# Sailboat Stability

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```					Sailboat Stability
by Douglas S. King The basics of sailboat stability are rooted in some fairly simple physics. However, it becomes complex rapidly when considering hull shapes, ballast type and placement, dynamic effects of waves, the effect of heeling on any boats handling characteristics, and other factors. Most important may be the emotional effect of heeling on the boats crew! It is no wonder that most sailors skip over the simple beginnings and launch directly into a justification of their prejudices (and all sailors have them) regarding hull shapes, ballast, etc. Stability is why boats return to an upright position when tipped or leaned over- the result of equal and opposite effects of gravity and buoyancy. Newton had a few things to say about this. Gravity pulls downward with a force equal to the boats weight, bouyancy pushes upward with a force equal to the amount of water that the boat's hull displaces. While gravity pulls downward separately on each part of the boat, the mast, the skipper, the engine, etc etc, it is more convenient to imagine all these weights as balanced around a single point, and consider gravity a pulling at this central point with a force equal to the summed weight of all objects on board. This central point is called the Center of Gravity, simply enough. Gravity and buoyancy produce this anti-heeling force, or righting moment, by shifting relative to each other, creating a lever arm. In real boats they both shift simultaneously, but it greatly simplifies the problem to consider them separately. First we will look at stability from the standpoint of the center of gravity with the boat acting as a pendulum. It should be intuitive to anybody that a greater weight, or the same weight placed lower down, will increase stability. We can get beyond this with a little geometry and math to produce explanations of why boats sail the way they do, and why different boats sail differently. We'll begin with a very simple hull shaped like a cylinder. Obviously it spins freely at first, and that it rotates around the center of the circle which is it's cross section. Equally obvious is that if we add a weight attached to one point of the cylinder, it becomes stable. The weight always wants to sit at the lowest point, and tries to pull the rest of the hull with it. Our cylindrical hull now produces a righting force or moment.

Now let's look at the shift in buoyancy. This is due to the fact that most boats are not shaped like cylinders. A flat-bottomed hull will show the buoyancy contribution to stability most dramatically, but any non-cylindrical boat (and very very few boats are shaped thus) will have a buoyancy component to her stability.

What happens is this: As the boat heels, the part of her hull on the low side sticks down further. Simple! If you look at the situation in detail you will realize that of course the high side is being lifted clear of the water, and equal volumes must be immersed or lifted on each side of the boat's center. Thus the force of buoyancy pushes upward much harder on the low side. Very simple, but as we'll see, it can get complex and subtle when we look at it in real life.

Even if we only consider the gravity contribution to stability, this stabilizing force or righting moment behaves oddly. When our imaginary cylindrical hull is sitting upright, there is no righting moment because the lever arm between buoyancy and gravity is zero. As the hull rotates or heels, the lever arm gets longer, and this too is intuitive, but the increase in lever arm and thus righting moment is not continuous. If we graph the leverage of the righting moment, or "righting arm," as the angle increases we get what looks like a sine wave. There is a point where the stability is increasing rapidly, then drops off, then starts to decrease as the angle surpasses 90×. This graph will be different for differentlyshaped hulls, and boats with different ballast configurations. It is intuitive that a wide, flat-bottomed boat is more stable than narrow roundbottomed one, but again a close look at the graph of righting moment can give some skippers a surprise. A wide, flatbottomed boat will gain righting moment quickly, as the centers of bouyancy and gravity shift in opposite directions. Then it's righting moment will drop slowly. This curve still has elements of our sine wave. This effect is exaggerated for small boats using the crew for live ballast, and is even more extreme for catamarans. We're ready to look at combining these effects, and with this approach through basic physics, take a step beyond the intuition that most skippers use to decide what sort of boat they think is "best." We can even consider what sort of boats suit which functions, and thus arrive a limited sense of "best" boats for a given type of sailing. Going back to the cylinder, the closest type of sailboat to this would be the narrow, deeply ballasted keelboat. The righting arm graph will not follow a sine wave precisely, but again, there are elements of that curve in it. We see slight initial stability, which might lead some sailors to conclude the boat is tippy or tender. Then the curve veers upward as the centers of buoyancy and gravity begin to shift in opposite directions. This is the source of some boats being said to heel only so far, then becoming steady as a rock. If we look at the basics, this is obviously not true. It is certainly possible for simple wind pressure on the sails & rig to heel the boat right past this point to around 90× into the range wherein righting moment is beginning to decrease again. Some features which can increase stability at this point of the curve are high freeboard, raised decks, flared topsides. This is termed "reserve stability" and

can be very important to any sailboat. Sailors who have been in a knockdown will appreciate all the reserve stability they can get. So what do we get with the opposite type of hull shape? The extreme scow or catamaran is very stable initially, very reassuring to those who do not like heeling. The large shift in bouyancy at small angles will generate great sail-carrying power. It holds the rig more upright where it can drive the boat forward more effectively. Lastly, this type of hull does not generate much weather helm for the skipper to battle, so there is less drag from the rudder and a feeling of greater control. So the big advantage is speed! However in gusty weather the skipper must keep in mind the diminishing righting arm, ease off, and not try to sail as though driving one of those "heel just so far and then steady as a rock" type of boats. The skipper who knows only this style of sailing will get an ugly surprise as he approaches a knockdown. And the crew who didn't like heeling will decide that this boat is too tippy also! While the wind itself cannot tip a keelboat past 90×, a combination of wind and waves definitely can. This is a part of the stability curve that ocean passagemakers consider as critical to safety. They discuss negative righting moment, and the limit of positive stability. This is the point where a boat will tend to stay upside-down. Obviously this range should be minimized, but some features which produce the highest limit of positive stability are not compatible with good sailing. Apparently our best hull in this regard is the cylinder, which would not provide a very secure deck surface to work on. It might be safe in high seas, but would always be turning around to pick up crew overboard! When looking at maximizing reserve and minimizing negative stability, it is important to not overlook buoyancy. By the time conditions are extreme enough to put a boat to these tests, it is quite common to have water getting into the boat. This is bad for a number of reasons, including the reduction of stability. For some it may not be intuitive, but since water runs downhill it will collect in the lowest part of the hull and reduce buoyancy just where it is most needed. And if we are to consider dynamics, the momentum of a lot of water sloshing around inside a boat can turn it over just by what engineers call the "free surface effect." So we have looked at overall boat stability, some differences among different types of boats, and a means of evaluating three components of sailboat stability: initial stability, reserve stability, and range of positive stability. Water Ballast The concept of water ballast is not new, it dates back to the clipper ships or further. In fact it has been incorporated into ship design since the conversion of steamships from coal to fuel oil around the time of World War One. A relatively recent development in recreational sailing, water ballast has two different applications. In ocean racers, water ballast tanks are placed as

far off to the side as possible. This gives the same effect as a hiked-out crew in a small boat. Sail-carrying power is greatly increased at small angles of heel. Some of the smaller ocean racers use forward centerline tanks to put the bow down and increase momentum for driving through waves. Many trailerable cruisers use centerline water tanks as their main ballast. It can be drained when on the trailer, thus reducing the weight pulled along the highway by car. This has resulted in an outcry from some that water cannot be used as ballast. Some point out that the water has no effectiveness when below the waterline, saying "water doesn't weigh anything in water." While this may sound like valid physics, it does not take into account one factor of basic stability. Filling a tank built into the hull with water will significantly lower a boats center of gravity. The tank is part of the hull, and when completely filled with water, the water may as well be considered part of the hull. Please note that partially filling the tank may actually reduce stability, and may have a noticeable free surface effect. How do we know that filling the tank lowers the center of gravity? Because the displacement is increased by the weight of the water. The boat sinks deeper into the water just as it would if an equal weight were loaded on board from the dock. Gravity pulls on the water in the tank and doesn't care if that weight is composed of lead, or bricks, or feathers. The tank filled with water becomes one component of the boats center of gravity, and it is in the lowest part of the hull. Then it is sometimes said that water ballast "doesn't work" because ballast needs to be more dense than water. Look back at the very first diagram showing the center of gravity. Our example has a cooler stowed in the cabin. That cooler, full of ice and drinks, would certainly float and thus is less dense than water. That cooler most definitely makes up part of the boats displacement, and is a component of the boats center of gravity. Now, would that boat be more stable with cooler stowed down below in the cabin, or higher up on the deck? So it is obvious that water ballast does "work." Lead is far more dense, could be placed outside the hull and still function as ballast, and even if inside the hull would take up less room than a tank of water. Wouldn't lead make better ballast? Of course! Gold would also make excellent ballast, since it is even denser. Depleted uranium would be better yet. But for our trailerable boats one would then have to get a heavier-duty trailer and tow car. We would have to haul that lead around with us on the road. The ocean racers would have to either carry it with them all the time even in light winds, or dump it over the side and then not be able to get it back when the wind picked up. They would have to give up the advantage of variable displacement and being able to change their righting arm and momentum to suit variable conditions. Does this mean that water ballast is "best" for trailerable boats, or offshore racers? No, it is a compromise. It has advantages for some types of sailing, and might be considered "best" only in a limited way. The wise sailor realizes that any vessel must be suited to her usage, her local conditions, and the temperament of her skipper. That is what makes her the best! Douglas S. King doug888@bellsouth.net

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