This author's recent paper on the zeros of the tracking error for various Löfgren alignments showed that the formula originally derived in 1941 for tracking angle zeros in the case of the Löfgren A alignment method ("minimax" optimization of distortions) provides accurate results in practice, but the approximate formula often used for the Löfgren C alignment (Least Mean Squares optimization) does not appear to work as well. The zero tracking error radii were found to be in error by up to 0.6 mm, causing practically all protractors for Löfgren C alignment to be slightly miscalibrated. This paper investigates the Löfgren C case analytically and presents some new formulae for the optimum offset angle, overhang, and zero tracking error radii, which match the numeric optimization results very well.

Author: Jovanovic, Vladan M.
Affiliation: Consultant, Bloomington, IN
JAES Volume 70 Issue 3 pp. 199-207; March 2022
Publication Date: March 8, 2022

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