The balance along the vertical axis, becomes : 

(2) Lift = Weight cosγ 

1.2.1. Climb Gradient (γ) 

The climb gradient (γ) and the angle of attack (α) are usually small enough so that : 

sinγ≈ tanγ≈γ (in radian) cosγ≈ 1 and cosα≈ 1 

As a result: 

(3) Thrust = Drag + Weight γ 

(4) Lift = Weight 

From equation (3), Thrust -Drag = Weight γ. Then: 

Conclusion: At a given weight and engine rating, the climb gradient is maximum when (Thrust – Drag) is maximum (i.e. when the drag is minimum or when the lift-to-drag ratio is maximum). The best lift-to-drag ratio speed is called Green Dot (or Drift-down) speed. In case of an engine failure, flying at green dot speed permits maximizing the aircraft’s aerodynamic efficiency and compensating for the power loss. 

1.2.2. Rate of Climb (RC) 

The Rate of Climb (RC) corresponds to the aircraft’s vertical speed. As a consequence: 

Conclusion: At a given aircraft weight, the rate of climb is maximum when TASx(Thrust – Drag) is maximum. In terms of power1, the rate of climb is maximum when (Pthrust – Pdrag) is maximum. 

1.2.3. Speed Polar 

The following Figure (G2) illustrates both the thrust and the drag forces versus the True Air Speed. 

To fly at a constant level and speed, the thrust must balance the drag. As a result, drag can be considered as the thrust required to maintain a constant flight level and a constant speed. Climb is only possible when the available thrust is higher than the required thrust (excess of thrust). 

The above equations indicate that, for a given weight: 

The climb angle (γ) is proportional to the difference between the available thrust and the required thrust. 

The rate of climb (RC) is proportional to the difference between the available power and the required power. Moreover, as RC = TAS γ, the maximum rate of climb is obtained for a TAS higher than green dot (when dRC/dTAS = 0). 

The force power (Pforce) represents the force multiplied by the speed (TAS). The unit is watt (W). 

It can be observed that it is not beneficial to climb at a speed lower than green dot, as it would require a longer distance and time to reach a given flight level. 

1.3. Influencing Parameters 

1.3.1. Altitude Effect 

Due to air density reduction when pressure altitude increases, climb thrust and drag decrease. But, since the drag force decreases at a lower rate than the available thrust, the difference between thrust and drag decreases. Therefore, the climb gradient and the rate of climb decrease with pressure altitude, due to a lower excess of thrust.

1.3.2. Temperature Effect 

As temperature increases, thrust decreases due to a lower air density. As a result, the effect is the same as for altitude. 

1.3.3. Weight Effect 

As seen in the previous section: 

Therefore, at a given engine rating, altitude, and climb speed (TAS), any increase in weight leads to a decrease in the climb gradient and rate of climb. 

1.3.4. Wind Effect 

A constant wind component has no influence on the rate of climb, but changes the flight path. 

GS = Ground Speed 

TAS = True Air Speed 

γg = Ground climb gradient 

γa = Air climb gradient 

As shown in Figure G3, the air climb gradient remains unchanged, whatever the wind component. So, the fuel and time to the Top Of Climb (T/C) remain unchanged. 

2. CLIMB IN OPERATION 

2.1. Climb Management 

2.1.1. Thrust Setting 

The standard climb rating is called “Maximum Climb Thrust”. At the reduction altitude, pilots have to reduce thrust from takeoff power to climb power by setting the thrust throttles to the climb (CL) gate (Figure G4). This must be done prior to a maximum time of 5 minutes after brake release. 

2.1.2. Energy Sharing 

Aircraft energy is provided by the engines. To fly, an aircraft needs: 

Kinetic energy : Energy necessary to maintain speed and accelerate. 

Potential energy : Energy necessary to maintain altitude and climb. 

The sum of the kinetic energy and the potential energy cannot exceed the total aircraft energy. Consequently, the total energy has to be shared between the need for speed and the need for altitude. 

The FMGS manages this energy sharing during the climb (70% for speed, 30% for altitude). As a result, when: 

TAS increases: The climb gradient and the rate of climb decrease, as potential energy is converted into kinetic energy.