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Do commercial flights continue with an engine failure? If you look closely at the attached picture it seems that one of the engines has a much smaller contrail than the other three. This seems to suggest that the aircraft is flying on three engines with the one at reduced (idle?) power. Is this normal?

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    $\begingroup$ The chemtrail tank for one of the engines ran dry. Perfectly normal. Try not to think about it. $\endgroup$
    – Bob Jarvis - Слава Україні
    Commented Mar 3, 2019 at 23:48

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The image looks like four engines running at the same cruise thrust. The wake vortex is blowing the exhaust of the inboard engines down and the exhaust of the outboard engines out and in the perspective of this image this makes the lower two streams look merged while the upper ones further apart. Close behind the engines it is clear there is four of them and all have similar strength.

That said, a four-engine aircraft may continue on three engines as far as it has enough fuel and there is no other damage (so not if the engine flamed out after a big bang). With one engine out it can't maintain as high altitude, so it has to drift down to lower altitude where it flies slower and thus has shorter range. However if they have enough contingency fuel, they can continue to destination. Or return back to departure point, or proceed towards the destination, but land somewhere short. The dispatcher will consider the repairs, taking care of the passengers, rebooking them, the next flight the plane was scheduled for and other things and tell the pilots which is the preferred option.

In contrast a two-engine aircraft shall land as soon as possible. One engine out of two means there is no redundancy left and that is an emergency and shall be handled as such. Note that as soon as possible does not necessarily mean closest airport—the aircraft will cover over 100 NM during normal descent from cruise altitude, so if there are more options in about 150 NM, the pilots and dispatcher still get to choose.

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    $\begingroup$ "Land as soon as possible" may give the wrong impression, since twin engine aircraft are routinely used for flights over oceans. In fact the longest flight certification for a twin engine aircraft after an engine failure is now 370 minutes (just over 6 hours) before landing for the Airbus A350XWB. $\endgroup$
    – alephzero
    Commented Mar 3, 2019 at 23:20
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    $\begingroup$ @alephzero If the nearest airport is indeed 370 single-engine minutes away, then there's no choice. But FAA rules (Part 121.565) are specific in that you must land with the least amount of flight time unless there's a safety reason, and in that case you must file a report with the FAA. The common term is "land at nearest suitable airport". $\endgroup$
    – user71659
    Commented Mar 4, 2019 at 0:30
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    $\begingroup$ @JanHudec Those are the two usual terms used in emergencies and have a distinction. "Land as soon as possible" means to get the plane down as fast as possible and consider places such as too short runways, closed airfields or the Hudson river (Airbus would call it a red LAND ASAP). "Land at nearest suitable airport" means no immediate danger and consider runway length, crash services, familiarity, terrain, etc (Yellow LAND ASAP in Airbus philosophy). The term "nearest suitable airport" is written into regulation (121.565) $\endgroup$
    – user71659
    Commented Mar 4, 2019 at 6:27
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    $\begingroup$ @wrtlprnft 100 NM isn't well outside of your glide range in an airliner at cruise altitude. That's actually pretty close to your glide range. Airliners can glide a really long way from cruise altitude. Also, midway between two airports 100 NM apart, you are 50 NM from each of them, well within the glide range of most airliners. $\endgroup$
    – reirab
    Commented Mar 4, 2019 at 9:07
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    $\begingroup$ @wrtlprnft If you're "right above" an airport, and at or near cruise altitude, you can't land at that airport, at least not immediately. It takes time - distance - to descend. If you have no other good options where to land then you certainly can do something like a circling descent (think corkscrew, or descending while flying something similar to a holding pattern), but you wouldn't be getting down much sooner because of it. So if you're at cruising altitude straight above an airport and need to land, that airport 100 NM away with a longer runway or better weather may well be a better option. $\endgroup$
    – user
    Commented Mar 4, 2019 at 12:06

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