The same way your car calculates how fast you're driving, you can figure out how quickly an object rotates using its angular velocity. This measurement of how fast an object is turning or rotating is important to vehicle speed as well as hard disk usage.

## Rotational Latency

**Rotational latency** measures how long an object with an angular velocity goes through an entire rotation or revolution. You can imagine a car making a turn as part of a circle that includes that turn. Or you can think of the tires of a car rotating on their own axis as the car moves. The **angular velocity** measures this velocity of rotation or revolution.

The speedometer on your car is one example of rotational latency, and the concept is also used for data storage on hard disk drives for computers. You can learn more about rotational delay and disk access time to figure out how these devices use rotational latency. When hard drives read information from a disk, the disk rotates with an angular velocity. In the context of hard drives, you measure the rotational delay of the hard drive.

## Hard Drive Rotational Delay

In hard drives, platters, double-sided magnetic disks that store data, are arranged like a record with each disk at the same center. You can group these tracks, or each disk stacked on top of one another, into sectors, the units of data transfer. In this setup, the surface has a head which performs the reading and writing.

For hard drives, the *seek time* tells you the delay time, the *rotational delay* is how long it takes to get to the correct sector, *transfer time* is how long the data reading process takes and *overhead* is the disk space used for location and timing of the information itself. You can calculate **transfer time** by dividing the size of a byte sector by the transfer rate.

## Calculating Rotational Delay

To calculate **rotational latency**, or rotational delay in the context of hard drives, first you need to know an object's angular velocity per unit time. This could be a hard drive velocity of 7,200 rotations per minute. Convert the time unit to seconds. For 7,200 rotations per minute, you divide the number by 60 seconds to get 120 rotations per sec.

The delay is the inverse of this value, or the number 1 divided by the value, which would be 1/120 seconds, or about .0083 seconds. Make sure you measure rotational delay with the same units of time that you want for the disk access time.

## Disk Access Time Example

You can also obtain average disk access time as the sum of average seek time, average rotational delay, transfer time, queuing overhead and and queuing delay. Queuing time is how long it takes for a disk to become free. If you had a hard drive with 8 kb (kilobytes) transfer size, average seek time 12 ms, rotational velocity 8,200 RPM (rotations per minute), transfer rate of 4 mb/s and controller overhead of .02 seconds, you can calculate average disk access time.

First convert the rotational velocity to seconds and the average seek time to seconds to get 136.67 rotations per second and .01 seconds, respectively. Divide .5 rotations by 136.67 rotations per second to get .0037 seconds for an average rotation. Use .5 rotations because you want to cover half of a rotation when calculating an average time for rotation. You can do this by assuming, for random reading and writing, the disk spins halfway on average.

Convert the transfer size 8 kb to mb by multiplying it by 0.001 to get 0.008 mb, and divide it by the transfer rate 4 mb/s to get .002 seconds. Add these numbers in units of seconds as 0.002 + 0.002 + 0.012 + 0.0042 to get a total average disk access time of 0.0202 seconds.

All this happens through the process of reading from a disk, and you can calculate the response time by adding together seek time, rotational delay, transfer time and overhead.

References

- Computer Hope: Rotational delay
- ScienceDirect: Rotational Latency - an overview
- University of Washington: Lecture 26
- UCSD: Solutions 2
- Computer Hope: Disk access time
- Villanova: The average disk access time formula
- Power Admin: Current & Average Disk Queue Length Counters
- Duke University: Disk Access Time Example

About the Author

S. Hussain Ather is a Master's student in Science Communications the University of California, Santa Cruz. After studying physics and philosophy as an undergraduate at Indiana University-Bloomington, he worked as a scientist at the National Institutes of Health for two years. He primarily performs research in and write about neuroscience and philosophy, however, his interests span ethics, policy, and other areas relevant to science.