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Best angle of climb vs. best rate of climb

There are a number of designated airspeeds relating to optimum rates of ascent.

Vx is the indicated airspeed for best angle of climb.

Vy is the indicated airspeed for best rate of climb.

Vx is slower than Vy.

Climbing at Vx allows pilots to maximize the altitude gain per unit of ground distance. That is, Vx allows pilots to maximize their climb while covering the least amount of ground distance. In other words Vx is what you need to clear an obstacle with maximum margin.

This occurs at the speed for which the difference between thrust and drag is the greatest (maximum excess thrust).

Climbing at Vy allows pilots to maximize the altitude gain per unit of time. That is, Vy, allows pilots to maximize their climb in the shortest time. Vy is what you need when you want to climb as quickly as possible.

This occurs at the speed for which the difference between engine power and the power required to overcome the aircraft's drag is the greatest (maximum excess power).
Climb rate is proportional to excess power.

A trick to remember: X comes before Y in the alphabet. And to know how to clear an obstacle obviously comes in priority before knowing how to climb fast. Therefore Vx is the best obstacle clearing speed, and Vy gives you the fastest climb.