I have finally got around to reading the Embry-Riddle paper posted here by @raven.
It just reads like a repeat of the countless papers containing formulae which claim to describe principles of flight.
Obviously there are some basic rules, but are they accurate enough to be really usable in practice?
Some are obviously true; for example
2. Maximum endurance (time aloft) corresponds to minimum fuel flow (FF) and engine power output required to maintain altitude.
but this one
Maximum range CAS and AOA are constant for a given weight, independent of altitude.
is really subtle because both CAS and AOA are going to vary with lots of other things, over altitude.
And even if the airframe behaved perfectly “per the maths” you still have engine efficiency issues where the fuel flow per HP varies a lot with the power output.
I would think some of the models are pretty good. I was involved with a company that produced much of the software for commercial flight sims under contract with Redifon and I was impressed when attending a number of sessions and chatting to pilots and trainers just how accurate they were / are.
Peter wrote:
but are they accurate enough to be really usable in practice?
IMO they are accurate in so far that “secondary” effects can be ignored.
Peter wrote:
Maximum range CAS and AOA are constant for a given weight, independent of altitude.is really subtle because both CAS and AOA are going to vary with lots of other things, over altitude.
Absolutely – the key words here, though, are “maximum range”. While CAS and AOA vary with lots of things, there is just one CAS/AOA combination that will provide maximum range – and this combination is independent of altitude (which might be surprising to some).
Without having read the text yet, I’d bet there is one assumption for this statement you didn’t not quote: This maximum range CAS/AOA statement is only true at a given COG, because it does change with balance.
There really is much more to it, only those things are not relevant for a typical GA aircraft. They fly too slow to have any practical effect on operational parameters, and when the only relevant operational parameter is FF. If you read about WW2 piston aircraft, there is a whole new world opening up. Ram air effects and altitude effects are part of the design, particularly for cooling drag and engine power. Just the cowling of the FW-190-A variants is a masterpiece in engineering where ram air effects are considered. The plane gains 2-300 hp with speed (15-20%), and at alt, the thrust from the exhaust adds another 20% in addition to the thrust from the propeller. Irrelevant stuff for a GA aircraft, but all out important when you effectively are in for a race in which the loser dies, and you have a BIG engine 
One thing I can’t explain is why the cruise speed of the TB20, at a given engine setting, hardly varies with the loading.
I was involved with a company that produced much of the software for commercial flight sims under contract with Redifon and I was impressed when attending a number of sessions and chatting to pilots and trainers just how accurate they were / are.
Many years ago I visited the (as it then was) Redifon and talked to a guy who wrote some of the code. It was a vast amount of Fortran, and they were basically solving partial differential equations at a fixed frequency of something like 20Hz. Clearly far more effort goes into airliner simulation than into anything we fly.
Peter wrote:
One thing I can’t explain is why the cruise speed of the TB20, at a given engine setting, hardly varies with the loading.
Most if not all GA aircraft cruise way above the speed for minimal drag. That means that parasitic drag totally dominates induced drag. Since parasitic drag doesn’t depend on load, load has a very minor effect on total drag and thus on cruise speed.
I can’t replicate the effect much even at lower speeds.
Some other stuff is going on; perhaps elevator drag varies in the opposite direction.
“Maximum range” depends CAS/AOA depends on winds which depends on altitude 
The dependency on altitude from zero to ceiling will go away if you include the time it takes to climb & descend if you staying near that “global max range minima”, if you are not flying max range, of course the resulting range will depend on altitude if you are not flying max range (not much rocket science here)
Of course, as Malibuflyer said all assuming weight remain the same (otherwise it’s only max range AoA that matters, as max range CAS is linked to weight)
One can think of it in terms of “optimal best L/D geometry” which indeed cancels out any benefit of going up/down along the Z-axis, this applies in power off decent while fuel is used to maintain climb rate or cruise level, hence, max range is fully determined by best L/D AoA drag amount and the required fuel loss to match it (or fuel converted into altitude if you like a different unit of energy)
In other words, you can climb up to ceiling at best L/D AoA then switch engine off and glide at best L/D AoA, it will be the same outcome in terms of range as flying best L/D AoA on cruise at low power
There are second orders of course like too much rich mixture & density altitude impact on engine, it may not be able to cruise level, let alone climb, at best L/D AoA
Ibra wrote:
One can think of it in terms of “optimal best L/D geometry” which indeed cancels out any benefit of going up/down along the Z-axis
One might argue that exchanging speed for alt or vice versa is a waste of energy, as converting one form of energy to another form always includes losses.
