I been thinking about space elevators, lately. Not because I think it a practical solution, but mostly because I think it's interesting. A space elevator requires a material which is strong enough to lift it's own weight when it's tens to hundreds of miles long and in order be able to be +30,000 miles long and be strong enough lift payload it must be tapered.
NASA is paying for studies on Space elevators and their solution involved nano carbon fiber- which would be theoretically strong enough. Nano carbon fiber almost qualifies as unobtainuim. Space elevators are "predictably" something NASA would spend money researching. It's perfect to spend years studying, and can be justified because it could be "breakthrough" technology. Now, NASA is NOT spending a lot of money on this, but maybe it's something NASA might "get" to waste huge globs of money on. And the "good news" is that if a space elevator were to actually be build it's fits perfectly the socialist model of having a molopoly to space access controlled by the state. Anyhow, for the dingbats who think space is viable AND want something "PC", space elevators are exciting.
I don't think it's at all likely that a Space elevator will be built within two decades and to me space elevators are about as distant future as a probe being sent to another solar system [and after being launched getting there before another century has past]. I see large telescopes on the Moon before space elevators. I'm I making myself clear, that I don't think Space elevator are a near term solution? Now, space elevators are "sold" as a near term solution, but I don't "buy in" to that fantasy.
Now, making a space elevator out of some present day unobtainuim which is light and very strong, could be how space elevator will actually be made. BUT what interests me is the question could a space elevator be made of material which we currently have. And more specifically can it be made out of steel. Now, there is stronger and lighter material than steel- spider thread is much stronger, but steel is what is actually used for things like big suspension bridges and the limit on suspension bridges is the tensional strength of the material (the steel used]. It is my guess, that if we were serious about building a space elevator and IF a "serious" engineer was willing to do this and was tasked with building it within 10 years (an almost impossible task) and "had the money" he/she would use some steel alloy. As I've said before I am not a engineer. Steel is normally rated in pascel or ksi, but I don't how this relates it's strength to weight. I see different ranges given for steel, the highest I've seen is 5 GPa and supposively piano wire is 3 GPa. Btw there is also a material called ZYLON which is rated at 5.8 GPa and has low density: 1.5 (steel is 7.8). Anyways I found table for bridge steel which gives the strength per it's weight:
http://www.inventionfactory.com/history/RHAbridg/sbtd/sgsbstrd.html
I don't know what this steel is rated at, but...:
Per 1/2" diameter it weighs about .52 lbs per foot and lift about 15 tons (57692' weighs 15 tons).
[Added note: As far as I can fiqure, steel which is rated at around 100,000 psi strength yield
(690 MPa) can hold it's hold weight if 5.6 miles long [without permanently being
stretched- though above cable is pre-stressed] therefore this bridge steel is equal to
around 200 ksi (1.4 GPa). Therefore piano wire which was 3 GPa would be able to have twice
the length.]
This means that if you had 10.9 miles hanging in mid-air it could support itself but if you
added say a ton of payload weight to it it couldn't support it. Now, if I taper this cable it
will support more weight. So what I'm going to do is make a standardized unit which will be used
for entire space elevator- so you might be buying a million or more of these strands which are
all the same (would have customized specification). If you take this 1/2" diameter strand and have
it so it only had 25% of it volume at the bottom and 75% of volume at the top, this 10.9 mile tapered
strand will weigh 7.5 tons (15,000lbs) and will able to lift a payload of 25% of 15 tons (7500 lbs).
The next segment will need to be 3 strands- one to lift payload two to lift the first strand.
{At this point I will breifly address how the payload could climb the cable. [Warning, we are entering
the wacky zones, get out your tin hats.] In addition to having these cables being tapered
they will also be magnetized* (say narrow bottom being South and top larger end being North). At
the lower end of space elevator their won't be much steel, but as the structure goes up it becomes
more massive, and even if this cable can only be modestly magnetized, the quantity might make up
for lack of quantity. Now there might problems with this, e.g., the magnetic power of elevator might
create a hole in ozone or conversely the magnetic affect might not extend as far I hope it would and
general have little or no effect. I'm not the sure of affects would be of a magnet which is thousands
of mile long. As fallback if magnet idea doesn't work there will three cables which are held straight
by tensional force, which in some manner can be pushed and pulled against. Now instead of cable capable
of lifting payload of 7500, there would cables 3 1/3 size [each able to lift 2500lbs]. The cable would
be arranged in a trianglar configuration with payload traveling up the middle.}
Anyways back to the exponential growth. The first seqment weights 15,000. The second segment will have 3
cables (2 to lift the previous cable & 1 to lift payload, so with total of 4 cables each weighing 15,000 lbs
[as describe above there is actually 12 cables each weighing 1/3 of 7.5 tons, but we will refer to these
3 cables as one cable]. So next segment needs to lift 30 tons plus the 7500lbs of payload [67,500 lbs],
so it needs 9 cables, these 9 weigh 67.5 tons [135,000lbs]. The 4th segment needs to lift 202,500 lbs
requiring 27 cables [these weigh 27 times 15000 = 405,000 lbs]. The 5th section must lift 607,500 lbs,
requiring 81 cables [which weigh 1,215,000 lbs]. 6th needs to lift 1,822,500 lbs (911.25 tons) requiring
243 cables [which weighs 3,645,000 lbs]. 7th needs to lift 5,467,500 lbs requiring 729 cables [which
weighs 10,935,000 lbs (5467.5 tons)]. The 8th section needs to lift 16,402,500 lbs requiring 2,187 cables
[which weighs 32,805,000 lbs]. The 9th section needs to lift 49,207,500 lbs requiring 6,561 cables [weigh
98,415,000 lbs]. The 10th section needs to lift 147,666,500 lbs (73,811 tons) requiring 19,683 cables
[which weighs 295,245,000 lbs].
Let's stop here and take a look at this. So far the total weight of this structure is about
442,904,000 lbs + the 7500 lb for payload (which would need to include any "added weight" due to any
acceleration). So this is over 200 thousand tons- around 4 aircraft carriers in steel. The approx
bundled diameter of cables at botton of 10th segment is 18" sq with about 53" sq at the top of seqment.
Further comparsion, it's so far "only" about 1/4 of the total weight of the Golden State bridge but
it's more than the weight of it's two cables (@ 3' diameter and 7,650 ft long), but the space elevator
has barely begun it's 35,000 km journey. If we are using steel with 200 ksi (1.4 GPa) strength, then
the total cable length is 109 miles [steel which if has more tensional strength would require less steel
and could have longer length]. 109 miles is about 1/200th of the distance. It seems fairly hopeless.
And I don't disagree that the whole idea is "pie in the sky". The total mass so far, has easily exceeded
all mass that has ever been lifted to LEO or beyond by all nations since Sputnik. And if an Aircraft
carrier costs 4 billion, then at miminum at a very rough estimate, assembling 4 aircraft worth of steel
straight up will cost over 16 billion. If you made a better steel, eg, the piano wire of 3 MPa then
this roughly means to go the same distance you would use half the quantity of steel, roughly saving
8 billion. Or another way saying this is it is at least worth 7 billion to develop the steel, meaning
steel shaped, tempered [and other forms of treatment], designed to join easily to other strands, not
losing strength and not adding excessive weight, plus possibly magnetizing it to high enough level that
it adds to overall strength. This is another reason I stop at this point, once the cable reaches
significant size the magnetic strength could become a meanful factor. Plus another factor enters in
and that is the gravitation force of the mass of the cable affecting itself. Now, I don't have the
answer. The questions I leave you with is, "What would be the gravitation force at the ends of two
chunk of steel each meter in diameter and say 100 km long?" And "What be the force of the attraction of
these chunks of steel if they were modestly magnetized?
Note: Another factor is if you are halfway to GEO, your orbital speed and the lessen affect of Earth's
gravity should make your weight about 1/2 (remember this is "all about" having material which can lift
it's weight over distance- halving it's weight effectively doubles it's tensional strength). And at GEO
your weight is zero, therefore if you have enough mass at GEO, gravity can provide all the "tensional
strength" needed

Various notes:
* reference for magnetic steel:
http://www.arnoldmagnetics.com/products/alnico/pdf/Cast_Arnokrome_III.pdf

Kevlar 49:
Density
g/cm^3: 1.44
Tensile Modulus
GPa: 131
Tensile Strength
GPa: 3.6--4.1
Tensile Elongation
%: 2.8

100 ksi equals 690 MPa
150 ksi equals 1040 MPa [1.04 GPa]

Kg/mm2 = KSI x .7031
Newtons/mm2 or MPa = KSI x 6.895
http://www.fiskalloy.com/pdf-pages/wa-bronze510.pdf

Discussion on truck construction:
AR235 is an abrasion-resistant steel, while AR514 is a Grade B steel with 265 BHN,
100,000 psi yield strength, and 120,000 psi tensile strength.
100X, or Domex, has 250 BHN, 100,000 psi yield strength, and 110,000 psi tensile strength.

In the carbon line, A569 is a mild steel with 36,000 psi yield strength,
137 BHN and 50,000 psi tensile strength.
When discussing AR400, or Handox (the Swedish manufacturer's trade name),
he said it has 145,000 psi yield strength and 400 BHN, and 180,000 psi tensile strength.
http://trailer-bodybuilders.com/ar/trucks_primer_picking_best/

By changing the amount of Chromium and Molybdenum we were able to obtain a totally new
high strength steel alloy we call C2M30 which has over 300,000 psi yield strength with a
modulus of 26 million psi - 2 million psi lower and thus more elastic than maraging steels
and Aermet. http://www.clubwerks.com/wooddetail.asp?ID=45