One key assumption Löfgren made in calculating the distortion is that the lateral stylus tip velocity is 10cm/s. It seems others followed this assumption and for instance the Ellison Excel sheet is based on it. This will scale all the calculations and hence is key in understanding the magnitude of the problem. This assumption was made in the time of 78s without RIAA correction, so I’m wondering about the extent that it’s still valid.
Here’s the quote in Löfgren (p. 355):
Die Schnellenamplitude überschreitet wohl selten 10 cm/s (11), entsprechend einer Lichtbandbreite (12) von etwa 25 mm.The citations (11) and (12) are:
(11) H. J. von BRAUNMüHL und W. WEBER, Einführung in die angewandte Akustik. Leipzig 1936, S. 106.
(12) G. BUCHMANN und E. MEYER, Eine neue optiselle Meßmethode für Grammophonplatten. Elektr. Kachr.-Techn. 7 (1930), H. 4, S. 147—152.
Just came across Gilson’s 1981 article in Wireless World that is quite interesting. I’ll just leave these quotes here without any comment (p. 61):
It shows simply that the lowest possible tracking angle errors can be achieved only at the cost of increasing the values of F and t; and conversely forces F and t can only be reduced by accepting increased angular errors. In the absence of published information on the audible effects of the opposing factors, the optimum balance is anybody’s guess, but it is hard to see justification for the assumption that the lowest possible angular error must necessarily be the best condition.
In thinking about these problems, it is necessary to keep a sense of proportion; tracking error is only one source of distortion and possibly a minor one. Probably the worst source is tracing error, which can easily run into double figures percentage at the inner grooves, particularly with slight stylus wear. Then there is vertical tracking angle error, which is difficult to avoid. Another source is that due to any longitudinal compliance in the stylus/armature system; it is usual to mount the cantilever in an elastomeric grommet or block, and this is not adapted to providing much rigidity in the longitudinal direction.