This website is a nice companion to Aerodynamics for Naval Aviators and Introduction to Flight by Anderson, it even has the original Carson paper.
http://www.nar-associates.com/technical-flying/technical-flying.html
RobertL18C wrote:
This website is a nice companion to Aerodynamics for Naval Aviators and Introduction to Flight by Anderson, it even has the original Carson paper.
Thanks, looked at few articles before but that website package is brilliant !
Yeah – the famous David Rogers PhD. He was one of the first “GA pilot educators” when the internet de facto started about 25 years ago. All the “techy” pilots got into that stuff.
Ibra wrote:
Thanks, looked at few articles before but that website package is brilliant !
Me too. It is indeed!
UdoR wrote:
In the end, power delivery of the engine is a matter of air mass, rather than MP.
Yes you are right:that is the key concept when ROP.
UdoR wrote:Constant MP leads to higher output power with increasing altitude, which is an effect of the decreasing temperature with altitude, where same MP puts more air mass into the cylinders.
Well this is clearly so when NA, but not so much for TN or TC: as you said what matters is air mass going into the cyls. For a given MP, all else being equal, this is driven by air temperature in the induction manifold (IAT), not OAT. NA or TC/TN at relatively low MP, you get decreasing IAT with altitude . However, at higher MP’s, the turbocharger compression provides for increased IAT with altitude (on our aircraft higher than 100C before the cooler at FL200 with -25C OAT) .
In such cases, OAT at altitude will drive how much air mass can be processed by the aircraft’s induction system and turbocharger (this is typically the limiting factor for power at high altitude high OAT on TC aircraft). However, if capable of achieving the required (high) MP, then it is manifold air temp or cylinder induction air temp (IAT) rather than OAT that will determine how much mass flows into the cylinders.
Another factor is that at high compressor pressure ratios (high altitude) the turbine also experiences a similar pressure drop increasing back pressure at cylinder exhaust, and lowering power output. This is one of the reasons why Tornado Alley Turbo quoted that charge air coolers do not necessarily drive the high power benefits quoted by aftermarket cooler manufacturers in the 80’s: the higher induction pressure loss (through the cooler) also means a higher turbine pressure loss in the exhaust (or a more closed wastegate) partially negating the increased power for the cooler induction air. What’s not negating is the beneficial cooling effects.
This backpressure effect combines with the higher compressor discharge temperature (CDT) and IAT to diminish power output at high altitude vs low altitude for the same (high) MP.
You can see such effects (not the intercooler, but the turbocharger CDT/IAT and exhaust pressure) in the Conti graphs above.
Going back to the OP, In the end, at high altitude (required for efficiency) these effects overwhelm any efficiency variations due to RPM.
UdoR wrote:
I’m quite disappointed to see that so few pilots concern about efficiency.
Oh I think quite a few are very interested in efficiency, otherwise neither the Comanche nor the whole Mooney brand would never have been as successful as they were.
POH’s do give quite a bit of information on efficiency too, if you are willing to dig deep and make your own calcs based on the figures given in the performance section. Some of the older manuals will give a wealth of power settings with GPH, TAS and (often quite optimistic) range figures. If I remember right Piper prefers graphs for this kind of stuff while others like Mooney put pages full of numbers down.
When searching for the sweet spot where range, speed and fuel flow combine for the best MPG or the best compromise if the best MPG is only achievable with undesirable power settings, these tables help quite a lot once you get used to them.
In practice, the way to go about it is to put together an excel or similar table where you can use the figures in the POH to create (more) realistic flight data and then compare those with your own airplane.
What I have found in my work with many airplanes is that often there may not be one sweet spot but several which, in the end result, are close together but sometimes quite far apart in terms of what kind of power setting you want to use.
Mooney for instance provides some sort of ultra long range cruise at 1900 RPM. What that does however is to bring your speed down to below 100 kts, which is hardly why anyone would buy a fast airplane. When analyzing MPG however, some figures are quite interesting, just to give an example. (MPG being defined as statue miles per US gallons here).
The ultra long range cruise they show is based on 1800 RPM, which yields speeds between 95 and 114 kts TAS at 2500 and 15000 ft respectively. For this regime, the best MPG is around 20 at 15000 ft with roughly 6.5 GPH consumption and19.8 at 10’000 ft @ 106 kt and 6.15 GPH .
The interesting bit here is that normal long range cruise with 2300 RPM yields 19.5 MPG at 15000 ft as well, but with 136 KTAS and 7.9 GPH fuel flow.
A cruise with Carson speed IAS yields 19.0 MPG @ 15000 ft with 150 kt, 2600 RPM and 8.9 GPH. The funny bit is, that this also corresponds to high speed cruise at that altitude.
In general, the MPG of the different cruise regimes which realistically get used are all between 18 and 20 MPG, generally at around 10’000 ft to 15000 ft. The question will of course be, will anyone for the sake of say 1 Mile per gallon more sacrifice 50 kts of TAS or even does that make any sense at all?
It should not be forgotten in the efficiency calculation that flight time also means cost even without the fuel involved. In the 100 hrs I have available between Annuals for the normal use of the airplane, Carson cruise will carry me 15’000 miles using 890 USG. Ultra long range cruise however will carry me roughly 10’000 miles using 650 USG. Turned around however, to achieve 15000 miles with ULRC would cost 975 USG and would mean significantly more flight time.
So facturing fixed costs like periodical maintenance (50/100 hrs checks) into the picture, I think we can show that the cruise which gives the best MPG does not necessarily have to be the most efficient in the sense of cost.
There is another factor in terms of MPG which often gets confused when the obvious comparison with cars comes up. What must not be forgotten in that calculation is, that cars usually need to cover a LOT more distance from origin to destination as they hardly can simply go straight as airplanes do. The increased distance can easily go up to 30% mileage. Consequently, even with better MPG, the actual consumption of the cars does not necessarily have to be better.
It is sometimes quite fun to play with those figures and find that our sometimes 60 year old airplanes can, if operated accordingly, be as efficient as a reasonably priced motorcar to use the old Top Gear moniker.
@Mooney_Driver wrote “It is sometimes quite fun to play with those figures and find that our sometimes 60 year old airplanes can, if operated accordingly, be as efficient as a reasonably priced motorcar to use the old Top Gear moniker.”
I totally agree with this sentiment, I often do this excercise when deciding how to travel to places more than 2hrs away.
I don’t know about anyone else but I am finding the debate about on the step confusing.
What I learnt as being on the step, if one puts aside boating or float plane analogies comes as a result of another debate.ie is it more efficient when reaching cruising altitude to reduce power to cruise power on levelling out, in which case the aircraft will take more time to reach cruise speed and therefore longer before the aircraft can be trimmed for cruise. Or is it better to keep climb power on at the cruise altitude until reaching cruise speed, before reducing both power and trimming for the cruise.
This argument developed into some saying that it is better to climb to 100ft or so above cruising altitude,(the step) reduce power on levelling out then dive down the 100ft to your cruising altitude, thus getting to cruising speed and cruising attitude quicker.
Please don’t ask any questions as I have never understood the answers and if you’ve got 2 oldish instructors within hearing range it nearly always causes an argument using algabreic equations which go totally over my head. As does the constant use of the Greek alphabet in any mathematical equation to do with aviation.
My rule of thumb is that Carson speed is around 15%-20% above best glide IAS, and that, like best glide, it reduces with weight. Hence the constant alpha concept (apologies for the Greek).
Now it seems either through design consensus, or the laws of aerodynamics, this equates to around 45% power; and 45% power is typically full throttle close to a practical service ceiling in a NA engine.
OTOH I subscribe to the thesis that these engines are happiest at 65% and above, and reducing power below 65% is either due to needing to build reserves on a diversion, or related to a ferry flight. Any fuel savings are not going to be repaid with engine longevity.
Indeed the optimal engine thermomechanics best longevity is not inline with optimal aerodynamic best efficiency speeds, so if you have to pick between, 60% is a good number, one needs to back test engine cost & fuel cost over 30years on same engine+airframe to tell otherwise, by then things like WTI price, local winds, altitudes, specific times of your flight would also explain you efficiency numbers far better than the Carson paper 
The efficiency of “MPG*Speed” goes high near 30% best glide and 45% power, Cason speeds are somewhere near 1.9*VS or 1.3*VBG but you need to increase it with headwind and decrease it with tailwind, and adjust for weight, otherwise it’s a worthless number….
Mooney_Driver wrote:
UdoR wrote:
I’m quite disappointed to see that so few pilots concern about efficiency.
Oh I think quite a few are very interested in efficiency
I agree…be it because of fuel costs, total operating costs, environmental or other reasons, a lot of us are interested in efficiency.
I just think that in a typical European flying environment, efficiency is much more driven by factors other than RPM as discussed above. Not least because as discussed not all the available RPM range is practical for a variety of type-specific reasons.
In my view the following factors play a bigger role than RPM in the trip efficiency, beyond mpg (ie fuel or other cost to go from A to B ) with a guess-number of resulting variability on a given flight all else being equal:
Of course they are influenced by flight rules, weather, aircraft type, loading, trip distance, tripgoals (sightseeing?), pilot-aircraft contractual relationship, etc…
A very interesting discussion , but it is diverting way beyond the OP into overall efficiency!
