Scenario 1. A two-engine airliner experiences rapid depressurization and makes an emergency descent to 10,000 ft, and diverts to the nearest airport.

Scenario 2. The same two-engine airliner experiences rapid depressurization after it has lost one of its two engines and makes an emergency descent to 10,000 ft, and diverts to the same nearest airport.

In which scenario between the two does the airliner consume a greater amount of fuel, and why?

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    $\begingroup$ (1) I'm not sure it's reasonable to refer to "cruise" at 10,000 ft for an airliner. (2) Are we to assume identical airspeed in scenarios one and two? (3) With one engine inoperative of two (for any reason), how does the aircraft maintain directional control? What does that do to the amount of drag the engine must overcome? $\endgroup$
    – user
    Aug 9 '19 at 11:16
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    $\begingroup$ All the other conditions not mentioned above were assumed to be the same. Therefore, the speed is the same, and no additional drag is being made to the one-engine aircraft due to the one-engine condition. $\endgroup$ Aug 9 '19 at 11:39

For an A320, at FL 100 and weight 50 tonnes and ISA, the FF is 1028 kg/h per engine, so two engines is 2056 kg/h.

Now for the same but OEI: the FF is 1891 kg/h (just the one engine).

Scenario 1 is higher fuel flow rate. I'll explain why based on scenario 2.

In scenario 2, with one engine inoperative (OEI), the remaining engine will run at higher power setting, which improves the SFC (see image below), and therefore will improve the endurance (time in the air; how fast the fuel is used).

► It will diminish the range though, as range requires speed, which will be limited with OEI (and also due to the low altitude), i.e., don't mix the improved FF and endurance with why not always fly with one engine (ignoring the safety issues).

enter image description here
Source: Jet Transport Performance Methods, Boeing

(Don't miss the text left of the graph.) That's also why coast guard C-130s orbit with an engine deliberately turned off. Being a turboprop (gas turbine), the SFC relation holds.

Related: Why is max endurance different for jet and props?

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    $\begingroup$ What about the drag from using the rudder to counteract the asymmetric thrust? I guess the coast guard doesn't care about that while orbiting, but does this argument still hold when flying straight? $\endgroup$
    – Bianfable
    Aug 9 '19 at 11:36
  • $\begingroup$ From performance manuals, it holds yes. Also too much rudder can be offset by a slight bank. I'll add figures. $\endgroup$
    – ymb1
    Aug 9 '19 at 11:37
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    $\begingroup$ @ymb But flying straight with a bank means a uncoordinated flight, and that implies a higher drag from ailerons, rudder and body, as well as less lift (to be compensated with a higher airspeed) caused by a slightly lower projection on the horizontal plane of the wing planform. All that means more fuel consumption... $\endgroup$
    – xxavier
    Aug 9 '19 at 11:55
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    $\begingroup$ @ymb It's interesting, and seems paradoxical, too... $\endgroup$
    – xxavier
    Aug 9 '19 at 12:13
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    $\begingroup$ @Bianfable: The higher speed is due to the MCT power setting. Bigger bang but certified to not do damage (e.g., better cooling due to the faster fan). The slower speed is the most economical when both engines are working. $\endgroup$
    – ymb1
    Aug 9 '19 at 12:15

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