6. Vertical Equilibrium

	Rhino command name RV_tna_vertical	source file RV_tna_vertical.py

In RhinoVAULT, the ThrustDiagram representing the thrust network, is an instance of the FormDiagram, with the only difference being the $z$ coordinates. A ThrustDiagram is simply an alternate visualisation of the FormDiagram with updated $z$ coordinates. When a FormDiagram is successfully created, the ThrustDiagram is automatically created.

A ThrustDiagram is represented by the mesh datastructure.

---

Algorithm Parameter

Target Height

Once the FormDiagram and ForceDiagram have been created and horizontal equilibrium has been found, the distribution of horizontal forces in the system is fixed. The actual magnitude of the horizontal forces depends on a scale factor and will determine the target height of the final ThrustDiagram. A higher scale factor results in higher horizontal forces and therefore a shallower shell. Vice versa, a lower scale factor results in lower horizontal thrust and thus a deeper solution.

The meaning of the scale factor and the magnitude of horizontal forces is related to the magnitude of the loads, which in turn are related to the self-weight of the resulting three-dimensional geometry. Rather than asking you to "guess" the scale factor to get the three-dimensional shape you want, RhinoVAULT will determine the scale for you based on the desired height of the final solution. The default value for the target height is 25% of the length of the diagonal of the bounding box of the FormDiagram (essentially of the bounding box of the footprint of your shell). This value tends to produce well-proportioned geometries.

Animation showing the varying geometry of the ThrustDiagram with different target heights.