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I once meditated on the fact that a car, in downhill, would consume more fuel when in neutral to keep the engine on, rather than in gear. To keep the engine on when in gear, in fact, you mostly need the gravity and enough thrust to keep it rotating, and therefore no fuel (just motor oil).
This is what I'd expect cars to do but I'm probably missing something. How's actually the story? And if it's not like this, would/could my idea work somehow? (note: patent pending :P)
Note: This is specific to gasoline based engines.
Assuming your car was produced after the ~1990's it is equipped with a Deceleration Fuel Cut-Off (DFCO) system which cuts the fuel flow to the engine when the gas pedal is not depressed and the car is in gear. In this case it is more fuel efficient to stay in gear because you are letting gravity run the engine instead of fuel. In addition, it saves wear on your brakes because the partial-vacuum created in the engine leads to engine-braking.
In many states in the US it is actually required that you stay in gear when going downhill so that you have better control over the vehicle. To quote the Wikipedia article on energy-efficient driving:
Coasting with a vehicle not in gear is prohibited by law in most US states. An example is Maine Revised Statues Title 29-A, Chapter 19, §2064 "An operator, when traveling on a downgrade, may not coast with the gears of the vehicle in neutral."
The answer depends a great deal on the control system around the engine, and how fast you are going down the hill relative to the gear you are in.
For a basic engine system, like 1960s or earlier, at idle throttle setting the fuel usage would go up a bit with engine speed. The higher engine speed would make a higher vacuum, which would pull in more fuel-air mixture. If the downhill speed and gearing come out to the same engine speed as idle, then the fuel usage would be the same as idle. If you used a higher gear so that the engine would go slower, then it might use a little less fuel. However, there isn't a lot of engine speed room below idle. You run the risk of the engine bucking, which is not a good idea to subject the power train to.
To meet late 1960s pollution limits, some cars were equipped with a "decel valve". This sort of effectively stepped on the gas for you when the engine was undergoing rapid deceleration, or was externally driven (rapid deceleration is being "externally" driven from the momentum of the engine). The reason was that this condition with low fuel input would cause more pollutants to be emitted. The short term expedient was to give it more fuel. In such a case, running the engine faster than idle due to coasting down a hill in a sufficiently low gear would definitely use more fuel than idling in neutral down the hill.
With more modern control systems, it's hard to know. Some cars detect this condition and effectively shut down the engine. In that case, you are better off with the engine engaged than in neutral. For example, my Honda Civic hybrid routinely shuts down the engine and re-starts it as the conditions dictate. Going down a hill uses no fuel at all, and actually charges the battery a bit depending on speed and gear. Many modern cars are also capable of shutting off some of the cylinders under light load. In that case it again would take less fuel to keep the engine engaged than to let it idle.
