Chapter 5 · Four forces, one wing
How planes fly
Four forces in balance
Every aircraft has four forces acting on it. Lift pushes it up, weight pulls it down, thrust from the engine or propeller pulls it forward, and drag, the push of the air, holds it back. In steady level flight they balance in pairs: lift equals weight, and thrust equals drag. For a small plane of 1,100 kg the weight is W = m·g = 1,100 × 9.81 ≈ 10,800 N, so the wings must give exactly that much lift. If lift is bigger, the plane climbs; if it is smaller, it sinks. The glowing arrows in the picture are drawn to scale, so watch them grow and shrink as the plane climbs or dives.
Air turned downwards
A wing works by turning air. Its curved top and slightly tilted front push the passing air down, and, as Newton's third law says, the air pushes the wing up. The streamlines in the picture bend over the airfoil, the wing's cross-section, and leave it heading downwards. Lower pressure above the wing and higher pressure below it describe the same push in another way. More air turned more sharply means more lift, and that is exactly what the next formula counts.
The lift formula, with numbers
Engineers write lift as L = ½·ρ·v²·S·C_L. Here ρ (rho) is air density, 1.225 kg/m³ at sea level, v is the speed in m/s, S is the wing area and C_L is the lift coefficient, which depends on the wing's shape and angle. Take a light aircraft with S = 16 m² and C_L = 0.5. For level flight, L must equal 10,800 N, so v² = 2 × 10,800 / (1.225 × 16 × 0.5) ≈ 2,204, and v ≈ 47 m/s, about 169 km/h. Because v is squared, doubling the speed gives four times the lift.
Tilting the wing until it stalls
The angle between the wing and the oncoming air is the angle of attack. Raise it a little and C_L grows. At C_L = 1.5 the same plane needs only v ≈ 27 m/s, about 98 km/h. But C_L rises almost in a straight line with the angle only up to about 15 to 16 degrees for many wings. Past that critical angle the air can no longer follow the curve. It separates from the surface and breaks into turbulence, and the lift collapses. This is a stall. Often one wing stalls first, so the plane drops that wing and falls. In the picture it tips over and sinks.
Undoing the stall, then trying it
To recover, the air must cling to the wing again, so the angle of attack has to come down. First lower the nose, even though the ground is below. Next bring the wings level. Then add power so that thrust builds the speed back up. Only when the wing is flying again does the nose rise gently. Pulling up too early brings the stall back. Now rescue the plane yourself in the simulator under the picture. It starts in a stall and falls. You control pitch and throttle. This is a game of physics, not a flying lesson: real pilots learn it with an instructor.
Flying without an engine
What if the engine stops? The plane does not drop like a stone. It glides: the wing keeps making lift and drag, and the plane settles onto a gentle slope. The glide ratio says how far you go forward for each unit you sink. A ratio of 15:1 means 15 km forward for 1 km of height lost. A sailplane is built for this and reaches 40:1 to 60:1. An airliner manages about 15:1 to 20:1. From 10 km up, an airliner at 15:1 can glide about 150 km with no engine at all.
The Gimli Glider
On 23 July 1983 an Air Canada Boeing 767, flight 143, ran out of fuel at about 12,500 m after a mix-up between pounds and kilograms. Both engines stopped. Captain Robert Pearson, who was also an experienced glider pilot, and first officer Maurice Quintal had to find a runway. They glided the airliner to a former air base at Gimli, Manitoba, and landed it. All 69 people aboard survived, and the aircraft became known as the Gimli Glider. It shows that lift and drag keep working even when the engines do not.
In numbers
- 47 m/s
- level-flight speed in the worked example
- 15–16°
- angle of attack where many wings stall
- 40–60:1
- glide ratio of a good sailplane