Cantilever Truss Simulation

A radial siphon needs something like a cantilever truss. And this has never been modelled. It would have to be a dynamic model, just like the siphon.

It seemed plausible to simply re-use the ties and masses in a siphon simulation to construct a cantilever truss, with the masses as nodes, and the ties as the bracing between the nodes. This cantilever would then be subjected to gravitational and centrifugal and coriolis forces in exactly the same way as the siphon - except that the cantilever truss would act to counteract coriolis forces.

In the following preliminary model, a terrestrial cantilever was constructed using node masses with rigid ties (that could sustain compression as well as tension). The cantilevers ties and struts were not initialised using any prior analysis, and the structure was allowed to fall and rise.

One problem with this simulation is that when attempts are made to increase truss rigidity by increasing the tie spring constant k, the resulting forces exerted by the ties are greater, and the node mass accelerations are higher, and so the time step used has to be reduced. But, at some point, the whole cantilever appears to fly apart. Problem not investigated.

To stop the animation, move the cursor over the applet. To start or restart, move it off the applet.

A cantilever truss used in an radial siphon would (or should) have all its ties in tension, and have no need for compressive strength.

There would be a problem of initialising the node locations and tie tensions prior to starting the siphon. One option would be to do this analytically, as is at present done with the siphon. Another option might be to begin with a non-rotating massless Earth, and slowly add mass and angular velocity until the correct values had been reached. Hopefully, this would result in an unstressed cantilever gradually becoming stressed, and adopting an equilibrium position.

A further problem would be that of 'holding' a rising siphon against the truss. This might simply entail using a string of truss nodes as a pathway along which the siphon is constrained to move. So, at any point, the direction of motion of siphon masses would be towards the next highest node in the cantilever node pathway. If there are sufficient nodes, this should make for a path without significant sudden changes of direction.

A simulation using a cantilever truss would contain many more masses than the siphons modelled so far. There could easily be 3 or 4 times as many masses. And the simulation would run slower.

The expected behaviour of a cantilever truss siphon simulation would be for the cantilever truss to bend back from the direction of rotation along its length in a manner not dissimilar to the terrestrial cantilever truss modelled here - since both are subject to an evenly distributed load along their length. And since this would result in maximum bending at the base, it might help to widen the base, to form something not unlike the Eiffel tower.