As you mentioned the maths is fairly simple, 

Area of the pack is pi(2.25^2   -  1.125^2) = 11.9 in^2

11.9/0.0015 = 7948 inches of tape

So 7948/7.5

=1059seconds of audio

So around 17 minutes.

From experience that sounds about right.

Here is a link to a spreadsheet that applies the relevant formula if you enter the data.

 Best, Stuart.
Archival AV Technician,
School of Scottish Studies Archives.

The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.

-----Original Message-----
From: Association for Recorded Sound Discussion List [mailto:[log in to unmask]] On Behalf Of Nick Patterson
Sent: 25 October 2018 19:55
To: [log in to unmask]
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 and authoritative reference for similar calculations for *partially* full reels.

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 harshly

best regards, /Nick

Nick Patterson, Music Librarian
Music & Arts Library, Columbia University
701 Dodge, 2960 Broadway
New York, NY 10027