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

[Joseph Mack NA3T]

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 
bit/area)

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
      = 2*pi*r

This number of bits is the same on all cylinders, so the 
total storage is

        2*pi*r(R-r)

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

        2*pi*(R/2)^2/pi*R^2=1/2

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?

Thanks 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
Homepage http://www.austintek.com/ It's GNU/Linux!