Arc Angles: Optimizing Tonearm Geometry


If you've been reading audio magazines for the past 30 years or more, you may recall that in the late 1970s there was a short-lived furor, first in the US and then in the UK, about forgotten lessons of tonearm/cartridge alignment. It turned out that seminal work on the subject by H.G. Baerwald, published in 1941(footnote 1) and refreshed by J.K. Stevenson in 1966 (footnote 2), had been disregarded by many pickup-arm designers, presumably because they'd never been acquainted with it. (It has since come to light, principally through the work of Graeme Dennes (footnote 3), that Erik Löfgren first published the optimum alignment equations more generally credited to Baerwald over three years earlier, in 1938. Perhaps because Löfgren's paper was in German and Baerwald's in English, the latter's became the recognized reference. Löfgren's paper has since been translated by Klaus Rampelmann (footnote 4)).


To do the history part right, we have to go back before Löfgren and Baerwald, and turn our gaze to England in 1924, the second year of publication of The Gramophone, cofounded and edited by novelist (later Sir) Compton Mackenzie. The magazine's technical editor was the remarkable Percy Wilson, a larger-than-life character whose mathematical background was used to good effect at the time, not only in modifying the flare of the exponential horn on the more realistic assumption of spherical rather than planar wavefronts, but also by being applied to what, in an article published in the September and October 1924 issues (footnote 6), he termed "needle track alignment."

What was then already understood was that (using modern terminology) because tonearms or pickup arms were pivoted, but cutter heads ran on a linear drive mechanism, angular errors were inherent in record replay—and exactly the same remains true today (footnote 7). The cutting stylus traverses a radius of the disc, so that the lateral groove modulation is nominally at right angles to a tangent to the groove at all times—whereas the replay stylus traverses an arc, so that the modulation is generally read with some angular disparity, which generates distortion (footnote 8). Today we know that angular disparity as lateral tracking error (LTE), and the resulting nonlinearity as lateral tracking error distortion (LTED).

Wilson calculated what alignment of the replay components would minimize LTE across the disc, basing his figuring on the assumption—wrong, as we will see—that this would also minimize the resulting distortion. To achieve this, he found, the radius of the stylus (needle) arc had to be greater than the distance from the arm pivot to the center of the disc, by a distance that today we term the overhang; and the pickup cartridge had to be twisted relative to a line joining stylus to arm pivot by an angle termed the offset. This overhang-plus-offset geometry, Wilson's great contribution to arm/cartridge alignment, is still used today, even though his equations for calculating the two parameters have been superseded.


Footnote 1: H.G. Baerwald, "Analytic Treatment of Tracking Error and Notes on Optimal Pick-Up Design," Journal of the Society of Motion Picture Engineers, December 1941.

Footnote 2: J.K. Stevenson, "Pickup Arm Design," Wireless World, May and June 1966.


Footnote 4: Erik Löfgren, "On the Non-Linear Distortion in the Reproduction of Phonograph Records Caused by Angular Deviation of the Pickup Needle," originally published in German in Akustische Zeitschrift, November 1938, Vol.3, pp.350–362; downloadable in English translation here.

Footnote 5: Such as and

Footnote 6: Percy Wilson, "Needle Track Alignment," The Gramophone, September (pp.129–131) and October (pp.167–169) 1924. Available from Gramophone's online archive, these articles can be downloaded, a bit laboriously, as PDFs. Only the September article contains alignment equations.

Footnote 7: I ignore here radial-tracking (aka linear-tracking or parallel-tracking or tangential-tracking) arms since they remain rarities, and those pivoted arms with headshell-rotation mechanisms—such as that on the Garrard Zero 100 of yesteryear because they are rarer still.



scho2684's picture

Hi there,
Thanks for this very interesting explanation.

There are 2 things though:
It is stated that it would be good to have a alignment tool delivered with cartridges that obviously is referring to the cartridge body:

I have found that cantilevers and styluses are never 100% aligned correctly, so how to deal with this?

The other thing is the Lofgren B method on which you comment that the approach does not make sense to you because of, as I read it, the higher distortion at the end of the disc.

If I look at my records, most of them don't have modulated grooves there where Lofgren B is exceeding the distortion of the max mid area distortion of the Bearwald, so therefore I think that Lofgren B is the better one...(for me at least)