Mac,
Here's what you're looking for.
The weather vane effect or 'weather cock' effect is only and I repeat
ONLY applicable when the airplane is on the ground.This is due to the main wheels acting as a pivot somewhere pretty close to the centre of gravity of the airplane.Therefore if hypothetically,you had a V1 of 99 kts and a Vr of 200 kts and a left engine out at 100 kts IAS combined with a nasty crosswind from the left,i'm quite certain that you'd have a darn tough time keeping the airplanne straight on the runway for takeoff.Combine that with a slippery runway and I could bet my last dollar that you'd be off the runway!
HOWEVER......things are quite different when in the air.Out 'there',in the air,its the drift associated with the engine fail that matters.And with the absence of a 'pivot' fulcrum point ie the main wheels on the runway,the plane does
not weather cock,rather it 'drifts'.And this is where the simplest of laws of physics will apply.Wind from left,combined with failure of the rhs engine will simply drift the airplane to the right due to:
1)Loss of thrust on the rhs thus resultant vector to the right
2)More lift from the lhs due increased wind component from the lhs.Therefore resultant lift vector will make airplane roll AND yaw to the right...
To cut a long story short,the downwind engine IS the critical engine in case of EO(systems dependability notwithstanding of course!).
Same goes for Engine out landings...
Hope I could be of some help(albiet minuscle,but nevertheless)....
Happy X winds...
