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"Slinky" Primary / Sloped Archimedes Spiral Primary Equation


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From:  Bert Hickman [SMTP:bert.hickman-at-aquila-dot-com]
Sent:  Tuesday, August 18, 1998 8:45 PM
To:  Tesla List
Subject:  Re: "Slinky" Primary / Sloped Archimedes Spiral Primary  Equation

Tesla List wrote:
> 
> ----------
> From:  John H. Couture [SMTP:couturejh-at-worldnet.att-dot-net]
> Sent:  Monday, August 17, 1998 2:41 PM
> To:  Tesla List
> Subject:  Re: "Slinky" Primary / Sloped Archimedes Spiral Primary  Equation
> 
>   Bert -
> 
>   These questions came to mind as I was using the equations you show for
> the TC inverse cone type primary.
> 
>   1. What are the advantages/disadvantages of the cone type primary?

An inverse conical primary will couple better to secondaries with a high
H:D ratio. This is oftne the case for small diameter secondaries (on
small coils) where H:D ratios may exceed 10:1. However, as we the
elevate the outer primary turns, we also tend to reduce the standoff
voltage to the between it and the toroid. For larger 2-coil systems,
this can become the coil's performance limiting factor, since it leads
to excessive torroid-to-strikerail hits and excessive corona losses.

>   2. How would you determine the optimum angle?

It's not clear that there really IS an optimum, John. As long as the
coupling coefficient, gap quenching, and voltage standoff are all
"tuned" to:
  - avoid overvolting the secondary
  - prevent primary:secondary flashovers
  - minimize toroid:strikerail hits
then ANY of the three primary construction techniques can work well.
There are representative coilers on this list who have achieved
excellent performance using any of these three primary styles.

>   3. What are the advantages/disadvantages of using a cone type primary 
> with a raised secondary?

The main reason one needs to raise the secondary is to reduce the
coefficient of coupling to match the voltage withstand capability of the
secondary to the gap's quenching ability and the degree of streamer
loading. Like much of Tesla Coiling its a balance of tradeoffs. The
second reason would be to provide a bit more distance between the toroid
and the strikerail to reduce strikerail hits. This often becomes
necessary as the coiler begins to increase power levels. Most higher
power coilers tend to be driven towards "flatter" primaries in order to
reduce e-field stresses between the toroid and the primary. E-field
control takes on critical importance as you try to achieve streamers
longer than 2.5-3X+ coillength.

>   4. How would you determine the best cone angle and best approximate
> location for the secondary for later tweaking?

Knowing that it's not critical, I'd select an angle that makes
construction simple and that's not too steep - such as 30 degrees. And,
if I knew I was going to go to higher power levels, I'd skip using a
conical primary altogether! I'd make provision for the secondary to be
adjustable within a fairly large range, instrument measure the coupling
coefficient and tuning of the system, and begin ramping up power,
looking for any evidence of overcoupling or clearance problems. In the
final analysis, there's absolutely no substitute for experimental
tweaking!
> 
>   I found that for the typical TC spiral primary as the angle is increased
> from zero degrees (flat spiral) to about 30 degrees the inductance
> increases slightly. As the angle is increased more the inductance begins to
> decrease until it is about one third the zero degree value at 90 degrees or
> the coil value. The inductance increases then decreases only slightly up to
> about 45 degrees so the flat inductance value could be used for all cone
> type primaries under 45 degrees because the differences are within the
> error tolerance.
> 
>   With a fixed secondary and inductance (Ls) the secondary voltage varies
> as the   sqrt(Ls/Lp).    This would indicate a coil type primary (Lp) would
> give more secondary voltage and spark length than the spiral primary
> because the inductance is less. We know this is not correct so what are the
> optimum spiral primary design criteria?
> 
>   John Couture
> 
<SNIP>

The key criteria is we must maintian LpCp = LsCs so that both the
primary and secondary continue to resonate at the same frequency. If
nothing is changed in the secondary side, and we force Lp to be lower,
we must correspondingly increase Cp in order to stay in tune. If we
leave the gap breakdown voltage the same, then the "bang" energy must
increase since we've increased primary capacitance. Since the maximum
output voltage can also be expressed as a function of sqrt(Cp/Cs), it's
clear that the voltage would, indeed, increase... so that it the
sqrt(Ls/Lp) relationship still applies.

-- Bert --