Forces in Flight
Gravity, Lift, Thrust and Drag.
Gravity is a force that is always directed toward the centre of the earth. The magnitude of the force depends on the mass of all the aircraft parts. The gravity is also called weight and is distributed throughout the aircraft. But we can think of it as collected and acting through a single point called the centre of gravity. In flight, the aircraft rotates about its centre of gravity, but the direction of the weight force always remains toward the centre of the earth.
Lift is the force generated in order to overcome the weight, which makes the aircraft fly.
This force is obtained by the motion of the aircraft through the air
Lift force is therefore dependent on the density of the air r, the airspeed V, the type of airfoil and on the wing’s area according to the formula below:
Lift Force = 0.5 * r * V2 * Wing's Lift Coefficient * Wing Area
Where the Lift Force is in Newton, Wing Area in m2 and the airspeed in m/s. The standard density of the air is 1.225kg/m3.
The wing's lift coefficient is a dimensionless number that depends on the airfoil type, the wings aspect ratio (AR), Reynolds Number and is proportional to the angle of attack (AoA) before reaching the stall angle.Thrust is the force generated by some kind of propulsion system. The magnitude of the thrust depends on many factors associated with the propulsion system used:
- type of engine
- number of engines
- throttle setting
- speed
The direction of the force depends on how the engines are attached to the aircraft.
The glider, however, has no engine to generate thrust. It uses the potential energy difference from a higher altitude to a lower altitude to produce kinetic energy, which means velocity.
Gliders are always descending relative to the air in which they are flying.
Drag is the aerodynamic force that opposes an aircraft's motion through the air.
Drag is generated by every part of the aircraft (even the engines).
There are several sources of drag:
One of them is the skin friction between the molecules of the air and thesurface of the aircraft.
The skin friction causes the air near the wing's surface to slow down.
This slowed down layer of air is called the boundary layer.
The boundary layer builds up thicker when moving from the front of the airfoil toward the wing trailing edge.
Another factor is called the Reynolds effect, which means that the slower we fly, the thicker the boundary layer becomes.
Form drag is another source of drag. This one depends on the shape of the aircraft. As the air flows around the surfaces, the local velocity and pressure changes. The component of the aerodynamic force on the wings that is opposed to the motion is the wing's drag, while the component perpendicular to the motion is the wing's lift. Both the lift and drag force act through the centre of pressure of the wing
With cambered airfoils, the Centre of Pressure position varies with changes in Angle of Attack, whereas with symmetrical airfoils, its position is fixed and coincident with the airfoil's Aerodynamic Centre (AC).
For rectangular wings at subsonic speed, the Aerodynamic Centre lies at 25% of the chord length measured from the leading edge.
Induced drag is a sort of drag caused by the wing's generation of lift. One cause of this drag is the flow near the wing tips being distorted as a result of the pressure difference between the top and the bottom of the wing, which in turn results in swirling vortices being formed at the wing tips. The induced drag is an indication of the amount of energy lost to the tip vortices. The swirling vortices cause downwash near the wing tips, which reduces the overall lift coefficient of the wing
The picture below shows the downwash caused by an aircraft
The Cessna Citation has just flown through a cloud.
The downwash from the wing has pushed a trough into the cloud deck.
The swirling flow from the tip vortices is also evident.
The wing geometry (aspect ratio AR) also affects the amount of induced drag:
Long wing with a small chord (high AR) has low induced drag, whereas a short
wing with a large chord (low AR) has high-induced drag.
For the same chord, the wing with a high AR has higher lift coefficient, but stalls
at lower angle of attack (AoA) than the wing with a low AR.
Also, aircraft with high AR wings are more sensitive to elevator control.
The induced drag increases with increasing of the wing's actual lift coefficient
being generated and it's proportional to the square of the angle of attack.
And since a slower airspeed requires a higher angle of attack (AoA) to produce
the same lift, the slower the airspeed is, the greater the induced drag will be.
So, the induced drag is also inversely proportional to the square of the airspeed.
In order to minimise tip vortices some designers design a special shape for
the wing tips.
With drooped or raised wing tips, the vortex is forced further out
However, this method will cause an increase in weight since they need to be
added to the wing tip.
An easier and lighter method is by cutting the wing tip at 45-degrees.
With a small radius at the bottom and a relatively sharp top corner, the air from
the secondary flow travels around the rounded bottom but can't go around the
sharp top corner and is pushed outward
There's also the Interference drag, which is generated by the mixing of
streamlines between one or more components, it accounts for 5 to 10%
of the drag on an airplane.
It can be reduced by proper fairing and filleting which allows the streamlines
to meet gradually rather than abruptly.
All drag that is not associated with the production of lift is defined as
Parasitic drag.
The graph below shows the induced and the parasitic drag versus airspeed.
Total drag is the induced drag plus the parasitic drag
Since during constant speed and level flight the thrust is equal to the total drag
the graph also shows how much thrust is needed at different level flight speeds.
At take-off (just above the stall speed), a high AoA is needed to get enough lift
which increases the total drag and also the thrust needed.
As the speed increases, the AoA needed to get the same lift decreases and so
does the total drag until the minimum drag speed is reached, above which the
total drag starts increasing exponentially (and so does the thrust needed).
The plane's max level speed will be limited by the prop's pitch speed or by the
max thrust available, which altogether means by the max power available
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