Re:[Paddlewise] Stability

I'm mostly in agreement with Robert Livingston concerning what he wrote
regarding primary and secondary stability. Certainly there is no official or
even a generally accepted definition of "Secondary Stability" in Naval
Architecture or even kayaking. In fact, the words seem to rarely be used
together outside of the Kayak and Canoe realm. I put "secondary stability"
into Google and with the exception of a few mentions in relation to dental
materials and one concerning fluid mechanics and Gortler vortexes (which I
have never heard of couldn't understand at all upon viewing the article) the
vast majority of the first one hundred Google results seemed to be related
to kayaking or canoeing. 

This brings up a question. Who first used this term and when? Let's see who
among Paddlewiser's can find the earliest documented example of this term
used in relation to boats. Given its present usage level of usage there, I
suspect it will be in the realm of canoeing or kayaking. I've been looking
at our earliest brochures and see that I used the term in the very earliest
Escape brochure we printed (probably in early 1982). By the next printing of
the Escape brochure though, I wrote about "dynamic stability in waves"
instead. (That turned out to be a mistake, as I found out much later, there
already was a defined term in Naval Architecture for "dynamic stability" and
it doesn't mean what I had meant. Such is the hazard of making up terms and
then not researching them I guess. I can't remember where I may have gotten
the "Secondary Stability" term but I looked to see if I can find it in John
Dowd's or other early sea kayaking texts. Perhaps it was just the obvious
term to make up to separate it from "Primary Stability" and I made that up
like I did with "Dynamic Stability". [I couldn't find the term in any of
John Dowd's many editions, but I found that Randel Washburne called it
"large-angle stability" in his 1983 "The Coastal Kayaker" book). I'll try to
look at some mid 1970's and later Canoe magazine buyers guides and early
British kayaking books (when I get back to work) to see if it was used there
at all. 

I liked Robert's example of pushing against a door with someone pushing
back. My one nit-picking point of disagreement comes with his interpretation
of where on the curve the decrease in pushing back is important. In the Sea
Kayaker comparison and explanation of the stability curves the term
stiffness is used (this article is probably most easily found in its
entirety on our website--near the end of the Mariner XL review--unless one
happens to have the Spring 1987 issue). Here is part of what is written
there (used with permission):
  
"At any selected point on these curves the righting moment measured in
lbs.ft. may be read on the vertical axis, and the angle of inclination
measured in degrees on the horizontal axis. The area under the curve to that
point represents the work done in inclining the kayak to that angle and, if
the angle is measured in radians (1 radian = 57.30 ), the units of work will
be directly in ft.lbs. The slope of the rising part of the curve at that
point represents the stiffness, which is the rate of increase of the
righting moment as the angle of inclination increases. Units of stiffness
come out as lbs.ft./degree. For a boat to be in a stable state, an increase
in heeling force must be balanced by an increase in righting moment, after
an appropriate increase in inclination. So stability requires stiffness and
the two terms are often interchanged.
The slope of a curve can be derived at any desired point by drawing a
tangent at that point, and that is a straight line coincident with the curve
at the point of contact. Its value can be calculated by making a right
angled triangle from this tangent and dividing the vertical height by the
horizontal length."

Apparently, the guy on the other side of the door varies in strength (to
resist) in relation to the angle you swing open the door and at some point
if you get enough angle on him he can be overpowered and you will likely
fall through that door when that happens (unless you can suddenly quit
pushing). This surely will happen at the top of the curve. I contend that,
due to momentum, the kayaker is likely to feel about to capsize when the
angle of the stiffness curve begins to significantly decrease (even though
it is still rising).

One other nit-picking point, while hull's width is an important parameter to
initial stiffness it is not as significant a factor as the area of the water
plane in determining stability. (This applies to stiffness at any point of
lean). With two boats of the same width with vastly different water planes
the one with the most water plane area at a given angle will be the stiffest
at that point of the curve. Imagine a hollow diamond shaped water plane
compared with a full rounded shape of the same length and width. Since
longer length also increases the water plane, longer length increases the
static stability of the kayak if width and other factors are held constant.

How about this for a simple definition of secondary stability: "The
stiffness against further angle of tilt when the hull is already tilted to
three-fourths of its maximum righting moment divided by the hulls initial
stiffness."  I invite refinements (and simplifications of terms). The goal
will be to get to a definition that matches the subjective feel experienced
by a paddler but while using measurable and well defined parameters.

Robert wrote: 
<Snip>>>>>>>As for "secondary stability" since that has no "scientific"
definition, I
cannot make the same statement. But the effect of width on the entire curve
of stability is so paramount that again it is hard (impossible?) to find any
"commercial-like" design where the stability curve for 0 to 45 degrees will
be greater at ANY point than a commercial-like design with a waterline width
that is 1 inch greater.<<<<<Snip>

I'm afraid a little more nit-picking follows (or at least some contrary
evidence that argues against Roberts challenge). The Nimbus Puffin was 7/8"
narrower in max. beam than the Aquaterra Chinook. Lengths and prismatic
coefficients were about the same. The Chinook was a little more initially
stable but if you get the Winter 1986 edition of Sea Kayaker you can see
that the curves overlap at 17 to 18 degrees of tilt (both are still
ascending) so that at all angles of lean well above 18 degrees the Puffin
has far greater stability. The Puffin was 1 3/8" (one and three eights inch)
narrower at the waterline as well. The Puffin has much fuller bilges and the
Chinook tends to more approach John Winters' V-bottom computer model (where
the chines were at the surface). Sea Kayaker placed the center of gravity of
150 pounds (representing the paddler) 10" above the seat bottom when
measuring a kayaks stability (with a torque wrench). Perhaps the seat height
was higher in the Chinook (Sea Kayaker didn't publish the seats height at
that time). 

The flatter bottomed Sea Runner (in the same issue) was 1" narrower than the
Chinook in beam (3/4" narrower at the waterline) but had far greater
stability than either the Chinook or Puffin. Another possible confounding
factor could be the height of the gunnels. Higher gunnels will have better
stability at high angles of lean. The Sea Runner holds its width over more
of its length than does the Chinook and has a much flatter bottom. Same
caveat about the seat height as before. I should state that these were
measured in a tank (rather than computer modeled) results so there is
greater chance that some measurement error was involved. My point is that
width isn't the whole story even when we are just considering a kayaks
static stability. 


Matt Broze
http://www.marinerkayaks.com
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