Hello again,
Here is one of the formulas i found back around mid 1980's ... i think i have more notes about this i'll have to find though.
time in seconds:
t=2*pi*(C2-C1)*[w*(C1+C2)+1]*s
tape thickness w=100/407125 inches
linear tape speed s=70498/180000 inches per second
C1=start count
C2=end count
Notes:
1. The counts for the deck i was using at the time are the 3 times the counts above, so divide all counter counts by 3 here.
2. The tape thickness and tape speed are curve fit values and may or may not reflect actual values in real life as measured.
3. The time is in seconds so we divide by 3600 to get the time in hours.
For example, the max count for a T120 tape was 5885 on that deck, and so if we ran the entire tape from start to finish then we'd see counts:
c1=0
c2=5885
but the counts in the above formula for that deck would be entered as:
C1=0
C2=5885/3
Alternately this can be entered into the formula of course.
To test this formula, we can look at the entire tape time from counts of 0 to 5885 (t1) and compare that to the sum of the times of counts that takes us from zero to 1/2 of the total count (t2) and from 1/2 of the total count to the full count (t3), and the sum should be the same as the total (all times in hours and tape deck on fastest speed):
t1=t2+t3
It turns out that (times in hours):
t1=1.987039
t2=0.831993
t3=1.155046
so:
t2+t3=1.987039
and so t2+t3=t1
and so this sanity check works out well.
We can also do a sanity check on the length, which is about 712 feet.
I turns out that at the given speed the calculated length is 705 feet, so the total length is off by 7 feet. It is not known what the tolerance of a T120 tape length is however, and i dont remember where i got that length of 712 feet from unfortunately. Perhaps there iis more info about this on the web, and keep in mind it could have been the result of a curve fit not a direct measurement.
The basic premise for the above formula is simply the arc length of an Archimedes spiral. I dont remember if i implemented any approximation such as leaving part of the formula off because after something like 5 turns the formula can be greatly simplified. I might go over this again and see if i can remember what i did back then
Here is one of the formulas i found back around mid 1980's ... i think i have more notes about this i'll have to find though.
time in seconds:
t=2*pi*(C2-C1)*[w*(C1+C2)+1]*s
tape thickness w=100/407125 inches
linear tape speed s=70498/180000 inches per second
C1=start count
C2=end count
Notes:
1. The counts for the deck i was using at the time are the 3 times the counts above, so divide all counter counts by 3 here.
2. The tape thickness and tape speed are curve fit values and may or may not reflect actual values in real life as measured.
3. The time is in seconds so we divide by 3600 to get the time in hours.
For example, the max count for a T120 tape was 5885 on that deck, and so if we ran the entire tape from start to finish then we'd see counts:
c1=0
c2=5885
but the counts in the above formula for that deck would be entered as:
C1=0
C2=5885/3
Alternately this can be entered into the formula of course.
To test this formula, we can look at the entire tape time from counts of 0 to 5885 (t1) and compare that to the sum of the times of counts that takes us from zero to 1/2 of the total count (t2) and from 1/2 of the total count to the full count (t3), and the sum should be the same as the total (all times in hours and tape deck on fastest speed):
t1=t2+t3
It turns out that (times in hours):
t1=1.987039
t2=0.831993
t3=1.155046
so:
t2+t3=1.987039
and so t2+t3=t1
and so this sanity check works out well.
We can also do a sanity check on the length, which is about 712 feet.
I turns out that at the given speed the calculated length is 705 feet, so the total length is off by 7 feet. It is not known what the tolerance of a T120 tape length is however, and i dont remember where i got that length of 712 feet from unfortunately. Perhaps there iis more info about this on the web, and keep in mind it could have been the result of a curve fit not a direct measurement.
The basic premise for the above formula is simply the arc length of an Archimedes spiral. I dont remember if i implemented any approximation such as leaving part of the formula off because after something like 5 turns the formula can be greatly simplified. I might go over this again and see if i can remember what i did back then