Finding the Length of a CoilDate: 07/07/99 at 14:19:09 From: Robert Johnson Subject: Finding the length of a coil I am looking for a formula to figure the length of a coil or spring when given the diameter and pitch and number of turns. Date: 07/07/99 at 17:32:09 From: Doctor Rick Subject: Re: Finding the length of a coil Hi, Robert. Imagine that you take a paper triangle like this: /| / | / | L / | / | P*N / | /| | / P| | /_________pi*D____|__________________________________________| pi*D*N L = length of coil D = diameter of coil N = number of turns P = pitch Wrap it around a cylinder the diameter of the coil. It will wrap around exactly N times, since Pi*D is the circumference of the cylinder. At each turn, the diagonal edge (hypotenuse) of the triangle is a distance P farther along the cylinder than on the previous turn; this is the pitch. The hypotenuse follows the path of the coil, so its length L is the length of the coil. You can find it from the Pythagorean theorem: L^2 = (pi*D*N)^2 + (P*N)^2 = N^2 * (pi*D)^2 + P^2) L = N*sqrt((pi*D)^2 + P^2) where sqrt() means the square root of the expression in parentheses, and P^2 means P squared. If you have any questions about this, feel free to ask. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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