Jim Lux wrote:
On 6/30/11 4:40 AM, Brian Hall wrote:I am looking for formulas to calculate the inductance of an elliptical coil, for use as a primary or secondary, in the shape of a flat spiral, or vertical helix, or conical spiral. Google showed me something about elliptigal integrals but I was never that good at calculus (that and 15+ years between being taught calc and not having used it since). Does anyone know of such formulas, to determine inductance in henries or microhenries, and would be willing to share?I think you're going to have a tough time finding an analytical expression for this. What I would do is calculate the inductance for a circular coil with the diameter = major axis, and then for diameter = minor axis. You know the elliptical coil will be somewhere in between.
If the ellipcisity isn't very much I think that would give quite an accurate answer. For short coils inductance varies approximately as N^2, not N.
The good analytical inductance equations were all developed early in the 20th century by E.B.Rosa at what became the NBS. If you google "rosa inductance" you'll get plenty of hits for the (not copyrighted) document. The units used are a bit weird (inductance in centimeters, eh?) because back then, there were 4 or 5 different systems of units used (abamperes, statcoulombs, etc. in addition to cgs vs mks, and SI was only a gleam in the eye of future metrological hegemony at BIPM)
I have a little book intended for use as a primer for experiments to be performed in a phyics lab. Cover page is signed by a student at West Point and the date is 1893!!!! If I remember right it lists a total of 8 different systems of units in use than and compares them numerically. It mentions the 'new' convention names of volt, ampere, etc. Earlier terms were pressure and quantity...
There are also tables and equations from Grover ( who worked at NBS, for Rosa, as it happens). Grover's book is available in softcover from Dover for about $10. (it might also be out of copyright.. original date was 1947)
Very valuable if you can find one. Didn't realize Dover still had reprints. Are you sure? I'd like to get one for my bookcase at work because I don't want to leave my original there. You didn't mention Bureau of Standards C74 which has lots of useful equations from the same original source.
A bit of googling shows that elliptical coils might be used in MRI, but that same googling says that the coils are designed using Finite Element methods, not analytical expressions..
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