Re: How do I work out secondary former diameter?

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

Original poster: Mddeming-at-aol-dot-com 



---------- Forwarded message ---------- 
Date: Wed, 06 Dec 2000 18:58:34 +1300 
From: Seth Fischer <aureo-at-xtra.co.nz> 
To: Tesla List <tesla-at-pupman-dot-com> 
Subject: How do I work out secondary former diameter? 

Are there any rules of thumb for decicing the secondary former diameter? 
What are the advantages/disadvantages? 

I will be using a 15/60 NST, 1600 turn secondary, not sure what size 
toriod yet. 

TIA 
Seth Fischer 


Hi Seth et al. 

Your question, if looked at in detail, is not a simple one, although there 
are many rules of thumb and conventions (e.g., Height to Diameter ratio 
should not exceed 5:1). The selection of the coil size is not entirely 
arbitrary.   
As I recall the physics of the situation from too many years ago, the maximum 
standing wave is established in the secondary (Max voltage at very top) when 
the length of wire used to wind the secondary is equal to 1/4 the wavelength 
of the resonant frequency. This would be length=75,000,000/f , where f is the 
frequency in Hz and length in meters. For the metrically challenged, this 
would be about 246,000,000/f feet. The frequency depends in turn on the 
effective inductance and capacitance of the secondary & toroid as: 

f=1/(2pi*sqrt(LC)) 

The inductance (L) depends in turn, on the geometry of the secondary. For a 
close-wound, single-layer coil, a good approximation can be given by: 

L=(rN)^2/(9r + 10h) 
    
   Where L is in uHy,  r is the radius of the coil in inches N is the number 
of turns, and h is the height of the winding (not the form) in inches. If you 
have already selected N=1600, then r & h will depend on the size wire you are 
using. The capacitance C depends on the coil geometry, the shape, size, and 
position of the topload and the proximity of the coil to other stuff in the 
area where it will be running. As a first approximation, the capacitance (in 
pf) of an isolated toroid made with outer diameter d1 and cross-section 
diameter d2 is: 

C=(1+(0.2781*-d2/d1)*2.8*sqrt((pi*(d1-d2)*d2/4)) 
        ( per Chris Hill <http://www.hills2.u-net-dot-com/tesla.htm>) 
The over-all effective capacitance will usually be somewhere between this 
value and 35% greater to include capacitance of the coil itself and the 
surrounding "stuff" 
The E-tesla6.11 program can be used iteratively with these equations to get a 
better approximation of C. Another item to consider is the resistance. A very 
thin wire will have higher resistance meaning a lower Q for the coil, and a 
larger proportion of the energy going into heating the coil rather than 
generating sparks. Also, if R>=2*sqrt(L/C) no oscillation will take place. 
        Since the discharge capacitor needs to resonate with the secondary 
of your power supply at or below the supply frequency (50-60 Hz) and must 
also resonate with your Tesla primary at the resonant frequency of the 
secondary, a frequency that is too high or too low can give you some really 
odd size requirements for the primary. 
        The inductance in (uHy) for a pancake primary with inner and outer 
radii of ri and ro, is approximately: 

L= (r'N)^2/(8r'+11B) 
    
where N is number of turns, r'=(ri+ro)/2 in inches, and B=ro-ri (in inches). 
Physically, the minimum value for ri obviously cannot be less than the 
diameter of your secondary form PLUS enough distance to prevent arc-over. ro 
is limited by the size of your coil platform. Also the distance between 
turns, r'/N-t, must be large enough to prevent arcing between turns of the 
primary coil. (t is thickness of wire) 
In the primary circuit, we must again have R<2*sqrt(L/C) to have oscillation 
and here, C is large and L is small, which is why copper tubing is usually 
used for the primary to minimize R which is the AC resistance and includes 
eddy currents and skin effect. 
    On the purely mechanical side, a very tall, skinny coil with a large 
toroid is unstable and may flex and be prone to falling over or arcing to 
wires, pipes, etc., in the ceiling. A very short, wide coil, with its top 
located too close to the ground will not produce long streamers.  Wide coil 
forms are more expensive and heavier than narrow ones but are more stable. 
Thin wire is lighter and smaller than thick, but has higher resistance and a 
wide coil requires more wire for a fixed number of turns than a narrow one. 
(Double the diameter means double the length of wire for the same height 
coil) 
        As you can see, a good coil is a balancing act between often 
contradictory constraints. I can be contacted on or off list for further 
discussion. 

The Light willing, 
Matt Deming