Looking at the old cassette tape,

Cassette Tape Image

From the POV of the head, let's say that it reads at speed \$v\$ (the magnetic medium scrolls at speed \$v\$).

But looking at the right wheel, which is the one that's pooling the magnetic medium - its radius is growing(!) over time.

Now, \$v=r\omega\$, where \$\omega\$ is the angular velocity, i.e. a constant

Question

I don't think that's true. What is really going on here? Radius is growing over time, for sure. I also assume that \$\omega\$ is constant. so did \$v\$ increase?

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  • 3
    Would Engineering be a better home for this question? – Qmechanic Jun 25 '17 at 9:57
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    For whatever its worth: The Phillips Mini-Cassette worked by turning the takeup reel at a constant speed. – Solomon Slow Jun 25 '17 at 17:55
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    in any case, assuming that the tape was recorded at the same speed it is played at, having the tape go faster shouldn't have a negative impact on playback quality, does it? since it always matches the recording speed. – Florian Castellane Jun 26 '17 at 13:50
  • @FlorianCastellane, If the tape doesn't move at constant speed, then it won't be used as efficiently. Suppose that the slowest part of the tape is moving just fast enough to give satisfactory playback fidelity. That means that every other part of the tape is moving faster than what is needed for satisfactory fidelity. And, that means, You could have gotten more recording time for the same length of tape (or used less tape for the same length of time) if it moved at a constant speed. – Solomon Slow Jun 26 '17 at 18:54
  • Running the tape at higher speeds than the mfg'r recommends would cause the Chipmunk Effect, where it sounds like ...chipmunks. +(delta)v = ce – Tim Spriggs Jun 28 '17 at 14:13
up vote 36 down vote accepted

The details of how a cassette drive works are well covered by this Wikipedia article. The tape is pulled by a capstan next to the playback head, and this capstan pulls the tape at a steady rate.

Tape drive

(picture from the Wikipedia article)

You probably need to click on the picture to see it full size. I have indicated the capstan by a red arrow. The take-up spool doesn't rotate at a fixed speed. It uses a slipping drive, as badjohn says in his answer, so it takes up the tape at the speed the capstan moves it.

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    Would I be wrong in thinking that the capstan disengages and the spools themselves govern the speed when fast-forwarding or rewinding? – Sandwich Jun 25 '17 at 12:45
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    @Sandwich: correct. – John Rennie Jun 25 '17 at 12:59
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    Indeed, some of us are. I still have a working, near mint condition Nakamichi 480Z cassette deck that I bought new about 35 years ago. Interestingly, it has dual capstans. – Alfred Centauri Jun 25 '17 at 15:16
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    @AlfredCentauri: this is one of those I'm not worthy moments :-) I couldn't afford a Nakamichi as a teenager, and by the time I could afford one compact disk had come alone. – John Rennie Jun 25 '17 at 15:20
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    Just in case anybody cares: "Capstan" is a nautical term. It's the name of the winch that is used to weigh (i.e., haul up) the anchor. The capstan of a tape drive and the capstan on a ship both stick up out of the deck and rotate on a vertical axis. – Solomon Slow Jun 25 '17 at 17:49

The specific mechanisms for cassette players and decks largely depended on how much you paid for them.

On inexpensive players, the capstan, feed reel and take up reel would be driven by the same motor, connected by belts. On the best decks, the capstan and the reals would each have a separate motor. Mid priced decks could have two motors, one for the capstan and one for the reels.

On a one or two motor system there would be a slip mechanism driving the take up and feed reels. The feed reel need to put reverse pressure on the tape to maintain tension across the heads.

The clutch that allowed the reels to turn at variable speeds could be a simple as letting the belt slip on the pulley. I saw a number of these when disassembling broken players as a kid. On three motor systems, the reels would be driven in the appropriate direction by its own motor. Presumably it was a relatively low torque motor so it would not stretch the tape.

Either way, the rotation of the capstan, pressing against the pinch roller would govern the speed of tape travel. The 1 7/8 inch per second speed was the standard, but some players could play at other speeds, usually to extend the recording time for low fidelity used, such as voice notes.

During fast forward or rewind the pinch roller is pulled back from the capstan. On a one motor system, the capstan would spin at a faster rate. On a multi-motor system the capstan would be still.

Auto-reverse decks added more mechanisms and had two capstans and pinch rollers.

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    Actually, on the most luxurious units the capstan is turned by a crew of sailors pushing on levers attached to its hub. – Hot Licks Jun 25 '17 at 22:08
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    Where'd they find such tiny sailors though? – Doktor J Jun 26 '17 at 15:32

The speed past the head is constant: 1⅞ inches per second. A slipping clutch allows the take up reel to vary its speed as required.

  • I wonder how the speed is governed – ja72 Jun 25 '17 at 10:02
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    I don't understand. The radius is changing , so does V. so how do you say that V is constant ? – Eris Jun 25 '17 at 10:05
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    @Royi I am not sure how the speed of the motor for the roller that drives the tape past the head is governed. For the take up wheel, if unrestrained, it will run a bit faster than ever required to keep the tape under tension. However, it is not firmly connected to the spool. It goes via a clutch. Can you drive a manual car? Imagine that you partially depress the clutch. The speed of the car can now change even while the engine speed is constant. – badjohn Jun 25 '17 at 10:26
  • @ja72: See my answer to electronics.stackexchange.com/questions/229723/…. – Transistor Jun 26 '17 at 19:14
  • Constant speed of the capstan motor is easily achieved if it a synchronous AC motor (as invented by Tesla in the 19th century). The motor turns at a constant speed unless excessive torques are applied. With modest torque, the motor can advance or retard a bit, but not more than one pole position. – richard1941 Jul 4 '17 at 8:02

The reason you are getting confused, is that you are under the impression that the speed of the tape is controlled by the motion of the supply and take-up reels. This is not correct. The speed of tape travel (v) is controlled by the "capstan," which has a constant radius (r) and constant rotation (w). Therefore, v is constant!

The very early cassette players did not have capstan drive. The tape was driven from the takeup spool. As a result, the speed of the tape did vary. That was not a major problem as long as you record and playback on the same device. The device was meant to be cheap, not high quality.

Later cassette devices, driven by the high fidelity craze of the 1960's, incorporated capstan drives that maintained a constant tape velocity over the record/playback head, as previous responders have noted above. That made tapes portable from one device to another. The cassette drive manufacturers would try to outdo each other with wow and flutter specifications, and the devices became more expensive. I just trashed mine because the rubber rollers and belts inside are shot and there are no replacement parts available.

I wonder if I could fabricate rollers from RTV silicone caulk... possibly chilling the material with dry ice and turning it on a lathe... Hmmm...

  • "The very early cassette players did not have capstan drive." Are you sure? I don't think so. – Transistor Jul 3 '17 at 6:30
  • Yes, I am sure. I remember one that sounded like Alvin the chipmunk on the telephone at one end of the tape, and smoky the bear at the other end. When I went shopping for a cassette recorder, I took a lot of trouble to find one with capstan drive. This would be some years before the Sony Walkman, which did have capstan drive. – richard1941 Jul 4 '17 at 8:05

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