Rule of thumb: Groove geometry, Depth-to-width ratio


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Rule of thumb: Groove geometry, Depth-to-width ratio

Unread postby Steve E. » Thu Jan 02, 2014 6:19 pm

This came out of this thread. Thanks to boogievan for starting the topic.
I'm going to continually reedit this top posting as new information comes my way, so it is a convenient sticky.

The question is: When we measure a groove width, how DEEP is the cut? This is an important question if we don't want to cut so deep that we hit aluminum and kill our styli on acetate lacquers. (Which are apparently roughly 7 mils deep). We need extra leeway, too, because we cut deeper for a moment when making a locked groove....especially if we don't have the protection of something like an advance ball.

Recent postings of old literature (viewtopic.php?f=9&t=4564) indicate to me that, at least since the 1940s, most cutting styli have been in the 87º to 90º range. There used to be a few outliers of 70º, 95º, and even 100º. And in the wax era, who knows?

The big difference in the shaping of pre-1948 standard "coarse" groove styli (for 78 rpm records, and for the old 33 1/3 radio transcription discs) and the post-1948 microgroove styli was in the radius of the curved tip at the bottom. Microgroove styli are closer to pointy, producing a cross section that is almost like a triangle. I am not sure how many mils shallower-per-width a more rounded stylus would be, so I don't know how I'd do the math. Is it a negligible difference in depth? or does such a groove have trapezoid math applied to it?

Anyway, the math here assumes a near-triangular cross section.

Depth of a modern 87º groove: negligibly more than 1/2 of its width. (=.52689)
Depth of a modern 90º groove: 1/2 of its width. (=.5)

That's all the info that 98% of people on the board will ever need on the subject.

OK. For anyone using atypical styli, and keeping in mind that the high radius of the tip of a non-microgroove cutting stylus may give you additional uncalculated leeway:

In a theoretical groove with a 53.2º angle, the depth would be ~1/1 of the width (=.9985)
In a theoretical groove with a 60º angle, the depth would be ~6/7 of the width (=.866025)

Depth of a 70º groove would be ~5/7 of its width (=.71407)
Depth of a 95º groove would be a little less than ~1/2 of its width (=.45817)
Depth of a 100º groove would be ~2/5 (or ~3/7) of its width (=.41955)
Depth of a theoretical 110º groove would be ~1/3 of its width (= .350104)

The formula for calculating depth:

If the groove width is w, and the angle of the base of the groove is G, the depth d is:

d = w * .5 * TAN[90-(G/2)]


d = (w/2) * TAN[90-(G/2)]

So the depth to width ratio is:

d/w = .5 * TAN[90-(G/2)]
d/w= 1/2 * TAN[90-(G/2)]
d/w= [TAN(90-(G/2))]/2

The "90" of this math assumes degree units. Keep in mind, if calculating this using Microsoft Excel, the TAN function expects radians so you need to convert your angles from degrees.

A related piece of useful information, which I am gathering solely from boogievan's posts: Apollo lacquers are optimally 7 mils thick, then you hit aluminum.

I welcome any corrections. This seems like a pretty crucial batch of info, but I'd like to corroborate it.
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Re: Rule of thumb: Groove geometry, Depth-to-width ratio

Unread postby Stevie342000 » Sun Feb 07, 2016 5:49 am

Here is some information I came across on Groove Geometry for Micro-Groove Discs & Recording Characteristics - see attached files.
Recording Characteristics Wireless-World-1952-11.pdf
Microgroove Recording Wireless-World-1949-04.pdf
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