Re: [Paddlewise] Bad Forward Sweep

From: "PeterO" <rebyl_kayak_at_iprimus.com.au>

> Mike said
> > Strictly speaking, the hull can be seen as pivoting around any point.
> > Rotation is rotation and the rotation is the same regardless of
> > inertial reference frame chosen.
> 
> G'Day,
> 
> Mike, You put forward an intriguing proposition and I'll try hard not to
> misinterpret but looking at Matt and John's explanations I don't think they
> are saying the same thing with different frames of reference. Their use of
> phrases such as rotating around various points (John) and "pivot point"
> (Matt) were fairly specific and I think in the context of the discussion
> could be taken as synonymous. Surely also they are both using a common frame
> of reference (latitude and longitude)?

Their frames of reference are implicitly the centers of rotation they discuss,
which are a few centimeters apart.  One is the same as the other with a bit
of translation involved.

> If the frame of
> reference were latitude and longitude in both cases then the physical
> ramifications of each interpretation would be quite different.

Long and lat are not the reference frame, so that's why you're likely
confused.  While the two approaches may result in slightly different
answers for some things, the answers are equivalent.  For example,
if they both applied numbers to calculations, they might discover that
they came up with the same forces but different moments (torques).  
However, the difference in the moments would be the relevant force
times the distance between the two centers they chose.  

If they tried to use the answers to see how the kayak would respond 
(i.e F=ma or the rotational equivalent M = I x alpha where I is the 
moment of mass [equiv to mass but for rotation] and alpha is angular 
acceleration), they'd get the same answer assuming they correctly 
calculated the effects of where the center of gravity is relative to 
their chosen center of rotation (i.e. recalculate "I" about the 
center of rotation and not about the center of gravity). If they 
chose the center of gravity, such effects disappear, making the 
calculations simpler - hence why naval architects often use CG.

> I found Matt's explanation of center of lateral resistance (the pivot point)
> very clear.
> John's points about effective arm extension differences in moving vs
> stationary boats were compelling.

They are.  I'm not saying they are wrong - in fact they are just looking
at the same thing from two perspectives.  I'm just being a bug and trying
to emphasize that the chosen center of rotation is somewhat arbitrary and
that one shouldn't try to be definitive about which point is relevant.

Mike

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