RE: [Paddlewise] paddle sizing and Technology guides design

Well, this is going to get very technical, although it only really
requires high-school physics, so those of you who don't like that
should delete this now.



"Peter A. Chopelas" wrote:
} Subject: RE: [Paddlewise] paddle sizing and Technology guides design
>
> Because the perceived resistance is a function of the square of the 
> relative fluid velocity, the same paddle pulled back rapidly through the 
> water would have more resistance (less perceived "slip"), and pulled slowly 
> would have less resistance (more perceived "slip").  So it is non-sensical 
> to say the less slip you have in the water the more efficient the paddle 
> design, they are not related.  The only practical comparison of efficiency 
> is comparing the total power required to push the same kayak, at the same 
> speed, in the same conditions.

Slippage and efficiency are related, and what is more, it can be 
mathematically related to power required.

> The perceived resistance against a solid object is a direct function of the 
> speed you push against it (not a square of the speed as in a fluid), and 
> the slippage against the solid object would indicate a loss of perceived 
> resistance (remember sliding friction is always lower than static 
> friction).  This is why the idea of slippage in a fluid, which comes from 
> this model of pushing against a solid object, is invalid.  Thrust as a 
> result of fluid motion is not comparable to slippage.

Wrong.

> Get the idea of "slippage" out of your vocabulary when considering fluid 
> generated thrust.  Power is a work rate, to define efficiency with anything 
> other than "power in", or reduce it to something not related to power, is 
> clearly invalid.

Power = force*velocity, remember.  So if you pull the paddle blade
backwards faster than the kayak moves forward (slippage), you're using
more power than is going into propelling the kayak. (The forces must
be equal by Newton's third law.)  That's a direct measure of
efficiency.  Yes, it's true that there is no way to have zero slippage
- that's why it is impossible to have 100% paddle efficiency.  It's
still desirable to minimize the slippage.

Where is the extra power going?  Kinetic energy of the water.

The power required to propel a kayak must counteract the drag, a
force.  To do that, we push/pull the water backwards, resulting in a
momentum transfer from the water to the kayak, producing thrust to
counteract the drag.  The mathematical relation is force = dp/dt,
momentum transfer rate.  So for a given kayak velocity, we need to
have a given momentum transfer rate.

Now, let's look at the water.  Momentum is mass*velocity, so for
a given momentum transfer, we can move either a large mass of water
slowly, or a small mass of water quickly.  Which is better?
Well, let's look at kinetic energy.  Kinetic energy is 1/2 mv^2,
proportional to the square of the velocity.  So if we move a smaller
mass of water more quickly, it will have more kinetic energy than
if we moved a larger mass of water more slowly (but using the same
momentum transfer).  If we want maximum *energy* to go into propelling
the kayak, and not into pushing the water backwards, we must move
as large a mass of water as possible, as slowly as possible.  And
if we do this with the same amount of momentum transfer, we will have
exactly the same thrust.

BTW, this same problem comes up in aircraft propulsion - it's much
more efficient to move larger quantities of air more slowly than
small amounts of air very quickly.  That is why modern fanjet engines
are so large in diameter - most of the thrust is "bypass" thrust
generated by the very large fans.

> You want to accelerate the mass of the water exactly aft so you get forward 
> thrust, accelerating the mass of the water in any other direction (as in 
> turbulence) results in wasted effort.  The cleanest way to accelerate the 
> mass of water mostly aft is with the least amount of turbulence, this is 
> done with a high aspect ratio surface with a foil shaped cross section. 
>  This is a FACT of fluid mechanics, if you do not understand this, nor 
> simply can not accept it as a fact, than there is nothing else I can do for 
> you.

This "FACT" is simply not true.  And you need to give some
support for your assertion beyond just saying it is a "FACT".

> > Is it really? Please re read it. Any force you apply parallel to the
> > motion of the boat will be useful for moving the boat in that
> > direction. Are you suggesting that forces don't create reactions in
> > the direction they are applied?
>
> The fact that a propeller moves perpendicular to the line of travel to make 
> forward thrust demonstrates your statement is false. 

A propeller moves perpendicular to the line of travel, but applies a force
parallel to the direction of travel.  Nick's statement is true - he
said force applied parallel, not motion parallel.

> If you can increase the amount
> > of water you move without increasing the velocity at which you move
> > it, you will be more efficient.
> 
> False, it is unrelated.  If this were true why not use giant paddle blades? 
>  You would increase the amount of water you push back at the same velocity, 
> but YOU WILL NOT INCREASE EFFECENTCY.  Efficiency is a measure of power 
> consumption compared to useful work done.  Power is a work RATE, i.e. it is 
> time related, units are foot-pounds per minute, velocity is measured as 
> feet per minute.  They are not related, and for a kayak the only thing that 
> is useful is to compare the amount of power it takes to move the same 
> kayak, at the same speed, in the same conditions.  Paddling fast or slow is 
> not by itself a measure of power consumed.

Again, see above.  It is entirely related; and giant paddle blades would be
very efficient if you could use them practically.


> > >>  As long as you move the paddle parallel to the direction of motion
> > >>  desired all the force applied will go directly to propelling the
> > >>  boat.
> > >
> > >This is totally false and again based on uninformed intuitive ideas.
> >
> > Is it really? Please re read it. Any force you apply parallel to the
> > motion of the boat will be useful for moving the boat in that
> > direction. Are you suggesting that forces don't create reactions in
> > the direction they are applied?
> 
> My statement is correct, you have not thought this through.  Just because 
> you pull a paddle strait back does not mean your effort "will go directly 
> to propelling the boat".  You will push water in every direction (including 
> backwards), but you also get turbulence. Turbulence heats the water and 
> pushes it in directions not useful for forward movement, using up power and 
> therefore it is wasted effort, i.e. poor efficiency.

He didn't say his "effort" will go into propelling the boat; he said
the force applied.  And this is true; Newton's Third Law is not
repealed for fluid mechanics.  But as discussed above, the *power*
applied will not all go into propelling the boat; some of it will go
into propelling the water.  Again, be careful not to confuse momentum
and energy here - you must have an equal amount of momentum propelling
the water and the kayak by the Third Law, but you want maximum *power*
(energy/time) going into boat propulsion, not water propulsion.

Turbulence, etc. is all part of the kinetic energy of the water.  
All that factors into the amount of slippage.


> You want to accelerate the mass of the water exactly aft so you get forward 
> thrust, accelerating the mass of the water in any other direction (as in 
> turbulence) results in wasted effort.  The cleanest way to accelerate the 
> mass of water mostly aft is with the least amount of turbulence, this is 
> done with a high aspect ratio surface with a foil shaped cross section. 
>  This is a FACT of fluid mechanics, if you do not understand this, nor 
> simply can not accept it as a fact, than there is nothing else I can do for 
> you.

You're confusing airplane & glider wings (and propellers) with
paddles.  The FACT of fluid mechanics is that a high aspect ratio wing
on an airplane gives you is a maximum lift/drag ratio.  This is
important for airplanes because the lift counteracts gravity to allow
it to fly, while the drag must be counteracted with engine thrust.
And propellers give maximum thrust for minimum rotational drag with a
high aspect ratio.  But it's very unclear to me that a high lift/drag
ratio is important in a paddle - please demonstrate why.  

> > Once the fluid is set in motion it makes absolutely no difference
> > what it does.  The momentum has been applied and has been conserved
> > by the resulting reaction of the boat. How that momentum dissipates
> > itself in the water is irrelevant.
> 
> THIS IS LUDICRUS!!!  Any fluid that is not moving aft, is wasted effort, 
> F=Ma.  If it is does not accelerate backwards, it is not useful for moving 
> you forward.  All of the power it takes to move the water in any direction 
> beside strait back is wasted, and it comes only from your efforts, wasted 
> effort.  The only momentum that is going into your boat, is equal to the 
> amount of momentum of the water going back!  Vortexes, turbulence, lateral 
> water movement is LOST POWER.

You're confusing momentum and energy.  Nick is right; how the momentum
dissipates itself is unimportant.  What is important is how much power
(energy rate) goes into moving the water vs. moving the boat.  You
need a given momentum transfer rate to counteract drag, and what you
need to do for maximum efficiency is move the water as little as
possible to create that momentum - which means moving as large a mass
of water as possible.

> Realize that the idea of the "thrust" face of the paddle is also 
> inaccurate, on a well shaped blade 75 percent (or more) of the thrust comes 
> from the low pressure side, the face opposite the "thrust" face.  This is a 
> fact of fluid mechanics, do not argue with it.  

References for this "fact" of fluid mechanics?  Where is there a
technical discussion of *paddle* thrust that we can find this
demonstrated for typical paddle usage?

I think you're confusing paddles with propellers & wings again.

I really love all these assertions followed by "do not argue".


> > However:
> >   - Everything else being equal the paddle with the largest blade area
> > will be the most efficient.
> 
> WRONG!  size is not related to efficiency.

Yes it is, everything else being equal, because a larger paddle will
move a larger amount of water, more slowly.  The same momentum transfer
will result in a higher proportion of energy being applied to the kayak 
(counteracting drag) and a lower proportion to the water.  Again, this
is because momentum is proportional to velocity, and kinetic energy
to velocity squared, so for the mimimum water kinetic energy, you need
mimimum velocity.  Efficiency is all about converting the power applied 
into thrust, not kinetic energy of the water.

Larger blades are more efficient.

--------------------

That doesn't make them easier to use, however.  Personally the paddle
I most enjoy using is a Betsy Bay greenland-style paddle.  I just like
the feel of it, and I find it more fun to roll with.





***************************************************************************
PaddleWise Paddling Mailing List - Any opinions or suggestions expressed
here are solely those of the writer(s). You must assume the entire
responsibility for reliance upon them. All postings copyright the author.
Submissions:     PaddleWise_at_PaddleWise.net
Subscriptions:   PaddleWise-request_at_PaddleWise.net
Website:         http://www.paddlewise.net/
***************************************************************************