This is a topic that comes back regularly, so let's try to understand it a bit better: how does the effective length vary when we modify the Vertical Tracking Angle by changing the height of the tonearm pivot?
If the pivot of a tonearm arm is raised, this will result in the stylus changing its position on the record. In effect, the stylus won’t trace the arc of the protractor anymore, but will be inside the arc (although still tracing an arc concentric to the proper one, since the pivot/spindle distance hasn't been modified). The question then is, by how much is this distance modified?
Starting with an effective length of 263 mm (at VTA = 0 mm, for reference), the following graph gives the result of the changes in the distance stylus-pivot axis obtained by raising the VTA by increments of 1 mm:
If, as an example, we examine more closely the results for a 5 mm change in VTA, here is what we find, following Löfgren A geometry (all calculations done using the John Elison spreadsheet):
VTA setting: reference position + 5 mm
Effective length: 263 mm 262.952 mm (resulting effective length (1))
pivot-spindle distance: 247.37 mm 247.32 mm
Offset angle: 20.812 degrees 20.816 degrees
Distortion, at null points:
66 mm 0.00014 (%) 0.00014
120.9 mm 0.00019 0.00019
Outside the null points:
57 mm 1.03511 1.03533
95 mm 0.48333 0.48343
140 mm 0.42205 0.42214
The variations in distortion are extremely small: between 0.00022% and 0.00009%.
But perhaps the main problem is that, while we modified the resulting effective length by raising the VTA, we did not change the pivot-spindle distance. So in effect, we left the Löfgren geometry. Then again it's probably not that significant because, even if we wanted to, we wouldn’t be able to adjust the pivot-spindle distance by 0.05 mm (247.37 - 247.32 = 0.05 mm) ...
Note that there is one more element entering in play here: the VTF will oftentimes be affected when modifying the height of the tonearm pivot. If, for example, the change in height results in an increase of the tracking force, the cantilever will be pushed down, and that will affect the VTA, as well as the resulting effective length. This in turn will have an effect on the stylus rake angle (SRA). Less pressure on the cantilever will have the opposite effect.
Typically, on tonearms where a change of height of the pivot results in a change in VTF, lowering the pivot increases the VTF; raising it diminishes the VTF. So it would appear that the two parameters, effective length and VTF, are working in the same direction: raising the height of the pivot can decrease the effective length and lower the VTF. The diminished tracking force results then in less pressure on the stylus and, as a consequence, a larger SRA, which in turns brings the stylus even further from the arc. Whether this can be measured is another question...
Adjusting the VTF after modifying the VTA should restore the proper geometry and maintain the variations in distortion within the limits given in the table above.
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(1) What is called here “resulting effective length” is the length of a horizontal line drawn from the stylus to the vertical axis of the pivot point--as opposed to the distance stylus-actual pivot point (inside the armwand) which remains constant. But the “resulting effective length” is the one of relevance here because it is the one on which the alignment geometry is based, and the one that varies with VTA changes: the stylus does not remain in the same position on that horizontal line.
