On diagrams, force vectors applied to an object are often drawn as arrows.\u00a0 The direction of the arrow shows the direction in which the force is applied.\u00a0 The placement of the arrow shows where the force is applied.\u00a0 The length of the arrow shows how much force is applied (the longer the arrow, the more force).<\/p>\n
![\"\"](\"https:\/\/kanatasailingclub.com\/staging\/wp-content\/uploads\/2017\/05\/force-diagram.png\")
<\/p>\n
We use vectors in sailing to understand how forces affect the boat, how apparent wind changes as the boat moves, and to understand how the heck we can sail “into” the wind.\u00a0 Don’t worry, we won’t be doing number-crunching.\u00a0 We’re more concerned with “push here to turn left”, not “calculate how fast you turn left when you push here exactly this hard”<\/p>\n
Breaking down and summing vectors<\/h4>\n
Just like scalars can be added together (8 + 6 = 14) vectors can be added.\u00a0 If the vectors are in the same direction, adding them up is just like adding numbers (if the wind is blowing 6 knots from the north, and speeds up by 6 knots from the north, then the result is that it is blowing 12 knots from the north).\u00a0 When vectors have different direction, the adding is not quite as simple (if the wind is blowing 6 knt from the north, then speeds up by 6 knts from the east, then the result is 8.5 knots from the north-east).\u00a0 We won’t be doing any number crunching or trigonometry, it’s just something to be aware of.<\/strong><\/p>\n Just like adding two vectors into one vector, a vector can be broken down into two (or more) smaller vectors called components.\u00a0 In the above example, a 8.5 knot wind from the NE can be thought of as “6 knots from the N and 6 knots from the E”.\u00a0 Vectors are usually<\/em> broken down into components that are perpendicular to each other (like N and E), but you can break them down into components of any direction as long as they add up to the same thing.<\/p>\n We’ll see summing and breaking down vectors more as we analyze how the foils counter the sail and how the apparent wind works.<\/p>\n In the real world, when we push or pull on something off-centre, it tries to turn.\u00a0 Let’s take the example of a canoe floating beside a dock.\u00a0 If we push on the middle of the canoe, it moves sideways.\u00a0 If we push on one end, it moves sideways, but also tries to turn.\u00a0 This turning force is called “torque”.\u00a0 If we want to turn the canoe only (without it moving sideways) than we can push on both ends of the canoe in opposite directions.\u00a0 The “sideways” parts of the pushes cancel each other out, but the torque from each push is added.<\/p>\n The torque produced is proportional to the distance from the pivot point.\u00a0 That is, if you push with the same force at a distance twice as far from the pivot point, then the torque is doubled.\u00a0 That’s why it’s easier to loosen a bolt with a long wrench than with a short one.<\/p>\n Dealing with tonnes and tonnes of vectors is hard.\u00a0 Often times though we can replace lots of vectors with one vector.\u00a0 Let’s say that you have a bunch of people pulling or pushing on an object to move it.\u00a0 For the purpose of analysis, you could replace all the forces that people are applying with a single force that represents the sum of their effort.\u00a0 As long as the equivalent vector applies the same net force as all the individual efforts, and the same torque as all the individual efforts, you can concentrate only on the one vector to make the math easier. The Sail, and Centre of Effort (CE) The wind blowing across a sail generates a force on the sail.\u00a0 This force is part forwards, part sideways.\u00a0 Got it?\u00a0 Good!\u00a0 Hey, that was easy!<\/p>\n While the sail actually has lots of little forces pushing against the sail all over it (perpendicular to the sailcloth), you can imagine it as one big force.\u00a0 This force (which we’ll call the effort<\/em>) is applied about 1\/3 the way along the sail and about 1\/3 the way up the mast (in other words, not quite the middle, but pretty close to where the sail is “baggiest”).\u00a0 The point at which the force is pushing is called the Centre of Effort, or CE.<\/p>\n The direction of effort is (roughly) perpendicular to the sail at the sail’s deepest point.\u00a0 It generally points forwards some amount, and to leeward some amount.\u00a0 A fuller or tighter sail can change the direction somewhat, but it’s okay to think of\u00a0 it as pretty much perpendicular to the sail.<\/p>\n CE on Boats with 2+ Sails<\/strong><\/p>\n The above talks in terms of CE in a boat with a single sail.\u00a0 The principals are the same for a boat with a jib.\u00a0 Some points before we take a look at double-handers:<\/p>\n This means that the force generated by the main is a bit farther back in the boat, but we have a new force generated by the jib forward.\u00a0 The jib force is generally smaller than the main.\u00a0 The sum of these two forces is between the two individual forces, but closer to the main force.<\/p>\n The total CE generated by the sails will generally be close to the mast, but a little bit behind.<\/p>\n Some boats have a third sail that goes in front of the jib called the spinnaker (typically only raised when going downwind).\u00a0 This sail also generates force and the CE will be moved forward farther when the spinnaker is raised.\u00a0 The same principals apply on boats with multiple masts, or multiple sails.<\/p>\n The Foils, and Centre of Lateral Resistance (CLR)<\/strong><\/p>\n This one is not quite as intuitive as the sail(s).<\/p>\n Picture a canoe.\u00a0 The canoe is easy to push forwards\/backwards, but tougher to push sideways, right?\u00a0 The shape of the canoe (narrow in one dimension, wide in the other) resists the sideways motion.\u00a0 This is called “lateral resistance”.<\/p>\n Sailboats have hulls that produce some lateral resistance, and the rudder produces some as well (when it’s straight), but the majority of the lateral resistance comes from the centreboard (or dagger board, or keel, or whatever you call the “fin” that sticks down into the water — I’ll just call it the centreboard).\u00a0 A few sailboats (like the Hobie 16) don’t have boards, so the hull is shaped to provide extra lateral resistance.\u00a0 For the purpose of this analysis, we’re talking about boats with boards.<\/p>\n Just like we were able to take all the little forces on the sail and come up with an equivalent force applied at the centre of effort, we can take all the little lateral resistances and do our analysis based on a single force generated at the “centre of lateral resistance” or CLR.\u00a0 Since we’ve already mentioned that the centreboard is providing most of the lateral resistance, you won’t be surprised to learn that the CLR for the whole boat tends to be pretty close to the middle of the centreboard.<\/p>\n Sailboats generally produce a lot of lateral resistance, much more so than a canoe.\u00a0 They make so much, that we often “cheat” in our analysis and say that the boat doesn’t move sideways at all.\u00a0 If we apply 100 pounds of sideways force to a sailboat, we’ll say that the boat produces 100 pounds of resistance, and doesn’t move sideways.\u00a0 It actually does move sideways a little bit, but for the purpose of this write up we’ll say it doesn’t.<\/p>\n A note on terminology — “foils” or hydrofoils are the thin blades move through the water and generate forces.\u00a0 In the boats we’re talking about, the centreboard and rudder are the foils.\u00a0 There are a few types of boats which have horizontal or angled foils.\u00a0 Rather than produce a force to resist the boat moving sideways these produce an “upwards” force to help lift the hull out of the water.\u00a0 You can get some pretty amazing results<\/a> with this, but when this page talks about “foils” we’re taking centreboard and rudder, not lifting foils.<\/p>\n Drag<\/strong><\/p>\n Just like a boat resists moving sideways, the hull and foils of a boat also resists moving forwards or backwards.\u00a0 This resistance is called “drag”.\u00a0 Drag is usually much less than lateral resistance though.\u00a0 (Warning: math incoming) Drag tends to increase proportionally to the square of speed of the boat.\u00a0 That is to say, a boat going twice as fast generates four times as much drag, everything else being equal.<\/p>\n In a moment we’ll see a sail generate a forward force on the boat.\u00a0 We know that an unbalanced force causes something to accelerate (Newton’s 2nd law).\u00a0 As the boat speeds up, the drag grows until the forward force equals the drag force (at our top speed).\u00a0 Later on in the class, we’ll be (I assume) talking about things we can do to reduce drag to increase our top speed.\u00a0 For now though, our analysis does not take drag into account.<\/p>\n We’re going to first consider a beam reach (we’re sailing perpendicular to the wind) because it makes more intuitive sense, at least to me.<\/p>\n For the purpose of this analysis, we’ll consider all forces as if they act on the “middle” of the boat, without generating torque.\u00a0 That part comes later…<\/p>\n Terms to know – weather helm and lee helm<\/strong><\/p>\n I’d like to talk about two terms we’ll be using.\u00a0 For some reason, the direction the wind is coming from is sometimes called “wind” (as in “windward”) but it’s also sometimes called “weather”.\u00a0 The direction the wind is blowing to is “lee”.\u00a0 The various forces on the boat might be exerting a torque on the boat, trying to turn it into the wind (“weather helm”) or away from the wind (“lee helm”).\u00a0 Most boats are designed to have a small bit of weather helm when sailed properly.\u00a0 This will turn the boat into the wind and stop the boat if the skipper falls off or lets go of the rudder, or something.<\/p>\n Probably the easiest effect of torque to understand is how a boat stays upright.\u00a0 That’s because we’ve all hiked out on a boat, and we’ve all experienced the effects of moving around while hiking.<\/p>\n We have the wind pushing on the sail.\u00a0 For this analysis, we’re looking at just the “sideways” part of how the wind pushes, and not the forward part.\u00a0 The wind is pushing some distance up the mast, at CE.\u00a0 Counter to this, we have the lateral resistance in the opposite direction somewhere below the waterline.\u00a0 Remember our canoe example at the top of this post?\u00a0 The two forces pushing in opposite directions some distance apart are working together to torque the boat around a pivot point.\u00a0 In the diagram below, these forces (red) are producing the red clockwise torque around the pivot (purple X).\u00a0 This is the torque which will heel the boat and capsize if you don’t do anything to stop it<\/p>\n To counter that torque, we need to exert an equal amount of torque in the counter-clockwise direction.\u00a0 We do this by hiking.\u00a0 Gravity exerts a force on our body, which is transferred to the boat using our legs as levers.\u00a0 The heavier we are (the more downward force) or the taller we are (the farther away from the pivot the force is applied) the more torque is generated.\u00a0 Jason uses this as an excuse to have a second helping of desert.\u00a0 You want to apply just the right amount of torque such that the boat stays flat.<\/p>\n Let’s look what happens when the boat heels.<\/p>\n First, there is less sail area presented to the wind, so the sideways force (red arrows) become smaller.\u00a0 Second, the CE moves “down” toward the waterline as the mast tilts.\u00a0 The CLR moves “up” as well.\u00a0 All this means the red vectors (which are smaller anyway) are vertically closer to the pivot point, providing less torque.\u00a0 The net result — less hiking force is needed to keep the boat steady.<\/p>\n In strong winds, even the tall heavy sailors can’t generated enough torque to keep the boat flat.\u00a0 Most of the time, you’ll see a fleet of Lasers sailing along, all with a bit of heel according to the skipper’s ability to generate righting force.\u00a0 Good Laser sailors know that sheeting out to spill some wind (reducing the size of the red vectors) results in a flat boat and less drag, and generally go faster than the kids who try to hold all the wind in their sail and heel too much.\u00a0 To put it another way, the good sailors will generate as much torque with their body as they can, and then adjust their sail to their body.\u00a0 The other sailors will try to generate as much sail power as they can and then wrench their body trying to tame it (and fail to do so).<\/p>\n If you get a chance to watch Steve Harrington on the water at a KSC club race, he’s a perfect example.\u00a0 The guy’s 145 pounds, 5’6″ and his Laser is dead flat in even the strongest winds.\u00a0 He’s also winning every race.<\/p>\n Let’s look at the boat from the top.\u00a0 This is similar to what we did when we looked at how we sail upwind, but now we’ll look at the torques the different forces generate.<\/p>\n The boat will tend to pivot at some point between the CE and CLR.\u00a0 The two sideways components (blue and purple) will together torque the boat in one direction.\u00a0 If CE is behind CLR, then they’ll be rotating the boat into the wind (weather helm).\u00a0 If CE is in front of CLR, then they’ll rotate the boat away from the wind (lee helm).\u00a0 If they are perfectly lined up with each other, then they won’t be torquing the boat at all.\u00a0 The forward component of the sail (green) will however torque the boat (weather helm), even if CE and CLR are perfectly in line, since it’s pushing forwards off-centre to the pivot point<\/p>\n Moving CE\/CLR to steer<\/strong><\/p>\n Let’s take a look what happens to CE and CLR around the boat.<\/p>\n Let’s say you were to move CE forward in the boat.\u00a0 What would happen?\u00a0 The sideways components (purple and blue, above) wouldn’t have has much leverage around the pivot point, and you’d have less weather helm.\u00a0 If you move CE so far forward that it’s in front of CLR, you’re actually generating lee helm with those sideways forces.<\/p>\n Now what about that green “go forward” component?\u00a0 If you roll your boat to windward (that is, towards the right side of the diagram above) then you can move your CE to the point where it is directly above CLR.\u00a0 This would eliminate the green torque component.<\/p>\n How would you move CE forward (or back) in the boat?\u00a0 Sheeting the main in would move CE farther back and in towards the centreline.\u00a0 Sheeting out would move CE forward, but away from the centreline.\u00a0 Sitting farther forward in the boat would tilt the mast forward (and tilt the centerboard backwards) to move CE\/CLR forward\/back.\u00a0 Hiking the boat to windward would move CE towards the centreline, and heeling to leeward would move it away from the centreline.<\/p>\n So to steer without a rudder you would:<\/p>\n On a double-handed boat, you can also use the jib.\u00a0 Picture the scenario where you let one sail (either the main or the jib) do all the work, while the other one just flaps around<\/p>\n Thus, it’s quite easy for a single sailor to sail a double-hander without a rudder — let one sheet loose, and yank on the other.\u00a0 You can play with how much of each sail you’re applying until you find a balance that keeps you straight.<\/p>\n I’m not touching this one.<\/p>\n There are countless articles written about how a sail generates force, many of which contradict each other.\u00a0 Most resources you’ll find online either<\/p>\n In other words, it’s the airfoil teaching effect:<\/p>\n (image used with permission, original source https:\/\/www.xkcd.com\/803\/<\/a>)<\/p>\n In my humble opinion, knowing how to use the force is more important than knowing the details of how it is generated.<\/p>\n I will speak briefly on turbulence.\u00a0 A fluid (air, water, etc) will tend to flow in nice straight lines (laminar flow).\u00a0 When it encounters an object, it has to go around the object.\u00a0 If the object is fairly small, is nice and smooth, and allows for gradual flow around the object, you can have laminar flow around it.\u00a0 If the object forces abrupt changes in the direction of the fluid, you create turbulence, and eddies or swirlies are introduced into the system.<\/p>\n When laminar flow is established can be harnessed to generate the sail and foil forces with minimal drag.\u00a0 When a flow becomes turbulent the amount of force we can generate drops significantly, and the amount of drag increases.\u00a0 To put it another way, we’d like all the fluids moving around our boat to have laminar flow if possible.<\/p>\n How do you know you have laminar flow?\u00a0 Look at the tell tales on your sail.\u00a0 If they are streaming backwards, they’re getting caught in the laminar flow as the wind blows across your sail.\u00a0\u00a0 Great!\u00a0 If your tell tales are spinning around, flapping forwards and then back, or other erratic behaviour, then they are getting caught in one of the eddies, which indicates you have turbulent flow.\u00a0 Turbulent flow means your sail is not generating as much power, and there is more drag on your rig.<\/p>\n We can’t see tell tales on our foils, but we can look at the water behind the boat.\u00a0 If the water in our wake is relatively smooth, then then foils are not generating much turbulence.\u00a0 If our wake is full of bubbles, and little whirlpools, then its and indication that our hull is dragging significantly.\u00a0 Reducing hull drag is beyond the scope of this write-up, but try sitting farther forward in the boat and using less rudder if possible.<\/p>\n True wind<\/strong> is what the wind is doing relative to the ground (or water, or other stationary point).\u00a0 You may be in a lull, or a gust, or just steady wind.\u00a0 Whatever the case, if the wind is blowing 10 knots from the North relative to the surface, then that is the true wind at this point in time.<\/p>\n Induced wind<\/strong> or boat wind<\/strong> is the wind that’s created by moving across the surface.\u00a0 If the true wind is dead still, but you’re riding a bicycle at 30 km\/h then you “feel” a wind on your face as if it’s blowing 30km\/h right at you.\u00a0 That’s induced wind — wind created by your motion over the ground.<\/p>\n Apparent wind<\/strong> is the combination of the two.\u00a0 Let’s say the wind was blowing at 10 km\/h and you were riding a bike at 30 km\/h directly into the wind.\u00a0 You would “feel” 40 km\/h (10 km\/h true wind, plus 30 km\/h induced wind).\u00a0 If you were biking away from the wind, you would feel 20 km\/h.\u00a0 If you were biking sideways to the wind, you’d “feel” the wind come at you at about 32km\/h from and angle about 32 degrees.<\/p>\n When you are travelling slow, the induced wind is small, and apparent wind is pretty close to true wind.\u00a0 When you are travelling very fast the apparent wind becomes closer to the induced wind.<\/p>\n You’re sails operate on what they feel — the apparent wind.\u00a0 So if you’re at a standstill on a beam reach, your sails “feel” the true wind coming from directly beside you.\u00a0 As your speed increases, you’ll be generating more induced wind.\u00a0 This will make the wind “appear” to come from more in front of you.\u00a0 As you speed up, the boat may move from a beam reach to a close reach, even to close hauled just be speeding up.<\/p>\n Another example is gybing a Laser in strong wind.\u00a0 You want to be going as fast as possible when you gybe.\u00a0 If the wind is blowing at 20 knots, and you’re going 5 knots in the direction of the wind, then there’s 15 knots of apparent wind coming behind you.\u00a0 Tough as hell to gybe that.\u00a0 But, if you’re going 15 knots downwind, then there’s only 5 knots of apparent wind coming behind you.\u00a0 That’s a walk in the park!\u00a0 So catch a wave, get up on a plane, do whatever you need to do to speed up that boat heading into that gybe!<\/p>\n Side note<\/strong> – Some boats can sail faster than the true wind on reaches.\u00a0 That’s because it’s not the 5 knots of true wind that is operating on the sail, it’s the 20 knots of apparent wind that the sail is using.\u00a0 The 29er, for example, will sail at a speed of about 18 knots on a broad reach in 12 knots of wind, and you’re actually “tacking” through the apparent wind when you gybe.<\/p>\n <\/p>\n","protected":false},"excerpt":{"rendered":" Introduction This off-the-water class was concerned with the physics of sailing.\u00a0 Tom did his “Theory from Hell” lecture (thanks, Tom!) and Reese spoke about how to apply the forces generated to the actual boat. I’m going to present the information in a bit of a different order than was listed in the class.\u00a0 I’ll talk … Continue reading Advanced Sailing Skills, – May 15, 2017<\/span> ![\"\"](\"https:\/\/kanatasailingclub.com\/staging\/wp-content\/uploads\/2017\/05\/vectors.png\")
<\/p>\nTorque<\/h4>\n
![\"\"](\"https:\/\/kanatasailingclub.com\/staging\/wp-content\/uploads\/2017\/05\/canoe.png\")
<\/p>\nEquivalency Vectors<\/h3>\n
![\"\"](\"https:\/\/kanatasailingclub.com\/staging\/wp-content\/uploads\/2017\/05\/equivalenecy.png\")
<\/p>\nForces on the Boat – CE and CLR<\/h2>\n
\n<\/strong><\/p>\n![\"\"](\"https:\/\/kanatasailingclub.com\/staging\/wp-content\/uploads\/2017\/05\/CE.png\")
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![\"\"](\"https:\/\/kanatasailingclub.com\/staging\/wp-content\/uploads\/2017\/05\/double-hander.png\")
<\/p>\n![\"\"](\"https:\/\/kanatasailingclub.com\/staging\/wp-content\/uploads\/2017\/05\/CLR.png\")
<\/p>\n![\"\"](\"https:\/\/kanatasailingclub.com\/staging\/wp-content\/uploads\/2017\/05\/CLRresistance.png\")
<\/p>\nApplying CE\/CLR<\/h2>\n
Analysis without considering torque — how does a boat sail\u00a0 upwind?<\/h3>\n
![\"\"](\"https:\/\/kanatasailingclub.com\/staging\/wp-content\/uploads\/2017\/05\/beam-reach.png\")
<\/p>\n![\"\"](\"https:\/\/kanatasailingclub.com\/staging\/wp-content\/uploads\/2017\/05\/close-hauled.png\")
<\/p>\nAdding Torque to the Equation<\/h3>\n
Torque to roll the boat<\/h4>\n
![\"\"](\"https:\/\/kanatasailingclub.com\/staging\/wp-content\/uploads\/2017\/05\/hiking.png\")
<\/p>\nTorque Affects of CE and CLR on weather helm and lee helm<\/strong><\/h3>\n
![\"\"](\"https:\/\/kanatasailingclub.com\/staging\/wp-content\/uploads\/2017\/05\/weatherhelm.png\")
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How a Sail Generates Forces<\/h2>\n
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![](\"https:\/\/imgs.xkcd.com\/comics\/airfoil.png\")
<\/p>\nTurbulent and Laminar Flow<\/h2>\n
![\"\"](\"https:\/\/kanatasailingclub.com\/staging\/wp-content\/uploads\/2017\/05\/flow.png\")
<\/p>\nApparent Wind<\/h2>\n
![\"\"](\"https:\/\/kanatasailingclub.com\/staging\/wp-content\/uploads\/2017\/05\/apparentwind.png\")
<\/p>\n