av8a,
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.
Regards Again,
TOGA_Party