RE:[Paddlewise] Secondary stability

A few clarifications I think are in order, I never wrote that secondary 
stability was meaningless, I just speculated that it could be something not 
relevant to large commercial vessels since you can not rapidly shift the CG 
to alter the ships response like you would on a kayak.

I also question Nick's proposed definition of using the location of the 
inflection point as indicative of the perceived secondary stability.  If 
Matt is not thoroughly confused by now the inflection point is where the 
RATE of CHANGE of a curve reverses.  For example a strait line from the 
"zero, zero" point has a constant rate of change, for each degree of roll 
you get the same increase of correcting moment; for a concave curve the 
rate of change is increasing, for each additional angel of roll the 
increase in correcting moment gets larger, for a convex cure the rate of 
INCREASE of correcting monument gets smaller, BUT IT IS STILL INCREASING, 
just not as much.  If the curve has an inflection point it is where the 
RATE of increase reduces below zero so the RATE of change is getting 
smaller, it would be where the concave cure meets the convex curve.

If you have a "low" stability hull, where large increases in the roll angle 
only result in a modest increase in correcting moment, I think most people 
would say it has low secondary stability, regardless of where the 
inflection point is. I do not think the infection point is something 
perceptible in the seat of the pants, because even if it the RATE of CHANGE 
is decreasing, the CORRECTING moment is still INCREASING as you roll the 
kayak over on its side.  I.E. the more you roll it, the higher the 
resistance to the roll, it would be where you feel the resistance drop off, 
when you are over the top of the curve, where you start feeling like you 
are going over.

I would also think that if the curve had a sharp peak, it would feel less 
forgiving since the correcting moment would drop off rapidly with little 
warning once you pass a certain roll angle.

It seems to me that the secondary stability would be (taking the paddlers 
skill out of the picture) a combination of what is the absolute resistance 
to rolling is at a given perceived angle of roll, and how much margin you 
have from this point to the peak, and how much warning you get before the 
correcting moment drops off.  So if you roll up to say 30 degrees and the 
slope of the curve is at some given angle, but if you have little margin 
and a real shape break you would likely perceive this as poor secondary 
stability.  OTOH if you have a kayak with a lower slope at 30 degrees angle 
of roll, but a large margin (i.e. a lot more angle of roll to the top of 
the curve) and the curve had a flatter top giving you more warning, you 
would say it had good secondary stability.

In fact I would say the higher the peak of the curve on the chart (i.e. 
highest absolute rolling resistance) would have more influence over the 
perceived secondary stability than the location of the inflection point. 
 And the overall rate of increase, or average slope, would also have a 
powerful influence of the perceived secondary stability.

I do not claim to be anykind of an expert on hull design but I have spent 
many years analyzing aircraft stability and control curves know well how to 
read a chart and its derivatives, you have to look at how the changes 
affect the "human factors", hard to predict from purely a mathematical 
stand point.

I would suggest someone get together a group of paddlers of various skill 
levels and compare perceived secondary stability with all kinds of curve 
properties in various hull designs.  If you can find any kind of 
correlation (which you may well not find) then we might have a working 
definition, and something to look for in a cure (maybe an article idea for 
SK mag?).  As one of my engineering professors used to say, one simple 
experiment is worth a thousand expert opinions.

Peter

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