Tall Towers

I’ve had a major side diversion into the idea of extreme compression towers. A couple of years ago I wrote some basic Mathematica tools for looking at truss towers using the finite element method combined with some slick automatic modeling functions. For space applications, it is always assumed that compression towers were impractical and the focus has been on tensile structures such as the space elevator. While compression structures are certainly challenging because of stability issues, I had never seen a complete treatment that covered all the major structural requirements. So before creeping old age made me loss the earlier work I spent some time working on the analysis tools. It turned out to be a significant slug of work, at least for a retired guy, and thus the two months since my last post.The main website page for extreme tower work is here.

Of course, a 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.

I’m 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.

So far, only the analysis package and a user’s guide have been written. The guide walks through the design of a 10 km tall tower 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. I need to complete the tools to allow for breaking down the structure into finer level trusses. For now, there is a basic truss structure in which the truss elements are assumed to be cylindrical tubes. The tubes are weight optimized with strength, wall stability, and Euler buckling stability constraints. However, for a structure of this scale, the elements of the main truss structure should also be trusses. And so on as in a fractal geometry. I’m currently working on automatically breaking down the structure to finer level trusses. One motivation is to reduce the area presented to a wind load.

It will also be fun to look at some of the geometric systems that have been devised by civil engineers of earlier times. One promising concept is to use hyperboloid arrangements.

Hyperboloid Pylon Structures. Shukhov Oka Towers. photo by Igor Kazus

 

 

 

2 thoughts on “Tall Towers

  1. I’ve been working on the package used to design and analysis tall towers and discovered a mistake in the optimization algorithm. The analysis results
    where correct, but the truss-rod dimensions above the first repeating unit where not being updated after the first iteration. Thus, the structures where not in any sense “optimized”. The current package corrects this problem. The user guide has been rerun with the new package. The user guide text has not been updated, so the optimization results and the text discussing the results may not always
    match up. The new package includes a lot of new work on beam analysis that will enable multi-level truss structures, but the functions have not yet been made public functions. If you have downloaded the package, please pick up the new version.

  2. Hello Mr. Flanagan

    From what I read It appears we have some common goals. You are concentrating on finding a solution to the compressive stress that a tall tower must support. I am working on minimizing the mass of the trusses by using Lighter-than-Air building blocks (similar to air beams).

    I have pulled down the original website I had due to the fact that some patent trolls were trying to take advantage of an easy catch (not Prof. Quine of York University). See http://ksjtracker.mit.edu/2009/07/01/space-shaft-or-the-story-that-would-have-been-a-bit-finer-if-only-one-had-known/

    Perhaps we ought to exchange ideas and contact info?

    best regards

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