March 06, 2021, 01:44:46 AM

Author Topic: Geometry problems using cylinders and strings  (Read 1338 times)

Offline TomToad

Geometry problems using cylinders and strings
« on: November 05, 2017, 06:10:06 PM »
Trying to figure out some problems here and hoping someone can help out, or point me to the correct information. I'll divide the problem into three parts

Part 1
Suppose you have a fixed cylinder, such as a column, and wrapped around the cylinder is some string.  To keep things simple, the thickness of the string is negligible.  Let's label the radius of the column as 'r'.  Now suppose that you unwrap a portion of the string, take the loose end and pull it until it is taught.  We will label the length of the loose part from where you are standing to where it makes contact to the column as 's'.  Now I want to calculate the distance 'd' from where you are standing to the center of the column.

I believe I have the answer, but am not sure.  The line segments s, r, d form a right triangle where the angle between s and r are 90 degrees.  So d should be calculated as Sqr(s*s + r*r). is this correct?

Part 2
Suppose I start to walk around the column so that the string unwinds itself.  Say the angle I walk around is 'a'. How much string will now be unwound and what is now the current distance?

I believe you would need to divide the circumference by 360/a.  So c = 2*pi*r then s = s + c/(360/a)

Part 3, the part I am heading to and most confused by
Suppose that the string is wrapped around two or more columns?  How would it affect the calculations above?

Answer: no idea!
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8 rabbits equals 1 rabbyte.

Offline Matty

Re: Geometry problems using cylinders and strings
« Reply #1 on: November 05, 2017, 07:35:52 PM »
Part 1 and Part 2 seem good to me...you've got them fine.

Looking at Part 3 now...give me a moment and see if I can imagine it in my head properly.
I eat cheese in the trees when its eight degrees

Offline Matty

Re: Geometry problems using cylinders and strings
« Reply #2 on: November 05, 2017, 07:39:48 PM »
Okay looking at part 3.

The question isn't entirely clear but let me see if I can give an answer that points in the right direction.

As far as I know the only column that matters is the last one.

For each full revolution of the last column you will have the amount of string lagging of the end that you calculated above c*360/a

The difference is now that a doesn't just go from 0-360 but from 0-n where n could be any angle.

So for example if the final column did two revolutions then a would be 720.

Does that help?
I eat cheese in the trees when its eight degrees

Offline ENAY

Re: Geometry problems using cylinders and strings
« Reply #3 on: November 07, 2017, 02:00:06 AM »
Are you trying to work out much string is needed?

Offline TomToad

Re: Geometry problems using cylinders and strings
« Reply #4 on: November 07, 2017, 08:57:45 AM »
@enay: no, the amount of string needed is already known.  I am trying to calculate the path the person takes as he unwinds the string from the columns.  For example, here is the path around a single column.

Ultimately, I want to be able to alter the path by arranging more columns at different configurations.

I haven't had much time to work on it due to my regular job being busy this time of year.  Can't find much online to help.  I know trigonometry will help here, especially laws of sine and cosine, so I am close.  Just need a bit more time to work on it.
 
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8 rabbits equals 1 rabbyte.

Offline TomToad

Re: Geometry problems using cylinders and strings
« Reply #5 on: November 07, 2017, 09:26:21 AM »
Grrr, thinking about the problem and I realized one of my assumptions was wrong.  I assumed that when you make one full rotation around the column, the string releases one full rotation.  In reality, it releases slightly more than one rotation due to the fact you are now further away from the column.  So the neat, consistent spiral in the above example should actually get slightly wider as you move away from the column, and so my formula of s = s + c/(360/a) needs to be revised.

Thinking now that I should focus on looping string length and calculate angle, instead of the other way around.
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8 rabbits equals 1 rabbyte.

 

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