## How A Sail Gives Lift

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How a Sail Gives Lift Arvel Gentry corrects this most misunderstood theory By Arvel Gentry SAIL Magazine June 1973 How many times have you heard that a sail gives lift todrive a boat because the air travels faster on the lee sidefor it has farther to go than it does on the windward sideSo the pressures are different and you get lift Well that iswrong Even a perfectly flat thin airfoil with the same December 1999distance on both sides has lift when it is at an angle to thewind So try to forget everything you know or think youknow about how a sail gets its lift The real explanations ofhow a sail gives lift may seem a bit complicated at first butonce you get the idea it is really quite It is true that the pressures over much of the lee side of asail are lower than the freestream pressure and thepressures on the windward side are higher These do result from the air flowing faster on the lee Figure 1side and slower on the windward side Bernoullis condition were not satisfied and the air coming off of theprinciple But what causes the air to flow in this manner lee side of the leech were to travel faster than the air Early mathematicians tried to solve this problem and coming off the windward side as is implied in the flowthey derived a set of equations The streamlines these first diagrams in many sailing books If there were gave are illustrated in Figure 1 for a simple flat speeds we would have different pressures fromairfoil at an angle to the flow Their equations and solutions Bernoullis principle on the two sides of the line dividingwere correct but the flow lines were exactly the same on the lee side and windward side flows downstream of theboth sides of the airfoil turn the page upside down and leech With different pressures and the sail fabric no longeryoull see what I mean separating the two different speed regions we would have Because the flow lines are the same on both sides the nothing to keep the highpressure air from taking over andpressure forces therefore must be the same and the airfoil pushing into the lowpressure regionwould have no lift at all This would mean that man could What happens in a real flow is the total region aroundnot fly and birds could not fly But birds do fly and early the airfoil adjusts itself so that the air flowing off the twomanmade gliders even with flat uncambered wings also sides of the airfoil at the leech has the same speeds andflew Something obviously was missing from their pressures Again this adjusting process is called the Kuttasolutions condition by It is an important principle Examining the calculated flow around the edges of the to remember for it influences the entire flow field aboutairfoil gives the clue Note that these mathematically the saildetermined streamlines in Figure 1 make sharp turns as Mathematicians found that the Kutta condition couldthey go around the leading and trailing edge of the airfoil be satisfied by adding another type of flow solution calledthe luff and leech of our sail For a thin airfoil this means circulation to that already determined and shown inthat the air must have high velocities at these points in Figure 1 Circulation is a special mathematical floworder to get around the sharp corners The velocities solution where air rotates around the airfoil The the luff can be reduced by bending the airfoil of the circulation flow goes forward over the windwarddown into the flow cambering the airfoil but what about surface around the luff and then toward the rear on the leethe leech side of the airfoil The circulation flow velocities are higher In real life we find that the flow around the leech varies close to the surface and they decrease as you get fartherfrom that shown in Figure 1 as the air first begins to move away from the surfacepast the airfoil It changes so that the air leaves the airfoil at The combination of noncirculation flow andthe leech smoothly with the same speed and pressures on circulation flow is illustrated in Figure 2 When the twoboth sides This fact of aerodynamics is known as the Kutta flows are added together both the velocities and named after the man who first discovered it in are taken into account in the entire area around the airfoil1902 They are added together just as one adds boat speed and You can understand this Kutta condition requirement if true wind speed to get apparent wind strength andyou stop and visualize what would happen if the Kutta direction In the mathematical solution circulation air speeds are circulation causes some of the air that was going to go on the windward side to be diverted around to the lee side We can also see this from the fact that the stagnation streamline at the left side of Figure 2 is much lower than it was in Figure 1 The Kutta condition must always be satisfied for any lifting airfoil However if the flow separates from the airfoil before it reaches the leech the Kutta condition will not be satisfied at the leech of the airfoil itself Instead it will be satisfied at the trailing edge of the separated region well behind the airfoil However since the flow at the trailing edge of the separated region has a smaller angle to the freestream than does the actual leech of the airfoil the airfoil with separation has less lift and much more drag This is shown in Figure 3 Figure 2adjusted so that the Kutta condition at the leech is satisfiedthe calculated air flow speeds and pressures are the sameoff both sides of the leech The resulting air speeds of the Figure 3circulation part of the flow are smaller than the noncirculation solution speeds On the top of the airfoil the Note that nowhere in this discussion have I flow direction is the same as the noncirculation anything about the density of the air or about the airflow direction This means that the two flows added having farther to go on the lee side or about the air will give a higher speed flow striking the sail The air just does not behave like that Also On the bottom side the circulation flow direction is note that the airfoil used was perfectly flat and thin Ofagainst the noncirculation flow so the two flows cancel course our cambered sail is more efficient than the flateach other a little bit to give a slower speed flow airfoil but from the example given we see that a sail does With slow speed flow on the bottom of the airfoil and not have to have thickness either real or imaginary tohigh speed flow on the top we get high pressure on the have lift The air flows about the sail and the way that itbottom and low pressure on the top which gives us the flows is governed by the shape of the airfoil and it is basicnecessary pressure difference between the two sides of the noncirculation flow plus the effects of the circulation thatsail to maintain the cambered shape and to give the lifting must be added to satisfy the Kutta condition at the leechforce to drive the boat Air does not strike the sail like so many grains of You might ask if the results from this mathematical blowing sand Instead air behaves like a fluid as it flowsexercise noncirculation plus circulation flow are really past the sail When air sees it is approaching the sail itmeaningful The answers are indeed accurate and they starts to move and change direction in preparation formatch test data almost exactly passing the sail But air also has a certain resistance to a Examine the stagnation streamlines marked S in change in direction It doesnt want to change 1 and 2 In Figure 1 the stagnation streamlines any more than it has to in flowing past the sailcome into the airfoil close to the edges Notice that at point The stagnation streamline divides the air that is goingA in Figure 1 the windward streamline is quite far from the to pass on the two sides of the sail The air that is going toairfoil surface flow on the lee side does not move any further to leeward At this point we should expect low speed flow in the than it has to to get past the sail and still satisfy the Kuttadirection indicated by the arrow Circulation flow at this condition at the leech The leeside streamlines thereforepoint is just equal to this speed and opposite in direction pass very close to the forward part of the sail They haveand it therefore cancels out the noncirculation flow This high velocities and low pressures in this regionpoint becomes the place where the new stagnation On the windward side the air is a bit lazy it comes into the airfoil when we have circulation want to move up into the convex region of flow that isas shown in Figure 2 formed by the airfoil and the stagnation streamline The At point B in Figure 1 the flow on the surface has a windward side streamlines spread out a bit the air slowsslower speed than point A so the circulation flow is not down and the pressure gets higher But the final airspeedonly able to cancel out the noncirculation flow direction pressure and direction of flow at the leech must be thebut can actually make the flow go in the opposite direction same as on the leeward surface for the Kutta condition toaround the luff of the airfoil From this we see that the be satisfied 2 In Part 1 SAIL April 1973 we learned what is a drawing In Part 2 last month we introducedthe boundary layer and separation effects And so far inPart 3 we have learned how a sail gets its lift Now lets putall this aerodynamic knowledge together to see how asingle sail works Figures 4 and 5 show accurately drawn an airfoil representing a jib at two different relativewind angles for the centerline of the boat 25 and 35degrees The stagnation streamline dividing the flow thatpasses on each side of the sail is identified by the letter SThe first leeside streamline is marked A and the firstwindward line is B Figure 6 Figure 4 Figure 7 point Line A then tends to move gradually away over the Figure 5 rest of the airfoil The detailed pressure distributions for the two boat With this flow we would expect to have an increase inangles are shown in Figures 6 and 7 In these drawings the air speed to the point where streamline A is closest to thenegative or suction pressures less than atmospheric are airfoil followed by a gradual decrease in speed as the by arrows pointing away from the sail The is approached If you remember that air pressure goeslower surface pressures are usually higher than down when speed goes up Bernoullis principle youatmospheric positive pressures and are represented by therefore get a decrease in pressure over the front leepartarrows pointing toward the sail of the sail followed by a gradual increase in pressure Below each airfoil drawing is an engineering type of toward the leechplot showing this same information in terms of pressure In Figure 4 streamline B tends to resist moving up a long the surface of the sail The difference the convex region formed by the airfoil and the the leeside and windwardside pressures at a streamline so that it gets further away from the airfoilgiven point on the airfoil represents the pressure surface Therefore there is a decrease in wind speed and andifference across the sail fabric increase in pressure in this area Figure 6 shows how all this If you study Figures 4 and 6 together you can see how turns out in terms of the pressure along the airfoil surfaceall this information youve learned previously fits together For the 35 degree boat angle case in Figures 5 and 7 weIn Figure 4 the stagnation stream line S goes smoothly into have a higher angle of attack for the sail and a airfoil luff Line A gradually gets closer to S and the different streamline picture and resulting surfaceairfoil surface as it approaches the maximum camber pressures The stagnation streamline comes into the airfoil 3on the windward surface a little way back from the luff Obviously the term backwinding of a sail is not really aStreamline A passes close to the luff and then immediately very good descriptive term for it implies that air strikesstarts getting farther from the surface over the rest of the the sail And now we know that air does not behave in thisairfoil All the air between lines A and S must pass through waythe little space at the lee side of the luff You should also note in Figures 6 and 7 that the higher We would expect to see much higher air speeds and angle case would have higher lift if the flow did notlower pressures close to the luff than we had for the lower separate Where does this higher lift come from Theboatangle case We would also see a rapid increase in streamlines in Figures 4 and 5 clearly illustrate this Thepressure as the flow continues downstream from the luff higher angle of attack requires a higher circulation tosince streamline A moves rapidly away from the surface satisfy the Kutta condition at the leech Higher circulationThe pressure drawings and plot in Figure 7 show that this means that more air is diverted to pass on the top or leeis exactly what happens side of the sail We can see this from the fact that the Previously it was learned that the boundary layer does stagnation streamline in Figure 5 is lower further tonot like rapid increases in pressure and it tends to separate windward than it is in Figure 4 Again to get more lift weunder these conditions In real life the boundary layer for must cause more air to pass on the lee side of the sailthe highangle case shown in Figures 5 and 7 would If you have read carefully the first three parts of thisprobably separate and the airfoil would stall As soon as series you should be able to predict what will happenthis happens the streamlines shown in Figure 5 would no when two sails the jib and main are used togetherlonger be true for we would get a completely different Between now and next month look at some of theflow picture about the airfoil similar to Figure 3 drawings in the sailing books that show how the slot However by being able to calculate the airflow with the works and read their explanations Then see if you cancomputer as though there was no separation we are able figure out why they are wrongto study just what causes the separation to occur and whatcan be done to prevent it from separating Next month jib mainsail and the slot effect In the streamline drawings in Figures 4 and 5 the linesA and B are the same distance away from the S at the leech as they were way out in front ofthe airfoil This means that the airspeeds and pressures onboth sides of the leech are about the same as the The detailed calculated results show a speed at 95 ofthe airfoil length about 14 higher than with the speed and pressure recovering to nearfreestream values by the time the trailing edge is reachedThese facts will become very important when I describetwo airfoils together Another important point can be inferred from the datapresented in these figures Because all sails are very thinwith relatively sharp leading edges they are very sensitiveto the angle of the wind An increased angle of attack will cause the to come into the windward side of the sail Thiswill cause excessive pressure gradients on the lee side asthe air tries to recover from its rapid turn around theleading edge and return back to near freestream values atthe leech As a result the flow will separate and we willhave a stalled condition As the angle of attack to the wind is reduced the boatheaded up the stagnation streamline will shift around tothe luff and then the lee side of the sail The distribution will cause the sail to change its shapesince there may be a higher pressure on the lee side than onthe windward side It is in a luffing condition Note that the air is not actually striking the sail like somany grains of sand and making it shake It is just that thefluctuating pressure and unstable shape of the sail cause itto shake as it responds to the pressures created by the flow 4

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