AE 1350 Lecture Notes #7We have looked at..Topics To be StudiedUses of AirfoilsEvolution of AirfoilsAirfoilAn Airfoil is Defined as a superposition ofAngle of AttackLift and Drag Forces acting on a Wing SectionSectional Lift and Drag CoefficientsNote that...Pressure Forces acting on the AirfoilSlide 13Slide 14Relationship between L´ and pRelationship between L´ and p (Continued)Pressure Coefficient CpWhy use Cl, Cp etc.?The Importance of Non-Dimensional FormsSlide 20Once Cl, Cd etc. are found, they can be plotted for use in all applications - model aircraft or full size aircraftCharacteristics of Cl vs. aSlide 23Mathematical Model for Cl vs. a at low angles of attackDrag is caused bySkin FrictionLaminar FlowTurbulent Flow“Time-Averaged” Turbulent FlowIn summary...AE 1350Lecture Notes #7We have looked at..•Continuity•Momentum Equation•Bernoulli’s Equation•Applications of Bernoulli’s Equation–Pitot’s Tube–Venturi Meter–Pressures and Velocities over AirfoilsTopics To be Studied•Airfoil Nomenclature•Lift and Drag forces•Lift, Drag and Pressure CoefficientsUses of Airfoils•Wings•Propellers and Turbofans•Helicopter Rotors •Compressors and Turbines•Hydrofoils (wing-like devices which can lift up a boat above waterline)•Wind TurbinesEvolution of AirfoilsEarly Designs - Designers mistakenly believed that theseairfoils with sharp leading edges will have low drag.In practice, they stalled quickly, and generated considerable drag.AirfoilChord LineCamber LineEqual amounts of thickness is added to camberin a direction normal to the camber line.An Airfoil is Defined as a superposition of•Chord Line•Camber line drawn with respect to the chord line.•Thickness Distribution which is added to the camber line, normal to the camber line.•Symmetric airfoils have no camber.Angle of AttackVAngle of attack is defined as the angle between the freestreamand the chord line. It is given the symbol .Because modern wings have a built-in twist distribution, theangle of attack will change from root to tip.The root will, in general, have a high angle of attack.The tip will, in general, have a low (or even a negative) .Lift and Drag Forces acting on a Wing SectionSectional Drag, D´Sectional Lift, L ´The component of aerodynamic forces normal to the freestream, per unit length of span (e.g. per foot of wing span), is called the sectional lift force, and is given the symbol L ´.The component of aerodynamic forces along the freestream, per unit length of span (e.g. per foot of wing span), is called the sectional drag force, and is given the symbol D ´.VSectional Lift and Drag Coefficients•The sectional lift coefficient Cl is defined as:•Here c is the airfoil chord, i.e. distance between the leading edge and trailing edge, measured along the chordline.•The sectional drag force coefficient Cd is likewise defined as:cVLCl221cVDCd221Note that...•When we are taking about an entire wing we use L, D, CL and CD to denote the forces and coefficients.•When we are dealing with just a section of the wing, we call the forces acting on that section (per unit span) L´ and D ´, and the coefficients Cl and CdPressure Forces acting on the AirfoilHigh PressureLow velocityHigh PressureLow velocityLow PressureHigh velocityLow PressureHigh velocityBernoulli’s equation says where pressure is high, velocity will below and vice versa.Pressure Forces acting on the AirfoilHigh PressureLow velocityHigh PressureLow velocityLow PressureHigh velocityLow PressureHigh velocityBernoulli’s equation says where pressure is high, velocity will below and vice versa.Subtract off atmospheric Pressure p everywhere.Resulting Pressure Forces acting on the AirfoilHigh p-p Low velocityHigh p-p Low velocityLow p-p High velocityLow p-p High velocityThe quantity p-p  is called the gauge pressure. It will be negative over portions of the airfoil, especially the upper surface. This is because velocity there is high and the pressures can fall belowatmospheric pressure.Relationship between L´ and p EdgeTrailingEdgeLeadingsideupper sidelower EdgeTrailingEdgeLeadingsideupper EdgeTrailingEdgeLeadingsidelower ppppsideupper on Force-sidelower on the acting Forces direction wind the tonormal ForcedxdxdxLVRelationship between L´ and p(Continued)    EdgeTrailingEdgeLeadingsideupper sidelower EdgeTrailingEdgeLeadingsideupper sidelower ppppdxppdxLDivide left and right sides by cV221EdgeTrailingEdgeLeadingupperlowercxdVppVppcVL222212121We get:Pressure Coefficient CpFrom the previous slide,EdgeTrailingEdgeLeadingupperlowercxdVppVppcVL222212121The left side was previously defined as the sectional liftcoefficient Cl.The pressure coefficient is defined as: 221VppCpThus,  edgeTrailingedgeLeadingupperplowerplcxdCCC,,Why use Cl, Cp etc.?•Why do we use “abstract” quantities such as Cl and Cp?•Why not directly use physically meaningful quantities such as Lift force, lift per unit span , pressure etc.?The Importance of Non-Dimensional FormsConsider two geometrically similar airfoils.One is small, used in a wind tunnel.The other is large, used on an actual wing.These will operate in different environments - density, velocity.This is because high altitude conditions are not easily reproduced in wind tunnels.They will therefore have different Lift forces and pressure fields.They will have identical Cl , Cd and Cp - if they are geometrically alike- operate at identical angle of attack, Mach number and Reynolds numberThe Importance of Non-Dimensional FormsIn other words, a small airfoil , tested in a wind tunnel.And a large airfoil, used on an actual wingwill have identical non-dimensional coefficients Cl , Cd and Cp - if they are geometrically alike- operate at identical angle of attack, Mach number and Reynolds number.This allows designers (and engineers) to build and testsmall scale models, and extrapolate qualitative features,but also quantitative information, from a small scale modelto a full size configuration.Once Cl, Cd etc. are found, they can be plotted for use in all applications - model aircraft or full size aircraftCharacteristics of Cl vs. Angle of