Re: optimal aspect ratio

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Malcolm Watts by way of Terry Fritz <twftesla-at-qwest-dot-net>" <m.j.watts-at-massey.ac.nz>

Hi Herwig,

On 29 Jul 2002, at 0:21, Tesla list wrote:

> Original poster: "by way of Terry Fritz <twftesla-at-qwest-dot-net>"
<herwig.roscher-at-gmx.de>
> 
> 
> Fellow coilers,
> 
> The latest edition of a German radio amateur magazine is dealing with 
> the optimal aspect ratio of cylindrical single layer air core coils 
> (like the solenoid type primaries in our TC systems).
> 
> The author proofs, that coils with an aspect ratio length/diameter of 
> 0.45 provide maximal inductance and minimal resistance.
> 
> The number of turns is calculated from
> 						7.43 x 3rd root(L in µH/dia in mm) 
> 
> Unfortunately there is no URL available (the publisher wants to sell 
> the copies of course).
> 
> Cheers,
> 
> Herwig

The proof is easily obtained by starting with a fixed wire length, 
diameter, and h/d ratio (say 2 for example) and iteratively 
increasing diameter as height/length is decreased until inductance 
hits a maximum. In fact differentiation applied to Wheeler's formula 
does much the same thing in fewer steps.

      While that obtains a maximum inductance, it doesn't score the 
highest Q.

Regards,
malcolm