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Re: Air resistance



Hi Ludwik-
You write, in response to:
***************************************************************
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.
*****************************
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

Howdy,

We'll be renovating one of our labs to use MBL equipment in the next couple
of years. There will be about one dozen Macs and associated ULIs, probes
and other stuff.

I've taken a few MBL courses based upon the experiments that are already
published for using the ULI, etc., but am still very uncomfortable trying
to put together new labs for precisely the reason we have been seeing here.
It seems that sampling rates as well as sampling times, moving averages,
etc., are critical in getting results that make some sense to our students
(or even to us!). What I NEED is a course, or at least a good book, that
explains all of this and how to go about choosing reasonable data rates,
etc., for a given situation.

I'm not trying to "pull the wool over the student's eyes." I just want
them to have reasonably satisfying experiences in the lab and to be able to
learn from those experiences.

Good Luck,

Herb Schulz
(herbs@interaccess.com)