Major aerodynamic forces on aircraft: Lift = L Drag = D Pitching Moment = M Thrust = T Weight = W
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Transcript of 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