Turn the primary up the secondary and the arc gets longer. It is the first thing anybody tries and it is the wrong way round. Coupling does not buy length. It buys the ratio of the arc to the coil that threw it, and those are different things that happen to be measured in the same units.
What raising k does to the tank
The secondary is not a separate machine. Its losses appear across the primary as a resistance, and the size of that resistance is set by the coupling:
R_ref = w^2 · k^2 · L_p · L_s / R_sThe square is the whole argument. Double the coupling and the secondary looks four times as lossy from where the bridge is standing. The bridge is a voltage source into a series circuit, so the current it can push through that circuit is what falls:
I_pk = (4/pi) · V_bus / R_totalRaise k and R_total goes up, I_pk comes down, and the power going into the arc comes down with it. Nothing about that is subtle and nothing about it is controversial. Uspring puts it as the primary looking lossy: the transfer of power to the secondary is itself what takes the primary current down.
What the record holders actually run
If coupling bought length, the longest arcs would be the most tightly coupled ones. They are the opposite.
- BrOdin throws 460 to 520 cm at
k= 0.146 to 0.185, off a large secondary. The longest arcs on this list, at the loosest coupling on it. - Anders Mikkelsen gets 318 cm off a 16.4 cm secondary at
k= 0.497. That is 19.4 times the coil, and a fifth of BrOdin's metres. - ZakW gets 122 cm off a 5.0 cm secondary: 24.4 times the coil, and a quarter of BrOdin's length.
- Daniel Eindhoven's RAIKIRI staff gets 350 cm off a 14 cm secondary, at 25 times the coil the highest ratio here, on a 900 V bus into a full bridge of silicon carbide.
The metres sit at the bottom of the coupling range. The ratios sit at the top. The two highest ratios on the wall come off fourteen and five centimetre secondaries, throwing three and a half metres and a metre respectively; BrOdin's coil throws more than either and does it at k = 0.15.
An ordinary DRSSTC lives at 0.13 to 0.17. A QCW lives at 0.30 to 0.50, which is the same trade taken deliberately: a QCW is trying to make a long arc off a short coil, so it pays current for ratio on purpose.
The wall on the other side
There is a reason nobody simply winds the primary tighter and accepts the lost current. Racing sparks have been caught at k = 0.185, which is inside the range an ordinary DRSSTC would call ordinary. The turn to turn voltage up the secondary is not distributed the way the coupling coefficient suggests, and the coil flashes over its own winding before any of the arithmetic above has a chance to matter.
So what does buy length
Energy, and slowly. Across the measurements that exist the arc goes as the cube root of the energy in the bang:
L ~ E^n, n = 0.31 to 0.33A cube root is a hard master. Eight times the energy for twice the arc, and the eight has to come from somewhere: a higher bus, a longer ontime, more capacitance in the tank, and each of those has its own wall. That is why millimetres per kilowatt does not work as a figure of merit. It assumes a straight line through a curve, and it is not even defined until you say how long the bang lasted.
At the bench
- Set the coupling from the geometry you can survive, not from a length you want. Start looser than you think and creep up.
- Measure the primary current before and after every change to
k. If it fell and the arc did not, the coupling was not the limit. - When the arc stops growing, look at the bus and the ontime before you look at the coil. The cube root means the coil is rarely the cheapest thing to change.
- Treat the first racing spark as the ceiling for that winding, permanently.
The figures above are collected from published builds rather than measured here, and the ratios are arithmetic on the builders' own numbers. Three of them have been read at the source: RAIKIRI, and Gao's QCW 1.5 and ramped SSTC. The rest came off a compilation of forum threads, and the records page keeps them apart from the ones that did not.