Re: [TCML] charging reactors - Inductance formulas

[Frosty <frosty90@xxxxxxxxx>]

Hi all
Heres my 'two cents' on inductance;

I have a rather old book here called "Electrical engineering Circuits" by
"H.H Skilling". In the book there is a general formula for the inductance of
"a long coil" given as:

L=(u*N^2*A)/l  henries
u is the permeability of air
N is the number of turns
A is the crss sectional area (square metres)
l is the length (metres)

But the author does go on to explain that this equation assumes that all the
flux links with all the turns of the coil. They also mention that the
cross-sectional shape dosen't matter, and they say nothing of wire spacing
etc. (this is for a single layer solenoid).

It is then explained that the innacuracy of this formula obviously comes
from the fact that not all flux links with every turn, and that the leakage
occurs mostly near the ends of the coil. They also say that if the length is
10 times the diametre the true inductance is 4 percent less than the
calculated value (with the above formula).

They then say that for a short coil of circular turns, a modification of the
above formula to take into account the leakage is:

L=(u*N^2*A)/(l=0.45*d) henries

and acording to the author "this formula is good for a coil however long,
and is accurate to witin 1 percent when the length of the coil is about half
the diametre"

the author then goes on to say it may be more convenient in the form:

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

r is radius and all units are in inches

They also go on to mention that all these assume relatively fine wire or
very low frequency, so that stray induced currents are small; so for "high
frequency" i.e. tesla coils, it would seem that these formula would differ
in accuracy, by how much I don't know how to calculate (maybe someone here
does), but one would assume that if the wire thickness is very small, these
would still be fairly accurate at moderately high frequency.

They also mention that this last formula is credidted to H. A. Wheeler. I
think this is what most of us refer to when refering to the "Wheeler
formula". It would appear that all of the various "Wheeler aproximations"
are all possibly based on the first formula, but make corrections for
leakage assuming a circular cross section, straight solenoid circular wire
etc.

Cheers,
Jesse
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