major aerodynamic forces on aircraft: lift = l drag = d pitching moment = m thrust = t weight = w

Figure 1. Aerodynamics: The science of the air flow around as well as the forces and moments acting on a structure in a moving airstream

Major aerodynamic forces on aircraft:

• Lift = L• Drag = D• Pitching Moment = M• Thrust = T• Weight = W

Steady level flight:

Lift = Weight

Thrust = Drag

M = 0

Airfoil Geometry

• b = span

• c = chord

• S = planform area

• Aspect Ratio = b2/S = A

Sail Geometry

Camber = t/c

Aspect Ratio: A = b2/SA

SA = Sail Area

Forces on Wing & SailWing

Sail

L = Lift

D = Drag

R = Resultant

V = Relative Wind

Forces on a Sailboat

A 6-Metre yacht

Equilibrium of forces in the close-hauled sailing condition, Vt = 12 knots

LWL = 23.5 ft

Beam = 6.5 ft

Draft = 5.4 ft

Displacement = 94 lb

Sail Area = 600 sq ft

Lateral Area (hull) = 70 sq ft

Angle of heel = 20°

Basic properties of the atmosphere required for sailing or winged flight

Density (function of p & T) Viscosity

If air had density but no viscosity Balloon flight is possible No sailing or winged fight is possible Early inviscid theory predicts no lift

Consequences of viscosity Skin friction drag (unavoidable) Boundary layer creation → lift

Boundary LayerVelocity Gradient in Viscosity of Surface of an Airfoil

Laminar Flow:Relatively low skin friction dragB.L. separates at relatively low αLaminar separation → large pressure drag

Turbulent Flow:Relatively large skin friction dragB.L. remains attached to higher α

Transition Laminar to TurbulenceDetermined by Reynolds number Re

Re = VAl/ν

= velocity x distance ÷ viscosity value

v = called kinematic viscosity.

It is basic property of air

Boundary Layer → Circulation

← Circulation: air velocity higher on top

surface than bottom

By Bernoulli’s theory, pressure on top surface > pressure on bottom surface

Typical airfoil pressure distribution

Simplest (Quantitative) Theory of Lift & Drag(Based Upon Concept of Dynamic Pressure – q)

Dynamic pressure = air density x airspeed2

q = ρv2/2Sea level standard dayρ = .0024 slugs/ft3 = air densityequivalent to .0768 lb/ft3

v must be in ft/secv(ft/sec) = 1.47 x V(mph)Example: at 100 mph (SLSD)

q = 26 lb/ft2

Actual Lift Produced by a Wing Depends Upon:

• Dynamic pressure – q• Wing area – S• Angle of attack – α

• L = qSCL

• CL = lift coefficient

• CLvaries with α

Drag

Drag – retarding force

D = q S CD

CD = drag coefficient

3 Physical sources of drag

Skin friction

Pressure drage (due to separation)

Induced drag (varies with lift)

Drag Coefficient

• CD = CDo + CDi

• CDo due to skin friction and pressure drag

• CDi induced drag coefficient

• CDo is nearly constant C (for a given aircraft)

• CDi = C2L/πeA

Physical Origin of Induced Drag – Wing Tip Trailing Vortices

Lifting line or bound vortex

Downwash at Wind Due to Trailing Vortices Tips Local Velocity Vector Down

Downwash

Induced Velocities (Downwash) Due to the Tip Vortex Action

Induced drag is a function of lift alone and has nothing to do with the angle of incidence except to modify it through the

introduction of an induced angle

Illustration of Downwash

Telltale Action vs AOA

Influence of Foresail on Airflow

Influence of Camber on Force Components

Force Components Sailing With the Wind

Vortex Shedding