Explanation of e vs a chart
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Explanation of e vs A Chart. The chart is empirical and assumes that the aircraft drag polar can be expressed as C D = C D min + K(C L – C L min ) 2

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Explanation of e vs a chart
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).


Subsonic e vs aspect ratio
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



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