I've got a question that has been puzzling me for awhile, and figured I'd reach out to the collective wisdom of the group.

Bombardier makes a line of personal watercraft under the Sea Doo brand name.  From 1998 to about 2004, they installed a tempermental engine made by Rotax in a line of high performance watercraft.  This engine was called the model 947, with 951cc, 2-stroke, oil injected, reed valve induction, variable exhaust pipe tuning via their RAVE technology & water injection.  These engines put out 130 HP, nothing major from a racing engine perspective, but pretty healthy for a consumer recreation vehicle.  These are direct coupled to a jet pump that provides the motive power for the PWC out the back.

They are notoriously unreliable, many go south with under 100 hours usage, many self destruct with broken piston skirts ending up first in the crankcase, then all over the inside of the hull as the aluminum case shatters.....

But my question has to do with runaway.  I rebuilt one and proceeded to get it running "on the hose", i.e. out of the water using a garden hose plumbed into the cooling system.  The engine started and ran for a short time, and proceeded to runaway.  When this happened, I quickly hit the stop button (which does nothing), and pulled the choke (which killed it) I knew to pull the choke, because this engine is known for runaway, and I had read that pulling the choke was the best way to stop it.

Bombardier specs call for setting the "out of water" idle at 3000 RPM, which results in an idle "in the water" of about 1500 RPM.  Mine was set for about 3200 RPM.  A well-known tuner of Sea Doo's recommends an out of water idle speed of 2800 RPM to prevent runaway on this engine.  I set mine down to 2800 RPM and the runaway problem stopped.

What puzzles me is the mechanism for runaway on this particular engine.  2-strokes are well known for runaway if an extremely lean condition exists, but this particular engine does it when it is properly set up and jetted.  I did a plug check at idle, and it showed a fairly rich condition.  (plug check at WOT showed a nice tan color)

These engines don't have excessive compression, and are designed to run on 87 octane pump gas.  A compression check reveals 135 PSI, which is right on spec for this engine.

This engine is newly rebuilt, so no carbon deposits are present for autoignition.  It didn't run long enough for the plugs to get super hot for autoignition. The compression is relatively low for autoignition.

Can anyone present a hypothesis on why this particular engine does this at a slightly high idle setting?

A while back, Honda was playing with a two-stroke engine that used controlled auto-ignition; they called it ARC (Active Radical Combustion). The residual exhaust from the previous stroke has enough heat and chemical reaction going on to ignite the next stroke without needing the spark plug. You're probably experiencing something like that. There is almost no frictional load or pumping losses in a roller-bearing two-stroke (compared to a four-stroke) so it's conceivable that even the slightest amount of fuel delivery would let it run away.

This is a very interesting topic. I would like to make two comments.
 Firstly, I have seen several high compression SI 4-stroke engines that would continue to idle very roughly after the ignition was turned off - but, they certainly would not run at high RPM in "compression ignition" mode. Maybe 2-strokes behave differently.  
 Secondly I have witnessed very odd behaviour from a 4-stroke motorcycle engine with transistorised switching of the primary circuit triggered by a sender unit on the crankshaft. Switching off the ignition would stop the engine - but, disconnecting the battery would not always stop the engine which would continue to idle happily - certainly not in any type of autoignition mode. The workshop manual wiring diagram showed that the ignition switch cut the connection to the battery so it should have had the same effect as disconnecting the battery.
 Anyhow the point I am trying to make is that Mr. Waterstreet's engine may well have a similar type of crank-triggered spark - maybe when he turns the ignition off the sparks continue.
  It may be tricky to do but possibly Mr. Waterstreet should check to see if the plugs are firing as the engine "runs away'.  

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