@floris2burn,
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.
