> “My guess is the pilot turned off the good engine with a hope of a crash landing in the river. But just did not have the altitude to pull it off.”
Not my guess. If the good engine was producing more torque than could be controlled by the ailerons and tail (a long shot for a commercial airliner), they might have reduced the power on the good engine slightly, not shut it off.
One of the two pilots guessed wrong (for whatever reason) on which engines was out.
Since the good engine was producing maximum thrust and the bad engine zero thrust, laws of physics would immediately want the aircraft flying sideways. If the aircraft has not gained enough altitude at the point of engine failure, it must be difficult to level the aircraft with ailerons and tail manipulations.
The pilot was hoping by killing the good engine, the plane could be leveled and a crash landing in the river was the only way out.
The main question in my mind is, were both engines adequately tested before attempting takeoff? If yes, what makes one engine fail so quickly and completely? It can’t be overheating or fuel running out or metal fatigue.
You’ve almost got it.
All the speculation about intentionally shutting down the good engine to maintain controllability is nonsense. All FAR Part 25 aircraft (virtually all western airliners) can climb with 1 engine, and maintain controllability. These aren’t light twins, where it is all somewhat guesswork and blue-line discipline. Part 25 aircraft guarantee every take off can achieve second-segment climb at V2 to V2+10, or the takeoff does not begin.
The reason the good engine was shut down should be obvious: in their hurry to restart the flamed out engine they shut down the good one in error.
This illustrates differences in training at airlines outside the U.S. Here, the only time you can troubleshoot is ABOVE critical altitude, usually 1,000’ above field elevation, and possibly with a fire. We train pilots that unless they are sure a fire is uncontainable, they must WAIT until above critical altitude to do ANYTHING except fly the aircraft. That way, the emergency can be handled in a methodical and disciplined way.