Re: [Paddlewise] Impact loading of tow lines.

From: <juliom_at_cisco.com>
Date: Mon, 18 Oct 1999 14:25:18 -0700 (PDT)
> Therefore    F = V sqrt(kM).
> 
Cool formula! Awesome work!  

> Substituting weight for mass   F = V sqrt( k w/g)  where g = acceleration 
> of gravity.
> F =  52.8 sqrt[ (1.6 * 300)/ (386.4) ] = 58.8 lb.

Water tends to be horizontal, though. Or are you referring to the case where
both boats become airborne and during the trip down one of them
gets entagled in a tree?  :-D

The acceleration is the key factor here.  And apparently you used
the acceleration of gravity to find your k's.  

But I digress.  

The maximum acceleration that the human body can
withstand for a very short period of time without suffering injury
is 20 g's.  So it is precisely the acceleration that we should
be concerned about to find out k.  Let us use 

  F = M*a    and your formula   F = V sqrt(kM)

then, equating the forces F=F
  
     M*a = V sqrt (kM)    so   a = V * sqrt(k/M)

Doing some algebra

    k = a^2 * M/V

given that    a < 20 * g for a 70Kg person walking (without a kayak) 
at about 3 knots, which is about 1.5 m/s  we need 
                               
   k < 9.81^2 * 70/1.5    then 

                   k < 4491.2 meter^2/second^3 

There you have it, k for a spring to prevent injury on a towing paddler.


Hey, you guys! wake up! class is over.  :-D
- Julio


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Received on Mon Oct 18 1999 - 14:27:44 PDT

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