If you have a strong cross wind from the right and you have an engine fire, you will probably surmise that the right engine is your critical engine. That being cos u will have to turn right in order to stop a total hull engulfment by the flames.
I believe the critical engine on jet aircraft is the upwind engine. Because "weather-cocking" due to x-wind combines with engine out yaw to provide the most critical controlability scenario.
To try and explain things a little more clearly.
Imagine you are lined up on the runway,you advance the power and proceed on your take-off run. You will soon reach a speed called V1.
This speed can be equal to Vrotate (which is the speed at which we can pitch the nose of the aeroplane up,in preparation for lift-off). V1 and Vrotate MUST be equal to or greater than Vmcg. Vmcg is the "minimum control speed-on ground",which by definition means that we can keep the aeroplane undercontrol with aerodynamic devices alone,ie rudder and ailerons.
So lets say that today V1 and Vrotate are at the same speed and the wind is from the right. You pitch the nose up and the right engine fails.
A failure on the right side will cause the nose of the aircraft to swing right.Right!? And with the wind from the right striking the fin on the right,will cause the the nose of the aircraft to swing right. It's the these two effects when added together MAY overcome our ability to keep the aircraft under control with aerodynamic devices alone. Remember the nose wheel is off the ground so no steering available!
There's a bit more to it than that,but,all aircraft are put throught an exhaustive set of "certification" trials which plot aircraft performance and all V-speeds are derived from these trials.
ON a prop aircraft it is the engine that would be most critical to loose. The downgoing blade gives thrust (power) if the nose is up, which would be normal flight attitude, hence the left engine thurstline is closer to the centerline of the aircraft. This is the engine you don't want to loose(!). The yaw moment if flying on righy engine only is therefore greater.
On jet aircraft it is normally not defined. The wind direction changes and so does your flightpath in the patter, which yould shift the critical engine from one side to the other. Not practical
The critical engine is the one which gives the most directional control problem if it fails.
As you cavort down the rw with a wind from the left, you have right rudder applied to stay straight (counteracting the weathercocking effect of the fin). This reduces the amount of right rudder available should the left engine (upwind) fail, so the critical engine is the upwind one.
I'm completely miffed! Try as I might I cannot visualise what your suggesting with regard to the HS125. I can see that with thrust lines close to the fore-aft axis there would be little yaw when an engine fails. But are you saying that in nil wind the HS125 yaws AWAY from the failed engine?
Mystified of Perth!
Morse, sorry to disappoint, from the BAe 146 AFM, page 1 of section 4.21.1,
The critical engine is the outer engine on the upwind side
av8a, if on the 146 you consider the outer left engine as being #1, and for this exercise, the wind coming from the left.
Should #1 fail, the subsequent yaw will be to the left ( one engine producing thrust LHS, two engines RHS). Until airborne, the wind from the left will strike the left side of the aircraft. With more surface, including the vertical stabiliser, aft of the CoG, the resultant yaw will also be to the left.
The critical engine is that one whos failure has the most adverse effect on controlability of the aircraft, in the scenario I've described, #1 is the critical engine.
There can be more than prop rotation to be considered, e.g. some aircraft have split hydraulic systems with the Landing Gear on only one. When the engine driving that system fails the gear will be retracted only by the auxillary pump and therefore performance is predicated on gear retraction time in this worst case. Therefore that engine is declared as 'critical'.
In point of fact the only effect is probably an undeclared bonus if flying on the non-critical engine during the retraction segment. The matter of critical engines is probably only academic.