# Section 2.1 - Structural Methods

We begin our review of space transport methods with the structures category. Surviving artificial structures appear as early as 23,000 years ago, in the form of a rough stone wall at the entrance to Theopetra Cave. The wall was probably intended to block cold winds, since that time was near the Last Glacial Maximum. A "tower whose top is in the heavens" is famously mentioned in Genesis 9:3, although the baked brick, stone, and tar technology of the first Millenium BC would not have been up to the task. It is only since the late 20th Century that structural materials like Carbon Fiber became available, that are strong enough to perform useful space transport functions. A structure only needs to be built once, but can be used multiple times. The cost per use thus goes down the more often it is used, and the longer the structural life is. This is a very different economic situation than single-use rockets, the main space transport method used to date.

## Structures in General

For space transport purposes, we want to know how useful a structural material is in and of itself, rather than as part of a vehicle with other propulsion. To find that out we can derive performance measures from the material's properties. Then we compare these measures to the transport job of reaching orbit from the surface, or changing orbits. The measures are relative to a body's gravity well or orbit velocity.

### Gravity Wells

Conceptually, a Gravity Well is related to water wells with steep sides, which you must climb if you find yourself at bottom, requiring energy to get out. For large bodies, the "depth" of a gravity well can be expressed as the surface gravity times the radius of the body, which has units of m2/sec2. This may be thought of as climbing one radius above the surface at constant surface gravity is the same amount of work as climbing to infinity under the actual inverse square decrease of gravity with distance. For Earth, that is 6,378,000 meters at 9.80665 m/ss (standard surface gravity) or 62,547,000 m2/sec2. This is derived from the formulas for potential energy and gravitational force in the Physics section:

The formula for potential energy is ${\displaystyle -GMm/r}$ where G is the Gravitational Constant, M is the mass of the large body, m is the mass of the object of interest, and r is the radius of the large body. Since gravitational force g is ${\displaystyle GMm/r^{2}}$, the potential can be expressed as ${\displaystyle -gr}$. Since generally ${\displaystyle F=ma}$, dividing g by the object mass gives the potential per mass as ${\displaystyle -ar}$, where a is the surface acceleration of gravity and r is the radius. This is a convenient form for calculations, since both surface gravity and radius are usually known for large bodies.

This derivation of gravity well depth assumes a non-rotating, uniform, spherical object. Real bodies depart from these assumptions in varying degrees. Determining the "depth" of any point on a real body can be done by corrections to the simple formula if they are small. For fast-rotating or irregularly shaped objects a numerical integration of the gravity field may be required.

### Scale Length

In physics in general, a Scale Height H is a distance over which quantity changes by a factor of the mathematical constant e (2.718...). It is most often applied to change in atmospheric pressure with altitude due to gravity. The variation in pressure due to gravity for gases also happens in solids. So for structural engineering purposes we can also calculate a scale height for columns or length for cables. A vertical column or cable with a constant horizontal (cross-section) area has a mass m of

${\displaystyle m=DAh}$

where D is the density in kg/m3, A is the cross sectional area in square meters, and h is the height in meters. The compressive force at the bottom (for columns), or tensile force at the top (for cables), due to its own weight, is found by the usual F = ma formula, where acceleration a in this case is the local one due to gravity. Dividing by the area A gives force per unit area, or pressure P as

${\displaystyle P=DAha/A=Dha}$

The tensile or compressive strength of a material, S, also has units of force per area. Equating them and solving for h then gives the maximum height or length, H, the material can sustain before failing as

${\displaystyle S=Dha}$ becomes ${\displaystyle H(scale)=h=S/Da}$

A taller constant width column or longer constant width cable will exceed the strength of the material and therefore collapse or break. Structural limits can be reached from other causes than gravity, such as centrifugal acceleration. We therefore call the general case Scale Length because it is not always due to height. As examples, common steel has a strength of 275 MPa and a density of 7800 kg/m^3, and Earth surface gravity is 9.81 m/s^2, so the scale length is 3600 meters. A very strong carbon fiber/epoxy composite column has a strength of 1300 Mpa and a density of 1650 kg/m^3 and so a scale length of 80 km. Since the Earth's radius and equivalent gravity well depth is 6378 km, the gravity well to scale length ratio for this material is 80:1.

Scale length is a theoretical value like the ultimate tensile strength at which materials fail. Real designs will always use some value below that so loads are well below the failure point. We can define the Working Length as the scale length divided by the design Factor of Safety, FS. This is a ratio of ultimate stress at failure to design stress. It is based on experience and detailed understanding of how materials fail. The chosen value is intended to reduce failure probabilities to an acceptable level for the given purpose. The Margin of Safety, MS, is the Factor of Safety - 1. It represents the amount of added stress above those caused by expected loads which the structure can withstand. Both safety values are intended to account for known and unknown variations in loads, and the actual strength of a structural element vs it's theoretical design strength. For example, a space structure may be degraded by impact damage or exposure to the space environment, and no longer be as strong as intended.

### Efficient Design

Constant area columns or cables are simple to design and calculate for small structures, but are not an efficient design for large ones. This is because the load is a maximum at only one end of a large structure - the bottom for a column and the top for a hanging cable. A constant stress, rather than constant area, design makes the best use of the material by using all of it at it's safe stress limit. Therefore the cross sectional area must vary to suit the local loads. This results in minimum weight and cost, since you only use as much structure as you need at any point. For example, the support columns of skyscrapers are typically larger and thicker near the bottom because they are supporting the whole building and its contents, while near the top floors they are supporting much less weight above them.

For a column where the mass you are supporting is at the top, each part of the column below the top has to support that weight plus the part of the column above that point. Therefore the column has to support an increasing load as you go down, and needs a larger area to keep the stress per area the same. Similarly for a cable with a mass at the bottom, each point along the cable supports that mass, plus all the cable below that point. So the cable cross section area should increase to support the increased mass as you go up. The amount of increase in both columns and cables is 1/(working length) per meter, since the working length is over how many meters the stress will increase by 100% due to the structure itself. The fractional increase is based on the sum of supported + structural mass beyond that point. The constant fractional increase in load per meter results in an exponential taper, by a factor of e (2.718...) per working length. In other words the cross section Area Ratio, AR, where h is the total length, is

${\displaystyle AR={\frac {A(bottom)}{A(top)}}=e^{h/(H(scale)/FS)}}$

In theory there is no limit on the area growth, you can just keep making the structure thicker at the bottom or top. So in theory you can build a structure of any height or length with any material. In reality, the exponential growth in area from a real material implies a similar growth in structural mass and cost. At some point the design becomes infeasible to build. Where that point is depends on what the purpose of the structure is. Feasibility is especially significant for large bodies like the Earth, where the ratio of gravity well to working length is high. This produces a large exponent in the area ratio formula if you try to span the entire gravity well with a single structure.

### Tip Velocity

Some large structures involve rotation about a center, rather than being vertical in a gravity well. This still results in a tapered design, but the loading force comes from centrifugal acceleration rather than gravity. The general formula for centrifugal acceleration at any radius on a rotating object is

${\displaystyle a=v^{2}/r}$

where v is the velocity and r is the distance from the center. The distance traveled per rotation period is ${\displaystyle 2\pi r}$ , so the velocity of any point between the tip and center is proportional to r. Thus the acceleration at any point varies linearly with radius, and the average acceleration over the radius is half that at the tip. The same type of constant stress design as for a vertical structure leads to a tapering area from center to tip of a rotating one. Instead of a near-constant gravity along the length of a vertical structure, we have a strongly varying acceleration in a rotating one. When a rotating structure is near a large body, we have gravity forces in addition to the centrifugal ones. As the structure rotates, the direction and strength of gravity will vary relative to the centrifugal acceleration of rotation. If the structure is also in orbit, it also has centrifugal acceleration of orbital motion, which can largely cancel that from gravity.

A rotating structure made of a given material will accumulate stress from the varying accelerations from center to tip. Since the acceleration grows linearly from zero at the center, the average is half the tip acceleration. Where a(tip) x r(tip) x 0.5 equals the working length, we have the same accumulated stress as a vertical structure under constant gravity. The velocity of the tip, v(tip) is then a characteristic value for the material. We can compare the characteristic tip velocity at one scale stress to the orbit velocity for the planet or body it operates on or near. This gives us a measure of usefulness for rotating structures in that location. For example, if tip velocity = orbit velocity, you can build a device on the surface which mechanically throws payloads into orbit, or reach down from orbit at zero ground velocity if tip velocity cancels orbit velocity. As with vertical structures, you can build devices which rotate faster than their characteristic velocity, but at the cost of increasing taper factor, and thus increasing mass, relative to the supported load or payload. For a large body like the Earth, large taper factors are needed to match orbit velocity, but useful designs can be built with lower tip velocities.

Figure 2.1-1. Example material properties.

### Material Properties

There are a vast number of known materials, each with their own structural properties, and new ones are developed on a regular basis. Materials Science is the field involved in understanding, developing, and applying materials. It is a well-developed subject, which can be explored in textbooks, handbooks, and online courses, such as from MIT's Department of Materials Science and Engineering.

Figure 2.1-1 gives some examples of common materials used on Earth, and a few that can be used for space projects where high strength is needed. Strength is not the only important property for material selection. When doing a detailed design you should do a full search for available materials and also consider all relevant properties before a final selection. Real designs will have a factor of safety, which is not included in this table, and will also have structural overhead for items like connector fittings and coatings. The overhead can be treated as extra loads to be supported or a reduction in the useful strength of the material.

The strongest materials are fibers which are strong in tension. In order to use them for compression structures, they have to be embedded in a matrix of some other material to give them stability. Otherwise they would simply bend like a thread. An example is carbon/epoxy, which encapsulates carbon fibers with an epoxy matrix. A typical ratio by area is 60% fiber and 40% matrix. The epoxy is relatively strong as a plastic by itself, but most of the strength comes from the fibers. We do not list carbon nanotube fibers or single-crytal solids like Diamond because we do not yet have ways to produce them in large enough pieces or quantities for large space projects. They have extraordinary strength, but until they can be mass-produced, they are not yet useful for large structures.

## A. Static Structures

Structural methods are divided into two main groups, static and dynamic. Dynamic ones are discussed in the next section. Static structures have parts which are mostly fixed in relation to each other. The structure as a whole may move with respect to the ground, such as the main truss of the International Space Station. Large structures are primarily governed in their design by the ratio of strength to density, or specific strength. That ratio is converted to a scale length by dividing by the local acceleration. Other important properties for a large structure include stiffness, temperature dependence of properties, and resistance to decay from the surrounding environment.

Some method to travel the height or length of the structure is often required. These methods include: conventional elevator (which does not need further explanation), incremental winch, linear motor or rails, and fluid transfer:

Incremental winch - A hanging cable, as is used with conventional elevators, that spans the entire height of a tall structure, ends up duplicating the loads of the main supporting structure and would be quite massive. An incremental winch has a small motor-driven trolley which pulls a length of cable behind it as it climbs up the structure. The cable is unreeled from a spool on the elevator compartment. The trolley then hooks the cable to a fixed point on the structure some reasonable distance up. The cargo elevator remains attached to the next lower point on the structure during this time. The elevator then reels in the spool like a winch to pull itself up from one attachment point to the next. By this method the cable length and mass are kept relatively low. The elevator car requires power for the winch. This can be by rails or wires attached to the main structure, solar arrays or other power source attached to the elevator compartment, or beamed power from an outside source.
Linear Drives - Instead of a cable, this uses either traction or magnetic force to climb the structure. Traction would use friction pressure against a rail or cable, or geared drivers against a linear toothed rail. Magnetic forces would use coils functioning as an electric motor, but instead of the coils being in a circle and producing rotation, as in an ordinary motor, they are in a line producing a linear motion. Magnetic Leviataion (MagLev) trains work this way. As with the winch, it needs an power source such as wires or conductive rails.
Fluid transfer - Rather than moving an elevator compartment, a pipe could be used for higher volume transfer. Dr. Dana Andrews, formerly with Boeing, suggested pumping Oxygen gas generated on the Lunar surface up to the Lunar L2 point on a Lunar space elevator. A column of Oxygen at .1 atmosphere at L2, and a temperature of 1000 K (a solar heated pipe can be used to keep the gas hot) would have a pressure of 2310 atm (234 MPa) at the bottom. So a single pressurized pipe section puts heavy loads on the design. A better approach is to have pumping stations spaced along the elevator, to keep the pressure rise at each station low. A pipe could also serve as a pneumatic system to transport cargo besides gases. The depth of the gravity well will determine the practicality of this method.

Regardless of the method used, lifting a mass against gravity or centrifugal acceleration takes energy according to the change in potential energy = mah, where m is mass, a is acceleration against which you are lifting, and h is the height. For example, a 2000 kg passenger elevator climbing 10 meters per second in Earth gravity requires 2000 x 10 x 9.81 = 196,200 Watts.

### 1. Towers

Alternate Names: Space Tower, Megastructure
Type: Potential Energy via Mechanical Traction

Figure 2.1-2. Tokyo Skytree.

Description:

Towers are self-supporting compression structures, whose main purpose is not habitation. When the main purpose is to house people, we call them tall buildings, or Skyscrapers. The Eiffel Tower is probably the most famous example, but they are also commonly used as transmitting towers, such as the w:Tokyo_Skytree (Figure 2.1-2). As noted in the example material properties table above, advanced aerospace materials have scale lengths of many kilometers, so it is possible to build towers in that size range. Such towers can be used as a high altitude astronomical platform, a launch platform for a propulsive vehicle, or a support structure for an accelerator system.

Design - In theory a tower of unlimited height could be built. At some height, though, the exponential growth of the base area and total structural weight and cost makes it impractical to go higher. For example, let us assume a structural factor of safety of 2.5, and that a launch tower is used many times. The tower mass might then be limited to 100 times the rocket and equipment mass at the top. A carbon fiber/epoxy tower on Earth would then be limited to about 150 km in height.

In a real structure, the load, the mass you are supporting besides the structure itself, probably won't all be at the top. Design calculations then have to account for where the loads are distributed along the height. Additionally, for the bottom 20 kilometers or so on Earth, wind loads, ice build-up, and other environmental effects have to be accounted for. Above 20 km, ultraviolet light and atomic oxygen can attack certain structural materials. This is not commonly a problem at low altitude, so you need a protective layer for the structure or choose different materials.

A large tower would typically be built as a truss, like the Tokyo Skytree example. The space between the vertical elements in a truss gives it stability, but it does not have to be a solid structure to support most reasonable space-related loads. Truss elements will bend if too much load is placed along their length - imagine pressing on the ends of a drinking straw or spaghetti noodle. Stiffness or Elastic Modulus is a material's resistance to this bending. To make best use of the material strength, the design is often made so that buckling (failure from bending) and crushing (failure from direct load) happen at the same time. For high strength materials this results in individual elements roughly 20 times longer than their smallest cross section. It also results in the tower as a whole being roughly 20 times taller than the base width. These are only generic values, the real ratio would be determined by structural analysis of the actual design conditions.

Construction - These types of towers can be built 'from the top down' in order to avoid human construction work in a vacuum. In this process, the top section of the tower is assembled at ground level. Hydraulic jacks then raise the tower up by one section length. The next section down is then installed underneath the top section. The progressive jacking process is repeated for the whole tower height, so all the construction work takes place near ground level. Special anchoring provisions are required to stabilize the tower while being built in this fashion. Since the tower is typically tapered, anchor masses, jacks, and assembly cranes must gradually move outward from the center as the tower grows. If remote controlled robots are used for construction, then the standard method of building from bottom to top can be used. Wind loads are significant below 20 km altitude, where the product of atmospheric pressure and wind speed produces maximum Dynamic Pressure. To reduce these wind loads, the structural elements can be enclosed in pivoting airfoils, which have a much lower Drag Coefficient than circular or triangular struts.

Status:

The tallest man-made above-ground structure is the Burj Khalifa, in Dubai at 830 m (2723 ft or 0.51 miles ). The tallest freestanding structure is the Magnolia Tension Leg Platform, which is 1580 m ( 5200 ft) from the sea floor to the top of the surface platform. The tallest building under construction is the Jeddah Tower, in the Saudi Arabian city of the same name. It is estimated to be 1000 meters (0.63 miles) high when completed. A number of larger Tall Buildings and Structures have been proposed but not yet started construction. Civil engineering and construction are very well developed fields. Suitable materials exist for multi-km tall towers, though they may require a advances in construction techniques. The economics of such towers is more limiting at the present time.

Variations:

• 1a Unguyed Tower - This type is self-supporting from its base, like a Pine Tree. Like trees, such towers may need an extensive underground structure to distribute the weight and tipping forces like wind. The base diameter will typically be 5-10% of the height to prevent bending. In the lower part of the tower, wind loads may require the base to spread more than the upper part, which only depends on buckling for its necessary width. This approach assumes that most of the loads on the tower are vertical, as in an elevator riding up and down the tower height. Carbon-epoxy materials can support up to 700 MPa in compression. The largest rocket in development is about 2.55 million kg in mass. If we allow 10 million kg total for an example use like rocket launch platform on top of the tower, the load is about 100 MegaNewtons (MN). This load can then be supported by 1/7 of a square meter of cross section of carbon-epoxy columns. This is far less than the minimum launch platform size of about 2500 square meters. So the columns can be hollow tubes, and the tubes spaced apart from each other in an open truss (Figure 2.1-2). The spaces between the vertical structural elements can be used for other purposes.
• 1b Guyed Mast - Masts are structures stabilized by diagonal supports like ropes or wires, as in the Rigging of sailing ships. Diagonal supports can better resist sideways forces like wind. This is commonly done with television and radio towers because the antenna itself is not very heavy, and so the main loads are winds on the lightweight tower structure. A very tall structure may combine diagonal supports in the lower 20 km, where wind is significant, and be self-supporting in the upper portion.
• 1c Series of Towers - An electromagnetic accelerator for people and delicate cargo may be hundreds of km long, with the upper end many km high to avoid aerodynamic drag and heating, forming a long ramp. To support the device you can use a series of towers of increasing height as supports, with connecting structure similar to a suspension bridge between them.
• 1d Inflatable Tower - Many materials are stronger in tension than compression, so concepts like the ThothX Tower have been proposed, using internal gas pressure to put the structure in tension and support loads.

References:

### 2. Space Elevator

Alternate Names: Skyhook, Beanstalks, Jacob's Ladder, Space Bridge, Geosynchronous Towers, Orbital Tethers
Type: Potential Energy via Mechanical Traction

Figure 2.1-3. Basic space elevator concept.

Description:

In 1895, astronautics pioneer Konstantin Tsiolkovsky was inspired by the recently built Eiffel Tower. He envisioned a tower that would reach all the way to Geostationary Orbit, where orbit period matches the Earth's daily rotation. We now refer to any similar concept as a Space Elevator, because you could use an elevator rather than a rocket to reach space. Since the top end matches local orbit velocity, you can merely let go and are in orbit. Tsiolkovsky's concept was more a thought experiment than a practical design, because in 1895 no materials existed with anywhere near the required strength

A more modern version of the concept (Figure 2.1-3) assumes a cable in tension rather than a tower. This is because fibers like PAN-derived carbon are currently the highest strength available bulk materials, and bulk quantities are needed to build a space elevator. The part of the elevator below stationary orbit sees more gravity than centrifugal acceleration, and would fall down if unsupported. Therefore this version requires a counterweight above that orbit, where centrifugal acceleration is higher than gravity, and the weight then pulls upward on the attached cable. This version of the space elevator is often used in popular illustrations, but early 21st century materials are still not strong enough to make this size elevator practical. Smaller versions with shorter cables, however, can result in feasible designs. We can call these Staged Elevators since they only provide part of the velocity to reach orbit, in the same sense that the stages of a multi-stage rocket do. A different transport method or multiple elevator stages are needed to do the full job of reaching orbit.

If staged elevators are not connected to the ground, they are not required to be centered on a 24 hour orbit, nor rotate at the same rate the Earth does, creating a whole class of possible designs. They can be located in whatever orbit is needed, and will appear to be in motion when viewed from the ground. For bodies smaller than the Earth a full elevator is more feasible, because the lesser gravity well can be spanned with existing bulk materials. If future materials about 3 times stronger than current carbon fiber become available, the original single-stage elevator would become feasible from a structural materials standpoint. It would still be a very large construction project, and have other technical challenges to overcome. The rotation state of the elevator can be vertical, which is one rotation per orbit when seen from inertial space; swinging, where it varies by some angle from vertical but does not do a full rotation relative to the ground; or rotating where it does rotate relative to the ground. The rotation sense can be forward, where it is the same direction as the orbit around the planet, or backward where it is opposite. Normally it would be forward, since that results in lower velocity at the bottom end relative to the ground, and higher velocity at the upper end for injection into transfer or escape orbits.

For any type of space elevator, the structure can be used multiple times over it's design life. So the construction cost is divided by the number of times it is used. The larger the structure is, to gain more performance, the higher the cost. When maintenance and operations are added to the construction cost, there will be an optimum size and cost for a given traffic level. Mass and cost grow exponentially with size and performance, and construction cost per use only decreases as the inverse of the number of uses. So at some point the lower cost from many uses is overcome by the increasing mass and cost of a larger structure no matter how many times it is used. Therefore economics is a limiting factor on large space elevators.

Figure 2.1-4. Staged elevators: rotating (left) and vertical (right).

Gravity and Stress - Where a tower has to resist the compression force created by gravity against the solid surface of a body, a space elevator needs to resist the tension force created by the difference in gravity between it's parts, or from it's own rotation. Structural elements can store and transfer momentum and potential energy to vehicles or cargo, and support objects away from the structure's center of mass or under rotation. Structures in orbit will naturally tend to align vertically (Figure 2.1-4, right) because gravity forces decrease as the square of distance. So the lower end of a vertical cable has a lower potential relative to the center by more than the higher end sees a higher potential. The total energy of a vertical cable is then less than that of a horizontal one, so it tends to fall into that state. The difference in gravity (otherwise known as tides) provides tension to keep the structure extended.

Staged elevators can be built any size up to the practical limit of the materials used. In the lower limit of zero length a space elevator reduces to a simple object in orbit. For intermediate lengths and vertical orientation, the velocity of the bottom end is the velocity of the center times bottom/center distances r from the center of the body. This simply reflects that the center and bottom travel paths of length 2πr in the same orbit time. The bottom's velocity can be further reduced if you rotate the entire cable such that the bottom end travels opposite the orbit direction relative to the center (Figure 2.1-4, left). The tip's maximum rotation velocity relative to the center is then governed by the mass and cost of the structure growing exponentially as you make it more capable. For the Earth, and current bulk materials, it is not practical to counter all of orbit velocity with rotation, but about half can be. On smaller bodies the entire velocity can be countered by rotation, so that the bottom end momentarily comes to rest relative to the body's surface.

The remaining velocity of the bottom end relative to the surface has to be provided by some other method. When a body rotates, like the Earth does, some of the remainder can be supplied that way. In our planet's case, equatorial rotation velocity is 465 m/s, or 5.88% of orbit velocity. The roughly half of orbit velocity not supplied by the elevator's or the Earth's rotation is a substantial improvement over needing to supply all of it. The difficulty of building a transport system like a chemical rocket is also non-linear with velocity. For example, if it could provide 3.5% of launch mass as payload to orbit doing the whole job, it could increase payload to 27% if it only needs to do half, an increase 7.7 times. By using a rocket + elevator as a two-stage system, the sum of smaller mass exponents is less than each exponent by itself, so the total cost and difficulty is less using both than using either one for the entire job.

The rocket stage does not place itself fully in orbit. It docks temporarily at the tip of the cable, and only the cargo travels further using the elevator. This is less total energy per delivery than if the rocket stage hardware had to travel all the way to orbit. The elevator cable serves as a momentum bank to store orbital kinetic energy, which can be transferred to the payload. The kinetic energy can be stored by running an electric propulsion system, which is much more efficient than conventional rockets. Using an elevator stage lowers the overall difficulty of reaching orbit, and can lower the overall cost if well designed. Material strength to density ratio is the critical criterion for designing these types of transport systems. Their mass is highly non-linear with strength because doubling the strength reduces the exponent part of their mass ratio by half.

Structural Dynamics: - The forces affecting a space elevator design vary with time, so they are dynamic forces rather than static ones. This includes arriving and departing vehicles, internal movement of cargo along the structure, deployment of extension cables if used, thrust for orbit maintenance and rotation, varying gravity in an elliptical orbit or if the elevator is rotating, varying tidal forces from the Sun, Moon, or planetary satellites, and thermal stress from going into and out of shadow as it orbits. Elevator designs can be truss-like, with sufficient compressive structural elements to keep a stable shape against these varying forces. They can also be cable-like, with primarily tension elements, and the structure allowed to flex with the applied forces, or they can be a mixture of the two. Active damping for vibrations can be applied with shock absorber/spring combinations or with thrusters along the structure. Design for dynamic forces is similar to the design problem of a suspension bridge, which must withstand static forces from its own weight, and dynamic ones from vehicle traffic and varying winds. In both cases, the design must not exceed safe working stresses at any point in the structure, under any combination of forces.

Because of the typically high slenderness ratio (ratio of length to maximum width) and varying forces noted above, the structural dynamics will be complex and require a good theoretical understanding and likely computer simulation. A further complexity is unlike terrestrial skyscrapers, which are constructed empty and then loaded when complete and not usually changed afterwards, a space elevator may grow over time while already operating. This is likely because a large elevator can assist in it's own construction by reducing the work for a launch system, and can help offset it's cost by operating as soon as possible. So instead of analyzing a completed building and then checking construction loads do not exceed design loads, a growing elevator would need analysis over a continuous range of sizes.

Maintenance and Repair - Space elevators, like large structures on Earth, are subject to environmental degradation and occasional sudden damage. These include atomic oxygen, electrostatic discharge, solar UV and high energy particles, trapped radiation belts, impacts from natural meteoroids and human-made orbital debris, and accidental vehicle collision or pressurized system failure. For long-term operating life and safe operation, a space elevator has to be designed for all these causes, with a program for maintenance and repair. In case of catastrophic damage, the design should minimize risk to people and property.

Status:

The Elevator on Earth dates as early as Archimedes in 236 B.C. The modern safety elevator was introduced in 1852 by Elisha Otis, and a descendant of his company is still the largest manufacturer of vertical transport. Ropes and cables have long been used on Earth for hoisting loads and stabilizing tall structures such as ship masts and transmitting towers. A space elevator refers to a complete transportation unit. A Space Tether refers to a cable in space that has a number of possible uses, one of which is the structural element of a space elevator. A number of Space Tether Missions have been flown as experiments, but not yet as an operational transportation system. The largest rigid structure in space to date is the ISS Integrated Truss Structure, which is 108.5 meters long. Taller structures on Earth await economic reasons to build them, they have not reached the limits of available materials. Space elevators require enough traffic to similar orbits to justify their construction. Significant traffic exists as of 2016 to synchronous orbit, but not enough to justify a synchronous-capable elevator system.

A Variable Gravity Research Facility has been proposed in Earth orbit to study the effects of partial gravity on people and growing plants. Such partial gravity levels are found on the Moon and Mars, and it is currently unknown what gravity level is necessary for health and plant growth on long missions. Such a facility would include large space structures to generate artificial gravity, and can also serve as a test bed for tether dynamics and operations. It would be a step towards required knowledge to build an operational space elevator system.

Variations:

• 2a Orbital Vertical Elevator - This is the most commonly presented space elevator concept. It has a cable kept vertical in smaller versions by tidal forces, or in larger versions by sufficient cable or counterweight past GEO to apply tension to the part below GEO. Mass grows exponentially with gravity well depth. Therefore a compressive tower built up from the ground meeting a cable from above results in lower total mass, because it splits the structural task into two smaller exponentials. Despite that, current materials are not sufficient for a full vertical elevator on Earth. They are for smaller bodies such as the Moon or Mars.
• 2b Momentum Transfer Slingshot - If a payload is released from the end of a vertical elevator, the other end of it's orbit will be changed about 7 times the initial distance from the elevator center of mass. This is because while attached the payload is forced to move at a different velocity than a free object would at that altitude. Once released, it then follows the free orbit defined by its release velocity. This variation increases the orbit change by adding partial rotation and dynamic extension of a cable.
A variation from vertical cables is the orbital slingshot. This would take advantage of the tendency of a long object to auto-rotate from horizontal to vertical orientation about the center of mass due to "tidal" effects. A relatively light-weight vehicle, launched conventionally, would dock with a much more massive "orbital momentum bank" (largely consisting of discarded rocket stages left at the bank with each launch), and be hooked to a cable reel. The vehicle would be pushed out to a somewhat higher orbit, where it would fall behind the momentum bank, with cable being paid out at a matching rate. After sufficient tether has been paid out, it would be braked to a halt, putting it under tension. The momentum bank would slow and fall inward, while the vehicle would be accelerated and fall outward. It is released at the desired orientation and velocity to transfer to a higher orbit. Unlike an "elevator" system, the tether need not be long enough to continuously reach the ultimate orbit, as the vehicle will be "slung" outward up to 14 times the cable length.
The momentum bank loses velocity in this maneuver, but could use highly efficient solar-powered electric engines (plasma, ion, or magnetic) to recover that loss over an extended period. Multiple momentum banks can be used in series the achieve higher orbits or greater final velocities. If the momentum bank uses an elliptical orbit (cheaper for a rocket launched vehicle to intercept), it may be possible to insert objects into near-circular orbits by slinging at apogee. The vehicle can also take on fuel at the momentum bank, as the empty rocket stages already have propellant tanks that can be re-used. The slingshot approach has a moderate size and velocity capacity.
• 2c Orbital Rotating Skyhook - This is an idea devised around 1980, where a cable is kept in tension by sufficient rotation rate. On smaller bodies, where the cable end can dip low enough to grab cargo and lift it to orbit, the Skyhook name is generally used. For Earth reaching that low is difficult because of the high tip velocity and mass needed. Instead a vehicle coming from the ground provides enough velocity to meet a slower rotating tip. This version is often called a Momentum Exchange Tether or Rotovator (rotating elevator). The momentum being exchanged is between a vehicle/cargo and the and the elevator system. Again, both launch vehicle and Skyhook mass ratios are exponential in velocity, so splitting the job lowers the overall difficulty.
• 2d Atmospheric Elevator - For this concept an aircraft or balloon/airship uses a cable to lift an object to altitude, after which it continues to orbit by other methods. With an aircraft this can be a simple tow cable where one vehicle pulls another, or a cable system which dynamically snatches and accelerates a vehicle, possibly tossing it higher than the aircraft flies. It requires less modification of the towing aircraft and not having to deal with combined aerodynamics. For an airship type lifter, it avoids having to build a tower that height, although cargo mass is relatively limited.

References:

• Rotating Elevator -

• Baracat, William A., Applications of Tethers in Space: Workshop Proceedings Vols 1 and 2. (Proceedings of a workshop held in Venice, Italy, Octover 15-17, 1985) NASA Conference Publication 2422, 1986.
• Anderson, J. L. "Tether Technology - Conference Summary", American Institute of Astronautics and Aeronautics paper 88-0533, 1988.

#### 3. Aerostat

Alternate Names: High altitude balloon, Airship, Inflatable Tower

Type: Potential Energy by Aerodynamic forces

Description: This method uses lift generated by pressure and density differences but not primarily from velocity such as wing lift. One approach to minimizing drag and gravity losses for a launch vehicle is to carry it aloft with a high altitude balloon or airship. Research balloons have carried ton-class payloads in the range of 15-30 km high, which is above the bulk of the atmosphere. Another approach that has been proposed is to use pressure-supported structures of great height. The highest strength materials are strong in tension, so an inflated structure in theory can support itself. Wind loads on a large pressurized structure are a major design issue. If a less dense gas is used than the surrounding atmosphere, the structure will be partially buoyant and not require the same scaling as one that depends on compressive strength. Sufficiently large structures, which would have low surface to volume ratios, could float just from heating the interior air.

Status: Balloons, airships, and pressure supported structures have been in use for a number of years, and some experiments have been done to launch a rocket from a balloon. They have not reached orbit yet.

Variations:

• 3a Balloon Carrier - A device producing lift and carrying an instrument package or launch vehicle, but not a propulsion system of it's own. They have been used extensively on Earth for science, and been proposed for other planets.
• 3b Airship - A device combining buoyant lift and and some combination of aerodynamic lift and forward propulsion.
• 3c Orbital Airship - This concept has been proposed by JP Aerospace. It involves a very lightweight airship which starts from a floating platform and accelerates via solar-electric thrusters to orbital velocity. It is not known if this is technically possible.
• 3d Geodesic Sphere - A triangulated frame supporting a pressure skin can float with merely a temperature difference between inside and outside if sufficiently large. Since structure mass goes with area, and lifting force goes with volume, if built sufficiently large it will float.
• 3e Pressure Supported Tower - Uses lift force from higher interior pressure to raise a structure. This can be generalized to pressurizing any structural element to help support it.

References:

#### 4. Low-Density Tunnel

Alternate Names:

Type: Kinetic Energy by Aerodynamic Forces

Description: Traveling to or from a large body with an atmosphere, such as the Earth, can produce large losses from drag and heating. Aerodynamic drag has a gas density factor in it's formula. This concept reduces or avoids those losses by using a lower density gas or vacuum. Lower density can be obtained by using a gas with a lower atomic weight, such as Hydrogen, or by pumping out some or all of the gas. This is not a transport method in and of itself, but rather a way to avoid losses.

Status: Low pressure pipes are a common device. It has not been tried for space transport.

Variations:

• 4a Light Gas Tunnel - One or more light gas balloons or pipes are strung along the path of a vehicle or projectile. The gas has a lower density than air. The formula for drag is 0.5*C(d)*Rho*A*v^2, where Rho is the density. Thus the lower density will lower drag. High speed travel through any gas will develop shock waves, so the size of the projectile relative to the size of the tunnel needs to be small enough that the shock waves will not damage the structure.
• 4b Evacuated Tunnel - An evacuated tunnel is supported up through the atmosphere by a combination of towers or it's own lift from displacing air.. A launch system such as an electromagnetic accelerator fires a projectile up through the tunnel. Drag losses are minimized within the tunnel, and are low in the remaining part of the atmosphere beyond the tunnel. The top end requires some way to keep air from flowing in and filling the tunnel - such as a hatch that remains closed until the accelerator is about to fire.

References:

#### 5. Magnetically Supported Structure

Alternate Names: Startram

Type: Magnetic Storage by Magnetic Field

Description: A static or time varying magnetic field produces a force to support a structure. For example, a series of large superconducting coils stacked so they repel each other and support a cargo. Alternately current carrying wires generate repulsion between the ground and the structure.

Status: Startram is a concept proposed using magnetic levitation, but has not reached experimental versions yet.

Variations:

References:

## B. Dynamic Structures

Static structures rely on constant forces such as from the strength of materials to hold themselves up. Dynamic structures rely on the forces generated by rapidly moving parts to hold up the structure. The advantage of this approach is it can support structures beyond the limits of material strengths. The disadvantage is that if the machinery that controls the moving parts fails, the structure falls apart.

#### 6. Fountain/Mass Driver

Alternate Names:

Type:

Description: An electromagnetic accelerator provides a stream of masses moving up vertically. A series of coils decelerates the masses as they go up, then accelerates them back down again, at a few times local gravity. When they reach bottom, the accelerator slows them down and throws them back up again, at a high multiple of local gravity. Thus the accelerator is many times shorter than the fountain height. The reaction of the coils to the acceleration of the fountain of masses provides a lifting force that can support a structure. The lifting force is distributed along where the coils are located. This can be along the length of a tower, or concentrated at the top, with the stream of masses in free-flight most of the way.

Status:

Variations:

References:

#### 7. Super-Orbital Mass Stream

Alternate Names: Launch Loop

Type:

Description: A strip or sections of a strip are maintained at super-orbital velocities. They are constrained by magnetic forces to support a structure, while being prevented from leaving orbit. A vehicle rides the strip, using magnetic braking against the strip's motion to accelerate. Several concepts using super-orbital velocity structures have been proposed. One is known as the 'launch loop'. In this concept a segmented metal ribbon is accelerated to more than orbital velocity at low Earth orbit. The ribbon is restrained from rising to higher apogees by a series of cables suspended from magnetically levitated hardware supported by the ribbons. The ribbon is guided to ground level in an evacuated tube, and turned 180 degrees using magnets on the ground. A vehicle going to orbit rides an elevator to a station where the cable moves horizontally at altitude. The vehicle accelerates using magnetic drag against the ribbon, then releases when it achieves orbital velocity.

Status:

Variations:

• 7a. Birch Ring - Consists of two parts. One is a constellation of one or more low-altitude "geostationary" satellites with a space elevator attached, at a distance from the ground that would be LEO in a normal orbit. This constellation of satellites (which can also called geostatites, since they are stationary with respect to the ground) are kept from falling despite to their low velocity, by a pelletized or solid mass stream that weighs more and is moving at a rate somewhat higher than orbital velocity. The mass stream maintains a lower orbital altitude by deflection from the statite constellation onto shorter arcs. In the case of a low-mass stream, the hyperorbital path is close to a straight line, and a higher number of statites is needed to divert it around the earth without cutting through the atmosphere (in a polygon-like pattern). In the case of a high-mass stream it moves only slightly higher than orbital velocity, but has a lot more mass than the statites.
Alternate Names: Orbital Ring System (ORS), Jacob's Ladder, Skyhook

#### 8. Multi-Stage Space Elevator

Alternate Names:

Type:

Description: A multi-stage space elevator has more than one structural element, with the parts in relative motion. For example, a vertically hanging cable in Earth orbit can have a rotating cable at it's lower end. The advantage of such an arrangement is to lower the mass ratio of cable to payload compared to a single cable. The mass ratio of a rotating cable is approximately proportional to exp(tip velocity squared). If two cables each supply half the tip velocity, then the ratio becomes exp(2(tip velocity/2)squared), which is a smaller total mass ratio. Another feature of a multi-stage elevator is that the tip velocity vector of the two stages add. Since one rotates with respect to the other, the sum of the vectors changes over time. Given suitable choices of tip velocities and angular rates, one can receive and send payloads with arbitrary speed and direction up to the sum of the two vectors. The dynamics of a multi-stage elevator are complex.

Status:

Variations:

• 8a Hanging/Rotating Elevator - This consists of a vertical/nonrotating space elevator structure with a rotating second stage at one or both ends. This is more suited for within a gravity well, where the gravitational gradient will stabilize the first stage.
• 8b Rotating/Rotating Elevator - This consists of two stages, both of which are rotating, to get reduced mass ratio for a given velocity. This is more suited for free space application where the lack of varying gravity across the structure will simplify the dynamics.

References: