Twin Wing Parametric Study

These figures present the results of a parametric study of the key geometry variables in a twin rigid wing rig (some of which are depicted here). The study used the Cmarc panel code to calculate the lift and induced drag of the two isolated wings in combination, including ground effects. An NACA 0012 airfoil was used (although the actual choice of airfoil should not affect the results of this inviscid analysis).

When compared on the basis of equal rig heights, the twin wing was superior in nearly every respect to a comparable analysis performed on a single wing rig. However, the actual performance may differ because of Reynolds number effects (the twin wing's Reynolds number is less than half that of the single wing) and compromises necessay to provide adequate structural stiffness to the twin wing's long, slender panels.

Two key figures of merit were used. The first, axial force coefficient, is the component of the aerodynamic force that is parallel to the yacht centerline. This is what drives the boat, and is primarily a light wind metric. The second is a metric which I call drive efficiency, which is a measure of how much driving force is produced for a given amount of heeling moment. This is a heavy wind metric, since it takes into account the fact that the yacht is limited by its stability. When this latter metric is formed using nondimensional coefficients, the results have to be adjusted for the fact that the rolling moment coefficients are nondimensionalized using different spans, and must be placed on the same basis when comparing configurations with different luff lengths.



Configurations analyzed:
Half Apex Angle, q, degrees Aspect Ratio, H2/S Apparent Wind, b, degrees Left Panel Deflection, d1, degrees Differential Deflection, d2-d1, degrees Gap Ratio, Gap/H Taper Ratio, Ct/Cr Height, H, feet Length, L, feet Root Chord, Cr, feet Tip Chord, Ct, feet
Run Theta Aspect Beta d1_ d2md1 GapRatio Taper H L Cr Ct
1 12 6 -15 0 0 0.1 0.5 18.8149 19.2352 2.0449 1.0224
2 14 6 -15 0 0 0.1 0.5 18.8149 19.3909 2.0284 1.0142
3 16 6 -15 0 0 0.1 0.5 18.8149 19.5731 2.0096 1.0048
4 18 6 -15 0 0 0.1 0.5 18.8149 19.7831 1.9882 .9941
5 20 6 -15 0 0 0.1 0.5 18.8149 20.0224 1.9645 .9822
6 12 8 -15 0 0 0.1 0.5 21.7256 22.2109 1.7709 .8855
7 14 8 -15 0 0 0.1 0.5 21.7256 22.3907 1.7567 .8783
8 16 8 -15 0 0 0.1 0.5 21.7256 22.6011 1.7403 .8702
9 18 8 -15 0 0 0.1 0.5 21.7256 22.8436 1.7219 .8609
10 20 8 -15 0 0 0.1 0.5 21.7256 23.1199 1.7013 .8506
11 12 4 -15 0 0 0.1 0.5 15.3623 15.7055 2.5044 1.2522
12 14 4 -15 0 0 0.1 0.5 15.3623 15.8326 2.4843 1.2422
13 16 4 -15 0 0 0.1 0.5 15.3623 15.9814 2.4612 1.2306
14 18 4 -15 0 0 0.1 0.5 15.3623 16.1529 2.4351 1.2175
15 20 4 -15 0 0 0.1 0.5 15.3623 16.3482 2.406 1.203
16 16 6 -15 0 -5 0.1 0.5 18.8149 19.5731 2.0096 1.0048
17 16 6 -15 0 -10 0.1 0.5 18.8149 19.5731 2.0096 1.0048
18 16 6 -15 0 -15 0.1 0.5 18.8149 19.5731 2.0096 1.0048
19 16 6 -15 0 -20 0.1 0.5 18.8149 19.5731 2.0096 1.0048
20 16 6 -15 0 -25 0.1 0.5 18.8149 19.5731 2.0096 1.0048
21 16 6 -15 0 0 0.1 0.4 18.8149 19.5731 2.1531 .8612
22 16 6 -15 0 0 0.1 0.3 18.8149 19.5731 2.3187 .6956
23 16 6 -15 0 0 0.1 0.2 18.8149 19.5731 2.5119 .5024
24 16 6 -15 0 0 0.1 0.1 18.8149 19.5731 2.7403 .274
25 16 6 -20 -5 0 0.1 0.5 18.8149 19.5731 2.0096 1.0048
26 16 6 -25 -10 0 0.1 0.5 18.8149 19.5731 2.0096 1.0048
27 16 6 -30 -15 0 0.1 0.5 18.8149 19.5731 2.0096 1.0048
28 16 6 -15 -5 0 0.1 0.5 18.8149 19.5731 2.0096 1.0048
29 16 6 -15 -10 0 0.1 0.5 18.8149 19.5731 2.0096 1.0048
30 16 6 -15 0 0 0.2 0.5 18.8149 19.5731 2.0096 1.0048
31 16 6 -15 0 0 0.05 0.5 18.8149 19.5731 2.0096 1.0048
32 16 6 -15 0 0 0.1 0.6 18.8149 19.5731 1.884 1.1304
33 16 6 -15 0 0 0.1 0.7 18.8149 19.5731 1.7731 1.2412
34 16 6 -15 0 0 0.1 0.8 18.8149 19.5731 1.6746 1.3397
35 16 6 -15 0 0 0.1 1 18.8149 19.5731 1.5072 1.5072
Average Chord, CMAC, feet Link Length, Lp-L, feet Pivot Length, Lp, Feet Length Ratio, Lp/L Width, W, feet Root Y, Yr, feet Root Z, Zr, feet Pivot Height, Hp, feet Tip Clearance, Wt, feet Tip Clearance, Fraction of Tip Chord Tip Y, Yt, feet Tip Z, Zt, feet
Run MAC Link Lp LenRatio W Yr Zr Hp Wt Wt/Ct Yt Zt
1 1.5336 2.4051 21.6403 1.125 8.9985 4.4993 1.8815 23.0489 1.0001 .9781 .5 20.6964
2 1.5213 2.0339 21.4248 1.1049 10.3663 5.1831 1.8815 22.6699 .9841 .9703 .492 20.6964
3 1.5072 1.752 21.3252 1.0895 11.756 5.878 1.8815 22.3805 .9659 .9613 .4829 20.6964
4 1.4912 1.5298 21.3129 1.0773 13.1721 6.5861 1.8815 22.1513 .9455 .9511 .4727 20.6964
5 1.4734 1.3493 21.3717 1.0674 14.6191 7.3096 1.8815 21.9643 .923 .9397 .4615 20.6964
6 1.3282 2.0829 24.2938 1.0938 10.1019 5.051 2.1726 25.9355 .8661 .9781 .4331 23.8981
7 1.3175 1.7614 24.1521 1.0787 11.6858 5.8429 2.1726 25.6072 .8523 .9703 .4261 23.8981
8 1.3052 1.5173 24.1184 1.0671 13.2959 6.6479 2.1726 25.3567 .8365 .9613 .4182 23.8981
9 1.2914 1.3248 24.1684 1.058 14.9369 7.4685 2.1726 25.1581 .8188 .9511 .4094 23.8981
10 1.276 1.1686 24.2884 1.0505 16.6143 8.3071 2.1726 24.9962 .7993 .9397 .3997 23.8981
11 1.8783 2.9456 18.6511 1.1876 7.7556 3.8778 1.5362 19.7798 1.2249 .9781 .6124 16.8985
12 1.8632 2.491 18.3236 1.1573 8.8658 4.4329 1.5362 19.3156 1.2053 .9703 .6026 16.8985
13 1.8459 2.1458 18.1272 1.1343 9.9931 4.9965 1.5362 18.9612 1.1829 .9613 .5915 16.8985
14 1.8263 1.8736 18.0265 1.116 11.141 5.5705 1.5362 18.6804 1.1579 .9511 .579 16.8985
15 1.8045 1.6526 18.0008 1.1011 12.3133 6.1566 1.5362 18.4514 1.1304 .9397 .5652 16.8985
16 1.5072 1.752 21.3252 1.0895 11.756 5.878 1.8815 22.3805 .9659 .9613 .4829 20.6964
17 1.5072 1.752 21.3252 1.0895 11.756 5.878 1.8815 22.3805 .9659 .9613 .4829 20.6964
18 1.5072 1.752 21.3252 1.0895 11.756 5.878 1.8815 22.3805 .9659 .9613 .4829 20.6964
19 1.5072 1.752 21.3252 1.0895 11.756 5.878 1.8815 22.3805 .9659 .9613 .4829 20.6964
20 1.5072 1.752 21.3252 1.0895 11.756 5.878 1.8815 22.3805 .9659 .9613 .4829 20.6964
21 1.5072 1.5017 21.0749 1.0767 11.618 5.809 1.8815 22.14 .8279 .9613 .4139 20.6964
22 1.5072 1.213 20.7861 1.062 11.4588 5.7294 1.8815 21.8623 .6687 .9613 .3343 20.6964
23 1.5072 .876 20.4491 1.0448 11.2731 5.6365 1.8815 21.5385 .4829 .9613 .2415 20.6964
24 1.5072 .4778 20.0509 1.0244 11.0536 5.5268 1.8815 21.1557 .2634 .9613 .1317 20.6964
25 1.5072 1.752 21.3252 1.0895 11.756 5.878 1.8815 22.3805 .9659 .9613 .4829 20.6964
26 1.5072 1.752 21.3252 1.0895 11.756 5.878 1.8815 22.3805 .9659 .9613 .4829 20.6964
27 1.5072 1.752 21.3252 1.0895 11.756 5.878 1.8815 22.3805 .9659 .9613 .4829 20.6964
28 1.5072 1.752 21.3252 1.0895 11.756 5.878 1.8815 22.3805 .9659 .9613 .4829 20.6964
29 1.5072 1.752 21.3252 1.0895 11.756 5.878 1.8815 22.3805 .9659 .9613 .4829 20.6964
30 1.5072 1.752 21.3252 1.0895 11.756 5.878 3.763 24.262 .9659 .9613 .4829 22.5779
31 1.5072 1.752 21.3252 1.0895 11.756 5.878 .9407 21.4398 .9659 .9613 .4829 19.7556
32 1.5072 1.971 21.5442 1.1007 11.8768 5.9384 1.8815 22.5911 1.0866 .9613 .5433 20.6964
33 1.5072 2.1643 21.7374 1.1106 11.9833 5.9916 1.8815 22.7768 1.1931 .9613 .5966 20.6964
34 1.5072 2.3361 21.9092 1.1194 12.078 6.039 1.8815 22.9419 1.2878 .9613 .6439 20.6964
35 1.5072 2.6281 22.2012 1.1343 12.2389 6.1195 1.8815 23.2226 1.4488 .9613 .7244 20.6964


Results:

CA: Axial Force Coefficient; Positive is AFT (negative is good)
CA/Cl: (Axial force Coefficient/Rolling Moment Coefficient)
Drive Efficiency: (Axial force Coefficient/Rolling Moment Coefficient)*(H/Href)
Gap: Distance between foot and surface
Taper Ratio: Chord at head divided by chord at foot
Ar: Aspect ratio (span^2 / area)
Beta: Apparent wind angle
Trim: Rotation of wings to adjust angleof attack

ChartObject Twin Wing Summary Results

CN, Angle, Variation, AR= 4, 6, 8

CA Angle, Variation, AR= 4, 6, 8

CY Angle, Variation, AR= 4, 6, 8

CA/Cl, Angle Variation, AR= 4, 6, 8

Cl, Angle Variation, AR= 4, 6, 8

Eficiency, Angle Variation, AR= 4, 6, 8

CA/Cl, Taper Ratio Variation Ar = 6, Gap = 0.1 H, Beta = 15 deg

CD, Taper Ratio Variation Ar = 6, Gap = 0.1 H, Beta = 15 deg

CL, Taper Ratio Variation Ar = 6, Gap = 0.1 H, Beta = 15 deg

CD, Gap Variation Ar = 6, Gap = 0.1 H, T= 0.5, Beta = 15 deg

CL, Gap Variation Ar = 6, Gap = 0.1 H, T= 0.5, Beta = 15 deg

CA/Cl, Gap Variation Ar = 6, Gap = 0.1 H, T= 0.5, Beta = 15 deg

CA/Cl, Apparent Wind Variation Ar = 6, Gap = 0.1 H, T = 0.5

CA/Cl, Trim Variation Ar = 6, Gap = 0.1 H, , T=0.5, Beta = 15 deg

CA/Cl, Differential Trim Variation AR= 6, Taper= 0.5, Gap= 0.1 H Beta= 15 deg

Cl, Differential Trim Variation AR= 6, Taper= 0.5, Gap= 0.1 H Beta= 15 deg

CY, Differential Trim Variation AR= 6, Taper= 0.5, Gap= 0.1 H Beta= 15 deg

CA, Differential Trim Variation AR= 6, Taper= 0.5, Gap= 0.1 H Beta= 15 deg



Last Updated on 1/16/99
By Thomas E. Speer
Email: tspeer@gte.net

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