# How do I calculate the necessary velocity of two reels of tape to maintain constant tension on the tape?

I have a real-world problem that I'm quite certain can be solved with a formula. Unfortunately I myself am not particularly skilled in the realm of physics or math. Any and all help is very much appreciated!

I have a cassette tape. It's on a transport that does not use a capstan to drive the tape. As the tape travels from the first reel to the second, the first reels diameter decreases while the second reels diameter increases as the tape moves from one to the next.

In this situation, both reels have independent speed control. At what rate does motor A need to increase/decrease in speed, in proportion to motor B, to maintain constant speed and tension on the tape between the two reels?

I want to calculate the velocity from the radius. To know the radius, we have to know where we are on the tape.

If I were you, I would use torque control on at least 1 of the motors. That way you can keep constant tension on the tape. You could possibly control speed on one of the reels and torque on the other.

To answer your question, though, every revolution of a reel will move the tape linearly the same distance as the circumference of the reel. You also know that for every revolution, the diameter of each reel will decrease by 2 times the thickness of the tape. From those two pieces of info, you should be able to figure out a formula. But as I said in the first paragraph, I think you'd be better off with torque control on one of your motors.

• Thanks Brad! I'm using steppers, so torque control is out of the question. I'm working on a formula based on your info. – ViuLab May 27 '14 at 6:20
• What are you using for sensors to determine the amount of "wrap" on each reel? In addition, sans capstan, how do you propose to maintain constant speed across the read head? The amount of uncertainty in the "cm/sec" rate at the read head will define how accurately you need to know the current tape radius on the reels. My honest advice would be to throw out the transport and get one that does have a capstan drive. – Carl Witthoft May 27 '14 at 12:15