Date: Tue, 21 Mar 1995 01:05:03 -0500
Message-Id: <199503210605.BAA07006@postbox.acs.ohio-state.edu>
To: baidarka@imagelan.com
From: hazel.2@postbox.acs.ohio-state.edu (Paul W Hazel)
Subject: Re: Paddling...
Bob Myers wrote in response to Guillemot:
>
>Wait a minute - it's not useful to separate lift and drag in this manner.
>You don't have to move the paddle in either up-and-down or horizontally
>back; you can combine the two motions. If you do so appropriately, there is
>no wasted force or energy. Think of it this way: lift and drag are merely
>the two perpendicular components of the hydrodynamic force. The part of
>that force that is parallel to the direction of motion of the paddle is
>called drag, and the part that is perpendicular to the direction of motion
>is the lift. If you take that total hydrodynamic force vector, instead of
>worrying about whether you're using "lift" or "drag", you should be able to
>move the paddle so that the total force vector is horizontal, pulling the
>kayak forward - without any wasted force.
It is perfectly possible to move the paddle in a way that the force vector
is exactly horizontal. Take for example a flat bladed paddle: insert it in
the water so that the blade is perfectly straight up and down ( a line drawn
from one edge of the paddle to the other and extended to the surface would
be perpendicular to the surface). Now pull.
Assuming a symmetrical blade, any tiny amount of lift that might be
generated as water flows over the top edge of the paddle will be canceled by
the same amount of negative lift created by water flowing under the lower
edge. The net lifting force will be zero, and therefore all of the generated
force will be in the horizontal plane - by definition "drag".
As Bob pointed out, lift and drag are perpendicular to one another -
therefore the only way that the vector sum of the two forces can be
perfectly horizontal (or perfectly vertical, for that matter) is if the net
value of one of these forces is exactly zero.
Otherwise, that added value will pull the vector away from a perfect 90
degrees (horizontal).
The point here is that it's not a good idea to try to get perfect horizontal
force, because then you lose the benefit gained by adding the two vectors.
As seen by the different styles of paddles wich intentionally generate lift,
there is certainly an advantage to this. By designing a blade that optimizes
lift AND drag, it is routinely possible to generate a vector sum of the two
forces which is significantly greater than either force by itself can be.
But that vector sum will NEVER, EVER, be perfectly horizontal. The
mechanical efficiency of the paddle in terms of its hydrodynamics is
directly dependent upon the angle between the perfectly horizontal and the
actual vector sum of lift and drag.
For this argument, I assumed a more or less conventional paddle and stroke,
i.e. the paddle is pulled through the water more or less horizontally with
respect to the surface for most of the stroke. I have only seen a modern
"wing" paddle once, and I have never seen it in use. The forces on it will
be the same of course, but I'm guessing that a different frame of reference
might be necessary for analysis.
Paul Hazel
hazel.2@osu.edu