AOA and Jet Engine Performance Questions

I’m trying to understand how jet engine performance is optimized at each phase of flight. Any insight or helpful references would be greatly appreciated.

Do you mean something like this for take off and landing?

could you elaborate a little more?

That’s a great reference, thank you! Impressive the time put into that. I’m actually looking for all phases of flight, trying to understand the engine setting goals for each. So looking at your link, for take-off, looking through the various aircraft types, and ignoring for the moment, flap settings and rotation speeds, the take-off power settings increase for increasing load factors. Seems natural enough. So my question for take off performance: is engine stress (decreased engine life/higher maintenance) the only factor in not going full throttle under all take off conditions? In other words, it has nothing to do with fuel used per unit of thrust (fuel economy), during take-off?

I asked the OP of the post mentioned above if it would be possible to add the same stats for taxi, cruise, climb and descend. He said he would consider it, (but already stated how much work there would go into researching that, which I can imagine).

Also, I assume that your windspeeds, elevation, flaps and trim settings will affect your fuel burn on take-off and departure.

Yeah, I’m trying to separate out airframe and engines and consider them separately. Then put the concepts back together again. I know that sounds a bit odd, but… Anyway, I think I’m pretty confident with the airframe stuff. But I seem to keep hitting roadblocks with nailing down the engine issues…

Eureka!, finally a google hit that gives another little piece of the puzzle:
(I hope the quote and reference meet guidelines):
http://www.boeing.com/commercial/aeromagazine/articles/qtr_4_08/article_05_3.html :

“From a fuel consumption perspective, a full-thrust takeoff and a full-thrust climb profile offer the most fuel economy for an unrestricted climb. However, from an airline’s cost perspective, this must be balanced with engine degradation and time between overhauls, as well as guidance from the engine manufacturer. The airline’s engineering department must perform the analysis and provide direction to flight crews to minimize overall cost of operation when using takeoff derates or assumed tempera­ture takeoffs and climbs.”

little pieces of (engine) fuel economy puzzle:
1)flap extension for TO to the bare minimum for safe operations
2)as much thrust as possible without compromising wear and tear (noise abatement too)
3)get up to flap retraction speed and retract, as fast as possible
4)climb at the maximum rate of climb to cruise altitude
fingers crossed…

Coming from an ATPL Performance perspective :

@adit As you said in your post above, the idea is to run the engines in a way that produces the best compromise between performance and engine wear.

As we all know, jet engines are most efficient at high altitude and relatively constant speed. However, something not a lot of people know is they are also most efficient at high engine speeds (around 95%), hence why those sorts of speeds are used in the cruise. The reason for this is a load of complicated performance stuff though, so I won’t go in to that.

As for your other question, there are a few factors that determine what engine power setting is used for takeoff: aircraft weight, runway length, air temperature, humidity and pressure, wind speed and direction, initial climb requirements, maintenance requirements, operator procedures… You get the point, the list goes on.

NADP

Just a quick thing on your 3rd point.
“Get up to flap retraction speed and retract as fast as possible…”

Well, sort of. But also no.

The standard departure is to climb at V2 + 10-20kts up to 1500ft AAL at which the thrust is reduced to climb thrust and the acceleration begins. However, there can be many things dictating the thrust reduction and acceleration height (the point at which you begin accelerating the aircraft from V2 + 10-20kts towards 250kts, or whatever the limit given by ATC). If not given by the aircraft charts or documents, the noise abatement procedure would typically default to something called an NADP - Noise Abatement Departure Procedure. There are two of them, NADP1 and NADP2.

NADP1 is designed to reduce notice in areas close to the airfield. This is where you climb at V2 + 10-20kts until 3000ft AAL, reducing thrust at 800ft AAL, before accelerating.
NADP2 is designed to reduce noise further away from the airfield. This is where the thrust is reduced again at 800ft AAL and the aircraft is then accelerated, at climb thrust, at that height.

I hope this all makes sense and feel free to message me with any more questions!

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Thanks so much for your detailed response. I have a few questions, if I may:

As we all know, jet engines are most efficient at high altitude and relatively constant speed. However, something not a lot of people know is they are also most efficient at high engine speeds (around 95%), hence why those sorts of speeds are used in the cruise.

I’ve seen graphs showing an apparent exponential relationship between rpm and thrust (better thrust growth at higher rpms). Does fuel have a more linear relationship to rpm rather than thrust (at lower rpm’s, less fuel is going to thrust production)?

The standard departure is to climb at V2 + 10-20kts up to 1500ft AAL at which the thrust is reduced to climb thrust and the acceleration begins

So NADP, engine stress, and ATC speed limits are the only limitations (big limitations to be sure) to higher power settings? Those aside, highest power, and highest climb rate would have given best fuel performance (in an ideal world)?
(edit to the limitations: speed safety margin for loss of an engine)

I got into this in the first place from an obsession with AOA as a possible means for maximizing certain flight goals, in particular in this case, fuel consumption economy.

So I have come to understand there is one and only one AOA at each flap setting (for a particular aircraft type), that maximizes thrust to fuel consumption (the max L/D AOA)? So, theoretically, if you could target that AOA continuously up to the altitude at which you can no longer maintain that AOA due to power settings/speed limitations, that would give an optimum fuel efficient climb and ceiling? (and ideally it would be continuous climb rather than stepped?)

So if targeting that max L/D AOA, (over whatever range of airspeeds and altitudes where you can still maintain that AOA), it gives you the best fuel range possible at whatever given altitude (even 1000msl).

If true, the summary might be, for (theoretical max fuel range)?:
1)peg max L/D AOA whenever possible (at every altitude and every speed needed for the range of flight phases)
2)get high as fast as practical due to engine fuel burn optimization issues.
3) and high for the biggest gap between GS and IAS

Of course, I’ll do my best to answer them!

For the first one, an increase in fuel flow will indeed result in an increase in thrust. As to whether this relationship is linear or not I don’t honestly know, but I would hazard a guess that (for a constant altitude and speed) it would be more of an exponential curve.

For takeoff an climbout, pretty much. Aircraft performance is often the most limiting one for thrust used on takeoff though, but the other factors you mentioned are all to be taken into account too!

That is, as I understand it, correct. During flight school you’re taught that the most efficient AoA (i.e maximum L:D ratio) is 4° and, therefore, you should aim to fly at a speed that gives this AoA during cruise if you’re looking for best fuel economy.
This is, incidentally, why aircraft usually pitch up slightly during cruise.

Not necessarily for climb. When climbing you normally want to get up as quick as you can. That is why aircraft climb at close to takeoff thrust for most of the climb. As for cruise, if you fly at the most efficient engine speed, aircraft speed and AoA then you should get your best fuel economy.

Correct.

Pretty much, yes. The higher you go, the thinner the air gets and the less fuel you need to put in to the engine so the more efficient the aircraft gets.

Almost. GS is sort of irrelevant when talking about the aircraft. True Air Speed (TAS) and Mach speed are more important at high altitude. The GS is just the TAS when combined with wind speed.

Hopefully that all makes sense.

Regarding takeoff thrust there are actually a few reasons for not doing a full power takeoff:

  • Engine life
  • Too fast acceleration, which may lead to gear or flaps over speed, or too high pitch which is uncomfortable for passengers

In cruise, it’s actually not always true that cruising at the ceiling for the given weight is always most efficient. For example, this stackexchange answer contains a table which shows that FL410 is worse that FL390 on the 787 at 420000lbs. https://aviation.stackexchange.com/questions/37164/for-a-b787-in-cruise-what-is-the-altitude-speed-and-angle-of-attack

There are also noise restrictions at a lot of aerodromes, particularly near populations. So although you might comply with a speed restriction by increasing the climb rate, only reducing thrust can help avoid noise issues.

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Thanks again. These are very helpful answers! A couple follow-up questions, if it’s ok?:

Not necessarily for climb. When climbing you normally want to get up as quick as you can. That is why aircraft climb at close to takeoff thrust for most of the climb. As for cruise, if you fly at the most efficient engine speed, aircraft speed and AoA then you should get your best fuel economy.

1)So with power set close to takeoff thrust during the climb (when cleared to do so), do you mean you would be at a higher AoA than that at max L/D (4° in your case)? In other words, it pays to have higher rate of climb at expense of the increased induced drag (induced drag being higher at AoA > 4°), for the sake of getting the engine up to best operating altitudes - a trade off advantage?

(edit note: I’m now getting somewhat different definitions for induced drag, but whatever you call it, I’m referring to the increased drag caused by AoA increasing beyond the max L/D AoA; and from graphs, it it appears to increase rather sharply from that point up to the stall)

2)The value of max L/D AoA, I assume would be aircraft dependent (aerodynamic design dependent), but again is independent of weight, altitude or speed for each particular aircraft?

Thanks! I knew I must be missing something in my list of limitations. Imagine getting all one’s ducks in a row except for the design extension speeds. Would not go down well!

I need to now read your link and understand that.

Nowadays liners have a flight director and from what I’ve seen it’s only taken into consideration by pilots after climb thrust is engaged. My simple guess is that it’s all computer calculated if not “ignored” for the climb phase.

However I assume the AOA is mostly coming from the design and not necessarily pilot or autopilot in normal operations.

I get that idea from the fact that the AOA doesn’t change much unless actively inducing pitch or speed changes.

So I looked at the table in your link. Thanks for that. I think it makes sense that the aircraft can fly higher than the most efficient altitude that the step profile is trying to capture. And from what I understand, the factors that keep you in that highlighted step region, is to be at the highest altitude you can fly at (max engine efficiency), while being able to still maintain (close enough to) AOA max L/D. I’m going to call it AOAe (most aerodynamically efficient angle of attack). As you rise above that “best economy ceiling”, to the service ceiling, you can no longer maintain AOAe. The actual AOA starts growing toward the stall limit. The service ceiling is of course below the stall limit, but with degraded AOA, so more drag requiring more thrust and therefore more fuel flow.

If I understand correctly the FMC would make primary, managing the flight around the most aerodynamically efficient AOA. There is apparently only one value for that most efficient AOA, which I was referring to as AOA max L/D, but I’ll use my shorthand again of AOAe. The thing that I had to wrap my head around, was the fact that a cleaned up aircraft has one and only one AOAe for all airspeeds, and altitudes. If you target that value for all your operations, you get best performance from the airframe. Of course it gives you more benefit at higher altitudes, but at every altitude, it’s the most efficient AOA at that altitude (even just above sea level). If not for having to share efficiency needs with the engine, then your climb would even be most efficient by pegging the AOA at AOAe. So why would you not do that in a climb? Because you might get more benefit from degrading to a more parasitic AOA (greater than AOAe), because of dividends paid to you by getting the engine up to altitude ASAP. This is the best to my current understanding anyway. So presumably the FMC has this kind of design consideration in it’s software.

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Apologies for my late reply, I’ve had a couple of busy days.

Correct, during a climb the AoA will exceed the 4° we previously discussed. This is because AoA is a factor that affects the coefficient of lift. In other words, increase the AoA and the lift produced increases.

Side note: this increase in lift will have the direct consequence of increasing (lift) induced drag.

So yes, when climbing we do indeed trade off some of that efficiency for an increased rate of climb.

As I mention above, this is indeed induced drag, or lift induced drag to give it the full name. As for that drag increasing up to the stall point… You’re correct, but we’re getting into some pretty deep principles of flight here now.

Beforehand I mentioned the coefficient of lift, aka CL. This is a number that varies based on a number of factors (AoA, wing area, camber, aspect ratio, wing shape etc). For a symmetrical wing, CL has a value of 0 at 0° AoA. For a cambered wing, the value of CL is positive at 0° AoA. Assuming all other factors stay constant, CL will increase if AoA is increase up until the stall point. This is usually around 16° AoA (again, this number does vary slightly), which is called the critical AoA or ‘Alpha Crit.’ as AoA is usually represented by the alpha symbol.
The relationship between AoA and CL is actually pretty linear, but can vary with aspect ratio and wing sweep, and it’s typically shown on a CL Alpha curve (googling that phrase will bring up an image of what I’m referring to).

So yes, the value of Max L/D ratio will vary from type to type, but the number won’t move far away from the number I originally gave. That said, it’s worth noting that the max L/D ratio coincides with the point of minimum drag, the point at which the induced drag and parasite drag curves intersect on a total drag graph. In other words, the most “efficient” way to fly is at the pint of minimum drag. Pretty logical, right?

That said, airliners actually very rarely fly at that point. They almost always fly faster. But that’s another different PoF lesson altogether!

I really hope this all makes sense, as I said it’s been a busy couple of days for me and I’m pretty tired at the moment so do let me know if you would like me to clarify anything at all!

Cheers!

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Thanks so much for your answers. I fully appreciate and respect your time priorities! Brilliant answers btw! I’ll give a bit more reply, hopefully before long…

Please get good rest! And thanks again. A further question I have is below. But please don’t be in a hurry to answer, and only do so when and if able.

One point that’s been bugging me is the difference between what I’ll call AOAe (best endurance) and AOAr (best range). It does seem very logical, as you said, that AOAe occurs at the bottom of the valley of the total drag curve: Lowest drag at a given speed = lowest fuel consumption to maintain that speed.

So fuel consumption is minimized at AOAe, which means your fuel load lasts longer, in time - maximizing duration.

But of course it doesn’t address what speed does for you in that duration. So I understand you need to target maximizing speed/fuel flow, which, doing the math, moves you up the drag curve (to the MSR point?). So, in a sense, a bit of extra drag effectively pays for greater distance (for a given fuel load)

But (also from recent reading), due to the “flatness of the valley” of the drag curve, and other benefits achieved, it’s standard practice to move just touch further up out of the valley, to 99% of MSR (maximum specific range), which is designated as LCR (long range cruise).

So my question would be: Just to verify, the 4° discussed earlier is for endurance AOAe (max L/D AOA)? If so, what might be the max range AOA? I’m trying to get a rule of thumb sense for the AOAr number. And also would the difference between the MSR and LCR AOA be splitting hairs, from an IF user perspective?