RE: Short, Fat Resonators?

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

Original poster: "Loudner, Godfrey by way of Terry Fritz <twftesla-at-qwest-dot-net>" <gloudner-at-SINTE.EDU>

Hello Greg

A similar result exist for an Archimedes spiro primary. Let R = the average
radius of the coil and W = the width of the coil. For a fixed length of
wire, the coil will have maximum inductance when W = 8R / 11. One would have
to be suspicious of results like these because they come from using
empirical formulas for inductance about which the range of validity is in
doubt. Otherwise the derivation of these results for optimal inductance is a
simple exercise in differential calculus. I think it would be interesting to
explore very low aspect ratio resonators on a smaller scale than that of N.
Tesla. 

Godfrey Loudner


> -----Original Message-----
> From:	Tesla list [SMTP:tesla-at-pupman-dot-com]
> Sent:	Monday, July 30, 2001 10:21 PM
> To:	tesla-at-pupman-dot-com
> Subject:	Re: Short, Fat Resonators?
> 
> Original poster: "by way of Terry Fritz <twftesla-at-qwest-dot-net>"
> <Mddeming-at-aol-dot-com>
> 
> In a message dated 7/30/01 12:49:29 AM Eastern Daylight Time, 
> tesla-at-pupman-dot-com writes: 
> 
> 
> 
> >
> > Original poster: "Gregory Hunter by way of Terry Fritz
> <twftesla-at-qwest-dot-net> 
> > " <ghunter31014-at-yahoo-dot-com> 
> >
> > Has anyone on the list experimented with very low 
> > aspect ratio (1 to 2 diameters tall) resonators? On 
> > another thread somebody made some real interesting 
> > statements about the beneficial properties of wide, 
> > squat secondaries, and I'm wondering if anyone has any 
> > hands-on experience to share. I've been eyeballing 
> > those 5 gal plastic buckets that are so common these 
> > days. They are made of polyethylene, and "clean" 
> > buckets with no printing on them are available at 
> > Wal-Mart & similar stores. I bet one of these would 
> > make a fine secondary form for a low aspect ratio 
> > coil. I'm not serious about building anything yet. I'm 
> > just thinking about it, doodling with designs, etc. 
> >
> > Greg 
> > http://hot-streamer-dot-com/greg 
> >
> 
> 
> 
> Hi Greg, All, 
>         It can be shown mathematically that the highest inductance for a 
> given length of wire occurs in a coil when h=0.9r. This also means that
> the 
> Q-ratio XL/R is at a maximum, since inductive reactance, XL, is
> proportional 
> to L, and resistance, R, is proportional to wire length. The only person I
> 
> know of who actually built coils to these proportions was Tesla himself.
> (40" 
> diameter coil 18" high). While this might be desirable because Vout ~ 
> sqrt(L2/L1), extremely short coils require much higher insulation since
> the 
> voltage drop per inch of coil length dV/dh is extremely high. For example,
> a 
> 30" high coil at 300KV has a nominal gradient of 10kV/inch or about 
> 250v/turn. Under the same conditions, a 10" high coil has a gradient of 
> 30kV/inch or 750v/turn. Insulation breakdown and arcing are much more
> likely 
> under these conditions. Like everything else in a TC, it's a trade-off.
> The 
> rule-of-thumb is usually to keep "small" coils to 5:1 ratio h/d or less
> and 
> "big" coils to 3:1 or less. The division between "big" and "small" is, of 
> course, very murky. I can provide the derivation of the opening statement
> off 
> list, if requested. 
> 
> Hope this helps, 
> Matt D.
>