The most fuel efficient engine for your car is the engine which produces, at it's peak, the peak power you'll need. The reasons why:
The average car engine is most efficient (fuel vs power) somewhere med-high up in it's rpm's. This is because of the way we control the engine. We limit the amount of air it can suck in by placing a door in the way (the throttle plate). This applies to gasoline engines only, diesels are different but the general rule at the bottom will still apply. This creates drag. More then enough drag to really hurt the fuel-power efficiency. As we open the throttle, this drag is reduced, and the fuel-power ratio increases until it peaks, then internal inefficiencies in the engine eventually start bringing it back down.
So you see that it will be most efficient at turning gas into power when you have your foot all the way down and the throttle plate completely out of the way . Unfortunately, unless you want to accelerate, this will produce way too much power.
You may find the most efficient engine in the world, but unless it's matched to the car weight/transmission/drag such that it's efficiency points are utilized, somebody who just picked the smallest engine that is sufficient to move the same car will get better mileage.
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