I am intrigued by the persistent use of the word "cycle" instead of "stroke". A two-cycle engine would only run for two revolutions if it was a two-stroke or four revolutions if it was a four-stroke. A cycle is the complete "suck-squeeze-bang-blow". A 2-stroke engine does a complete cycle in just two strokes of the piston or one revolution. A 4-stroke engine takes four strokes of the piston to do one complete cycle, or two whole revolutions.
Are you trying to be pedantic for a reason?
There have been many miniature 4-stroke engines designed and built. One reason for using a 4-stroke engine over a 2-stroke for model aircraft use is noise.
Lessee, why one might use a 4-cycle in an RC aircraft over a 2-cycle.
* Better fuel economy. Glow fuel costs $30 a gallon and planes tend to fly roughly twice as long on a given fuel load if a comparable 4-cycle is used in place of the 2-cycle. My NexSTAR is a fairly extreme example; on an OS 46AX two cycle(The recommended engine by Hobbico and what was included in the RTF versions even though mine was an ARF), the 270cc fuel tank it carries gave roundabouts 10-12 minutes of flying with ample reserve for landing under power. Swapping that engine out for a Magnum 52RFS 4-cycle increased my typical flight time from 10 minutes to nearly 30. I timed it; 33 minutes and change to run the tank till it quits.
* Larger props are more efficient. Swapping the 46AX out for a 52RFS meant I went from a 10-5 3-blade to a 11-7 3-blade. Total thrust stays roughly the same but the larger prop turning lower RPM helps with efficiency. I fly at around 35% throttle on the Magnum 52; the 46AX wanted about 1/2 throttle.
* Quieter. Kinda related to your point, though you didn't specify what aspect of the noise you were referring to. My Magnum 52 is worlds quieter than the 46AX ever was.
* More realistic sound. Real aircraft generally aren't powered by 2-cycle engines and 4-cycle engines tend to be a reasonably close facsimile. Especially with Cessna-like aircraft, which most trainers are.
* More aerodynamic. 4-cycles don't require massive aluminum tumors hanging off the side, which means they are much less of a drag generator than a comparable 2-cycle would be. More applicable in a cowled up aircraft(Like the Phoenix Typhoon I'm building over winter!) where the drag of the jug itself isn't all that much of a consideration, but the exhaust system poking out into the airstream is.
* Easier starting. 9 times out of 10 I have to fight my 2-cycles to get them to run in the correct direction. My 4-cycles...physically cannot run backwards. I can just bump them against compression in reverse with the glow driver attached and they kick right to life; my 2-cycles bounce a few times and it's potluck which direction they actually run in when they properly start.
* Better idle/low speed/trasition. Two cycles like to 'load up' and need to be cleared out when they're left idling, or at low power. Four cycles generally don't have this problem and, as long as the mix is within 90% of correct, they'll be much more reliable at low speed. And often they'll idle down lower besides.
* Less prone to failure due to a lean run. In my experience, two cycles will quite happily continue to run well after they've been leaned excessively, especially on the top end, which will burn them up right fast in a hurry. My 4-cycles quit on me within
seconds if I twist the HSN too far while on the ground. It's nigh impossible for me to run one lean enough to burn it up.
* Lighter. In some cases that huge aluminum tumor hanging off the side of a 2-cycle makes it heavier than the 4-cycle replacing it. 'Twas the case with my old Super Tiger GS45ABC. It weighed 100 grams more than a Magnum 52RFS in ready-to-fly configuration, even though it weighed 150 grams
less without a muffler. But you'd never fly it that way; be way too loud, inefficient, prone to ill temperment.
Generally speaking, I won't fly a 2-cycle without a good reason for it. And usually that reason is 'I can't get a 4-cycle small enough for this model'. Which ties into why I'm even asking about the feasibility of making one this small that's capable of flying something in the first place. Smallest one I can get is 3CC or so, smallest
brand new 4-cycle I can get is closer to 4cc, yet I have planes calling for just 1cc engines, planes which would never balance out with one of those large 4-cycles.
A 4-stroke engine has a lot more than half the power of a similar sized 2-stroke engine. The cylinder on a 2-stroke is never filled with a full charge. A lot of the fresh charge also goes straight out of the exhaust. In a 4-stroke, the valve timing more or less inhibits this, so the cylinder has a much better charge to burn.
A 4-stroke also has more torque than a similar sized 2-stroke.
Jack
Rule of thumb is about 30% more displacement to equate the two, though in some airplanes it gets closer. I only went up by 12% in displacement when I swapped my NexSTAR to 4-cycle, but being a trainer with a flat bottom high-lift wing, it didn't much care. If anything it flies better than it did on the 46AX; I cruise at 35% power whereas the OS had to run at half throttle or so. That might be even better if I could run a 12" prop...the 4-cycle I got LOVES a 12x6...but ground clearance issues forced me to use a 3-blade 11" prop.