A Challenging Endurance Problem

[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]

Originally Posted by megan

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]

A Challenging Endurance Problem: PART B

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"?

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]

An Associated Conundrum

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)
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
Oh and all their backup systems too - must have been quite an electric party
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 ....

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