The rest of the above I don’t understand. I think some words are missing, and/or puctuation?
I hope someone else understands it, it’s highly technical and not for everybody…
There is the article Dan published, I suggest that as start
Carson speed is multiplier of best L/D speed
That multiplier is said to be a constant.
The rest of the above I don’t understand. I think some words are missing, and/or puctuation?
Therein it is concluded that MPG increases over altitude
As the air is thinner, pumping losses reduce because the throttle can be more open. But there are many other factors e.g. prop efficiency varies (and in a complex way). Engine efficiency varies too, and this is a prime reason why best MPG is not obtained at best-l/d speed (at such low power settings, mechanical losses are proportionally bigger, as can be seen from the non-equal 0 intercepts on the axes here).
Pumping losses were known to be very important way back in ww2 – see here and in the book on WW2 engine development mentioned here.
Carson speed is multiplier of best L/D speed, the latter is pure geometric thingy where lift/drag angle remain the same irrespective of altitude when the power is off, in nil winds, for a giving altitude you will find that best L/D speed delivers max f(x) = max(distance) while Carson speed delivers max f(x) = max(distance*speed)
When flying with power straight and level, you are using power to “recover” altitude such it remains the sams but you still get those optimal f(x) 
in nil winds assuming as long as your engine have power to fly those said speeds while keeping altitude constant, you will find that changing altitude does not change you MPG at best L/D and does not change MPG*TAS at Carson speed
In reality, winds changes laterally & vertically, turbulent air, TAS/IAS does not follow ISA and piston engines are not designed for those speeds on hot days, plus it’s too slow !
As proxy Vld is near Vref, Carson is 1.3*Vld, so you are looking for 2*VS and maybe +15kts/-5kts depending on winds
Just found a book “Piston Airplane Cruise Performance” from Melville R. Byington Jr. that is free accessible and gives a huge amount of information:
https://commons.erau.edu/jaaer/vol4/iss1/6/
Therein it is concluded that MPG increases over altitude, see page 18 (that is page 6 of the PDF).
Although this seems naturally logical I don’t see this. So I’ll have to look for the other paper. By the way it’s Max Conrad, not Joe. Don’t know why I got that wrong before.
Efficiency has always been my primary goal, save for moments of pure madness 
, when either driving a vehicle, or flying. I followed and studied the CAFÉ reports as they were published starting in the eighties, propagated thru the EAA.
Not sure if already mentioned in the previous pages of the thread, but the original article by Carson is found here:
Fuel Efficiency of Small Aircraft
Peter wrote:
You list a turbo engine in your profile
That’s correct, but not so different at all in my case. Typically the Turbo’ed ones fly more economically at altitude. They’re designed to fly there, and have e.g. a lower compression ratio. In my case it’s a manual wastegate and the turbonormalized engine “operates” more or less like the normally aspirated, despite that I can let her inhale more air. Compression ratio etc. is exactly the same as the normally aspirated variant. That’s why I can fly low as efficient as with a non-turbo.
The RPM thing is true, but then the air is less dense at altitude, so that you need more RPM at altitude for the same efficiency against the air. I can fly 1900 RPM at 2000 ft, very efficient that way, but I can’t do that same thing at say FL100. The engine’s running a bit rough there LOP. And as I don’t know whether that’s still ok or not, I avoid a rough running engine whenever possible. I don’t know whether that’s a general rule or only true for my engine.
However, the same MPG over altitude seems to be some sort of rule. I was equally surprised when I found out that there’s no difference in MPG for non-turbo altitudes whether flying low or high. I once found a long explanation, that’s one of Carlson’s papers, and one with a Bonanza did some test flights for that.
What seems to be true, though, is that you can fly faster at altitude, but on a higher fuel flow, resulting in the same MPG. In my case, if I stay LOP, I see 150 KTAS at 2000 feet or at FL100 on the same fuel flow. The engine tends to be hotter at FL100 than at 2000 feet.
In my case, when I take the Turbo in I can do more speed, but not LOP. In principle it’s cutting down MPG a lot. I can adjust it very sensibly (just a little bit in) so that I can fly a bit more efficient than one would be without the turbo, but you arrive quickly on the edge of the red box when you want to stay on the lean side. I assume that an intercooler would help to keep the temperature low(er) and to increase efficiency, but this was not a 1970 development :-)
I don’t know enough to argue this but one factor is pumping losses which are much higher at say 3000ft / 23" MP than at FL100 and WOT.
Other second order effects exist e.g. with a lean mixture it is better to use a lower RPM, and I have measured this, just about, on some flights. It is only of the order of 2% extra. That is 2200rpm versus my normal 2400rpm. But also at a lower RPM the mechanical losses are lower – as one should expect.
I can fly LOP (I fly just a little LOP the whole time, in cruise) up to about FL160 (ISA). Above that, “best power” is needed to reach the ceiling.
You list a turbo engine in your profile, and that’s a very different thing. The TB21 gets less MPG and has a shorter range than the TB20, every time. I think ultimately one pays the price for a lower compression ratio; the SFC scales with the square root of the CR. A higher CR = free fuel
Peter wrote:
And I can confirm this – the TB20 the best MPG at around FL100-130. Wide open throttle (WOT).
I cannot, however. MPG should be more or less the same irrespective whether flying low or at FL130. Ask Joe Conrad about this. He really pushed that to any extremes you can imagine in his record breaking (and still holding) long distance flights.
What I see is that at lower altitudes it’s a hassle to fly, and there are turbulences, where at higher altitudes it gets increasingly impossible to fly LOP. That, in my case, defines the best altitude range.
There is a good article on Carson speed in a recent US AOPA magazine.
And I can confirm this – the TB20 the best MPG at around FL100-130. Wide open throttle (WOT).
Unfortunately for most of Europe you need to hold an IR to do this
