Abbe error, named after
Ernst Abbe
Ernst Karl Abbe HonFRMS (23 January 1840 – 14 January 1905) was a German physicist, optical scientist, entrepreneur, and social reformer. Together with Otto Schott and Carl Zeiss, he developed numerous optical instruments. He was also a co-ow ...
, 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%.
In machine design, some components are particularly sensitive to angular errors. For example, slight deviations from parallelism of the spindle axis of a
lathe
A lathe () is a machine tool that rotates a workpiece about an axis of rotation to perform various operations such as cutting, sanding, knurling, drilling, deformation, facing, and turning, with tools that are applied to the workpiece to c ...
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.
Abbe error can be detrimental to
dead reckoning
In navigation, dead reckoning is the process of calculating current position of some moving object by using a previously determined position, or fix, and then incorporating estimates of speed, heading direction, and course over elapsed time. ...
.
Formula:
:
the error.
the distance.
the angle.
References
{{reflist
Error
Trigonometry
de:Kippfehler