msb@lsuc.UUCP (Mark Brader) (07/16/85)
This will work if you have a tape counter that counts revolutions
of the take-up reel.... i.e., if it moves faster near the beginning
slower near the end. If your tape counter counts revolutions of the
source reel, you can still use these formulas, but c will have to be
replaced with m-c, where m is the counter reading at end of tape.
Of course, if your machine displays tape time directly, you can
ignore this message. I bought mine before those existed.
In this article the ^ means exponentiation, * multiplication, sqrt
square root; and SUM(x/y) means to take each of the observed values for
x, divide them by the corresponding values for y, and add all the results.
Okay, let c be the reading on the tape counter, and t be the time from
beginning of tape, in minutes. Then c and t are related by an equation
of the form
t = (c^2)/A + c/B
and the inverse formula is
c = sqrt(K^2 + A*t) - K where K = A/(2*B)
We want to find the values of A and B for the particular tape and the
particular VCR. (I put A and B in the denominator so that they would
be greater than 1 for typical equipment. On my VCR, with a 6-hour tape
I find A=17900, B=10.42; with a 3-hour tape A=17680, B=4.408.)
Now make a continuous recording over the whole length of the tape you want
to calibrate. If you have, say, a cable channel which continuously displays
the time of day, use that. Next best is a station which broadcasts time beeps
every half-hour. Failing that, use a network channel and choose a time when
most of the programs are half-hours, and assume they start on time.
Now rewind and clear the tape counter. Advance along the tape by convenient
intervals using the time of day indications just described. Spot each one
as exactly as possible and record the tape counter value. You want at least
about half a dozen values recorded; the more the better.
You now have a list of c and t value pairs. (For some people, this may
be sufficient information, and you can stop here.) Otherwise, let's
say you observed n different points, not counting t=0,c=0.
Then plug them into the following formula:
A = (n * SUM(c^2) - (SUM(c))^2) / (n * SUM(t) - SUM(c) * SUM(t/c))
And, using that result, you then compute
B = n / (SUM(t/c) - (SUM(t))/A)
And you're done.
If you use different lengths of tapes, and maybe even different brands,
you will have to do this for each one. (However, at least on my machine,
changing speeds has no side-effects; that is, instead of doing this at SLP (EP)
speed and using half-hour intervals, I got good consistent results by doing
it at SP speed and using 10-minute intervals which I counted as half-hours.)
For example, suppose you were measuring a very short tape and you just
made the 2 (=n) observations c=100,t=10 and c=200,t=30. Then you'd get
A = (2*50000 - 300^2) / (2*40 - 300*.25)
= (100000 - 90000) / (80 - 75)
= 2000
B = 2 / (.25 - 300/2000)
= 2 / .1
= 20
And sure enough, t = (c^2)/2000 + c/20 fits the observations exactly.
The inverse relation would be c = sqrt (2500 + 2000*t) - 50.
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Mark Brader and uw-beaver!utcsri!lsuc!msbalbert@ucbvax.ARPA (Anthony Albert) (07/24/85)
In article <709@lsuc.UUCP> msb@lsuc.UUCP (Mark Brader|LSUC|Toronto) writes: > >This will work if you have a tape counter that counts revolutions > t = (c^2)/A + c/B > >and the inverse formula is > > c = sqrt(K^2 + A*t) - K where K = A/(2*B) > >We want to find the values of A and B for the particular tape and the >particular VCR. > >Now make a continuous recording over the whole length of the tape you want >to calibrate. If you have, say, a cable channel which continuously displays >the time of day, use that. ... One thing to be careful of is that the counters might give different values during FF and REW than during play and record. At least that has been my experience. -- Anthony Albert ..!ucbvax!albert albert@ucbvax.ARPA