Nick wrote: <SNIP> >>>>>If the top of the curve is the beginning of the end, maybe the inflection point is the end of the beginning. One of the biggest problems I see with the inflection point theory is that many boats don't have an inflection point. For these boats the steepest part of the curve is at zero degrees of heel. I am not ready to say none of those boats have any secondary stability.<<<<< <SNIP> The peak of the stability curve has zero stiffness. This is a balance point where it takes only a little increase in the tipping force already applied (to get up to that angle of lean) to throw the static system into a capsize (if no other forces are applied). The problem with using the inflection point (beyond its non existence in many cases as Nick points out) is that it could be manipulated to be at anywhere along a long straight run of the curve when the differences in the curves were really only minute. Maybe too little for a person to even sense. A person can and does sense when the steepness (stiffness) of the curve begins to drop off significantly. The extra force applied that used to make the kayak tilt one degree more now moves it two degrees and a little further out the same increase in force will move it four degrees as the curve shallows out before reaching the peak. I propose that an angled straight line that touches (is tangent to) the curve before the peak might be agreed upon as the "risk" point. How to choose the angle of that line would then be the question. A fixed angle might be one solution but it would have to be extremely shallow to work (be tangent with) with very shallow curves. Of course maybe extremely shallow curves don't exhibit any point where the feeling of security is diminished because there never was a feeling of security in the first place. A fixed shallow angled line would probably make the tangent too close to the maximum point of the curve as well. A straight tangent line that is at an angle that is a percentage of the angle of the maximum steepness of the curve might give us a more realistic "risk" point (where we sense that it isn't going to take too much more lean to destabilize us). I propose we start out testing a tangent angle that is half the maximum steepness angle of the curve. I'm not sure we wouldn't sense danger at a steeper angle or even at an angle that is just beyond the maximum steepness but it might give us a model to experiment with. Any curve where the curve broke suddenly shallower (ala Pisces) would be pinpointed by a wide range of tangent angles. Using half the maximum steepness for the angle would mark the point on the curve where the stiffness was only half of its maximum stiffness. A notchy curve can create a situation where it takes a lot of force to get over the notch and this may lead to an overshooting of the risk point as the effort, once past the notch, must be quickly curtailed again and the possible adverse center of gravity shift used to shallow the steepness to overcome the notch must also be quickly corrected with a weight shift. This takes time. My "Risk angle system addresses this notchiness by increasing the tangent angle and thus moving the "Risk" angle further left. Notchiness combined with the reflex delay in the human nervous system will increase the risk of capsize at high angles of lean. Kayakers find kayaks with a wide range of initial stabilities to have good secondary stability or not but it isn't closely based on the height of the curve and as I pointed out too much initial stability seems to never lead an expert kayaker to comment that the kayak has good secondary stability. A few posts back I reported this definition from a military ship damage control class on the web teaching the fundamentals of Naval Architecture: "Danger Angle: One half the angle of the maximum Righting Arm." Has anyone come up with a reason for this definition? Is it really a danger angle where a ship without movable ballast greatly increases its risk? I think, as hula waisted kayakers, our "risk" point can be much closer to the maximum righting moment than a ships danger angle could be. A ship does not shift itself over into a list unless there is something wrong with the ship or some outside force has thrown it over to one side. With kayaks, an internal force (the paddler) can drastically change the lean angle and the consequences of going over even 180 degrees are usually small, at least for a prudent paddler, so we can probably increase the level of risk we are comfortable with. I propose we label the point on the curve we settle on as the "RISK" angle. I think it will tell us more about what a kayaker wants to know than the value of the maximum righting arm, its angle, the area under the curve, or the point of maximum stiffness (which is often zero--see Wind Dancer Curve at http://www.marinerkayaks.com in the XL review), or what the shape of the top or backside of the curve is. Matt Broze http://www.marinerkayaks.com *************************************************************************** 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. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************Received on Wed Nov 22 2000 - 01:06:28 PST
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