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Here is the correct solution...

Here is the equation you intended to present:

Fs = Ft * Sin(cartridge offset + tracking error)

This is certainly a valid equation when we define tracking error as negative in-between the null-points and positive outside the null-points.

Cartridge offset plus tracking error is the angle between the groove tangent at the stylus and the tonearm pivot/stylus axis. There's no question that tonearm manufacturers nearly always specify cartridge offset, so that's easy to find. However, the problem is that tracking error cannot be calculated without first finding the angle between the groove tangent and the tonearm's pivot/stylus axis. In other words, you have to find the total angle first, then subtract cartridge offset to get tracking error, then add them back together to get the angle you calculated in the first place. That just doesn't make any sense. Furthermore, it proves that tracking force is not a function of either cartridge offset or tracking error, but a function of the angle between the groove tangent and the tonearm's pivot/stylus axis. Let's call this angle " A " so the correct equation becomes:

Fs = Ft * Sin( A )

Okay! The parameters we need in order to derive an equation to calculate skating force Fs are as follows:

a = radial distance from the platter spindle to the stylus
b = tonearm pivot-to-stylus effective length
c = tonearm pivot-to-spindle mounting distance
VTF = vertical tracking force
f c = dynamic coefficient of friction for the stylus in the groove
C = angle at the stylus between the blue radial line and the green pivot/stylus axis
A = angle between the groove tangent at the stylus and the tonearm's pivot/stylus axis. A is the complement of angle C , which means that A + C = 90-degrees.



The vector Ft is a function of vertical tracking force and the stylus/groove coefficient of friction f c .

Ft = VTF * f c

Next, we can find angle A between the orange groove tangent and the green pivot/stylus axis by solving the pivot-stylus-spindle triangle for the complement of the angle at the stylus using the Law of Cosines. We've already defined the required variables:

a = radial distance from the platter spindle to the stylus
b = tonearm pivot-to-stylus effective length
c = tonearm pivot-to-spindle mounting distance
C = angle at the stylus between the blue radial line and the green pivot/stylus axis

Since angle A is the complement of angle C :

A = 90 - C

Angle A is also the angle between vectors Ft and Fa , which brings us back to the following equation:

Fs = Ft * Sin( A )

The interesting thing about complementary angles is that the Cosine of angle C is the Sine of angle A . Therefore, the equation above for Fs can be expanded as follows:

Fs = VTF * f c * ( a 2 + b 2 - c 2 ) / (2 ab )

I think this clearly shows that skating force Fs does not depend on either tracking error or cartridge offset, but on angle A between the groove tangent and the tonearm's pivot/stylus axis.

Best regards,
John Elison


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  • Here is the correct solution... - John Elison 08/30/1721:59:56 08/30/17 (0)

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