Stylus Rake Angle

A question was posed about why the angle of the cutter and angle of the stylus need to be the same.

The trigonometry dictates that for small angles of deviation it does not matter much as the cosine is changing extremely little for angles of 1,2,3 degrees. For instance, cos 3 degrees = .9986!

Visualize this: a pointed shovel whose shape is a "V", with the "V" portion 10 inches tall. Put the shovel straight into the sand to a depth of 5 inches, and then pull it along making a "V-shaped" groove in the sand.

Now, with the shovel in the groove, lean it 3 degrees forward or back. The "V" shape of the shovel fits the V groove almost perfectly at the 3 degree angle, even though the groove was cut with the shovel vertical, or at 0 degree lean angle. It has to: the cosine of 3 degrees is .999!

But, if you lean the shovel to 15 degrees you will see that only the upper part of the groove will contact the sides of the groove, the rest of the shovel will be pulled up away from the groove. We'll only have 2 short contact points.

The shovel represents the stylus, of course, the sand the record, and the V-groove the cut groove in the record.

So, in reality, small deviations of stylus angle compared to cutter angle mean very little. Large deviations represent a increasing compromise as the difference in angles gets larger.

Peterayer:

>I wonder if anyone has thought about designing an arm which would automatically compensate overhang and VTF for VTA changes.

Certainly. To maintain a constant VTF, the tonearm vertical bearing should be kept at the same height, regardless of VTA changes. It is probably best to align the vertical bearing axis to the LP surface, as doing so will minimize changes in effective arm length that would be induced by VTA changes or record warps.

To maintain a constant overhang requires that the tonearm pipe is raised and lowered on a curved rail or post that has the same radius as the stylus-to-tonearm-bearing distance. Easy to do with a linear-tracking tonearm (the Eminent Technology designs are a good example), a bit of a head-scratcher otherwise.

hth, jonathan carr

I think the Arche headshell (from Dertonearm, aka designer of the Axiom tonearm) allows for changing VTA at the headshell. I think this would fit Jonathan's requirement for changing VTA without changing the height of the vertical bearing, so as not to alter VTF. And of course the Arche could be used with most pivoted tonearms. I have no affiliation of any kind; nor do I own an Arche headshell. I don't find it to be a terrible bother to re-adjust VTF. What I usually do is get the VTF in the right ballpark, then settle on VTA, then finalize VTF, and Bob's your uncle. There is such a thing as "good enough".

There is such a thing as "good enough" indeed!

As for no VTF change with VTA change, it is complicated. Springs do NOT do acheive this as they are linear force per displacement devices, and VTF varies as a trigonometric function. Therefore, the compensation system for changing VTF with VTA to make VTF constant would need act in proportion to a trig function. Too complicated, best to adjust center of gravity height for minimum change in VTF with a given VTA change, and if you make a big enough change in VTA to actually change VTF meaningfully then just adjust VTF.

All tonearm guys who say their perfect height of the pivot point, the height of the counterweight, the underslung nature of their counterweight, or their spring, are not very good at trig, calculus, and running the experiments or they would know that they are wrong and then confirm it with the tests.

Changing VTA at the headshell brings with it several other problems while trying to solve a problem that readjusting the counterweight would have solved anyway.

Lew, I haven't carefully studied the Arche headshell, so take this with however much salt as you want.

Since the Arche's pivot for VTA adjustment appears to be placed above the top of the cartridge rather than at the stylus tip, it seems to me that it will alter the overhang and effective length along with the VTA.

hth, jonathan carr