Climb Aircraft Performances

Continuing with the Private Pilot and Air  Transport Pilot aircraft performance subject. We are writing about  two aspects that we can find in every climb. Rate of climb and angle of climb, Vx adn Vy .

We will solve some doubts that could have, such as what is de diffecence between Rate of climb and Angle on climb.

What is the essential condition to have a climb?

The only condition that provokes an aircraft to climb is an excess of power. Power available (Pa) is greater than Power required (Pr). If this it is not accomplished, it is not possible to climb.

For training purpose we are going to consider that TAS is constant.

What is the difference between climb angle and rate of climb?  

CLIMB ANGLE

In the picture above we can see which forces are actuating during a climb.
Considering that sine of c (angle of climb) is equal to c, for pedagogic reasons.

Angle of climb(c) = (thrust (T) – Drag (D))/ Weight(W).

C= (T-D)/W.

The greatest angle of climb is when the difference between thrust and drag is maximum, which means it is reached when we fly at the minimum drag speed (In some books it is said when T – D is maximum, because they care about decrease of the T, due to the drift of the blade).
For training purposes we considered the thrust as a constant.

RATE OF CLIMB

gamma is the climb angle (c on the equation above)

As you can see in the picture Rate of climb ( R/c) = TAS ( True air speed) * c, which is the same as R/c= TAS * (T-D)/W which is equal to R/c= (Pa-Pr)/W.

Rate of climb will be the greatest when the relation Pa – Pr is the greatest. We get that result when we fly approximately at the minimum power required speed.
So as you could observe Rate of climb is a vertical speed ( feet/min) and climb angle is a trajectory.

Where can I find de maximum angle of climb and the maximum rate of climb speed ?

In the flight manual of your airplane you can find this speeds:

SPEED OF BEST ANGLE OF CLIMB (Vx)

This speed allows us to gain the most altitude with the least horizontal distance. As we said it is the speed that makes the relationship T-D be the greatest. It is almost the same speed as the minimum drag speed, so all factors affecting the drag affects the Vx (the factors affecting the Vx are written in this post: Aviation power curves).

This speed is very useful for example, when we want to avoid obstacles near the runway

SPEED OF BEST RATE OF CLIMB

This speed allows us to gain the most altitude with the least time.  it is the speed that makes the relationship Pa-Pr be the greatest. Vy is almost the same speed as the minimum require power speed, so all factors affecting the require power affects the Vy. (the factors affecting the Vy are written in this post: Aviation power curves ).

We use this speed during take off, when there is not any obstacles that affects the rate of climb, because the earlier we are high the safer we are.