# Work by swimming

1. May 27, 2008

### catherines

I'm doing a science fair project about swimming. Is it crazy for a swimmer (just pulling, no kicking) swimming a length of freestyle pull only to take 400-700 J of work?

I'm using an equation W = kv^2s where k is a constant, v is velocity, and s is the distance. The k that is provided with the equation is 13.9, but I don't know if that is a correct estimation of the work done.

Also, does anyone know the coefficient of water (for friction)?

2. May 27, 2008

### rock.freak667

Not too familiar with the F=kv^2 since I've never done anything with turbulent flow. Have only done questions with lamina flow such that Stokes' law would hold. But I would guess that k has to involve the viscosity of water. If you can find out exactly what k is in terms of constants ( e.g. k would be $6 \pi \eta$ for F=kv) then you probably could get a better approximation.

3. May 27, 2008

### marcusl

I think you need a more sophisticated approach if you plan to enter a science fair competition. Here are some things to think about:

1) More energy is expended in heating muscles up than in moving the body. You'll need to research muscle and motion efficiency.

2) Get in the practice of being precise in your project, questions and analyses. How long is the pool? How fast is the swimmer going? Is it a sprint or one length out of a long workout? It all matters.

3) Think about how to make estimates as a cross check on your calculations. For example:
Is your estimate in the ballpark? Maybe, for someone not working too hard (doing some floating and coasting). Maybe not, for a sprinter in competition.

Here's how you might do a rough ballpark calculation of the latter:
It is known that a sprinter can put out power on order of 1000W for short times. The Olympic record in the 50m freestyle is around 20 seconds. The energy expended in a 20 second 50m sprint must therefore be in the ballpark of 20 kJ, or 20 to 50 times your estimate. (The actual number might be 15 kJ or 30 kJ, but it is more than an order of magnitude higher).

One length out of a longer race is a different matter, since sprinters rely on anaerobic metabolism that can be maintained for seconds but not minutes.

4) Your focus on water drag is quite appropriate. This is highly nonlinear, that is it becomes more important as speed rises. Again a good topic to look into further.

Start investigating some of these, then please come back with what you have found and with questions!

4. May 27, 2008

### jimvoit

On the internet, using the keywords displacement hull and resistance, you can get to the equations and data related to the naval architecture of dispacement hulls. There may be something there that will help you out.

5. May 27, 2008

### catherines

Oh! I got it! It turns out, the units of work for that equation wasn't given, so I just assumed it was Joules. But it was acutally kJ. And it turns out, for distance you had to use feet and I was using metres, so I got it all figured out now. Thank you so much for your help!