This is in response to the oft mentioned prospect of a space elevator. One problem is that there is no existing material that is strong enough for the cable. This was done to show how far away from any reasonable cable, material science is today.
Maybe, before we start, we need to look at what's needed. A synchronous earth orbit is about 22,000 miles high. That's the point at which one might anchor the top of the cable. But you're going to have to extend the cable much farther than that to counter the weight trying to pull the entire mess back down to earth.
Here, we're going to calculate how long a steel wire can be to be suspended, and not break of its own weight. For the calculation, I’ll use a 1 sq in cross section, to make the calculation easier. In fact, wire that thick is really bad, but I’m just interested in the math at the moment. First, how strong is steel? Here’s a tensile strength chart.
http://en.wikipedia.org/wiki/Tensile_strength
1700 MPa = 246,000 psi (steel tensile strength – Pounds / Square Inch)
steel strength = 250,000 psi (ie 1”^2 of steel will support 250,000 #s.)
Now let’s calculate the weight of a 1” section, 1 foot long.
water = 0.4333 #/ft (62.4/144 = 1 sq in section of water, 1' long)
steel = 3.38 #/ft (.433 * 7.8 1"^2 of steel, 1' long)
so, how long is 250,000 #s of steel?
250000/3.38/5280 = 14 miles.
A steel strand 14 miles long will just barely not break of its own weight.
A carbon nanotube, the strongest material in the chart, would be good for 510 miles.
(14*62,000/1,700 = 510 miles)
In order for a space elevator to work, it must reach far higher than 24,000 miles.
As if this is not enough, a space elevator must start on the equator, and go straight up. We all know that low earth orbit is filled with space junk, all traveling around 18,000 mph. Our cable is only traveling around 1,000 mph in this area, so a collision would be at something like 17,000 mph. That’s very unhealthy for a cable with a heavy strain on it.
Everyone’s welcome to disagree with me. In fact, I’d appreciate it.
Thanks.
Lin Lyons