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

[Craig Taylor]

Joseph,

I believe you're looking at it from an optimal bits per track point of view
... the optimal track may not be the inner track if total storage capacity
is brought into play. I'd much rather have 80gb of storage on a media that
is sub-optimal rather than 60gb optimal (#'s picked from air / not intended
to specify specific example).

On Wed, Aug 12, 2009 at 9:53 AM, Joseph Mack NA3T <jmack at wm7d.net> wrote:

> 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!
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-- 
-------------------------------------------
Craig Taylor
ctalkobt at ctalkobt.net