I already looked at ESPN's Sport Science episode where they calculate that Marshawn Lynch produces 54,000 watts when pulling some tires. Yes, that is way too high. However, what would happen if some was actually that powerful? What could that person do? How fast could they run 100 meters? That is what I am going to calculate.
First, I am going to assume that Marshawn has a mass of about 100 kg. Also, let me say that he can produce 54,000 watts no matter what his speed.
Take a short time interval. During this time, Marshawn will increase his speed from say v1 to v2 this would be a change in energy of:
And this would relate to the power by:
So, if I know this small time interval and the velocity he started at (at the beginning of the interval) then I can find the final velocity:
If the time interval is short, then the velocity is essentially constant (for very short time intervals) so that I can use the average velocity to write:
You see where I am going don't you? This is all set up for a numerical calculation. Here it is - I made it as simple as I could:
I changed my mind. Instead of using the average velocity to find the new position, I just used the velocity. Trust me, it is ok. Here - you can check. One good way of checking your calculations is to make the time interval (dt in this case) smaller and see if you get the same result.
So, what do I get. Here is a plot of the speed as a function of time:
There you go - 100 meter dash in under 3 seconds. Take that Usain Bolt. Note that Usain not only has a cool name (Bolt) but has the world record at 9.58 seconds. Another note - I just noticed that lists the wind speed for these records. Boom. That is another blog post.
Not only would 54,000 watts give you a 100 meter time under 3 seconds, you would be going over 50 m/s. Yes, that is like 120 mph.
How about another check. What if I put in a more reasonable power of 2000 watts? Here is what I get:
Seems better, doesn't it? Still a world-record time, but I did not take into account air resistance and I assumed the power would be constant. Oh, also that would give a speed of 40 mph - so that isn't quite right.
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The caption of the second plot should be Speed of 2000 Watts dude, no?
@anon,
Thanks for catching that - I fixed the title.
"What could you do with 54,000 watts?"
Produce one research paper on AGW?
Hmmm... On a quick glance there would seem to be a problem. 54000 watts is about 72 horsepower. Most cars have more than this and do not accelerate to 120 m.p.h. in the space of 100 yards.
Being at work and all, I haven't had time to think through whether there's an error in your calculations, your assumptions or my comparison.
@Rob,
Cars don't have a mass of 100 kg.
*smacks forehead* duh...
The ability of human muscle to produce power is very velocity dependent (obviously, otherwise everyone would ride 1-speed bikes).
Which is why the ability to apply 2 kW continuously might get you a world record time DESPITE the ability of sprinters to produce well over 2 kW of power. I think in a previous comment I mentioned that Usain Bolt's split times demonstrate a peak mechanical power production over 4 kW in his early acceleration. But he doesn't have gearing on his legs, so biomechanical inefficiencies at high velocities (and wind resistance) prevent him from reaching your times.
I still agree 54 kW is baloney.