[TriLUG] OT: the optimum location for inner track/cylinder on rotating media?
Joseph Mack NA3T
jmack at wm7d.net
Wed Aug 12 12:40:25 EDT 2009
On Wed, 12 Aug 2009, Steve Litt wrote:
> I didn't take the time to really think about it, but one
> thing you're missing is this equation: 2*pi*r(R-r)
> That's wrong -- if the inner radius is 0 that implies no
> bits -- clearly wrong.
this is my point. If r=0 then you store no bits on the
> When you did the area calculation, that was valid only if
> bits are constant over tangential lengths, not if they are
> constant over radial angles.
I did it both ways: bits/area are constant; bits/angle along
a cylinder is constant and I compared them.
I talked to a few people here at work about this. For
constant bits/angle the bits/platter is a maximum at r=R/2.
However the maximum, being a maximum is smooth at the top
and doesn't vary much for small changes in r. Here's the
capacity for other r's
We measured a CD to find r=1/3 and the CD looses 1/18th the
of its storage relative to the r=1/2 case. From what I
remember of vinyl records, r was about 1/3. To prevent irate
users complaining about the manufacturers short changing
them on storage by only usin the outer half of the record,
the manufacturers start at r=1/3 loosing only 5% or so of
The test of the theory (that the maximum is not used to
placate users) would be to measure r for a device that the
users can't see, like a floppy or hard disk. These should
all have r=R/2. I can't find any floppies to disassemble.
and I don't have any dead hard disks
I decided I was happy with capacity = 1/2 for r=1/2. Here's
a remapping of the problem
\ | | /
\ / h
The triangle holds a rectangle. At what height h is the
rectangle of maximum area and what is the area? (ans h=1/2
and the area of the rectangle is 1/2)
Joseph Mack NA3T EME(B,D), FM05lw North Carolina
jmack (at) wm7d (dot) net - azimuthal equidistant map
generator at http://www.wm7d.net/azproj.shtml
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