1. WING LOADING (W/S), SPAN LOADING (W/b) AND ASPECT RATIO (b2/S)
Span loading (W/b), wing loading (W/S)
and AR (b2/S) are related
Zero-lift drag, D0 is proportional to wing area
Induced drag, Di, is proportional to square
of span loading
Take ratio of these drags, Di/D0
Re-write W2/(b2S) in terms of AR and substitute into drag ratio Di/D0
1: For specified W/S (set by take-off or landing requirements) and CD,0 (airfoil choice), increasing AR will decrease drag due to lift relative to zero-lift drag
2: AR predominately controls ratio of induced drag to zero lift drag, whereas span loading controls actual value of induced drag

2. EFFECT OF THICKNESS: NACA 4412 VS. NACA 4421
Both NACA 4412 and NACA 4421 have same shape of mean camber line
Thin airfoil theory predict that linear lift slope and aL=0 should be the same for both
Leading edge stall shows rapid drop of lift curve near maximum lift
Trailing edge stall shows gradual bending-over of lift curve at maximum lift, “soft stall”
High cl,max for airfoils with leading edge stall
Flat plate stall exhibits poorest behavior, early stalling
Thickness has major effect on cl,max

3. FINITE WING DOWNWASH a: Geometric Angle of Attack
ai: Induced Angle of Attack
aeff: Effective Angle of Attack
Chord line
Finite Wing Consequences:
Tilted lift vector contributes a drag component, called induced drag (drag due to lift) → CL < cl and CD > cd
Lift slope is reduced relative to infinite wing (a < a0)

4. IMPORTANT STATEMENTS Fundamental Equation of Thin Airfoil Theory
“The camber line is a streamline of the flow”
Fundamental Equation of Prandtl’s Lifting-Line Theory
“The geometric angle of attack is equal to the sum of the effective
angle of attack plus the induced angle of attack”

5. GENERAL LIFT DISTRIBUTION (2/4)
Substitute expression for G(q) and dG/dy into fundamental equation of Prandtl’s lifting line theory
Last term on the right (integral term) is a standard form and may be simplified as:
Equation is evaluated at a given spanwise location (q0), just as fundamental equation of Prandtl’s lifting line theory is evaluated at a given spanwise location (y0)
Only unknowns in equation are An’s
Written at q0 equation is 1 algebraic equation with N unknowns
Write equation at N spanwise locations to obtain a system of N independent algebraic equations with N unknowns