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Re: Need Formula for length of spiral



Original poster: "Jim Lux by way of Terry Fritz <twftesla-at-qwest-dot-net>" <jimlux-at-earthlink-dot-net>


I don't have an exact one off hand, but one can derive it as follows:

The length of one turn is 2 * pi *(r1+r2)/2, where r1 and r2 are the
starting and ending radii.
This turns into pi *(r1+r2)

Now, turn it into the length of the "Ith" turn, where the turns are spaced
d apart

length (turn i) = pi * (r0+(i-1)*d + r0 +i*d), where r0 is the starting
radius of turn number 1)

bring the r0 out to get length(turn i) = pi * (2*r0 + d*( (i-1)+i)) or
length(turn i) = pi*2*r0 + pi * d * (2i -1)
length(turn i) = (pi*2*r0 + (-1* pi * d)) + pi * d * 2 * i  .... grouping
constant and varying terms

sum up N turns

total = length(turn 1) + length(turn 2) + length(turn 3)+... + length(turn N)
= N * (2 * pi * r0 - pi * d) +  2*pi*d * (1 + 2 + 3 + ... + N)

sum of (integers from 1 to N )= N*(N+1)/2

length of all turns = 2 * N * pi * r0 + pi * d * N^2
moving the pi out
= N * pi *(2*r0+ d*N)


Tesla list wrote:
> 
> Original poster: "John Tomacic by way of Terry Fritz
<twftesla-at-qwest-dot-net>" <tesla_ownz_u-at-hotmail-dot-com>
> 
> Hi everyone,
> 
> Does anyone have a formula that I can use to calculate the length of wire
> required in a flat spiral coil? I have the formula for inductance, however,
> I really need the wire length.
> 
> Thanks,
> 
> John
> SST coiling in Ottawa.
> 
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