV work of air displacement is generally neglected. As for the profile change, the best I can figure is that I can't figure out a way to exploit it. Of course, that doesn't mean that it's not possible, but the only ideas I get are of intricate and folding micromachines - machines that are simply not reasonable to produce.

Comments

It isn't so much that it violates entropy as that it violates conservation of energy. Whatever energy is being used to turn the turbine is being provided by the fuel consumed by the engine. The only time this would not be the case would be during braking wherein you could use it as an energy sink (like regenerative breaking in a hybrid) or when going down hill when gravity would be providing the energy.

It isn't a plane-on-a-conveyor problem. This is, however, a waste of time.
During braking, the majority of the energy comes from air that has not been affected by the car, and is a different mechanism for generating power, as is regenerative braking which is siphoning momentum.

I'd contend there is another case, where the device merely changes the shape of the vector field of the velocity differential between the air touching the car and the air at rest far away.
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to
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--.
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(dist from car ^ vs velocity -->)
The energy obtained by the 'turbine' is simply the hysteresis created between the profile before and after the installation of the working 'turbine' (the '.'). The turbine must not interact with air not displaced by the car, lest it merely burden the vehicle with additional drag (by forcing a larger volume of air to interact with the vehicle).

Again, this could be replicated by simply lowering the drag on the vehicle via streamlining the shape and/or polishing the surface. I mean, it's simpler and does the same thing at a billionth the cost.

Importantly, this is not generating energy in any sense that violates CoE or the 2nd Law. It's merely making use of some waste energy by shaving capacitated energy out off the air immediately next to the car before it diffuses out and mingles with the environment (at which point any energy gains are taken from the environment at the expense of lowered fuel efficiency from increased drag).

As you said though, this is largely a waste of time, or more precisely it no doubt lacks a useful payoff. The energy to be had is likely very small or not worth it, like trying to use 100C liquid water that comes out of a power plant. Sure there's something to be had, but the energy density is so low that only the most intricate (read: expensive) devices can provide usable power. Also, the 'turbine' may need to be microscopic, since the largest velocity gradation is right next to the no-slip surface.

I'm going to update the post to reflect this...
Even if the turbine only interacts with air that is displaced by the car (which seems like it may be a physical impossibility), it is still less efficient than if there were no turbine where the air is passing through. The reason is because any energy being used to run the turbine has to be accounted for as originating from some source in the system. Here, the source must be the car's engine.
Taken more simply, what you're proposing is to create a system wherein there is an engine which charges a generator by moving a fan through the air. Regardless of what sort of coupling you use between the engine and the fan, it will always be less efficient than simply coupling the generator to the engine itself because the pneumatic air-drive system is so incredibly inefficient.
This is entirely true - it's a horribly lossy way to go about it. As I said, you'd be better off just leaving off the 'turbine' and accepting the increase in aerodynamic efficiency. But the goal here is to reclaim waste energy, not generate new energy. The note that this may be physically impossible from the air being unconstrained is likely the deal breaker. The argument to simply hook up to the engine is a distractor, since it mangles the idea into generating new energy; the counter should be whether the environmental reservoir and the waste reservoir can be separated, and whether there are regions near the vehicle where the volume of air is largely influenced by the car and less so a part of the environment (since any additional influence by the environment will constitute additional losses upon the engine), and whether this proportion of waste-to-environment is ever large enough to compensate for the inevitable fractional losses to the environment.

If it can get back any of the waste energy, what are the limits, and if not, why? I'd imagine that it is possible to get *some* back, since microscopic devices can greatly change and manipulate the aerodynamic profile of the vehicle. This could exploit some of the design flaws of the vehicle and improve some cars' profile (think boxy Cadillacs, not streamlined sports cars).

We could stop there and just accept our gains in gas mileage, or we can buy them back (at a loss) by also including a 'turbine', converting some of the gains back into usable power.

This is the interesting part, since such a mechanism - if refined enough - could be very useful elsewhere (think of wind power driving electric generating shingles or wall paneling). The fact that this is not a wise thing to mount on a car is a foregone conclusion - the only case it becomes effective is when it can improve the net aerodynamic profile of the car, and by then, why not just take the gains and be happy instead of squandering them by converting to another energy form (an inherently lossy process). But if such a mechanism *could* be made, it's easy to see where the pursuit of it could be very valuable elsewhere.
The problem is that there is no waste energy to be recovered. Given any design pair of designs wherein you have one model with a turbine and another without, the one without will have worse efficiency if they otherwise have identical aerodynamic profiles. Any time where we are including a turbine to exploit aerodynamic efficiencies, what we've actually done is to cause the aerodynamic efficiencies to fall. The fall in efficiency will always be such that a greater amount of power will be used by the engine to power the turbine than it would take the engine to generate an equal amount of power with a directly connected generator.

Where 'turbine' is in quotes

It would seem that this is, in fact, a plane-on-a-conveyor problem.

I can only identify one form of gradient that can be modified, and that is the velocity differential between the surface of the car and the at-rest atmo in the environment. The turbine would need to accelerate the [air affected by the car] to bring it closer to the [environmental atmosphere]'s velocity, namely the air affected by the car must be accelerated in the direction of the car's velocity. This mechanism should be aimed to directly counter the effect the car had on the air, and thus provides a net reduction of drag via mechanical means.

The question left then is whether the air can be accelerated at a net gain in energy. This would seem to be impossible. Bringing the air to a speed closer to rest atmo velocity requires a back force on the vehicle, bringing the speed closer to the car requires additional energy.

The exception is when the velocities are just allowed to slip better - but air is about as good a lubricant as you're going to get, and no mechanical device will improve this, lest it dampen turbulence or something. That's why it is a plane-on-a-conveyor problem.
Incidentally, thanks for the conversation. Your comments on the thermodynamics of the situation answer why we can't just jam a turbine on the back of the car.

I was still left with explaining why one can't merely go to work on the part that's already been written off as waste. That part's the part I was hung up on, since there were two forms that seemed to provide work - PdV due to displacement (which requires further interaction with the environmental sink of air to release it's energy), and undoing the velocity differential (which requires a shove forward, clearly unhelpful). More so, though, is I suspect that the velocity differential doesn't actually store any useful work anyhow, though I am getting confirmation of this from a mechanical engineer I know; without the assumption that the waste energy (from hitting the air) lingers near the car in an exploitable manner (via streamlines), there is simply no way to reclaim energy period (thermodynamics aside).

Either way, I'm sure now that such a simple solution cannot do good, and any active reduction of drag will cost more energy. The only viable solution is to passively reduce the drag of the vehicle.

(This is my summary of the results for future reference)