The same physics applies to fast trains and other modes of transit. Fast electric trains have the advantage of not having to lug their fuel along with them at speed.
> consider that energy is a function of both power and time applied; if you double the speed to fly from say London to NY, would you cut the time to fly to less than 1/8th what it would otherwise be?
I think I understand what you’re trying to say, but note that by definition going twice as fast will get you there in half the time. Work and Energy are in alignment here because of the various efficiency losses you’re talking about.
The Concorde did have some reprieve in that it flew 20k feet higher than the usual cruising altitude.
https://aviation.stackexchange.com/questions/21881/at-what-a...
Ultimately high speed transport is not about conservation of energy. It’s about conservation of human time. Weighing that against the environment and other factors are important but few people weigh their total use of energy in a given day.
There are some military planes flying on biofuel, so ideally we’re not that far off.
HSR has its own unsolved problems. Like not being able to work over deep ocean... and insane infrastructure costs.
It’s bad, but not that bad. If you double the speed, you need 8 times the power, but only half as long for a given distance, so energy use is ‘only’ 4 times what you had.
(Of course, were talking about a very rough approximation that likely is so inexact that 8 might even be a better estimate)
To be clear, that's wrong, because of other factors; when you go faster in a given airplane, you can be more efficient at higher altitudes - mindful that wing size is dictated more by landing speeds than just how fast you want to go - if anything, you want smaller wings for weight, cost, and other considerations, but landing speed gets in the way. So, if you took the time to solve that equation for an airplane at, say, 30k feet, and for say 50k feet altitude, would you still get efficiencies over say, one of the modern , slower jumbo jets?
[1] https://web.mit.edu/16.unified/www/SPRING/systems/Lab_Notes/... (edited for line spacing)