Why does Vx increase with altitude and Vy decrease?

Question

As an airplane climbs, the best angle of climb airspeed (Vx) increases and the best rate of climb airspeed (Vy) decreases. I can't figure it out, why does it happen? I Hope someone explains it to me I appreciate

Answer 1

Vx is all about using higher angle of attack (slower airspeed) and excess thrust to climb. The more excess thrust one has, the steeper the angle one can climb.

As altitude increases, thrust output decreases. This is why the plane must lower its angle of climb, reduce its angle of attack, and go faster in order to continue climbing.

Vy is all about using a lower angle of attack and greater airspeed to climb. As thrust output decreases, the aircraft must increase its AoA and lower its airspeed to continue climbing.

At the absolute ceiling altitude, only the most efficient combination of (diminished) thrust, airspeed, and angle of attack will allow level flight. This is where Vx and Vy converge.

Answer 2

The details of this depend on the details of your propulsion model for your aircraft. I.e. how do maximum throttle thrust/power change with airspeed and altitude.

You also need to pay close attention to equivalent vs true airspeed.

$V_y$ is always greater or equal than $V_x$. However, at absolute ceiling, they are equal (and the climb angle and rate of climb are both zero).

So, to start apart and end up together, they either have to increase/decrease, both increase (but at different rates), or both decrease (but at different rates).

For a jet aircraft, we usually approximate the thrust available as constant with airspeed. In this case, Vx will occur at the speed for best L/D, which will be a fixed Ve. In order for Vy to start off greater, but to eventually equal Vx, Vy must decrease with altitude (in terms of Ve).

For a propeller aircraft, we usually approximate the power available as constant with airspeed. In this case, Vy will occur at the speed for minimum power required, which is the speed for best $C_L^{3/2}/C_D$. Which occurs at a fixed lift coefficient and therefore also occurs at a constant $V_e$ with altitude. So, in order for Vx to start off less than, but to eventually equal Vy, Vx must increase with altitude (in terms of Ve).

In reality, neither of these approximations is perfect, so the truth generally lies somewhere in-between. However, working it out to great precision requires very detailed models of the propulsion system.