[TriLUG] OT: the optimum location for inner track/cylinder on rotating media?
Joseph Mack NA3T
jmack at wm7d.net
Wed Aug 12 09:53:51 EDT 2009
Some storage media (vinyl records, hard disks, cd/dvds?,
floppies) rotate at constant angular velocity AND operate at
a constant data rate. Thus the number of bits
stored/cylinder is constant, whether the cylinder is near
the center of the platter or on the outside. If the media is
unifor (the maximum storage density is the same anywhere on
the platter), and you're interested in maximising the
storage, then the lower storage density used on the outer
cylinders represents wasted area. The maximum bit density is
determined by the physical length of the inner cylinder.
Here's the storage possible on a platter of radius R in
which bits are stored at maximum density (assume = 1
bits = pi*R^2
Let's derive the storage on a platter in which the max
density is determined by the inner cylinder of radius r.
number of bits on inner cylinder
This number of bits is the same on all cylinders, so the
total storage is
The maximum storage possible is 0 for r=0, r=R and has a
maximum at r=R/2. The storage relative to the platter at
constant density is
The maximum number of bits that can be stored on a disk
operating at constant data rate and constant angular
velocity is half that of the platter operating at maximum
storage density (I'm surprised that it's that high) and
occurs when the innermost track is at r=R/2.
If this is correct, then vinyl records and CDs etc should
all have their inner most track at r=R/2. However inspection
of these media shows that the inner track is much closer to
the center of the platter and would indicate that the amount
of storage used on the platter is sub optimal.
What am I missing?
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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