It's a beautiful Sunday for a deep-dive into the subject. So here's a paper on the math of skating https://drive.google.com/file/d/11saMtnPRpj8xZ-M_CGDhgbPbVfufSDV1/view linked to by AnalogMagik's coverage on the subject https://www.analogmagik.com/antiskate , and it appears their test LPs plus software (which measures distortion) is probably the best way to set this force; however, the whole thing costs $750 in the US. The paper also covers the solutions provided by some arms, and old skating force measurement devices, and the first patent on it dating back to 1931 from Bell Labs.
Excerpts:
<<As the turntable spins, the cartridge stylus of pivoted tonearms may experience uneven pressures on the groove walls, a side-thrust which makes the stylus lean harder against one side of the groove than the other. This side-thrust - normally compensated by an anti-skating adjustment - is caused by the offset angle for headshell, groove modulation, and other factors. If there is no compensation for the skating force, the distribution on the vertical tracking force on the groove walls is increased in the Left Channel (Inner Groove Walls, resulting in distortion in the Right Channel, and vice versa.>>
<<
The effects of Antis-kating is dependent on many factors:
Mass of the armwand
Vertical Tracking Force
Cartridge suspension
Stylus Shape
VTA/Azimuth/Alignment Geometry
Bearing chatter
Vinyl Materials
etc......
>>
<<On 12" tonearms tracking at 2g or above, you may notice a number where the L and R channel distortion is already very close, or you may observe that numbers do not correspond to anti-skating changes. In such cases, the anti-skating force is not required.
Some tonearm designs have inherent imbalances and will register numbers which will be skewed towards one channel, in such cases, nothing can be done. Some tonearms have too much anti-skating force even at the lowest setting, so the results are highly dependent upon equipment quality.>>
<<One must realize that the force exerted on the stylus is not linear, therefore the amount of anti-skating force required will be different depending on the relative location of the cartridge towards the record spindle. The curve is somewhat of a parabolic shape, with the skating force higher at the outer groove than at the inner groove, and lowest in the middle. Some tonearms designs have a mechanism which will increase anti-skating force gradually to counteract the non-linear nature of the centripetal force.
Optimizing anti-skating adjustment at the outer grooves where the skating force is the strongest will cause over-compensation across the inner groves. This is why the anti-skating track is placed near the inner grooves. >>
<<Anti-skating affects crosstalk measurements. We have observed that when anti-skating is set incorrectly, the imbalance will sometimes (but not always) cause crosstalk readings to be skewed so that in an optimal number can never be achieved. Therefore it is important to go back and forth between Anti-skating and Azimuth, as well as VTF and VTA to achieve an optimal set of numbers.
Again, we emphasize that no setup parameter can be optimized in isolation. >>

If a skating force is generated a different vector diagram is R* formed, with Fv + Fs as resulting vector. This resulting vector can R L be resolved into vectors R* and L*, with R* being shorter than L*.
<<The reaction force (to the friction force) of the tone arm passes through the arm pivot. These two forces combine as vectors and, because of the angle ? between groove tangent and effective length L, leave an unbalanced force, the skating force Fs. This force is at right angles to the groove tangent and tends to pull the arm towards the record's centre (see fig. 1). In fig. 1 the stylus tip is on a null point, therefore the skating force is directed exactly towards the record centre. The skating force is determined by the magnitude of ?, which varies across the record surface (? = angle between groove tangent and effective arm length = offset angle ? + tracking error ?, with ? varying across the record surface, (see fig. 10)),the cartridge’s mechanical resistance (cantilever damping). In fig.1 the angle ? is equal to the offset angle ?.>>
<<Skating force compensation enhances trackability by about 20-25 %.>>
[ack: This is very much in line with the out-of-phase test using my Ultimate Test LP that I posted earlier, where cancellation in mono improved from -8dB without anti-skating to -10dB with]
<<Higher modulation velocities result in increased skating force [1, 2]. Wright [6] could show experimentally
that the friction force increased for higher modulation velocities (for sinewaves).>>
<<The skating force Fs is a function of groove radius R, overhang D and effective arm length L>>
<<
Final remarks:
Since skating force is not constant across the record surface but describes a somewhat parabolic curve exact compensation is not possible: whatever the precision of setting the antiskating , the curve of the skating force will be intersected in two points at best.
From discussions on web forums it becomes evident that some people think that skating force is zero when the tracking error is equal to zero, as it is the case in the null points. This is true only for linear tracking arms, for pivoted arms this simply not correct. As long as the line connecting the stylus tip to the arm pivot is not tangential to the groove at the contact point, which is always the case for pivoted arms, a skating force is generated. For that very reason tangential pivoted arms like the Garrard Zero and the Thales still have anti-skating mechanisms.>>
Excerpts:
<<As the turntable spins, the cartridge stylus of pivoted tonearms may experience uneven pressures on the groove walls, a side-thrust which makes the stylus lean harder against one side of the groove than the other. This side-thrust - normally compensated by an anti-skating adjustment - is caused by the offset angle for headshell, groove modulation, and other factors. If there is no compensation for the skating force, the distribution on the vertical tracking force on the groove walls is increased in the Left Channel (Inner Groove Walls, resulting in distortion in the Right Channel, and vice versa.>>

<<
The effects of Antis-kating is dependent on many factors:
Mass of the armwand
Vertical Tracking Force
Cartridge suspension
Stylus Shape
VTA/Azimuth/Alignment Geometry
Bearing chatter
Vinyl Materials
etc......
>>
<<On 12" tonearms tracking at 2g or above, you may notice a number where the L and R channel distortion is already very close, or you may observe that numbers do not correspond to anti-skating changes. In such cases, the anti-skating force is not required.
Some tonearm designs have inherent imbalances and will register numbers which will be skewed towards one channel, in such cases, nothing can be done. Some tonearms have too much anti-skating force even at the lowest setting, so the results are highly dependent upon equipment quality.>>
<<One must realize that the force exerted on the stylus is not linear, therefore the amount of anti-skating force required will be different depending on the relative location of the cartridge towards the record spindle. The curve is somewhat of a parabolic shape, with the skating force higher at the outer groove than at the inner groove, and lowest in the middle. Some tonearms designs have a mechanism which will increase anti-skating force gradually to counteract the non-linear nature of the centripetal force.
Optimizing anti-skating adjustment at the outer grooves where the skating force is the strongest will cause over-compensation across the inner groves. This is why the anti-skating track is placed near the inner grooves. >>
<<Anti-skating affects crosstalk measurements. We have observed that when anti-skating is set incorrectly, the imbalance will sometimes (but not always) cause crosstalk readings to be skewed so that in an optimal number can never be achieved. Therefore it is important to go back and forth between Anti-skating and Azimuth, as well as VTF and VTA to achieve an optimal set of numbers.
Again, we emphasize that no setup parameter can be optimized in isolation. >>

If a skating force is generated a different vector diagram is R* formed, with Fv + Fs as resulting vector. This resulting vector can R L be resolved into vectors R* and L*, with R* being shorter than L*.
<<The reaction force (to the friction force) of the tone arm passes through the arm pivot. These two forces combine as vectors and, because of the angle ? between groove tangent and effective length L, leave an unbalanced force, the skating force Fs. This force is at right angles to the groove tangent and tends to pull the arm towards the record's centre (see fig. 1). In fig. 1 the stylus tip is on a null point, therefore the skating force is directed exactly towards the record centre. The skating force is determined by the magnitude of ?, which varies across the record surface (? = angle between groove tangent and effective arm length = offset angle ? + tracking error ?, with ? varying across the record surface, (see fig. 10)),the cartridge’s mechanical resistance (cantilever damping). In fig.1 the angle ? is equal to the offset angle ?.>>
<<Skating force compensation enhances trackability by about 20-25 %.>>
[ack: This is very much in line with the out-of-phase test using my Ultimate Test LP that I posted earlier, where cancellation in mono improved from -8dB without anti-skating to -10dB with]
<<Higher modulation velocities result in increased skating force [1, 2]. Wright [6] could show experimentally
that the friction force increased for higher modulation velocities (for sinewaves).>>
<<The skating force Fs is a function of groove radius R, overhang D and effective arm length L>>
<<
Final remarks:
Since skating force is not constant across the record surface but describes a somewhat parabolic curve exact compensation is not possible: whatever the precision of setting the antiskating , the curve of the skating force will be intersected in two points at best.
From discussions on web forums it becomes evident that some people think that skating force is zero when the tracking error is equal to zero, as it is the case in the null points. This is true only for linear tracking arms, for pivoted arms this simply not correct. As long as the line connecting the stylus tip to the arm pivot is not tangential to the groove at the contact point, which is always the case for pivoted arms, a skating force is generated. For that very reason tangential pivoted arms like the Garrard Zero and the Thales still have anti-skating mechanisms.>>
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