can anyone illustrate with a picture what does upwind engine and downwind engine mean? for example, i came across this - “The outer engines are critical. If there is any crosswind then the upwind outboard engine is the most critical. With a twin jet the upwind engine is critical for the same reason in a crosswind.”
Up wind is the same as windward, or into-wind side. If the crosswind is from the left, then the left engine is critical, because if it fails, you have the crosswind from the left, AND the asymmetric thrust from the right engine(s) trying to drive the nose to the left during the takeoff phase while the wheels are in contact with the surface.
Once you are clear of the ground, you can align the plane into the airflow with rudder, and if you do nothing else you will start to drift downwind as the crosswind carries you laterally, or, if you are able to think about it, you can do a slight turn into wind to establish a crab angle to maintain the runway axis on the climbout. But in any case, a few seconds after you are airborne, the crosswind is no longer relevant from a critical engine aircraft control standpoint.