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In SpaceX's webcast today they talked about the first stage getting back to Earth with twice the velocity as usual. I quote: "So 4 times as much energy means harder on the stage, and 8 times as much heating." I understand 2x the velocity means 4x as much energy, E=1/2mv^2, but why does that produce twice as much heat relative to the energy?

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    $\begingroup$ The energy is four times as much, but it is also delivered twice as fast, giving a factor of eight. $\endgroup$ – Ruben Verresen May 6 '16 at 22:28
  • $\begingroup$ @RubenVerresen make this an answer, it's great! $\endgroup$ – tfb May 7 '16 at 0:33
  • $\begingroup$ One should point out that this is also the case when you hit the wall in your car... twice the velocity means eight times the forces that will crunch the car and the driver/passengers... which makes it such a good idea to drive just a little slower... $\endgroup$ – CuriousOne May 7 '16 at 0:39
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Air friction is roughly proportional to the (magnitude of the relative) velocity squared. Power is equal to force times velocity (the time derivative of work, which is force times distance). Since the force is proportional to the velocity squared, then the power will be proportional to the velocity cubed.

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