The formula for the length of a spiral is (somewhere between a lot of paper - I have lost the paper war) but it may not be what you need for practical reasons.
The tension on the takeup reel may cause the ratio to change.
When one reels are close to empty the ratio will stay the same for almost one revolution of the empty reel where after it will jump for the next revolution.
I am curious as to your application.
Can you give more detail? (size of drums , belt thickness, belt length etc)
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