Re: Single vs Twin TCs

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

Original poster: "Bert Hickman by way of Terry Fritz <twftesla-at-qwest-dot-net>" <bert.hickman-at-aquila-dot-net>

Ralph,

I actually made a number of implicit (but unfortunately unstated)
assumptions in the previous posting:  

1. Tank cap and main spark gap firing voltage is the same for either 
system (i.e., same bang size)

2. The resonators and toroids used in all systems were identical

3. The primary inductance associated with each twin was 1/2 that of the
single TC so that the combined primary inductance remains the same 

4. Because of assumptions 2 and 3 above, the operating frequency remains
the same for both systems

Using a lumped model for simplicity, we know that the maximum voltage
output of of a TC will be proportional to the primary bang energy (Ep =
0.5*Cp*Vg^2) where Cp is the tank capacitance and Vg is the main gap
breakdown voltage. For a standard TC, the secondary energy in the
resonator/toroid after ring-up (E1) will be equal to the primary energy
less system losses. Let's ignore losses to simplify the calculation
(since we can assume that similar losses will exist for either the
single or 2-coil system). For the single coil case, the maximum energy
in the secondary (ala Conservation of Energy) will be the following
where Cs is the effective capacity of the resonator/toroid combination
and V1 is the maximum output voltage:

   E1 = 0.5*Cs*(V1^2) (where E1 is proportional to the primary bang size
Ep)

In the case of a balanced twin, the same energy/bang must be shared
equally between two identical resonator/toroids, so the maximum energy
(E2) available to each resonator in the twin system will be half of the
above. Letting V2 be the output voltage of each twin resonator:

   E2 = 0.5*Cs*(V2^2) = 0.25*Cs*(V1^2)   

Simplifying, canceling common terms, and solving for the ratio V2/V1:

   (V2^2)/(V1^2) = 0.5

   V2/V1 = SQRT(0.5) = 0.707 

   V2 = 0.707*V1

Thus, the voltage output per each resonator will be about 0.707 times
that of the single 2-coil TC case, all other things being the same
(which they never really are...).  :^)

Best regards,

-- Bert --  
-- 
Bert Hickman
Stoneridge Engineering
Email:    bert.hickman-at-aquila-dot-net
Web Site: http://www.teslamania-dot-com


Tesla list wrote:
> 
> Original poster: "by way of Terry Fritz <twftesla-at-qwest-dot-net>"
<Parpp807-at-aol-dot-com>
> 
> In a message dated 12/19/01 8:46:02 PM Central Standard Time,
> tesla-at-pupman-dot-com writes:
> 
> Bert and Steve,
> 
> My experiments now with my bipolar twin are producing a
> point to point discharge of 60 inches. That's an increase
> from the 43 inches I was getting from the horizontal bipolar.
> A good confirmation of the sq rt 2 value for the combined length.
> 
> Maybe the attractive E-field does increase the efficiency due to more
> of the energy going into the spark. The 1/8 steel rod I'm using for
> breakout points on each toroid is shaping the E-field so as to
> almost totally eliminate the corona losses that were so severe
> in the HBP.
> 
> Would you please explain how  the 0.707 (RMS?) voltage value
> relates to energy conservation?
> 
> Happy day,
> Ralph Zekelman
> 
> > So, let's assume that a
> >  single coil TC outputs a streamer length "X" for a given input power
> >  level. If we now apply the same power into a bipolar twin, it should be
> >  distributed equally between the twin resonators. This implies that the
> >  estimated spark length for EACH secondary would be about 0.707*X. The
> >  combination should be a resonator-to-resonator spark length of 1.414*X
> >  for the same input power

-- 
Bert Hickman
Stoneridge Engineering
Email:    bert.hickman-at-aquila-dot-net
Web Site: http://www.teslamania-dot-com