A Challenging Endurance Problem

[Wind_Tunnel]

Suppose I'm flying a Boeing 777-200ER (Trent 892), and am already at 500KTAS and 35,000ft. I weigh 217,800kg, of which 43,800kg is fuel.


Suppose my one and only goal is to stay in the air as long as possible. My only constraint: I must select a single speed (as fast or slow as I please) and altitude (as high or low as I please), head to it ASAP, and stay with it until flameout.


At what speed (in KTAS) and altitude (in ft) should I fly, and why?


Prize goes to whoever not only provides the answer, but PROVES how all OTHER combinations of speed & altitude MUST burn more fuel per hour.


Huge thanks to whoever tries to tackle this.

[megan]

All the information you need to work it out. :E

http://www.dept.aoe.vt.edu/~lutze/AOE3104/range&endurance.pdf

[Andrewgr2]

The objective is to stay airborne for as long as possible at a constant ALT and KTAS.
This will be achieved by picking the speed and altitude that results in the lowest average fuel flow.
As fuel is burnt off, an ever lower fuel flow will maintain the set ALT and KTAS.
So the problem is surely to find the ALT and KTAS with the lowest fuel flow at which the plane can just remain airborne at its initial weight?

Problem is complicated slightly by fuel used to get to the initial setting and glide time after fuel exhaustion, but I would have thought these considerations wouldn't significantly change the answer.

[zlin77]

Try entering cost index "0" in the FMC, then fly at Optimum Altitude, each aircraft will be a little different due to performance degradation..

[TyroPicard]

zlin
That will give max range, not endurance.

wind tunnel
Given your constraint of a single speed... Too difficult, because optimum endurance speed reduces as the a/c weight reduces due to fuel burn. Simple pilots don't have the tables to work it out.

[zlin77]

"Google' Boeing Fuel Conservation Strategies, Cost Index explained or email FlightOps.Engineering@ boeing.com they should be able to give you an answer..

[laardvark]

calculate optimum speed / alt at 50% current fuel weight ?

[Andrewgr2]

@laardvaark Sounds like a reasonable starting point but would the aircraft fly at that speed / alt and the current fuel weight?

[laardvark]

not sure but if approximated would still represent the optimum .

[Andrewgr2]

So, to get back to the question -

What alts / speeds would give minimum fuel flow at:
starting weight / 50% of starting fuel / nearly 0 fuel? If they are similar - not much problem. If very different, we have to think more deeply.

[hawk37]

Clearly, you would need detailed performance tables for the aircraft in order to answer WindTunnel's question. For starters, is there a holding table giving fuel flow at various altitudes based on weight of aircraft?

Secondly, is this table at the minimum fuel flow necessary to sustain flight at that altitude? If the answer is yes, then you have the solution to WindTunnel's question.

The general solution is for the aircraft to be nearly at its maximum altitude. This is because the engines would be required to operate at high power settings where the thrust produced per lb of fuel consumed will be greater than that at low altitudes and low power settings. Holding tables often demonstrate this, with lower fuel flow's at the higher altitudes

[AtoBsafely]

General thoughts:

Max endurance is a holding problem, so fly at optimum holding altitude and speed. To satisfy the constraint of of a single speed and altitude for the rest of the flight, you could use an average weight for the rest of the flight. However, fuel flow will be higher at the initial weight, so I would bias toward that. So optimum holding at 2/3 fuel of the initial condition is probably good.

Finally, I suspect for a B777 single-engine holding is a lower fuel flow than holding with both engines operating (one engine provides sufficient thrust while operating at a more efficient RPM).

I would look at optimum SE holding at 200 or 205T. Probably the altitude is in the high teens/low 20s. If you need to take the descent into account, use a SE descent at the hold speed.

[Andrewgr2]

It seems likely that any published figures would be for holding speeds safely above a minimum fuel flow which, I would expect to correspond to a speed not too far above the stall...

[FE Hoppy]

I like AtoBsafely's thinking.

Without any data to reference my instinct would be to shut down an engine and drift down on one at current OEI dftftdown speed to current OEI ceiling and stick with that speed and alt. reducing thrust as weight reduced.

To be honest the problem isn't worth any more thought than that as the constraints of single alt and speed make it nothing more than a theoretical Q with no practical application.

[G0ULI]

Nothing to do with MH370? :rolleyes:

The question, as posed, has some mutually incompatible parameters. As fuel burns off, the aircraft will tend to want to climb higher, reducing drag and increasing ground speed. Constraining the aircraft to a single speed and altitude will not result in maximum endurance in either time or distance.

[AdamFrisch]

Like with any aircraft - the max endurance is had at Vbg - best glide. If such is not published, it's pretty close to Vy, normally. I don't know how this pertains to jets, but the fundamentals are the same. And what else is that max endurance is independent of altitude - you get no benefit for flying high, at least not with pistons. I would assume the same would be true for turbines as they're both aspirated.

[Andrewgr2]

I think most of the points necessary to solve the Ops question have now been made:

Gouli - I was assuming that the intention was to set KTAS and ALT and then (for whatever reason :rolleyes:) leave the setting alone whilst the aircraft flew to flameout. The fact that this would not achieve max endurance was not relevant to the OP's specification and, so far as I can see, does not make the original question invalid.

AdamFrisch - Has raised the important point that what we need to do is minimise drag in order to get max endurance and that this is achieved at Vbg or Vy. This will vary with weight but if,as AtoBsafely has suggested, we assume 2/3 of the original fuel, we won't be far off.

AtoBSafely has raised the point that we would be more efficient operating on one engine at a higher power than two engines at lower power. Would the additional drag caused by asymmetric flight outweigh the advantage and would the on-board systems feed all the fuel to the one running engine without further intervention?

AdamFrisch has also suggested that endurance is independent of altitude. Instinctively this sounds right - maybe someone can comment on whether fuel flow varies for a given KTAS (approx Vy) at different altitudes.

So the question may boil down to - what is the fuel burn, independent of altitude, on a single engine, to fly at Vbg (or Vy)at approx 2/3 of the original fuel load? Given that we start with 43,800 kg of fuel, how long will this last?

[Linktrained]

AtoBsafely FEHoppy


Look up
Linktrained PPrune "Fuel not used"


Sorry not able to give a better reference.


The aircraft was a twin engined biplane ( ! ) and with own my lack of experience, I was reluctant to shut down my Port engine. I was required to fly at 3000 ft for the task, which I did.
Before it got dark, I had not been able to see that the Port exhaust was glowing (or not !). So the first hour was flown using both engines.
After returning to Liverpool The G/Es wanted to know why I had only refuelled one side. ( I hadn't !)
No performance information was available to me, anyway !

[Kefuddle]

Taking this as an academic question, I wouldn't know where to begin without knowing such specifics such as the drag values and fuel vs thrust.

From a practical perspective, one simply reduces thrust until minimum fuel burn is achieved. Given that the drag curve on a transport jet with a clean wing tends to be very flat at the bottom, there probably is negligible difference for a relatively wide range of speeds, but flaps up min maneouvering speed would probably be the best start point. If the situation is particularly dire, reduce below min manoeuvring speed if the fuel burn is lower.

Also, probably best to disconnect the A/T too, to prevent unnecessary thus lever movement.

[hawk37]

AdamFrisch - Has raised the important point that what we need to do is minimise drag in order to get max endurance and that this is achieved at Vbg or Vy. This will vary with weight but if,as AtoBsafely has suggested, we assume 2/3 of the original fuel, we won't be far off.

AtoBSafely has raised the point that we would be more efficient operating on one engine at a higher power than two engines at lower power. Would the additional drag caused by asymmetric flight outweigh the advantage and would the on-board systems feed all the fuel to the one running engine without further intervention?

AdamFrisch has also suggested that endurance is independent of altitude. Instinctively this sounds right - maybe someone can comment on whether fuel flow varies for a given KTAS (approx Vy) at different altitudes.

So the question may boil down to - what is the fuel burn, independent of altitude, on a single engine, to fly at Vbg (or Vy)at approx 2/3 of the original fuel load? Given that we start with 43,800 kg of fuel, how long will this last?

Gentlemen;
1. Re "AdamFrisch". Max endurance will not necessarily be at least drag for a 777. Max endurance will be at minimum fuel flow, and minimum fuel flow will be a function of not only drag, but engine thrust per pound of fuel consumed.

2. Re operating on one engine vice 2; it may be possible at low altitudes for a jet to have more endurance (less fuel flow on one than two), but I have not seen any numbers to suggest that this can be true at higher altitudes

3. max endurance (time) is certainly not independent of altitude. As I said earlier, the thrust specific fuel consumption is much higher at lower power settings than higher ones, hence higher power settings will give more thrust per pound of fuel burned. Caveat, I use the term "high power settings" to indicate those not far below maximum N1.

[FE Hoppy]

Hawk,
my reasoning was that we have to chose a single speed and altitude. Given that we are probably above OEI ceiling but below AEO ceiling we are already too low for optimum 2 eng endurance so we either climb now or start throttling back both. If we chose the single eng ALT and speed we get the bonus of height in hand. That gets us ahead of the game as we drift down with one at MCT. Then we only misuse on engine as we throttle back.

[hawk37]

Yes FE Hoppy, to get max endurance as the OP requested, it does seem best to be at single engine and almost a high as possible.

[AdamFrisch]

It is a known fact that max range (and I know this is difference from max endurance, but not by much) is achieved independent of altitude, as per Carson. Because L/D ratio increases with altitude. There is no benefit by going high, especially when you also have to account for the fuel to get up there.

Therefore, and this is an educated guess, I'm pretty certain that a jet will have no endurance benefit by going to higher altitudes. Take off, level off at lowest obstacle clearance altitude and pull back to max endurance (which will be lower than Vbg).

[Andrewgr2]

OK465: But the OP also said:
my one and only goal is to stay in the air as long as possible
so although your neat solution meets the constraints, it doesn't meet the goal. I think the goal has to be met within the constraints!

Hawk: I'm struggling a bit with the idea that min drag may not be the optimum speed for maximum endurance. Min Drag = Min Thrust. Assuming constant altitude, are there situations where a jet engine can produce more thrust whilst burning fuel at a lower rate? It's only the absolute rate at which fuel is consumed that is important here, not the efficiency with which it is consumed.

[FE Hoppy]

@AdamFrisch
It is a known fact that max range (and I know this is difference from max endurance, but not by much) is achieved independent of altitude,

what?

http://www.pprune.org/tech-log/399975-some-doubts-ace-technical-pilot-interview.html#post5416515

[framer]

AdamF,Like with any aircraft - the max endurance is had at Vbg - best glide.
Why do you think that all aircraft are the same AdamF?
The airframes obey the same laws but the engines are different animals. The minimum rate of fuel flow for a 777 will occur at a speed slower than min drag.

[Machdiamond]

The missing bit of information in this equation is the nature of the prize.

[hawk37]

Andrewgr2.

When I said max endurance will not be at minimum drag speed, I was primarily meaning that the minimum drag would be at low altitude, at the speed for L/D max. If one believes that thrust vs fuel flow is flat in at this speed, then minimum drag will be max endurance speed. However, the thrust to fuel flow curve depends on the engine, and for those I've seen, at low altitude, at higher speeds the fuel flow for the same thrust is higher. Hence, in this case, the max endurance speed will be slightly lower than the minimum drag speed.
Now let's add some altitude to the flying aircraft. With that comes extra drag due to compressibility. Hence, the minimum drag at that higher altitude is more than the minimum drag at the lower altitudes. A natural conclusion could be that the fuel flow would thus be lower at low altitude than at high altitude, for max endurance. This conclusion is normally wrong. If you look at holding charts for aircraft with jet engines, you will see that the fuel flow usually decreases with altitude. Now I know that holding speed is not necessarily max endurance speed, but it is normally close enough to demonstrate that higher is slightly better for max endurance.
What is the reason for that you ask? The reason is that when holding at low altitudes the jet engine is at a relatively low power setting, at low fuel efficiency, and this means less pounds of thrust produced for a given fuel flow than at the higher power settings, and higher fuel efficiency available when at the higher altitudes for a high level hold. So, although minimum drag is higher at higher altitudes, the lower specific fuel consumption of a jet engine at higher rotational speeds has a more profound effect on the fuel flow, and hence the fuel flow is slightly lower at higher altitudes.

Now shut down an engine and compare the fuel efficiencies and endurance.....that's would need further analysis...

I agree with FE Hoppy, of course maximum range increases with altitude.

Hope that helps.

[AdamFrisch]

I don't know enough about turbines, so I will happily defer that there are added benefits by going higher for these propulsive systems.

But.

Here's a specific reference saying that endurance is independent of altitude even for jets. Only max range benefits from higher altitudes as TAS goes up. So, I was half right since we were talking about endurance initially. My mistake was that I though they both were independent of altitude.

Aircraft Performance - Maido Saarlas - Google Books (http://books.google.com/books?id=Nl8VLz_oQAUC&pg=PA143&lpg=PA143&dq=max+endurance+independent+of+altitude&source=bl&ots=xKmM-tVMvp&sig=THasVLKVKd5MW9i3h5-12AUAUd4&hl=en&sa=X&ei=dz5EVJ6XKq2rjAL024CABQ&ved=0CC0Q6AEwAw#v=onepage&q=max%20endurance%20independent%20of%20altitude&f=false)

[megan]

Here's a specific reference saying that endurance is independent of altitude even for jetsAdam, I'm afraid he is incorrect as he has not taken into account the efficiency of turbine engines with respect to altitude. The higher the altitude the more efficient they are in terms of fuel burnt for the thrust produced. Higher means colder air for consumption, and the rotor/s are operating at higher RPM, both elements increasing efficiency. Theoretically a jet will have its greatest endurance at or near the tropopause. (As taught by the USN and USAF)

What is taught by the RAF and RAAFPrinciples

1. Broadly, since fuel flow is proportional to thrust, fuel flow is least when thrust is least; therefore maximum level flight endurance is obtained when the aircraft is flying at the IAS for minimum drag (VIMD), because in level flight thrust is equal to drag.

2. Maximum endurance is obtained at an altitude which is governed by engine considerations. Although for a given set of conditions the IAS for minimum drag remains virtually constant at all altitudes, the engine efficiency varies with altitude and is lowest at the lowest altitudes where rpm must be severely reduced to provide the low thrust required.

3. To obtain the required amount of thrust most economically, the engine must be run at maximum continuous rpm. Therefore maximum endurance is obtained by flying at such an altitude that, with the engine(s) running at or near optimum cruising rpm, just enough thrust is provided to realize the speed for minimum drag, or MCRIT, whichever is the lower. Above the optimum altitude little, if any, additional benefit is obtained, and in some cases there may be a slight reduction because burner efficiency decreases at or about the highest altitude at which level flight is possible at VIMD. In general, optimum endurance is obtained by remaining between 20,000 ft and the tropopause at the recommended IAS and appropriate rpm. The greater the power/weight ratio of the aircraft, the greater will be the optimum height. With aircraft having high power/weight ratios, maximum endurance is obtained at the tropopause.

4. Altitude should only be changed to that for maximum endurance if the aircraft is above or near the endurance ceiling, otherwise if the aircraft is climbed from a much lower altitude, a considerably higher fuel flow will be required on the climb thereby reducing overall endurance.

5. On engines having variable swirl vanes, the consumption increases markedly if the rpm are so low that the swirl vanes are closed. If the altitude is low enough to cause the swirl vanes to close at the rpm required for VIMD, the aircraft should either be climbed to the lowest altitude at which VIMD can be obtained with the swirl vanes open, or the rpm increased to the point at which the vanes open, accepting the higher IAS.
Effect of Weight

6. Drag and thrust at the optimum IAS are functions of the all-up weight; the lower the weight the lower the thrust and fuel flow. Endurance varies inversely as the weight and not as the square root of the weight as in range flying because in pure endurance flying the TAS has no importance.
Effect of Temperature

7. In general, the lower the ambient air temperature, the higher the endurance, due to increased thermal efficiency, and vice versa. However, the effect is not marked unless the temperature differs considerably from the standard temperature for the altitude. In any case, the captain can do nothing but accept the difference, since any set of circumstances requiring flying for endurance usually ties the aircraft to a particular area and height band.

Twin and Multi-Engine Aircraft

8. When flying for endurance in twin or multi-engine aircraft at medium and low altitude, endurance can be improved by shutting down one or more engines. In this way the live engine(s) can be run at rpm closer to the optimum for the thrust required to fly at VIMD, thus improving GFC. Provided that the correct number of engines are used for the height, altitude has virtually no effect on the endurance achieved.
Use of the Fuel Flowmeter

9. The fuel flowmeter is a useful aid when flying for endurance. If the endurance speed is unknown, the throttle(s) should be set at the rpm which give the lowest indicated rate of fuel flow in level flight for the particular altitude.

10. Whenever reporting aircraft endurance, the time for which the aircraft can remain airborne should be given. It is confusing and dangerous to report endurance in terms of amount of fuel remaining because of the possibility of mis-interpretation.
Conclusions

11. Maximum endurance is achieved by flying at an altitude where optimum rpm give the minimum drag speed. It will rarely pay to climb to a higher altitude unless the commencing altitude is very low; in any event, the instruction or need to fly for endurance may preclude this. At the lower altitudes, maximum endurance may be obtained either by flaming-out engines to use optimum rpm on the remainder, or by using near-optimum rpm to give VIMD. It should be remembered that:

a. The importance of flying at VIMD outweighs engine considerations, always assuming that an engine, or engines, will be stopped in the low level case.

b. At lower altitudes there will be a slight decrease in endurance due to the higher ambient temperature reducing engine thermal efficiency.

[hawk37]

Adam;

"endurance is independent of altitude even for jets" only applies if you consider two things:

1. there is no additional drag on the aircraft due to compressibility, and

2. the fuel required to produce a certain amount of thrust is independent of the aircraft's speed.

For simplicity, many aerodynamics texts make these assumptions.

[AtoBsafely]

Linktrained,

Just to be clear, shutting down an engine is being suggested in this hypothetical problem only. Not recommended for normal operations.

Megan,

Thanks for the reference. I was thinking of an older generation engine, and having reviewed data for a new engine I see that best holding is up high. So I revise my guess to fly at SE cruise ceiling and descend in a drift down.

[megan]

Just to be clear, shutting down an engine is being suggested in this hypothetical problem only. Not recommended for normal operations.Not hypothetical in the military, regularly used in the P-3 community, and sob, the Nimrod when it was with us. Not an airline though I would hope, though it might give a airline beancounter somewhere an idea if s/he hears of the procedure.

[Machdiamond]

Yes airlines too. Shutting down an engine in cruise was standard operating procedure with Aeroflot in the early 90's - at least that was my experience as a SLF back then. Personally I see nothing wrong with it.

AdamFrisch is correct with his reference that endurance (not range) is independent from altitude. These curves are normally not published in AFMs unless you operate a military patrol aircraft. When you look at these curves, best endurance is surprisingly flat between some low altitude like 10000ft right up to tropopause.

[BOAC]

From 'megan' and RAF the engine must be run at maximum continuous rpm - my understanding is that that related to 'standard' axial flow engines and now-a-days it should read 'at design rpm'.

Shutting down a donk was SOP on the Lightning if short of fuel (weren't we always......:)) for that very reason, plus there was very little trim drag associated with the event unlike a 'normal' twin.

[keith williams]

GOING BACK TO BASICS
The aircraft initially has a certain quantity of stored usable energy made up of:

a. Chemical energy by virtue of its fuel load.
b. Potential energy by virtue of its height.
c. Kinetic energy by virtue of its speed.

To achieve maximum endurable we must expend the stored energy as slowly as possible.

MINIMIZING CHEMICAL ENERGY EXPENDITURE RATE
The rate of expenditure of chemical energy is essentially:

Fuel consumption rate = Thrust required x Specific Fuel Consumption.

(SFC is the mass of fuel that is required per hour to generate each unit of thrust).

Looking at the above equation we can see that to minimize the fuel consumption rate a good starting point would be to minimize the thrust required and to minimize the SFC.

Thrust required is equal to drag, so our ideal speed should be VMD. The drag at any given EAS does not vary significantly with altitude until compressibility effects kick in, so provided we do not go too high, the altitude should not affect the drag, thrust required, or fuel consumption.

SFC is more problematic because it varies with a number of factors including air temperature, air pressure and RPM. The most significant of these factors is RPM.
At very low RPM the majority of the fuel energy is used simply in overcoming friction and keeping the engine running, so little thrust is produced for each unit of fuel burned. This means that the SFC is very high at low RPM. As RPM increases, the basic running costs (in terms of energy) represent a decreasing proportion of the total fuel flow. The aerodynamic and thermal processes also become more efficient. This means that the SFC gradually decrease as RPM increases. Most text books quote a between 90% to 95% RPM as the RPM range within which SFC is lowest. The precise value of the optimum RPM will of course vary from engine to engine, but the figure of 90% to 95% is a reasonable starting point for the purposes of this thread.

Combining the above factors shows that for our maximum endurance we need to fly at VMD with our engines (or engine) running at 90% to 95% RPM.

At low altitude the thrust of both engines running at 90% to 95% RPM will be too great to balance the drag at VMD. Increasing drag using spoilers or flaps would simply waste fuel so this is not an option. But the thrust at any given RPM decreases as altitude increases, so if we climb to suitably high altitude we will achieve the required balance between drag at VMD and thrust at 90% to 95% RPM. But even at this altitude, the fuel flow with both engines running at 90% to 95% RPM will be far greater than that with one engine shut down and the other running at 90% to 95%. So a better solution would be to fly at the altitude where single engine thrust at 90% to 95% RPM is balances the drag at VMD.


MINIMIZING POTENTIAL ENERGY AND KINETIC ENERGY EXPENDITURE RATE
The power required is the rate at which an aircraft expends energy. So to minimize the expenditure rate of stored potential end kinetic energy during the descent to cruise altitude, the best option would be to shut down both engines and fly at VMP. So ideally we would descend with all engine out at VMP then star one engine and run it up to 90%-95% RPM as we level off at cruise altitude at VMD.

Unfortunately this contravenes the requirements to “fly at a single speed” and to “reach the cruise altitude asap”. Reaching the cruise altitude in minimum time would require a maximum speed descent, but then maintaining max sped in the cruise would not achieve maximum endurance.

ADJUSTING FOR REAL-WORLD FACTORS
All of the above does not of course take into account the actual performance characteristics of the specified aircraft and engines. To do this we would need to examine the appropriate data and adjust our airspeed, RPM and altitude accordingly.

[FE Hoppy]

Well I don't have 777 documents but for the E190 the figures look something like this:

Speed - 210kt chosen because: a) I have numbers for this speed at all weights. b) Its just behind the drag curve at heavy weights and plenty ahead at light weights (probably the best compromise for fixed speed)

Driftdown not calculated.

Start weight 50T End weight 30T (only the lineage version can carry this amount of fuel)

All Engines operating
FL 300 - 869 minutes
FL 250 - 872 Minutes
FL 150 - 850 minutes

One Engine shutdown
FL 150 - 868 Minutes

These values assume Air conditioning AND Anti-Ice ON. (only tables with fixed speed) So the engine bleed will have them running at higher RPM which probably skews the results a little.

Not sure why I spent an hour on this but there you go.

[Linktrained]

AtoBsafely


I had explained in that quote:
"I throttled back the Port engine until the exhaust was dark enough although still giving some power..."
Of course this would be at an inferior specific consumption of petrol on the Port engine. The Starboard remained at its normal cruising power, whatever that may have been ! (My Type Rating has lapsed, now.)
I had remained close to Blackpool aerodrome, which I see has just closed after over a century of use.


I spent most of my time on 4 engines with a F/E, so operating with one shut down was a part of life, sometimes.

[Intruder]

I'd go to current Max Altitude and speed at the top of the yellow arc (min safe speed). Overall, for the rest of the flight, that would probably be closest to max endurance altitude and speed.

[megan]

my understanding is that that related to 'standard' axial flow engines and now-a-days it should read 'at design rpm'I don't know BOAC, not having the necessary experience, but as a 737 driver, how close to max continuous was your cruise RPM? The heavy drivers have an answer for their types? Do you in fact ever get close to max continuous (besides take off)?

[bubbers44]

I needed to hold in a B727 one day for morning fog so checked the charts and max endurance for holding was at FL250 so descended from FL350 to FL250 to extend holding time. If the alternate would have required a climb, of course, that would have negated the fuel savings. Higher isn't always better.

[BOAC]

how close to max continuous was your cruise RPM? - I'll have to pass on that one. Ball park stuff - Normal cruise ??85-8'ish??, MCT in the 90's, but remembering MCT was an EGT limit and as I said, your reference was for axial flow engines I believe. I suspect that running at MCT in a 737 for 'endurance' would shorten your time.

[deefer dog]

Megan, re your post #2. The link includes an unfortunate error. The diagram on page 19 illustrates the reverse of what is true in respect of speed to fly for max range in conditions of a tailwind.

It looks like a labelling error, but read quickly could easily mislead. (Text is correct though).

Despite that extremely informative.

[misd-agin]

777 AOA doesn't have any indices, like L/D, on it.


It has fixed marks at every 5 units. There is no guidance given on what units produce L/D, endurance, etc.


Cruise is typically in the mid to upper 2.x's. Indicates in even decimals - 2.2, 2.4, etc.


Stall margin indicator is approx. 6-7 units at cruise.
At 10,000' it's closer to approx. 10 units.




737 is very similar but cruise is typically 2.8 -3.0 and the stall margin indicator is closer to the 5 unit mark, or approx. 6 units.

[misd-agin]

I'm not sure if this PROVES your question -

Boeing 777 performance manuals -

weight at start of problem - 480,000 lbs.
fuel on board 96,000 lbs (nearest 1,000)
avg weight during problem - 432,000 lbs
weight at the end of the problem - 384,000 lbs.


Best holding altitude (minimum fuel burn) -
480,000 FL290
432,000 FL310
384,000 FL310

FL310 is the answer




Speed? In the aircraft I'd adjust the ZFW to generate an a/c gross weight of 435,000 lbs and fly the FMC generated holding speed (Vref +100 minimum).

Since we don't have an FMC available I'd use -

.64/234KIAS/381KTAS (*)


480,000 would be Vref +93
432,000 would be Vref +100
384,000 would be Vref +108

* - speeds estimated from charts and not calculated

[misd-agin]

If you choose the option of shutting an engine down the results are -


221 KIAS (approx. 265 KTAS)


10,000'


8% greater endurance vs. two engine holding.


480,000 Vref+80
432,000 Vref+87
384,000 Vref+95

[misd-agin]

L/D from the FMC? Not that I'm aware of.


Climb page at low altitude provides best angle speed. That would be close.

[Wind_Tunnel]

Thanks, all. Sorry for the delayed "judging". I owe beverages to all who took the time to work this through - especially those who saw through my clever disguise, and took this to be MH370-related.

Part B of the problem is simple: can you relate your answer to the performance limit given in Figure 3, p.5 of the ATSB's June 26 report: "MH370 - Definition of Underwater Search Areas (http://www.atsb.gov.au/mh370.aspx#)"?

Background: the south-eastern border of regions S1/S2/S3 is confirmed to be the ATSB's original Inmarsat arc-constrained performance limit. This limit is defined as the line connecting the fuel exhaustion points of a series of constant speed paths, each beginning at the NW tip of Sumatra at roughly 1836 UTC, and each passing through the Inmarsat arcs at their appointed time (but otherwise as straight as possible). Maximum endurance - according to the ATSB, anyway - is thus achieved at the speed corresponding to the path which overflies the final Inmarsat arc by the greatest proportion of its total length. This is almost - but not quite (must adjust for speed differentials) the point at which region S1/S2/S3 is at its fattest, as measured in the direction of the generating flight paths.

(I have back-solved for the maximum endurance speed according to this method: it is roughly 430KTAS. I just hoped someone could corroborate and/or explain it. Does this put hawk37 in the lead?...or is the ATSB out to lunch?)

[AdamFrisch]

FEHoppy wrote:

Start weight 50T End weight 30T (only the lineage version can carry this amount of fuel)

All Engines operating
FL 300 - 869 minutes
FL 250 - 872 Minutes
FL 150 - 850 minutes

One Engine shutdown
FL 150 - 868 Minutes

These numbers corroborate my initial statement that max endurance is independent of altitude.

[WeeWinkyWilly]

The original premise:
"I must select a single speed (as fast or slow as I please) and altitude (as high or low as I please), head to it ASAP, and stay with it until flameout." I'll venture just a similar hypothetical in the same vein - but with some vital differences peculiar to aircraft type. Disregarding cost index and fixed altitudes and speeds, can we look at a slightly different set of impertinent theoretical parameters?

In this scenario, my F/O has passed out after suddenly projectile vomiting. He's incapacitated and I'm starting to feel quite queasy myself. I'm not thinking straight and instantly find myself wondering whether it's hypoxia so I sweep my quick-donning mask on. I'm not ex-military and I've never done a hyperbaric or hypobaric chamber run, so I have no real idea what hypoxia is like at the onset. I'm feeling no better, my head is swimming and I'm losing focus so I decide to descend and so I disconnect the autopilot and lower the nose. Shortly thereafter, just before passing out, I suddenly realize that we both ate at the same mukkin cart outside Fatties just before heading to our beds last evening. We have a 772F freighter now not on autopilot and left to its own devices. The flight deck door is locked.... and access is not available.... not that there's anyone aft who can access the cockpit or likely to want or need to.

So having dispensed with its pilots (sorta like Arthur C. Clarke's computer HAL in "2001: A Space Odyssey" - but not in any extra-terrestrial context), what would my aerospaceship 772F now get up to? Once "left to its own devices", i.e. what exactly are those devices capable of?

Unlike an Airbus (an A320 like MS804 say), without its normal FBW system's protections, it won't enter a descending and tightening spiral . It has a completely different FBW system called the AFCS (an "Active' Flight Control System). Rather than different modes of degradation such as alternate 1 and 2 etc, Boeing's FBW design has quadruple redundancies and sports a multiplicity of fallback power sources and fault-tolerant workarounds - and it's not easily subjected to any degraded "laws". Its proclivities are to keep on aviating no matter what. Unlike the Airbus philosophy, my 772 won't disallow a pilot-selected overbank - but at anything above a pilot-selected 30 degs angle-of-bank, it will disproportionately increase the yoke's roll axis feedback in order to remind me that I shouldn't be unnecessarily trying to aerobat an airliner. But if it isn't a pilot roll input, my 772's FBW will "actively" impose a restorative rolling moment back towards wings-level. In fact it's so good at this inherently "active" sub-routine that it can pick up a gust-induced "dropped" wing of a mere 5 degrees AoB much faster than the speed of vomit.... and promptly get us back on an even keel. So even if my unpiloted 772 should enter some nasty ITCZ induced turbulence and get a little "upset", as soon as it exits it will phugoid a little and quickly resume wings level flight - albeit upon a new heading. And it can keep on doing this all day (and night). But, believe it or not, I'm blithely and blissfully unaware of this 772's model-specific peculiar pecadillo, as I've rarely hand-flown this noble beast - and certainly never broken the law and done it up there at height, where RVSM rules the roost. It's not in any simulator syllabus and I've never read it anywhere. But the Boeing test pilots know all about it and it's not for publication. What operator needs its pilots to go prove or disprove it? It's just a natural and little known adjunct to the Boeing FBW design philosophy. Keep the bank vector somewhere near vertical and the crashworthiness is never tested.

So there I am, firmly ensconced in the messy subliminal soporifics of regurgitated exotic Asian food fanciers (and even though erupting unconsciously at both ends), it matters not a whit - my trusty steed is "taking care of business". The Man of La Mancha and his rusty sidekick Sancho Panza are both out of the picture and quite non-interventionist - however Don Quixote's trusty steed Rocinante knows what to do. It's in his genes.

But back to the postulated conundrum. Once spat out on a heading that's going to take my 772F southbound and clear of the ITCZ, what's the effect of a static cargo and trim-state as fuel burns off? I'll help you out with this. The 772 will gradually climb as fuel burns off. If its AFCS is always going to oppose any bank angle's lift vector that's other than vertical and it's "a climber" due to fuel burn-off, why should it do other than "proceed" on course (whatever that course might happen to be)? In fact why should it meander more than 3 to 5 degrees left or right of its final spat-out recovery heading in ever-smoothening upper air? What's its anmpp (air nautical miles per pound of fuel or aka specific air range) going to be? I'll help you out again here. Eventually the 772F will be up at around FL440 and its range will be optimized..... as good as it's ever going to get and around 103% of a fixed FL350 LRC cruise... and 105% of a stepped climb profile.

The only question remaining is Rocinante's conduct and technical decorum at:

a. first flame-out

b. second flame-out

c. APU start-up

d. APU flame-out (i.e. what can the AFCS now achieve RAT-wise?). i.e. Rather pointless having a RAT deploy as a lender of electrons of Last Resort - if it can't help the batteries provide the ergs required for the flight-control system's final earthbound functionalities.

e. I'm assuming that a RAT-powered Rocinante will just fly a 12 to 15 degrees nose-up wings level glide attitude to a nice optimal ditching. It may dig a wingtip into a swell and shed a flaperon (in its full aileron deflection response) and maybe some aileron trailing edge on the same side - but that's not a Boeing design deficiency.

What say you? I'd be interested in some knowledgeable researched input.

I awake from my reverie, reach for my lunch-box and ruminate upon my boring freight-dawg existence. These projectile vomiting spasms sure leave you peckish. You can sign me up for one of these pilotless projects any day. It's a freightening prospect.

[Ian W]

Perhaps you should read the MH370 thread where all this was discussed and engine off from height was actually checked out in the flight simulators (hint search for phugoid not 15 degrees nose up) :hmm:
I suppose the ACARS, ADS-B and SSR ate at the same food stall but the SATCOM was not hungry thus they all went sick with the first officer :hmm:
Oh and all their backup systems too - must have been quite an electric party:hmm:
The uncontrolled reaction to turbulence could account for one such turn but not only the turn back after going dark. However, the night was clear and calm no ICTZ weather to speak of and there were more than one turn, initial turn back then several along the Thai border then descend over home town of captain then a right turn up the Malacca straits then a left around the top of Indonesia then just outside primary radar range another left onto South. Those non-existent ITCZ storms must be really well positioned and their turbulence got it right each time ....:hmm::hmm:

Now as you have lots of time you should read and understand what William of Occam was positing. :)