Re:XB-1 First Supersonic Flight [video]
by scythe on Tuesday January 28, 2025 @06:41PM
(#42859620)
>Naively, traveling twice the speed requires 8x the power, so going over 4x the usual 550mph should mean over 64x more fuel burn
You've forgotten to cancel the denominator. If you use the drag relation of speed to power, you're multiplying by time, but the time is reduced by the speed. It would be more straightforward to use the F ~ v^2 relation between speed and force. So going 4x as fast for the same distance would require 16x the fuel, while going 4x as fast for the same time would require 64x the fuel. But the latter would obviously never happen in practice as you'd circumnavigate the Earth.
You've forgotten to cancel the denominator. If you use the drag relation of speed to power, you're multiplying by time, but the time is reduced by the speed. It would be more straightforward to use the F ~ v^2 relation between speed and force. So going 4x as fast for the same distance would require 16x the fuel, while going 4x as fast for the same time would require 64x the fuel. But the latter would obviously never happen in practice as you'd circumnavigate the Earth.