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Wing Efficiency in Aircraft Drag Polars

Explanation of a chart showing empirical data of aircraft drag polars based on lift and drag coefficients. Includes formulas for viscous and inviscid drag contribution, aspect ratio impact on wing efficiency, and data from various aircraft models.

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Wing Efficiency in Aircraft Drag Polars

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  1. Explanation of e vs A Chart • The chart is empirical and assumes that the aircraft drag polar can be expressed as CD = CD min + K(CL – CL min)2 • The K in the drag-due-to-lift term is made up of the viscous drag-due-to lift K” (due to the viscous separation as seen in the airfoil drag polar) and the inviscid drag-due-to-lift K’(due to the influence of the trailing vortices on the wing ac). K’ = 1/pAe’ from finite wing theory where e’ depends on spanwise lift distribution and is typically 0.8 to 0.9. K” ~ 0.01-0.03 from airfoil data. The K’ and K” are combined as K = 1/pAe = 1/pAe’ + K”. • The aircraft flight test drag polar data is plotted CD min vs (CL – CL min)2 up to the drag break. The slope K is then determined. This K is a composite of the viscous and inviscid drag-due-to-lift (DDTL). The wing e is then determined from the expression K = 1/pAe. • The reason that e decreases with A is because the contribution from the inviscid DDTL decreases with increasing A and is very soon overwhelmed by the contribution from the viscous DDTL. If you increased A to 100 (unrealistic) the inviscid DDTL would be almost zero but the viscous DDTL would still be there. • Some of the aircraft drag polars in my data base are shown on the following charts. My value of e = 0.51 for the C-5A/B is from Lockheed – Georgia report LG1C22-1-1 where at Mach 0.75 the CD min = 0.0162, CL min = 0.15, CD = 0.026 at a CL = 0.5 (the cruise CL).

  2. Subsonic ‘e’ vs Aspect Ratio ‘e’ determined from drag polar CD = CDmin + K ( CL – CLmin)2 K = 1 / pAe SymbolMin CL ~ 0 ~ 0.1 ~ 0.2 ~ 0.3 Closed No Sweep Open Swept Wing 1.0 0.9 F-16C I-26 I-R3 0.8 U-2S F-15E F-104 RQ-4A ASW-12 Genesis 2 F-4C 0.7 Wing Efficiency Factor, e Cirrus Tier 3- Med-High Camber F-20 ASW-27B ASW 22 0.6 A-340 L-1011 LS-8A SB-13 B-52 B-707 F-5E Horten IV W570A B-747 C-5B 0.5 Mach 0.7 - 0.8 Sweep > 25 o Low-Med Camber ASW-20 Sweep ~ 15 o 0.4 0 5 10 15 20 25 30 35 40 Aspect Ratio

  3. High-speed Drag Polars for Large Transport Aircraft – Flight Test Data

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