# Power generated by elite runner.

1. Aug 29, 2008

### tedjan

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 [Broken]

Last edited by a moderator: May 3, 2017
2. May 10, 2011

### dansfma

tedjan,

I like this post. Was looking at power output in watts across several athletic areas - walking, biking, sprinting, weightlifting, etc.

I understand your reasoning on Usain but have a question: Usain achieved his kinetic energy by overcoming wind resistance - so didn't he have to put out even more than 1500 watts to get to his speed? Said another way: If you want to focus on just his acheivement of speed, then I agree with your answer. But if you wanted to measure exactly his output or effort to get to that speed, then it would be his speed + the forces working against him (like drag). Does that sound right?

3. May 10, 2011

### JaredJames

This thread is from 2008 and the OP hasn't been back since November 2009.

Check the thread details before responding to avoid necroposting.

4. May 10, 2011

### dansfma

JaredJames,

Thanks for tip on checking thread details. I'm new to these forums.

I was actually trying to follow laws of physics, not disobey them. If a 1000 kg car accelerates at a rate of 5 m/sec, then we could conclude the engine put out 5000 newtons of "thrust" forward (F=ma; 5000 = 1000 * 5). But if we knew that wind resistance was exerting a force of 200 newtons in the opposite direction, then the engine is putting out 5200 newtons to achieve the 5 m/sec acceleration. Although this example is with force and not power, it is the same concept I was trying to apply to Usain. Make sense?

5. Jul 19, 2013

### tedjan

Sorry to be out of touch on this post. I’ve been working in another problem area. Regarding the Bolt question the aerodynamic drag equation is very useful to estimating the drag. NASA has an excellent discussion at:

http://wright.nasa.gov/airplane/smeaton.html

Mr. Bolt’s velocity at 10 m/s is about 23 mph, his frontal surface area is approximately 8 ft^2. Then, 0.00327 * 23^2 * 8 or approximately 13 lbs of drag. I actually think it would be a single digit number value, about 6 lbs of drag.

Ted

6. Jul 20, 2013

### CWatters

I remember reading a book on manpowered flight in which the author suggested that a fit cyclist could sustain about 1/3rd of a horsepower and they tried to design their aircraft to use less than that. When looking for a suitable pilot they said they quickly discovered it was easier to teach a racing cyclist to fly than turn a pilot into a racing cyclist.

7. Jul 20, 2013

### tedjan

Yes, Brian Allen powered the Gossamer Albatross across the Channel with about 400w.

http://en.wikipedia.org/wiki/Gossamer_Albatross

Typical values are stated in terms of 'mass' spicific power of watts/kg. That works out to about 3.5 w/kg for continuous specific power output. Short term specific power can be multiples of 3.5 w/kg. Good continuous power examples are found in cycling, swimming (P/m=Fv/m) and stair racing (P/m=gh/t).

It's fun to measure your own specific power output by running up a few flights of stairs.

Ted

8. Jul 21, 2013

### A.T.

Recently a human powered helicopter hovered for > 1min and reached > 3m altitude. Here the info about the pilot/engine:

http://www.aerovelo.com/projects/helicopter/tech-info/ [Broken]
Here a plot of power vs duration:

Last edited by a moderator: May 6, 2017
9. Jul 21, 2013

### tedjan

10. Jul 21, 2013

### A.T.

For longer durations check out the Daedalus human powered aircraft. It flew for several hours. They switched the pilot several times during the project, and ended up with 3 professional cyclists in 3 day training rotation, to have one rested guy everday, when the right weather comes. The power is mentioned somewhere here:

11. Jul 31, 2014

### jimbostank

Ted,

What is the power for the 5k runner?

How fast do you think a 90 kg runner would have to run to produce the same power as an olympic runner who weighs 50-60 kgs?

Can someone aid me in calculating watts for running?

A.T. has been helping me a bit on a question I asked in the forum. The discussion is evolving now but if you're bored i'd be interested in your opinions.