Module 01
Flight theory (aerodynamics)
How a paraglider flies. Speeds, angle of attack, lift and drag, the polar curve, wing loading, and why the same wing behaves differently at altitude or when wet. This is the biggest section of the P4 exam (25 questions) and about a quarter of the P2.
What is in this module
Three speeds: wind, air, ground
Every pilot knows this with the body. The exam tests whether you know it with words and numbers.
- Wind speed is how fast the air moves over the ground.
- Airspeed is how fast the wing moves through the air. It is the speed the glider feels. Lift, drag, stall: all depend only on airspeed.
- Groundspeed is how fast you move over the ground. It is what a GPS shows. Groundspeed only matters for going somewhere and for landing.
The river picture
Imagine a boat on a river. The boat's engine gives it a speed through the water (airspeed). The river carries the boat along (wind). A person on the bank sees the boat's speed over the ground (groundspeed). The boat does not feel the river. The wing does not feel the wind. The wing only feels its airspeed.
The formula. Groundspeed = airspeed − headwind, or airspeed + tailwind.
| Situation | Airspeed | Wind | Groundspeed |
|---|---|---|---|
| Trim speed 32 km/h, headwind 8 km/h | 32 km/h | −8 | 24 km/h |
| Trim speed 32 km/h, tailwind 8 km/h | 32 km/h | +8 | 40 km/h |
| Trim speed 34 km/h, headwind 34 km/h | 34 km/h | −34 | 0 (you hang in the air, "parked") |
| Airspeed 36 km/h, headwind 40 km/h | 36 km/h | −40 | −4 km/h (you go backwards) |
Working backwards: how far above stall am I?
A glider flies downwind with a groundspeed of 50 km/h. The wind is 20 km/h. Stall speed is 25 km/h. How many km/h above stall is it? Airspeed = groundspeed − tailwind = 50 − 20 = 30 km/h. Stall is 25, so the margin is 5 km/h. Notice: it looks fast over the ground, but the wing is close to stall. This is the downwind stall trap.
Turning downwind does not change your airspeed
After you turn downwind, your groundspeed becomes faster. Your airspeed stays the same, if you keep the same brake position. Pilots see the ground rushing past, feel "too fast", and pull brake. Now the airspeed is slow, and the wing can stall. The downwind stall is caused by the pilot being fooled by groundspeed changes, not by airspeed changes.
Must-pass idea: wind is not the same everywhere
The wind at launch is never guaranteed to be the wind at the landing field. Wind changes with height (wind gradient), with terrain (venturi, rotor, wind shadow), with the time of day (valley winds, thermals) and with distance. A P2 † question tests exactly this: "The wind speed and direction are always the same in the landing field as at launch." False. Always look for wind indicators at the landing field before you commit.
How the wing makes lift
Air flows toward the wing. The angle of attack (AoA) is the angle between the wing's chord line (the straight line from the front edge to the back edge) and the air coming toward it (the relative wind).
- Small AoA → air flows smoothly over and under the wing → lift, low drag, faster.
- Bigger AoA → more lift and more drag → slower.
- Too big → the airflow cannot stay attached to the top of the wing. It breaks away. Lift collapses, drag becomes huge. This is a stall.
Where does the lift act? All the small lift forces along the wing add up to one force acting at one point: the centre of pressure. (The centre of gravity is different: that is where the weight acts, at the pilot.)
What do the brakes do? Pulling the brakes pulls the back edge of the wing down. This increases the angle of attack and increases drag. So the glider slows down for both reasons: more AoA and more drag. Pull too far and you pass the stall angle.
Must-pass idea: never hold the brakes fully down in the air
The most dangerous thing you can do at any height except flare height is to pull the control toggles all the way down. That stalls the wing. At flare height (the last metre) it is the correct landing technique. Anywhere else it is a stall. The P1 and P3 exams both test this as a † idea, and the P3 operating limits say: avoid applying either brake beyond ¾ of the way from full off to stall position.
Stall: the facts the exam wants
- A wing always stalls at the same angle of attack. It does not always stall at the same speed.
- Signs of a coming stall: slow airspeed, sluggish, heavy handling, the wing feels "mushy", then a sudden decrease in lift (the wing drops back). A low angle of attack is not associated with a stall.
- A stall is most dangerous near the ground: launch, landing approach, scratching close to a ridge.
- The only time you intentionally slow to a stall is just before landing (the flare).
- A spin is a stall of one side only: the inside wing stalls and the glider rotates around it. Recovery: hands up, let both sides fly again.
- Deep stall (parachutal stall): the whole wing has stopped flying forward and descends like a parachute, very high angle of attack, almost no forward speed, brakes feel light. Recovery: lower the angle of attack (push the A-risers, use speed bar, hands fully up). Do not pull brake.
Wet wing, heavy pilot, high altitude: same angle, different speed
Anything that makes the wing need more lift or gives it less air raises the stall speed (the airspeed at which the stall angle is reached):
- Heavier pilot (higher wing loading) → stalls at a faster airspeed.
- Wet wing → heavier and the fabric breathes differently → stall speed increases, and a deep stall is more likely. (Wet lines can also shrink.)
- High altitude, hot day → thin air → every true airspeed is higher, including the stall speed. You need a faster run at launch and you land faster.
The polar curve and the important speeds
A polar curve shows the sink rate of a glider at each airspeed, in still air, in straight stabilised flight, for one wing loading. Every important speed is a point on it.
| Speed | What it is | When to use it |
|---|---|---|
| Stall speed | Slowest speed the wing can fly. Below it, no more lift. | Never, except the flare. |
| Minimum sink speed | The speed where you go down slowest. A little faster than stall. Some brake. | To stay up longest: thermals, weak lift. But the wing is close to stall and handling is sluggish. |
| Trim speed | The speed with no brake input, "hands up". Set by the manufacturer. | Normal flying. Trim is between minimum sink and best glide on most wings. |
| Best glide speed (best L/D) | The speed where you go furthest forward for each metre of height, in still air. | To fly furthest in still air, to get away from a hill, to reach a landing field. |
| Top speed | Full speed bar. | To penetrate strong headwind, to escape lift or a cloud, to get out of sink quickly. Beware: the wing is less stable at full speed. |
Longest time in the air is NOT the same as longest distance
- Most time aloft → minimum sink.
- Most distance in still air → best glide (best L/D). Best glide is a little faster than minimum sink. So if you are flying at minimum sink and want maximum glide, you fly slightly faster.
- Best manoeuvrability (the wing answers your inputs quickly) → around best glide, not at minimum sink where the wing is sluggish and close to stall.
L/D ratio (glide ratio). Lift divided by drag, which is the same as distance forward divided by height lost. A glide ratio of 8:1 means 8 m forward for every 1 m down. Best L/D is the best glide ratio the wing can do.
Speed to fly: headwind, tailwind, sink and lift
The polar tells you the best speed in still air. In real air you adjust:
| Air | Best speed for distance over the ground | Why |
|---|---|---|
| Headwind | Faster than best glide | The wind eats your groundspeed. Spending less time in the air loses less ground to the wind. |
| Tailwind | Slower (toward minimum sink) | The wind helps you; stay up longer and let it carry you. |
| Sinking air | Faster | Get through the bad air quickly. Time in sink costs height. |
| Rising air | Slower (minimum sink) | Stay in the good air longer. |
Exam-style example
To cover the most ground into a headwind, in a glider whose best glide speed is 40 km/h, the pilot should fly at… more than 40 km/h. Into wind, best glide over the ground is always faster than best glide in still air.
A glider in rising air still sinks relative to the air. If the air rises faster than the glider sinks, you climb relative to the ground. The glider always descends compared to the air around it.
The polar and the angle of attack when the air moves
Must-pass idea: what happens to the angle of attack in lift and sink
Flying into rising air, the air meets the wing more from below: the angle of attack increases, lift and drag increase (the resultant force grows), and the wing pitches back. Flying into sinking air, the angle of attack decreases and the wing surges forward. The P4 marks this as a † question. Learn the pair: lift → angle of attack up; sink → angle of attack down.
When you fly into rising air, the air now comes at the wing from a little more below. The angle of attack increases, lift increases, and the wing pitches back a little (you feel pushed up, the wing "hangs back"). When you fly into sinking air, the angle of attack decreases and the wing surges forward. This is why active flying works: in lift, you may ease the brakes; in sink or when the wing surges, you check it with a little brake.
Drag: the two kinds
- Parasitic (form or shape) drag: from the shape of everything that is not making lift: your body, the harness, the lines, the fabric. Sitting upright on final glide increases your shape drag. Fewer, thinner lines and a smooth harness reduce it.
- Induced drag: the price of lift. It comes from the lift itself (mainly from the air spilling around the wing tips as vortices). It is biggest at slow speed and high angle of attack, smallest at high speed.
Total drag = parasitic + induced. The best glide speed is where the total is lowest compared to lift.
Drag grows with the square of speed
Double the airspeed → four times the drag (and four times the turbulence behind an object). Wind of 40 km/h makes 4× the drag and turbulence of 20 km/h. Three times the speed → nine times. Exam questions say "an airflow of 40 km/h produces 4 times as much drag as 20 km/h" → true.
Wing loading
Wing loading = total flying weight ÷ wing area (kg per m²). A heavier pilot on the same wing = higher wing loading. Compare two identical gliders, one flown heavy (high loading) and one light (low loading):
| Effect of higher wing loading | Result |
|---|---|
| Every speed on the polar (stall, minimum sink, trim, best glide, top) | Faster |
| Minimum sink rate | Higher (sinks faster) |
| Best glide ratio (L/D) | The same (in theory; the whole polar shifts, its shape does not change) |
| Stall angle of attack | The same |
| Stall speed | Higher |
| Control and stability in turbulence | Better: more solid, more responsive, less collapse-prone |
| Turn rate for a given bank | Faster |
Three classic exam puzzles about wing loading
- Two identical gliders, different weights, fly at the same airspeed toward a distant cloud. At normal transition speed (faster than best glide for the light pilot), the heavy glider is closer to its own best glide, so it glides better: the lighter pilot arrives lower.
- Two identical gliders, different loading, enter a big area of lift at minimum sink. The lighter glider has the lower minimum sink rate, so it gains the most height.
- How does a heavy pilot stall compared with a light pilot? At the same angle of attack but a faster airspeed.
A pilot has more control of the glider when wing loading is high (within the certified range). Flying at the very light end of the weight range makes the wing feel floaty and is a common cause of pilot-induced oscillations.
Aspect ratio, stability, turns
Aspect ratio = span² ÷ area. A wing with a 10 m span and 25 m² area has an aspect ratio of 100 ÷ 25 = 4.0. Higher aspect ratio → better glide, less induced drag, but less stable and harder to recover from collapses.
Inherent (positive) stability means: after a disturbance, the glider returns to normal flight by itself, in pitch, roll and yaw. A paraglider has strong pendulum stability because the pilot hangs far below the wing.
Axes of movement: pitch (nose up and down), roll (one wing tip up, one down), yaw (nose turns left or right).
Turns. You start a turn with weight shift and inside brake. The inside wing slows and its drag increases, so the glider slips into the turn at first. In a steep turn the wing must make more lift (load factor rises), so the stall speed rises. This is why steep turns close to the ground are dangerous. A spiral is a steep, fast, diving turn that can keep steepening by itself; you exit with weight shift to the outside and outside brake, gradually.
Pilot-induced oscillation (PIO): swinging from side to side under the wing. It is caused by quick, stabbing brake inputs followed by badly timed corrections. Fix: smooth, slow inputs; if in doubt, hands up and let the pendulum stability calm the wing.
Control inputs should be smooth and slow, not quick and short, not long and deep. Quick inputs at the wrong time create oscillations.
Altitude, temperature and air density
Thin air makes less lift at a given true airspeed. Air is thin when it is high and when it is hot. So:
- A high-altitude launch needs a faster run: the wing must move faster through the thin air to make the same lift. Your groundspeed at lift-off and landing is higher than at sea level.
- The worst performance condition is high altitude in hot weather (both make the air thin). The best is low altitude in cold weather.
- Your indicated airspeed (the airspeed the wing "feels") for stall, trim and best glide does not change. The true airspeed and groundspeed do.
Nepal bridge: Sarangkot is high, Canada is often higher
Sarangkot launch is about 1,500 m (5,000 ft) ASL, so you already know the faster run and the faster landing of altitude. Many Canadian mountain sites are 2,000–2,500 m ASL and it can be 30 °C at launch. Expect an even longer run. Also, in Canada you can climb legally to 10,000 ft (3,000 m) and, with oxygen rules, higher: Module 09 covers hypoxia.
Ridge lift: the two conditions for soaring
To soar on a ridge you need both:
- A glide ratio better than the slope of the hill (or you fly into the hill), and
- A sink rate less than or equal to the upward part of the wind blowing up the slope.
Ridge lift is strongest where the wind hits the slope squarely (perpendicular) and where the slope is steep: a cliff gives the most lift for a given wind because more of the wind is turned upward.
Wing damage and tangles: how the wing reacts
- A tangle (knot) in two A-lines on the outer left side pulls that part of the leading edge down: the glider tends to turn left.
- Tangled or damaged lines must be replaced with original manufacturer parts: line length and stretch (elasticity) are part of the design. A "stronger" or "thicker" line is not safe.
- A glider that consistently turns one way with brakes off has a problem (trim, lines, damage). Take it to the dealer. Do not fix it by shortening a riser or tightening a leg strap.
- The stress on the ribs is greatest at the line attachment points in the front half of the canopy, where the loads are highest.
Key numbers from this module
- Groundspeed = airspeed − headwind (+ tailwind). The wing only feels airspeed.
- Drag ∝ speed². Double speed → 4× drag.
- Aspect ratio = span² ÷ area (10 m span, 25 m² → 4.0).
- Glide ratio 8:1 → 8 m forward for 1 m down.
- Speed to fly: headwind or sink → faster; tailwind or lift → slower.
- Longest time → min sink. Longest distance (still air) → best glide. Best control → around best glide.
- Heavier: all speeds up, sink rate up, same best L/D, same stall angle, higher stall speed.
Check yourself
These are practice questions written for this guide. They are not the exam questions. Answer, then read the explanation, even when you are right.