A hard disk is made of a material with a linear coefficient of expansion of 1.5 × 10 ?6/°C. The track?to?track spacing is 1,000 nm. Assuming that the head is perfectly aligned over a track at a radius of 2 in. and that the error rate increases if the head strays 20% off track, how much temperature rise can we afford? What do you conclude from your answer?

What will be an ideal response?

We are going to assume that the expansion (movement) is in the disk for the sake of simplicity. If the tracks
are spaced by 1,000 nm than a 20% error in tracking corresponds to 200 nm. The head is 2 inches from the
center and thermal expansion must not move the track by more than 200 nm. If the disk heats up by one
degree, then the track moves by 2 × 1.5 × 10 ?6 = 3.0 × 10 ?6 inches. Since one inch is 25,400,000 nm, the
expansion is 3.0 × 10 ?6 × 2.54 × 107 = 76.2 nm/°C.
If the tolerance is 200 nm, the required change of temperature would be 200/76.2 = 2.6°C. This is a small
temperature change which implies that the temperature change in hard drives should be small, or there must
be a dynamic head tracking mechanism (which there is) to compensate for temperature changes.