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**Concepts we are going to use :** Forces at take off and Aviation Power curves

What is the 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).

Note : For training reasons we are going to consider the TAS is constant

When we are climbing The forces acting on the aircraft are :

**CLIMB ANGLE**

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 maximun, which means it is got when we fly at the minimun drag speed ( In some books it is said when T – D is maximun, because they care about decrease of the T , but for learning and having very clear the concepts I assume T 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.

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

Rate of climb is a vertical speed ( feet/min) and climb angle is a trajectory.

**SPEED OF BEST ANGLE OF CLIMB (Vx)**

This speed allows us to gain more 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.

When do we use it ?

To avoid obstacles on the initial climb.

**SPEED OF BEST RATE OF CLIMB**

This speed allows us to gain more altitude with the least time. As we said it is the speed that makes the relationship Pa-Pr be the greatest. It is almost the same speed as the minimum require power speed, so all factors affecting the require power affects the Vy.

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