[TriLUG] OT: the optimum location for inner track/cylinder on rotating media?

[Joseph Mack NA3T]

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 
platter.

> 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

r	capacity
R/2	1/2
R/3	4/9
R/4	3/8

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 
storage.

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)

Joe

-- 
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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