For those of you who followed the "Lifting bows w/foresails"-thread in rec.boats.racing: Here´s a computer run for the Cherub-dinghy, with an asymmetrical spinnaker in an apparent wind of 20 kn at an apparent wind angle of 70°.
I only give a short explanation below. You can figure out the rest from the listing at the end of the article, if you´re interested.
View from behind & below
Asymmetrical - section forces [N] & moments [Nm]
Section DriveF SinkF HeelF HeelMom YawMom PitchMom 1 24 -13 12 3 1743 -19 2 143 -97 141 151 5116 77 3 182 -122 153 343 2646 332 4 171 -140 124 408 -1247 533 5 123 -161 73 311 -3031 585 6 26 -53 10 48 -558 174 Total 669 -586 513 1265 76 1682
The third column, SinkF, is the sail force component perpendicular to the sea surface. Negative sink is LIFT, so the kite is lifting the boat at a force of 586 N, or about 59 kilos. The asymmetrical is driving the boat at 67 kilos, so the sail is lifting the boat nearly as much as it is thrusting it forward.
Considering that the boat weighs (incl. crew) some 250 kg, the lift of the asymmetrical is important in terms of reducing displacement. No wonder Cherub sailors will tell you their boat is merely skimming on the surface, leaping from wave to wave.
MainSail - section forces [N] & moments [Nm], including mast
Section DriveF SinkF HeelF HeelMom YawMom PitchMom 1 46 -5 38 31 -2691 42 2 78 -9 61 102 -5615 142 3 73 -11 56 145 -6003 207 4 65 -12 49 174 -5760 250 5 60 -15 46 205 -5461 293 6 35 -12 23 125 -2052 211 Total 356 -65 273 781 -450 1146
Even all sections of the main are lifting (negative SinkF). I have assumed a realistic bow-up trim of the boat (from photos) - the mast leans so heavily aft that the main is actually working like your book cover opened. Nevertheless, both sails are pitching the bow down (positive pitching moment), the asymmetrical even more so than the main.
Together, the lift of the main and the asymmetrical corresponds to approximately 30% of the boat's displacement.
MACSAIL DATA SHEET: Asy.10xaero & Main.10xaeroª AWA: 70.0°
* INPUT VALUES *
Rig measurements
I= 5.650 J= 3.000 BAS= 0.600 Rake at Fstay= 1.100
Sail scaling
Headsail luff= 6.500 Mainsail luff= 5.480
Mast diameter
Up to hounds= 0.000 At mast head= 0.000
Apparent Wind
App. wind angle= 70.0 App. wind speed= 10.0 VelScale= 20.0
Sheeting angles
Mainsail= 47.0 Headsail= 49.0
Boat attitude
Heel angle= 0.0 MRPL(%)= 10.0
Headsl tack h.= 0.250 Freeboard h.= 0.5
* PANEL CONFIGURATION *
CutNumber= 6
Panels in Headsail
Segments= 6 Sectors= 10 Total panels in Sail= 60
Panels in Mainsail
Segments= 6 Sectors= 10 Total panels in Sail= 60
Wake alignment:
HeadSail Steps: 3, Steplenght (m): 0.1000
MainSail Steps: 3, Steplenght (m) = 0.1000
* AERODYNAMIC COEFFICIENTS *
* HeadSail Area = 13.0 m2
HeadSail - Shape description
Section Height Chord Girth Camber Twist Entry/CL
1 0.184 3.229 3.629 21.5 % -11° 86° Fris 22-16
2 0.886 2.938 3.341 22.7 % -6° -82° Fris 55-14
3 1.929 2.604 2.948 22.3 % -2° -76° Fris 55-13
4 3.005 2.119 2.432 23.5 % 2° -70° Fris 51-13
5 4.219 1.307 1.535 25.6 % 7° -61° Fris 46-13
6 5.258 0.400 0.482 27.6 % 12° -54° Fris 41-14
HeadSail - Lift, drag & flow
Lift coeff. CL = 0.993 Drag coeff. CD = 0.335
Drive coeff. Cx = 0.818 Heel coeff. Cy = 0.654
Section Section cl Luff flow Leech flow
1 0.28 luffing Sep. at x= 0.74
2 0.85 luffing Sep. at x= 0.80
3 1.16 Ideal - low Sep. at x= 0.84
4 1.22 Ideal incidence Sep. at x= 0.80
5 1.11 Lee bubble - short Sep. at x= 0.79
6 1.23 Lee bubble - long Sep. at x= 0.74
HeadSail - section forces [N] & moments [Nm]
Section DriveF SinkF HeelF HeelMom YawMom PitchMom
1 24 -13 12 3 1743 -19
2 143 -97 141 151 5116 77
3 182 -122 153 343 2646 332
4 171 -140 124 408 -1247 533
5 123 -161 73 311 -3031 585
6 26 -53 10 48 -558 174
Total 669 -586 513 1265 76 1682
HeadSail - Center of effort distance from mastfoot [m]
Vertical CE Horisontal CE Pitching CE
-17.386 m 0.064 m 1.340 m
* MainSail Area = 8.2 m2
MainSail - Shape description
Section Height Chord Girth Camber Twist Entry/CL
1 0.339 1.795 1.809 5.5 % 1° 59° Fris 21-20
2 1.157 1.786 1.813 7.5 % 2° 66° Fris 22-19
3 2.116 1.724 1.764 9.3 % 4° 73° Fris 23-18
4 3.077 1.577 1.622 10.3 % 6° 78° Fris 24-18
5 4.044 1.299 1.337 10.6 % 8° 82° Fris 26-17
6 5.019 0.633 0.651 10.6 % 9° 84° Fris 27-16
MainSail - Lift, drag & flow
Lift coeff. CL = 0.859 Drag coeff. CD = 0.270
Drive coeff. Cx = 0.715 Heel coeff. Cy = 0.548
Section Section cl Luff flow Leech flow
1 0.77 Lee bubble - short
2 0.88 Lee bubble - short
3 0.85 Ideal - high
4 0.81 Ideal incidence
5 0.90 Ideal - low
6 1.03 Lee bubble - long Sep. at x= 0.25
MainSail - section forces [N] & moments [Nm], including mast
Section DriveF SinkF HeelF HeelMom YawMom PitchMom
1 46 -5 38 31 -2691 42
2 78 -9 61 102 -5615 142
3 73 -11 56 145 -6003 207
4 65 -12 49 174 -5760 250
5 60 -15 46 205 -5461 293
6 35 -12 23 125 -2052 211
Total 356 -65 273 781 -450 1146
MainSail - Center of effort distance from mastfoot [m]
Vertical CE Horisontal CE Pitching CE
3.755 m -0.716 m 2.725 m
* Combined coefficients, both sails together
HeadSail MainSail Combined
Lift coefficient 0.993 0.859 0.941
Drag coefficient 0.335 0.270 0.310
Drive coefficient 0.818 0.715 0.778
Heel coefficient 0.654 0.548 0.613
Heel.moment coeff. 5.035 4.948 5.001
Ratios
Lift/Drag ratio 2.965 3.179 3.037
Drive/Heel ratio 1.251 1.305 1.270
Drive/Heel.momnt r. 0.163 0.144 0.156
* Forces & moments in apparent wind 10.0 m/s, 70.0°, no leeway
HeadSail MainSail Combined
Driving force 0.650 0.357 1.007 kN
Heeling force 0.520 0.274 0.793 kN
Heeling moment 1.265 0.781 2.046 kNm
Yaw moment 0.076 -0.450 -0.374 kNm
Pitching moment 1.682 1.146 2.827 kNm
Center of effort distance from mastfoot [m]
HeadSail MainSail Combined
Vertical CE -17.386 3.755 15.116
Horisontal CE 0.064 -0.716 -0.207
CE for pitching 1.340 2.725 1.687
* Forces in apparent wind 10.0 m/s, 70.0°, leeway= 4°
Driving force 0.685 0.375 1.060 kN
Lateral force 0.473 0.248 0.721 kN
Aerodynamics calculated in 172 seconds
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