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Maths formula needed please

Community Veteran
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Registered: 06-11-2007

Maths formula needed please

I need to work out how much wire I will need to make a coil for my radio....
coil former size is 150mm length, by 30 mm diameter
I need to have 150 turns of wire on the coil former.
wire size is 22SWG or 0.71mm
is there someone out there who can give me the formula to work out the length of wire needed, please.
Thanks. Wink
8 REPLIES
Community Veteran
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Registered: 15-06-2007

Re: Maths formula needed please

A relatively simple method if a tiny bit inaccurate is to assume that the windings are a number circles of diameter (30 + 0.71) and then each winding has a length of (30 + 0.71) x PI
Then 150 turns requires 150 x  30.71 x PI mm or 14.47 metres - say 15 metres to allow for it not being dead tight to the former and the helical effect
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Re: Maths formula needed please

2*pi*r is the basis.  Wink
(or pi*d)
If the coil former is 150mm long you'll get 150/0.71 = 211 (roughly) turns along the length so no multiple layers to confuse things.
pi=3.1412 roughly
d=30mm (ignoring the wire thickness)
So 150*30*3.1412 = 14135mm
So less than 15 metres or 47 feet.
Community Veteran
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Re: Maths formula needed please

Thanks very much guys.... much appreciated... will log that on my notes (somewhere safe !  Roll eyes ) for future ref .
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Re: Maths formula needed please

Hi guys....
I have been struggling to do a "reverse" of the formula given....
I now need to know the length of the former required to acommodate a specified length of wire....
and despite several/many many tries to change the formula layout  -- transferring known quantities across the = sign and dividing etc.... I don`t seem to be able to get a coherent answer....
so here are the known quantities
Length of wire..... 23.35 feet  (7.11708 mtr)
Dia of former..... 27mm
(number of turns = irrelevant in this case)


Community Veteran
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Re: Maths formula needed please

Referring back to my first reply
You get the length of wire per winding (27 + 0.71) x 3.1416 = 87.05 mm where 0.71 is the diameter of the wire
Number of windings 7117 / 87.05 = 81.75 mm - assume 82 mm
Length of former 82 x 0.71 = 58.2 mm
Community Veteran
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Re: Maths formula needed please

Sorry Jim.... seem to have confused myself and you !
I don`t need the number of windings... (turns)  I need to find the Length of the Former for the specified amount of wire...(23.3 ft or 7.1017mtr) (sorry about the mm error)
so what is the formula, using the given amounts above....?
Community Veteran
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Re: Maths formula needed please

That is what I gave you
To combine the whole lot together you get
Length of former = Diameter of wire x number of windings =  Diameter of wire x (length of wire / length per winding) = 0.71 x (7117 / ((27 + 0.71) x 3.1416)) = 58.04 which is a bit less than previously as you need to round up the number of windings which in Excel means that the formula is
+0.71*round((7117 / ((27+0.71)*3.1416)),0) giving the result 58.22
But it is much better to do it in steps
Community Veteran
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Re: Maths formula needed please

Ok Thanks Jim.... I`ll have a play around with that, on my other lengths.... cheers  Wink