Re: [Paddlewise] speed with versus against the current

Winters wrote:

> > Jerry wrote:
> > >
> > >It has always seemed to me harder to paddle against the current as opposed
> > >to with.  I mean that even with my eyes closed I think I can feel the
> > >difference, i.e., without looking at the fixed shoreline.  I always
> > >attributed this to my imagination since I can't think of a physical reason
> > >it could be true.
>  
> I believe this has to do with one's normal stroke rate. If you are paddling
> at your normal still water stroke up current the force on your paddle will
> be less because the paddle speed through the water is lower. To get the
> same velocity [through] the water you have to increase the paddle velocity
> relative to you.  Even though the paddle force is the same your rate is
> higher and that may give the sensation of greater work.

I have about the same experience as Winters, and agree with John's
analysis here.

There is another effect, however.  It is most apparent at the transition
time when one crosses from water going WITH you to water going AGAINST
you.  In fact, most times when I paddle across a shear line onto a "new"
batch of water which is moving AGAINST my motion, it momentarily "feels"
easier.  Here's my tentative analysis:

Imagine yourself paddling in water which is traveling in the same
direction you are, and at a comfortable cadence and paddle force, at a
CONSTANT velocity.  In the language of physics, the forces of resistance
on the paddler/boat system are exactly balanced by the propulsive forces
on the system, so the NET force on the system is zero.  (To slow down or
speed up, the NET force has to change.)  The resistive forces are:  1.
water resistance (FW), and, 2. air resistance (FA).  The propulsive
force (FP) is that from the paddle interacting with the water.  So, the
relationship is:  FP = FW + FA

As you slide across the shear line onto water which is going AGAINST
your motion, the momentum of the paddler/boat system will maintain your
velocity for a second or so.  BUT, because the water is now sliding past
your boat at a greater relative velocity, you will find that
(momentarily) paddling gets "easier" at the *same* cadence you had
before.  In other words, (momentarily) the paddle force drops -- that's
why it feels "easier."  (This is like the effect which occurs as one
briskly walks on fixed ground and steps onto a treadmill moving AGAINST
your direction -- it feels like your feet will fly out from underneath
you!  Try it!)

Of course, soon you notice you have slowed down relative to a fixed
point on the shore, and you increase your cadence (and paddle force) to
regain the same effort you were putting out before.  BUT, because of the
opposing current, your true speed *over ground* will be SMALLER.  This
makes the resistance due to the air, FA,  SMALLER because you are
travelling less rapidly through the air.  Now go look at the little
equation I wrote above.  If FA is smaller than it was before, and you
are truly putting out the same "effort" -- meaning FP is about the same
magnitude as before -- then the resistance due to passage through the
water (FW) must be GREATER.  This can occur only if your hull speed
through the water is greater, so your craft will be moving *through the
water* a little faster.  No, you won't be travelling over the ground
faster than before, because the opposing current offsets some of that
hull speed.  BUT, you may experience the sensation of "easier" travel,
if you focus on the water and notice you are travelling through it
faster than before.

That's what I experience when paddling against a current -- exactly the
opposite sensation which Jerry experiences.  In fact, when paddling
*with* the current, I notice I have to apply a markedly GREATER force on
the paddle (at the same cadence), and feel I am working harder going
*with* the current -- which makes sense, because there is greater air
resistance at the greater speed over the ground.

Sometime I should paddle with Jerry and we should discuss these
"sensations" and try to sort out the differences in our perceptions.

Sorry for going on so long.  Took a lot of words to get this out.

-- 
Dave Kruger
Astoria, OR
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