I tried the formula that you suggested to calculate the self resonate
frequency of a secondary. With my specifications, it came out to 254 khz.
Then I calculated the self capacitance of the coil and using the coils'
inductance, calculated the resonate frequency and came up with 257 khz. The
two give the same answer within 1% and your formula is easier to use, all you
need to know is the dimensions and # of turns.
Speaking of how large toroids can be used to drop the resonate frequency:
When I run this coil with my 40" toroid, I measured about 130khz. By
calculating the capacitance for this toroid (37.85pf) and recalculating the
resonance, I get 126khz - close to the actual running frequency. I have
found the frequency of the coil changes as I really crank up the power.
Going from 2kva to 8kva, I find I need to increase the primary tap by about
1/2 turn. Richard Quick says he has noticed this also and is due to the
extreme electron field effectively increasing the capacitance of the toroid -
if I remember his explanation correctly.