2-D Source of Aerodynamic ForceSource of Aerodynamic ForceAerodynamic Lift, Drag, and MomentsCenter of PressureAerodynamic CoefficientsAerodynamic CoefficientsAerodynamic CoefficientsReference Area, SVariation of Coefficients with Parameterscl vs. acl vs. Recmc/4 vs. a and ReAirfoil Data-NACA 2415cd vs. clcd vs. Re and cmc/4Airfoil Data-NACA 2415cl vs. High Mach #’scd vs. High Mach #’sCalculating the Aerodynamic CenterCalculating the Aerodynamic CenterCalculating the Aerodynamic CenterNACA Airfoil NomenclatureNACA Airfoil NomenclatureDesigning an AirfoilFour Digit AirfoilsFive Digit Airfoils6 Digit AirfoilsDesign Lift CoefficientDrag Bucket-6 Series Laminar AirfoilP-51 MustangLift and Drag BuildupFinite Wing GeometryWing Tip Vortices and DownwashInduced and Effective Angles of AttackHigh Aspect Ratio Straight WingEffect of Aspect Ratio on Lift CurveCompressibility CorrectionEffect of Mach Number on Lift SlopeLow Aspect Ratio Straight WingsLow AR Wing Lift ApproximationsWhen do we want a low AR wing?Swept WingsSwept Wing Geometry and ApproximationsSwept Wing, Compressibility CorrectionsSupersonic Swept WingsEstimating Lifting Properties of Supersonic WingsSwept Wings OverviewDelta WingsDelta Wings-Subsonic FlowVortex LiftFeatures of Vortex LiftApproximate Calculation of Lift-Delta WingsWing Body CombinationsDragSubsonic Drag-AirfoilsSkin Friction DragPressure Drag (Form Drag)Subsonic Drag-Finite WingsSubsonic Drag-Finite WingsSubsonic Drag-Finite WingsSubsonic Drag- FuselagesSummary of Subsonic DragOther Types of DragTransonic DragReduction of Transonic DragArea RuleSupercritical AirfoilSupercritical AirfoilSupersonic DragSupersonic DragZero Lift Wave DragCalculating Supersonic DragCalculating Supersonic DragThe Drag PolarDrag BreakdownWetted Area EstimationWetted Area EstimationThe Drag PolarParasite DragWave DragDrag PolarDrag PolarGraphic Drag PolarGraphic Drag PolarInformation from PolarGeneral Drag Polar NotesGeneral Drag Polar NotesReferences for Chapter 2AE 3310 PerformanceChapter 2- Aerodynamics of the Airplane:The Drag Polar2-D Source of Aerodynamic ForceOnly 2 sources of resultant aerodynamic force (R): Integral of Pressure Integral of Shear StressNewton’s 2nd Law:Conservation of Momentumgives the relationship betweenpressure and velocityp0 = p1 + ( ) ρ V12 = p1 + ( ) ρ V121212Friction (Viscous Forces)No slip condition at the surface createsshear stressAffected by:Affected by:airfoil shapeangle of attackshocksvorticessmoothnesswetted areaAE 3310 PerformanceChapter 2- Aerodynamics of the Airplane:The Drag PolarSource of Aerodynamic ForceA body immersed in an airflow will experience an Aerodynamic Force due to:PressureSp=p(s)τ=τ(s)SShear Stressacts perpendicular to the surfaceacts parallel to the surfaceIntegrate around the surface of the bodyto get the total force:R = ∫∫ ∫∫+SSSdk Sdn pτnkdSAE 3310 PerformanceChapter 2- Aerodynamics of the Airplane:The Drag PolarAerodynamic Lift, Drag, and MomentsαV∞RLD“free stream velocity” or “relative wind”(defined as parallel to V )∞(defined as perpendicular to V )∞(not perpendicular to V )∞AERODYNAMIC FORCES MOMENTScMMLEc4By convention, a moment whichrotates a body causing an increase inangle of attack is positive.AE 3310 PerformanceChapter 2- Aerodynamics of the Airplane:The Drag PolarCenter of PressureQuestion: At what point on the body do the lift and drag (or R) act?Answer: The forces act at the centroid of the distributed load, called thecenter of pressureLDc.p.NO moment!LDMc4c4==Same force, but move it tothe quarter chord and add amomentLMDLESame force, but now it’sat the leading edge, alongwith a moment about theleading edgeQuestion: So why don’t we use center of pressure as reference point in aircraftdynamics?Answer: Because c.p. shifts when angle of attack is changed. Use quarter chord.AE 3310 PerformanceChapter 2- Aerodynamics of the Airplane:The Drag PolarAerodynamic CoefficientsFrom intuition and basic knowledge, we know:aerodynamic force = f (velocity, density, size of body, angle of attack, viscosity, compressibility)L = L(ρ∞, V ∞, S, α, µ ∞, a ∞)D = D(ρ∞, V ∞, S, α, µ ∞, a ∞)M = M(ρ∞, V ∞, S, α, µ ∞, a ∞)To find out how the lift on a given body varies with the parameters, we could run a series of windtunnel tests in which the velocity, say, is varied and everything else stays the same. From this wecould extract the change in lift due to change in velocity. If we did this for each parameter, and eachforce (moment), we would have to conduct experiments that resulted in 19 stacks of data (one foreach variation plus a baseline).This is bad: wind tunnel time is very expensive and the whole process is time consuming.AE 3310 PerformanceChapter 2- Aerodynamics of the Airplane:The Drag PolarAerodynamic CoefficientsInstead, let’s define lift, drag, and moment coefficients for a given body:CL =Lq∞ SCD =Dq∞ SCM =Mq∞ Scand q is defined as the dynamic pressure:q = ρ V∞ 212c is defined as a characteristic length of a body, usually the chord lengthNow define the following similarity parameters:Re = ρ ∞ V ∞ cµ ∞Reynold’s Number(based on chord length)M ∞ =V ∞a ∞Mach NumberAE 3310 PerformanceChapter 2- Aerodynamics of the Airplane:The Drag PolarAerodynamic CoefficientsUsing dimensional analysis, we get the following results. For a given body shape:CL = f1( α, Re, M ∞)CD = f2( α, Re, M ∞)CM = f3( α, Re, M ∞)If we conduct the same experiments, we can now get the equivalent data with 10 stacksof data.But more fundamentally, dimensional analysis tells us that, if the Reynold’s Number andthe Mach Number are the same for two different flows (different density, velocity,viscosity, speed of sound), the lift coefficient will be the same, given two geometricallysimilar bodies at the same angle of attack.This is the driving principle behind wind tunnels.But…be careful. In real life, it is very difficult to match both Re and M.AE 3310 PerformanceChapter 2- Aerodynamics of the Airplane:The Drag PolarReference Area, SS is some sort of reference area used to calculate the aerodynamic coefficients.S as wetted area - not common, but is the surface upon which thepressure and shear distributions act, so it is a meaningful geometricquantity when discussing aerodynamic force.S as planform area - the projected area we see when looking down atthe wing or aircraft (the “shadow”). Most common definition of Sused when