That's an interesting post, Pilot DAR, but I would take you to task on two important points.
Carb heat hot = richer mixture = greater detonation margin.
That's too simplistic and takes the squabble with barrow way too far. Of the thermodynamic variables that come into play when carb heat is selected, mixture strength is but one. What actually happens is:
1. an increase in temperature of the incoming charge increases CHTs;
2. a change to the combustion event from enrichening the mixture (due to the reduced air density) reduces CHTs; and
3. a reduction in power (due both to the reduced mass flow and to the over-richness) reduces CHTs.
It's a complex interaction but allow me, too, to fall foul of massive oversimplification by hanging some numbers on these factors following selection of carb heat to full when the engine is developing, say, 85% rated BHP:
1. temperature of incoming charge air will increase by circa 100degF ... because of the complex interaction with other variables, I don't believe this will be fully reflected in increased CHTs, but a significant increase will occur;
2. mixture will enrichen by circa 15% which, assuming the cylinders were already operating rich of peak CHT, will reduce CHTs by circa 15degF;
3. power output will reduce by circa 13% (according to Lycoming), which will reduce CHT's by circa 15 degF
Simplistic? Of course, but nonetheless I would expect CHTs to
rise slightly following the application of carb heat ... although certainly not by a sufficient amount to cause detonation problems on a 4-cylinder, naturally-aspirated Lycoming or Continental. It is certainly the case that I see higher CHTs on take-off in Southern Europe compared with the UK, where differences in charge temperature could be in the order of 50degF. I think the admonition not to use carb heat at high power due to detonation risk is a hangover from the days of the big radials, where the combination of charge-temperature rise from both the supercharger and carb heat very definitely could take you into detonation territory.
But hey, there's no need to speculate on this. Would someone out there with a carburetted Lycoming or Continental, in an aeroplane fitted with a multi-cylinder engine analyser, please go out, experiment and report back!
And the other thing I must take you to task over is:
I do not operate engines lean of peak. We did not operated lean of peak when we flew pistons transatlantic.
It's not clear if you are talking there about specific transatlantic operations that you've been involved in, or are referring to the piston airliner heydays of DC-7s, Constellations, etc. If the latter, then you are simply wrong! The reason we know so much about lean of peak operation and, with certain safeguards, can undertake it quite comfortably (in the process, reducing fuel consumption and increasing cylinder life) is because literally millions of hours were accumulated operating Wright Cyclones, Pratt & Whitney Wasps, etc lean of peak. It's your choice not to operate LOP, but quite wrong to suggest that in, former times, it wasn't the norm.