Inches per second of grooves @ diameters, TT speeds

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Inches per second of grooves @ diameters, TT speeds

Unread postby Steve E. » Tue Oct 27, 2015 5:40 pm

I was chatting with one of the rare guys who cuts on cylinders recently. This is a guy who can get absolutely phenomenal results out of acoustic (non-electric) recording.

He was talking positively about the fidelity at "160 rpm." (Earlier cylinders ran slower. According to the current wikipedia article, the earlier standards were 120 or 125, then 144.)


This got me wondering what that actually means compared to other formats, as it's a bit apples and oranges: It's a hill and dale groove traversing a 7-inch circumference cylinder, with minimal tracking error. How wide is the groove, etc?

At the very least, what part of what disc at what speed is comparable?

So, here's the math. 160 rpm x 7 inches per rotation = 1120 inches per minute, or 18.66 inches per second.

78 rpm discs:
The outer groove of a 12" 78 rpm, US: 78.26 rpm x 2 x π x 5.75 (radius) = 2827.4 per minute, or 47.12 inches per second.
The inner groove of a 12" 78 rpm, US: 78.26 rpm x 2 x π x 1.875 (radius) = 921.98 ipm, or 15.37 inches per second.
The outer groove of a 12" 33.33 rpm: 33.33 rpm x 2 x π x 5.75 (radius) = 1204.28" per minute, or 20.07 inches per second.
The inner groove of a 12" 33.33 rpm: 33.33 rpm x 2x π x 2.375 (radius) = 497.42" per minute, or 8.29 inches per second.

So, the speed is close to the inner groove of a 78 or the outer groove of a 33. If I had a little more time right now I could figure out the exact radiuses that it matches. Maybe someone else can do that, and figure out how 45s fit in, too.

Again, the width/depth and shape of the groove, and the material being cut on or pressed into, are huge factors in terms of possible fidelity.
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Re: Inches per second of grooves @ diameters, TT speeds

Unread postby Steve E. » Wed Oct 28, 2015 9:11 am

OK. So, now, knowing that 1120 inches per minute is our target, we can just reverse this process to figure out the radius at different rpms that will achieve this.

___rpm x 2 x π x r = 1120 ipm

r = 1120/(___rpm x 2 x π)

So, for 78s...
r = 1120/(78.26 rpm x 2 x π) = 1120/491.72 = 2.27 inch radius

for 45s
r = 1120/(45 rpm x 2 x π) = 1120/282.74 = 3.96 radius (in other words, the very outer edge of an 8 inch record)

For 33s
r = 1120/(33.333 rpm x 2 x π) = 1120/209.44 = 5.35 radius

These are the radiuses/radii that each of these disc speeds are the same groove speed as on a late-period standard Edison cylinder. For what it is worth. and if my math is correct.
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Re: Inches per second of grooves @ diameters, TT speeds

Unread postby Steve E. » Wed Oct 28, 2015 9:13 am

Subject for further research....The one inch or so of groove real estate on a 7" 45: in terms of inches per second, where would that map onto a 12" 33 1/3? It appears that it would.
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