Hey guys, I'm new here, but I have been using this site for a while and just decided to make an account.(adsbygoogle = window.adsbygoogle || []).push({});

Here is my problem, I hope someone can help me out:

I have a duct tape rolling machine which takes larger duct tape rolls and rolls them into smaller rolls. Because the machine is not regulated based on length of tape, I am trying to put together an equation that will allow me to input a length and get an output of the diameter of the roll.

I started out by taking the number of layers on the newly rolled duct tape roll by doing this: (D_o-D_i)/(2t)

Where Do is the total diameter of the new roll, Di is the core diameter of the roll, and t is the thickness of the tape.

I then took the average circumferance of the layers by doing this: pi(D_o+D_i)/2

This comes out to be the length of the material is L=(pi/4t)(D_o^2 - D_i^2)

I am pretty sure that is correct.

I then rearanged the equation so that the output is Do.

D_0=√((4L*t)/pi+D_i^2 )

Now, I am pretty sure all of this is correct, if you would like you could check the math, but I ran into problems when I tried to implement the equation.

I'll give you an example and then explain what I think the problem is:

Let's say I have used the rolling machine to roll a 1.625 inches (41.275 mm) roll with a core diameter of .375 inches (9.525 mm). The thickness of the duct tape rolled (based on the number on the store bought roll) is .012 inches (.3048 mm).

If I input this information into the equation, I get 163.625 inches (4389.2 mm) Although this seems reasonable, when I actually unrolled the tape, I was getting about 185 or so inches which is about 5 yards.

What I believe is the problem is that when the rolling machine pulls the tape off of the larger roll and rolls it onto a smaller roll, the tape is stretched or compressed due to the friction of the *sticky part* (I forget the word) of the tape.

Is there anyway I could implement this into the equation? Also, if the equation is wrong, could you suggest another way of finding the diameter based on length?

Thank You! If you need any more information, just ask.

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# A Problem With Rolling Duct Tape

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