how to i model a long (1000 ft) tape (of zinc covered plastic) rolled up around a core?

how to i model a long (1000 ft) tape (of zinc covered plastic) rolled up around a core?

Here is a mathematical model:

The radius of one loop is

R(n) = (n-1)T+Rc

where n is the number of the loop from the center, T is the thickness of the tape and Rc is the radius of the center tube that you are wrapping around.

The length of the nth loop is

l(n) = 2 pi R(n)

The length of N loops is

Solving for N

Plugging in T = .02 in, L = 1000 ft and Rc = .125in, you get 437 loops, which my computer has been trying to rebuild for about 10 minutes unsuccessfully.

As a check, compare the side area of the wound tape to the side area of the flat tape.

And, in case you were wondering, the radius of this wad of tape is R(N) = R(437) = 8.73 in.

So, if you want to just model this as a disc, which has the advantage that your computer can actually do it, here are the equations you need.

wow! thank you! Im relatively new at this, but i do understand your equation...but where would i input this? I have the core of the roll already modeled, now i need to do a similar rolled up thing as you did.

You could put this in as equations. But you don't have to. What you really need is N, which is the number of loops in order to model a sweep. The equations above tell you that

Where you get to choose T, Rc and L. Rc is the radius of your core, T is the thickness of your tape, L is the length of your tape==keep the units that same. You need to know N to create a helix for a sweep. But your computer will barf if you try to sweep this.

If you want to just model this as a disc, which I recommend, you only need to know the radius of the disk, which is

R = (N-1)T + Rc

thank you Mike,

but where do i enter this info? I only know how to use the sketching commands, just getting into equation driven curves, but where and how do i enter this info so it spits out a curve? thank you again, you're awesome

Sketch a circle with radius Rc.

Then select the sketch, click insert/curve/helix.

Under "Defined By", select "Spiral".

Under "Pitch:", enter the thickness of your tape.

Under Revolutions: enter N.

Now you have a spiral.

Start a new sketch on the same plane as your spiral and circle.

In the sketch, offset the spiral with a distance of zero.

Extrude the sketch thin with a width of your thickness minus .002 inches or so, to provide clearance.

I would still recommend against this.

Make spiral over the core and then use sweep tool