Re: [Paddlewise] Paddling efficency

Michael Edelman wrote:

> David Carlson wrote:
>
>> If the boats have the same drag and are going the same speed, then
>> the power
>> output from the paddles is the same.
>
> Absolutely.
>
>> If the stroke lengths of each paddler are
>> the same, then obviously the paddle/paddling technique with the
>> higher cadence
>> is only half as efficient as the slower cadence.  Why?  Because
>> force generated
>> in the direction of boat motion must be the same for each paddler,
>> and power is
>> force times velocity, and the paddle with the higher cadence must
>> moving with
>> twice the velocity.
>
> That's wrong. You're taking paddling speed as the absolute measure of
> power input- but that's only part of the equation. The other half is
> effort. Without it, we have no idea what the energy exerted by the
> paddlers is.

My discussion was considering only  how much work is being done by the
paddle vs. how much work goes to propelling the boat.  The paddle puts
out exactly as much power as was put into it. There is no significant
friction or other energy dissipating mechanism internal to the paddle.
So the difference between effort (paddler output) and paddle output is
nil.  The only effort I am neglecting to consider is physiological, and
internal to the paddler.

>
>
> Say we have 2 kayaks moving through the water with a kinetic energy of
> 50 watts measured on our kayak-o-meter. We have paddler A doing 50
> strokes/minute and paddler B doing 100. Is A twice as efficient as B?
>
> Answer: We can't say. We don't know how much effort either paddler is
> putting out.
>
> To complete the equation, we need to know that paddler A is working
> against a resistance of (say) 5 lbs and B against a resistance of 3
> lbs, or whatever it turns out to be. Then we can compute the work done
> by each paddler, and compare it to the energy of the kayak.

Remember that we said that the boats had the same resistance and same
speed.  Hence the resistance force on the boats are the same and the
power is the same (your 50 watts).  I said that under these conditions
and if the stroke length was the same, then the paddle doing 50
strokes/minute is more efficient.  If the stroke length of the paddle
doing 100 strokes/min is half that of the paddle doing 50 strokes/min,
then the efficiencies are the same.  The effort the paddler is putting
out is strokes/minute times feet/stroke times force on the paddle.

>
>
>
>>  Thus, the power input to the faster paddle is more than
>> that to the slower paddle.
>
> Incorrect, for reasons above.

No, please read what I wrote very carefully.

>
>
>> If you're paddling boats with the same resistance the same speed,
>> then the
>> force on the paddles must be the same ( ignoring rest time between
>> strokes).
>
> This assumes that force input to a paddle equates with thrust, which
> has the implicit assumption that paddle design is irrelevant, and that
> all paddles and paddlers are exactly as efficient as each other. This
> is a very large assumption, and not one I think can be justified.

There is no assumption here.  The only forces on the boat are resistance
and, by means of the paddler, the force of the water on the paddle.  For
a boat traveling at constant speed the component of the force of the
water on the paddle that is parallel to the direction of travel of the
boat must be exactly equal to the force of resistance on the boat.  You
can draw a free body diagram of the boat/paddler/paddle system to
visualize this.
This does not imply that paddle design is irrelevant.  Some paddles will
take more velocity to generate the required force.  Power=Force*Paddle
Velocity=Force*strokes/min.*feet/stroke.  The constant is Force in the
direction of boat travel.

>
>
>> So the conclusion that the larger paddle requires significantly more
>> more
>> driving force is incorrect.
>
> Except that was never claimed.
>
> What I said was this:
>
>> > If I'm using a Greenland paddle at 120 strokes and you're using a wider
>> > paddle at 60 and we're keeping pace, and all other factors are equal,
>> > then I'm probably more efficient.
>>

I quote from your post: "While larger blades
can generate more power, that doesn't mean they're more efficient. They
also require more driving force, and the payback is not necessarily
greater per unit of input. "

> In that posts, and the preceding ones, I stressed that I was talking
> about the paddler, and not the paddle. I never claimed that skinny
> paddles are more efficient than wider ones; they may well be less
> efficient, for all I know. This seems to have escaped a number of
> posters who keep claiming I'm wrong when I say narrow paddles are more
> efficient!

Read from your last sentence: "... when I say narrow paddles are more
efficient!"  Are you talking about the paddler or the paddle?

It is entirely possible that for some people, paddling at a higher
cadence is easier.  If that is the thrust of what you and many others
are saying, then I agree.  I only meant to point out that in our case of
the 50 stroke/minute vs 100 stroke/minute paddles that, if the stroke
lengths are the same and the boats are going the same speed and have the
same resistance, the paddler doing 100 strokes/min. has a lot of
inefficiency to make up for.

>
>
> Quoting myself once more:
>
>> Generally, with humans, as you increase power
>> > output you get diminishing returns in terms of effort per energy output.
>>
> And that was my central point.

OK.  Just remember that in the example of my previous paragraph, the
paddler going 100 strokes/min is putting out twice the power as the one
doing 50 strokes/min.  Per your quote, that means that the paddler going
100 strokes/min must be putting out more than twice the effort of the
paddler with the slower cadence. Obviously, the example of my previous
paragraph is implausible.  The only explanation for the faster paddlers
efficiency is that his strokes are less than half as long!

Regards,

Dave Carlson

>

>

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