This is simple calculation:
Tape length L =Pi /4 /t*(D+d)*(D-d)
Where Pi =3.14, t = tape thickness, d =hub diameter, D =tape-pack Diameter
In your example t =1.5 mil =0.0015 inch, d =2.25 inch, D =4.5 inch
So, L =3.14/4/0.0015*(4.5+2.25)*(4.5-2.25) =7948.125 inch
Duration T =L/S
Where S =Tape Speed. In your example S =7.5 ips.
So, T =7948.125/7.5 =1059.75 sec =17.6625 min =17 min 39.75 sec
This calculation is correct for tight tape winding.
G e n n L a b
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Tel: +64 21 238 3056
----- Original Message -----
From: "Nick Patterson" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Friday, October 26, 2018 7:54 AM
Subject: [ARSCLIST] Estimation of the time used on *partially-full*
open-reel audio tapes - seeking good reference
> Dear collective ARSC wisdom,
> I'm looking for reference resources for the estimation of the time used on
> *partially-full* open-reel audio tapes.
> I'm aware of resources that calculate timings (based on various factors)
> for *full* audio tape reels, such as:
> But, I'm wondering if anyone might be able to point me towards a stable
> authoritative reference for similar calculations for *partially* full
> So, a sample problem would be:
> What is the duration on a reel which is 7", 1.5 mil tape, recorded at 7.5
> ips, and has a tape-pack diameter of 4.5 inches on the reel (assuming a
> 2.25 inch center hub)?
> We have a working estimation method in place, for the project I'm current
> working on, but I'd like to find an authoritative reference in the
> community, that documents this.
> If anyone knows of such a resource, I'd appreciate any info!
> P.S. the engineers amongst you may scoff that this is simply math, but,
> math is not my strongest suit, hence my search for a stable reference,
> rather than back-of-the-napkin calculation - please don't judge too
> best regards, /Nick
> Nick Patterson, Music Librarian
> Music & Arts Library, Columbia University
> 701 Dodge, 2960 Broadway
> New York, NY 10027