A space elevator need not be based on the popular carbon nanotube tether reaching a to a counterweight beyond GEO. There is another model that can be used for assisted launch at LEO and other human activities. Such a system goes by the name of a SpaceShaft and it is not as sexy as the CNT system but it can be used for other applications that the CNT system cannot be used for.
I will present a short qualitative description of it. And I will recommend you visit
http://spaceshaft.org for some illustrations and online calculators.
Unlike the CNT system it is not a tether but a dynamic structure that can be compared to a spar-buoy, but rather larger than a semi-submersible platform used by the oil industry. For those who do not know what a spar-buoy is I recommend to Google for images, but in a nutshell it is a tubular buoy with an anchor-chain at one of its ends that force the object to stand upright half submerged an the other half floating out of the water.
Metaphorically we can compare the atmospheric environment of our planet to that of the oceans while space is the counterpart of the atmosphere. Because buoyancy can happen on both fluidic environments, a device that harness the energy of gravity can be implemented as to generate unlimited upthrust beyond both weight and distance and both products are simply based on the volume of the object displacing the environment in which it is submersed. However, there will be trade-offs like with any other system and these I may discuss later.
The deployment of such a system is gradual, and uses a FI-FO (First-In - First-Out) sequence of events for its construction. But before describing the process in further detail I will describe a little bit the atmospheric environment in which it will have to operate and do some simple math to give an idea of the potential and magnitude of the system. The following description of the deployment stages will exemplify the ease by which such a structure can be implemented.
As you may know, the atmosphere is dense at Sea level and very thin at half way to the Karman line, that is at a altitude of 50 km (see Wikipedia). If throughout this distance a large buoyant object can be made to stand upright, it will cumulate all the upthrust energy from the gaseous displacement of significantly dense regions of the atmosphere in which it is embedded. As an example of the cumulated energy; it will be anywhere between 9800 N to 4.90E7 N for a structure with a diameter of 100 meters, which is equivalent to a lifting capacity of 5000 t (tonnes).
The effect a thin atmosphere on a very large science balloon at an altitude of 50 km is that of stagnation, i.e. it will no longer ascend. However, because of the underlaying buoyancy the top section will be forced still further towards space until an equilibrium between weight and upthrust is achieved. As a simple example assuming that the atmosphere had a continuous density, half of the object would reach into space, i.e 25 km, and the other half will be submersed in the atmosphere, i.e. 25 km.
You could point out that; "optimistically this effect would only bring us up to an elevation of 75 km". But if the object was engineered in such a way that it could be controlled during its ascent, and that new buoyant sections could be regularly added at the base, such limitation would be eliminated and the resulting object will be a utility that could be regarded as a unidirectional elevator system that could reach beyond 100 km, and could also provide the necessary infrastructure needed for activities such as rocket assisted-launches, (e.g. space tourism,) and for other applications such as observation platforms for atmospherical and astronomical purposes.
Let us now look at the deployment method.
Assume that large, tubular balloons, with a diameter of 5 meters can be manufactured and forced to a “ring” shaped element that we will be identifying from now on as sectional-rings.
Note: It will be very important for accurate results to know the material properties from which the shells of these balloons are made of. And so, if not more important, it will be to know the precise air-density values, found within the “US Standard atmosphere” tables, but for simplicity and due to the lack of time these properties and subsequent calculations will not be taken into account at this forum.
Assume that each of these sectional-rings can contain 3600 cubic meters of Helium, i.e. the individual lift capacity of each ring, at sea level, is 3.6 t. Also assume that the sectional ring is moored by several mooring lines forcing it to lay horizontally. Also assume that the mooring lines can control the ascent of the sectional-ring enough as to insert a second sectional ring below the first one. Once this is done, both sectional-rings are securely attached and mooring lines are attached to the lower sectional ring and removed from the top sectional-ring. What you now have is an object with 7.2 t of lifting capacity. Keep repeating the mentioned steps until the system has reached 50 km of elevation.
You will notice the very large numbers of lifting capacity resulting from buoyancy throughout the atmospheric layers of the troposphere and lower stratosphere, (for your calculations use the air densities found at Wikipedia). And how this effect rapidly decreases when accessing the mesosphere, to a point in which the balloons become pure weight. Nevertheless, even with the pressurized balloons being on a pure weight condition the resulting net upthrust force is plentiful as to extend the structure into space.
I have superficially described how a SpaceShaft works, I am aware that there are many points that need further explanation, including how to keep the structure from being tossed around by weather disturbances, etc, but I hope I have given you another option to think about when considering space elevators.