I'm not sure how to describe this, but the problem came about as I was computing some acceleration profiles. Let's say you want to get up to Mach 3 (939 m/s) quickly. If you accelerate at 3 g's, this will take 31.923 seconds (not bad), and in level flight would cover a ground path of 14.991 km (kind of a lot, but not really comparable to typical flight lengths).

Only problem is, when it comes time to land, you have to slow down. If you want to do that quickly too, well, 3 g's in the "eyeballs-out" direction is a little hard on the eyeballs. Doing 1 g would take 3 times longer but also cover a ground path more than three times longer because of that pesky time squared in the equation for uniform acceleration ($\Delta x = \frac12 at^2$, if initial x and inital v are zero).

So you could gradually slow down over an even longer distance, or...is there some other, quicker way that doesn't involve much eyeballs out? Could you maybe fly a circle over the airport and decelerate that way, so that you feel the g-force mostly pointing down into your seat? Is there some other way you could "cut into another plane"?

The goal is to decelerate quickly so that the average flight speed (over the whole journey) is very close to Mach 3.

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    $\begingroup$ I'm voting to close this question as off-topic because this question belongs on Physics SE. $\endgroup$ – Simon Jun 27 '15 at 6:55
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    $\begingroup$ I really don't want to imagine someone circling the airport at Mach 3! $\endgroup$ – Dan Hulme Jun 27 '15 at 7:27
  • $\begingroup$ @DanHulme well okay, circle before they airport such that when your 360 degrees is done, you are lined up with the runway a few miles out. $\endgroup$ – DrZ214 Jun 27 '15 at 7:30
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    $\begingroup$ Just turn your seat around. $\endgroup$ – Peter Kämpf Jun 27 '15 at 8:48
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    $\begingroup$ As far as coping with the deceleration without your head snapping forward, you could always perform a maneuver like Pugachev's Cobra, essentially nosing up suddenly into an extreme AOA and then nosing back down. That both slows the aircraft and diverts the deceleration force downward in the direction of the pilot's seat, which pilots train to withstand. However, you'd likely either rip the wings off or send the pilot's head into his lung cavity if you turned the aircraft's main airfoils into airbrakes at Mach 3. $\endgroup$ – KeithS Jun 29 '15 at 20:30

If you need to have an average speed of Mach 3, then cruise at a speed higher than Mach 3 and land at Mach 0.2. And decelerate at a comfortable rate.

Or fly in a cryogenic wind tunnel to get the speed of sound down so much that Mach 3 is actual a very low speed.

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