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Re: Inductance, h/d ratio

Subject:      Re: Inductance, h/d ratio
       Date:  Mon, 5 May 1997 11:53:56 +1200
       From:  "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
Organization:  Wellington Polytechnic, NZ
          To:  tesla-at-pupman-dot-com

Hi Alfred, all,

>   From:   "Alfred A. Skrocki" <alfred.skrocki-at-cybernetworking-dot-com>
>     To:   Tesla List <tesla-at-pupman-dot-com>
> 
> 
> On Fri, 2 May 1997 18:53:30 +1200 Malcolm Watts
> <MALCOLM-at-directorate.wnp.ac.nz> wrote;
> 
> > Hi Alfred, all,
> >                 I wrote a program to calculate the optimum former h/d 
> > ratio for a given length of wire. Method: start with a length of wire 
> > and h/d = 50, then increase d as l is decreased. The answer the 
> > program gave me was just under 0.5. Not great for coiling except with 
> > a gigantic coil because of the height. Not the same as maximum Q 
> > (without terminal) either. That turned out to be h/d=1, confirmed by 
> > measurement.
> 
> What were you using as your determinant of optimum? I remember back 
> in college that the largest inductance for a given length of wire was 
> something close to a h/d ratio of 3. It's not talked about in modern 
> text but if you have access to the older radio enginering handbooks
> say from 1910 through 1950 I'm sure you will see it's close to 3 .

I beg to differ. A recent post from Bert H. also referred to this in 
Morecroft's book. You could try it by either using calculus or
writing the program or you could wind a couple of coils.
     Glancing at Wheeler's formula for single-layer solenoids 
shows that L decreases as H gets bigger and increases as R gets 
bigger - to a point. That point is probably where mutual inductance 
between turns is a maximum. It is obvious that as one increases the 
diameter, N^2 gets smaller and smaller. Infact, inductance is 
proportional to D and N^2 so you can see the tradeoff occurring. I'd 
have to go digging for references but will if sufficiently pressed. 
Morecroft is a start.

    Might just take the opportunity also to quote from one of Terman's
books regarding coil Q which supports my ideas on L vs R in the 
secondary. Curves are given relating three different wire sizes over 
a range of frequencies to Q for three coils that are otherwise 
identical: "The largest wire size (No. 20) has over six times the 
cross-section of the smallest (No. 28), and yet the latter has a 
value of Q only about 35% less."  If H and D are the same, it is 
obvious the coil wound with the smallest wire will be space wound.
    
    To address another point: why go for low frequency in a TC?  
Increasing primary energy means either having to increase voltage or 
capacitance or both. Problem with increasing capacitance is that for 
a given frequency, it has to be at the expense of L so the primary Q 
starts degrading. On the other hand, one might read TCBOR's 
information regarding trying to elevate primary voltages beyond a 
certain point - decidedly not easy beyond 25kV or so. So, by running 
a low frequency, one can increase cap size while still maintaining a 
high primary L/C ratio.

FWIW,
Malcolm