GMD for more than 3 conductors

[applepieordie]

I've seen 2 different equations  from 2 different references for finding the GMD for 4 conductors.

-one used (D12 x D23 x D13 x D14 x D24 x D34)^(1/4)

-the other used (D12 x D23 x D13 x D14 x D24 x D34)^(1/6)

i assume one of them is wrong? which one is correct? im leaning towards the 6 root one to be correct, can someone please confirm?

what is the general eqn for n number of conductors? i assume nth root of the product of n possible distances.

Thanks in advance for help.

 

[Stephen2awesome]

(d1+d2+....dn)^(1/n)

 

[rg1]

GMD (D12*D13*D14*D23*D24*D34)**1/6 is correct for 4 conductors.It is always a multiplication and then 1/n th root if n is the nos.

 

[applepieordie]

@Stephen2awesome @rg1

i thought so. Thank you for your replies.

 

[Stephen2awesome]

@Stephen2awesome @rg1

i thought so. Thank you for your replies.

you're welcome. Where did you see the other?

 

[supapowa]

The other formula looks like for gmR instead of gmd

 

[Bonsai]

This is one of those situations where stepping back and thinking about the meaning of the question really comes in handy. Geometric mean is not specifically an engineering term, it is a mathematical one. It is always the nth root of the the total product of n measurements of available data. For GMR, that data is radii, one for each conductor. For GMD, that data is distance, for which you will have the total number of distances between any two conductors (n =1 for 2 conductors, n = 3 for 3 conductors, n = 6 for 4 conductors, etc).