User:Danielravennest/papers/Space Elevators



Dani Eder

The Seed Factory Project,

6485 Rivertown Rd, Fairburn, GA 30213



Author's email: danielravennest@gmail.com

Introduction
Space Elevators are an attractive idea in principle. They replace the loud, inefficient, and expensive chemical rockets we use today with an "elevator ride", which is imagined as quiet, efficient, and cheap. However, as presented in media articles and illustrations, the idea is simplified too much. Many of the details are wrong or obsolete. This paper tries to give a more realistic overview that accounts for how things are designed and built in the real world.

Some Definitions
In the writings about space elevators, you will often see mention of Space Tethers. These are long, flexible cables which are used in space for any of a number of purposes. A tether can be part or all of the structure of a space elevator. But a complete elevator would also include cargo pods, a lifting mechanism, a power supply, etc. In engineering, tethers fall into the category of "large structures", along with tall buildings and bridges. A large structure is one where the mass of the structure itself is a large part of the total load. The load of the structure on itself then must be factored into the overall design.

History
The idea of a space elevator dates back to space pioneer Konstantin Tsiolkovsky in the late 1800's. (See:|Konstantin Tsiolkovsky and the Origin of the Space Elevator, Pearson, 1997). He imagined it as a "thought experiment", among other ways to get into space. He did not consider it a feasible project that could be built. The idea in the original form has caught people's imagination, despite now being out of date. Since 1960, other people have worked on and improved space elevators, large structures, and related ideas. The first use of a tether in space was on Gemini 11, in 1966. Since then a number of other Space Tether Missions experiments have flown to space, but fully operational tethers or space elevators are still in the future.

Economics
Any large structure, whether on Earth or in space, has a large cost attached to it. So it is important to understand if the cost is justified. The questions to ask are (1) is a space elevator better than what we have now (rockets)?, and (2) is it the best choice among other ways to get to space? The second question is very complicated, and beyond the scope of this overview. If you are interested you can look at this | Space Systems Engineering Wikibook for an introduction.

Payback Time
Turning to the first question, any project consists of one-time costs and repeat costs. For an existing rocket, like the Falcon 9, the one-time costs included design and testing, building the factory, and the launch pad. Those are past now. The repeat costs for each launch include the new rocket hardware used up each time, fuel, shipping to the launch pad, and launch and mission operations. If you graph the future cost vs kg to orbit, it will be a line of constant cost/kg slope, starting at (0,0). For a new system like a space elevator, you will have significant one-time costs: research, design, manufacturing the elevator parts, and delivering them to orbit. The repeat costs should be lower because you don't need new hardware or fuel each time. So the line will start well above 0 cost at 0 kg, then have a lower cost/kg slope once you start to deliver things. The two lines will therefore cross at some point, after which the space elevator is cheaper. How long it takes to reach the crossover point is called the "payback time". It can be measured in terms of kg of traffic or in years of operation. The latter can be estimated from (1) how many kg of traffic needs to go to space, after accounting for the changed market due to the lower cost/kg, and (2) the fraction of the total traffic the space elevator will capture. The latter will not be 100% for several reasons, including the orbits the payloads want to go to, physical characteristics, or national programs that choose to use their own systems. If there is enough traffic to go past the crossover point, then the space elevator is the cheaper overall option. However, time is an element also. How many years does it take to reach payback? If the answer is many years, the economic return, in % per year, may be too low for a business or government to want to pay for it. That is because there are always other things to spend their money on, that could bring a higher return.

Economic Analysis
The calculations just described are a simplified analysis, mostly useful to see if the project makes sense at all. A more detailed analysis takes into account additional factors:


 * Traffic to space and competing rocket costs are not constant. Traffic tends to increase, and rocket costs in a competitive environment tend to fall.  A better calculation would project the costs and kg delivered year by year, usually in a spreadsheet.


 * Some space elevator designs can start small, and be built up over time. In that case, the one-time costs to get started are less, and the upgrades are deferred until revenue is coming in.  The peak investment is then less.  Since available investment funding is limited, the feasibility of the project may depend on lowering peak investment.  A partly-built or small space elevator can literally bootstrap its own later construction.  This can have a dramatic effect on the total cost.


 * A full space elevator does 100% of the job of carrying traffic to space. Some designs allow for the elevator to do less than 100%, and a rocket to do the rest.  For physics and engineering reasons, both space elevators and rockets get exponentially more expensive as the job they do increases.  If each does part of the work, the sum of their costs may be less than either one by itself.  In that case, there will be an optimum division of the work which results in the lowest total cost.


 * Technology is not static. Generally, better structural materials, and methods to make them, are developed over time.  Less materials that cost less per kg lowers the cost of building the elevator.  In the future, elevator materials may come from the Moon or asteroids.  These would require less energy, and thus less cost, to deliver to the point of use.

Scale Height
Since space elevators are large structures, we will now look at some basics of structural engineering. Consider a column of steel, 1x1 meter in area, and variable height. The density is 7870 kg/m^3 and standard Earth gravity is 9.80665 m/s^2. Multiplying, we find gravity applies 77,178 Newtons of force on the base of a 1x1x1 meter steel cube. Since the area is 1 square meter, it is also 77,178 Newtons/m^2 = 77,178 Pascals (Pa). This compressive load is from the steel itself, before you add anything for the steel to support. As we increase the height of the column, gravity will increase the compressive load proportionally, because there is more steel above the same area. The "yield strength" of a given steel alloy is 305,000,000 Pa (305 MPa). This is the load at which the steel will start to deform and collapse. Dividing yield strength by load per meter of height, we find that a column 3,951 meters tall will reach yield strength at the base, and cannot support itself any higher. 3,950 meters is thus the "scale height" at 1 gravity for this kind of steel. You can do this calculation for any other material using their density and strength. It only considers the material itself, without any supported payload. It is also theoretical. You would never build something to the point of failure. For example, for steel buildings, the combined maximum loads from the steel itself, contents of the building, winds, earthquakes, etc. are limited to 60% of yield strength. A space elevator cable hanging from orbit is in tension (trying to be pulled apart) rather than compression (trying to be squeezed together). So the tensile strength rather than compressive strength is the appropriate value to use (they can be somewhat different).

Loads
In orbit, centrifugal acceleration upwards from your orbit velocity and gravity acceleration downwards vary. The net acceleration is what creates loads on the cable, so it must be calculated at each point. You must also add the loads from any equipment, cargo pods, etc. to the loads of the cable on itself. Our example of a steel column had the same area at all heights. This is not required. Instead, you find the loads at each point of the elevator cable, and give it enough area to support that load. Typically, for a hanging cable, the load is greatest at orbit height, since the whole cable and all the attached items are hanging from that point. As you go down, there is less cable and attachments below a given point, and so the cable area can be lower. This results in a tapered cable.

Structures can theoretically be rigid (break before bending) or flexible (bend before breaking). Real objects like a piece of lumber are somewhere between. They can bend a little before breaking. For a real structure, the question is what forces create bending and breaking loads, and how much movement is allowed from these loads. Generally the lower the ratio of length to width, the more rigid and less flexible a structure is. Thus tall buildings must have a certain width in relation to height. If they are too thin, wind loads would bend them like a tree, and make people sick or interfere with the elevator shafts.

Loads can be constant (static) or variable (dynamic). In a space elevator, a static load would be the Earth's gravity acting on the structural mass. Variable loads would be the Moon and Sun's gravity, since their distance and direction varies with time, and acceleration or deceleration of cargo pods. Obviously the structure must be designed for peak loads combined, plus a multiplier above that, called a "Factor of Safety". Dynamic loads which are sideways to the structure can cause vibration (rhythmic bending). If the timing of the loads matches the vibration period, the bending can become larger each time, unless damping is designed into the structure.

In modern design, all the loads are analyzed using structural analysis software or a custom simulation. If an initial design gives an unsatisfactory result, it can be modified and analyzed multiple times until a good result is obtained. During the early concept exploration phase of a project, simpler analytical formulas and approximations can be used.

Space Environment
Any engineering design must account for the environment it will operate in. For a large space structure this includes gravity, impact, radiation, and thermal environments:


 * As mentioned above, gravity from the Earth is constant at a given location and altitude. However a non-stationary or rotating elevator (described below) will see variable gravity at each point of the structure, and the motion of the Moon and Sun apply variable gravity even on a stationary elevator.


 * Space is filled with small objects moving at high velocity. Near the Earth this is mostly artificial satellites and their debris.  In addition, at all locations there are natural meteoroids.  When you look up at the night sky, you can see these meteoroids hitting the atmosphere as "shooting stars".  Both natural and artificial objects move fast enough to cause damage if they hit part of your elevator.  The larger the elevator, the more area that can be hit.


 * Space is also not an empty vacuum. Near the Earth, highly reactive atomic Oxygen (decomposed by UV from normal oxygen) is present, and at higher altitudes heated ions.  The Sun's ultraviolet light is about 100 times more intense in space than the ground.  Earth has radiation belts trapped by it's magnetic field.  The field itself is not uniform and can induce currents and static charges in the spacecraft structure.  Solar flares and galactic radiation can affect electronics.  All of the above can affect space elevator materials, and some of it is a hazard for people.


 * Most materials change properties like strength and dimensions with temperature. Moving from sunlight to shadow as a space elevator orbits or rotates can change the temperature by hundreds of degrees C. Change in length per degree C is usually small, a few parts per million.  But when the temperature range is 200 C, and the length is up to 60,000 km, the length change can amount to 10's of km.  Such large changes have to be accommodated in the design.

Material Selection
For any space elevator of significant size, the scale height of the structural material is of paramount importance. Extraordinary theoretical strengths can be derived from the strength of carbon bonds in nanotubes (tensile) or diamond (compressive). However, theoretical is not the same as laboratory measurements, and neither is the same as a usable structural material. Usable materials have defects (even if of atomic scale) from manufacture and handling, and must be produced in enough quantity and at reasonable cost for a project. At present, carbon fiber is the best overall usable material. We can speculate about the properties of future carbon nanotube cables, and we can do research to move nanotubes from the laboratory to practical use, but at present they are not ready. Carbon fiber is well understood, and has been used for decades in aerospace projects like passenger airplanes and satellites. Bare carbon fiber chosen for strength has a scale height of about 360 km in tension. With realistic factors of safety and structural overhead, a usable scale length is 150 km. Unfortunately the Earth's gravity well has an equivalent depth of 6,378 km, which leads to a taper ratio of e^(6378/150) = 3x10^18 for a full stationary elevator. This is much too high to be practical. A realistic projection of nanotube cable properties is three times stronger than current carbon fiber. This leads to a taper ratio of 1.4 million. This is still too high to be practical, but much better than 3 billion billion. For near-term designs, we must look at other options than the original space elevator concept.

Safety
Safety is an important part of any engineering project. Three aspects should be considered in the design: (1) Safety to the public. For example, a space elevator should not break and fall down, causing damage to people below, (2) Safety to crew and passengers on the elevator itself. For example, a passenger pod climbing the elevator should not lose pressure and kill the occupants, and (3) Project safety. These are hazards and losses during construction and operation, which accrue to the elevator owners. Examples are meteoroid impact that cuts the cable, or dropping a spool of cable during construction, which re-enters and is lost.

No project is without risks, but if there is too much risk to the public, you might not be allowed to build the space elevator at all. If you kill crew and passengers, you may lose future customers and cargo traffic. If the project has too many losses during construction and operation, it may drive up costs or insurance beyond what makes economic sense. From a design standpoint, the question is how to make it as safe as possible without driving up costs too much.

Redundancy & Modular Design
Redundancy is using multiple units that perform the same function. That way, if one unit fails, the other units can continue to perform their job. For a space elevator, using multiple redundant cables is a primary way to increase safety. Impact hazards can't be entirely eliminated, so cable breakage can be handled by having, for example, 20 total cables. The design loads would be handled by 14 of the cables, and the other 6 are spares. If one or two cables are broken by impacts, there are still enough to support the elevator, and you have time to repair the broken ones.

Modular design is providing smaller, easily replaced units in a larger project. A space elevator is too large to be built or delivered all at once. The cables can be divided into smaller sections, for example 5 km long each, which can be wound on spools and delivered as reasonable size payloads. The 5 km sections of the 20 parallel cables can be cross-connected to distribute loads around a broken section. Replacing a 5 km section of a longer cable is easier and requires less mass than replacing the entire cable. Another benefit of modular design is the space elevator as a whole can start smaller, and with fewer cables. As payload traffic and mass increase, the elevator can grow incrementally to handle the demand. This lowers up-front costs and smooths the expansion costs.

Optimization
It is not obvious when starting a space elevator design what the optimum answer will be. The way you find it is vary parameters of the design one by one, and look for the best result. Parameters include length of the elevator, payload capacity, orbit, structural materials, and many others. Changing one parameter often changes other parts of the design, so a semi- or fully-automated method of calculating the changes is desired, such as a spreadsheet or simulation.

Elevator Concepts
Massive bodies such as the Earth have a gravitational field. You must add potential or kinetic energy to move an object to a higher orbit or destination. Rockets do this by burning fuels, which generates thrust. This pushes on the payload, adding energy to it. An elevator adds energy by mechanical methods, like a cable lifting the payload, or a magnetic levitation track on the side applying force. Space elevator concepts differ in where they are located, how big they are, and how they add energy to a payload. The choice of an elevator concept among all the options will depend on what the job is, in terms of destination and traffic, and considering all the other factors like safety and economics.

Stationary Elevators
Geostationary orbit is 35,800 km above the Earth's equator. This orbit has a period of exactly one day, therefore objects in that orbit move at the same angular rate as the ground. They appear to be stationary from the ground perspective. This is exploited by communications satellites, since ground antennas don't have to move to track them. The original space elevator concept (Tsiolkovsky, 1895) imagined a tower reaching from the ground to geostationary orbit. The top of the tower would be sweeping the orbit at the same speed as a satellite would. Therefore if you climbed the tower and let go at the top, you would be at the right velocity to stay there and float nearby. Since many materials are stronger in tension than compression, instead of building up from the ground, you can build a cable down from stationary orbit. To keep the center of mass stationary, you must then build up also, to balance the mass hanging down.

We will call towers or cables that match the motion of a large body "stationary elevators". The Earth is not the only place you can build a stationary elevator. It is much easier to build them for the Moon, Mars, or a large asteroid like Ceres. The height to stationary orbit is generally less, and their gravitational field is weaker. That creates smaller loads, and therefore you need less structural materials.

Both towers and hanging cables get exponentially more massive as the job they do increases. For large bodies like the Earth, the least mass design is then a tower and hanging cable who meet at their tips. The least cost design will depend on the relative costs of building the tower and orbiting cable parts.

Moving Elevators
Stationary orbit is the special case where you match the rotation of the body you orbit and are directly above the Equator. Orbits in general can vary in a number of ways from this case. They can have different durations (period), tilt to the equator (inclination), and shape (eccentricity). If the shape is not a circle (eccentricity > 0.0), then the height above the surface will vary over time. You can place your elevator where gravity and motion are balanced between two objects (Lagrange points), or even detached from orbiting a body. In that case, you would be orbiting the Sun, rather than the Earth or Mars.

When viewed from a distance, a stationary elevator rotates at the same rate as the body it orbits, like the hand of an analog clock relative to the central pivot. This is also a special case. It can tilt back and forth relative to the ground, like a pendulum, or make complete rotations faster than it orbits. It can also have no rotation at all (inertial).

Elevator Systems
A single space elevator, like a single rocket stage, may not do the whole job you want to do. You can therefore build elevator systems made up of more than one part. An example of a two-part system is a vertical cable in orbit around the Earth, with a rotating cable attached to the lower end. A multi-part network could be built with elevators in different orbits or around different bodies. Finally, a space elevator can be combined with a different method, like a rocket, to do the full transportation job.

Elevator Size
The early space elevator designs reached from the ground to stationary orbit, plus some distance beyond to balance the center of mass location. That made them more than 35,000 km long. Aside from sheer size, comparable to the distance around the Earth (40,000 km), such large sizes expose them to very high structural loads, thermal changes from day-night cycles, meteor impacts, and tides from the Moon and Sun. Smaller sizes can relieve these problems. Because structural loads, and thus mass, is exponential with size, often the economics will favor smaller sizes. This is despite complicating the job by requiring a rocket or second elevator to complete the system. Optimum size depends on the traffic it is carrying. So an elevator installation may start smaller for today's traffic, and grow over time. This is similar to airports or highways, which start small, and grow over time.

Elevator Operations
We next turn to how the elevator adds energy to objects. On Earth, elevators mostly use a cable attached to the top of the car, a counterweight to balance the average loaded weight of the car, and an electric motor to drive the cable up and down. In space this would be impractical, since a counterweight would double the load, and the lifting cable would duplicate the load capacity of the main structure. The fastest cable-type elevators, in the Taipei 101 tower, move at 60 km/hr. A full synchronous orbit elevator, with a counterweight well above 35,800 km altitude, might be 60,000 km long. Therefore the elevator ride would take 1000 hours (41 days 16 hours), which is clearly too long for practical use. So we must look at other options for large elevators, and more efficient ones for smaller ones.

Sequential Climber
Rather than a cable and counterweight that runs the entire length of the space elevator, we can substitute a spool-type winch that climbs the elevator in stages. The winch carries a spool of cable attached at the end to the cargo pod. For each stage of lifting, the winch climbs ahead of the pod, letting out the cable. It then anchors to the elevator structure, and winds in the cable, lifting the pod. The winch carries it's own power supply. This might be solar panels, batteries, or beamed power. The alternative of the pod directly climbing the structure requires a track or rail strong enough to support the pod load, along the entire length of the elevator. That would be much heavier than a simple cable one stage length long - perhaps a few km, and individual attachment points spaced out the same distance. A sequential winch would be no faster than a conventional elevator, and thus not suited for very large space elevators. They don't require much new technology, since winches are very common mechanical devices.

Magnetic Levitation
"Maglev" operates using magnetic fields, rather than mechanical contact, to provide lifting forces. Since the moving cargo pod does not have to touch the elevator structure, it can go much faster. Up to 600 km/hr has been demonstrated on Earth, and in a vacuum higher speeds are possible. The drawback is requiring a track with coils and a power supply, or permanent magnets, along the length of the elevator, which would be heavy. It would also require a lot of power. A 10 metric ton cargo pod rising at 600 km/hr near the Earth requires 16.3 MW of energy at 100% efficiency. The benefit for the largest space elevators is shortening the trip time by a factor of 10 or more.

Orbital Mechanics
A vertical cable in orbit is in tension due to tidal forces. Gravity is stronger at the bottom, and weaker at the top relative to the center. Conversely, centrifugal acceleration is higher at the top. All parts of the cable complete one orbit in the same time. The top follows a longer path, and thus the acceleration is higher by the formula a = v^2 /r. The net force is thus upwards at the top and downwards at the bottom. The orbital velocity of a detached object decreases with altitude, while the velocity of an object climbing the vertical cable is increasing. Thus at the top it is moving faster than local orbital velocity. If it is released at that point, it will be in an elliptical orbit with a high point about 7 times higher than the tip-to-center distance of the cable. Thus rather than a continuous single elevator cable, you can have a system of shorter segments, and use orbital mechanics to travel between them. Eliminating most of the cable length is lighter and cheaper by a large factor, and it can also be faster if the altitude is gained fast enough between segments.

A rotating cable can amplify this effect by adding more centrifugal acceleration and tip velocity. In this case, the centrifugal loads on the cable will exceed the gravity loads, and the design will be based on a centrifuge or flywheel rather than a tower or cable. With current materials like carbon fiber, tip velocities in the range of 2-5 km/s are feasible, which is a large fraction of Earth orbit velocity. 3.3 km/s are required to reach Earth escape from low orbit. A cable with a tip velocity of half this, in an elliptical orbit, can pick up a payload in low Earth orbit and add twice the tip velocity to reach escape. If the tip is at 1 gravity centrifugal acceleration, the tip-to-tip length will be 555 km. This is about a factor of 100 shorter than a stationary elevator. No climbing mechanism is required, merely holding on for half a rotation, which takes 9 minutes.

The energy added to the payload via orbital mechanics is not free. By conservation of momentum the cable will slow a corresponding amount. Therefore it needs a propulsion method to make up the lost energy. Around Earth this can be via electrodynamics (interacting with the Earth's magnetic field), and elsewhere via electric thrusters. Near Earth the power for the propulsion can be beamed with lasers or radio frequencies. Alternately solar or nuclear power can be used elsewhere.

Space Tower
Tsiolkovsky's original thought experiment was a tower that reached from the ground to stationary orbit. A quick search shows the highest strength-to-density compressive material is | Unidirectional Boron Fiber. It has a theoretical scale height of 143 km, and accounting for overhead and factor of safety, a usable scale height of 60 km. Over each scale height, a minimum mass design increases in base area and total mass by a factor of e (2.718). We will assume a practical tower will not mass more than 1000 times whatever it is holding up or lifting. Otherwise the cost of the tower becomes too high, or the number of objects it can lift one at a time becomes too low. e^6.9 = 1000, thus a space tower today can be at most 60 x 6.9 = 414 km tall. That is tall enough that gravity on average will be 6.6% lower along the tower height, so the actual height we can reach is 440 km. This is far short of the 35,800 km required for the original concept, and future materials are not likely to be nearly 100x stronger. The maximum theoretical strength of diamond is only 45x stronger, which is still not enough. So Tsiolkovsky's original idea is not feasible on Earth, though it may be on smaller bodies.

There are still many uses for towers up to 440 km tall. They can be a launch platform for rockets, who then can avoid atmospheric drag and other losses from starting at sea-level. The tower can be the base of an elevator which hangs down from higher orbit. The tower can support a centrifugal catapult, electromagnetic accelerator, or other space launch method. They can also be communications relays, tourist attractions, and all the other uses that towers on Earth are put to.

Orbital Research Platform
Before large space elevators are built in real life, we will need much more data about how they function. A number of tether experiments have been flown, but not any of large scale or duration. An orbital research platform is therefore a needed early project. Once designed for space elevator technology and research, it can also be used for other space science. For example, a rotating structure to test elevator dynamics and payload transfer can also be used for variable gravity research. We obviously have lots of experience with 1.0 gravity, and some experience aboard space stations with 0.0 gravity, but very little data in between. How will people and growing plants do over long periods at Lunar or Mars gravity? How much artificial gravity is needed to maintain health on long missions or permanent habitats? Right now we just don't know. Finally, an orbital platform can be used to "scoop mine" the upper atmosphere for supplies. That is possible because space solar panels can generate up to 200 W/kg today. In low orbit they are in sunlight 60% of the time, and orbital kinetic energy is 31.3 MJ/kg. Therefore they can provide the energy to orbit their own mass in 3 days. With a typical life of 15 years, they can therefore supply orbital energy to 1800 times their own mass. Dropping a scoop into the upper atmosphere to mine air causes drag, and the collected gas must be accelerated to orbit velocity, but it seems solar panels can supply the energy. Avoiding launching this mass would save on current launch costs, but the idea is new and needs a lot more development. A research platform would be a good place to do it.

Rotovator Network
A Rotovator (from "rotating elevator") is a space elevator whose rotation period is significantly shorter than its orbital period. The center moves at orbit velocity, and the tips have a constant velocity around the center. At the bottom of the rotation, the tip is moving at v(orbit) - v(tip) relative to the ground, and at the top of rotation the tip moves at v(orbit) + v(tip). A payload which attaches at the bottom and lets go at the top is then accelerated by 2 x v(tip), and the Rotovator is slowed somewhat as a reaction. Conversely, if a payload attaches at the top and lets go at the bottom, it is slowed by 2 x v(tip), and the Rotovator gains velocity. For small bodies like the Moon and Mars, 2 x v(tip) can be all of the velocity from the surface to escape. For the Earth, with existing materials like Carbon fiber, a practical limit is about 6-8 km/s, while escape is 11 km/s. If you place one Rotovator in low orbit, and relay the payload to a second one in high orbit, you can achieve more velocity change with lower mass. If you also place Rotovators in Lunar and Mars orbits, you can have a network that relays payloads across the Solar System.

A Rotovator requires on-board propulsion to maintain its orbit if the payload traffic is more in one direction than the other. However, this can be electric propulsion, whose exhaust velocity is 30-50 km/s. Otherwise, in landing and taking off from a large body, you need high thrust chemical rockets with exhaust velocities of 3-4.5 km/s. Electric thrusters require ten times less propellant per increment of velocity, and even less when a rocket has a large fuel-to-payload ratio. Although a single Earth-orbit Rotovator cannot reach zero velocity relative to the ground, it can substitute a large portion of the velocity. The remainder still has to be done with a rocket or other launch system, but it can be much smaller.

The advantages of a Rotovator over a stationary elevator include:


 * Loads are at a maximum at the tips, and fall to zero at the center. Therefore on average they are half that of a stationary elevator which sees constant gravity load along its length.  Rotovators can be built with lower mass, and weaker materials.


 * Rotovators can be much shorter than a stationary elevator. For example, one with v(tip) = 3 km/s in Earth orbit would be 1835 km from tip to tip.  2 x v(tip) would provide over half the velocity range from the ground to Earth escape, while being only 3% the length.  The smaller length exposes them to less impact risk.


 * The Rotovator reduces or eliminates the climbing mechanism. If you want the maximum velocity change, in the previous example you hold on for half a rotation, which is 16 minutes.  If you want a variable velocity change, the maximum climb is 918 km to the center, or 1.5% of the time to climb a stationary elevator.

Dual Rotovator
It is not feasible for a single Rotovator to span the full 11 km/s to escape Earth using today's materials. However, it is possible to put two Rotovators on the ends of a cable or structure connecting them. Two wheels with a connecting structure resembles a bicycle, so this is humorously called a "Bicyclevator". By dividing the velocity change between two units, it is possible to span the full velocity range. However, such a Dual Rotovator would be a very large and complex construction. From an economics standpoint it is likely to be better to use a smaller orbiting elevator, and a rocket or other method to reach the lower tip.