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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
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updated Sept 26, 2013