Re: [Paddlewise] Impact loading of tow lines.

Michael Daly wrote:

> Some time ago, Julio and others discussed the use of shock absorbing
> materials in towing lines as a means of reducing the impact load on
> the person (or kayak) doing the towing.  Julio tried to calculate the
> forces, but got bogged down by not knowing the formulae to describe
> the physics of the situation.  I wanted to follow up on this, but
> haven’t had the time until now.
> 
> The problem is that if a towed kayak is impeded in its motion, the
> sudden rise in tension in the tow line could injure a paddler if
> attached to the tower’s waist.  Alternatively, the force could damage
> the kayak if the line is fixed to it.  In order to analyse this, I have
> made a few assumptions
> 
> 1. We will look at a worst case scenario - a towed kayak comes to a
>    complete stop while the towing kayak continues.
> 2. All energy is absorbed by a bungie in the tow line, none by the tow
>    line itself, the kayak etc.
> 3. The bungie is a nice, linear-elastic material

[snip of physics leading to the conclusion]

> Let's assume a paddler weighing 175lb, in a kayak that is 55 lbs carrying
> 70 lbs of gear for a total weight of 300 lb.  We’ll also assume a velocity
> of 3 miles per hour.  Plugging the results into our equation (with conversions
> to get everything in inches, pounds and seconds)
> 
> 3 mph =  3 (5280 * 12)/3600 =  52.8 inches per second.
> 
> G = 32.2 ft/sec**2 = 32.2 * 12 = 386.4 in/sec**2
> 
> F =  52.8 sqrt[ (1.6 * 300)/ (386.4) ] = 58.8 lb.
> 
> This sounds good; 58.8 lb is within the range that some folks considered
> reasonable when it was discussed a while ago.  And that’s a worst case.
> However, this requires the bungie to stretch under this load:
> 
> X = F/k = 58.8/1.6 = 36.8 inches!
> 
> Note that this is the _change_ in length.   I’ve noticed that the bungies
> are "comfortable" stretching to twice their length, so this means that the
> bungie has to start with a free length (exclusive of knots) of around a
> yard!   I’ve seen folks using bungies that are only 8 to ten inches long.
> They’d probably reach their limit of stretch before fully absorbing the
> load and then the force would shoot up to a higher level with a bit of
> a shock.

Wow.  Thank you Michael for a nice piece of work.  Really appreciate the
effort, and the talent, which went into it.  

My small addendum is that because of the assumption that the towed kayak is
stopped dead in its tracks, the figures you got are somewhat high relative to
the peak forces generated in a "realistic" case.  The upshot is that I think
your analysis shows the maximum force the tower will actually experience is a
lot less than the 58.8 lbs quoted above.

And, of course, this means the 1/4-inch bungie need not be three feet long,
though as a safety measure, perhaps this would be a good place to start.

Re:  doubling or tripling the 1/4 inch bungie:  perhaps a single 1/4 inch
bungie is safer, in that the peak force will be reached less rapidly (and with
more elongation of the bungie), allowing the paddlers to adjust to the sudden
jerks.  What do you think?

-- 
Dave Kruger
Astoria, OR


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