Well, that took an embarrassingly long time. For background, I started off trying to determine the limits for building compression towers high into the atmosphere. The ground rules were that the tower had to be stable with only passive structure, withstand realistic wind loads, and be built using conventional, current materials. With this goal in mind, I developed a Mathematica package called ttas.m (Truss Tower Analysis System) that would automatically generate a finite element model, run an analysis, and iteratively size the truss elements to satisfy local failure criteria (Euler buckling of the element, local wall buckling, and strength).
I wanted to actually use ttas package to do parametric studies of towers up to about 50 km in height. I quickly discovered a lot of inadequacies in the approach. One big problem was that in my first few examples global buckling was easily satisfied, so I assumed that with minor tweaks to the geometry a user could set a reasonable slenderness ratio and buckling would not be an issue. Not true. I eventually designed a system that simultaneously satisfies the global buckling criterion, and local strength criteria. My initial set of parametric studies is up on the web site now. Pretty satisfying that I got this far, and the results are definitely interesting. In the process, the analysis package got a major upgrade, and the new version has been posted, along with new user notes.See the main web site page on tall towers for links.
The results can pretty much be summarized with the log-log plot of mass versus height for various materials, shown below. We have assumed a 70 m/sec wind over the entire height of the tower, where air density is a function of height. We also assumed a 10^5 kg mass at the top of the tower (although another result is that total mass is a weak function of the top mass). The tower mass forms a straight line in log-log space, and the curves for different materials are nearly parallel. A typical model is also shown with the truss tubes drawn to scale.
I don’t know where I’m going next. In the tower study, it became obvious that I need to look at multi-level trusses (truss elements are made from additional trusses), but the amount of work required may not be justified. I feel like I left sub-orbital refueling incomplete, and would like to get back to that subject. I’ll take a few days off and see what moves me. The joys of hobby engineering.