# Power calculation for a sprinter

1. Jul 4, 2007

### luzirahs

Power generated by a 100m sprinter.

hai all,

i've been thinking about how much horsepower does a human generate during a 100m sprint...
(after my friends joking with me by telling me running on dyno machine's roller to measure my horsepower. )

is it possible for me to use P = (F*d)/t, where
F is the sprinter weight, (coz i think its the only force/mass that been moved, or got any other force involve, too?)
d is 100m and
t is his sprint time.

let's say mass of the sprinter is 60kg,
therefore his weight is 60kg*9.81m/s^2 = 588.6N
and his 100m sprint time is 10s sharp.

so, power generated by the sprinter is,
P = (588.6*100)/10
P = 5,886W
P = 5,886W*(1hp/746W)
P = 7.89hp

its so true that if the sprinter can sprint 100m less than 10s, his horsepower generated for the sprint will be higher, which is make sense to me.

am i correct?

thanx all.

Last edited: Jul 4, 2007
2. Jul 4, 2007

### mgb_phys

The force isn't his weight - unless he is sprinting vertically up! Draw a sketch - it will help.
You could assume that the sprinter is always accelerating and use F=ma.

I suspect that sprinters reach maximum velocity in a couple of seconds and then it is a more complicated question of air resistance and the force of lifting each leg on each stride. Sprinters try and run so that their centre of gravity remains level.
You could estimate how much a leg weighs and how far it moves up and down on each stride.

As a tip - human powered vehicles generally reckon on about 1/4 - 1/3Hp from a cyclist!

Last edited: Jul 4, 2007
3. Jul 4, 2007

### luzirahs

in this kind of problem, i assume that the sprinter accelerates w a constant acceleration from starting block to finishing line.

here's the calculations (referred from that link)...
----------------------------------------------
sprinter mass = 60kg,
his sprint time is 10s.

his final speed is,
v = 100m/10s = 10m/s

* this is average speed, along the sprint.

In order to find the force wee need to know the acceleration.
Using SUVAT equations of motion we have,

s = 100m
u = 0m/s
v = 10m/s
a = ?
t = 10s

using,
s = ut + (0.5)at^2
s = (0.5)at^2 (we lose ut because 0x10 = 0)

therefore,
100 = (0.5)*a*10^2 ...rearrange to find a,
a = 2 m/s^2

This acceleration is an average acceleration along the sprint...a constant one.

Then,
F = ma
F = 60x2 = 120N

After that,
Work done = Force x Distance Travelled
W = 120x100 = 12,000J

Power = Work done / Time taken
P = 12,000J/10s = 1,200Watts

Finally, to get Power in horsepower unit, divide Power by 746.
P = 1,200W*(1hp/746W)
P = 1.6hp

Last edited by a moderator: May 3, 2017
4. Jul 5, 2007

### mgb_phys

If he completes the 100m in 10s and is constantly accelerating the final speed is not 10m/s - although you don't use it in the calcs.
1.6hp sounds a lot but I suppose as it is only for 10secs it is possible.