Peter wrote: > It had not even occurred to me until Matt mentioned that it does not show > up on the stability curves. John responded: It does show up in the stability curves if you know what to look for. I don't think I ever said that secondary stability doesn't show up on the curve but I do believe it is hard to define in strictly objective terms. if I did say it I don't think I meant it how Peter has interpreted it here. I think Nick did a very good job of defining what I mean by secondary stability (if I am interpreting what he said correctly as I'm not familiar with the terms inflection points and what the derivatives are). Nick can you explain those points a little clearer or maybe look on the Sea Kayaker review of the XL at http://www.marinerkayaks.com and look at the stability curves of the Wind dancer, Pisces, and XL and use them as examples of where you would find the inflection point on each curve. I think we are in agreement here but I'd like to get the definition down to a way more folks than mathematicians can understand. Thanks Nick. Sorry to be so testy John. 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/ ***************************************************************************
[Paddlewise] Content-Type: text/plain; charset="us-ascii" ; format="flowed" Sender: owner-paddlewise_at_paddlewise.net Precedence: list X-Listname: Paddlewise Mailing List X-Subscription-Info: paddlewise-request_at_paddlewise.net The Mariner XL does not have distinctive secondary by my proposed definition. http://www.guillemot-kayaks.com/MarinerXL.gif shows a replotting of the data, traced (crudely) from the web site and then put into Excel. The first derivative is just the slope of the curve at any point. The Magenta line shows this by taking a simple rise-over-run calculation. The Red line does the same thing again to get the rate of change of the slope of the curve. http://www.guillemot-kayaks.com/Example.gif shows the same stuff for an extreme example design of what would likely be a very cranky boat. This boat has negative initial stability so it really wants to fall over to one side. It then becomes somewhat stable while resting on its flat side. While it's overall stability may be "bad", my theory would predict this boat to have "good" secondary stability. In the Example boat notice that the Magenta line rises as the slope of the curve rises and then drops down. The red line is positive where the slope is increasing or shaped like the bottom of a "U" and negative where the slope is decreasing and shaped like the top of an "n". The "inflection point", where the curve changes from "U" shaped to "n" shaped, corresponds to the steepest slope on the curve (maximum 1st derivative). Another example of in inflection point is the middle of an "S". Where the curve is "U" shaped, the stability is increasing at a faster rate the more you lean, so the more effort you put into leaning, the less effect it has. Where the curve is "n" shaped, more lean will have progressively more effect. What the Mariner XL does have which the Wind Dancer and Pisces do not appear to have as much, is an initially very straight stability curve. The slope stays fairly constant out to about 25 degrees. It is neither "n" shaped or "U" shaped but just goes "/". The others appear to be more consistently "U" shaped. However, I didn't take the time to replot them to be certain. By my system, this would appear to make the XL very predictable while leaning: You lean a bit, the boat heels a bit, you lean some more it responds the same until you get to about 25 degrees. The Pisces, looks like it starts out straight and then becomes "n" shaped at around 15 degrees. The Wind Dancer appears to accelerate throughout the lean: more lean produces more and more heel as you go. I can't comment on whether any of this is true, but that is what my proposed theory would predict. To summarize "U" shaped parts of the curve indicate a boat that stiffens up as you lean, "n" shaped indicates a boat that gets looser as you lean. Straight parts of the curve indicate a constant ease of leaning a little bit more. Regardless of whether or not looking at the slope of the stability curve (a.k.a the 1st derivative) is going to be accepted as a way to predict, "secondary" stability, I think it is useful to look at the slope to understand everything the curve can tell you. The slope tells you how hard it will be to lean the boat just a little bit more. And looking at the rate of change of the slope (aka the 2nd derivative) will tell you if the boat gets harder or easier to lean just a little bit more. Nick At 6:24 PM -0800 11/17/00, Matt Broze wrote: > Peter wrote: >> It had not even occurred to me until Matt mentioned that it does not show >> up on the stability curves. > >John responded: >It does show up in the stability curves if you know what to look for. > >I don't think I ever said that secondary stability doesn't show up on the >curve but I do believe it is hard to define in strictly objective terms. if >I did say it I don't think I meant it how Peter has interpreted it here. > >I think Nick did a very good job of defining what I mean by secondary >stability (if I am interpreting what he said correctly as I'm not familiar >with the terms inflection points and what the derivatives are). Nick can you >explain those points a little clearer or maybe look on the Sea Kayaker >review of the XL at http://www.marinerkayaks.com and look at the stability >curves of the Wind dancer, Pisces, and XL and use them as examples of where >you would find the inflection point on each curve. I think we are in >agreement here but I'd like to get the definition down to a way more folks >than mathematicians can understand. >Thanks Nick. >Sorry to be so testy John. > >Matt Broze >http://www.marinerkayaks.com -- Nick Schade Guillemot Kayaks 824 Thompson St, Suite I Glastonbury, CT 06033 (860) 659-8847 Schade_at_guillemot-kayaks.com http://www.guillemot-kayaks.com/ >>>>"It's not just Art, It's a Craft!"<<<< *************************************************************************** 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/ ***************************************************************************
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