Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Air resistance



On Sun, 7 Dec 1997, LUDWIK KOWALSKI wrote:

There must be a misunderstanding somewhere. I am reposting the data
at the end of this message. Just plot R=f(v) on the log-log paper
and get n="the best slope". Without doing this I can say that n=2
(plus or minus of up to 20%). Here is my reasoning. The region in
which good data were collected spans from about 2.49 to 4.63 m/s
Thus (v2/v1)=1.8. The corresponding ratio of air resistaces, R2/R1
is 3.0. What is n when 1.8^n=3? It is close to 2.

For your values on n=5 and n=0.2 the force ratios would be 19 and 1.1,
respectively. The experimental data are not perfect but they are
certainly not so bad as to accomodate your range of n. And this has
nothing to do with the value of b (=m*r) in your R=b*v^n formula.

Ludwik,

The point is that you didn't *measure* v and you didn't *measure* a; these
values are *calculated* from your measured d values using a processing
method that makes certain assumptions. Thus, any results you obtain from
your values of v and a reflect those assumptions.

The only defensible measure of the "goodness" of some particular "fit" is
how well it reproduces your *measurements*. All of the fits that I have
provided--including constant acceleration at 9.57 m/s^2--do so admirably
with rms errors in d of .7 to .9 mm, somewhat less than the apparent 1 mm
resolution of your data. Although the F_drag ~ v^2 (n=2) model produces
one of the better fits (rms errors of ~.7 mm), it is simply not *enough*
better to make any very compelling statements about the value of n.

John
-----------------------------------------------------------------
A. John Mallinckrodt http://www.intranet.csupomona.edu/~ajm
Professor of Physics mailto:ajmallinckro@csupomona.edu
Physics Department voice:909-869-4054
Cal Poly Pomona fax:909-869-5090
Pomona, CA 91768-4031 office:Building 8, Room 223