This is how sails are simulated in the computer. For the simulation the sails are divided into small squares, panels, and the pressure difference between the windward and leeward side of each panel is calculated. The pressure difference (*P) at each panel can be regarded as a force acting in the middle of the panel, at right angles (perpendicular) to its surface. By summing up all the little pressure forces acting upon the individual panels, the total (resultant) force acting on each sail can be found. The total force on each sail can be divided into two components:

The driving force is pointing forward, while the heeling force acts sideways. Even more important than the heeling force is the heeling moment, which takes into account the point where the force is applied, approximately 1/3 up the height of the sail. The sail efficiency is best measured by the drive to heeling moment- ratio. In addition to the heeling moment, the computer program also calculates accurately the longitudinal yaw moment, which determines the balance or helm of the boat. When the calculated sail forces & moments are fed into a Velocity Prediction Program (VPP), the influence of sail shape on boat performance can be assessed.

The panel method suits itself excellently for the calculation of sails, since they have hardly any thickness. To simulate aeroplane wings or sail boat keels & rudders, thousands of panels are needed because of the thickness of these bodies. While Boeing or McDonnel-Douglas supercomputers are used for keel simulations, sails forces can be calculated with only 100 - 200 panels, at a satisfactory accuracy, and thus sail simulation can be performed on regular (powerful) desktop PCs. From the sample output below you can read, for instance, that some 380 kilos (750 lbs) are needed to power a maxi boat to its upwind speed of 9,5 kn.

The development of MacSail, the proprietory aerodynamic sail simulation program by WB-Sails, started in 1987 together with the Helsinki University of Technology. Since then, the program has been the subject of two thesis and has been brought to an advanced level, where viscous effects and flow separation are allowed for. The program is used in fairing out flaws of existing sail designs and in developing new, ever more efficient sail shapes. 

1. Aerodynamic coefficients, forces & moments. Sample output from MacSail
2. Pressures & velocities on panels. Sample output from MacSail
3. Cp-curves at one section. Sample output from MacSail
4. Velocity vectors on leeward side. Sample output from MacSail
5. Technical description of the MacSail-program

Numerical output sample from MacSail Aerodynamic coefficients, forces & moments

 MacSail run for the sails of Maxi Yacht Nicorette - sail flying shapes are scanned from photographs
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 Dimensions:

• ° [degree] - it may not show right on some browsers - sorry.
• 1 N [Newton] roughly 0.2 lbs
• 1 kN [kiloNewton] roughly 200 lbs
• 1 m roughly 3.3 ft
• 1 m/s roughly 2 knots

MACSAIL DATA SHEET: Nicorette

                    WB G1 8/95 26° 8xaero & WB M 8/95 24° 8xaero. AWA:23.0°

* AERODYNAMIC COEFFICIENTS *

* HeadSail             Area = 138.6 m2

  HeadSail - Shape description

  Section  Height   Chord    Girth   Camber    Twist  Entry/CL 
      1    3.177   10.436   10.575    7.1 %      1°     28°     Fris 22-16
      2    7.416    8.265    8.596   12.3 %      5°     42°     Fris 21-16
      3   11.551    6.158    6.541   15.3 %      9°     52°     Fris 21-16
      4   15.613    4.185    4.484   16.4 %     13°     59°     Fris 21-16
      5   19.646    2.320    2.480   16.1 %     18°     64°     Fris 22-16
      6   23.151    0.748    0.795   15.4 %     21°     68°     Fris 23-16

  HeadSail - Lift, drag & flow

Lift coeff. CL = 1.607 Drag coeff. CD = 0.125 Drive coeff. Cx = 0.513 Heel coeff. Cy = 1.528 

Numerical output sample from MacSail Flow velocities & pressures

 Note: Nicorette - but different run from forces & moments

MACSAIL DATA SHEET: Nicorette 

                    WB G1 8/95 26° 8xaero & WB M 8/95 24° 8xaero AWA: 21.0°

* INPUT VALUES *

Rig measurements
      I= 26.000    J= 7.300     BAS= 2.180     Rake at F´stay= 1.500     

Sail scaling
      Headsail luff= 25.500     Mainsail luff= 27.450    

Mast diameter
      Up to hounds=   0.000     At mast head=    0.000     

Apparent Wind
      App. wind angle= 21.0     App. wind speed= 8.0  VelScale= 20.0 

Sheeting angles
      Mainsail=         0.0     Headsail= 9.0  

Boat attitude
      Heel angle=      20.0     MRPL(%)= 10.0 
      Headsl tack h.= 0.100     Freeboard h.= 1.6  

* PANEL CONFIGURATION *
      CutNumber= 6

Panels in Headsail
      Segments= 5      Sectors= 8      Total panels in Sail= 40

Panels in Mainsail
      Segments= 6      Sectors= 8      Total panels in Sail= 48

Wake alignment:
      HeadSail Steps: 3, Steplenght (m): 0.1000
      MainSail Steps: 3, Steplenght (m) = 0.1000

      - Deny y-trailing vortex

* FLOW VELOCITIES & PRESSURE COEFFICIENTS in each panel*

* HEADSAIL velocities & pressures, panels from head to foot/luff to leech

Ulee/uƒ          Leeward velocity to apparent wind velocity ratio
Uw/uƒ            Windward velocity to apparent wind velocity ratio

Cplee            Leeward pressure coefficient
Cpwind           Windward pressure coefficient
*Cp              Panel pressure coefficient (delta Cp)
 
Panel    Ulee/uƒ   Uw/uƒ (U/Umax)^2  Cplee   Cpwind    *Cp    Luff/leech flow
Section #5
  1, 1    1.223    0.713    0.537   -0.496    0.492    0.988  Lee bubble - short
  1, 2    1.594    0.615    0.794   -1.540    0.621    2.161  
  1, 3    1.735    0.560    0.950   -2.012    0.687    2.698  
  1, 4    1.779    0.525    1.000   -2.164    0.725    2.889  
  1, 5    1.760    0.497    0.978   -2.097    0.753    2.850  
  1, 6    1.648    0.492    0.852   -1.716    0.758    2.474  
  1, 7    1.481    0.604    0.680   -1.193    0.636    1.829  
  1, 8    1.327    0.849    0.476   -0.762    0.280    1.041  
Section #4
  2, 1    1.085    0.847    0.353   -0.177    0.282    0.459  Ideal - low       
  2, 2    1.497    0.627    0.673   -1.242    0.607    1.848  
  2, 3    1.718    0.529    0.887   -1.953    0.720    2.673  
  2, 4    1.821    0.465    0.996   -2.317    0.784    3.101  
  2, 5    1.825    0.423    1.000   -2.330    0.821    3.151  
  2, 6    1.739    0.420    0.908   -2.024    0.824    2.847  
  2, 7    1.593    0.466    0.763   -1.539    0.783    2.322  
  2, 8    1.388    0.596    0.579   -0.927    0.645    1.572  
Section #3
  3, 1    1.070    0.885    0.365   -0.145    0.217    0.362  Ideal - low       
  3, 2    1.449    0.671    0.670   -1.101    0.550    1.651  
  3, 3    1.666    0.571    0.885   -1.774    0.673    2.447  
  3, 4    1.771    0.503    1.000   -2.136    0.747    2.882  
  3, 5    1.752    0.471    0.979   -2.070    0.778    2.848  
  3, 6    1.674    0.480    0.894   -1.803    0.770    2.572  
  3, 7    1.550    0.541    0.766   -1.402    0.708    2.110  
  3, 8    1.384    0.685    0.611   -0.916    0.530    1.447  
Section #2
  4, 1    1.205    0.839    0.529   -0.452    0.295    0.747  Ideal incidence   
  4, 2    1.437    0.711    0.751   -1.064    0.495    1.558  
  4, 3    1.587    0.633    0.916   -1.518    0.599    2.117  
  4, 4    1.658    0.580    1.000   -1.747    0.664    2.411  
  4, 5    1.611    0.574    0.944   -1.594    0.671    2.265  
  4, 6    1.542    0.605    0.866   -1.378    0.634    2.012  
  4, 7    1.448    0.682    0.763   -1.096    0.535    1.631  
  4, 8    1.332    0.824    0.646   -0.774    0.321    1.095  
Section #1
  5, 1    1.309    0.701    0.902   -0.714    0.509    1.223  Lee bubble - short
  5, 2    1.427    0.739    0.909   -1.036    0.454    1.490  
  5, 3    1.478    0.717    0.975   -1.185    0.486    1.670  
  5, 4    1.497    0.702    1.000   -1.241    0.508    1.748  
  5, 5    1.445    0.723    0.932   -1.089    0.477    1.566  
  5, 6    1.392    0.770    0.865   -0.937    0.407    1.345  
  5, 7    1.311    0.839    0.767   -0.719    0.297    1.015  
  5, 8    1.223    0.925    0.668   -0.496    0.144    0.639  


* MAINSAIL velocities & pressures, from head to foot

Panel    Ulee/uƒ   Uw/uƒ (U/Umax)^2  Cplee   Cpwind    *Cp    Luff/leech flow
Section #6
  1, 1    1.224    0.735    0.628   -0.498    0.460    0.958  Lee bubble - short
  1, 2    1.504    0.620    0.831   -1.263    0.616    1.879  
  1, 3    1.603    0.559    0.943   -1.569    0.688    2.257  
  1, 4    1.637    0.530    0.984   -1.680    0.720    2.400  
  1, 5    1.650    0.503    1.000   -1.724    0.747    2.471  
  1, 6    1.558    0.523    0.891   -1.428    0.726    2.154  
  1, 7    1.412    0.570    0.732   -0.994    0.675    1.670  
  1, 8    1.212    0.656    0.539   -0.468    0.570    1.038  
Section #5
  2, 1    1.000    1.000    0.103    0.001    0.001    0.000  luffing           
  2, 2    1.144    0.991    0.521   -0.309    0.017    0.326  
  2, 3    1.429    0.953    0.813   -1.042    0.092    1.134  
  2, 4    1.545    0.852    0.950   -1.387    0.273    1.660  
  2, 5    1.585    0.798    1.000   -1.512    0.363    1.875  
  2, 6    1.512    0.757    0.910   -1.286    0.427    1.712  
  2, 7    1.380    0.734    0.758   -0.905    0.461    1.365  
  2, 8    1.195    0.749    0.569   -0.429    0.439    0.868  
Section #4
  3, 1    0.999    0.999    0.112    0.002    0.002    0.000  luffing           
  3, 2    0.854    0.992    0.342    0.270    0.016   -0.254  
  3, 3    1.202    0.959    0.676   -0.444    0.081    0.525  
  3, 4    1.397    0.865    0.913   -0.952    0.252    1.203  
  3, 5    1.462    0.817    1.000   -1.137    0.333    1.470  
  3, 6    1.432    0.781    0.959   -1.049    0.390    1.440  
  3, 7    1.337    0.762    0.837   -0.788    0.419    1.207  
  3, 8    1.184    0.777    0.656   -0.401    0.396    0.798  
Section #3
  4, 1    0.999    0.999    0.198    0.003    0.003    0.000  luffing           
  4, 2    0.827    0.992    0.381    0.316    0.016   -0.300  
  4, 3    1.084    0.964    0.655   -0.175    0.070    0.245  
  4, 4    1.261    0.886    0.886   -0.589    0.216    0.805  
  4, 5    1.323    0.851    0.975   -0.749    0.276    1.025  
  4, 6    1.339    0.818    1.000   -0.794    0.331    1.124  
  4, 7    1.297    0.796    0.939   -0.683    0.367    1.050  
  4, 8    1.184    0.796    0.781   -0.401    0.367    0.768  
Section #2
  5, 1    0.792    0.950    0.416    0.373    0.098   -0.275  Windward bubble   
  5, 2    0.891    0.919    0.525    0.207    0.156   -0.051  
  5, 3    1.047    0.826    0.726   -0.096    0.317    0.414  
  5, 4    1.165    0.809    0.900   -0.358    0.345    0.703  
  5, 5    1.208    0.812    0.966   -0.459    0.340    0.799  
  5, 6    1.229    0.810    1.000   -0.509    0.345    0.854  
  5, 7    1.209    0.820    0.968   -0.462    0.328    0.789  
  5, 8    1.141    0.849    0.862   -0.301    0.280    0.581  
Section #1
  6, 1    0.953    0.709    0.750    0.092    0.497    0.405  Ideal - low       
  6, 2    0.944    0.800    0.735    0.110    0.360    0.250  
  6, 3    1.016    0.826    0.852   -0.032    0.319    0.351  
  6, 4    1.079    0.825    0.962   -0.165    0.319    0.484  
  6, 5    1.100    0.829    1.000   -0.211    0.313    0.524  
  6, 6    1.099    0.837    0.998   -0.208    0.300    0.508  
  6, 7    1.078    0.858    0.959   -0.162    0.263    0.425  
  6, 8    1.043    0.899    0.897   -0.087    0.192    0.279

Pressure difference at the head section of the genoa. Leeward side (green), windard side (red), pressure difference Delta Cp (blue). Leech separation point on leeward side is indicated by arrow. In the separation zone the pressure coefficient is constant (in this cace Cp= -0.95). Note how, due to the leeward side separation, pressure drops (flow accelerates) near the leech on the windward side. In separated flow the pressures on the leeward & windward side are no longer equal at the leech, as is the case in attached flow.

Velocity vectors (flow speed) on leeward side.

 MacSail is based on the vortex-lattice method (VLM), which suits itself best for thin, highly cambered foils and allows reasonable calculation times even with (fast) microcomputers. Because of the large camber and twist of the sails it is necessary that the horseshoe vortices are placed on the sail surface (instead of the mast-boom plane), for good results. The vortices are on each element´s 1/4-line and the control point is on the 3/4-line. The free vortices shed by the element bound vortex pass through the elements behind, until the leech. To satisfy the Kutta condition, the first trailing vortice is placed in the plane of the leech panel. Up to 8 trailing vortice panels can be specified, before the trailing vortices are shed into the free stream direction, but there is no self-alignment procedure of the wake.

This is perhaps the weakest link of MacSail as it is now, but experimenting with different trailing vortice configurations, we have found very little difference, and on the other hand wake alignment would be very costly on computational time. In the vertical plane, the wake can be constrained (parallel to the water surface), and this is what we are doing. For the mainsail, it is sufficient to use one trailing element (for Kutta condition), before letting the wake follow the apparent wind, while for the jib it is more appropriate to follow the main surface for a while before relaxing the wake.

 A mirror image of the rig under the water surface is used to reflect the effect of the free surface, as usual. The distance of the jib foot from the water surface can be varied, but no other attempt as to simulate the effect of the hull on the sail flow is done. MacSail has been verified with the University CFD-code (American commercial program by Hess), and the results are very similar, so there is at least no programming error in the basic code.

 Drag

 We have chosen to calculate drag by direct panel pressure summation (PPS), and get good results with that. Although PPS has a bad reputation in drag calculation of aerodynamic bodies, due to small differences in opposite signed integrands, it suits itself for the case of thin profiles with sharp leading edges such as sails. One aspect about sail flow rarely appreciated is the lack of the leading edge suction: due to the sharp luff, in the real world there can be no leading edge suction similar to aerofoils. This yields a drag component of an order of magnitude larger than the viscous drag of typical aerofoils. We have found our PPS to be in good agreement with the 2D-foil tests performed by Milgram.

 No aerodynamic code for sails is reasonable unless separation is allowed for. Due to high camber and triangular planform, separation is almost always present in some parts of the sails. To complicate the matter, the sharp leading edge also yields separation bubble(s) at the luff. We have opted for a semi-empirical separation prediction, following a method by Cebeci-Smith, and have adjusted the algorithm empirically to agree rather satisfactorily with the 2D water tunnel tests by Milgram (see enclosed comparison for the NACA a=0.8-15 meanline). We also predict separation bubbles at the luff and adjust the lift of the panels involved - this is especially important to get better yaw-moment estimates, but also important for the drag. We are currently working on a correction similar to that of the separation bubbles, to allow for the harmful effect of the mast - again relying on the empirical results of the all-mighty Milgram.

 Thus we have a model that can predict sail flow long into stall angles - important, since the optimum sheeting conditions for sails often involve partial stalling (light winds and particularly reaching & spinnakers). This can be realized when transporting force coefficients into a VPP.

Copyright © 1995 WB-Sails Ltd. All rights reserved.

email: Mikko@wb-sails.fi