Are you well informed enough to be aware of 16" 33 1/3 records issued by the U.S. Dept. Of War Special Service Division circa 1945? Interested?
Welcome to the Straight Dope Message Board!
In keeping with the tradition of including a link to the column in question, I am assuming that this is what you are referring to?
With the column dating from 1976, apparently this was a time traveler asking the question.
The anachronistic reference to CDs was added in the 1990s, when the Cecil’s archive was first placed online. Since dates are now included, it looks a little odd, so I’ve restored the original.
“If the groove speed were held constant instead of the turntable speed (in much the same way that a reel of film plays out at a steady 24 frames a second), it would be possible to record over 90 minutes of material on a single side.”
My instinct says this statement of Cecil’s is a wild exaggeration, but let’s take a look.
There’s no conceptual limit to how long an LP side can be, but there are practical reasons that make it desirable to set a limit. Most mastering engineers seem to informally agree that 20 minutes per side is reasonable - more than that and you have to lower the modulation which affects the signal-to-noise ratio. Longer sides, say side 2 of “Bitches Brew”, are not uncommon but we’ll stick with the 20 min. limit to make the engineers happy.
So if we have a turntable running at 33⅓ revolutions per minute, that means that in 20 min. it rotates 666 times. Though the groove is actually a long spiral, for purposes of our thought experiment let’s pretend each rotation is a separate circular groove, so that’s 666 circular grooves nested one within the other.
An LP is 12 inches in diameter. (Sorry, fans of the metric system but phonograph standards were set in English units; please feel free to convert if desired.) Our outer groove has a diameter of 11.5 (allowing for a ¼ inch lead-in from the edge to allow you to plunk the needle in front of track one, though some people like your girlfriend may have trouble hitting the strike zone).
Let’s peg the innermost groove diameter at a generous 5.25 inches, a bit bigger than what’s on my Abba “Arrival” album which I took a ruler to. Multiply by pi and you get a diameter of around 16.5 inches. Do the same with the outer groove at 11.5 equals a rounded-down 36 inches. Average them to get 26.25. Times 666 rotations = 17,482.5 inches (about 1,457 feet) your stylus must travel in 20 minutes.
Assume that the velocity of the innermost (slowest moving) groove is sufficient to provide hi-fi sound, we calculate 16.5 x 33.3 ÷ 60 ≈ 9.16 in./sec. If we build a turntable that plays at constant linear velocity, dividing number of inches (17,482.5) of an optimally cut groove by 9.16 gets about 1,909 seconds or 31 min. 49 sec. - a heck of a lot less than 90. Sorry.
You may be assuming constant pitch (the distance between adjacent grooves). But most lathes provide variable pitch, where a preview head on the source tape machine reads the sound level the equivalent time of one groove in advance and modifies the pitch accordingly. Loud passages cause the grooves to be farther apart, soft ones, vice-versa.
So a very soft level allows for tighter pitch and more minutes. How much tighter, I don’t know; I am not a recording lathe engineer.
20 minutes per side is really an underestimate. The most I recall was Janet Jackson’s Rhythm Nation 1814, with over 30 on one side, I think over 35.
Using your efficiency factor of 1.59 (which I double checked a different way), that would get you about 55 minutes per side.
ETA: Here’s a cite for a total length of 61:19, so i trust my memory of over 35 minutes.
True enough, and presumably if a piece of music is mostly quiet with a few loud passages you can get more on a side. That’s the case whether your disc is rotating at constant angular velocity (a normal LP) or constant linear velocity (Cecil’s hypothetical record that turns faster the farther down it plays).
There was a French label in the 1970s called Trimicron that put out a bunch of classical LPs that were said to contain an hour per side. I’ve never heard one, but I imagine you really had to crank them, plus any surface imperfection would be a real problem. My 20 minute limit was just for the sake of argument here.
About 30 minutes a side was normal for opera and other large-scale classical music.
More disastrously, who says the 90-minute side is recorded at the average linear speed? And it took me only four tries to find a center smaller than 5.25".
By the way, CDs do have constant linear speed.
Vashbul assumed the slowest linear speed, the speed of the innermost groove, was used.
How small? I was just using Vashbul’s size measurements.
Call me lazy, but I haven’t measured my LP centers recently. Nevertheless, if you make the diameter too small, changers will pick up and return the tone arm before the groove is finished, so you can’t just keep shrinking the hub to make more groovy room.
Groovy room, Man. 
Okay, wise guy, let’s say that all 33s have a playing time of 30 minutes a side. (Opera records can get away with this because they tend to have lots of dynamics, and the variable pitch mentioned by Musicat means the softer parts are cut with the groove iterations closer together, saving space. Other types of music, like Abba, might not be so lucky.)
And let’s say we can use all the area up to the locked groove at the side’s end, which has a diameter of 4 1/8 inches - by the time the stylus hits it, linear speed is about 7.19 inches/second, at this speed you’re already starting to compromise resolution at the high end.
So, calculating as above, you have a groove that’s 24,480 inches long; if you played it at CLV (constant linear velocity) of 7.19 ips that’s 56 min 45 sec.
But wait, as long as we’re in linear-land, why not get rid of the label and use the whole surface right up to, say, one inch surrounding the hole in the middle (you don’t want your tone arm to hit the spindle)? Doing this would (my estimate) give you an extra 430 or so rotations. That might seem like a lot, but remember your disc is spinning faster as you reach the center, so it doesn’t actually add much playing time - about 8 min. I reckon.
Bottom line: 64 min. 45 sec., impressive but nowhere near the hour-and-a-half claimed.
I’m not sure about this. If you listened to 30 minutes of straight Abba, “lucky” is not exactly the word I’d apply in this situation.
Is averaging the thing to do here? I have a feeling that you’re underestimating the length of the entire groove. I’ll have to calculate it (aka ask my son) later.
Mmm, it seems right to me, but I flunked calculus so let me know what result your son arrives at.
I think you meant circumference there.
I remember the first computer I ever used, an ACT Sirius, had a variable speed floppy disk drive that allowed the data density to be the same across the media. I’ve no idea how it worked but the added complexity must have made it too expensive to continue with.
The original Macintosh diskettes also had variable speed. The drive motors were pretty noisy so you would hear various humming tones as files were read. I think the variable speed was used for the 400 KiB and 800 KiB (double-sided) diskettes, but they dropped it when they introduced 1.44 MiB high-density diskettes (the Mac diskette drives still had to support it for older diskettes).
In the 1980s, video laserdiscs came in two varieties: constant linear velocity (CLV) and constant angular velocity (CAV). CLV had about 1 hour per side, CAV only about 30 minutes. In low-end drives at least, only the CAV discs allowed features such as Still, Step, Goto, etc.