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Oswald efficiency estimation function

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26 Oct 2012 (Updated )

Finds Oswald efficiency factor for purposes of approximating a simple parabolic aircraft drag polar.

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Description

This function lets you use different methods to estimate Oswald efficiency factor, e, for purposes of approximating a simple parabolic drag polar:
C_D = C_D0 + C_L^2/(pi*e*AR), where C_L is lift coefficient.
 
Based on some or all of the following:
- Wing aspect ratio
- Wing sweep
- Parasite drag coefficient (drag independent of lift)
- Ratio of fuselage diameter (or width) to wing span
- Planform efficiency - usually .98 < u < 1

You can also choose between two common methods as proposed by Raymer ("Aicraft Design: A Conceptual Approach") or Shevell ("Fundamentals of Flight"). OSWALDFACTOR can also calculate using both methods and return the most pessimistic or optimistic result or a weighted average of the two results.
 
Example: Replicate Shevell's Figure 11.8.
        u = .99; df_b = 0.114;
 
        ARx = linspace(0,12,25);
        [CD0,AR] = meshgrid([.01 .015 .02 .025],ARx);
        e = oswaldfactor(AR,0,'shevell',CD0,df_b,u);
        plot(ARx,e); axis([0 12 .6 1]); grid on
        xlabel('Aspect Ratio'); ylabel('Efficiency factor, e')
        legend('C_{D,0} = 0.01','0.015','0.02','0.025')
        text(8.5,.63,'u = 0.99 s = 0.975')
 
        sweepx = linspace(0,40,41);
        [AR,sweep] = meshgrid([4;8;12],sweepx*pi/180);
        e = oswaldfactor(AR,sweep,'shevell',0,df_b,u)./...
             oswaldfactor(AR, 0 ,'shevell',0,df_b,u);
        axes('pos',[0.25 0.25 0.3 0.25]);
        plot(sweepx,e); axis([0 40 .9 1.02]); grid on
        xlabel('Sweep, \Lambda (deg)'); ylabel('e_\Lambda/e_{\Lambda=0}')
        legend('AR = 4','8','12','Location','SouthWest')

Required Products MATLAB
MATLAB release MATLAB 8.1 (R2013a)
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Comments and Ratings (1)
05 Nov 2012 Andante  
Updates
30 Oct 2012

improved math and curve fit coefficients; added example

31 Oct 2012

added weighted average method; changed exponent from 2.3 to 2.2 so as not to be too optimistic; better input handling

21 Nov 2012

improved n-dim input handling

26 Dec 2012

name change to help differentiate from lifting line e

09 Sep 2013

minor: documentation and input handling

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