by Nikolay Yotov

PARAGLIDING AERODNAMICS

for beginners

Airflow around a wing, aerodynamic force, lift

            Every object that moves through air interacts with it by creating an aerodynamic force.

            The speed of movement of a wing through the air is called airspeed (V).

Airspeed and aerodynamic force exist, no matter if the wing moves through the air or the air moves around a stationary wing, as in aerodynamic tunnel, for example.

Any force can be split into different components based on different coordinate (reference) systems. The aerodynamic force (R) depends on the direction and speed of movement; the direction and speed of air flow around the wing (the vector of airspeed V). The component perpendicular to V is called lift (R_y), and the component opposite to V is called drag (R_x).  Furthermore, we’ll continue using these popular names, but we must 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 a basic explanation of how a wing works. A wing is more efficient if it produces more lift and less drag.

            Lift can be created by:

• an airflow around a body that is asymmetrically positioned in it;
• an airflow around a body that has an asymmetrical shape;
• a combination of both above – an airflow flowing around an asymmetrically positioned body with an asymmetrical shape.

            When a symmetrical body is placed asymmetrically in airflow, the airflow causes pressure on its exposed surface and creates an aerodynamic force perpendicular to it.

            The angle between the body’s surface and the direction of airflow is called the angle of attack α and is a crucial flight parameter. It determines the direction and magnitude of full aerodynamic force i.e. the magnitude and ratio between its lift (Ry) and drag (Rx) components.

A typical example of an asymmetrically positioned body in airflow 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). Even small angles of attack increase lift and push our hand upward. Higher angles of attack produce more drag and push our arm backward. A 90  ̊angle of attack produces maximum drag and no lift at all. A 0  ̊angle of attack minimizes drag and allows our hand 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 racing car designs, where special spoilers create a downward aerodynamic force, which increase the pressure towards the ground and the friction of the tyres. This allows racing cars to make tighter turns with smaller radii and higher speeds.

            Another way to create lift is through the interaction of airflow with an asymmetrically shaped body. It uses the flow conservation law based on the fact that matter and motion don’t appear from nothing and don’t disappear into nothing i.e. the incoming flow is the same as outgoing flow. As a result, where the flow is restricted, it increases its velocity V, and vice versa:

            You can increase the flow velocity by restricting the exit of a garden hose with your finger, spraying water further away.

The river flow increases its speed where river banks become narrower and slows down where river banks become wider and further apart.

Wind increases over hills and mountain ridges because flow’s cross-sectional area is restricted from below compared to free-from-obstacles airflow at the same altitude.

            You cannot blow a ping pong ball out of a cooking funnel because its greatly widening cross-sectional area rapidly reduces airspeed.

            Parallel to the above processes, in areas where the speed of the fluid (V) increases, the surrounding pressure (p) decreases and vice versa. This is known as Bernoulli’s principle.

Airbrush painting devices use fast airflow to suck paint from below.

If you blow air between two sheets of paper, parallel and close to each other, it decreases the static pressure between them, causing them to come closer, pushed by the relatively higher surrounding 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 and can result in suction, potentially crashing them into each other.

            The classic wing profiles have a convex upper surface, which acts like an obstacle: it reduces the cross-sectional area of the flow, accelerates it, and creates a zone of reduced pressure, sucking the wing upward.

            Usually, the lift creation by airflow around an asymmetric profile is combined with the creation of lift by an asymmetrically positioned body in the flow.

The aerodynamic force R and its components lift and drag depend on:

– wing’s profile;

– angle of attack α;

– square of airspeed V² ;

– wing’s surface area S;

– air density ρ.

            The increase of the angle of attack directly increases lift production, but beyond a certain angle of attack, the airflow above the top surface tears sharply away from the wing, causing it to lose most of its lift. A stall occurs – the wing no longer flies but falls down fast, creating only drag.

            The stall is dangerous, because:

– it develops quickly and suddenly;

– the fall is fast and furious;

– the chaotic flow around the wing makes it difficult to control.

DO NOT FLY WITH TOO HIGH ANGLE OF ATTACK!

As it’s difficult to observe and measure the angle of attack, to avoid stall, it’s easier to pay attention to the airspeed – the feeling of the wind in your face. Any pull of brakes increases the angle of attack and slows down the paraglider.

Thus, if during a gliding flight we:

• feel a slowing down (reduced feeling of wind on the face)
• see our hands pulling the brakes too much, below our hips
• feel the too much resistance from the wing to our brake pull

then we’re close to stall and have to restore our airspeed immediately by releasing the brakes – HANDS UP!

            The stall shouldn’t be confused with a collapse, where the wing reaches a negative angle of attack. The airflow comes from above, deforming and folding the leading edge – the frontal part of the wing. The stall can also deform the wing, but this happens at the trailing edge – the back part of the wing, and the reason is reaching too high angle of attack.

Forward motion

            After learning how the airflow around the wing profile creates lift, keeping us in the air, we may wonder how this airflow is created when there is no engine pushing us through the air?

Why do paragliders fly forward?

            Because the specific wing profile has the ability to transform downward motion into forward force and motion.

            The downward motion is driven by Earth’s gravity and the paraglider’s weight, including the pilot and wing. This downward motion creates an airflow coming from below, which interacts with the specific wing profile to create forward force and motion.

            For example, if we put a body with circular symmetrical profile into a constant vertical flow, the acceleration of the flow around the sides will produce two self-balancing sideways lift forces, R_y . If the body’s profile has a semicircular shape, then there will be only one unbalanced sideways force, R_y, meaning 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 а wing is, the greater forward force and motion it creates:

            The magic is the shape! The wing can be made of wood, sail, metal, fiberglass, but its specific profile shape is what makes it fly forward.

            Two wings with identical shape but different mass glide along the same trajectory, just the heavier one flies faster, both vertically and horizontally.

In aerodynamics, forces, velocities and accelerations, or their components  parallel to the Earth surface, are called horizontal and are marked with the index “х”  (e.g. Fx , V_x , a_x). Components perpendicular to the Earth’s surface are called vertical and are marked with the index “y” (e.g. F_y , V_y , a_y). Apart from the “Earth’s” point of view, exactly the same forces, velocities and accelerations can be seen in relation to the wing surface.  Components parallel to the wing surface  are called tangential and are marked with the index “_T” (e.g. R_T , a_T). Components  perpendicular to the wing surface are called normal and are marked with the index “_N“.

Using the wing as a reference system with its normal R_N and tangential R_T components of the aerodynamic force is needed for explaining the self-driven gliding flight. The other components – lift (R_y) and drag (R_x) come from engine-driven airplane aerodynamic theory and cannot explain the forward motion and paragliding dynamics.

            The wing has the inductive ability to transform normal (perpendicular to its surface) motion and airflow (V_N) into tangential (forward and along its surface) force (R_T). In physics, induction means indirect influence. Indirect, because the object does not move in the same direction as the force acting upon it but it moves in a completely different direction. The gravity pulls the wing downward, but it reacts by going forward. The more you pull it, the faster it flies.

The inductive ability depends on:

•  The shape of the profile. It’s more pronounced with thicker profiles with a bigger top surface curve and roundness around the leading edge;
•  Airspeed. The higher, the stronger the inductive ability. That’s why stall recovery of small-sized wings causes more aggressive forward surges;
• Angle of attack. The higher the angle of attack, the bigger the share of normal component V_N from the overall airspeed V (more air comes from below, perpendicular to the bottom surface). There is an optimum angle of attack range where R_T and inductive ability are the strongest, depending on the shape of the profile. Too high angles of attack are not the best as they engage only a small part of the wing’s surface (the curve at the nose of the profile). Note that forces like R_T have an accumulative effect – the longer you let it work, the greater acceleration a_T and forward motion it will produce.

If we drop a paraglider in the air, it will accelerate downward pulled by gravity. This creates an airflow from below which is additionally accelerated by the roundness of the leading edge, creating suction and forward force there. This tangential force R_T will add horizontal motion to the vertical fall. Initially 90  ̊, the angle of attack will decrease, and airflow will come from a new direction, engaging a larger part of the curved top surface behind the leading edge (camber). This adds more forward motion, which further engages the top surface and starts producing lift until a balance is reached. The vertical fall transforms into a gliding flight forward.

            Another example of inductive ability is the rising of the wing during takeoff. It demonstrates that the forward force and motion can be created without using gravity as an engine when the wing is not horizontal:

            The inductive ability explains a lot in paragliding! It helps understand what happens if you sit too early at takeoff, paraglider’s stability and behaviour in thermals and turbulence, wind gradient effect, acrobatics, spirals, stalls, spins, collapses, take offs when pulled by a winch, why shark-nose profiles are more prone to stall, etc. etc.

Gliding flight

            The inductive ability cannot accelerate the wing indefinitely. The more forward motion is added, the more the angle of attack decreases, directly reducing the forward motion engine – the tangential force R_T. The rise of airspeed also increases exponentially (V²) the drag of elements carried by the wing – lines, pilot’s body, and harness.  Thus, at a certain moment, equilibrium of forces is reached, and a gliding flight is established – uniform linear forward motion with a slight descent.

            Usually, 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 only way to change a paraglider’s gliding trajectory is to change its angle of attack.

The angle of attack can be increased by pulling the brakes. This folds down the trailing edge, increases the profile curve, and its interaction with airflow. A more curved profile produces more lift but also more drag. The glider goes to a new flight mode with slower speed and descent and with steeper gliding trajectory. At a certain point, the minimum sink mode (V_{y min}) is reached, which gives maximum flight time duration (t). If we continue pulling the brakes and increase the angle of attack, we’ll reach the 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 our 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 also a steeper gliding trajectory. With the fully applied speed system, we reach the minimum angle of attack and the maximum speed flying mode (V_{x max} ).

When the brakes or the speed system are released, balanced (trim) flight mode restores, which is usually the best glide ratio mode (V_x/V_y = max). It gives maximum gliding distance.

            Regardless of the flying mode, the gravity and the inductive ability are the engine of the gliding flight. The height is the fuel.

            Why do we need different flight modes?

            Usually, the paragliders are balanced to fly at the best glide ratio (trim speed), but this is in relation to the air or to the ground when there is no wind. 

            When the wind blows (the air mass moves along the ground), if it’s a headwind, then its speed (V_{x wind}) is subtracted from the horizontal component of airspeed (V_x) to obtain the speed of movement relative to the ground V_{x ground} = V_x – V_{x wind} . And vice versa – if it’s  back wind, then its speed is added to the airspeed to obtain the ground speed V_{x ground} = V_x + V_{x wind} .

            In both cases, the flight duration time (t) is the same (speed of descent V_y=const), but we cover different distance (s) along the ground as s=V_{x ground} .t

            If the headwind speed is higher than the paraglider’s airspeed, then we will fly backward in relation to the ground but forward in relation to the air. The airspeed, or the feeling of wind on pilot’s face, is the same, whether flying with a 20 km/h backwind, no wind, or with a 300 km/h headwind because there is exactly the same airflow, angle of attack, and aerodynamic force. The paraglider’s weight (G), wing’s profile and inductive ability make it move through the airmass, which has its own movement relative to the ground.     

            When a paraglider flies through sinking air (-V_{y wind}), it increases its speed of descent relative to the ground (V_{y ground} = V_y – V_{y wind} ), reducing the flight duration time (t) and distance (s), while the ground speed (V_{x ground}) and airspeed (V_x) remain the same.  

            And vice versa. When a paraglider flies through rising air (+ V_{y wind}), this speed is added to the paraglider’s speed of descent through the air V_y , and the paraglider decreases its speed of descent relative to the ground (V_{y ground} = V_y + V_{y wind} ). This increases flight duration time and distance relative to the ground.

            If the airmass rises faster than the paraglider’s own descent through the air (V_{y wind} > V_y ), then the paraglider will gain height relative to the ground (V_{y gr} > 0 ).

            Again, no matter if we fly in rising or sinking air, the angle of attack, aerodynamic force, airspeed and feeling of wind in our face is the same, determined by our flying mode – how much brakes or speed system is applied.

            Usually, pilots try to increase their gliding distance by changing the flight mode (angle of attack), which partly compensates for or takes advantage of the influence of the wind. If we want to glide further, we should fly slower in backwind or rising air and faster in headwind or sinking air.

            Beginners should remember that in head wind or sink, they’ll fly shorter distance and in backwind and lift they’ll fly longer. So, they should be prepared to land in different place, than initially planned. The shorter gliding distance also means less choice of landing places.

Paraglider control

            The paraglider has two types of control: aerodynamic and balanced.

            Aerodynamic control is activating by moving or bending a part of the wing’s surface, which changes the magnitude and direction of the aerodynamic force.

            Balanced control is unbalancing the alignment of weight force G and aerodynamic force R, until a new balance (flying mode) is reached. The aerodynamic force is applied at the paraglider’s centre of pressure (CP), while the weight force G is applied at the centre of weight (CG), located somewhere above the pilot’s belly button. Balanced control is achieved by weight shifting of pilot’s body.

            The paraglider brakes serve as aerodynamic controls and work in the following way: pulling both brakes evenly folds down the trailing edge, creating creates extra drag, which slows down the wing relative to the pilot. This increases the angle of attack, temporarily increasing its lift but also slowing down the whole paraglider. If the brakes remain pulled down at a certain position, after a short transition, the paraglider establishes a new flying mode with increased angle of attack, decreased airspeed and steeper gliding trajectory.

Flying at a slower airspeed with steeper gliding trajectory is mostly used during landing, when we want to land shorter to avoid overshooting the landing spot. However, flying at a slower speed brings us closer to stall speeds, making the the paraglider more vulnerable to turbulence and wind gradient effects. The slower airspeed also results in decreased internal pressure, making the canopy  more prone to collapses.

            Apart from long-lasting control of flight modes, the brakes are mostly used briefly to stop self-accelerations of the wing due to external disturbances (thermals, gusts, turbulence), or improper piloting (take-offs, stalls, spiral exits, acrobatics).  Paraglider’s self-accelerations are problematic because they make the wing overshoot the pilot, leading to a potential collapse if it reaches negative angles of attack. The sudden aggressive overshoots of the wing usually require an aggressive deep pull of brakes, sometimes beyond normal flight mode. To prevent stalling the wing, hard braking should be only for a short moment (1 sec), and then the brakes need to be released to allow the glider to recover its vital airspeed. The pitch-control exercise of SkyNomad’s Active Flying course teaches pilots about the safe limits of brake pulls and the fun of paraglider’s dynamics.

            If only one brake is pulled, it folds down the trailing edge of the corresponding half-wing. This increases its drag and slows it down, while the other half-wing continues flying forward with its normal speed. The paraglider turns toward the slowed side of the 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 normal flight mode.

            Another way of turning a paraglider is through balanced control, using the weight-shift turn technique. The pilot shifts its body sideways, moving the centre of weight. This loads one half of the wing more than the other, causing that side to rises and the paraglider banks (leans, tilts) sideways at an angle γ from the vertical position. 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 motion causing the paraglider to turn. The greater the bank angle, the larger the sideways component of R, and the more intensive the turn becomes.

            A proper weight shift turn requires the pilot to lean fully sideways. Crossing the outer leg over the inner one adds more weight shift. Beginner pilots need to trust their harness, which holds their body secure while leanning sideways. Stable beginner’s EN A paragliders are more difficult turn by weight shift compared to sensitive high-performance EN D wings.

            The weight of the pilot is carried by the horizontal projection of the wing’s surface. The wing bank reduces vertical component of the full aerodynamic force to R.cos γ, which opposes weight G, and this increases paraglider’s descent. A banked wing is like an overloaded wing – it has higher descent rate (V_y) and horizontal speed (V_x).

Often, beginner pilots don’t pay attention to the increased speed and descent during a banked turn. They should be careful when flying close to terrain because every turn causes extra descent. Avoid turning close to the ground!

Apart from the weight shift turn, a wing bank can also be achieved by a deep pull of one of the brakes, slowing down this half of the wing and reducing its aerodynamic force. The wing banks because the outer part of the wing flies normally, with higher airspeed and greater lift.

Beginner pilots should avoid making small-radius turns by hard pulling on a brake, as this may increase the angle of attack too much, and lead to a sharp tear of airflow and stall. This may slow down the half of the wing and increases its angle of attack, leading to a sharp tear of airflow and stall. The half-wing-stall is called spin, as it spins the wing around its vertical axis. The spin is more dangerous than stalls or collapses due to its aggressive behaviour, which can lead to a cascade of big asymmetric collapses, stalls, line twists, and canopy cravats. There is no such danger with the weight shift turns, so beginners should turn with maximum weight shifting and minimum braking. In paragliding, turns begin with weight shift first, followed by a brake pull. 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, far from stall speeds and angles of attack.

            Apart from spin, a prolonged hard pull of the brake can cause such an intensive turn, which suddenly may become a spiral dive – a high-speed descent and G-force autorotation manoeuvre. The spiral dive is not as difficult to control as the spin, but it can disorient and restrict pilot movements. The 2-3 G forces during a spiral can lead to loss of vision and blackout to untrained pilots. If the spiral is not exited with sufficient altitude, it can kill the pilot by the impact with the ground (V_y = 10-20  m/s , V_x > 80 km/h). The spiral is a commonly used technique for rapid descent, for example, when escaping a thunderstorm’s cloud suck. SkyNomad’s Active Flying course teaches students how to do spirals. Stalls and spins are practices separately, on safety training courses over water (SIV).