Lundin's Inductance Formula

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Ed Phillips by way of Terry Fritz <twftesla-at-qwest-dot-net>" <evp-at-pacbell-dot-net>

Here are formulae for calculating inductance using Lundin's
APPROXIMATION for Nagaoka's constant.  This is much, much more
convenient to use or program than the old way which involved
double-difference table interpolation, and the results are almost as
accurate.

"Calculation of inductance by Lundin's approximation to Nagaoka's
constant.
[Letter to Proceedings of the IEEE, Volume 75, Number 9, September 1985
pp 1428 =1429]

FOR A SOLENOID OF DIMENSIONS:
DIAMETER  (INCHES) = D
LENGTH  (INCHES) = LE
NUMBER OF TURNS = N

CALCULATE

X=D/LE
X2=X^2

A(X)=(1+.383901*X+.017108*X^2)/(1+.258952*X)
B(X)=(.093842*X+.002029*X^2-.000801*X^3)

IF X = > 1 
K = (.6366198#/X)*((LOG(4*X)-.5)*FNA(1/X2)+FNB(1/X2))
INDUCTANCE =.0250688*D*X*N^2*K    MICROHENRIES
 
IF X < = 1
K=FNA(X2)-.42441318#*X
IND=.0250688*D*X*N^2*K    MICROHENRIES

 I can't find the original letter, so the stuff above is a rewrite of
the expressions in the Basic program I wrote at the time; hope I didn't
make any mistakes.  "Just in case" here are the original Basic
statements:

INPUT "DIAMETER, LENGTH, (INCHES) AND NUMBER OF TURNS"; D,L,N
DEF FNA(X)=(1+.383901*X+.017108*X^2)/(1+.258952*X)

DEF FNB(X)=(.093842*X+.002029*X^2-.000801*X^3)
X=D/L
X2=X^2
IF X<1 THEN LT1
K=(.6366198#/X)*((LOG(4*X)-.5)*FNA(1/X2)+FNB(1/X2))

LT1:
K=FNA(X2)-.42441318#*X

IND=.0250688*D*X*N^2*K    ' INDUCTANCE IN MICROHENRIES

Ed