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Based on the laws of thermodynamics, shouldn't it be theoretically impossible for a non plug-in hybrid vehicle to ever be more fuel-efficient than a vehicle that connects the same engine directly to the wheels without converting it into electricity first?

The only energy input on a non plug-in hybrid is the gas tank, and therefore any energy leaving the vehicle in the form of torque must have originated in that tank. When the vehicle is driven, electrical energy leaves the battery and is converted into kinetic energy by the motors.

Once the battery is depleted, the gasoline engine begins turning, converting chemical energy into kinetic energy, which turns the wheels directly as well as turning an alternator which converts the kinetic energy into electrical energy, charging the battery.

But since all this energy is, no matter what, coming from that gas tank, it really doesn't matter what form it's in when it's turned towards moving the vehicle; it still started out as the same amount of chemical energy!

Furthermore, no conversion of energy can ever be one hundred percent efficient: some is inevitably lost to heat and other forms of unusable energy. So chemical -> kinetic -> electrical -> kinetic will always be less efficient than chemical -> kinetic.

The only ways I can think of a hybrid being more efficient is through energy recovery; the regenerative breaking system turns kinetic energy back into electrical instead of turning it into heat and wasting it like in normal brakes. But will the energy recovered by this method ever be greater than the energy lost by the extra conversions, as well as the increase inertia from the heavy components?

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Short answer: most of the gas you burn goes into heating the breaks, not into moving. At least the way most people drive. So recovery opportunities are enormous. Also, hybrids tend to go hand-in-hand with being able to turn their engines off while not needed - idling wastes a non-negligible amount of fuel too. –  Chris White Jun 3 '13 at 2:06
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What you say is correct in principle, but ignores the important fact that practical car engines are horribly inefficient, and their effeciency changes quite a bit over the range of speed and power required to move the car. Note that this is the point of transmissions. At best they don't loose any power, but they make the overall process more efficient by allowing the gasoline engine to operate at a more efficient point.

In one way, you can look at a hybrid as having a wide-ranging finely adjustable transmission, but there's more to it than that. The efficiency of a gasoline engine is in part related to what fraction of peak power it must put out. If the gas engine is the only mechanical output in the car, then it must be sized to supply peak power. However, most of the time much less than peak power is needed, so the engine often runs at a inefficient point.

With a electric motor available to fill in the when peak power is demanded, the gas engine can be sized smaller and it is easier to make it more efficient over most of the normal operating range. It also allows for the option of not using the gas engine at all at very low power levels where it would be very inefficient. Instead it can effectively be run in bursts of more efficient operation. For example, if the gas engine is 3% efficient at 500 W, but 6% efficient at 1 kW, then you're better off running it at 1 kW half the time instead of at 500 W all the time. With a hybrid, you have this option. With just a gas engine, it's stuck having to produce whatever power is demanded at the moment, regardless of how efficient that is.

I have a Honda Civic hybrid, and I can tell you this stuff really works. I routinely get 50 miles/gallon minimum on the highway, often substantially more. The engine is physically small for the size car, and it has been specially designed to be easily shut down and restarted. Going down a hill, even at highway speeds, the engine often turns off. If the hill is steep enough, the motor is run as a generator and charges the battery. When I get to the bottom of the hill, I can see that for a little while the control system uses the electric motor to keep the car going at the set speed (this is all with cruise control engaged), then eventually gives up and switches on the gas engine. I can feel a slight klunk when that happens, and the charge indicator goes abruptly from discharge to charge.

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Just to note, I wasn't debating that the technology works- just asking how it works. That clears it up, though, thanks. –  Schilcote Jun 2 '13 at 21:46
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Regenerative braking is one thing, another thing is that in practice large powerful engines are generally less efficient than small engines (because a substantial fraction of driving time the engine is not fully loaded, see detailed explanation in Wikipedia on Active Fuel Management), and having an auxiliary electric motor allows using a smaller gasoline engine - that's why hybrid wins in overall efficiency.

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I figure it'd be because each part of the engine would have less inertia in a small engine. But unless Toyota has unlocked the secret of over-unity, that motor is not going to be able to help the engine out after the battery empties. –  Schilcote Jun 2 '13 at 20:51
    
Large engines are less efficient than smaller engines... Really? Do you have any reference to back that assertion? –  Deer Hunter Jun 2 '13 at 21:42
    
The article in Wikipedia explains this well, under light load a gasoline engine does not operate efficiently, see en.wikipedia.org/wiki/Active_Fuel_Management –  Maxim Umansky Jun 3 '13 at 1:51
    
Maxim, please revise the answer so that it could be less confusing. "Large engines are less fuel-efficient than smaller engines at the absolute loads required for cruising" - or something to that effect. –  Deer Hunter Jun 3 '13 at 6:33
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