Re: Air resistance

["JACK L. URETSKY (C) 1996; HEP DIV., ARGONNE NATIONAL LAB, ARGONNE, IL 60439" <JLU@hep.anl.gov>]

Hi Ludwik-
	You write, in response to:
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> I don't understand the data.  Look at the values from 1.600 s on. The
> space increments, with two exceptions, increase from increment to
> increment by .05.  The two exceptions tell me that the position 
> measurements are uncertain in their last place, and the velocity 
> differences are unccertain in their first significant digit.  The 
> accelerations are not good to more than 1 signifigant digit, and the 
> differences are garrbage.

That is precisely why averaging is essential. You should have seen the
data at the averaging of 3 to appreciate how much improvement is due
to averaging.

Assuming the limit of accuracy is one lambda (0.0085 meters for the 
ultrasound at 40 kHz) the designers of the instrument probably decided to 
truncate data (number of bits in the ADC unit) to that level, more or less. 
This limitation is corrected through avearging. I am only guessing. The 
technology was borrowed from the auto-focusing cameras where high accuracy
is not needed.
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	I think that you have forgotten that the average of garbage is
smooth garbage.   More precisely, if the error on 1 measurement is sigma,
and IF SIGMA IS THE SD OF A NORMAL DISTRIBUTION, then the error on
N measurements is sigma/sqrt(N).  I have no reason to believe that
the fluctuations in the first digit of of difference of differences of the
position measurements bear any resemblance to a normally distributed
random variable.
			Regards,
				Jack