[pf] the Physics of darning stressed material, like jeans.

**  I'm wearing the next pair of jeans after the one I describe below (Aug.
'98), but they also have required darning in the seat; I used monofilament
nylon fishing line, which is too slippery for regular darning, but works
fine if you use the catenary method below.

**  I expect to double the normal life of the jeans this way.


>In a message dated 04/08/98 21:45:07 EDT, David M. wrote:
><< My jeans also have holes at the knees etc. and I've finally
> found a way of holding such highly stressed holes together.  I use very
> strong thread, sometimes fishing-line, but the main thing is the thread
> picks up 3 to 5 pieces of cloth (i.e. in-and-outs) 
> on each side of the slit to be darned, before going 
> back over the slit to the other side. Call them wide arcs.
>  I worked it out by thinking about the catenary shape that the top cables
> of a suspension-bridge form, with a large number of pulls all in the same
> direction (downward, for the bridge or a loosely hanging chain).  
> The final result looks quite a lot like Lissajous Figures 
> for a 3-to-1 to 5-to-1 frequency ratio.
>  Sorry about the physics - it's been my life. >>
>
At 05:21 5/08/98 EDT, KaiforChi wrote, in Subject: Re: Repairs--please
explain more about the physics:
>David, I'm interested in the physics! LOL! Could you elaborate a bit more?
>Perhaps an illustration?
>
>Thanks,
>kai
>
** I can't draw a catenary; just hang a necklace loosely between your two
hands

**  This diagram will only work in an equally-spaced font, like Courier.
        You may need to Copy-&-Paste it onto a new word-processor page, 
where you
can choose the font. (I'm doing it with Eudora, set at "Courier New", 9.)

   .--^--.  .--^-.        .--^--.  .--^-.
  /       \/      \      /       \/      \      .--.
 /        /\       \    /        /\       \    /    \
|~~~~~~~~|~~|~~~~~~~|~~|~~~~~~~~|~~|~~~~~~~|~~|~~    |
   (^split^) \       \/        /    \       \/      /
              \      /\       /      \      /\     /
               --.--    --.--         --.--   --.--

**  This is the first half-to-2/3 of all that I do.  One more left-to-right
is usually enough.

**  Each arc: |          |  is supposed* to be a catenary, which spreads 
               \        /   the pull equally among the places where the 
                \      /    force acts, so in this case the thread  
                 --.--      shouldn't pull holes in the cloth.  Note: the 
                            pattern is for strength not looks; the edges 
of the split would have to be held together in the ordinary way.  I make
the arcs about an inch in both directions partly to grab a hold of stronger
material away from where it wore through.
                           (* Mine are very approximate.)

{ More physics: each link of a chain has the earth ("gravity") pulling down
on it with the same force as on each of the other, identical, links.  They
also pull on each other in varying degrees: near the ends the weight of the
middle bunch has to be held up in addition to the force from the neighbour,
while in the middle it's only the neighbour force acting. So the slope is
steeper at the ends. (You can see the effect of the neighbour force if you
remove a link.)}

David.
(David MacClement) davd@ihug.co.nz 
www.geocities.com/Athens/Delphi/3142/Pg1-AD11.html
 or better: http://www.emucities.com.au/member/davd/
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