This articlerelies largely or entirely on asingle source. Relevant discussion may be found on thetalk page. Please helpimprove this article byintroducing citations to additional sources. Find sources: "Abbe error" – news ·newspapers ·books ·scholar ·JSTOR(July 2020)

Abbe error, named afterErnst Abbe, also calledsine error, describes the magnification of angular error over distance. For example, when one measures a point that is 1 meter away at 90 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%.^[1]

In machine design, some components are particularly sensitive to angular errors. For example, slight deviations from parallelism of the spindle axis of alathe to the tool motion along the bed of the machine can lead to relatively large (undesired) taper along the part (i.e. a non-cylindrical part). Vernier calipers are not free from Abbe error, while screw gauges are free from Abbe error. Abbe error is the product of the Abbe offset and the sine of angular error in the system.^[2]

Abbe error can be detrimental todead reckoning.

Formula:

${\displaystyle ϵ=h\sin \theta }$

${\displaystyle ϵ}$ is the error.

${\displaystyle h}$ is the distance, sometimes called theAbbe offset.

${\displaystyle \theta }$ is the angle.

• Error
• Trigonometry

• Articles needing additional references from July 2020
• All articles needing additional references