by Shapley » Thu Sep 25, 2003 8:13 am
Barfle:
I looked at the article on the space elevator for which Lliam was kind enough to provide a link. I noted a few items of interest:
The article suggests the use of carbon fiber tubing "thin as newspaper and about 36" in diameter". I will estimate it at 38 3/16" diameter, since the 10' circumfence makes my calculations easy. The article also says it has "about 1/5 the weight of steel". I can only assume the article is written by a journalist, rather than a physicist, since mass, not weight, is the issue of concern. weight is a relative measurement, and will vary widely in our application. In fact, it would be ideal if our total weight were zero once the cable is in place. I have no idea how thick a newspaper is, but I will use 1/64" for the thickness, which will give our cable a density of about 100 lbs./cu. ft., or about 1.3 lbs./ft of cable.
The article also says that the platform will be beyond geosynchronous orbit. This makes sense, since the desire is to use the platform as a launching pad for interplanetary craft. No information is given on the size or design of the platform, however. Since the platform is a spacecraft launching station, sort of a deep space aircraft carrier, I will use an aircraft carrier as the design basis for the platform. (This lets me tie yet another thread into my rope.) The Navy website lists the displacement for an aircraft carrier as 97,000 tons. Since an aircraft carrier (other than this one) ideally spends its career at sea-level, then we can figure the displacement, weight, and mass as equal figures, so our platform has a mass of 97,000 Tons.
The article says the cable extends 63,000 miles to the platform. This is well beyond our 22,500 mile figure for geosynchronous orbit. Of course, this makes sense. since the desire is not to launch our aircraft into orbit, but to launch them out of orbit. The mass of our cable will therefore be about 216,000 Tons. Again, not an insignificant figure, but less than my 7,000,000 ton rope. It is also more than our aircraft carrier, which could be a problem. However, since we are beyond geosynchronous orbit, while maintaining our velocity in synch with the earths orbit, the linear velocity is greater than our rate of descent, and our aircraft carrier would be moving away from the earth (falling up?). However, it is anchored to the earth by the cable, since the article says that the cable will be anchored to the earth by an off-shore platform. Aircraft launched from our carrier, however, if they are launched "into the wind" (wind?) from the deck of our carrier (towards the direction of rotation) will similarly "fall up" and away from the earth, which is very much our desire.
Having the platform off-shore is a political requirement, I believe, rather than a physical one. The idea is to use the elevator and the aircraft carrier as an international launching platform, and being offshore keeps if free from governmental interference in that noble objective. It also gives a level of control over access to it, and keeps kids from climbing on it, thinking its a giant beanstalk or something. The article does say that it is anchored, so they are in agreement with me on that issue. There is even a drawing of the platform, and it looks quite massive. But then again, it has to handle the elevator car, and 10,000 ton payloads coming and going (10,000 tons is their figure). It also has to handle wind and wave and the other issues an offsore platform deals with. Since the illustration seems to show it off the coast of Central America, I assume it has seismic considerations as well, but those are easily dealt with.
Since our cable is anchored to the earth and extends 63,000 miles, nearly two thirds of it is exerting an outward stress on the cable, as it falls away from the earth, while the remaining third is pulled towards earth by gravity. Since no other explanation is given for the 63,000 mile figure, I assume (there's that dreaded word!) that they agree with me that the mass of the aircraft carrier and the mass of the cable beyond 22,500 miles has to be sufficient to overcome the gravitational effect on the remainder of the cable. People more educated than me have most likely done the math and decided that 63,000 miles is sufficient to achieve this effect. The desire will be to have an average end reaction of zero. However, that will be an average, and our cable end treatment must deal with the peak postive and negative stresses encountered by our cable. I feel vindicated already.
Our cable, like eveything else in the universe, will have a modulus of elasticity, and thus will undergo strain as various stresses are applied to it. This includes the dynamic load of the elevator as it moves at varying velocities along the cable, feeling the varying effects of wind and gravity as it climbs. Those calculations are pretty rudimentary, however, and I'm sure Benito could figure them out during coffee break on a Monday. We also have to deal with gravtional pull from various sources beyond the earth, including that great lump of cheese we call the moon. Since the moon can lift the oceans, and the arcraft carriers that ride on it, by as much as twenty feet or more while they sit on the surface of the earth, I'm sure its effects on our aircraft carrier 63,000 miles above the rest of them will be somewhat greater. Of course, it also pulls it towards the earth when it is on the opposing side of the earth, sort of an interplanetary low tide.
I read an article a while back that states that geosynchronous orbitals are not spherical, but vary widely as the earth rotates. This is due to planetary influences, and the earths tendency to "wobble" on its axis, among other things. However, our aircraft carrier is anchored to the planet by a more or less fixed length of cable. This means that our orbital will be held to spherical shape within the elasticity limits of the cable. This will induce stresses within the cable as well, and they have to be dealt with by our end treatment. Basically, our aircraft carrier is a giant yo-yo, with our cable as a string. As you know, a yo-yo doesn't fly off into space because it is anchored to our finger. Let go of the string, and the yo-yo no loner yoes, it goes.
There are other factors, such as radiation embrittlement of the cable fibres, temperature considerations, etc. But none of these make the endeavor impossible, just more challenging. Have fun, Benito!
Unless you have another explanation for the figure of 63,000 miles, I rest my defense. My fate is in the hands of the jury (oops, lawyer thread again). I'm sorry I failed your class, professor. Hopefully my other subjects will keep by GPA, like my aircraft carrier, above sea level.
V/R
Shapley
Quod scripsi, scripsi.
