OK, what’s the fastest a human can run the Olympic 100m?
I’m guessing we should be able to work out some theoretical limit but I’m not sure where to start.
There must be a point where the forces required become impossible to sustain without breaking yourself, any thoughts? Or some limit on the amount of energy availble over time? Or something?
Well, the most basic theoretical limit for any kind of matter or information to cover 100 m is 3.3x 10^-7 seconds (one third of a nanosecond).
The perfect race for the attention impaired. 
Purely theoretical, I know powerlifters aren’t sprinters, but here’s a thought experiment. Ronnie Coleman (Mr. Olympia from 1998 to 2005) weighs 285lb and has leg pressed 2300 pounds. Let’s assume that, since he only has one leg on the ground at a time, that he’s exerting a constant force of 1150 pounds. If we assume 285 of that is used to hold himself up, that leaves 865 pounds to act in the horizontal direction. 865 pounds is 3.85kN, and 285 pounds equivalent to 129 kg. F = ma, giving an acceleration of 29.76 m/s[sup]2[/sup].
Asafa Powell, in Athens, was recorded at 13.33 m/s. For our theoretical runner to get up to that speed, it would take .48 seconds, and they would have traveled about three meters. the remaining 3 meters would take 7.275 seconds. 7.25 + .5 gives 7.75. Adding another tenth of a second for reaction time (anything less than that gives a false start) gives us an answer of 7.85 seconds.
Santo Rugger,that leg press is a one time maximum lift. Mr. Coleman would not be able to exert that force on each of the 30-40 steps he would be taking in the race along with the fact that he could not apply that level of effort at the required speed.
Well, it’s still a better lower bound than 333 picoseconds.
We could start by looking at the fastest time for any animal in the animal kingdom, which would give us a time that we know is achievable by organic matter. Not exactly the direction you’re looking, but it might add a bit of information to the puzzle.
At what sort of g-force does the human circulatory system cease providing adequate blood flow? That’d be a pretty firm limit.
There was some research earlier this year out of France that suggested that 9.5 seconds was about the limit, after which time we’d have to resort to measuring times in the 1/1000th of a second.
http://www.sportsscientists.com/2008/08/beijing-2008-men-100m-report.html
It also takes something like an order of magnitude longer to perform one rep of a leg press than to take one step in a sprint. A dump truck can exert huge torque but you can’t extrapolate that to how it would do in a 1/4 mile drag race.
Also, when Chuck Norris sprints, he doesn’t move, the Earth rotates under him. 
Note that I just used that level of acceleration for half a second. I concede that I made a -lot- of assumptions, hence the “purely theoretical” and “thought experiment” disclaimers in the post. If you guys have a better method, feel free to share them. 
The static coefficient of friction between rubber and dry asphalt is 0.5 - 0.8. Seems to me that implies that a runner could apply a force equal to 0.5 to 0.8 times his weight before he starts slipping.
Sprinters wear running spikes, and don’t run on asphalt.
So what’s their frictional coefficient?
I think you slipped a decimal there. In one nanosecond light travels 30cm (299.7+ to be precise)* so I make it 333 nanoseconds, 0.333 microseconds minimum, to complete a 100 meter dash.
*I remember because I saw a film where the incomparable Grace Hopper held up a foot-long piece of wire and proclaimed, “This is a nanosecond,” explaining that’s how far light would travel in that time.
Nano-, micro-, what’s three orders of magnitude between friends?
(I think I got it right in terms of seconds, just slipped a gasket on the prefix for 10^-6)
Hell if I know. This is GQ, so while I know that the rubber/asphalt bit doesn’t apply, I’m not throwing out a WAG as far as the correct frictional coefficient.
“More” is about all I got.
She also handed out packets of ground black pepper, labeled picoseconds.
I seem to recall it as a foot per femto-second
too lazy/busy to do the math now
Blll
Wow, excellent answers. Thanks everyone.