Lift and Drag Review and Renew - How Flies the Albatross and Drag Review and... · 2014-05-25 ·...

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


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


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


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


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

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 /d

Aspect Ratio, A

Normalized Lift‐slope ~ Test Data Vs. Theory

‐10 TO 1527 to 3438 to 4659 to 60

c/2

to


Lift slope data and validation of theory

PelicanAero Group 7


Helmbold-Diederich ~ Low-speed lift slope of any wing

42cos2/

)cos/(

22/

2/

FFddc

AF

c

L

c

PelicanAero Group 8


Helmbold-Polhamus ~ Low-speed lift slope of any wing

222/ 4)cos/(2

4)2/(

/

c

L

AAddc

PelicanAero Group 9


Test data ~ rectangular wing lift ~ effect of thickness

PelicanAero Group 10


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

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


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


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



The Thin-wing Induced-drag Surprise ~ Circa 1950

10%

6%

4%

Rectangular wing linearized drag polarA=4, Effect of thickness, NACA TN 3501


‐0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

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


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)]



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



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



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



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:

[email protected]


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 - How Flies the Albatross and Drag Review and... · 2014-05-25 ·...

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