4.lift-and-bernoulli. Lift and Bernoulli's Principle
Lift is the upward aerodynamic force that opposes weight and supports the airplane in flight. It is produced by the dynamic effect of air acting on the wing (airfoil) and acts perpendicular to the flight path through the wing's center of lift. Two complementary physical principles explain how a wing generates lift: Bernoulli's principle and Newton's third law of motion. The PHAK presents both because each captures part of the same phenomenon.
Bernoulli's Principle. In a steady flow of a fluid, an increase in velocity is accompanied by a decrease in static pressure (and vice versa), so that the total energy of the flow remains constant. Expressed simply:
static pressure + dynamic pressure = total pressure (constant)
A classic demonstration is the venturi tube. As air flows through the constricted throat of the venturi, the streamlines are forced closer together, the velocity increases, and the static pressure drops. A wing works on the same principle. The cambered upper surface of a typical airfoil acts like one half of a venturi, with the free airstream above acting as the other boundary. Air accelerating over the curved upper surface experiences a reduction in static pressure, while the relatively slower air beneath the wing remains at higher pressure. This pressure differential between the lower and upper surfaces produces lift.
Newton's Third Law. For every action there is an equal and opposite reaction. A wing meeting the relative wind at a positive angle of attack deflects a mass of air downward (downwash). The reaction to accelerating that air mass downward is an upward force on the wing. Mathematically, the lift force equals the time rate of change of momentum imparted to the air. Both explanations describe the same flow field — the pressure distribution that Bernoulli describes is what physically produces the downwash that Newton describes.
The Lift Equation. Pilots should recognize the standard lift formula because it identifies every variable a pilot can influence:
L = CL × ½ρV² × S
Where:
- L = lift (lb)
- CL = coefficient of lift (a function of airfoil shape and angle of attack)
- ρ (rho) = air density (slugs/ft³)
- V = true airspeed (ft/s)
- S = wing surface area (ft²)
The term ½ρV² is dynamic pressure (often called q). Several practical truths fall out of this equation:
- Lift varies with the square of velocity. Doubling airspeed quadruples lift at a given angle of attack.
- Lift varies directly with air density. On a hot day, at high field elevation, or with high humidity, density drops, so for the same indicated airspeed the airplane needs a higher true airspeed and longer takeoff roll.
- Lift varies with CL, which the pilot controls through angle of attack and flap setting. CL increases with angle of attack up to the critical angle of attack, beyond which the airflow separates from the upper surface and the wing stalls.
- Wing area S is fixed by design, but extending flaps effectively increases both S and camber, raising CL at a given airspeed.
Airfoil Terminology. A few terms tie the theory to the wing:
- Chord line — straight line from leading edge to trailing edge.
- Mean camber line — line equidistant between upper and lower surfaces; its curvature defines camber.
- Relative wind — the airflow direction relative to the airfoil; opposite the flight path.
- Angle of attack (AOA) — the angle between the chord line and the relative wind. AOA, not pitch attitude, determines whether the wing is producing lift or stalling.
Pressure Distribution and Center of Pressure. The lift force is the integrated effect of pressure over the entire airfoil surface. At low AOA, the area of lowest pressure sits well aft on the upper surface. As AOA increases, the low-pressure peak migrates forward and grows stronger, increasing CL. At the critical angle of attack (typically 16°–20° for general aviation airfoils), the boundary layer separates near the leading edge, the low-pressure region collapses, CL drops sharply, and the wing stalls — regardless of airspeed, attitude, or weight.
Putting It Together in Flight. During takeoff at a heavy weight or a high density altitude, the pilot must achieve the same lift = weight balance with reduced ρ, so V (true airspeed) must be higher; this is why takeoff distances grow on hot, high days. In cruise, lift equals weight; in a level coordinated turn, lift must equal weight divided by the cosine of the bank angle, which is why load factor and stall speed both rise with bank. Understanding that lift is the product of CL, ½ρV², and S — and that only AOA controls CL — is the foundation for everything from slow flight and stalls to performance planning.