What you are describing is called asymmetric thrust and it is a problem.
Pilots have to compensate with trim, they adjust the airplanes control surfaces to keep the plane flying straight and to counter the force of that one engine.
On commercial planes the thrust of one engine isn’t enough to cause a *flat spin* like you describe, at least not easily.
In military jets though this is a real problem. The engines are far more powerful especially with afterburner and the jets are much lighter.
This is why a lot of military jets have the engines close together, to help prevent this from happening.
The famous crash in Top Gun when Goose is killed is an example of this problem. The first version of the F-14 was prone to compressor stall meaning that one engine could shutdown, and the engines were far enough part to cause excessive yaw leading to a flat spin… which is what we see in the movie.
The F-14 also doesn’t have enough rudder to counter this force. In order to make it fit in the aircraft carrier hangers they couldn’t put a tall enough rudder on the jet so they put 2 smaller rudders on it instead.
The later version of the F-14 used a different engine that solved this problem.
The SR-71 also had massive problems with engine unstarts. The J-58 engine was incredibly powerful and the two were mounted very far apart. If one engine stalled the SR-71 would veer sideways harshly and the pilot had to catch it and re-start the engine quickly.
The short version is: yes, it wants to turn because the thrust comes from the far side, but planes also have very big rudders in the tails. Adjust it a few degrees to the side to compensate and the plane can fly straight and turn both ways. You can “trim” it, permanently setting the “center” position as said few degrees to the side.
That said, planes will usually need to reduce speed and descend from their ideal cruising altitude since they’ve lost some power and that rudder to the side is going to cause a decent amount of drag.
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