Human Horsepower on the Water

ForeverSwim

I was curious the other day, after racing a low-power boat at Keystone Lake, how much horsepower a swimmer could generate on the water. After briefly researching this topic, I found out that the UCLA Physics department was able to calculate the output (horsepower) of a human, by timing (seconds) the human (weight) up a flight (distance) of stairs.

The calculation is as follows:

Weight (lbs) x Distance (feet) / Time (seconds) X 1/550ft-lbs-sec (1hp)

If this were the case, I figured that I would like to see how much horsepower a swimmer could generate over a shorter distance as well. I thought a 25-yard freestyle sprint would make for the highest amount of output (horsepower). I used my personal statistics as an example:

225 (lbs) x 75 (feet)/10.5 X 1/550 =

16,875/10.5 X 1/550 =

1,607.14/1 X 1/550 =

1,607.14/550 = 2.922hp

In conclusion, a 225lb person, swimming 75 feet in 10.5 seconds would generate 2.922hp. I cannot say I am a physics scholar, so please let me know if I am wrong in assuming the length of a pool would be the same in this calculation as the flight of stairs!

Just thought everyone would enjoy this calculation!

bobswims

Sorry, but weight (or mass) has no meaningful contribution to calculating horsepower of an object through a fluid. The horsepower needed is to overcome drag. Moreover, the power needed to push an object through a fluid increases as the cube of the velocity.

Generally:

Power = 1/2(density of the fluid)(velocity cubed)(reference area)(drag coefficient)

Which is also why it is much more efficient to maintain a constant speed while swimming. It just requires less power. Remember it's velocity to the 3rd power!

evmo

If people are familiar with power racks (Darren, you must have done a few of these in college)... I'm wondering if this might better approximate the meaning of "horsepower" in swimming. Since you are actually pulling weight (like horses do), in addition to moving your own mass through water...

ForeverSwim

@bobswims, I'll let you handle that equation, ha! Let me know what you find out..
@evmo, funny, I never actually used one of those things, however we did do the "stretch cords", which were the rubber tubing-block-swimmer devices. I wish I would have, might have made me more of a meat-head than I am today

ssthomas

I'm sending this to my physics major/math minor smartie pants little sister to see what she has to say. I'll let you guys know what she comes up with for us. :-)

Bill

Here's a quick calculation:

Power = Force x Velocity
Force = (1/2) x (density) x (velocity)^2 x Drag Coefficient x Area

Assume: Drag Coefficient = 0.5, velocity = 2.27 m/s, Area = 0.15m^2

Power = (1/2) x (1000 kg / m^3) x (2.27 m/s)^2 x (0.5) x (0.15 m^2) x (2.27 m/s)
Power = 438 Watts
Power = 0.58 hp

evmo