Peli 1 P dc 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 Renew Correlating 50 Years of NACA / NASA Test Data for the Effects of Wing Planform and Thickness 21 April 2013 Update J. Philip Barnes Pelican Aero Group c N c F c T c T v o a u a u
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Lift and Drag Review and Renew Correlating 50 Years of NACA / NASA Test Data
Lift and Drag Review and Renew Correlating 50 Years of NACA / NASA Test Data for the Effects of Wing Planform and Thickness 21 April 2013 Update J . Philip Barnes Pelican Aero Group. c T . u. a. c N. a. v o. u. c T. c F. Presentation Purpose and Contents. - PowerPoint PPT Presentation
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Induced drag transition ~ Prandtl-Jones to PolhamusK ≡ dcD/dcL
2 ; t ≡ ( K-KPJ ) /( KPo-KPJ )
Prandtl-JonesdcD/dcL
2 = 1/(pA)
Polhamus cD ≈ a cLdcD/dcL
2 ≈ 1/(dcL/da)
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
21 April 2013 Update J. Philip Barnes Pelican Aero Group
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Pelican Aero Group
2Lift 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
Pelican Aero Group
3Lift 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
5Lift 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-L)
dcL/da = p A/2Induced drag: cDv = cL
2/(pA)
PrandtlLift slope (any-A, low-L)
dcL/da ≈ 2pA/(A+2)Induced drag: cDv ≈ cL
2/(pA)
Prandtl-JonesInduced drag: cDv ≈ cL
2/(pA)But what about thickness?
Pelican Aero Group
6
0.0
0.1
0.2
0.3
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 /da) / 2ph
Aspect Ratio, A
Normalized Lift-slope ~ Test Data Vs. Theory
-10 TO 1527 to 3438 to 4659 to 60
Loc/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 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
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/(
/
hh
hp
a
L
c
L
AAddc
Pelican Aero Group
10Lift 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 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 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 PolhamusK ≡ dcD/dcL
2 ; t ≡ ( K-KPJ ) /( KPo-KPJ )
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
PreliminaryEmpirical
Correlation
t = e-a(t/c)-b(t/c)2
Prandtl-JonesdcD/dcL
2 = 1/(pA)
Polhamus cD ≈ a cL dcD/dcL
2 ≈ 1/(dcL/da)
t/c
t ≡ [dcD/dcL2 - 1/(pA)] / [1/(dcL/da) - 1/(pA)]
Pelican Aero Group
14Lift 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
2 / (dcL/da)• 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
Pelican Aero Group
16Lift 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
02. Loop on specified angle of attack, a (say from 0o to 10o) 03. Compute the lift slope, dcL/da (Diederich or Polhamus)04. Compute the lift coefficient, cL (given a and dcL/da)05. Compute Prandtl-Jones induced drag coefficient, cDv_PJ
07. Get induced-drag transition (t) at thickness ratio (t/c)08. Compute induced drag coefficient (cDv) given (t) 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 a or cL
Pelican Aero Group
17Lift 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
Lo
Application: Me-163 Assume: a) no twist, low Mach number b) 9% thickness (t/c) c) section h = 0.95 Measure from sketch: a) Leading-edge sweep (Lo)
b) Span (b) c) Root (centerline) & tip chords Tasks: 1) Get parameters S, A, r, Lc/2
Phil Barnes has a Master’s Degree in Aerospace Engineering from Cal Poly Pomona and a Bachelor’s Degree in Mechanical Engineering from the University of Arizona. He has 31-years of experience in the performance analysis and computer modeling of aerospace vehicles and subsystems at Northrop Grumman. Phil has authored diverse technical papers and studies of gears, computer graphics, orbital mechanics, aerodynamics, and propellers, including internationally-recognized studies of albatross dynamic 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