# How fast would someone have to run to run over water?

I was thinking about Flash, the superhero, or the little boy in the Incredibles.

There is one Yahoo answer that doesn't answer a lot. Especially, I don't think surface tension would help a lot for a human to run over water, I think one would have to build on the inertial effect of the water.

There is one empirical approach based on figuring out the speed at which bare-footed water skiing is done, but I wasn't able to find a decent number. Still the difference may be that a hypothetical runner would have to propulse herself over the water, which may or may not make the thing more difficult.

Hence, I raise the question here.

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I think it might not matter how fast you run, but how much you push down. – Alan Rominger Aug 20 '12 at 20:05
@AlanSE, I think one would have to assume that the downward component of force would be equal to (or slightly more than) the weight of the runner; I'm not sure how this could be varied. – AdamRedwine Aug 20 '12 at 20:43
Well, if you could run this fast... – Mike Dunlavey Aug 20 '12 at 21:02
@AdamRedwine if you are running with your feet hitting at an angle to the water then it will be a component of your forward speed. This is the limit to the speed of sprinters on a track, how hard they can push down, and so how much friction they can generate – Martin Beckett Aug 20 '12 at 23:14

## 1 Answer

Unsurprisingly this has been the subject of several scientific papers. In particular Google for papers by J. W. Glasheen and T. A. McMahon. They studied the basilisk lizard, but their results can be extrapolated to humans. It's debatable how reliable such a large extrapolation is, but the result is that the required speed is so far beyond human ability that we can safely conclude it's impossible without some artificial aid.

There's a summary of the results from the papers in this article and a more general summary here. The conclusions are that you have to run at a speed of 20-30m/sec, which doesn't sound too bad, but you'd need to generate a mechanical power of 12kW to do it. Trained athletes can just about manage half a kW, and most of us would struggle to generate 200W.

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Perhaps you should specify a kW of mechanical power, because it's quite common to expend over a kW of chemical energy - a difference that might matter to some calorie counters. – Alan Rominger Aug 21 '12 at 12:16
kW is a unit of power not energy. I think a human body produces about 100W of heat at rest. Obviously this will rise if you're exercising, but I'd guess only by a factor of two or three. If you were generating 12kW you would be nicely roasted. – John Rennie Aug 21 '12 at 14:22
100W of thermal power would correspond roughly to a 100 lb individual sleeping, which burns 89 calories per hour. That same individual doing intense biking can burn 1000 calories per hour, or 1.2 kW, but the bike would see a mechanical power of 200 W. I think that the 12 kW in your answer is mechanical power, necessitating not one, but two orders of magnitude higher energy expenditure than the intense biking example. – Alan Rominger Aug 21 '12 at 14:46
Ok, I think you have a fair point. If you were generating 12kW of mechanical energy you'd be be producing around 120kW of heat as well and you'd probably be too heavily charred to be worth eating. – John Rennie Aug 21 '12 at 14:53