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From: wjk@ihuxf.UUCP (Bill Krauss)
Newsgroups: net.video
Subject: Elapsed time vs. numbers on VCR display
Message-ID: <2196@ihuxf.UUCP>
Date: Mon, 14-May-84 14:07:58 EDT
Article-I.D.: ihuxf.2196
Posted: Mon May 14 14:07:58 1984
Date-Received: Tue, 15-May-84 05:44:45 EDT
Organization: AT&T Bell Labs, Naperville, IL
Lines: 35

The following info may be useful to VCR owners:
On my video recorder, I've noticed that the numbers that go by as I'm
recording or playing don't go by at a constant rate.  They go faster
when I'm at the beginning of the tape than when I'm near the end.
So, assuming that they are proportional to the number of revolutions of
the take-up (left) reel, and that the tape moves at a constant speed,
I came up with the following equations, which relate the time elapsed
from the beginning of the tape to the number displayed.


n  =  (ne / (re - rs)) * ( sqrt( ((re^2 - rs^2) / te) * t + rs^2 ) - rs )

t  =  (te / (re^2 - rs^2)) * ( ( ((re - rs) / ne) * n + rs )^2 - rs^2 )

dn/dt = ( ne * (re + rs) ) / ( 2 * te * sqrt( ((re^2 - rs^2) / te) * t + rs^2))

      = ( ne * (re + rs) ) / ( 2 * te * ((re - rs) / ne) * n + rs )

dt/dn = ( 2 * te * sqrt( ((re^2 - rs^2) / te) * t + rs^2)) / ( ne * (re + rs) )

      = ( 2 * te * ((re - rs) / ne) * n + rs ) / ( ne * (re + rs) )


where	rs = the radius of the left reel at the start (when it's empty)
	re = the radius of the left reel at the end (when it's full)
	te = time elapsed at the end (when the tape runs out)
	ne = number displayed at the end (assume number was 0 at the start)

and the variables are	n = number currently displayed (anywhere in tape)
			t = time elapsed up to this point

For the tape I was using, which I guess is a standard tape,
	rs = 13 mm, re = 39 mm, te = 6 hours, ne = 1827

			Bill Krauss     ...!ihnp4!ihuxf!wjk