Power to overcome drag is a cube of speed. If this is what you were trying to say you should have said it, though that doesn't really matter to what I was trying to point out.He changed his initial post from 2x speed is 4x fuel to 2x speed is 4x "power".
I say "power" because his use of "power" is wrong. He is discussing drag force. Power is Force x Velocity or P = Fd*v. If we only discuss Drag force (and neglect any other forces), then Fd = 1/2*rho*A*Cd*v^2 where rho is air density, A is cross sectional area, Cd is coefficient of drag and v is velocity. So Power, P = (1/2*rho*A*Cd*v^2)*v. Assuming that A, Cd and rho are constant between the 2 states, P ~ v^3. So power required for maintaining steady state at speed V2 = 2*V1 you get P2/P1 = (V2/V1)^3 = ((2*V1)/V1)^3 = 8 => P2 = 8*P1.
For anyone reading this, If you disagree with me, please be respectful in your reply.
edit: tagging @WuNgUn
The point I was making doesn't matter whether it is specifically 4x or 8x, and doesn't really matter if we are talking specifically fuel or power. You sure seemed to be implying that changing gears to keep the engine RPM at 2000 when increasing speed from 25 to 50 would require an insignificant amount of additional fuel/power. I was pointing out that If you were trying to say that it would take a lot of extra power/fuel to increase the RPM from 1000 to 2000 once you shifted, just not 8x a lot, then you did bad job of communicating that. You did seem to keep implying through your posts that the transmission makes a much more significant difference in required power/fuel when doubling speed then it actually does during normal driving.
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