# primary inductance

```Original poster: "Loudner, Godfrey by way of Terry Fritz <twftesla-at-qwest-dot-net>" <gloudner-at-SINTE.EDU>

The self inductance of a flat spiral coil made of cross circular conductor
is approximated by the formula L = (NR)^2/(8R + 11W) where R = the average
radius in inches, W = the width in inches, and N = the number of turns. I
visited two internet sites where I backward engineered the R and W being
employed. Let a = the inside distance from the center of the spiral to the
beginning of the first turn, b = the diameter of the conductor, and c = the
spacing between the turns.

use
W = Nb + (N - 1)c and R = a + [Nb + (N - 1)c] / 2.

DeepFried Neon at
http://homepage.ntlworld-dot-com/stephen.bell5/tesla_frame3.html use
W = Nb + Nc and R = a + [(N + 1)b + Nc] / 2. This site calculates L to the
third decimal place value without rounding off.

Using an averaging integral from calculus, I have always used
W = (N + 1)b + Nc and R = a + [(N + 1)b + Nc] / 2.

For a = 6.397", b = 0.37", c = 0.37", and N = 12, we have L(Cad) = 91.37uF,
L(Neon) = 94.13uF, and
L(Calculus) = 92.11uF. There is not a whole lot of difference between the
values.

But is there any agreement was to what W and R should be in this situation?

Godfrey Loudner

```