# Stupid Math Error

Discussion in 'Math' started by Wendy, Feb 25, 2014.

1. ### Wendy Thread Starter Moderator

Mar 24, 2008
20,772
2,540
I am having a massive senior moment, all day long.

I want to roll an inductor 1.27uH. I have chosen a drill bit 0.228" in diameter, and I will use 24 Ga enamelled wire.

L=(N^2 * r^2) / (9 r + 10 l)

where

L = micro Henrys
N = Number of turns in the inductor
r = mean radius of inductor
l = Length of inductor

I have empirically solved this to be 21 turns. However I have a hard head, and would like to do this with math. So I redefine some of the variables to make tracking easier.

Redefine:

x = N
g = 24Ga = 0.02010
i = l, which also = g x

So, the formula becomes

L = (x^2 * r^2) / (9 r + 10 i)

here is where it gets interesting

9 r + 10 i = (x^2 * r^2) / L
9 r + (10 g x) = (r^2 / L) x^2
0 = (r^2 / L) x^2 - (10 g) x - 9 r

This is the weakest step for me, where I feel I have most likely made the error. I have translated this into a quadratic equation.

OK, the variable numbers are:

x = Number of turns
r = Mean radius = (dia of core * dia of wire) / 2 = 0.124
g = .0201
L = 1.27

x = ( -b +/- sqr( b^2 - (4 a c)) / (2 a)

where

0 = a x^2 + b x + c

I get x = 2.5, which is a non-starter. I know I'm messing up somewhere. Help?

Last edited: Feb 25, 2014
2. ### WBahn Moderator

Mar 31, 2012
18,085
4,917
Your problem most likely stems from sloppy units in the original equation.

What is the length of the inductor in? cm? or m? or inches?

If we know what the units are then we can figure out what the units on the coefficients need to be and then we can track them through.

3. ### panic mode Senior Member

Oct 10, 2011
1,328
305
since it is late, i did not go as far as evaluating it though, so i cheated
just opened excel and typed in formula and all known parameters, plugged in 3 numbers to get to N=21 which produces 1.27053uH

4. ### panic mode Senior Member

Oct 10, 2011
1,328
305
ok without cheating i get solutions N=-4.38891 and N=20.99388
of course negative one is to be discarded so N=21 stands.
i think you simply made a typo somewhere while using quadratic equation (calculator...?).
what you posted looks good, i got
a=0.012117
b=-0.2012
c=-1.11645

then two terms to be added/subtracted are
-b/(2a) = 8.302486
+/-sqrt(b^2 - 4ac)/(2a)= +/-12.6914

which produces mentioned sum and difference of -4.38891 and +20.99388

Last edited: Feb 26, 2014
5. ### Wendy Thread Starter Moderator

Mar 24, 2008
20,772
2,540
If you had referenced the link provided (the source for the equation) you would have noted all dimensions are in inches. Given I am using a standard set of dimensions that would not explain a fundimental math error,

6. ### Wendy Thread Starter Moderator

Mar 24, 2008
20,772
2,540
The 21 agrees with my empirical solution. About to step out so I will go through the math again later.

May 11, 2009
5,939
1,222