(HP-67/97) Tonearm Geometry

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An extract from Tonearm Geometry and Setup Demystified, AUDIO {magazine}, JAN 1980, pgs 76-88

"Optimum geometry of tonearms has been the subject of several articles over the past three decades, the earliest complete mathematical study being that of H.G. Baerwald in his paper on optimum geometry in 1941, where an analytical study of tracking error distortion showed that optimum geometry of a tonearm of given effective length will have a corresponding offset angle and overhang. Further, the arm should zero at two positions on the grooved surface of a
phonograph record given the minimum and maximum radii where the signal will be encountered … In these "modern" times of computers and high technology, it is interesting to note, according to our calculations, that only a small group of manufacturers of tonearms are utilizing optimum lateral geometry. One would assume there would at least be agreement on this design parameter. Recently, Paolo Nuti used simple trigonometry to present some easy-to-use equations for measuring and calculating lateral tracking error, and provided a program for use on the Hewlett-Packard 67 /97 scientific programmable calculators …
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Geometric Considerations
Basically, optimum geometry can be summarized in three simple equations - the determination of null radii, the optimum offset angle. and the optimum overhang for a given effective length …
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Calculator Hints
With the advent of inexpensive yet sophisticated scientific calculators, solution of the equations presented in this paper becomes a practical consideration for interested audiophiles as well as engineers. Those who have programmable scientific
calculators such as the Hewlett-Packard 67 /97 …
Equations 2 and 4 are of the most interest since they calculate offset angle and overhang.
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The procedures are general and may not be directly applicable to all calculators. Since the output column gives the intermediate results, one can modify the routines for his own calculator.
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Table VI - Calculator steps for calculation of optimum offset angle
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Table VII-Calculator steps for calculation of mounting center and stylus overhang
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