On 10-Mar-2005, Kieran wrote:

Hmmm... this seems to be the part I'm missing. How do you get power
without knowing the path of the force?

Determining the moment in the shaft at some point allows you to resolve
the force at another point (say, centroid of area of the blade). Knowing
the paddle motion, from the video analysis you can do, will allow you
to determine the velocity of that centroid. Hence the power out. Since
power is a scalar, not a vector, you don't have to worry about direction.

However, that is total power in, not power that drives the kayak forward.
That is, if you calculate (estimate) the power to drive the kayak (total
hull resistance times hull velocity), it will be less than the power that
the paddle generates.

Mike

Michael Daly wrote:
On 10-Mar-2005, Kieran wrote:


Hmmm... this seems to be the part I'm missing. How do you get power
without knowing the path of the force?


Determining the moment in the shaft at some point allows you to resolve
the force at another point (say, centroid of area of the blade). Knowing
the paddle motion, from the video analysis you can do, will allow you
to determine the velocity of that centroid. Hence the power out. Since
power is a scalar, not a vector, you don't have to worry about direction.

Yes, all this I already knew... basically you're saying you DO need to
know the path of the force to get power. It seemed that Alan was
implying there was another way, just by knowing the force-time relationship.

However, that is total power in, not power that drives the kayak forward.
That is, if you calculate (estimate) the power to drive the kayak (total
hull resistance times hull velocity), it will be less than the power that
the paddle generates.

Actually, that's kind of the point. We want to know how much power the
paddler develops and puts into the paddle.

-Kieran

Kieran writes
Tinkerntom wrote:

Force on the paddle shaft, at the handgrip.
Makes me think of a big torque wrench. Do you get any deflection of
the
paddle shaft while paddling? Use a smaller shaft until you do, Take
video, or measure the deflection of the needle! Then in the lab,
measure the force needed to duplicate the deflection. You should then
have an idea of what the possible force exerted on the shaft would be
for a particular paddler.
The potential force would be based on as wolfgang points out the
effectiveness of the engine mount, the paddlers seat and feet, the
grip, and other loss of efficiency factors that could be isolated for
significance. TnT


The problem is not how to measure the moment (torque) on the shaft.
Strain guages have been around for ages that will allow me to do that,
and I'm well familiar with how to implement them. The problem is
determining power from that force.

The force balance in the kayak system is weird, as there is no fixed
pivot point on the paddle. So, the pivot point is a "virtual" one.

I'm making progress, but still wonder if anyone has done this already.

The only way I can see to determine power at the hand grip is to record
3D kinematic video of the motion, so that the actual 3D vector of the
handgrip velocity is known. Then Power=FxV. But I wonder if there's a
better/simpler way to do it.

I did find a paper (Aitken, 1992) that measured paddle shaft torque
(bending) with strain guages, then used the hull velocity through the
water to get power. I don't see how this is valid, though, since hand
velocity is not equal to hull velocity. But then I suppose it would
depend on what your frame of reference was... Hmmmm....

Any other bright ideas out there? :-)


Keiran -

Your getting lots of feedback, but the complexity of the problem is vast
and the simplifications on offer may be too simplistic, although you've
made that point in some you've answered already.

Trying to assess fluid drag on the boat from towing measurements is not
going to give a great answer, since no kayak goes in straight lines.
And even if you could measure a more accurate power loss for the hull
that gives you no handle on the power losses around the immersed paddle.
A paddle is probably more efficient than an oar, but how efficient is
it, & how does its propulsive efficiency vary through the stroke?

Could one "catch" all the energy added to a finite but significant
volume of free water surrounding the path of the paddle stroke? Are
there ways to track the 3-D motion within that volume over time (it
sounds like a real-time tomography problem, perhaps done by laser scans
using suspended reflective particles), & feed that back into a CFD
program to sum up momentum transfers and frictional losses.

Now, if you could strain gauge a paddler........ It'd be great if the
means existed. Then you'd be able to measure the forces & speeds of
action at every bodily joint. Does that mean you'd have to build a
robotic paddler & tune him until he imposed the same loads & speeds of
action as a human on real paddles in a real moving boat? Or is there
any feasible way to take such direct measurements?

The answer may still be 42, of course.

Good luck there -
Carl
--
Carl Douglas Racing Shells -
Fine Small-Boats/AeRoWing low-drag Riggers/Advanced Accessories
Write: The Boathouse, Timsway, Chertsey Lane, Staines TW18 3JY, UK
Email: Tel: +44(0)1784-456344 Fax: -466550
URLs: www.carldouglas.co.uk (boats) & www.aerowing.co.uk (riggers)

Kieran:

As a person who did considerable white water kayaking in the 60's
(since then it's been mostly C-1 and rafting), plus a combined-fields
background (B. of M.E. and Ph.D. physics), I hope I can offer some
constructive comments.

First, let us just consider measuring the forces in sufficient detail.
I agree with the suggestion of Carl Douglas on February 28 that strain
gaging the paddle shaft is probably the most effective way to go.

Strain gage arrays can be designed to do each of the following:

(1) Measure flexursl (bending) moment.

(2) Measure axial force.

(3) Measure perpendicular (shear) force.

(4) Measure torsional (twisting) moment.

Incidentally, I prefer using "arrays" instead of "rosettes" because a
rosette most often is used to denote two or more adjacent strain gages
mounted on the same backing sheet. "Array" is more general, as it can
also include strain gages mounted on opposite sides of the paddle
shaft.

Thus, a combination of strain gage arrays between the paddle blade and
the paddler's hand can measure all necessary force components. A
similar combination of arrays, rotated by 90 degrees with a feathered
paddle, would be mounted between the other paddle blade and the
paddler's corresponding hand.

This leaves the question of forces in the paddle shaft between the
paddler's hands. We should not assume that these are zero. Strain
gage arrays can be mounted at the middle of the shaft. Again, all of
the above (1-4) can be measured. Measuring flexural moments at the
midpoint can even resolve possible flexural moments exerted by the
paddler's hands.

Thus, we are talking about a total of 12 strain-gage-array measurement
channels. But with all of them, the forces and moments on the
paddler's hands become statically determined. Possible extrapolation
to forces at wrists, elbows and shoulders remain separate problems.

Using strain gages sounds deceptively simple. At risk of telling you
what you already know, let me recommend "Strain Gage Users's Handbook"
(1992) edited by Hannah and Reed, most highly. It is published by the
Society for Experimental Mechanics, Inc. Bethel, CT. Among other
things, it is not advisable to mount strain gages on plastic or
composite surfaces. This has to do with heat-sinking. Metal surfaces
are best. Thus, if the kayak paddle has an aluminum tube core (as many
do), suggest stripping the outer, plastic layers off before installing
the strain gages.

Regarding the problem of velocity measurements (to get the power), I
suspect that the video method which you proposed would be most
effective, especially as I got the impression that some people in your
department already have some experience with that. The alternative
idea of using 3-D arrays of six accelerometers is also intriguing.
Effects of error propagation in integrating acceleration can induce
serious inaccuracies, unless great care is exercised.

Overall, my reaction is the following:

(1) The project is certainly feasible, and has exciting potential.

(2) Considering its scope (if done thoruoghly) it may be too much for a
Master's thesis, and more appropriate for a Ph.D. thesis. You may wish
to talk with your professor about that.

Please feel free to contact me directly.

Andres Peekna
Innovative Mechanics, Inc.
5908 North River Bay Road
Waterford, WI 53185-3035




Kieran wrote:
Allan Bennett wrote:
In article j1tUd.66306$8a6.13749@trndny09, Kieran
wrote:

That's the general idea, but because the paddling motion is 3-d,
it's
not very easy to determine power just from the strain in the paddle

shaft.


The flex in a paddle-shaft will be a reflection of all the forces
acting upon
the blade in the water. Using the force profile: t v deflection)
and
suitable calibration, it will be possible to determine the power.

Hmmm... this seems to be the part I'm missing. How do you get power
without knowing the path of the force?

You need to know instantaneous velocity (direction and magnitude)
at every
moment. In a fixed-pivot environment like rowing, you can just
put a
potentiometer on the oar-lock. But the kayak/canoe paddle has no
fixed
pivot point. So, I imagine that a virtual pivot point would have
to be
derived via 3-d kinematic video analysis.


It seems there is a virtual point (see Plagenhoef, 1979 and
others), just as
there is a virtual point where all the forces that propel the boat
seem to
meet - a valuable tool for those athletes with adequate
imagination.

Thanks for the reference. I'll see if I can find that publication.
Would that be a book or a journal article?

I haven't yet sat down and done a free-body of the system, but in
my
head, it seems like it's going to be an indeterminant system... not
fun.


..and the ultimate purpose?

Trying to come up with a master's thesis for my degree in
biomechanics.
A research prof here has an ongoing project that considers at a
high
(systems) level the energetics of different forms of human locomotion

through/in/on water, including surface swimming with/without fins,
submerged (e.g. scuba) swimming, rowing, and kayaking. There's very
little published research that we can find on kayaking, so that's the

part I'm tackling.

Thanks for your input!
-Kieran