# Abbe error

Abbe error, named after Ernst Abbe, also called sine error, describes the magnification of angular error over distance. For example, when one measures a point that is 1 meter away at 45 degrees, an angular error of 1 degree corresponds to a positional error of over 1.745 cm, equivalent to a distance-measurement error of 1.745%.

As Abbe errors those deviations are referred to in the length measurement, resulting from the fact that the axis of the reference length and the movement axis do not coincide and the relative movement of the measurement object to Antastsensor with guide deviations such as Pitch or yaw angle errors is afflicted.[1]

In machine design, some components are particularly sensitive to angular errors. For example, if the shaft of a lathe is angled slightly, the part will have errors in diameter far down the part.

Abbe error can be detrimental to dead reckoning.

Formula:

$\epsilon = h \sin \theta$

$\epsilon$ the error.

$h$ the distance.

$\theta$ the angle.

## References

1. ^ "Determination of Abbe Errors". Technewss. Retrieved 12 December 2014.