1. 8,000’ is typically best speed - true, if power is limited to max recommended 75%. But best efficiency - not at all.
2. 12,500’ is max vfr cruising altitude w/o O2? Sometimes true, sometimes not true.
3. At 12,500’ you’ll be down to about 65% power, and slightly slower (but not 20 mph). True, you’ll be saving gas, which is why 12,500’ is more efficient than 8000’.
I agree with Bob. Better efficiency is found going higher than 8000 feet. We've done a fair amount of testing up to 20,000 feet on the RV-10. Does some amazing numbers up high if you have O2.
I agree with both you Gent's you are 110% right. No one said going higher than 12,500 msl can't add efficiency. However a 160HP O320, 160HP at gross weight, hot day not getting to FL200. Sorry. If it got there it would not be efficient nor fast. Seems to be a contest to see how high we can fly. Let me say Steve Bohannon in his modified RV-4 went to 47,500 feet, missing the absolute record by 300 feet set by a B29. There is also Dave Anders, Cafe' Foundation Triaviathon winning RV-4. Most RV'ers are not IFR O2 sucking with high HP high compression/stroked Lycs. We are talking flying near the corner of the performance envelope. However average RV's and pilots can fly well into the teens, but there are times that is a very inefficient things to do or not practical.
I never meant to imply 8,500 to 12,500 are the ONLY altitudes thou shall fly cross country. I said 8,500 is a good compromise in no wind conditions which produces a balance of efficiency and speed. That is my story and I am sticking to it.
Part the reason (in general) is you get 75% Pwr with WOT, which is goodness for non turbocharged Lycoming's in wear and tear, temps, and SFC (specific fuel consumption). Although Lycoming recommends 65% power as optimal long life. Having full wide OPEN throttle, the throttle plate is wide open, reducing engine "pumping losses". 75% is a happy place in the SFC range while scooting along. Of course 55% is better for lower fuel burn, so you fly higher (do not reduce throttle). There is no magic about 55%, could be 50% or 59%.
12,500 I suggest is just because it's max altitude for no O2.
However for the average RV driver, A/C weight, HP, Prop, atmospheric conditions, winds, terrain, length of the flight segment will determine best XC altitude. If you have O2 and IFR capability for flight over 12,500' or even FL180 may be a good option, but it's not within reach for all RV's due to weight and HP. That is why 8500-12500 ft rule of thumb, practical. There are diminishing returns on how high a SE normal asperated airplane can or should go, regardless of HP, wing, etc. and size of your O2 Bottle or size .
My old RV4 with O320 150HP Hartzell I'd fly in the mid teens fairly often solo. Going from Seattle to Phoenix in the winter. When a high WX system was off the CA coast flying of Sierra Nevada mountains I saw ground speeds over 210kts sometimes. Also I needed altitude for terrain. I love that trip.
However on the flip side, another trip flying from WA State to Oshkosh, summer, same 150HP RV-4, Max gross, max aft CG on a very hot day. I struggled to get to 12,500 MSL, and had toasty CHT engine temps. I went back down to 7,500'. An "average" RV can fly into the upper teens, but just because you can does not mean you should. We don't want to mislead folks.
Back in the day, I flew at FL210 to FL250 (Ted Smith unpressurized twin turbocharged Aerostar) sucking O2 from a mask for many hours. It was fun and topping weather is great. HOWEVER if the weather builds above your service ceiling (even in a jet) and you fly into icing, turbulence near your stall and/or Vne/Vmo/Mmo not fun. You can't climb and a high altitude "upset" is possible. You can get down drafts. SE planes near service ceiling need to be careful topping weather.
Walking around Oshkosh this year I did not see a lot of O2 systems or masks. (May be they were hiding it?). it may be best to stay on the deck at 25 square (if there are howling headwinds aloft). In one case I had tail winds down low and head winds aloft. Sometimes I fly 22 square 2000 ft AGL and enjoy the countryside just cuz. Obstacles and clearance is important.