Tall Compression Towers

Introduction

When it comes to easy access to the near regions of space, nothing could be conceptually easier than building a very tall tower. Of course, the tower can only get you above the atmosphere. Climbing to the top provides only a tiny portion of the total energy needed to travel in space. Still, there could be some useful applications. Getting above the bulk of the atmosphere does reduce the total velocity change needed to reach orbit by reducing or eliminating atmospheric drag (see, for example Landis, 2003). As discussed elsewhere one the website, vertical accelerators can be used for deep space applications (geosynchronous or beyond). One novel proposal combines a rotating tether with a tall tower to launch payloads (www.fisherspacesystems.com). A tower into the jet-stream might be a great place to put a windmill. And then there's all the conventional uses of towers such as transmitting and observation.

We'll start by acknowledging that in all likelihood, extreme towers are not going to be cost effective for any application. But I think it will be a fascinating project to see if one can be designed that meets the most basic criteria for strength and stability with a reasonable total mass.

There are a number of speculative papers that start to address the physical possibility of extreme tall towers. For our purposes, "extreme" means getting above a major part of the atmosphere, say starting at 10 km. Alexander Bolonkin has written about conventional compression towers, gas-filled towers, and structures based on electrostatic repulsion. These papers focus on the compression strength aspect and gloss over global stability and wind issues. Finally, there are a whole host of what I call kinematic structures. These use the momentum of a moving mass stream to keep a structure in tension. I'd like to study kinematic structures elsewhere on the site in the future.

The Alna Space Program is wary of assuming an active control system can be used to manage structural buckling. In tower discussions, one sometimes hears buckling dismissed by saying there will be some active system that keeps the tower perfectly aligned. While an active system can certainly balance a broomstick or a structure with a finite number of degrees-of-freedom, it is hard to imagine how it would work in a continuously flexible tower. In addition, the restoration forces involved for a structure with a mass of a few million kilograms would be huge. Therefore, we will demand that our tower have natural stability. I'm sure that active controls will be necessary to damp vibrations, and possibly improve alignment, but a control system should not be required to simply stand up.

We will also start the studies with free-standing towers only. Intuitively, it may be hard to scale guy-wire supported structures to heights of 10-100 km. This is also a limitation in what can be done easily with analysis. I'd like to keep the analysis linear, but extremely long guy-wires will have a great deal of sag and therefore a nonlinear force-deflection response. Guy-wires to help resist wind loads are more promising than wires to provide stability. Finally, we'll limit the studies to conventional structures and materials. I don't dismiss pneumatic structures, but let's try to obvious first

The blog page for leaving comments or questions on this work is here.

Some interesting truss towers

Warsaw radio mast. Second tallest structure ever built at 646 m. Collapsed in 1991 due an error while exchanging guy wires. Wikipedia
Shukhov Towers on the Oka River - hyperboloid electricity pylons. 68 m. Wikimedia
Interior of Shabolovka tower in Moscow, 160m. Wikipedia

Top

Some links on Tall Towers

Top

Studies

Notes on support cables for exteme towers

First published; 5/26/2012

In the study "Mass of Extremely Tall Truss Towers", I made the statement that support cables (or "guys") might not be suitable for extremely tall towers. At the time, I was concerned about the degree of sag that would be inevitable with very long guys, and the force-displacement nonlinearity the sag would introduce. This study looks at the classical equations for a cantenary in order to determine the shape of the guy. The shape equations can be used to find a tension force distribution, which in turn can be used to compute an elastic elongation. The elastic elongation of geometric straightening action are combined into a single force-displacement relationship. Finally, using some non-dimensional parameters, we can compute the highest guy cable possible with a particular combination of material strength, stiffness, and density (assuming a 45 deg path to the ground). For a high-strength sythetic material such as Kevlar, it appears that it would be feasible to use guys up to 6 km in height. Further study would be needed to determine if using a guy would reduce the mass of an extreme tower, where the tower height may be in the range of 40 k

The CDF document contains a couple of interactive widgets that will be static in the PDF version


Computable Document Format PDF Version

Mass of Extremely Tall Truss Towers

First published; 5/7/2012

This study makes use of the ttas package (Truss Tower Analysis System) to perform a number of parametric analyses for towers in the range of 1-40 km in height. The automated sizing/optimization functions are used to design towers that are naturally stable and can resist hurricane force winds. The study looks at three and six leg trusses. Various geometric parameters are considered, such as slenderness ratio, taper ratio, and the height of the repeating truss units. Analyses are performed for several engineering materials. One of the goals of the studies was to demonstrate the potential performance of the tower using current materials with realistic properties. One finding is that tower mass as a function of height forms a straight line when plotted in log-log space. Another interesting finding is that over the range considered, the tower mass is a weak function of the mass being supported at the top.

In the study, the truss elements are treated as cylindrical tubes. I call this a "first-order" truss. For a structure of this scale, it is likely that the major truss elements would also be truss structures. There may be further levels of trusses, as in a fractal regression. Most likely, higher order trusses would result in a significantly lighter structure, if for no other reason than a reduction in wind area. Analysis of multi-level trusses is a future goal.

The study motivated a number of changes in the ttas package. A new version of the package is being released with the study. The calculation notebook can reproduce all of the figures and tables presented in the study. The 3-D figures in the study are interactive in the CDF version, so I recommend downloading the Wolfram reader. The calculation notebook requires a full version of Mathematica. The analysis code is a Mathematica package file. It will only run in Mathematica, but the file is in plain text if you just want to review the methods.


Computable Document Format PDF Version HTML Version Calculation Notebook Analysis code

Truss Tower Analysis System

First published; 2/15/2012. Last update: 5/1/2012. User's Guide updated 5/1/2012

These files present the analysis functions that can be used to start designing a tower. The Truss Tower Analysis System (TTAS) is a finite element based analysis which also includes rapid modeling tools and a first-order optimization process. The finite element system only includes 1-dimension bar elements which can be used to model a truss structures. A linear static analysis is performed to determine nodal displacements and bar element loads. An eigenvalue analysis can also be performed to determine the factor-of-safety for buckling and the buckling mode shape. The analysis automatically incorporates gravity loads and a wind load model. The wind loads address the change of atmospheric density with height

The modeling tools allow the user to set up the topology of a basic unit which is repeated as necessary to build up the tower. The tower radius can be a user defined function with height. The optimization works by finding the minimum weight truss tube that meets strength, wall stability, and Euler buckling stability constraints. There is an overall loop so that after the tubes are sized, the global finite element analysis is repeated to update the tube loads and the tube optimization is repeated. The loop continues until the relative tubes dimensions changes are less than a specified tolerance. There is no global geometric optimization (the nodes do not move). The optimization does not guarantee that global buckling will be satisfied. The user must change the tower geometric, for example by increasing the base radius, to satisfy global buckling.

The notebook and corresponding CDF file are the user's guide for the analysis system. The guide includes examples of 10 km tall towers using a conventional, intermediate strength composite material. The examples are meant to demonstrate the system and show a preliminary feasibility of an extremely tall tower. Using a material with specific strength of 2.25E5 (m/sec)^2, and supporting a 10,000 kg mass at the top, the total tower mass was 6.4E8 kg. For comparison, that's about 1.4 times the mass of one of the World Trade Center Towers. The design withstands a hurricane force wind (90 m/sec) over applied to the entire height. More complete studies and tradeoffs using the system are planned. The package file is also linked. The package file contains the actual Mathematica programming, including a complete finite element system

A current limitation of the system is that the truss modeling tools only work one-level deep. For a structure of this scale, instead of solid tubes, the elements of the overall truss should also be trusses. The subdivision could continue more levels down in a fractal sense. Tools for performing this multilevel analysis are in progress.

PDF and HTML versions of this study have not been provided because the images in the notebook export to a very large (600MB) PDF. Besides, if you don't have Mathematica or at least the free CDF reader, the files will not be of much use.

The 5/1/2012 release of the package and guide are major updates from the original 2/15/2012 version. There are many new functions, a whole new tower data object system, and some error corrections.


Computable Document Format Notebook Version Package

Top