AERODYNAMICS THEORY FOR BEGINNERS PARAGLIDING PILOTS
Airflow around a wing and aerodynamic force
Every object, which moves through the air, interacts with it by creating an aerodynamic force.
Any force can be divided by different components based on different coordinate (reference) systems. In classic aerodynamics, the aerodynamic force is seen through the direction of movement (the vector of speed V); its perpendicular to V component is called lift Ry and its opposite to V component is called drag Rx. Further on, we’ll continue using these popular names, but we have to remember that these are not independent forces but only components of a single force – the full aerodynamic force R.
Lift and drag are convenient for an initial description of how the wing works: a wing is more efficient if it produces more lift and less drag.
Lift can be created by:
- airflow around asymmetrically positioned body;
- airflow around a body with asymmetric shape;
- combination of both – airflow around asymmetrically positioned body with asymmetric shape.
When asymmetrically positioned body is placed in an airflow, the air causes pressure on its surface and creates an aerodynamic force perpendicular to its surface.
The angle between the body’s surface and the direction of the flow is called the angle of attack α and is an outstandingly important flight parameter, which determines the magnitude and the tilt of the full aerodynamic force i.e. the magnitude and ratio between its lift and sink components.
Typical example of flowing of an asymmetrically positioned body is when we put our hand outside the window of a moving car. Then, we can feel the full aerodynamic force by changing the tilt of our palm (the angle of attack).
Small, positive angles of attack increase lift and push our arm upward. Higher angles of attack produce more drag and push our arm backward. 90 ̊ angle of attack produces maximum drag and no lift. 0 ̊ angle of attack minimizes drag and allows our arm to cut more easily through the air. Negative angles of attack produce downward lift which pushes our arm downward.
Negative angles of attack are used in car racing, where spoilers create downward aerodynamic force , which increases the pressure toward the ground and the friction of the tyres i.e. allows cars to make tighter turn with smaller radiuses with higher speeds.
In order to learn how airflow around asymmetrically shaped body creates lift, first we have to mention the flow conservation law (the flow materia and its movement doesn’t appear from nowhere and dissapear into nowhere). As a result, where the flow is restricted, it increases its velocity V and vice versa:
You can increase the speed of the flow by restricting the exit of a garden hose with your finger.
If river banks get closer, then river increases its speed. If they get wider, then river flow slows down.
You cannot blow a ping pong ball out of a cooking funnel, because its increasing section reduces air speed.
Also, according to the Bernoulli’s principle in areas, where the speed of the fluid V increases, the surrounding pressure p decreases and vice versa:
Airbrush painting devices use fast airspeed to suck paint from bellow.
If you blow air between two sheets of paper, parallel and close to each other, this decreases pressure between them and they come closer pushed by the higher pressure outside. Because of this effect, two ships on opposite courses shouldn’t pass too close to each other, as increased relative flow speed between them will reduce pressure between them and can suck them and crash them into each other.
The classic wing profiles has convex upper surface, which acts like an obstacle: reduces the section of the flow, accelerates it and creates a zone of reduced pressure (sucking the wing effect from the airflow above)
The speed of a wing movement through the air is called airspeed V.
Airspeed and aerodynamic force exist, no matter if the wing is moving through the air or the air moves around a stationary wing – for example in an aerodynamic tunnel.
Usually, the lift creation by flowing of an asymmetric profile is combined with the creation of lift by asymmetrically positioned body in the flow.
The aerodynamic force R depends on:
- shape of the profile
- wing shape and dimensions when seen from above
- surface of the wing S
- angle of attack α
- square of airspeed V2
- air density ρ .
The increase of the angle of attack directly increases the lift production, but beyond certain angle of attack, the flow above the top surface tears sharply away from the wing and the wing loses most of its lift. A stall occurs – the wing doesn’t fly but falls down with high vertical speed.
The stall is dangerous, because it develops quickly, because the fall is fast and because the chaotic flowing of the wing makes it difficult for control.
DO NOT FLY WITH TOO HIGH ANGLE OF ATTACK!
The stall shouldn’t be confused with a collapse, where reaching too low and even negative angle of attack causes deformation and folding of the leading edge (frontal part of wing profile) by the air flow. The stall can also deform the wing but at the trailing edge (the back part of the wing profile) and the reason is reaching too high angle of attack.
With unpowered aircrafts like paragliders, flying with too high angle of attack slows down the wing i.e. to avoid a stall we shouldn’t fly with a very low airspeed.
As it’s difficult to observe and measure the angle of attack, to avoid stall, it’s easier to pay attention at the airspeed (the feeling of the wind in our face) or by knowing the relation between the increase of the angle of attack and the slowing down the glider (pulling the brakes). Thus, if during a gliding flight we feel a slowing down (reduced feeling of wind in the face) or if we see/feel that we pulled the brakes too much (close to our ribs and hips), then we should know that we’re close to stall.
If we’re close to a stall we have to restore our airspeed immediately (release the brakes).
Now, we know how the flow around the wing creates aerodynamical force, which keeps us in the air and prevents us from falling like a stone.
Still, how is the flow created, when there is no engine pushing us through the air?
Why we fly forward?
Because the wing has the ability to transform downward motion into forward force and motion.
For example, if we put a body with circular symmetrical profile into a flow, the acceleration of the flow at the it sides will produce two self-balancing sideways lift forces Ry . If the body is with asymmetric semicircular profile, the sideways force Ry will be unbalanced i.e. the downward motion will create sideways force and motion. The same analogy is valid for the classic wing profile, where the roundness around the leading edge creates “forward suction”:
The downward motion is usually driven by the weight force i.e. a weightless wing cannot fly forward and the more loaded is а wing, the bigger forward force and motion it creates:
Usually, in aerodynamic text books and in this material, the force, velocity and acceleration components, which are parallel to the earth surface are called horizontal and are marked with the index "х" . For example Fx , Vx , ax .
The perpendicular to the earth surface components are called vertical and are marked with the index "y" . For example Fy , Vy , ay .
Apart from the "Earth" point of view, exactly the same forces, velocities and accelerations can be seen in relation to the wing surface. The parallel to the wing surface components are called tangential and are marked with the index "T" . For example RT , aT .
The perpendicular to the wing surface components are called normal and are marked with the index "N".
Using wing as reference point with its normal and tangential components of the aerodynamic force is not about making students life difficult. The other components – lift and sink come from driven by engine airplane aerodynamic theory and cannot explain forward motion and other paraglider dynamics.
The wing has the ability to transform initially perpendicular to its surface motion into forward force. This so called inductive ability depends on:
- The shape of the profile. It’s more pronounced with ticker profiles around leading edge;
- Airspeed. The higher, the bigger. That’s why stall recovery of smaller size wings is more aggressive (higher VN causes bigger RT );
- Angle of attack. Too high angles of attack are not the best as they engage only small part of wing surface. Mind that RT force has accumulative effect – the longer you let it work, the bigger acceleration aT and forward motion it will produce.
Induction means indirect influence.
Example of inductive ability:
If we drop a paraglider in the air, it will accelerate downward by gravity. The airflow from bellow will create suction around the roundness of the leading edge, which will accelerate the wing forward. The tangential force RT will add horizontal movement to the vertical fall. Initially 90 ̊, the angle of attack will decrease, but due to the convex shape of the top surface after the leading edge (camber), the tangential force will continue to exist and increase adding more forward motion until balance is reached.
Another example of inductive ability shows that forward force and motion can be created even when the wing is not horizontal:
The inductive ability cannot accelerate the wing infinitively. The more forward motion is added, the more the angle of attack decreases and thus the inductive ability. The rise of airspeed also increases the drag of elements carried by the wing (lines, pilot body, harness). Thus, at a certain moment, force equilibrium is reached and a gliding flight is established – uniform linear forward motion with a slight descent.
Usually, the gliders don’t change their weight during a gliding flight, and even if they do so (e.g. dropping a ballast), this doesn’t change the ratio between acting forces. The ratios are determined by the wing design and can be changed only by changing the angle of attack.
The angle of attack is increased by pulling the brakes, which fold down the trailing edge, increases the profile curve and create drag. The glider goes to a new flight mode with slower speed and descent and steeper gliding trajectory. At certain point, minimum sinking mode (Vy min) is reached, which gives maximum flight time t duration. If we keep pulling the brakes and increase the angle of attack, we’ll reach minimum or stall speed. A stall starts beyond it.
The angle of attack can be decreased by the speed system, where pushing a stirrup with legs, pulls a rope, which pulls consecutively down A, B and C risers. The wing goes into a new flight mode with higher speed and descent and steeper gliding trajectory. With fully applied speed system, we reach minimum angle of attack and maximum speed flying mode (Vx max ).
When the brakes or the speed system are released, balanced (trim) flight mode restores, which is usually the best glide ratio mode (Vx/Vy = max). It gives maximum gliding distance.
Why do we need different flight modes?
Usually, the paragliders are balanced to fly with the best glide ratio (trim speed), but it is calculated in relation to the air or ground, when there is no wind blowing.
When wind blows (an air mass moves along the ground), if it’s headwind, then its speed Vx wind is subtracted from the airspeed Vx, to receive the speed of movement in relative to the ground Vx ground = Vx - Vx wind . And vice versa – if it’s back wind, its speed is added to the airspeed to receive the ground speed Vx ground = Vx + Vx wind .
In both cases, the flight time duration t is the same (speed of descent Vy=const), but we cover different distance along the ground S=Vx ground .t
If headwind speed is higher than the paraglider airspeed, then it will fly backward in relation to the ground (Vx ground < 0), but will have exactly the same airflow and aerodynamic force as in the same flying mode (angle of attack) in no wind or backwind.
When a paraglider flies through sinking air (-Vy wind), it increases its speed of descent in relative to the ground Vy ground (Vy ground = Vy – Vy wind ), reducing the time duration t of the flight and the gliding distance S, despite the ground Vx ground and airspeed Vx remain the same.
And vice versa. When a paraglider flies through rising air (+ Vy wind), this speed is added to the paraglider speed of descent through the air Vy and the paraglider decreases its speed of descent in relative to the ground Vy ground (Vy ground = Vy + Vy wind ). This increases flight time duration t and gliding distance in relative to the ground S.
If the airmass rises faster than the paraglider’s own descent through the air (Vy wind > Vy ), then the paraglider will gain height in relative to the ground (Vy ground > 0 ).
Usually, pilots try to expand their gliding distance by changing the flight modes (angle of attack), which partly compensates or takes advantage of the influence of the wind.
The beginners should remember that in head wind or sink, they’ll fly shorter distance and in backwind and lift they’ll fly longer. The shorter distance means less choice of landing places.
The paraglider has aerodynamic and balance type of control.
The aerodynamic control is activation (movement/bending/folding) of certain areas from wing surface, which changes the magnitude and the focus of the aerodynamic force.
The balanced control is disbalancing the alignment of weight force G and aerodynamic force R, until a new balance (new flying mode) is reached. The disbalance is achieved by moving the weight force center (weight shift).
The paraglider brakes are aerodynamic controls, which work the following way:
The pull of both brakes evenly, folds down the trailing edge and creates a drag, which slows down the glider in relative to the pilot and increases the angle of attack. The increased angle of attack temporarily increases the lift, but also slows down the whole paraglider. If the brakes remain pulled down in a constant position, after a short transition, the paraglider establishes a new flying mode with increased angle of attack, decreased speed and steeper gliding trajectory.
Apart from longitudinal control of flight modes, the brakes are mostly used for stopping self accelerations of the wing due to improper take off, outside disturbances (thermals, gusts) or due to stall recovery. Self accelerations are problem because they cause wing overshooting the pilot and collapsing when reaching negative angles of attack. Pilots have to remember that in most cases, the sudden aggressive overshoots of the glider require more brake pull than possible for a normal flight mode. In order not to stall the wing, the hard braking should be only for a short moment (1 sec) and then brakes need to be released quickly to allow the glider recover its normal airspeed.
If only one brake is pulled, it folds down the trailing edge of the corresponding half wing; it increases its drag and slows down, while the other half wing keeps flying forward with its normal speed. The paraglider turns toward the slowed half wing and keeps turning until the brake is released. When the brake is released, the paraglider leaves the turn tangentially and keeps flying straight forward restoring its balanced flight mode.
Another way of turning is by balance control - applying weight shift turn technique – the pilot shifts his body sideways and moves its centre of weight. This loads half of the wing more than the other half and the glider banks (tilts sideways at an angle gamma - γ). The full aerodynamic force R tilts sideways too. The newly created sideways horizontal component R.sinγ of the full aerodynamic force is added to the initial forward movement and the paraglider turns. The bigger the bank, the bigger the sideways component of R is and the more intensive the turn is.
The wing bank also reduces the vertical component of the full aerodynamic force to R.cos γ , which increases the share of weight force G and increases descend. Simply said, the weight of the pilot is carried by the horizontal projection of wing surface. The bigger the bank, the smaller horizontal projection of wing surface (R.cos γ) opposes the vertical force G. A banked wing is like an overloaded wing - it has higher descent (Vy) and horizontal speed (Vx).
Often, beginner pilots don't pay attention to the increased speed and descent during a banked turn and have to be careful when close to the terrain.
Avoid landing during a turn!
Apart from the weight shift turn, a wing bank can also be achieved by sharp pull of one of the brakes, which slows down the half of the glider and reduces its aerodynamic force. The wing banks because the other half of the wing flies with higher speed and bigger lift.
Beginners should avoid small radius turns by hard pulling of a brake. This, slows down the half wing too much, increasing the angle of attack, leading to a sharp tear of airflow and a stall. The half wing stall is called spin (asymmetric stall) and its recovery is difficult and often has dangerous consequences (big asymmetric collapses, line twists, canopy cravats). There is no such danger with the weight shift turn. Beginner pilots should try to turn with maximum weight shifting and minimum braking. Throughout their development, pilots learn to doze their weight shift and brake application in order to achieve an efficient coordinated turn with minimum sink and radius.
In case of too high rate of turning by progressive braking and banking the wing, the paraglider suddenly enters a spiral – a high speed, descent and G-force autorotation mode. The spiral dive is not as difficult to control as the spin, but it can disorientate, and constrain pilot movements. If the spiral is not exited with sufficient altitude, it can kill by the impact with the ground (Vy = 10-20 m/s , Vx > 60 km/h). Spirals and spins are practices on safety training courses over water (SIV).
Summary, the paraglider control is aerodynamical (brakes), balanced (weight shift turn, speed system) or combined.
Note: This material is written for SkyNomad 6 days paragliding beginners course assuming that this might be the only training opportunity for some of our world wide students. Therefore, this material tries to give the basics of paragliding aerodynamics and most essential safety advices. Paragliding aerodynamics requires more efforts and abstract thinking, than meteorology for example, but once you understand, accept and aware its basics, then you can free yourself from natural fears and progress further. Of course, there are excellent pilots and even champions, who probably don't know the half of what's written here, using their natural tallents, but they cannot teach much others.
Re-reading this material is strongly recommended as its knowledge is quite condensed and every word has its place and meaning.
Keep on learning and fly safe!
Any feedback is welcome.
Nikolay Yotov, 2013; Nikolay Tsarov, 2007