The split cycle engines work, and despite what they're saying in the article, have been built. They are able to fire the plug ATDC because the jet of air coming from the compression cyllinder makes so much turbulence in the chamber of the combustion piston. Without turbulence, gasoline would burn at the laminar rate, which is only a few meters per second. That is why we have to fire all of our engine BTDC. Add turbulence and the mixture burns logarithmically faster. That's why you don't have to continually advance your ignition timing as engine RPM goes up. Faster piston speed also increases turbulence (kinetic energy from the piston is transferred to the mixture).
The key to a fast, complete combustion cycle is turbulence. Get as much turbulence in the combustion chamber as possible, and your fuel will burn that much more quickly. Their engine runs cooler than a conventional engine because of the ignition timing. In a normal engine such as our SOHC4, the spark plug is fired at 40 deg BTDC. That means the combustion chamber is in contact with the burning air from that point all the way through the exhaust stroke. If you fire the plug at or near TDC, you're taking away 40 degrees of revolution that would normally be heating the engine. If you can get the A/F mixture to burn quickly enough, you can retard your ignition advance and get the same power. In any crankshaft/piston engine, you want the maximum pressure level to be at 14 deg ATDC. If you can keep the pressure there but with retarded ignition timing, you've made your engine more efficient. Not only heat-wise, but mechanical-wise because the piston doesn't have to push through the building pressure.
