Single Wing Efficiency Study

These are the results of a parametric study I did to examine the effects of rigid wing rig planforms. The study used the Cmarc panel code, and all wings had an NACA 0012 airfoil (although the results should not be affected by the choice of airfoil as this was an inviscid analysis). This study was also used as a comparison case for a similar study that looked at twin wing "A" frame rig geometries. The results of this analysis showed that constant chord wings are surprisingly efficient, and the conventional single taper planforms may not be such a good choice.

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.

CA: Axial Force Coefficient; Positive is AFT (negative is good)
CA/Cl: (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)

ChartObject Single WingAspect Ratio VariationTaper Ratio = 0.5, Gap = 0.1 H, Beta =15 deg

ChartObject Single WingTaper Ratio VariationAr = 6, Gap = 0.1 H, Beta = 15 deg

ChartObject Single WingGap VariationAr=6, Taper=0.5, Beta=15 deg

ChartObject Single WingTrim VariationAr=6, Taper=0.5, Gap=0.1 H, Beta=15 deg
Configuration Matrix
Aspect Ratio, H2/S Apparent Wind, b, degrees Panel Deflection, d, degrees Gap Ratio, Gap/H Taper Ratio, Ct/Cr Span, H Reference Chord, CMAC
Case Aspect Beta d1 GapRatio Taper H MAC
1 6 -15 0 0.1 0.5 18.81489 3.135815
2 8 -15 0 0.1 0.5 21.72556 2.715695
3 4 -15 0 0.1 0.5 15.36229 3.840573
4 6 -20 -5 0.1 0.5 18.81489 3.135815
5 6 -25 -10 0.1 0.5 18.81489 3.135815
6 6 -30 -15 0.1 0.5 18.81489 3.135815
7 6 -15 -5 0.1 0.5 18.81489 3.135815
8 6 -15 -10 0.1 0.5 18.81489 3.135815
9 6 -15 0 0.2 0.5 18.81489 3.135815
10 6 -15 0 0.05 0.5 18.81489 3.135815
11 6 -15 0 0.1 0.4 18.81489 3.135815
12 6 -15 0 0.1 0.3 18.81489 3.135815
13 6 -15 0 0.1 0.2 18.81489 3.135815
14 6 -15 0 0.1 0.1 18.81489 3.135815
15 6 -15 0 0.1 1 18.81489 3.135815
16 6 -15 0 0.1 0.8 18.81489 3.135815
17 6 -15 0 0.1 0.7 18.81489 3.135815
18 6 -15 0 0.1 0.6 18.81489 3.135815

Results
Case Normal Force Coefficient, CN Axial Force Coefficient, CA Side Force Coefficient, CY Pitching Moment Coefficient, Cm Yawing Moment Coefficient, Cn Rolling Moment Coefficient, Cl Drive Efficiency, CA/Cl Adjusted Efficiency (CA/Cl)/(H/Href)
CN CA CY Cm Cn Cl
1 -0.0268 -0.2264 1.1844 -0.7803 -0.0031 -0.6751 0.3353577 0.335357725
2 -0.0188 -0.2645 1.3225 -1.2265 -0.0021 -0.7575 0.3491749 0.302394349
3 -0.0434 -0.1741 0.9796 -0.385 -0.0054 -0.5529 0.3148852 0.385653974
4 -0.0268 -0.3288 1.1603 -1.1305 -0.0031 -0.6613 0.4972025 0.49720248
5 -0.0268 -0.4288 1.1273 -1.4722 -0.0031 -0.6424 0.6674969 0.667496887
6 -0.0268 -0.5255 1.0857 -1.8028 -0.0031 -0.6186 0.8494989 0.849498868
7 -0.0122 -0.1704 0.7919 -0.5856 -0.0024 -0.4515 0.3774086 0.377408638
8 -0.0032 -0.0944 0.3958 -0.3238 -0.0013 -0.2257 0.4182543 0.41825432
9 -0.0222 -0.2204 1.1653 -0.8986 -0.0031 -0.7839 0.2811583 0.281158311
10 -0.0374 -0.2334 1.2087 -0.7231 -0.0032 -0.6235 0.3743384 0.374338412
11 -0.0331 -0.224 1.1714 -0.7636 -0.0034 -0.658 0.3404255 0.340425532
12 -0.0402 -0.2202 1.1526 -0.7399 -0.0037 -0.6354 0.3465534 0.346553352
13 -0.0484 -0.2149 1.1266 -0.7064 -0.0042 -0.6051 0.3551479 0.355147909
14 -0.0572 -0.2044 1.0822 -0.6459 -0.0049 -0.5584 0.3660458 0.366045845
15 -0.0043 -0.2306 1.2105 -0.8193 -0.0029 -0.7211 0.3197892 0.319789211
16 -0.0118 -0.2299 1.2049 -0.8091 -0.0029 -0.7079 0.3247634 0.324763385
17 -0.0163 -0.2292 1.2003 -0.8019 -0.0029 -0.6992 0.3278032 0.327803204
18 -0.0212 -0.2281 1.1937 -0.7926 -0.003 -0.6885 0.3312999 0.331299927


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

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