Ok, Most people think you would
have to be a math genius to build a Tesla coil. You don't, but it
doesn't hurt. Here are some equations to aid in the design
stages, and to allow you to know approximately what your baby is
putting out. But first, some terminology.
I = Current in Amperes.
V = Voltage in Volts
kV = 1000 Volts, but the "k" works for other units as well.
mA = 1/1000 Amps, but the "m" also works for other units.
C = Capacitance in Farads, or uf (microfarad) or nf (nanofarad), make
sure you convert to solve the equations.
L = Inductance in Henries
R = Resistance in ohms
sqrt = Square root of (whatever is next to it)
P = power in watts.
VA = Power in volt amps (which is a watt according to ohms law)
sec = Secondary (or relating to it)
primary = The Primary or relating to it.
AC = Alternating current
DC = Direct current
eJ = effective cap energy in joules = 0.5 x C(tank) x eVp^2.
BPS = break per second.
eVp = effective cap voltage = x_vp*(1-pow(2.7182818,(-rsg_fr/rsg_t1))).
x_vp = transformer peak output voltage.
rsg_fr = rotary gap firing rate (1/bps).
rsg_t1 = time for cap to charge to one time constant based on cap size
and transformer current.
RMS voltage = Peak voltage *.707 And the other way around of
course. The .707 is actually the sqrt of 2, which is a
trigonometry thing, as AC is normally a sine wave.
And now for the formulas, please note, this list is forever growing,
the TC is not something that can be completely predicted, there is a
lot of guesswork, these formulas are mostly worked backwards from real
results, using known inputs.
I = V/R, P = IV, P = V^2/R, P =
I^2R, Ohms law.
Output in inches = 1.78*sqrtVA input. This formula gives a rough
estimation of arc length, it is not very accurate.
Vsec = Vprimary*sqrt(Lsec/Lprimary)
This formula gives the theoretical peak voltage of a
TC secondary.
Energy = .5CV^2 this formula is used on both sides (energy in =
energy out) and balanced to get secondary voltage out (left C is tank
capacitance, right C is secondary capacitance, get it?)
Spark Length (inches) = sqrt(VA) + sqrt(eJ x BPS x 1.263) This is a much more accurate formula for spark length output.