For a flight at constant speed in level flight, the drag force must balance the engine thrust. As a general rule, when engine thrust is higher than drag, the aircraft can use this excess thrust to accelerate and/or climb. On the other hand, when the thrust is insufficient to compensate for drag, the aircraft is forced to decelerate and/or descend.
Angles definition
The Angle of Attack (AoA) is the angle between the flight path and the aircraft longitudinal axis.
The Flight Path Angle (FPA) is the angle between the horizontal axis and the flight path.
The aircraft attitude or pitch angle is the angle between the horizontal axis and the longitudinal axis.
pitch angle = (AoA) + (FPA)
Forces diagram
In flight, four forces are applied to an aircraft : Thrust, drag, lift and weight.
If the aircraft is in steady level flight, the following balance is obtained :
• The thrust for steady level flight (T) is equal to drag (D = ½ ρ S V2 CD),
• Weight (mg) is equal to lift (L = ½ ρ S V2 CL).
> Weight, applied on the center of gravity of the aircraft, directly proportional to the mass of the aircraft.
Weight = mg
> Lift and drag are aerodynamic forces that depend on the shape of the aircraft
Lift is directed perpendicular to the flight path and applied on the center of pressure of the aircraft.
Lift = ½ pS(TAS)2 CL
Drag is directed along the flight path.
Drag = ½ pS(TAS)2 CD
> the thrust is determined by the engine type and the power setting selected by the pilot, and is directed in the aircraft axis.
With
m = aircraft mass
p = air density
S = wing surface
TAS = True Air Speed
CL = lift coefficient
CD = drag coefficient
NOTE: The lift and drag coefficients depend on the Angle of Attack (AoA), the aircraft aerodynamics (mainly flaps and landing gears configuration) and the True Air Speed.
Along the flight path, the balance is expressed as:
Lift + Thrust ∙ sin (AoA) = weight ∙ cos (FPA)
and
Thrust ∙ cos (AoA) = drag + weight ∙ sin (FPA)
The motion of the aircraft through the air depends on the relative magnitude and direction of the various forces:
> For a flight at constant speed and in level flight, the drag force balances the engine thrust. And the lift balances the weight.
> When engine thrust is higher than drag, the aircraft can use the excess thrust to accelerate and/or climb.
> On the opposite, when the thrust is insufficient to balance the drag, the aircraft is forced to decelerate and/or descent.
As a function of the Mach number
Lift and drag equations may be expressed with the Mach number M. As a result, the equations are:
As a function of Po (Pressure):
The pressure ratio δ is introduced into the lift and drag equations:
δ = Ps / Po
With
Po = Pressure at Sea Level
Ps = Pressure at Flight Level
Therefore, the following equations are independent of pressure altitude:
Load factor
During a turn, an aircraft is not only subjected to its weight (W), but also to a horizontal acceleration force (Fa) directed towards the center of the turn to counteract the centrifugal force. The resulting force is called apparent weight (Wa), and its magnitude is equal to the load factor times the weight.
The load factor can be expressed versus the bank angle:
During a balance turn, the lift equals the apparent weight.
Lift-to-drag ratio
Because lift and drag are both aerodynamic forces, the ratio of lift to drag is an indication of the aerodynamic efficiency of the aeroplane. The lift-to-drag ratio L∕D is the amount of lift generated by a wing, divided by the drag it creates by moving through the air.
A higher or more favorable lift-to-drag ratio is typically one of the major goals in aircraft design; since a particular aircraft required lift is set by its weight, delivering that lift with lower drag leads directly to better fuel economy and performance.
aviation performance 