wjk@ihuxf.UUCP (Bill Krauss) (05/14/84)
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