Mike, this is a topic I really enjoy researching and thinking about
compression ratio should be in the 6~8 range for easy starting and running of a model on regular unleaded regardless of what the original had, modern autos running on regular unleaded have 9~10 but in a model there's nothing to be gained, we're not trying to dyno test our engines and get good milage! Similarly you don't scale oil pressure, but various modelers have their own favorite regulator settings, Jerry Howell uses 20 PSI, George Trimble 30 PSI, and Paul Knapp 40 PSI (I'm aiming for Paul Knapp's 40 PSI).
similarly valve timing should be for easy starting and running, we're not trying to get great MPG or optimize power and torque, all my engines use 130-deg three-arc cams (I'm guessing effectively 120-deg after tappet clearance) with zero overlap, and lift = 1/4 valve diameter.
my starting point for my Merlin and Duesenberg were technical drawings that I photo(Xerox) enlarged or reduced as necessary to match my desired cylinder bore (1" for the Merlin, and 15/16" for the Duesey) and took all measurements from them.
things like head bolts scale perfectly, the tension on them scales with the head area and the strength of the bolts scales with their cross section area. Many parts of the engine scale this way, though I generally leave my crankcase and oil pan with much thicker walls by not milling out so much on the inside.
the scaling laws indicate problems when there are weird exponents/powers in the equations, this comes out in flywheel inertia (smaller scale engines need larger than scale flywheels), springs (my valve springs use thinner wire and less turns than scale). Ken notes that torsional strength also doesn't scale (in the same way that flywheels don't scale), smaller engines need larger diameter shafts than scale. The full size Merlin suffers from not stiff enough cam shafts, so I should have enlarged mine for both reasons, but didn't and so far so good, keeping my fingers crossed, making new cam shafts is a LOT of work...
to get anywhere near the power-per-cubic-inch of the full size a model needs to be run at the scaling factor times the RPM, IE a quarter scale model should run at four times the RPM. this same scaling factor works for centrifical superchargers. but I never actually run my engines this fast.
Since we're not delivering power to a drive train I just scale the gears and don't worry about them, but it would be interesting to investigate the forces and such in the Merlin's supercharger gears and propellor reduction gears some day.
things that are influenced by Reynolds Number don't scale if you cross the laminar/turbulent boundary, but don't know that anyone has ever tracked a problem down to this in a model engine.
One issue that I don't have a clue about is cooling, how much coolant surface area is needed, how much coolant flow rate is needed. One thing I do know is that every working model Merlin is under cooled and over heats, mine included, Argh!
Spark ignition also doesn't scale, you still need a minimum spark energy to ignite the mixture regardless of its volume, so we mostly use full size coils hidden inside wood box display stand (I use moped coils, they're pretty small but still do the job).
then there are lots of rule-of-thumb that I build to (many gleaned from "Aircraft Engine Design", Liston, 1942), like piston-cylinder clearance per inch of bore, etc...
HTH,
Peter.
