An Impulse (in Physics) is force applied over a period of time to effect a change in momentum. More force over a shorter period of time is equivalent to less force over a longer period of time, and more force over a longer period of time generates the most change in momentum of all. (I'm assuming static mass, by the way, as if we're talking about alterations in the running of one person)
Winning a race is just a matter of attaining the highest average velocity. This is done by having the highest sum change in momentum (assuming all runners are of equal mass). This, in turn, is done by applying the greatest amount of force to propel forward. Assuming that the force generated by the athlete remains the same, then there are only two ways to increase the force that the athlete is generating at point of contact with the track. One of these is to increase the length of the lever being used to propel the athlete (make his leg longer. Not very practical thing to change, though it does suggest an advantage in the MaxV phase for taller athletes) and the other is to increase the amount of time force is being applied to the track propellling the athlete forward. Longer contact time.
So, theoretically, an athlete who has a longer ground contact time, while generating the same amount of force per unit of time within that contact time, will apply more force to the track and should propel himself faster.
Practically, however, this model fails. I'd like to see some reasoning as to why, because I'm having a hard time figuring out what causes the theoretical model (which I'm fairly sure is accurate) to fail when practically applied, and I'd like to know. I'm fairly sure its something rooted in the mechanics of running, such as stride recovery (applying force longer causes a longer duration needed for stride recovery maybe?) or something along those lines.
Quote from cockysprinter:
its simple math. lets say two sprinters have a ground contact of 1 second (ridiculous i know). 1 applies 80 pounds of force and another applies 100. the 100 pounds of force guy will be faster. there is room for variation of course, but thats the idea. if one guy has a longer ground contact, he needs to have a higher stride frequency or massive strides to make up. and both of these are dependent on power output. sorry but i dont remember much of physics, i took it a few years ago.
You're looking at things backward as to what I'm saying. Of course, if two athletes apply force for the same duration of time, then whoever applies the most force within that interval will run faster (provided mass is nominally equal). What I'm pointing out is that according to a theoretical model based off physics, then if two athletes are capable of applying the same force, then the one who can apply that force for a longer period of time will run faster. You were working off power being the variable, and I'm working off a model where duration is the variable.
Quote from Cockysprinter:
the average american male is 5'8.5" which mean 1 sprinter i listed is slightly short (5'8"), 2 are slightly above average (5'9"), 2 are tall (5'10, 5'11"), and the rest are 6'+. also if you discount ben johnson as the winner of 1988, greene is the only olympic gold medalist that is under 6'. i also believe that the 1980 winner was 6' or taller, i just dont remember who he is or what his height was. theres been a thread on this already where i did the same thing with more 100m gold medalists
Lookin at a chart for male height in the US, the mean is 5'8.5". A little over six foot is the upper bound of one standard deviation (according to the chart I'm using, which might be incorrect since it only accounts for white guys, apparently). I'd say its fair to say that within one standev of the mean can be considered within reason of not being very tall, since about 68% of the population falls within one standard deviation of the mean (in this case, about 4" +/- of 5'8.5"ish). Find me a better chart or table of american male height and I'll give you a more accurate estimation of standev and whatnot.
after describing the impulse concept more, i think i know why it fails. its the wrong concept to use :P. ive read analogy like this before but i dont remember where. try spinning a bicycle wheel using long less powerful motions. it gets the wheel moving, but cant keep up in the long term. the same concept applies to sprinting. a long impulse just doesnt supply the necesary power to keep a human moving at high speeds.
as for the height thing, i think youre looking at the same table i got my info from. i didnt know the standard deviation was 4", i saw the chart 3 years ago in math class. i suppose i can concede that sprinters are not overly tall, but i also dont know of many sprinters under 5'8" at the world class level. it would be interesting to get the heights and/or weights of all the sprinters who have run sub 10 to get a better picture.