Math Help rotation

Community General Discussion
1

Hi all,
Wasn't quite sure where to post this,

I have a math problem and im just not smart enough to work it out. ill post an image with the math at the bottom.
Basically, if anyone has ever used a audio cassette tape, reel to reel audio player or perhaps an old cine film projector you'll know that the reel that the film/audio is being removed from via the take up reel will slowly start the rotate faster as the diameter of the tape/film decreases. i need to work out the speed difference to two different sized reels. but i just don't understand higher math. i can barely count using normal math.

reel_math
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Original Article

Best Regards

Dave

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If the tape is being pulled out at constant velocity v, then the rotation rate of a reel of radius R in rotations per second is v/(2*Pi*R), or (tape velocity)/(reel perimeter).

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Then we need the perimeter change over time or tape length coiled up. That change unfortunately is nonlinear. Linear with number of rotations.

One more sleepless night or never ending nightmare?

Now I know why the tape decks had vacuum chambers at each side and light barriers telling when to start and stop winding a reel.

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4

Im really greatfull for that amazingly quick reply. But im still non the wiser. Is there a simpler way of explaining ? It ok if there isnt.

Dave

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The average reel radius decreases by one tape thickness per reel revolution.

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Do you understand the terms "tape velocity" and "reel perimeter"? Those can be measured: meters/second, feet/second, meters, feet, etc.

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Yeah i get that.

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Then divide the perimeter into the velocity.

To turn the problem around: roll a bicycle wheel along a path exactly one revolution.

Q: how far has it moved?
A: one bicycle wheel perimeter

Q2: what speed was the bicycle wheel moving?
A2: (one bicycle wheel perimeter)/(time for one revolution)

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9

I think i get it. Thanks. just need to work out how todo that with the arduino. Hopfully i might actually have some working code lol its only been three weeks.

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I forgot to mention. The tape is 200 feet long. 60960mm or 2500 inches

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Is this all i need (tape velocity)/(reel perimeter to work out the speed different between a full tape real and an empty one; if so. how would i then use this in an arduino sketch.

Dave

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For what purpose do you want to use it? Best math won't help if you cannot drive the reels exact enough to prevent highly unwanted tape jitter.

AFAIR HP has invented a perfect cassette drive with a single motor.

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i need to work out how much i need to slow down my takeup reel as the tape spools onto it increcing its inner diameter(perimiter)

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How will you drive that reel?

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... and how will you control tape tension?

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With a manual break gently rubbng on the tape reel.

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Stepper motor for pulling the reel and either a stepper or dc motor for the take up reel.

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So you have no idea of the current diameter of the reels? How then do you you want to calculate any rotational speed of the wheels?

IMO you can forget about higher math and concentrate on practical aspects of the drive.

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Look at my 1st post. The image. I added all the measurement to the image b4 i uploaded it

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And speed is constant, tape length is 200 feet