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# Re: air drag

Bob Muir and others,
We do the experiment of dropping coffee filters and finding their terminal velocities with a sonic ranger in our intro labs. It is part of a larger lab on freely falling bodies, and the students aren't actually asked to calculate the drag coefficient, just see if the relation between mass and vt is linear or non.
A couple of years ago I did a more careful experiment to see if it would be good to add to our lab. The results were presented at our local (Idaho-Utah) AAPT section meeting. An article came out in TPT (March 1999, p.181) about the same time doing a similar thing with muffin cups, so I never bothered to submit my results for publication. However, since you asked for numbers, and no else seems to have come forward yet with any, let me report what I got.
I was able to get multiple mass values by cutting a filter into quarters, then adding pieces to one filter, giving 1, 1.25, 1.50, etc. times the mass of one filter. That gave 10 data points, up to 3.25 mass units. A plot of v-squared vs. mass is acceptably straight. With a drag force of: F-drag = mg = c_2 vt^2 , I found a value of c_2 of about 6.6x10^-3 from the slope of the line.
The coefficient Griffin gives for a sphere is 0.22(diam.)^2, with the diameter in meters. The coffee filters we used vary from about 0.08m at the flat end, up to about 0.13m at the top. Spheres of these diameters should have coefficients of 1.4 to 4.0 x10^-3. Thus, the coefficient we found is a little bit higher. But then again the filters are not spheres, so you would expect more drag than for a sphere.
Hope this report is useful to you.
Rondo Jeffery
Weber State University
Ogden, UT 84408-2508
ps. I know Bob invited responses off list, but I would be interested to know if any others have results similar to ours.

muirrob@UNCG.EDU 02/06/01 08:05AM >>>
Has anyone determined drag coefficient in terms of cross sectional
area for coffee filters, i.e., c1 and/or c2 in the expressions:
Fdrag = -c1*v and Fdrag = -c2*v*v?

Fowles says that for spheres c1 = 1.55e-1 times diameter and
c2 = 0.22 diameter squared.
I expect these to be incorrect for something shaped like a coffee
filter.

My students are going to be studying this soon, so I'm interested in
having some independent results to compare with.

Feel free to respond off list.

Thanks,
Bob

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Bob Muir muirrob@uncg.edu
Physics & Astronomy 336-334-3255
UNC Greensboro, NC 27402-6170
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