I've read that you can calculate the horsepower output of a person by having them run up stairs; i.e. take their weight, time them going up the stairs, do some math, and voila, horsepower.
is there any way to calculate this on flat ground? or perhaps a conversion?
suppose a runner weighs 155 pounds. how much horsepower does he produce by running a mile in 4:00?
asafa powell weighs 195 pounds. what was his average horsepower for his 9.77 100m run?
The mechanical power output in level running is either 1. very easy or 2. very difficult to calculate. very easy method is not at all fully correct.
1. very easy. after max speed is acquired, the only work being done is against air resistance. you can find values for the air resistive force and multiply force in newtons by velocity in m/sec whch yields power in watts. that turns out to be quite small.
to calculate the inertial power in acclerating from v = 0 to say v= 10 m/sec, you can calculate kinetic energy (1/2 mv^2) and divide by the time it took to get to that velocity. e.g. 1/2 x 70kg x (10m/sec)^2 = 3500Joules divided by let's say 4 seconds = 875Watts. a horsepower is 760 watts, so 1.15 Hp. So, impressive in some ways, since the man can briefly put out as much power as a horse can do steadily. I'm not sure how Horsepower was originally defined.
2. very hard: one needs to also consider the kinetic energy changes of each segment of the body. that can be done with high speed video etc. but then one faces many decisions about hw to sum the segments, allow for passive transfer from say the thigh to the calf to the foot in a whip like manner.
most importantly, the muscles must do work against gravity to bounce. but much of that "work" is actually recovered from step to step using elastic (tendon) structures. that is also a very controversial conversion.
So, now I'll get back to my job which is to figure that stuff out.