PelicanAero Group 1PdPdLift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planformand Thickness www.HowFliesTheAlbatross.comJ. Philip BarnesApril 2013Lift and Drag Review and RenewCorrelating 50 Years of NACA / NASA Test Datafor the Effects of Wing Planform and Thickness 15 April 2013 Update J. Philip BarnesPelican Aero GroupPelicanAero Group 2Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planformand Thickness www.HowFliesTheAlbatross.com J. Philip BarnesApril 2013Presentation Purpose and Contents Review & renew: wing / body lift & induced drag Aspect ratio, sweep, & thickness Subsonic, linear range (moderate incidence) Elliptical wing and Prandtl's formula for lift ~ 1918 Helmbold's enhancement for low aspect ratio ~ 1942 Diederich's enhancement for sweep ~ 1951 Polhamus' enhancement for sweep~ 1957 Prandtl-Jones: "thick" wing or body induced-drag ~ 1918/1946 The thin-wing induced-drag surprise ~ 1950 Polhamus: "thin" wing or body induced drag ~ 1950 Transition, Prandtl-Jones to Polhamus ~ 2012 New: Synergy of airfoil & wing data thereof Summary and sample application of new methodPelicanAero Group 3Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planformand Thickness www.HowFliesTheAlbatross.com J. Philip BarnesApril 2013Configurations studied~ Data and theory references www.NTRS.NASA.gov www.AERADE.Cranfield.ac.uk www.Google.com www.NTRS.NASA.gov www.AERADE.Cranfield.ac.uk www.Google.com 114 configurations, thickness:02 - 20%PelicanAero Group 4Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planformand Thickness www.HowFliesTheAlbatross.com J. Philip BarnesApril 2013Wing geometry and aerodynamic termsS planareab spanc chord tipchord/rootchordt streamwise thicknesst/c thicknessratioA aspectratio=b2/S=b/cavo angleofattackcL liftcoefficientq liftslope/(2t)cDv vortexdragcoefficientAo leadingedgesweepAc/2 midchordsweepAc/4 quarterchordsweepS planareab spanc chord tipchord/rootchordt streamwise thicknesst/c thicknessratioA aspectratio=b2/S=b/cavo angleofattackcL liftcoefficientq liftslope/(2t)cDv vortexdragcoefficientAo leadingedgesweepAc/2 midchordsweepAc/4 quarterchordsweepSweepconversion(givenquarterchordsweep)tanAn =tanAc/4 +(4/A)(n)(1)/(+1)Sweepconversion(givenquarterchordsweep)tanAn =tanAc/4 +(4/A)(n)(1)/(+1)bct AoPelicanAero Group 5Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planformand Thickness www.HowFliesTheAlbatross.com J. Philip BarnesApril 2013Prandtl and Jones TheoriesLudwig PrandtlRobert T. JonesJonesLiftslope(lowA,anyA)dcL/do =t A/2Induceddrag:cDv =cL2/(tA)JonesLiftslope(lowA,anyA)dcL/do =t A/2Induceddrag:cDv =cL2/(tA)PrandtlLiftslope(anyA,lowA)dcL/do 2tA/(A+2)Induceddrag:cDv cL2/(tA)PrandtlLiftslope(anyA,lowA)dcL/do 2tA/(A+2)Induceddrag:cDv cL2/(tA)PrandtlJonesInduceddrag:cDv cL2/(tA)Butwhataboutthickness?PrandtlJonesInduceddrag:cDv cL2/(tA)Butwhataboutthickness?PelicanAero Group 60.00.10.20.30.40.50.60.70.80.91.00 1 2 3 4 5 6 7 8 9 10 11 12 13(dcL/do) / 2tqAspectRatio,ANormalizedLiftslope~TestDataVs.Theory10TO1527to3438to4659to60Aoc/2toLift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planformand Thickness www.HowFliesTheAlbatross.com J. Philip BarnesApril 2013Lift slope data and validation of theoryPelicanAero Group 7Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planformand Thickness www.HowFliesTheAlbatross.com J. Philip BarnesApril 2013Helmbold-Diederich ~ Low-speed lift slope of any wing4 2cos 2/) cos /(22 /2 /+ +=AA FF d dcA FcLctqoqPelicanAero Group 8Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planformand Thickness www.HowFliesTheAlbatross.com J. Philip BarnesApril 2013Helmbold-Polhamus ~ Low-speed lift slope of any wing2 22 /4 ) cos / ( 24) 2 / ( /q qqto+ A +=cLAAd dcPelicanAero Group 9Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planformand Thickness www.HowFliesTheAlbatross.com J. Philip BarnesApril 2013Test data ~ rectangular wing lift ~ effect of thicknessPelicanAero Group 10Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planformand Thickness www.HowFliesTheAlbatross.com J. Philip BarnesApril 20130.00.10.20.30.40.50.60.70.80 2 4 6 8 10 12 14 16 18 20LiftCoefficient,cLAngleofattack,ooDeltawingbodyLift(A=2)~EffectofThicknessNACARMA50K20,A50K21,A51K280.080.050.038%5%3%Test data ~ Delta wing-body lift ~ effect of thicknessMinor effect of thickness on lift Minor effect of thickness on liftPelicanAero Group 110.000.050.100.150.200.00 0.10 0.20 0.30 0.40 0.50 0.60InducedDragCoefficient,cDSquareofLiftCoefficient~cL2DeltawingbodyInducedDrag(A=2)~EffectofThicknessNACARMA50K20,A50K21,A51K28Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planformand Thickness www.HowFliesTheAlbatross.com J. Philip BarnesApril 20138%5%3%The Thin-wing Induced-drag Surprise ~ Circa 1950Induced dragcoefficient, cDvDelta wing-body linearized drag polarA=2, M 0.25, NACA RM A50K20, A50K21, A51K28PelicanAero Group 12Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planformand Thickness www.HowFliesTheAlbatross.com J. Philip BarnesApril 2013The Thin-wing Induced-drag Surprise ~ Circa 195010%6%4%Rectangular wing linearized drag polarA=4, Effect of thickness, NACA TN 3501PelicanAero Group 130.20.00.20.40.60.81.01.20.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22tStreamwise thicknessLift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planformand Thickness www.HowFliesTheAlbatross.com J. Philip BarnesApril 2013Induced-drag Transition ~ Prandtl-Jones to PolhamusPreliminaryEmpiricalCorrelationt= e-a(t/c)-b(t/c)2PreliminaryEmpiricalCorrelationt= e-a(t/c)-b(t/c)2Prandtl-JonesdcD/dcL2= 1/(tA)Prandtl-JonesdcD/dcL2= 1/(tA)PolhamuscD o cLdcD/dcL2 1/(dcL/do)PolhamuscD o cLdcD/dcL2 1/(dcL/do)t/ct [dcD/dcL2 1/(tA)]/[1/(dcL/do) 1/(tA)] t [dcD/dcL2 1/(tA)]/[1/(dcL/do) 1/(tA)]PelicanAero Group 14Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planformand Thickness www.HowFliesTheAlbatross.com J. Philip BarnesApril 2013Effect of thickness on induced drag ~ symmetrical sectionAssume elliptical loadingAssume small anglescL cN 2t (o+u) [1]u cN/(tA) [2]cD cN o cT + cF[3]Define thrust recovery: k cT/[cN tan(o+u)| cT/[cN (o+u)| [4]Combine [1,2,3,4]:Assume elliptical loadingAssume small anglescL cN 2t (o+u) [1]u cN/(tA) [2]cD cN o cT + cF[3]Define thrust recovery: k cT/[cN tan(o+u)| cT/[cN (o+u)| [4]Combine [1,2,3,4]:NomenclatureA aspect ratiovoflight velocityo angle of attacku upwash angle *cLlift coefficientcD drag coefficientcNnormal force coef.cFfriction force coef. ** cTchord thrust coef. ***k thrust recovery (0-1)NomenclatureA aspect ratiovoflight velocityo angle of attacku upwash angle *cLlift coefficientcD drag coefficientcNnormal force coef.cFfriction force coef. ** cTchord thrust coef. ***k thrust recovery (0-1)*Usually negative** Upper + lower, chordwise***Pressure integration, chordwisecNcFcTcT voououcD cF+ (cN2) / (tA)+ (1-k) (cN2) / (2t)cD cF+ (cN2) / (tA)+ (1-k) (cN2) / (2t)thin or sharp:k0 thin or sharp:k0"thick" : k1 "thick" : k1PelicanAero Group 15Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planformand Thickness www.HowFliesTheAlbatross.com J. Philip BarnesApril 2013Summary ~ Lift and Drag Review and Renew Prandtl: Good prediction of unswept wing lift slope Helmbold: Excellent prediction thereof particularly at low aspect ratio Diederich & Polhamus: added effect of sweep different formulas ~ quite-different curve shapes essentially identical results, nonetheless Prandtl & Jones: thick-wing or body induced drag totally independent methods & purposes Prandtl: any aspect ratio~Jones: Low-A same formula: cDv= cL2 / (tA) Polhamus: induced drag upper limit zero thickness, symmetrical section formula: cDv ocL cL2 / (dcL/do) Enhancements via our review & renew study:1) Showed Prandtl-Jones drag is limited to thick wings2) Suggested correlation for thick-to-thin drag transition3) New formula for induced drag with symmetrical sectionsPelicanAero Group 16Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planformand Thickness www.HowFliesTheAlbatross.com J. Philip BarnesApril 2013Application of method ~ "Neutral-trimmed" drag polar01. Set geom (aspect ratio, thickness, & sweep){A, t/c, Ac/2}02. Loop on specified angle of attack, o (say from 0oto 10o) 03. Compute the lift slope, dcL/do(Diederich or Polhamus)04. Compute the lift coefficient, cL(given o and dcL/do)05. Compute Prandtl-Jones induced drag coefficient, cDv_PJ06. Compute Polhamus induced-drag coefficient, cDv_Po07. Get induced-drag transition (t) at thickness ratio (t/c)08. Compute induced drag coefficient (cDv) given (t) 09. Est. zero-lift drag (cDo) {1stmention ~ use 0.02} 10. Compute total drag coefficient, cD = cDo + cDv11. Compute lift/drag ratio, L/D12. Plot all results versus o or cLPelicanAero Group 17Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planformand Thickness www.HowFliesTheAlbatross.com J. Philip BarnesApril 2013Sample application of method ~ homework assignmentbct AoApplication: Me-163Assume:a) no twist, low Mach numberb) 9% thickness (t/c)c) section q = 0.95Measure from sketch:a) Leading-edge sweep (Ao)b) Span (b)c) Root (centerline) & tip chordsTasks:1) Get parameters S, A, , Ac/22) Find L/D,o andcLat max L/D3) e-mail results to:Phil@HowFliesTheAlbatross.comPelicanAero Group 18Phil Barnes has a Masters Degree in AerospaceEngineering from Cal Poly Pomona and aBachelors Degree in Mechanical Engineeringfrom the University of Arizona. He has 31-years ofexperience in the performance analysis andcomputer modeling of aerospace vehicles andsubsystems at Northrop Grumman. Phil hasauthored diverse technical papers and studies ofgears, computer graphics, orbital mechanics,aerodynamics, and propellers, includinginternationally-recognized studies of albatrossdynamic soaring, regenerative-electric flight, and"German Jets."Phil Barnes has a Masters Degree in AerospaceEngineering from Cal Poly Pomona and aBachelors Degree in Mechanical Engineeringfrom the University of Arizona. He has 31-years ofexperience in the performance analysis andcomputer modeling of aerospace vehicles andsubsystems at Northrop Grumman. Phil hasauthored diverse technical papers and studies ofgears, computer graphics, orbital mechanics,aerodynamics, and propellers, includinginternationally-recognized studies of albatrossdynamic soaring, regenerative-electric flight, and"German Jets."About the AuthorLift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planformand Thickness www.HowFliesTheAlbatross.com J. Philip BarnesApril 2013