[Paddlewise] A Secondary Definition!

At 11:37 PM -0800 11/16/00, Matt Broze wrote:
>
>Imagine we make two ramps in the shape of a stability curve to roll a ball
>bearing up and over. The front side of the curves are identical but one then
>drops straight down to zero at its peak and the other falls away like most
>static stability curves do. Question: Which ball will reach the (ground)
>zero point on the back side the quickest (if you were to roll it over both
>ramps equally hard and with plenty of momentum to easily make it over the
>hump)?
>
>I don't believe the path (through space) the two balls would take would be
>any different with these two ramps. Both balls would be in free fall the
>whole way down, one would just have gotten further away from its ramp
>because its ramp dropped away more suddenly. You might not notice the other
>was not quite touching its ramp on the backside. Sort of like an orbiting
>satellite continuing to fall past the earth due to its speed. Of course if
>you could get the force just right so the ball barely clears the peak the
>backside ramp would slow the fall a bit.

I don't see how the analogy of a ball flying through the air is a 
good analogy for stability. A ball is free to fly so the shape of the 
ramp may not effect it's travel, but a boat must stick to it's curve.

There seems to be a growing consensus that because we are having 
difficulty defining "secondary" stability that it must be meaningless 
and if it means anything, it is the same as "overall" stability. I 
think many kayakers would dispute that. They can feel a secondary 
stability and know a boat that has it. Take an extreme example of a 
boat with a distinct "V" bottom and low flat deck (almost diamond 
shaped in section). This boat could have low "initial" but high 
"secondary". With the low deck, it may also be quite easy to turn 
completely over in which case the "overall" stability may not be 
great. In this case there is something between "initial" and 
"overall" which is significant. This is what people call "secondary".

Instead of throwing the baby out with the bath water, why don't we 
try to define what "secondary" is and how it differs from "overall".

If the stability curve crosses zero at 60 degrees, a paddler sitting 
bolt upright and doing nothing to recover at 59 degrees of lean will 
return to the upright position. The recovery might be slow, but if no 
other forces are applied, recovery is inevitable. This does not seem 
to me to be related to "secondary", but must somehow belong in the 
"overall" camp. Previously John has suggested the area under the 
curve as being indicative of overall stability. The area indicates 
the amount of work or energy required to capsize the boat until the 
point of no return, with an inert passenger. An inactive paddler is 
not realistic, but people are hard to predict, so we are stuck with 
it. By using area a boat with a high narrow stability curve and one 
with a wide flat curve are both shown to be hard to tip upside down. 
This seems to be what we want to know about "overall" stability.

Secondary is a little harder to pin down. I think what people call 
"secondary" is the feel that it is taking progressively more effort 
to effect a change in the lean. Some boats, you lean a little bit, 
the boat responds, you lean a little be more, it responds about the 
same, more lean, similar response. Some boats, you lean, it responds 
a bit, lean a little more and it responds more than before, more lean 
and an accelerated response. Other boats, you start leaning and the 
boat responds, you lean more, and the boat doesn't respond quite as 
much, more lean, even less response. These last boats tend to be 
characterized as having good secondary stability. The boat "stiffens" 
as it is leaned.

This tendency can be seen in the stability curve by analyzing the 
slope of the curve. The rate of change of the stability indicates 
whether it is going to take progressively more effort to create a 
given change or progressively less. Mathematical types will look at 
the derivative of the stability curve.

Some curves start out steep and bend continuously downward. Others 
start out relatively flat, then curve upwards before straightening 
out and starting to bend down. These are the boats which "stiffen". 
The inflection point, where the curve changes from upwards tending to 
downwards tending will probably tell us something about "secondary" 
stability. (for those mathematicians still following, the inflection 
point is the maximum of the derivative, or the zero crossing of the 
second derivative)

The possible characteristics to look at for this form of "secondary" 
stability are: the slope of the curve at the inflection, the height 
of the curve at the inflection, the angle of lean at the inflection 
or the area of under the curve until the inflection point.

After a little thought, I am going to say a boat with "good" 
secondary stability will be one where the angle of the inflection 
point is the highest. This will be the boat where you can lean the 
boat the most before the ability to recover starts to fall apart. 
Beyond the inflection point, less and less effort will be required to 
create the same effect on the boat until you reach the top of the 
stability curve where the slightest increase in effort will cause a 
capsize.

I am certain, that a lot of people won't agree with this definition, 
but I think it does address some of the concerns.

Nick
-- 


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!"<<<<

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