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I can understand why Vy decreases with altitude, because the engine produces less power. But why does Vx increase with altitude? I suppose if Vx were to decrease with altitude the airplane would be getting pretty close to its critical angle of attack, but I can't figure out the reason why it increases.
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Personal FAQ:
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An airplane climbs because it has more power available than the amount of power it needs for straight flight at a particular airspeed. This simply means, for example, that if you are flying an airplane that has a normal cruise speed of 100 kts at full power and you keep it at 80 knots with full power, it must climb.
Grab you book and look for the power available vs. power required chart. Vy is the airspeed at which the difference between the two curves is the greatest.
With altitude, power available decreases. As you get higher, it decreases a lot. The point at which the greatest difference exists between the curves moves down the airspeed scale.
Vx is a little different (and takes some visualization). Once you have power available for a climb, it's how high can you bring the nose and convert that excess power into thrust pointing upwards, so that you climb steeper, not faster. Vx is the point at which you'll get the maximum excess thrust.
The same loss of power with altitude means that there isn't as much excess thrust available. So, you have the lower the nose. And that means airspeed has to increase.
As altitude increases and power and thrust both decrease, Vy will decrease because there's less power available. Vx will increase because there's less thrust available.
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