Lift, Drag & the Stall
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.
Lift, drag & the stall, summary notes
- 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.
- 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)
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.
Lift, angle of attack & the stall
Drag & the minimum-drag speed
Lift & drag concept map
Lift, Drag & the Stall
Lift, drag & the stall quiz
Lift, Drag & the Stall, quiz
1. The dynamic pressure at 60 m/s in air of density 1.225 kg/m³ is about:
2205 Pa4410 Pa37 Pa2. The coefficient of lift of a wing is greatest:
Just before the stalling angleAt zero angle of attackAt the top speed3. A high aspect ratio wing has:
Lower induced drag than a low aspect ratio wingHigher induced dragNo effect on drag4. The graph shows lift coefficient against angle of attack. The point marked P is:
The stalling angleThe angle of zero liftThe best glide angle5. In the drag graph shown, the dashed curve that falls as speed increases represents:
Induced dragParasite dragTotal drag6. In the figure the arrows above the aerofoil point away from the surface. This indicates that the upper surface has:
Reduced static pressureIncreased static pressureNo pressure change7. An aeroplane has a wing span of 30 m and a wing area of 90 m². Its aspect ratio is:
1030.338. The dynamic pressure at 50 m/s in air of density 1.225 kg/m³ is approximately:
1531 Pa3063 Pa61 Pa