Lift & drag

081 Principles of FlightChapter 2

Schematic

CL rises linearly at low alpha, peaks at CL max, then drops at stall.

Schematic

Total drag minimum at VIMD — best range speed for jets is 1.32 x VIMD.

Lift generation

Key fact

Lift = component of total aerodynamic force perpendicular to undisturbed airflow. Generated when flow direction of a mass of air is changed. Upper surface produces the greatest proportion of lift at all speeds. Upwash ahead of wing; downwash behind (consequence of producing lift).

Formula — Lift equation

L = ½ ρ V² S CL
L = q × S × CL

At stall: (VS)² × CLMAX = (V)² × CL

Key fact

CL is mainly affected by AoA and camber. CLMAX reached at critical angle of attack (~16° for typical sections). At 1.3 VS in level flight: CL ≈ 59% of CLMAX (1/1.3²).

3D airflow & induced drag

Key fact

Spanwise flow: upper surface tip→root; lower surface root→tip. Creates wing tip vortices — strongest at high AoA, low aspect ratio, take-off. Vortices descend to lower levels; form on rotation, end when nosewheel touches down.

Formula — Induced drag

Di = ½ ρ V² S CDi
CDi = CL² / (π × AR)
CDi ∝ 1 / V²

Key fact

Induced drag increases with AoA, mass (higher AoA), decreases with speed. Reduced by high aspect ratio, wing tip tanks, washout, taper. Parasite drag increases when wing tip tanks installed (form drag).

Parasite (profile) drag

Key fact

Total drag = induced + parasite. Parasite drag ∝ IAS² and includes:

• Form (pressure) drag — reduced by streamlining (but skin friction increases)
• Skin friction drag — boundary layer; turbulent layer has more friction but less separation tendency
• Interference drag — mainly wing/fuselage junction

Key fact

Profile drag = form + skin friction. Minimum total drag when parasite drag = induced drag at VMD. Best L/D AoA ≈ 3–4°. Only one speed gives (CL/CD)MAX = VMD.

Factors affecting CL

Factor	Effect on lift
More camber	More lift
Higher aspect ratio	More lift (less tip vortex)
More sweepback	Less lift at same AoA
Larger nose radius	More lift
Compressibility	Lift reduced (density increases in venturi throat)

Drag vs altitude, weight & flaps

Key fact

At higher altitude: fly faster for same total drag — drag curve shifts right (TAS). IAS-based drag unchanged. Increased weight → more drag at same AoA, higher speed for level flight. HLDs increase drag, allow lower AoA → induced drag decreases, parasite increases.

Ground effect

Key fact

Significant within half wingspan height; affects low wing + low tailplane most. Entering GE: lift coefficient ↑, effective AoA ↑, induced AoA ↓, downwash ↓, CDi ↓ (~80% of induced drag lost). Exiting GE on take-off: vortices increase, lift decreases, pitch-up tendency — carry extra speed.

Exam trap

In ground effect aircraft may become airborne before recommended take-off speed (floating on landing). Induced drag is lowest in GE; highest at take-off (low speed, high AoA).

Boundary layer

Key fact

Laminar: thinner, lower friction, more separation tendency, less kinetic energy. Turbulent: thicker, higher friction, better resists adverse pressure gradient before separation. Transition point moves forward with AoA and velocity; ageing aircraft → more turbulent flow → more drag.