Michael Daly wrote:
On 4-Jun-2004, Peter wrote:


A study done by David Jones (The Stability Of The Bicycle; Physics Today,
April 1970, 34-40) used a variety of modified bicycle designs to
determine the key elements in stability.


An earlier analysis of this stuff is in Timoshenko's book on Dynamics.
It is indeed centripetal and (D'Alembert) centrifugal forces that
provide stability to a bike. The degrees of freedom in a bike are
coupled - if you turn the front wheel to the left or right, the
bike leans a bit accordingly. This changes its direction which
generates a counteracting centrifugal righting force.

Sure, there are plenty of references that make the theoretical claim
that gyroscopic forces result in bicycle stability. But Jones tested
those claims with an experimental arrangement where the gyroscopic
effects were canceled out by using a second counter-rotating wheel next
to the regular wheel. The resulting bicycle was found to still be very
stable and easy to ride whether the second wheel was turning backwards
(no gyroscopic effects), forwards (double the effect), or stationary.
Bicycles are still stable even in the absence of gyroscopic effects.

The steering geometry was found to be more significant, especially the
amount of trail between where the steering axis hits the ground compared
to the position of the contact patch of the tire.


But I would expect the
movement to help rather than hinder stability. The upper part of the
bow curves outward and if this surface is brought into contact with the
water by leaning the boat then the forward movement of this curved
surface should tend to produce an additional righting force.


OTOH, the water flowing over the surface may generate a normal force.
Water flowing over the surface results in less pressure on that surface.
hat that does in the end depends on the orientation of that force
relative to other forces.

I've been told that longitudinal stability is enhanced with motion, but
I have no idea what it would do to rolling stability of a heeled craft.
It seems to be below my threshhold of awareness, regardless.

As I wrote before, I expect the effect to be small at the relatively low
speed of kayaks. But the heeled-over surface of the upper part of the
bow has the leading edge higher than the trailing edge and when pushed
forward through the water it will tend to push the water downwards which
requires a corresponding upward push on that part of the boat. This
force will provide a net torque helping to keep the boat upright.

Peter wrote in message ...
Michael Daly wrote:
On 4-Jun-2004, Peter wrote:


A study done by David Jones (The Stability Of The Bicycle; Physics Today,
April 1970, 34-40) used a variety of modified bicycle designs to
determine the key elements in stability.


An earlier analysis of this stuff is in Timoshenko's book on Dynamics.
It is indeed centripetal and (D'Alembert) centrifugal forces that
provide stability to a bike. The degrees of freedom in a bike are
coupled - if you turn the front wheel to the left or right, the
bike leans a bit accordingly. This changes its direction which
generates a counteracting centrifugal righting force.

Sure, there are plenty of references that make the theoretical claim
that gyroscopic forces result in bicycle stability. But Jones tested
those claims with an experimental arrangement where the gyroscopic
effects were canceled out by using a second counter-rotating wheel next
to the regular wheel. The resulting bicycle was found to still be very
stable and easy to ride whether the second wheel was turning backwards
(no gyroscopic effects), forwards (double the effect), or stationary.
Bicycles are still stable even in the absence of gyroscopic effects.

The steering geometry was found to be more significant, especially the
amount of trail between where the steering axis hits the ground compared
to the position of the contact patch of the tire.


But I would expect the
movement to help rather than hinder stability. The upper part of the
bow curves outward and if this surface is brought into contact with the
water by leaning the boat then the forward movement of this curved
surface should tend to produce an additional righting force.


OTOH, the water flowing over the surface may generate a normal force.
Water flowing over the surface results in less pressure on that surface.
hat that does in the end depends on the orientation of that force
relative to other forces.

I've been told that longitudinal stability is enhanced with motion, but
I have no idea what it would do to rolling stability of a heeled craft.
It seems to be below my threshhold of awareness, regardless.

As I wrote before, I expect the effect to be small at the relatively low
speed of kayaks. But the heeled-over surface of the upper part of the
bow has the leading edge higher than the trailing edge and when pushed
forward through the water it will tend to push the water downwards which
requires a corresponding upward push on that part of the boat. This
force will provide a net torque helping to keep the boat upright.

Peter, for whatever it's worth I like your response the best, it does
seem more intuitive that the leaned bow and stern passing over moving
water would result in lift similar to that of a paddle brace. As
Michael also correctly noted moving water is a fluid which does
conform to the Bernoulli effect: the same law that produces lift on
airfoils. In the case of the Kayak airfoil however the pressure would
be greater on the side which was less wetted, tending to push the boat
further into the water. However, the speed of the fluid flow may be
inconsequential compared to the positive effect of the bow and stern
acting like a paddle with it's leading edge high. Oh well, time to get
into the lab (water) and test it out!!

Gene

On 4-Jun-2004, Peter wrote:

Sure, there are plenty of references that make the theoretical claim
that gyroscopic forces result in bicycle stability.

Umm,... Timoshenko showed that gyroscopic forces were essentially irrelevant.
I was confirming your point, but identifying earlier analyses exist than
Jones. I wouldn't be surprised if Jones referenced Timoshenko. It's a
classic text in mechanical engineering. Whitt and Wilson's book on bicycling
science also catalogued many studies on bicycle stability done before WWII.

Mike

"Michael Daly" wrote in message ...
On 4-Jun-2004, Peter wrote:

Sure, there are plenty of references that make the theoretical claim
that gyroscopic forces result in bicycle stability.

Umm,... Timoshenko showed that gyroscopic forces were essentially irrelevant.
I was confirming your point, but identifying earlier analyses exist than
Jones. I wouldn't be surprised if Jones referenced Timoshenko. It's a
classic text in mechanical engineering. Whitt and Wilson's book on bicycling
science also catalogued many studies on bicycle stability done before WWII.

Mike

Slightly different question: If you're familiar with SeaKayak magazine
reviews, they supply some interesting numerical data with respect to
the subject of stability. As an example, if given the same or equal
conditions, if it takes say only 10 foot lbs of force to heel a boat
25 degrees which represents the point of imminent capsize, that should
also mean that it requires the same amount of force applied opposite
to right the boat?

Now if another boat requires 20 foot lbs to heel the boat the same 25
degrees and with the same result i.e. imminent capsize, and the same
amount to resist or right the boat, which boat is more stabile? Which
is easier to control? Which would you rather paddle? while the charts
and numerical values can be wildly divergent, the reviews narrative
descriptions regarding stability frequently appear to be similar.

Gene

On 11-Jun-2004, (Gene Cosloy) wrote:

Slightly different question: If you're familiar with SeaKayak magazine
reviews, they supply some interesting numerical data with respect to
the subject of stability. As an example, if given the same or equal
conditions, if it takes say only 10 foot lbs of force to heel a boat
25 degrees which represents the point of imminent capsize, that should
also mean that it requires the same amount of force applied opposite
to right the boat?

No. The righting moment is the force that is pushing you back up. When
you heel a boat, it will resist the heel up to the point of collapse.
If you take away the heeling moment, the righting moment will push it
back to a neutral position.

Now if another boat requires 20 foot lbs to heel the boat the same 25
degrees and with the same result i.e. imminent capsize, and the same
amount to resist or right the boat, which boat is more stabile?

The greater the righting moment at a given angle of heel, the more stable
the kayak will feel.

Which is easier to control? Which would you rather paddle?

It is difficult to say. You can probably discount a kayak from these
graphs (since it would be wildly different than what you're looking
for) they say nothing that should make you choose a kayak. The final
judgement is only made in the water.

while the charts
and numerical values can be wildly divergent, the reviews narrative
descriptions regarding stability frequently appear to be similar.

The flaw in the graphs is in the way the data is determined and what
it means. The model is a kayak with a static paddler. Real kayaks
have live, moving paddlers. If the kayak starts to heel, a real
paddler will react and that changes the geometry and hence the behavior
of the heeled kayak. Remember that the reviewers are not beginners
or even intermediate paddlers. They can make any kayak perform and
can make up for differences that may be noticable (or difficult
to overcome) for beginners.

The way to read the graph in a useful way is as follows.

The slope at the origin (degree of heel near zero) indicates the initial
or primary stability. The slope here can be positive (inherently stable)
or negative (inherently unstable). The more positive it is, the higher
the initial stability. Beginners tend to like high initial stability,
while experienced and adventurous kayakers prefer low initial stability.
Racers will accept negative initial stability.

The maximum height of the graph indicates the degree of secondary stability.
A kayak with a very high graph will be more stable on edge than one with
a lower value. However, a key feature is what angle of heel this occurs at.
If the peak is at a relatively small angle of heel, the kayak will be
difficult to edge and will be (likely) harder to handle. If the peak is
further to the right and at a larger angle of heel, the kayak will roll
on edge easily and will sit well over solidifying its stability.

An example of a kayak with very low or negative initial stability is one
with a deep V hull or with a V and rounded hull. Some racing kayaks
cannot stay upright in the water without the active participation of
the paddler.

An example of a kayak with high secondary stability is a fat, wide kayak
like the Solstice GTHV, Necky Pinta or many of the foldable kayaks like
Kleppers. They are difficult to edge and tend not to carve turns
easily.

An example of a kayak that has moderate initial stability and solid
secondary at a higher angle of heel are many of the Greenland-inspired
designs like the Anas Acuta, Pintail, Explorer, Chatham etc. They are
easy to get on edge and can sit there comfortably. My Ellesmere is
twitchy at zero degrees of heel and is _more_ stable on edge. These
kinds of kayaks tend to be popular with advanced paddlers.

Mike