I think the problem is that you're viewing power output strictly as the product of how much fuel is going into the cylinder rather than how much fuel-air charge is going into the cylinder. That's an important distinction to make in this case.What's happening with the F4U is that it has to run extremely rich in military to avoid detonation. When ADI is used, the mixture can be leaned significantly. While a greater charge weight is entering the cylinder, fuel makes up a smaller portion of the charge. So the specific fuel consumption is reduced. The F4U is a bit unusual in that the fuel consumption is actually reduced with water injection. Most other planes with water injection will see a power gain with no or minimal increase in fuel consumption but not the big drop like you see in the F4U.Here's an excerpt taken from a 1951 Navy manual on aircraft fuel that explains it some."When water or water-alcohol is used for high power operation, the fuel-air ratio is usually reduced from about 0.10, which is normal at high power, to about 0.08 at the instant the water injection is started. By this means the specific fuel consumption plus specific water consumption will be of the order of 0.70 pound per brake horsepower hour, which is no greater than the specific fuel consumption at the maximum power permissible without water injection."Here's a better explanation from Vee's for Victory!"When one views a "carburetor curve" it is apparent that as power is increased to "high power" settings, that the fuel flow is increased proportionally. Much of this fuel is being wasted, for the resulting mixture is "rich"; in fact, all of the oxygen has been burned out of the mixture. This extra fuel is simply acting as an internal coolant, providing a degree of protection against detonation. It can be considered as a very expensive form of ADI. This is obvious from the extremely poor efficiencies shown by engines running at takeoff power, particularly those that are air-cooled. "Since ADI fluid replaced the need to use fuel as an internal coolant, there is an immediate improvement in the efficiency as measured by fuel consumption. Of couse ADI fluid is consumed in the process, and it has to be carried aloft as well, but there is a considerable difference in cost and engine performance. As a result of the need to reduce fuel flow when using ADI, manufacturers provide a "derichment" valve on their carburetors which reduced fuel flow in proportion to the amount of ADI required to produce the desired power."
