Re: [Paddlewise] The impact loading of tow lines - corrected version (long)

Michael Daly wrote:
> 
>The period of undamped vibration of this bungie will be (ref 2)
> 
>         T = 2*pi sqrt( M/k) = 6.28 sqrt ( 300 * 29 / 33.3) = 100 seconds.
> 
> This tells me that the system will not be too jerky - that is it won't tend to
> loosen and tighten do to the stretchyness of the bungie.  This is good.
> 

Goofed again (I've got to stop posting late at night)!

The equation wants Mass and I used weight! So:


  T = 6.28 sqrt( 300*29/( 33.3 * 386.4) ) = 5.2 seconds.

This is not as good.  You see, the paddler will be pumping energy into the 
system in an on-off pattern - right paddle stroke, nothing, left paddle stroke,
nothing, right... and so on.  Like a kid pumping a swing at a park, each time
the energy makes the swing go higher.  If we pump energy into the bungie at
regular intervals, the bungie stretches will get bigger and bigger.  The key
is how close in time the paddle strokes are to the period of the system.
If we assume one stroke per second, every fifth stroke will match the resonance
of the bungie system.  On the other hand, every fifth stroke means we're dealing 
with a harmonic and that won't be as bad.  The most important factor is that the
system isn't a free vibrating, undamped system, but a damped system, where the 
water will absorb the "jerky" energy.  Is this still a problem?

Are you still with me?

At this point I can only say it's time to stop with theory and get to testing.
Use the method described in the long post and get an estimate of the length 
of bungie you need.  Put together your tow rig of choice and test it.

1)  Test it by paddling to speed and then having the tow line stop you.
    Use your imagination - I can think of a couple of ways to do this.
    Find a spring scale with sufficient capacity to measure the force.
    You'll need a buddy to watch the scale.

2)  Tow a friend and see if the bungie jerks or rebounds too much under
    steady towing conditions.

If there's too much force or too much bounce, try lengthening the bungie
(assuming you won't buy a different diameter).  Don't be surprised if
the results differ from the calculations by as much as a factor of two!
That's why engineers use safety factors.

Mike

PS - for a discussion on safety factors, see "Two Moment Structural Safety
Analysis" by Carl Turkstra and Michael Daly, Canadian Journal of Civil 
Engineering, Vol 5, No 3 1978.

PPS just kidding.  But the paper does exist.
***************************************************************************
PaddleWise Paddling Mailing List - All postings copyright the author and not
to be reproduced outside PaddleWise without author's permission
Submissions:     paddlewise_at_lists.intelenet.net
Subscriptions:   paddlewise-request_at_lists.intelenet.net
Website:         http://www.paddlewise.net/
***************************************************************************