Here's One for All the Math Geniuses

[diamone]

For all you math geniuses out there - here's one very few people can solve.

1. You have a tape originally recorded at a Constant Angular Velocity (CAV/rim drive)
(i.e. recorded in RPM instead of IPS e.g. Living Letters tapes from the 60s)

2. You don't have a CAV tape deck so you are playing it back on a Constant Linear Velocity
(CLV/capstan drive) tape deck that has NO VARISPEED AND NO WAY TO PLUG IT INTO THE COMPUTER THIS IS IMPORTANT

3. The only thing it will plug into is a CLV disc recorder that ALSO has no varispeed.
(i.e. runs in IPS like a CD instead of RPM like a record - e.g. Grey Audograph)
and ALSO has no computer interface (no fair using a mic or tapping off e.g. a speaker)

4. You expect to be able to play the resulting CLV disc back on a standard CAV turntable
and be able to retrieve the original recording from the tape at the correct speed.

The only three variables on this are on the disc recorder:

1. The embossing stylus is capable of starting or ending within a half inch of the disc hole
2. There is a MANUAL groove pitch adjustment which must be set ONCE and left alone
3. there is a MANUAL IPS adjustment that also must be set ONCE and left alone.

What Other Parameters (besides these) do you need to know on
A) the tape and
B) the disc

How many oranges are in Train 1 and how fast is Train 2 going?
(How would you set these parameters to accomplish this?)

And yes it works just like the math says it would (once you know what the math is).
In the days before computers I had to
A) figure it out and then
B) do it for a lady so she could hear her dead husband's letters from Vietnam at the right speed.

[markrob]

Hi,

I think this approach is in the ballpark. Let me know if you see any errors in my thinking.

First you need to know the ratio of the outside to inside diameter of the take up reel on the original CAV recorder when packed and unpacked with tape to determine the ratio of linear velocity change from the start to finish as the tape is wound. You also want to know the actual starting linear velocity of the tape, so you can match it later on. You need the RPM of the CAV tape machine that made the original recording. If you measure the inner hub diameter of the take up reel along with its RPM, you can determine the starting linear velocity of the tape.

LVStart = (PI X Hub_Diameter X Tape_RPM) / 60

If you measure the final diameter after the tape has spooled to the end of the audio, you can determine the velocity ratio

VelRatio = End_Diameter / Hub_Diameter

You use the same diameter ratio on the disc to match the tape. Since the tape spools from low diameters to high, and the disc runs from high to low, the two will cancel out once you establish initial conditions on the playback disc. To do this you use the value LVStart calculated above.

Since the disc cutter has a fixed inner diameter of 0.5", you can use this along with the ratio obtained to determine the starting (outside) diameter of the disk cutter. That is given by:

DiscStartDia = 0.5" X VelRatio

Next you need to determine the fixed cutting pitch. You want to select a pitch such that it takes the same of revolutions at playback to move from outer diameter to the inner diameter as does the tape machine. If you measure the tape thickness and know the changes in diameter of the tape from start to finish, you can calculate the number of turns the take up reel turned from start to finish. That number is given by:

Reel_Turns = (End_Diameter - Hub_Diameter) / (Tape_Thickness * 2)

Assuming the tape is well packed. You could also count the turns or calculate by measuring time at the know RPM.

The LPI to be used for cutting is then:

LPI = Reel_Turns / (DiscStartDia - 0.5)

Now the only thing left is to match the initial tape linear velocity to the disc at playback so the pitch matches. We need to know the disc playback speed and the initial linear velocity of the tape recording so we can play back at the same on the disc. We set the IPS of the cutter to make that happen

IPS = (Pi X DiscStartDia X Playback_RPM) / 60

If you set the IPS of the cutter to match LVStart calculated above you should be good to go.

I'll bet that was a fun project to do back in the day.

Mark

[diamone]

1. OC ÷ IC = velocity ratio change from start to finish
2. RPM of original tape machine
3. starting LV (PI X Hub_Diameter X Tape_RPM) / 60
4. tape thickness
5. groove pitch

OK.....

Since the tape spools from low diameters to high, and the disc runs from high to low, the two will cancel out once you establish initial conditions on the playback disc.

BBBZZZZTTT only for a few seconds near the middle of the program.

Since the disc cutter has a fixed inner diameter of 0.5", you can use this along with the ratio obtained to determine the starting (outside) diameter of the disk cutter.

You are also assuming the disc recorder is
A) outside-in only
B) only capable of going into the center at the normal location - when I said
``the disc embosser can end OR START within a half-an-inch of the center hole''.

We set the IPS of the cutter to make that happen.

OK now do the math again embossing inside-out

I'll bet that was a fun project to do back in the day.

For mil-and-a-half and mil-tape, the Memovox embosser did fine on Soundscriber discs - we took off the disc drive pin and replaced the round shaft with a square-topped one because otherwise we'd be recording over the drive hole of the Memovox disc.

We were able to crank the pitch down to the same LPI as the thickness of the tape - start the Memovox at the same 3/4 of an inch from the same quarter-inch hole as the 3-inch reel of tape.

Then we divided out the RPM of the rim drive tape by the IPS of the Memovox and changed drive tires on the Memovox to give us an IPS which would match the tape rotation-for-rotation (on a 5-inch capstan player using two 3-inch reels) regardless of whether it was on a capstan player or a rim drive player.

So when we were done, we could play the CLV Soundscriber disc on a normal 33 RPM turntable and get a WHOLE lot closer to keeping the correct speed throughout the program than we could by cutting outside in.

The half-mil tape was another story.

See if you can figure out what we did and what kind of disc recorder we used instead when the smallest LPI on the disc recorder was still too wide to do rotation-for-rotation.

And apparently we weren't the only ones to figure this out. Years later I inheited a boatload of Memovox discs that HAD no drive holes manufactured in them (maybe they were error discs that never got their second hole drilled out and got sold for peanuts) and recordings going into (or as we were to soon find out - coming out of) the center within a half an inch of the hole in ADDITION to the ``regular'' program that had been embossed onto it previously.

We played the inner sections on the Memovox and couldn't figure out why they kept getting slower and slower and slower as the stylus moved outward.

Sure enough - the ``normal'' cuts played normally (CLV) on the Memovox while the inner cuts played close-enough to CAV on a turntable to where we assumed somebody else had figured this out as well and come to the same conclusion - because the material was all of the same Living Letters genre that you'd FIND on an old 3 inch rim drive player.

So yes it was fascinating.

[markrob]

Hi,

I get it! Thanks for pointing out the error in my thinking. Inside out makes much more sense.

Mark