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I was talking with a friend about what things would happen if you experienced engine problems in cruise. We were wondering the following:

What things would need to be changed to arrive in the optimal configuration for range?

Here I found that the speed is reduced to approximately 80% of the normal cruise value, but I can image that more things change, perhaps the altitude?

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The optimization problem is unchanged from the all engines operative (AEO) cruise optimization. You should still:

  • Climb as high as practical (colder, thinner air is better for range)
  • Set the lift coefficient such that drag is minimized for propeller aircraft ($c_{Di} = c_{D0}$). For turbojets, minimize energy per flight time ($c_{Di} = \frac{1}{3}\cdot c_{D0}$). For turbofans, pick a value between those two extremes.

For the computation of the theoretical optimum polar point please see this answer for a complete derivation including wind, or this answer for a shorter explanation.

Your flight altitude will certainly be lower, because you need to generate more thrust on the remaining engine (requiring higher density), which in turn will result in a lower TAS (true air speed). The CAS (calibrated airspeed) should stay about the same, however. The configuration (flaps, gear) should stay unchanged, only rudder deflection will be added for asymmetric thrust compensation. The resulting sideslip will increase the zero-lift drag of the airplane a little, so a slightly lower speed than in the AEO case would result.

In the unlikely case that the required density will result in an altitude below ground level, you will need to slow down and need to set flaps to stay airborne, and now the new optimum with flaps will result in a markedly higher lift coefficient because deploying flaps will increase the zero-lift drag quite a bit. If you have the flaps-down polar, the optimum is easy to find.

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Your guess is right.

In this article you can read about engine-out procedures. Because you can't maintain a certain altitude without sufficient thrust, losing an engine means you can't maintain the same cruising altitude without all the engines running. This is, of course, based on the fact that you're flying around the maximum altitude you can fly with both the engines operative given a certain aircraft weight.

It's worth nothing that when losing an engine on modern twin-engines airliners, usually the APU is started to provide electric power and pneumatic pressure (also, hydraulic pressure via electric pumps that runs on electric power produced by the only remaining engine's generator), but usually APUs can't be started and/or run over a certain altitude (20.000 - 25.000 ft, depending from the aircraft), so descending to lower altitudes is somewhat mandatory.

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  • $\begingroup$ Do you know at what point the engine operates? Is cruise thrust the maximum thrust and as such, losing an engine will always result in 50% loss of power, or is it possible to squeeze more newtons out of an engine, but at the cost of efficiency? $\endgroup$
    – ROIMaison
    Sep 28, 2015 at 12:48
  • $\begingroup$ Usually there are various power settings for the engines: TOGA (Take-Off/Go-Around) is the highest one, and it' used rarely (as it stresses the engines a lot). MCT (Maximum Continuous Thrust) is an high thrust power setting but can be maintained for longer timespans than TOGA. MCL (Maximum CLimb thrust) is the highest thrust setting used during climbs. Every aircraft has it's own thrust settings (and relative names, on Airbuses for instance, there is also the FLEX power setting) and it's own engine out procedures, that usually involve using an higher thrust setting on the remaining engine. $\endgroup$
    – Marco Sanfilippo
    Sep 28, 2015 at 13:17

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