To add to this interesting topic...
The reason why the barrier speed and Vx often differ is because of the configuration of the a/c. Flaps are generally the reason- the barrier speed will be slightly less than Vx, because the speed quoted for Vx is usually flapless, while the barrier speed has 10 degrees.
Vy is NOT excess thrust! Vy is the speed where the amount of EXCESS THRUST HORSEPOWER (THP) is greatest. What do I mean by excess??... well, a certain amount of power is required to fly straight and level at any speed. At low speeds (remember slow flight) lots of power is required because of the drag (mainly induced drag). At high speeds, high power is once again required because of the high drag (mainly parasite drag). There is some speed where the power requirement is minimized (this coincides with maximim endurance). If we fly at this minimum power speed, you are obviously not flying at full wide open throttle. This power that is not being used (i.e. it is not needed to maintain straight and level flight at that speed) represents the excess power that can be used to climb or accelerate to a higher (or slower) speed. It is a form of stored energy, waiting to be used.
Vx represents the speed where EXCESS THRUST is greatest. This condition does not depend on time- it depends on altitude gained per horizontal distance travelled. It is slower than Vy and will not register as high a rate on the VSI. You are climbing at a steeper angle, but you are not gaining as much altitude per TIME. You are gaining the most altitude per DISTANCE.
Now, someone mentionned that Vy coincides with the minimum drag speed (maximum range)... I disagree (recall: Vy represents the point where excess power is greatest). It technically coincides with the minimum power speed (maximum endurance). However, if you look through various POHs, the speed for Vy is generally closer to the maximum range speed than it is for maximum endurance, and there is a reason for this. The mimum power speed is usually very low (in my a/c it is around 55-60 knots). The minimum drag speed is higher (around 70-75 knots in my a/c). If the a/c tried to climb at such a low speed (55-60 IAS), the props would lose efficiency, and little THP would actually get developped. So, the solution is to use a slight higher IAS (Vy in my a/c is 75 knots, and maximum range speed is 73 knots). At this higher IAS, the power requirement is greater, but the props are more efficient, so you will get a better climb rate.
I hope this explanation did not confuse anyone. Remember, power and thrust are 2 different things. Power is NOT minimized at the point where drag is minimum.
