Re:air resistance

[John Mallinckrodt <ajmallinckro@CSUPomona.Edu>]

On Sat, 6 Dec 1997, LUDWIK KOWALSKI wrote:

> The air resistance data are no longer "quick and dirty". Propagation of 
> random errors of d --> "differences of differences" is very instructive 
> and worth emphasizing. The bottom line is that the R=F(v) curves are 
> quadratic. 
> ...
>       t(s)         d(m)         v(m/s)        a(m/s^2)         R(N)
>
>      1.400        0.608         1.773           9.63
>      1.425        0.655         2.013           9.65
>      1.450        0.708         2.254           9.65
>      1.475        0.668         2.494           9.64           0.09
>      1.500        0.835         2.734           9.60
>     ...

(rest of the data deleted)

Ludwik,

I assume the data point for d at t = 1.475 s is an error and 
should read "0.768 m."  With that correction I can (as with the 
previous data) obtain *excellent* numerical fits to your d vs. t 
data (i.e., rms errors in d less than 1 least sig fig) with drag 
exponents (i.e., the n in F_drag = b v^n) anywhere from 1/5 to 5.  
I get marginally better fits with n near 2, but certainly not 
significantly enough better to come to any conclusions about the 
precise value of n (which I, nevertheless, suspect *is* pretty 
close to 2 at these speeds.)

I believe that you are making an error in trusting the 
acceleration values for precisely the reasons that you note in 
discussing the need for averaging.  Furthermore, as you later write:

> Do not forget that high accuracy of a is essential because R is calculated 
> as m*(9.8-a). If a=9.44 (+/- 3%) then R is 0.2 (+/- 100 %).

Exactly, and, because of the gross errors introduced by double 
differencing and then averaging over large times, you will not 
likely get the accuracy you need.

Again, it is my opinion that this data simply cannot settle the 
question.  The data would have to be taken over a much larger 
range of v, probably with more precision in the distance data, and 
possibly with better time resolution.

John
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