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(Psst... just because the people work for a place who's name ends in "national laboratory" doesn't mean they have a direct pipeline to the wisdom of the ages. In fact, they are just as likely to be wrong as anyone else... I know... I work with these people from time to time.)
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Isn't it? I've always found vibrations to be an interesting topic.
The numbers were for comparison. Now, in the 'articles' you link, the authors stress how only a spindly, lightweight structure will be needed. Spindly, lightweight structures have extremely small bending (EI) stiffnesses. The Sears Tower is practically rigid compared with a 'space fountain' structure. Pick your favorite 'space fountain' design
(as the articles you linked surprisingly had no structure sizing) and perform a sinusoidal gust loading along the height... I imagine the tip displacement value will astonish you.
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Ok... I'll explain. The gust loading will not be even over the side area of the structure facing the wind. This difference in loading along the windward face will create a torque on the structure. And spindly structures have even lower torsional (GJ) stiffnesses than bending stiffnesses.
No... they just fail to say anything useful...
I'll assume you meant 'your' and not 'you are'. I saw no 'math' in your Wikipedia article and the only technical publication linked from there was on a 'launch loop', not a 'space fountain'. The wonderful catch-all in the Wikipedia article really means that the problems were manageable within the scope of the universe we occupy, not that the problems were practically solvable, or that they were economically practical. I would ABSOLUTELY LOVE to see that analysis done by Roderick Hyde. If you have it, please send me a link or a pdf. Also, always remember
Akin's Law of Spacecraft Design Number 17
No... I didn't say that they were science fiction. In fact, I am a huge proponent of rail gun technology. As soon as it becomes economically feasible, I think the military should put those bad boys on EVERYTHING. However, what I was referring to was the atmospheric drag that will suck momentum from these projectiles. Not only that, but the projectiles will need to be ferromagnetic in order to be redirected at the top and bottom of the tower. The atmospheric drag on a projectile traveling at Mach 6+ will cause tremendous heating and could exceed the Curie temperature of the material making it no longer ferromagnetic. Also, the velocity of the returning projectiles will will be limited by the terminal velocity of the projectile profile. All these losses will add up to necessitate a tremendous energy expenditure to bring the projectiles back up to speed at the bottom of the 'space fountain'.
Now look, maybe I started a little harsh, but I'm sick and tired of people thinking you can get to space easily by climbing successively taller trees. My goal it not to stifle creativity... far from it. However, I think a little realism and practicality needs to be brought into every discussion. Oh and I was serious about wanting to see that analysis...
Cheers...