## Formula

Enter your RPM and drive bolt thread details below to calculate the distance needed between your hinge and drive bolt.

#### Revolutions Per Minute

#### Thread

#### Presets

## Theory

Stars are always in a fixed position in the sky and appear to move across the night sky as the earth rotates. The rate at which the earth rotates relative to the stars in known as sidereal time and a sidereal day is the time it takes for the earth to perform a full rotation. Essentially, it is the time it takes for a any star in the sky to return to that same position.

A sidereal day on Earth is 23 hours 56 minutes and 4.091 seconds long or 1436 minutes (about 4 minutes shorter than a standard solar day) and we can use this time to calculate the rate at which the barn door tracker needs to turn.

If we think of the top board of the barn door tracker drawing an imaginary line as it moves, it will eventually draw a full circle if it is able to move 360° on it’s hinge. This means that any point on the board can be through of as the radius of an imaginary circle so we need to work out what size circle will match the sidereal rate of the Earth and this is dependent on the rate at which the top board will move which is determined by the size of the thread on the drive bolt and the speed at which it is turned.

One rotation of Earth is `2Π radians`

so the sidereal rate of the Earth is `2Π / 1436`

which is approximately `0.004375 radians per minute`

. Using this value we come to the final formula of:

`Radius (in inches) = RPM / ((2Π/ 1436) * TPI)`

or approximately `RPM / (0.004375 * TPI)`

where RPM is the revolutions per minute of the drive bolt and TPI is it’s threads per inch. The drive bolt should be centered at this distance from the hinge.