Tensile Shock Waves in Tethers

Years of flying small kites in hurricane-force winds on the US NW Coast had many exciting lessons for what Jet Stream wind is like. A particular incident involved a 1m2 parafoil lifter on ~200kg rated (~400kg breaking strength) UHMWPE line in ~30msec wind. A sudden wind burst sent an apparent shock wave down the line that smashed into the anchor-point, where the line failed instantly. A loose end was to come with the right search term- “Tensile Shock Wave”, to find relevant science. This 1969 paper does the job, just keep in mind any polymer supports elastic waves, not just natural rubber. The sonic-relativity physics is cool, that if Mach ramps up suddenly along a kite line, a shock wave forms, and this sonic boom can destroy tethers. Such a shock wave may easily form on a suddenly snubbed tether by a massive high-velocity kiteplane.

Production of Tensile Shock Waves in Stretched Natural Rubber

Nature volume 224 , page1301(1969)


IT may be shown theoretically that when plane mechanical pulses of finite amplitude travel in non-dispersive media, the velocity of propagation in space is given by c + V where c = ( S / ρ )1/2, S being the tangent modulus of the material and ρ its density, and V is the particle velocity associated with the pulse. If S increases with increasing amplitude of deformation, the head of the pulse will become steeper as it travels through the medium and it will eventually become a shock front, the gradient of which is limited by dissipative processes, such as internal friction and thermal conductivity. Such compressive shock waves are well known in fluids and in recent years similar shock waves have been produced and studied in blocks of solids1.


==== original Old Forum message =====

"dave santos santos137@yahoo.com

Feb 7, 2013 at 1:42 PM

Our advanced low-stretch tethers seem to have a unique vulnerability to shock-wave formation. The conjecture is- if the line is tensioned near its max working load, and there are high-energy harmonics on the line, rogue shock waves can form to crash into kite and anchor-nodes, and cause a line to fail well below its measurable static load. An elastic line absorbs shock peaks before they do damage.

I lost a small (1m2) single-line parafoil last year in a US NW Coast gale to a shock wave on the line (its still a hundred feet high in a tree). The kite was going nuts and the 400lb rated UHMWPE line, in good condition, was “jangling” wildly, but a padded belt around my waist made the 50lb estimated gust surge pulls quite manageable. A specially powerful gust hit the kite, and the jumpy line suddenly parted right at the hand winder knot on the belt.

Its well known that an ordinary knot weakens a line greatly, but there was more going on here, since this line was so over specified. There was no excessive tug before the line parted. It was rather clear the line had not parted by “static force” alone, but a sudden shock effect focused at the anchor-node seemed to be to blame. UHMWPE has a low melting temp, so the failure mode may have been a sudden local heating resulting in the break (rather than a break in progress releasing heat). The knot was a stress-concentrator node itself, and knot failures by shockwaves may be common. A corollary prediction here is that knots in stretchy line have a lesser weakening effect.

Rogue shockwave line failure is predicted to follow a certain classic pattern. The at-risk line is low-stretch, tension is high, and the harmonics on the line are energetic and chaotic enough to combine by chance into rogue peaks exceeding the breaking strength. The longer the line, the more energy it can store harmonically to focus on a node. If the line is being rapidly pumped, complex phase-shifts arise favorable to random shock wave formation. Wind turbulence on the line also destabilizes normal dynamics. Risky nodes are stiff and sharply discontinuous.

There is a luck factor to rogue waves, which can occur even in moderate “improbable” conditions. Shock waves can also hammer at a node, for accumulated damage. The node itself, say a composite airframe, might be directly damaged. Good shock absorption design is possibly essential to future AWES. Fishing poles are a good reference model for harmless shockwave absorption, but high efficiency line pumping is the competing trade.

This is another poorly understood topic in AWES design suitable for careful study…"