Nick, John, Matt, and all, The more I think about it the less I think the inflection point is relevant, that is I disagree with Nick In fact Matt just brought something to mind with his last posting that has not even been discussed, a kayak will capsize NOT when you are over the peak of the curve, but when the overturning moment caused by gravity acting on the mass, is greater than the righting moment cause by the buoyant force acting on the hull. So one could reach capsize way before you reach the peak of the curve, and hypothetically one could feel stable [high secondary stability] when heeled well past the peak. If you do not consider the effect of gravity acting on the mass you ignore HALF of the equation and you can NOT DRAW ANY CONCLUTIONS. And again the inflection point is irrelevant. In the current Dec. SK mag the latest Folbot was evaluated and it has no inflection point in its curve (it is a fully convex curve) and at least one reviewer found it has "good secondary stability". If a theory is wrong in one instance it is always wrong, especially since the Folboat does not really have any thing usual about it's shape. A big headed, muscle bound (i.e. high CG) paddler could find the same kayak has poor secondary stability than a lightweight person with a low center of gravity. Also the perception would be very different for the same hull shape depending on how heavy the hull is, Doug's 90 LB battle wagon likely feels more stable than it would if it weighs only 45 lbs. because of how much lower the CG would be for the kayak/paddler combination. Do the stability curves account for the effect of gravity or do they just calculate the righting moment caused by the buoyant forces? If gravity is considered what assumptions about the height of the CG are made and how accurate are they? Does the assumed height change for the different loading conditions, if they do not than I would contend that nothing meaningful could be determined from the curves by themselves. To have a complete picture you would have to plot the overturning moment [mass x grav x ht. of CG x cos(heel angle)] with the righting moments caused by the buoyant forces acting on the hull. Where the two curves cross is where capsize is imminent (where the paddler has to take action or a capsize will occur). I contend that how far you push a kayak over on its side and still feel stable is what most people would consider secondary stability. If you can only get 10 degrees of heel before you feel like you will capsize (no matter how much effort it took to get there), most would say it has low secondary stability. If you can push it way over to 40 degrees, most would say it has high secondary stability. Inflection points, the area under the curve, and other derivatives or second (and third order) effects do not show up on this curve because we are looking at it in a static, or quasi-static, condition. The derivative affects become very important for DYNAMIC effects, or time dependant responses, which to my knowledge has never been looked at, at least in the popular press, for a kayak. I would imagine that time dependant or dynamic effects would be relevant for advanced skills like in fast moving choppy seas, but not something most beginners would need to know about. A dynamic effect might be properties such as how quickly a heeled kayak will right itself when released, how far it overshoots past the zero point, how many oscillations and how much time it takes to stabilize back to zero. All of these are time dependant and the stability curves do not tell us enough information; we would need to know the dampening ratios [determined from skin friction, water viscosity, etc], the natural frequency of the system [dependant on the inertia of the system, gravity, etc.] and a bunch of other stuff. BTW these properties is where multi-chine, hard chine or rounded chine hulls would be noticeably different, you will never see it in quasi-static curves such as the common stability curves. There are noticeable differences in performance as you vary these properties though I imagine by the time a kayaker is skilled enough to notice how these things affect the kayak it is not really relevant. You choose a kayak by what behavior (and features) you like best not by it's dampening ratios. This is the same for how you buy a car, how a private pilot chooses and airplane, etc. Where this kind of analysis would be important is so designers can determine how the kayak will behave before they build it, knowing this also gives good insight into how design changes affects performance. For something as small and relatively inexpensive to build as a kayak it has been simply trial and error, and experience, that most designers depend on. If a kayak cost $150 million to build (like a jet fighter) and someone willing to pay that much for it, than there would be more analysis done on them. The third order affects that someone asked about are sometimes evaluated in complicated dynamic systems. This would be something like the rate of change OF the rate of change, as in how fast the acceleration is changing. Acceleration itself is the rate of change of speed. It can be important because mechanical systems, such as a gyroscope in a launch vehicle, may not keep up with the speed of change. Though it is generally ignored. But as far as secondary stability goes, without a lot of testing, I would guess that the farther you can heel a kayak and still feel stable, the higher the secondary stability. This might show up on a chart where the further to the right (high heel angle) that a curve of overturning or gravity forces crosses below a curve of the righting forces. Something you can not see on the stability curve of righting forces by itself. Peter *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. 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