Re: [Paddlewise] Greenland paddle - Throw-weight

We've been through a similar argument before. One of the problems, that John
alluded to, is that muscular work can not be calculated like physical work.
If you put a weight on a shelf, it can just sit there without the shelf
continually doing work on the weight. If you support a weight with a muscle
that is not fully extended (i.e. limp) then the muscle must continuously do
work, physiological work, to keep itself contracted against the pull of the
weight. An analogy might be a leaky tire: it won't stay up unless you keep
pumping air into it.

If you could support the paddle in some rigid device (think of a double
paddle wheel with only one paddle/blade on each side, with one blade up when
the other was down), and then move the pair of wheels by turning a crank,
the weight of the blades would be unimportant. The weight would be borne by
the paddlewheel bearings, whether the wheel were turning or not. But when
the wheel is turning, the bearings also need to hold it against vibration
because the wheel hasn't enough balance. It needs at least two blades on
each side to not vibrate. 

Because the real paddle is moving in a cone, not a circle, it too will cause
reaction against its supports, depending on the weight distribution. (It
can't move in a circle, because you're using one blade on each side of the
boat.)

Thus contrary to John's opinion (and contrary to mine the last time he and I
discussed this sort of thing), the weight distribution of the paddle (moment
of inertia) is important in the amount of (physiological) work one does,
supporting the paddle against its inclination to turn in a disc instead of a
cone.

In a sense it is the added effort to hold the paddle, but it is the added
effort to hold the paddle against this twisting, which depends on the radius
of gyration (a measure of the weight distribution) as well as the weight.

Hank Hays wrote:
[snip]
>The bottom blade actually does essentially stop in the water -  the boat
moves on past it (hopefully or you are going nowhere fast!) - and the upper
blade travels faster to make up for it.  Yup, start, stop, start, stop.....
 The center of the shaft travels the same speed as the boat.  If the bottom
blade stops, the upper blade has to be traveling at an average of twice the
speed of the boat to get ahead for the next stroke.  You are accelerating
the upper blade of the paddle from a dead stop to twice as fast as the boat
(or more for a short period of time).   And if you paddle unfeathered, think
of the wind resistance!  
[end quote from Hank]

The same argument will tell you that a bicycle wheel is also stopping and
starting continuously. You need to be working in a coordinate system that is
moving with the (mean motion of the) boat. Wind resistance is important, but
in the present argument is something of a red herring. But this does
indicate the reason for feathered paddles, which we inherit from the
flatwater racers. They race only in essentially calm conditions, so if
they're going at seven knots, the upper blade of the paddle is feeling a
breeze of fourteen knots.

Hank again:
>Yup, acceleration is expensive in energy costs.  But, does this matter as
much as you think?  The paddle shaft has a counterweight at the other end,
the string does not.  One paddle blade cannot go flying off on the tangent
into orbit because of the shaft and the blade on the other end.  Drill a
hole through the center of the shaft, insert an axle, mount the axle in
bearings and give the paddle a spin.  It will go in circles until air
resistance stops it (meaning pretty soon).  Forces keeping the blades
together balance so no energy expended in that regard.  People don't paddle
like this when in a boat, just when standing on the ground.    
[end quote from Hank]

Thank you, Hank. This illustrates my main argument nicely. If we go back to
my paddlewheel analogy, drill the hole obliquely through the centre of the
shaft, and see how hard it is to support the bearings.
Bruce Winterbon
bwinterb_at_intranet.ca
http://intranet.ca:80/~bwinterb

All states have laws to protect the rich from the poor.
Few attempt the more difficult task of protecting the
poor from the rich.

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