If you increase the thrust on the right engine, the plane rolls to the left. But why? And why does the plane roll to the right and not yaw to the right?
Note: I am not a pilot, nor have I followed any aerodynamic studies whatsoever.
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Increasing thrust on the right engine only will make the aircraft yaw and then roll to the left.
The thrust does generate a yawing moment to the left, but the secondary effect of yaw is roll. In simplistic terms, a yaw to the left means that the right wing not only momentarily moves through the air faster than the left, but more of the wing is exposed to the airflow. This generates extra lift from the right, putting the aircraft into a left roll.
A more technical explanation of this effect can be found here.