The lift and drag equations, C_L vs angle of attack and the stall, parasite/induced drag and the best-L/D (minimum-drag) speed.
Notes
Lift, drag & the stall — summary notes
Free
Main ideas
Lift L = C_L·½ρV²·S and drag D = C_D·½ρV²·S, where ½ρV² is the dynamic pressure and S the wing area; the coefficients C_L and C_D package the aerofoil shape and angle of attack.
C_L rises almost linearly with AoA up to the critical (stalling) angle — typically about 15–16° for a plain aerofoil — then falls sharply as the flow separates. The stall is an ANGLE-OF-ATTACK event: an aircraft can stall at any airspeed or attitude if the critical AoA is exceeded.
Total drag has two parts: PARASITE drag (skin friction + form + interference) which grows with V², and INDUCED drag (the price of making lift, from wing-tip vortices) which falls with V². Their sum is a U-shaped curve.
The bottom of that U is V_IMD — the minimum-drag speed — where induced and parasite drag are equal and the lift-to-drag ratio L/D is at its maximum; this is the most aerodynamically efficient speed.
Higher aspect ratio (long, slender wings) and wing-tip devices/winglets reduce induced drag by weakening the tip vortices — which is why gliders have very high aspect-ratio wings.
⚠ Exam trap: induced drag DOMINATES at low speed/high AoA (near the stall), parasite drag dominates at high speed; they are equal at V_IMD, which is also the best-L/D and best-glide speed.
Key formulas
Lift
L = C_L·½·ρ·V²·S
Drag
D = C_D·½·ρ·V²·S
Efficiency
L/D maximum at V_IMD (min total drag)
Solved examples
An aircraft is flying slower than its minimum-drag speed and total drag is INCREASING as it slows further. Which type of drag is responsible?
Below V_IMD the aircraft is on the 'back of the drag curve', where induced drag dominates. As speed falls the angle of attack must rise to keep L = W, strengthening the tip vortices and raising induced drag — so total drag climbs even though the aircraft is going slower. This is the region of 'speed instability' on the approach.