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tedjan
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I’ve been interested in finding out how much power in watts a runner can develop.
There are actually two cases that I was interested in; one was for sprinting and the other was for running at a constant speed for an extended period of time, such as, for a 5K.
The second one is a bit complicated, but the case of the sprinter is pretty easy if you look at the kinetic energy after they leave the blocks.
The kinetic energy is half the mass times the velocity squared. It’s measured in joules. If you divide that by the time, it gives you the power in joules per second or watts.
Usain Bolt is a good example. He weighs 198 lbs or 90 kg. He runs the 100 m in about 10 sec, so his average speed is about 10 m/s.
If he starts from a dead stop and accelerates to his average speed in about 3 seconds, then his kinetic energy at 3 seconds into the sprint is 0.5 x 90 x 10^2 or 4500 joules. If he generates that much energy in 3 seconds, he is generating about 1500 watts. That’s the same as 2 horsepower.
You can also calculate how much power a stair-runner generates when they run up a tall building. Then the energy generated would be the potential energy of the runner at the top of the building. (The potential energy at the bottom is zero.) The potential energy is the runner’s weight multiplied by gravity and by the height of the climb.
The Taipei 101 is a race to the top of a tall building. The race is 91 floors or 390 meters. If a 150 lb or 68 kg runner reaches the top of that building, they have generated 68 x 9.8 x 390 or 260,000 joules. If they do that in 16 mins or 960 seconds, then they are generating about 270 watts of power. That’s about a third of a horsepower.
Some cyclists train with hubs on their bikes that measure their power output. A cyclist may actually train at the 270 watt level, so about 250 to 300 watts is pretty reasonable for a stair racer.
I think that’s interesting,
Ted
http://members.aol.com/MathPhysicsModel/SM/SM.html
There are actually two cases that I was interested in; one was for sprinting and the other was for running at a constant speed for an extended period of time, such as, for a 5K.
The second one is a bit complicated, but the case of the sprinter is pretty easy if you look at the kinetic energy after they leave the blocks.
The kinetic energy is half the mass times the velocity squared. It’s measured in joules. If you divide that by the time, it gives you the power in joules per second or watts.
Usain Bolt is a good example. He weighs 198 lbs or 90 kg. He runs the 100 m in about 10 sec, so his average speed is about 10 m/s.
If he starts from a dead stop and accelerates to his average speed in about 3 seconds, then his kinetic energy at 3 seconds into the sprint is 0.5 x 90 x 10^2 or 4500 joules. If he generates that much energy in 3 seconds, he is generating about 1500 watts. That’s the same as 2 horsepower.
You can also calculate how much power a stair-runner generates when they run up a tall building. Then the energy generated would be the potential energy of the runner at the top of the building. (The potential energy at the bottom is zero.) The potential energy is the runner’s weight multiplied by gravity and by the height of the climb.
The Taipei 101 is a race to the top of a tall building. The race is 91 floors or 390 meters. If a 150 lb or 68 kg runner reaches the top of that building, they have generated 68 x 9.8 x 390 or 260,000 joules. If they do that in 16 mins or 960 seconds, then they are generating about 270 watts of power. That’s about a third of a horsepower.
Some cyclists train with hubs on their bikes that measure their power output. A cyclist may actually train at the 270 watt level, so about 250 to 300 watts is pretty reasonable for a stair racer.
I think that’s interesting,
Ted
http://members.aol.com/MathPhysicsModel/SM/SM.html
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