Private Pilot · Unit 2 · 30 min

How a Wing Generates Lift

The last lesson treated lift as a given. This one explains where lift comes from: two pieces of physics, the shape that exploits them, and the factors, some designed in and some in your hands, that decide how much lift you get.

Two pieces of physics

The production of lift is a complex phenomenon and can get extremely technical. For a pilot's purposes, two pieces of classical physics explain it well.

Newton's laws of motion

In the 17th century, Sir Isaac Newton presented three principles of motion:

• First law: a body at rest tends to remain at rest, and a body in motion tends to keep moving at the same speed and in the same direction. You met this one in The Four Forces of Flight: balanced forces mean nothing changes.
• Second law: when a force acts on a body, the resulting acceleration is proportional to the force and inversely proportional to the body's mass: the familiar F = ma.
• Third law: every force applied to a body is opposed by an equal force in the opposite direction. For every action, an equal and opposite reaction.

The third law matters most here. If a wing can be made to push air downward, the air must push the wing upward with equal force.

Bernoulli's principle

The second piece is named after Daniel Bernoulli, a Swiss mathematician. Simply stated: as the velocity of a fluid increases, its pressure decreases.

The figure below shows air moving through a tube with a constriction in the middle; such a tube is called a venturi. The fluid enters with a certain velocity and pressure. In the constriction it speeds up, and the gauges show what Bernoulli predicts: as the velocity rises, the pressure falls. Past the constriction the flow slows again, and the pressure recovers to its original value.

Hold onto that trade between speed and pressure. A wing is about to perform the same trick without the tube.

PHAK Ch 4, "Bernoulli's Principle"

The airfoil

An airfoil is a structure designed to obtain a useful reaction from the air moving past its surface. Slice a wing from front to back and the airfoil is the cross-section you get. Its parts have names, and the knowledge test uses all of them:

• The leading edge meets the airflow first; the trailing edge is where the flows over the upper and lower surfaces rejoin and leave.
• The chord line is an imaginary straight line connecting the two edges.
• Camber is the characteristic curve of the upper and lower surfaces. The mean camber line runs midway between the two surfaces, and the point where it bows farthest from the chord line is the maximum camber.

No single airfoil satisfies every flight requirement. The weight, speed, and purpose of each aircraft dictate the shape of its airfoil, from the deeply cambered sections of early airplanes to the thin symmetrical shapes of supersonic designs.

When the airfoil moves through the air, the flow divides at the leading edge. One stream runs along the lower surface; the other is diverted up and over the top, a flow called upwash. The streams rejoin at the trailing edge, and the combined flow leaves deflected downward. That departing, downward-bent flow is the downwash, and by Newton's third law, the wing's push on that air is answered by the air's equal push up on the wing.

PHAK Ch 4, "Airfoil Design"

Angle of attack

Understanding angle of attack is crucial to understanding how airplanes fly, which is why this course keeps returning to it. The angle of attack is the angle between the chord line and the relative wind, the airflow parallel to and opposite the airplane's flight path. Lift always acts perpendicular to the relative wind. And lift is proportional to the angle of attack: raise it and lift increases, up to a point this lesson reaches shortly.

Pressure distribution and the center of pressure

Here is where Bernoulli and Newton meet. The airfoil's shape and angle of attack make the air accelerate over the upper surface and decelerate along the lower one. Faster air above means lower pressure above; slower air below means higher pressure below. Around the airfoil, some regions sit at pressures above atmospheric and others below it, and the net force from all of those differences is the total lift the airfoil generates.

To simplify, we treat all of that distributed force as acting through a single point: the center of pressure. The point moves. Raise the angle of attack and the center of pressure moves forward along the chord, toward the leading edge; lower it and the center of pressure moves aft. Designers care about the limits of that travel because it affects the airplane's stability, and the lesson on stability and center of gravity picks the thread back up.

The full account of lift, then, has two components working together: the pressure difference (Bernoulli) and the reaction to downwash (Newton). Airfoils are designed to exploit both.

PHAK Ch 4, "Airfoil Behavior"; PHAK Ch 5, "Center of Pressure"

The coefficient of lift

Airfoils are tested in wind tunnels, and one measured number is key to understanding an airfoil's performance: the coefficient of lift (C_L), which relates the lift the airfoil produces to its angle of attack.

Follow the red lift curve: it climbs steadily, more angle of attack meaning more lift. Then it peaks. (The chart also traces the drag coefficient, which rises the whole way; drag gets its own lesson.) That peak is C_Lmax, the most lift this airfoil can produce, and the angle where it happens is the critical angle of attack. Any increase beyond the critical angle does not level lift off; lift decreases sharply, because the smooth airflow separates from the upper surface. That separation and loss of lift is the stall. It happens at the same angle of attack every time, regardless of airspeed, attitude, or weight, and it gets the whole of the next lesson.

PHAK Ch 5, "Lift"

The lift equation, and the pilot's share of it

Aerodynamicists compress all of this into one line:

Lift = C_L × ½ ρ V² × S

You will never compute it in the cockpit, but every factor in it is either set by the day or flown by you:

• C_L captures the airfoil's shape and its angle of attack. You control it with pitch: change the pitch attitude and you change the angle of attack.
• ρ (rho) is the air density, set by altitude, temperature, and humidity. Thin air makes less lift at the same speed and angle of attack, which is why hot days and high airports demand longer runways. Unit 9 turns this into numbers.
• V² is the airspeed, squared. At 120 knots a wing generates four times the lift it generates at 60 knots. The same relation runs in reverse: a 10 percent loss of airspeed on final costs about 19 percent of the lift.
• S is the wing area, fixed by the designer until you lower the flaps.

Total lift depends on both angle of attack and airspeed together. To hold level flight while slowing down, you must trade one for the other: as airspeed falls, the angle of attack has to rise to make up the difference. Every approach to landing is that trade, flown smoothly.

PHAK Ch 5, "Lift"

High-lift devices

Flaps exist to bend this equation in your favor at low speed. Lowering flaps increases the wing's camber, and with it the coefficient of lift, so the wing can produce the lift you need at a lower airspeed. That reduces the stall speed too, which is what lets you fly a slow, controllable final approach.

Designers have built the idea several ways. The plain flap hinges the trailing edge down; the split flap deflects only the lower surface; the slotted flap (the 172's kind) opens a gap that ducts high-energy air over the flap and delays separation; and the Fowler flap slides aft on tracks, growing the wing's area as well as its camber.

PHAK Ch 6, "Flaps"

How wings are designed

Before the airplane ever reaches you, its designer chose four things about the wing, and each choice shows up in how it flies:

• Camber. Increase the upper camber and the velocity difference between the surfaces grows, and lift with it, up to the point where the curvature starts disturbing the smooth flow.
• Aspect ratio: the wingspan divided by the average chord. At a given angle of attack, a higher-aspect-ratio wing lifts more efficiently, producing more lift for the same drag. Gliders run aspect ratios of 10 to 30; training airplanes sit around 6 to 10.
• Wing area. The wing must carry the whole airplane. Trainer wings produce roughly 14 pounds of lift per square foot, so supporting a 2,450-pound airplane takes about 175 square feet of wing.
• Planform: the wing's shape viewed from above. Elliptical wings are aerodynamically ideal but hard to build, and they stall near the tips first. Rectangular wings stall at the root first, which gives early warning while the ailerons keep working. Most trainers blend a rectangular inner section with tapered outer panels.

How designers arrange for the root to stall before the tip, using wing twist and stall strips, belongs to the next lesson, where the stall gets its full treatment.

PHAK Ch 5, "Wing Design"

Check your understanding

Answer from memory, without scrolling back up. Recalling it yourself is what makes it stick.