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Magnetic Tape Capacity

and the Effect of "Tape Blocking"

Note: This information is useful in making a more time and media efficient application using magnetic tapes,
- not of general interest to restoration ;-))

Background:
There is a 3/4 inch gap ("Inter-Record Gap") between Physical Tape Records on tapes of 200, 556 and 800 characters/inch tape format where no data is written. (The above describes the Model 729 tape drives on the restored the 1401s.)
- No user data is placed in this gap. (There is a check character which is written after the last data character - two character positions of no magnetic transitions then the check character is written.)

It is usually considered a good thing to put as many data records into one physical
tape record as practical. This permits more data per tape, and allows more data records to be written or read per second. Factors of physical memory available, statistics of tape defects per length of tape, and other factors, tend to limit the desirable size of physical tape records.

Background info on tape write error recovery:
A standard software recovery (simplified) from a detected tape write error is to
    - assume a small tape defect
    - back up over the defective tape block just written
    - write an end of file mark (three inches blank tape followed by a special character)
    - back up over the special character
    - re-write the tape block after the three inch blank area (containing the bad spot)

Because computers are so fast relative to physical I/O, the computer time to block and unblock physical records (as in sorting) is considered rather inconsequential.

Capacity of 2400 foot reel using 80 character records at 556 bits/inch and various tape blocking ( various 80 character records in one data block )
From Stan Paddock, Sept 2013

The Effect of "Tape Blocking"
- from Stan Paddock, Sept 28, 2013, was in .xls format
Basis Tape length 2,295 feet of tape used for data
Tape density 556 Bits Per Inch (6 bits wide)
Data record length 80 One 80 column card
Blocking Factor 1 to 20 Cards per data block
Maximum data 12,145,600 Maximum data
Blocking
factor 		Record length
+ IRG (inches) 		Data Length
(inches) 		Percent
data 		Number of
data blocks 		Characters
on tape 		Cards
on tape
1 0.894 0.144 16.1% 30,809 2,464,720 30,809
2 1.038 0.288 27.7% 26,537 4,245,920 53,074
3 1.182 0.432 36.5% 23,306 5,593,440 69,918
4 1.326 0.576 43.4% 20,776 6,648,320 83,104
5 1.469 0.719 49.0% 18,742 7,496,800 93,710
6 1.613 0.863 53.5% 17,070 8,193,600 102,420
7 1.757 1.007 57.3% 15,672 8,776,320 109,704
8 1.901 1.151 60.5% 14,486 9,271,040 115,888
9 2.045 1.295 63.3% 13,467 9,696,240 121,203
10 2.189 1.439 65.7% 12,581 10,064,800 125,810
11 2.333 1.583 67.8% 11,805 10,388,400 129,855
12 2.477 1.727 69.7% 11,120 10,675,200 133,440
13 2.621 1.871 71.4% 10,509 10,929,360 136,617
14 2.764 2.014 72.9% 9,962 11,157,440 139,468
15 2.908 2.158 74.2% 9,469 11,362,800 142,035
16 3.052 2.302 75.4% 9,023 11,549,440 144,368
17 3.196 2.446 76.5% 8,616 11,717,760 146,472
18 3.340 2.590 77.5% 8,245 11,872,800 148,410
19 3.489 2.734 78.5% 7,905 12,015,600 150,195
20 3.628 2.878 79.3% 7,591 12,145,600 151,820

There was a flury of e-mails in 2009, including :
From: Stan Paddock
Subject: Re: Question: How many equiv punched cards did a 2400-ft reel hold?
Date: October 15, 2009 7:48:40 PM PDT
To: ...

Bill,

Last Wednesday I ran a short program to try and figure this out.
  1. I tried to find the longest tape in our storage. (biggest diameter)
  2. I loaded the tape on drive one of the CT machine.
  3. My program wrote 1600 character (blocking factor 20 for cards) records at 556 BPI. 3/4 inch assumed for inter-record-gap.
  4. After each write, I checked for End-Of-Reel
  5. If not, I added one to a counter and went back to write.
  6. When End-Of-Reel was detected, I printed out the total number of records written.

7,591 records
151,820 80 character cards
12,145,600 characters
2,295 feet of tape used for data

Extrapolating to 800 BPI
10,014 records
200,280 cards
16,022,400 characters
2,295 feet of tape used for data

According to Ron Williams, most customers used 556 BPI because 800 BPI was not that reliable on the 1401.

Stan

From: Bob Feretich
Subject: Re: Question: How many equiv punched cards did a 2400-ft reel hold?
Date: October 13, 2009 8:01:18 PM PDT
To: ...

The 729-V drive didn't ship until later. The 729-II drive was available with the 1401. The 729-II maximum density was 556 CPI. Do some good record blocking, but still having inter-record gaps... and 441 CPI average sounds like a reasonable number.

Regards,
Bob

From: Jack Ghiselli < jghiselli@sbcglobal.net >
Date: Thu, May 18, 2017 10:55 am

And Stan’s data ... is a pretty good real-world estimate: about 130,000 cards (65 boxes) per tape reel.

I wrote business application programs for the 1401, and selecting a block size for tape files was kind of a balancing act, given the 16,000 character maximum memory size of the 1401. The larger the tape block-size, typically the faster your tape-heavy program would run. But, to write a tape block of, say, 10,000 characters, you need a 10,000 character memory buffer, leaving precious little room for your application program logic. So, we’d typically start with a compromise about double Stan’s blocking factor, say 20 card-images/block, for a block-size of 1600 characters. Consider a typical program which read an old master tape in, updated with add/delete records, and wrote a new master tape out. Our 1460 (a souped-up 1401) had “Tape Overlap”, which sped up run-time, but meant you needed two buffers for the input tape, and two for the output tape. That’s 6,400 characters for the tape buffers, already limiting our program size to about 9K, without considering other working tape files. As the users demanded adding more and more features (hence more memory) to the program logic, we’d reduce the tape block sizes, so we’d often end up more like Stan’s numbers. Funny how Stan always comes out right, doggone him.

I’ve attached an Excel spread-sheet which computes the capacity of tapes at various card-image blocking factors. Of course, not all tape files had records which were card images, but a card image is a useful rule of thumb.

One aside: Sometimes our master tapes grew large enough to require multiple reels. If the programmer (me) could increase the block-size enough to squeeze into a single reel, the operator didn’t have to wait around for the hours-long program to demand he dismount reel #1 and mount reel #2. Instead, the operator could go to coffee. He was very appreciative, and a wily programmer could convert this appreciation to increased computer access time for debugging.

Best regards,

--Jack

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updated Sept 26, 2013