Abbe error or sine error describes the magnification of angular error over distance. For example, if you are trying to measure 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, if the shaft of a lathe is angled slightly, the part will have errors in diameter far down the part.
