1 — The Lift Equation
Lesson 1 left us with one idea: lift must equal weight to hold height, and you have only two handles on it — speed and angle of attack. The lift equation makes that precise. It gathers everything a wing’s lift depends on into a single line.
- Cₗ — lift coefficient
- how effectively the aerofoil and angle of attack make lift; rises with angle of attack up to the critical angle
- ½ ρ V² — dynamic pressure
- the pressure of motion: air density ρ and the square of true airspeed V
- S — wing area
- the lifting area of the wing — fixed for a given aeroplane
Because lift grows with V², doubling the speed gives four times the lift — at the same angle of attack. So to hold lift at low speed the angle of attack must be large; that is why slow flight near the stall is flown at a high angle of attack.
Read it as a story. The dynamic pressure ½ρV² is the energy the moving air brings;
the wing area S is how much wing meets it; and the lift coefficient Cₗ is how
effectively this particular aerofoil, at this particular angle of attack, turns that
into lift. Of the four quantities, area is fixed and density is the atmosphere’s to
decide — so in the cockpit you are really only setting V and Cₗ.
2 — The Lift Coefficient and Angle of Attack
Cₗ is a dimensionless number that bundles together the wing’s shape (its camber and
section) and, crucially, its angle of attack — the angle between the chord line and
the relative airflow from Lesson 1. For a given wing the shape is fixed, so Cₗ is
essentially a function of angle of attack: raise the nose to the airflow and Cₗ
rises; lower it and Cₗ falls.
3 — The Lift Curve
Plot Cₗ against angle of attack and you get the single most important graph in this
subject — the lift curve. Drag the angle of attack and watch how the coefficient
responds:
Three features matter for the exam:
- The linear range: through the normal flying angles,
Cₗrises almost in a straight line with angle of attack. More angle, more lift coefficient. - The zero-lift angle: a cambered wing still makes some lift at zero angle of attack,
so
Cₗreaches zero only at a small negative angle. - The critical (stalling) angle, about 15–16°, where
Cₗreaches its maximum (Cₗ max). Beyond it the airflow separates from the upper surface,Cₗcollapses and the wing stalls — the subject of Lesson 4.
4 — Trading Speed Against Angle of Attack
Put the equation and the curve together. To hold level flight, lift must equal weight,
so Cₗ · ½ρV² · S is fixed. Area and weight don’t change minute to minute, so Cₗ
and V² must trade off:
- Fly faster and
½ρV²is large, so only a smallCₗ— a small angle of attack — is needed. - Fly slower and
½ρV²shrinks, soCₗmust be large — a high angle of attack — to make up the difference.
Slow down far enough and you reach Cₗ max at the critical angle: there is no more lift
to be had, and the wing stalls. That is exactly why the stall sets the lowest speed
at which the wing can still support the aeroplane.
5 — Why This Matters to the Pilot
Every speed on the airspeed indicator is really an angle of attack in disguise. When you slow to approach speed you are choosing a higher angle of attack; when you raise the nose to climb at a fixed power you trade speed for angle of attack. The lift curve is the map of that trade — and its right-hand edge, the critical angle, is the one limit you must never cross unintentionally.
Cₗ max. Knowing the curve is why a pilot respects a margin above the stall and treats
angle of attack — not just the airspeed needle — as the thing that keeps the wing flying.All numbers and the curve here are illustrative; your aircraft’s real coefficients, critical angle and speeds come from its POH/AFM.
