Date: 11/16/98 at 12:19:55
From: Doctor Peterson
Subject: Re: Calculating the length of two twisted copper wires
Hi, Roland. If we picture one of your wires making a helix of radius R,
with one turn taking H inches, it will look like this:
|<--R-->|
| |
******|****** |
** **
| ******o****** |----
| o| | ^
| o | | |
|. o | | |
ooo. | | |
| . | | |
| .| | |
| |. | |
| | . | |
| | . | H
| | .| |
| | | |
| | | |
| | o |
| | o |
| | o| |
| | o | |
| ******|****o* | |
** | o ** v
******o******------
The length of the wire can be found by unwrapping it from the cylinder
to form a right triangle:
o
o |
o |
o |
o |
o |
o |
o |
o |
L o | H
o |
o |
o |
o |
o |
o |
o |
o |
o |
*********************************************************
2 pi R
We'll get:
L = sqrt(H^2 + (2 pi R)^2)
as the length of one turn of wire, so the ratio of the length of the
twisted pair to the length of the wire will be:
L / H = sqrt(1 + 4 pi^2 (R/H)^2)
The radius of the cylinder about which the center of the wire will
spiral will be about the same as the radius of the wire itself:
******** oooooooo ********
*** ooo *ooo ***
** oo ** ** oo **
* o * * o *
* o * R o *
* o *----------o *
* o * o *
* o * * o *
* o * * o *
**** oooo* **oooo ****
******** oooooooo ********
So in your example, with R = .020 in and H = 1 in, we get:
L / H = sqrt(1 + 4 pi^2 .020^2) = 1.0079
and for a 100 ft pair, each wire is 1.0079 * 100 ft = 100.79 ft.
That doesn't sound like much difference. It will increase if the wires
don't touch tightly all the way around. You may have to adjust the
radius to correspond to reality!
***
how to calculate loss of length with twist
in Blacksmithing, General Discussion
Posted
From 1998:
http://mathforum.org/library/drmath/view/53155.html
***
Date: 11/16/98 at 12:19:55 From: Doctor Peterson Subject: Re: Calculating the length of two twisted copper wires Hi, Roland. If we picture one of your wires making a helix of radius R, with one turn taking H inches, it will look like this: |<--R-->| | | ******|****** | ** ** | ******o****** |---- | o| | ^ | o | | | |. o | | | ooo. | | | | . | | | | .| | | | |. | | | | . | | | | . | H | | .| | | | | | | | | | | | o | | | o | | | o| | | | o | | | ******|****o* | | ** | o ** v ******o******------ The length of the wire can be found by unwrapping it from the cylinder to form a right triangle: o o | o | o | o | o | o | o | o | L o | H o | o | o | o | o | o | o | o | o | ********************************************************* 2 pi R We'll get: L = sqrt(H^2 + (2 pi R)^2) as the length of one turn of wire, so the ratio of the length of the twisted pair to the length of the wire will be: L / H = sqrt(1 + 4 pi^2 (R/H)^2) The radius of the cylinder about which the center of the wire will spiral will be about the same as the radius of the wire itself: ******** oooooooo ******** *** ooo *ooo *** ** oo ** ** oo ** * o * * o * * o * R o * * o *----------o * * o * o * * o * * o * * o * * o * **** oooo* **oooo **** ******** oooooooo ******** So in your example, with R = .020 in and H = 1 in, we get: L / H = sqrt(1 + 4 pi^2 .020^2) = 1.0079 and for a 100 ft pair, each wire is 1.0079 * 100 ft = 100.79 ft. That doesn't sound like much difference. It will increase if the wires don't touch tightly all the way around. You may have to adjust the radius to correspond to reality! ***