At work, use computational fluid dynamics (CFD) to simulate air flow over aircraft, ships, things carried by aircraft, etc. I also get the chance to do a little bit of development work. This past year, some people have been asking for the capability to simulate *catenaries* — in other words, cables and systems of cables used to connect objects together in dynamic systems. These are used for all sorts of purposes, including towing objects behind boats, connecting a parachute to a jumper, lifting objects with helicopters, and (the thing that gets me excited) flying kites!

I always jump at the chance to do anything related to my hobbies for work, so I jumped at the chance to work on this. Without getting too much into technical details, here is the basic approach used to simulate a catenary. Each cable is divided into an equal number of segments. The mass of each segment is assumed to be concentrated in discrete points at the endpoints of each. Tension, gravity, and air flow apply forces to each of these points. Applying Newton’s laws of motion to each point produces a large nonlinear system of equations, which, when solved, gives the shape, speed, and tension in the catenary. The tension at the end of the cables then produces an equal and opposite force to whatever they are attached to, like a kite. The overall fluid properties (a.k.a. *flowfield*) and the motion of bodies other than the catenaries in the simulation are handled by the computation fluid dynamics code.

To test it out, I modeled my Barn Door kite and set up two catenaries: one for the bridle + kite line, and the other to model a tail. For now, the kite is assumed to be rigid in the simulation, and the bowing of the horizontal spar is built into the shape. The line is 200 feet long, and I made the bridle as close to the real 5-point setup as possible, with the mass and properties of the bridle and line intended to be similar to 200-lb-rated dacron line. In the simulation, the kite is flown in a steady, uniform, 7 mph breeze. I had to estimate the center of mass of the kite. At first, my estimate was too far back, resulting in the kite spiraling out of control:

This was a little surprising to me, because I was under the impression that an aft CG is always good for a kite. I guess there is actually a limit to that. The next test moved the CG forward, closer to the horizontal spar. That fixed the stability problems, resulting in a nice smooth simulated flight:

Encouraged by that success, the next step was to simulate KAP. An additional point mass of 14 oz was added 50 feet down the line to model a KAP rig. The results are kind of interesting. The shape of the line with the point mass looks right based on my experience with real KAP. The kite is also a bit less stable with the extra weight on the line, which is also consistent with my experience. The high-frequency “wobbling” motion of the kite happens in real life too, at least with the Barn Door design. My other kite, the Mini Dopero, doesn’t do that, so it might be interesting to try that kite in the sim too.

So what’s the use of this simulation? I’m not totally sure. Qualitatively speaking, it seems to produce results that are consistent with real life. CFD is computationally expensive, though; each of these simulations took a dozen or two hours on a couple hundred cores of a supercomputer. For now, they are somewhat limited in that the kite is assumed to be rigid, but some flexibility could be included in the sim using this CFD code (maybe not full sail billowing, but at least spar bending). Turbulence and gusts could also be included. For someone with the resources available, this type of simulation could maybe be used to study how sail shapes and mass properties affect kite stability. For now though, it was mainly for fun. I hope you enjoyed these videos!