PelicanAero Group 1
PdPd
Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planform and Thickness www.HowFliesTheAlbatross.com J. Philip Barnes April 2013
Lift 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 Group
PelicanAero Group 2
Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planform and Thickness www.HowFliesTheAlbatross.com J. Philip Barnes April 2013
Presentation 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 method
PelicanAero Group 3
Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planform and Thickness www.HowFliesTheAlbatross.com J. Philip Barnes April 2013
Configurations 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 4
Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planform and Thickness www.HowFliesTheAlbatross.com J. Philip Barnes April 2013
Wing geometry and aerodynamic terms
S ≡ plan areab ≡ spanc ≡ chord ≡ tip chord / root chordt ≡ streamwise thicknesst/c ≡ thickness ratioA ≡ aspect ratio = b2/S = b/cav ≡ angle of attackcL ≡ lift coefficient≡ lift slope / (2) cDv ≡ vortex drag coefficiento ≡ leading‐edge sweepc/2 ≡mid‐chord sweepc/4 ≡ quarter‐chord sweep
S ≡ plan areab ≡ spanc ≡ chord ≡ tip chord / root chordt ≡ streamwise thicknesst/c ≡ thickness ratioA ≡ aspect ratio = b2/S = b/cav ≡ angle of attackcL ≡ lift coefficient≡ lift slope / (2) cDv ≡ vortex drag coefficiento ≡ leading‐edge sweepc/2 ≡mid‐chord sweepc/4 ≡ quarter‐chord sweep
Sweep conversion (given quarter‐chord sweep) tann = tanc/4 + (4/A) (n‐¼) (‐1) / (+1)Sweep conversion (given quarter‐chord sweep) tann = tanc/4 + (4/A) (n‐¼) (‐1) / (+1)
b
c
t
o
PelicanAero Group 5
Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planform and Thickness www.HowFliesTheAlbatross.com J. Philip Barnes April 2013
Prandtl and Jones Theories
Ludwig Prandtl
Robert T. Jones
JonesLift slope (low‐A, any‐)
dcL/d = A/2Induced drag: cDv = cL2/(A)
JonesLift slope (low‐A, any‐)
dcL/d = A/2Induced drag: cDv = cL2/(A)
PrandtlLift slope (any‐A, low‐)dcL/d ≈ 2A/(A+2)
Induced drag: cDv ≈ cL2/(A)
PrandtlLift slope (any‐A, low‐)dcL/d ≈ 2A/(A+2)
Induced drag: cDv ≈ cL2/(A)
Prandtl‐JonesInduced drag: cDv ≈ cL2/(A)But what about thickness?
Prandtl‐JonesInduced drag: cDv ≈ cL2/(A)But what about thickness?
PelicanAero Group 6
0.0
0.1
0.2
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0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 1 2 3 4 5 6 7 8 9 10 11 12 13
(dcL /d
Aspect Ratio, A
Normalized Lift‐slope ~ Test Data Vs. Theory
‐10 TO 1527 to 3438 to 4659 to 60
c/2
to
Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planform and Thickness www.HowFliesTheAlbatross.com J. Philip Barnes April 2013
Lift slope data and validation of theory
PelicanAero Group 7
Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planform and Thickness www.HowFliesTheAlbatross.com J. Philip Barnes April 2013
Helmbold-Diederich ~ Low-speed lift slope of any wing
42cos2/
)cos/(
22/
2/
FFddc
AF
c
L
c
PelicanAero Group 8
Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planform and Thickness www.HowFliesTheAlbatross.com J. Philip Barnes April 2013
Helmbold-Polhamus ~ Low-speed lift slope of any wing
222/ 4)cos/(2
4)2/(
/
c
L
AAddc
PelicanAero Group 9
Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planform and Thickness www.HowFliesTheAlbatross.com J. Philip Barnes April 2013
Test data ~ rectangular wing lift ~ effect of thickness
PelicanAero Group 10
Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planform and Thickness www.HowFliesTheAlbatross.com J. Philip Barnes April 2013
0.0
0.1
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0.8
0 2 4 6 8 10 12 14 16 18 20
Lift Coefficient, cL
Angle of attack, o
Delta‐wing‐body Lift (A=2) ~ Effect of ThicknessNACA RM A50K20, A50K21, A51K28
0.080.050.03
8%
5%3%
Test data ~ Delta wing-body lift ~ effect of thickness
Minor effect of thickness on liftMinor effect of thickness on lift
PelicanAero Group 11
0.00
0.05
0.10
0.15
0.20
0.00 0.10 0.20 0.30 0.40 0.50 0.60
Induced Drag Coefficient, cD
Square of Lift Coefficient ~ cL2
Delta‐wing‐body Induced Drag (A=2) ~ Effect of ThicknessNACA RM A50K20, A50K21, A51K28
Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planform and Thickness www.HowFliesTheAlbatross.com J. Philip Barnes April 2013
8%
5%
3%
The Thin-wing Induced-drag Surprise ~ Circa 1950
Induced dragcoefficient, cDv
Delta wing-body linearized drag polarA=2, M 0.25, NACA RM A50K20, A50K21, A51K28
PelicanAero Group 12
Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planform and Thickness www.HowFliesTheAlbatross.com J. Philip Barnes April 2013
The Thin-wing Induced-drag Surprise ~ Circa 1950
10%
6%
4%
Rectangular wing linearized drag polarA=4, Effect of thickness, NACA TN 3501
PelicanAero Group 13
‐0.2
0.0
0.2
0.4
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0.8
1.0
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0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22
Streamwise thickness
Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planform and Thickness www.HowFliesTheAlbatross.com J. Philip Barnes April 2013
Induced-drag Transition ~ Prandtl-Jones to Polhamus
PreliminaryEmpiricalCorrelation
= e-a(t/c)-b(t/c)2
PreliminaryEmpiricalCorrelation
= e-a(t/c)-b(t/c)2
Prandtl-JonesdcD/dcL
2 = 1/(A)Prandtl-Jones
dcD/dcL2 = 1/(A)
Polhamus cD ≈ cLdcD/dcL
2 ≈ 1/(dcL/d)Polhamus cD ≈ cLdcD/dcL
2 ≈ 1/(dcL/d)
t/c
≡ [dcD/dcL2 ‐ 1/(A)] / [1/(dcL/d) ‐ 1/(A)] ≡ [dcD/dcL2 ‐ 1/(A)] / [1/(dcL/d) ‐ 1/(A)]
PelicanAero Group 14
Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planform and Thickness www.HowFliesTheAlbatross.com J. Philip Barnes April 2013
Effect of thickness on induced drag ~ symmetrical section
Assume elliptical loadingAssume small anglescL ≈ cN ≈ 2 [1]≈ cN /( [2]cD ≈ cN cT cF [3]
Define thrust recovery: ≡ cT / [cN tan≈ cT / [cN [4]
Combine [1,2,3,4]:
Assume elliptical loadingAssume small anglescL ≈ cN ≈ 2 [1]≈ cN /( [2]cD ≈ cN cT cF [3]
Define thrust recovery: ≡ cT / [cN tan≈ cT / [cN [4]
Combine [1,2,3,4]:
NomenclatureA aspect ratiovo flight velocity angle of attack upwash angle *cL lift coefficient cD drag coefficient cN normal force coef.cF friction force coef. ** cT chord thrust coef. *** thrust recovery (0-1)
NomenclatureA aspect ratiovo flight velocity angle of attack upwash angle *cL lift coefficient cD drag coefficient cN normal force coef.cF friction force coef. ** cT chord thrust coef. *** thrust recovery (0-1)
* Usually negative** Upper + lower, chordwise*** Pressure integration, chordwise
cN
cFcT
cT
vo
cD ≈ cF + (cN2) / ()
+ (1-) (cN2) / (2)
cD ≈ cF + (cN2) / ()
+ (1-) (cN2) / (2)
thin or sharp: ≈0thin or sharp: ≈0
"thick" : ≈1"thick" : ≈1
PelicanAero Group 15
Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planform and Thickness www.HowFliesTheAlbatross.com J. Philip Barnes April 2013
Summary ~ 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 = cL
2 / (A)• Polhamus: induced drag upper limit
– zero thickness, symmetrical section– formula: cDv ≈ cL ≈ cL
2 / (dcL/d)• 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 sections
PelicanAero Group 16
Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planform and Thickness www.HowFliesTheAlbatross.com J. Philip Barnes April 2013
Application of method ~ "Neutral-trimmed" drag polar
01. Set geom (aspect ratio, thickness, & sweep) {A, t/c, c/2}02. Loop on specified angle of attack, (say from 0o to 10o) 03. Compute the lift slope, dcL/d (Diederich or Polhamus)04. Compute the lift coefficient, cL (given and dcL/d)05. Compute Prandtl-Jones induced drag coefficient, cDv_PJ
06. Compute Polhamus induced-drag coefficient, cDv_Po
07. Get induced-drag transition () at thickness ratio (t/c)08. Compute induced drag coefficient (cDv) given () 09. Est. zero-lift drag (cDo) {1st mention ~ use 0.02} 10. Compute total drag coefficient, cD = cDo + cDv
11. Compute lift/drag ratio, L/D12. Plot all results versus or cL
PelicanAero Group 17
Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planform and Thickness www.HowFliesTheAlbatross.com J. Philip Barnes April 2013
Sample application of method ~ homework assignment
b
c
t
o
Application: Me-163
Assume:a) no twist, low Mach numberb) 9% thickness (t/c)c) section = 0.95
Measure from sketch:a) Leading-edge sweep (o)b) Span (b)c) Root (centerline) & tip chords
Tasks:1) Get parameters S, A, , c/2
2) Find L/D, and cL at max L/D3) e-mail results to:
PelicanAero Group 18
Phil Barnes has a Master’s Degree in AerospaceEngineering from Cal Poly Pomona and aBachelor’s 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 Master’s Degree in AerospaceEngineering from Cal Poly Pomona and aBachelor’s 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 Author
Lift and Drag Review and Renew - Correlations of 50 Years of NACA and NASA Test Data on the Effects of Wing Planform and Thickness www.HowFliesTheAlbatross.com J. Philip Barnes April 2013