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> The faster the plane goes, the more fuel it consumes due to the drag increase by the square of the speed

This is not actually true. Drag is at max at around mach 1. After that it goes down again. If you go fast enough you can be very efficient.



Drag goes back from the transonic peak but not below what was at subsonic speed.

The gain comes from being able to fly in thinner air if the plan be is designed to survive the the transonic regime and supercuise, because mach speed becomes lower higher you fly and the air thinner, so lift available to subsonic planes is limited




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