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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

414.0. "Disk blocks to tape inches" by R2ME2::STAN () Fri Dec 20 1985 16:43

From:	ALGOL::HARRIS       "What would it take to remove the hassles?" 20-DEC-1985 16:32
To:	STAN
Subj:	formula

Any rough guess as to how blocks on the disk convert to magtape inches?
Assume 1600bpi   (you wouldn't *believe* SDC wants length estimates, too
... or would you??)
-Tom
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414.1R2ME2::GILBERTFri Dec 20 1985 19:123
> Any rough guess as to how blocks on the disk convert to magtape inches?

All of them!?  :^)
414.2TOOLS::STANSun Dec 22 1985 18:2112
As far as the bits go:

	      1 tape inch   1600 bits   1 byte    1 block     1600
1 tape inch =		  X --------- X ------ X --------- = ------- blocks
			    tape inch   8 bits   512 bytes   8 X 512

which is approximately 200/500 = 0.4 blocks.

Unfortunately, the gaps on the tape are larger than the data bits,
so we must also factor in the number of record gaps and file gaps.

Does anyone know how long a record gap is (in inches)?
414.3AURORA::HALLYBMon Dec 23 1985 12:0633
Assuming one uses BACKUP to write the tape (e.g., for software distribution),
and one sticks to rather conventional defaults, then at 1600 bpi:

			1 foot ~= 32 blocks

For 6250 bpi the density is approximately 85 blocks/foot.

If your data consists primarily of a large number of small files, then
the density will be somewhat less, but that isn't a concern for distribution
purposes.  There's already some fudge (0.7) in the factors above which you'll
see if you do the same arithmetic I did.

Some notes of interest --

"bpi" is a linear measure.  For tapes, capacity is an area and things being
what they are, 1600 bits/inch works out to be 1600 Bytes/inch of storage.
Likewise for 6250.

BACKUP writes data onto the tape with a blocking factor of 8 KBytes, regardless
of file format or file size.  Inter-record gap is .4in for 6250 bpi and I think
its .75in for 1600 bpi.  I could be wrong about the .75 but not by enough to
make a significant difference since 8KB is already 5+ inches.

The figures above make sense when compared against our advertising specs --

A TU77 @ 1600 bpi, 125 ips operates at a bandwidth of 200 KBytes/second and 
can store  40 MBytes of data on a 2400 foot reel at 8 KBytes/block.

A TE16 @ 1600 bpi,  45 ips operates at a bandwidth of  72 KBytes/second and
can store  40 MBytes of data on a 2400 foot reel at 8 KBytes/block.

A TA78 @ 6250 bpi, 125 ips operates at a bandwidth of 781 KBytes/second and
can store 140 MBytes of data on a 2400 foot reel at 8 KBytes/block.
414.4RANI::LEICHTERJSun Dec 29 1985 19:496
Don't forget to add the overhead for BACKUP's redundancy blocks!  Every n
blocks (n=10, by default), BACKUP writes a block that is the XOR of the
n blocks just written.  Hence, the available space on the tape is n/n+1 times
what you think (about 10% lower, with the default redundancy group).

							-- Jerry
414.5AURORA::HALLYBThu Jan 02 1986 12:4930
Updating my previous answer to allow for Jerry's point and the correct values
for interblock gaps (1600 --> .6in, 6250 --> .3in, thanx to Howard Kaikow),
we have:

Assuming one uses BACKUP to write the tape (e.g., for software distribution),
and one sticks to rather conventional defaults, then at 1600 bpi:

			1 foot ~= 30 blocks

For 6250 bpi the density is approximately 108 blocks/foot.

If your data consists primarily of a large number of small files, then the
density will be somewhat less, but that isn't a concern for distribution
purposes.  There's already some fudge in the factors above which you'll see if
you do the arithmetic below.  One note of interest:  "bpi" is a linear measure.
For tapes, capacity is an _area_ and things being what they are, 1600 bits/inch
works out to be 1600 Bytes/inch of storage.  Likewise for 6250. 

BACKUP writes data onto the tape with a blocking factor of 8 KBytes, regardless
of file format or file size.  Every 10th block, BACKUP appends an 11th "XOR"
block for redundancy.  We therefore have:

	14.5454 user d_blocks = 16.00 data d_blocks = 8K bytes
	(8K bytes) / (1600 bytes/in) = 5.12in. / t_block "data"
	(5.12 in. / t_block "data") + (.6in "gap") = 5.72in. / t_block "net"
	So: 14.5454 user disk blocks = 5.72 inches of tape	
	or: 1 inch = 2.54 blocks	(1 cm = 1 block!!!)
	or  1 foot = 30+ blocks

  John