How to calculate the storage disk capacity & how much time required to access the stored data?

Disks are storage devices that hold enormous amounts of data, on the order of hundreds to thousands of gigabytes.

Disks are constructed from platters. Each platter consists of two sides, or surfaces. A rotating spindle in the center of the platter spins the platter at a fixed rotational rate, range between 5400 to 15000 rpm.

Each surface consists of a collection of concentric rings called tracks. Each track is partitioned into a collection of sectors. Sectors are separated by gaps where no data bits are stored. The geometry of multiple-platter termed as cylinders, where a cylinder is the collection of tracks on all the surfaces that are equidistant from the center of the spindle.

The maximum number of bits that can be recorded by a disk is known as Disk capacity.

The number of bits that can be recorded into a 1-inch segment of a track is known as Recording density which is measured by bits/in.

The number of tracks that can be squeezed into a 1-inch segment of the radius extending from the center of the platter is known as Track density, which is measured by tracks/in

The product of the recording density and the track density is referred as Areal density, which measured by bits/square inches.

\(Disk\;Capacity = \left(\frac{No.of\;Bytes}{Sector}\right)\;\times \left(\frac{Avg\;no\;of\;Sectors}{Track}\right)\;\times\left(\frac{No\;of\;Tracks}{Surface}\right)\;\times\left(\frac{No\;of\;Surfaces}{Platter}\right)\;\times\left(\frac{No\;of\;Platters}{Disk}\right)\)

The disk capacity is expressed in Gigabytes (GB).

Example

What is the capacity of a disk with two platters, 30,000 cylinders, an average of 300 sectors per track, and 512 bytes per sector?

Disk Capacity = (512/Sector) X (300/Track) X (30000/Surface) X (2/Platter) X (2/Disk)

= 18,43,20,00,000 = 18.43 GB

Disks read and write bits stored on the magnetic surface using a read/write head connected to the end of an actuator arm. The action of moving the arm back and forth along its radial axis is called seek. Disks with multiple platters have a separate read/write head for each surface.

Disks read and write data in sector-sized blocks. The access time for a sector has three main components: seek time, rotational latency, and transfer time.

The time required to move the arm to the target sector is called the seek time.

The waiting time of head for the first bit of the target sector to pass under the head known as Rotational Latency.

The maximum rotation time,

$$ T_{max\;rotation} = \left(\frac{1}{RPM}\right) \;\times \left(\frac{60\;secs}{1\;min}\right) $$

\( Avg.Rotation\;Time = \frac{1}{2} \;\times\; Max. Rotation\;Time\)

The transfer time for one sector depends on the rotational speed and the number of sectors per track.

$$ T_{avg\;transfer} = \left(\frac{1}{RPM}\right) \;\times\; \left(\frac{1}{avg. no\;of\;sector\;per\;track}\right)\; \times\; \left(\frac{60\;secs}{1\;min}\right) $$

The average time to access the contents of a disk sector as the sum of the average seek time, the average rotational latency, and the average transfer time.

\(Access\;Time = Avg.Seek\;Time + Avg.Rotation\;Time + Avg. Transfer\;Time \)

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