RE: [Paddlewise] Paddling in Space

At 12:59 AM -0700 7/27/02, Matt Broze wrote:
>
>Nick continued:
>>>>>.Imagine two kayaks paddling side by side at the same speed. Guy A has
>his paddle in the water for 1 second and then out for one second, the
>Guy B is paddling with in the water for 2 seconds and out for 1.
>They both will decelerate similarly between strokes, but Guy B will
>not need to accelerate as much during the time his paddle in the
>water. As a result he won't need to apply as much force and his
>stroke will be more efficient.<<<<<,
>
>I don't think I can agree with that. Given--for the sake of simplicity--that
>each paddler keeps his own paddling force equal throughout their stroking
>time (but not equal between paddlers). They will both need to accelerate up
>to the same speed again after each one second of rest and deceleration, but
>guy B will have twice as long to do it so his rate of acceleration will be
>only half that of guy A's. Guy A will make 6 strokes in 12 seconds while guy
>B will have only taken 4 strokes to work against the kayaks (same) drag over
>the same distance at the same speed. Therefore Guy B will be working against
>the kayaks drag for a total of 8 seconds and have had 4 seconds of rest
>while guy A will only be working against that same drag for 6 seconds of the
>12 and have had 6 seconds of rest between strokes. Guy B only has to
>accelerate back up to speed 4 times and guy A 6 times in the 12 seconds they
>traveled the same distance at the same speed. The questions are who is
>working harder and which strategy is most efficient? I don't know, and
>unfortunately I'm not up to trying to figure out the math right now, Any of
>the mathematically adept out there want to give it a shot?

I did a little analysis in Excel. Bottom line: Guy B (slower 
cadence,longer stroke, same rest) works less. Obviously, the amount 
of effort saved depends on drag. With no drag, Guy B applies 75% of 
the force to maintain the same speed. I haven't worked out the math 
yet, but this results in the same amount of work. As drag increases 
the relative force required by Guy B decreases. As drag increases Guy 
B needs to apply less than 75% of the force while maintaining the 
same cadence. The advantage accumulates slowly, but it is perceptible.

Because Guy B can apply his effort over a longer time he does not 
need to accelerate the kayak to as high a speed to maintain the same 
average speed. Since drag increases with speed he is working on 
moving a boat that has lower average drag. This means less force 
required and less overall effort.

Because the effect is drag dependant (Higher speed -> more efficiency 
due to longer stroke) the effect will be most pronounced at higher 
speeds.

While Guy B does not get as much rest, he is using less effort to 
maintain the same speed, so he does not need as much rest.

I also ran the analysis with Guy B going at the same cadence as Guy A 
(ie a stroke every 2 seconds) but with a shorter coasting time. And 
as expected this saved even more effort than stretching out the 
stroke.

BTW I chose the paddling rates based on being easy to deal with not 
because they were in any way reasonable. A 2 second long stroke is 
probably unreasonable, but it is easy to understand.
-- 
Nick Schade
Guillemot Kayaks
824 Thompson St
Glastonbury, CT 06033
(860) 659-8847
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