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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.

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Lift and Drag Review and Renew Correlating 50 Years of NACA / NASA Test Data

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  1. 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 cT u a cN a vo u cT cF 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

  2. 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 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

  3. Configurations studied ~ Data and theory references • www.NTRS.NASA.gov • www.AERADE.Cranfield.ac.uk • www.Google.com • 114 configurations, thickness: 02 - 20% 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

  4. Wing geometry and aerodynamic terms S ≡ plan area b ≡ span c ≡ chord r≡ tip chord / root chord t≡ streamwise thickness t/c≡ thickness ratio A ≡ aspect ratio = b2/S = b/cav a≡ angle of attack cL ≡ lift coefficient h ≡ lift slope / (2p) cDv≡ vortex drag coefficient Lo≡ leading-edge sweep Lc/2≡ mid-chord sweep Lc/4≡ quarter-chord sweep Lo b t c Sweep conversion (given quarter-chord sweep) tanLn = tanLc/4+ (4/A) (n-¼) (r-1) / (r+1) 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

  5. Prandtl and Jones Theories Ludwig Prandtl Prandtl Lift slope (any-A, low-L) dcL/da ≈ 2pA/(A+2) Induced drag: cDv≈ cL2/(pA) Jones Lift slope (low-A, any-L) dcL/da = p A/2 Induced drag: cDv = cL2/(pA) Robert T. Jones Prandtl-Jones Induced drag: cDv≈ cL2/(pA) But what about 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

  6. Lift slope data and validation of theory Unswept Prandtl Helmbold Swept Helmbold-Polhamus Helmbold-Diederich 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

  7. 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

  8. Helmbold-Polhamus ~ 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

  9. Test data ~ Delta wing-body lift ~ effect of thickness 3% 5% 8% Minor effect of thickness on lift 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

  10. The Thin-wing Induced-drag Surprise ~ Circa 1950 Delta wing-body linearized drag polar A=2, M 0.25, NACA RM A50K20, A50K21, A51K28 3% 5% Polhamus: cDv≈acL ≈ cL2/(dcL/da) 8% Induced drag coefficient, cDv Prandtl-Jones: cDv = cL2/(pA) 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

  11. The Thin-wing Induced-drag Surprise ~ Circa 1950 Rectangular wing linearized drag polar A=4, Effect of thickness, NACA TN 3501 4% 6% Polhamus: cDv≈acL ≈ cL2/(dcL/da) 10% Prandtl-Jones: cDv = cL2/(pA) 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

  12. Induced-drag Transition ~ Prandtl-Jones to Polhamus t≡ [dcD/dcL2 - 1/(pA)] / [1/(dcL/da) - 1/(pA)] Polhamus cD ≈ a cL dcD/dcL2 ≈ 1/(dcL/da) Preliminary Empirical Correlation t = e-a(t/c)-b(t/c)2 Prandtl-Jones dcD/dcL2 = 1/(pA) t/c 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

  13. Effect of thickness on induced drag ~ symmetrical section No sweep No twist Assume elliptical loading Assume small angles cL≈ cN≈ 2p (a+u)[1] u ≈ -cN /(pA) [2] cD≈ cNa -cT + cF[3] Define thrust recovery: k ≡ cT / [cNtan(a+u)] ≈cT / [cN(a+u)] [4] Combine [1,2,3,4]: Nomenclature A aspect ratio voflight velocity a angle of attack u upwash angle * cL lift coefficient cD drag coefficient cNnormal force coef. cFfriction force coef. ** cT chord thrust coef. *** kthrust recovery (0-1) cT u a cD≈cF + (cN2) / (pA) + (1-k) (cN2) / (2p) cN a "very thin": k → 0 vo u "thick" : k →1 * Usually negative ** Upper + lower, chordwise *** Pressure integration, chordwise cT @k = 0: cD≈cF + cNa consistent with Polhamus cF 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

  14. 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 = cL2 / (pA) • Polhamus: induced drag upper limit • zero thickness, symmetrical section • formula: cDv≈acL≈ cL2 / (dcL/da) • Enhancements via our review & renew study: 1) Showed Prandtl-Jones drag is limited to thick wings 2) Suggested correlation for thick-to-thin drag transition 3) New formula for induced drag with symmetrical sections 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

  15. Application of method ~ "Neutral-trimmed" drag polar 01. Set geom (aspect ratio, thickness, & sweep) {A, t/c, Lc/2} 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 06. Compute Polhamus induced-drag coefficient, cDv_Po 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/D 12. Plot all results versus a or cL 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

  16. Sample application of method ~ homework assignment 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 2) Find L/D, a and cL at max L/D 3) e-mail results to: Phil@HowFliesTheAlbatross.com Lo b t c 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

  17. About the Author 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." 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

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