Original poster: "Gerry Reynolds" <gerryreynolds@xxxxxxxxxxxxx> I forgot to answer the bottom half of your question.
Original poster: "Steve Ward" <steve.ward@xxxxxxxxx> Well, wouldnt any reasonable top capacitance pretty much destroy that perfect 3:1 ratio? How far off should the ratio be to avoid harmonics? I would guess that depends on the Q somewhat, as to whether or not you would excite that other mode. I must admit im having difficulty conceptualizing how the 1/4 and 3/4 resonances work when you have a big toroid on the end of the coil. Maybe i should read Paul's papers ;-).
Paul has a list of all kind of things that contribute to racing sparks (more than I can remember). As the topload is increased, the 1st overtone frequency drops faster than the 3rd overtone so the belief is the 3rd overtone gets excited less.
I still dont really believe that exciting higher harmonics in the secondary is what causes the racing sparks. It seems simple enough to me, put too much stress on the coil and its going to arc over, particularly near the bottom where the coupling is greatest. So if you relax the coupling some, the volt/turn should be lower, and in all of my cases of racing sparks, this has fixed the problem.
The key, I believe, is "the stress on the coil". Get that stress high enough and there will be an arc. Too much coupling into the lower portions of the coil will increase that stress. Too much overall coupling will increase the spectral separation between the two frequencies that coupled tuned circuits create. These frequencies can beat at a frequency of (fupper - flower) and cause local stresses if the beat occurs before ring down is completed. 1st and 3rd overtone frequencies can beat and cause local stresses. Out of tune systems can have two frequencies that are spectrally are more separated than in tune coupled systems and beat at a more rapid frequency and can cause local stresses before ring down is completed, etc...
Certainly more study is needed and perhaps some computer simulations that show the many frequencies properly and the stress they can create. I do want to work on that model when time permits.
Gerry R.