Coil wrapping math

[GoombahYah]

Hi all! I'm trying to calculate the number of turns required for a given resistance of a wire, and have bumped up against my rusty math skills. Through various sources, I've figured out a formula for calculating the length of a coil:

N = sqrt[ (πDT)^2 + (WT + P(T-1))^2 ] + d

Where:
N = Overall length of wire
D = Diameter (mean)
T = Number of Turns
W = Wire diameter
P = pitch (spacing)
d = Lead length

However, I'm having a hard time re-factoring this in terms of T (the number of turns for a specific length).

Can anyone whose math skills are better than mine lend a hand in this (or point out any errors in the formula above)? Thanks!

 

[Susan~S]

How about this instead. Here are a few links for you regarding building coils and getting the resistance just where you want it:

1. Steam Engine
2. Coil Toy Calculator

 

[Rsunderl]

... also, get an ohm meter to test once you have the coil made but before you fire it on your device. Never know when you have the perfect coil wrapped, but it has a short.

 

[GoombahYah]

Thanks for the links, but I'm trying to make a native iOS app that does (most of) what those online calculators do. Hence the request to check my math.

And I second Rsunderl's comment: no matter what calculator is used, always use an ohmmeter to check the results before firing. Even if these calculators are 100% accurate, imperfections in the coil, the wind, or the installation can cause unexpected variations.

 

[trophyfish711]

Steam Engine is the one I use.. spot on !!!!

 

[Bunnykiller]

I use this....

 

[Lessifer]

I think you're making it more complicated than necessary, for the size of coils we are making.

Wire Length In Inches:
3.14DN + LL1 + LL2 = Li
Key:
D = Inner Diameter
N = Total Coils
Li = Length (inches)
LL1 = Leg Length 1
LL2 = Leg Length 2

 

[rurwin]

The average circumference of a ring of wire will be:

c = pi x (InternalDiameter + WireDiameter)

In that distance a single turn of wire also moves from one turn to the next. In a tight micro-coil that's a distance of WireDiameter. So the length of a single turn will be

L1 = sqr(c^2 + WireDiameter^2)

The length of an N-turn coil will then be:

LN = L1 x N + LegLength1 + LegLength2

The cross-sectional area of the wire is:

A = pi x (WireDiameter/2) ^ 2

The resistance of the coil is then:

R = Resistivity / A x LN

The Resistivity of Kanthal A1 is 1.45 ohm mm^2/m, or 1,450,000 ohm m^2/m, or 0.001 45 ohm mm^2/mm. Choose the version you use depending on your units for length and area.