Review of path-length calculations for rectangular bending magnets with arbitrary pole-face angles

This document shows how to calculate the path-length of rectangular bending magnets in a beam line. The path-length depends on the pole-face angles and the body geometry, i.e. how the magnet is positioned in the line. The majority of bending magnets are installed with identical pole-face angles at the start and the end, but in certain cases the pole-face angles are different e.g. in the CERN PS BOOSTER BTP and BTY extraction lines, the BHZ10 magnet have a special positioning in order not to perturb the optics of any of the lines unfavorably. The path-length corresponds to the s-parameter in MADX, and must be calculated precisely, in order to get a correct survey, which needs to be correct to the 10 micron level.