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Space Transport and Engineering Methods/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 Millennium 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 $$-GMm/r$$ 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 $$GMm/r^2$$, the potential can be expressed as $$-gr$$. Since generally $$F = ma$$, dividing g by the object mass gives the potential per mass as $$-ar$$, 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

 * $$m = DAh$$

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

 * $$P = DAha/A = Dha$$

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

 * $$S = Dha$$ becomes $$H(scale) = h = S/Da$$

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

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

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

 * $$a = v^2/r$$

where v is the velocity and r is the distance from the center. The distance traveled per rotation period is $$2 \pi r$$, 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.

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

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 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:

 * Krinker, M., Review of New Concepts, Ideas, and Innovations in Space Towers, 2010.

2. Space Elevator

 * Alternate Names: Skyhook, Beanstalks, Jacob's Ladder, Space Bridge, Geosynchronous Towers, Orbital Tethers

 * Type: Potential Energy via Mechanical Traction

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.

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 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:

 * Pearson, J. Konstantin Tsiolkovski and the Origin of the Space Elevator, IAF-97-IAA.2.1.09, 48th International Astronautical Congress, Turin, Italy, 1997.
 * Cosmo, M. and Lorenzini, E. Tethers in Space Handbook, 3rd ed., Smithsonian Astrophysical Observatory, Dec. 1997.
 * Carroll, J. Guidebook for Analysis of Tether Applications, for Martin Marietta Corporation, Mar, 1985.
 * Multiple Authors, |Collection|NASA%20STI||17|Collection|NACA Space Elevator, search of NASA Technical Reports Server, approx 4775 items from 1916 to 2016.
 * Alpatov, A. et. al., Dynamics of Tethered Space Systems, CRC Press, Apr. 2010.

 * Rotating Elevator -

 * Carley and Moravec, The Rocket/Skyhook Combination, L5 News, March 1983
 * Ebisch, K. E., Skyhook: Another Space Construction Project, American Journal of Physics, v 50 no 5 pp 467-69, 1982.

 * 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 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 its 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:


text:
Space Transport and Engineering Methods/Guns and Accelerators

This section covers Guns and Accelerators. Although the details are quite varied, what they share is a larger fixed installation which provides acceleration to a smaller projectile or cargo. The construction of a large fixed device is justified if you use it many times and the maintenance per use is moderate.

Note: This section is continued at Guns and Accelerators 2 due to page size.

A. Mechanical Accelerators
As the name indicates, this group uses direct force from the device structure.

9 Leveraged Catapult
Alternate Names:

Type:

Description: A leveraged catapult uses a relatively large or heavy driver to accelerate a smaller payload at several gravities by mechanical means. Such devices date back to the Medieval period, but this is an updated version using modern materials. Devices such as a multiple sheave pulley or a gear train convert a large force moving slowly to a small force moving fast, and transmit the force along a cable. The mechanical advantage produces more than one gravity of acceleration. This concept may be one of the simplest to implement on a small scale. Despite the seeming simplicity of the concept, velocities of several km/s are possible, which would greatly reduce the size of a rocket needed to provide the balance of the velocity to orbit. The performance of this concept reaches a limit due to the weight, drag, and heating of the cable attached to the payload and the magnitude of the driving force, which is divided by the leverage ratio to yield the force on the payload.

Status:

Variations:

 * 9a Drop Weight - A falling mass is connected to a vehicle by a high strength cable running over a multiple-sheave pulley, cable reels with different diameters, or connected with a gearing ratio. Two types of natural locations with large height difference are possibilities - river gorges and mountain peaks. Locations such as the Grand Canyon and the Columbia River gorge have lots of vertical relief for the drop weight. At these locations the weight can consist of a large fabric bag filled with water from the river at the bottom. The bag can be emptied before hitting bottom. This reduces the weight that has to be stopped by a braking system. For mountain peak locations, the drop weight runs down a set of rails and is stopped by running into a body of water or running up an opposing hillside plus possibly wheel braking. The mountain location may be preferred because of the greater launch altitude. This example assumes a mountain with a solid weight sliding on rails:

We assume that a 15,000 kg cryogenic rocket using RL-10 engines is being thrown. An acceleration of 60 m/s^2 is tolerable by humans for the 20 seconds required to reach 1200 m/s assuming the human is in good health and properly supported. The linear path traversed would be 12,000 m (7.5 miles) at constant acceleration. The tow cable pulls with 900 kN (202,000 lb) of force on the rocket. High strength carbon fiber is available with tensile strengths of up to 6.9 GPa (1,000 ksi). Allowing for a factor of safety and a braided overwrap surrounding the fiber bundle (to protect the carbon fibers from abrasion), we assume a working stress of 3.45 GPa (500 ksi). The cross sectional area required is then 0.00026 m^2, or a circular cable 0.0182 m (0.72 inch) in diameter.

With a density of 1840 kg/m^3, the cable mass is 0.48 kg/m. For a 12,000 m long cable, the mass would be 5,760 kg without allowing for taper. Since the cable has to be accelerated also, the leading end, closer to the drive mechanism, has to be able to apply sufficient force to accelerate the rocket and all the cable in between the rocket and leading end. To a first approximation, the leading end must be 40% larger in cross section than the trailing end to account for the acceleration of the cable itself. The mean weight of the cable is then 0.576 kg/m, giving a cable mass of 7,000 kg. Something has to be done with the cable after it finishes the job of accelerating the vehicle. It can be taken care of by looping the cable back from the drive mechanism to the starting point (where the vehicle is at the start). At the completion of a launch, the loop of cable is moving at 1200 m/s, and is gradually allowed to come to a stop. Some method will be required to reduce hoop stress on the cable as it makes turns around a pulley at high velocity.

The return portion of the cable has to be able to accelerate the part of the cable past the drive mechanism at 6 g's. Given a 7000 kg lead section, we get a mass of 3200 kg. Thus the total mass accelerated at 6 g's is 25,200 kg, and the total accelerating force is 1.512 MN. Given a 45 degree slope on a mountain, we assume that the drop weight accelerates down at 3 m/s^2. Thus the gear ratio is 20:1, and the force of the drop weight on the drive system must be 30.24 MN. Since a free-falling weight on this slope would accelerate at 7 m/s, there is a 4 N/kg retarding force due to the drive system. Therefore the drop weight must be 7,560 tons. If it is a 4 meter square block of steel (about the cross section of a railroad car), it will weigh 124.8 tons per meter, and hence must be 60.6 meters long. The rails must be 12,000 m/20 long, or 600 meters long. vehicle at 3 g's to 1100 m/s. This requires a 20 km straight run of track. The rail cars needed would include:
 * 9b Locomotive Driver - A set of railroad locomotives provides the motive force, which is multiplied by a gear mechanism to a higher speed. Example: launching a 20,000 lb

 * 1 tank car for vehicle fuel
 * 1 special purpose car to carry the glider
 * 2-3 cars with tow rope guides to keep the tow rope off the ground.
 * 1 pulley system car
 * 30 locomotives in tandem.

We assume the locomotive top speed is about 27 m/s, therefore a 40:1 gear ratio will provide the desired speed at the vehicle. Locomotive traction averages 80,000 lb/engine, or 2000 lb per engine when reduced through the gear ratio. The gear-down mechanism and launch cable drum are mounted on a flatbed rail car. This car can be anchored to a foundation on either side of the railroad track to hold it in place when the combined pull of the locomotives is exerted. The starting traction of 30 locomotives is 1800 tons. Since the couplings between engines are probably not designed for this load, a set of steel cables on both sides of the locomotives are used to transmit the traction force from each engine to the gear mechanism. The vehicle is attached to the anchored rail car by a high-strength cable which is 20 km long. At 3 g's it takes this distance to accelerate to the desired speed.

Two or three rail cars are spaced out along the 20 km with towers with a pulley wheel on top, to guide the cable and keep it off the ground during the initial acceleration. The vehicle has glider type wings attached that will generate lift as it gains speed, so the vehicle will climb once it reaches 100 m/s or so. When the vehicle reaches the desired speed, the cable is released and the vehicle continues to climb under the glider's lift. Eventually the glider drops the vehicle, which proceeds under rocket power. Although 30 locomotives is a lot, you only have to lease them long enough to do a launch, after which they can return to normal railroad use.

A small prototype would consist of a single Locomotive driver. 1250 lb rocket @ 4 g peak. Final velocity = 700 m/s. Accel time = 17.5 sec distance = 0.5at2 = 6.1 km. Engine traction = 80,000 lb average @ 25:1 gear ratio.

 * 9c Jet Driver - This is similar to the locomotive case, but the gear ratio is lower since the jet can reach a higher speed on a take-off run. Example: an F-15 can tow 40,000 lb rope tension if near empty. @10:1 gear ratio can accelerate 1000 lb object @ 4 g's. Aircraft top speed on deck = 300 m/s. Object top speed in theory would be 3000 m/s. In practice would be limited by aerodynamics and cable heating (perhaps to 1500 m/s? limit is not well understood)

References:

10 Rotary Sling
Alternate names: Centrifuge Catapult

Type:

Description: In principle, this is a sling or bolo scaled up and using aerospace materials. Rotating cables can reach a significant fraction of orbit velocity on Earth, or all of orbit velocity on smaller bodies. A drive arm is driven in rotation by methods such as an electric motor, or a jet mounted on its tip. In larger versions a cable with the payload attached to the end is played out gradually as the system comes up to speed. The drive arm leads the cable slightly so the cable and payload see a torque that continues to accelerate them. When the desired payload velocity is reached, the payload releases and flies off. The cable is then retracted and the drive arm slows down. When it stops, another payload is attached. In smaller versions the cargo can be connected directly to the drive arm without a cable.

In a vacuum, such as on the Lunar surface, this is theoretically a very efficient system, as the sling can be driven by an electric motor and the mechanical losses can be held to a low value. Some method of recovering the energy of the arm and cable (such as by transferring it to a second system by using the motor as a generator), can lead to efficiencies over 60% in theory.

On bodies with an atmosphere, such as the Earth, the system is hindered by air drag. One method of reducing drag is to attach an aerodynamic shape to the cable material, so as to lower drag compared to a circular cable. Another is to mount the drive arm on the top of a large tower, so the cable is not moving in dense gas. A third is to generate lift along the cable or at the payload raising its altitude. The rapidly moving part of the cable near the payload then has less drag.

A counterweight is desirable in situations where the unbalanced load of the cargo would put too much stress on the pivot and supporting structure. The counterweight gets released at the same time as the cargo. Due to gyroscopic effects, the rotating cable will attempt to keep its axis of rotation fixed. When attached to a rotating body such as the Earth, the location and mounting of the cable will have to take that into account.

Design Example:

This example is for a terrestrial sling with a tip velocity of 1800 m/s, or about 24% of Earth orbital velocity, and a cargo of 10,000 kg including propulsion for going to orbit:

 * - Assume tip acceleration is 10 gravities (100 m/s2) for non-living cargo.
 * - Then r = 32,400 meters.
 * - For a 10,000 kg projectile at end, cable tension is 1 MN. If carbon fiber is used with a 3400 MPa design stress, then cable area is 1/3400 m2, or about 3 cm2.
 * - Cable mass is 0.6 kg/meter, adds 60 N/meter at tip. The implied scale length is 16.67 km. Acceleration falls linearly with radius, so effective radius is 16.2 km for load purposes, and cable mass ratio is 2.8:1.  Therefore cable mass is 18,000 kg.
 * - To spin up in 1 hour, we need an average accelerating force of 0.5 m/s2, or 5000 N.
 * - Drag counteracts the accelerating force. Assume the cable is shaped to be 1 cm tall by 3 cm deep. Since drag is proportional to velocity squared, and velocity goes linear with radius, drag over the entire length will be 1/3 that at the tip. At the tip drag is 0.5 Cd rho A v2. Cd = 0.04 for shaped airfoil. rho = 1.225 kg/m3 at sea level. A = 0.01 m2. v = 1800 m/s. Then tip drag = 2381 N/m, or 1/3 x 32,400 m x 2381 N/m = 25.72 MN at sea level.
 * - If we assume our drive motor can produce a peak of 4 times the average accelerating force, then peak drag can be at most 15,000 N. The motor is then driven to maintain a surplus of 5000 N force above drag. Since sea level drag is 1715 too high, we want to go to an altitude where density is that factor lower, or 7.14 x 10-4 kg/m3. This density is at 53 km altitude. The cable will drape in a curve due to the combination of radial and gravity forces, so the tower height will need to be approx 60 km.

Status: Slings and bolos are ancient devices. So far as is known, a modern one for space transport has not been built

Variations:

 * 10a Jet Driven Sling - A jet engine is mounted to the rotating arm in order to get high starting torque. The launch velocity is increased by the ratio of cargo radius to jet radius from the pivot point.
 * 10b Two Stage Sling - A second rotating cable or arm is mounted on the first one to reduce mass ratio of the entire system. This adds complexity, so is only an advantage where the mass ratio of a single stage version becomes too extreme.

References:

B. Artillery
Guns have been in use in the West since about 1300 AD. A "space gun" is merely one large enough, and with a high enough muzzle velocity, to be useful for space transport purposes. It also needs to point sufficiently above the horizon for the projectile not to hit the terrain, and lower the amount of air to travel through. The earliest illustration of using a cannon to reach orbit is from Isaac Newton's Principia Mathematica, where he was illustrating the concepts of gravity and orbits. Thus the idea is as old as orbit mechanics. In the 20th century rockets were developed for ballistic missiles and then placing payloads into orbit. They were able to reach higher velocities with lower maximum acceleration and infrastructure at the time. Even though guns have a much longer heritage, and both artillery and rockets are both still used by military forces, they were bypassed in the early part of the Space Age.

11 Solid Propellant Charge
Alternate Names:

Type:

Description: This method uses an explosive charge which vaporizes behind a projectile in a barrel. The high gas pressure generated this way accelerates the projectile to high velocity. Conventional artillery reaches speeds of around 1000 m/s. Velocities much higher than this are difficult to reach because the barrel mass becomes extreme at higher pressures, and the temperature and molecular weight of the resulting gas limits the internal speed of sound, which in turn limits muzzle velocity.

Status: Artillery has a long history and extensive use. The High Altitude Research Probe project attached two naval gun barrels in series and used relatively light shells to reach higher muzzle velocities than conventional artillery.

Variations:

References:

 * Newton, Isaac, Principia Mathematica.
 * Verne, Jules, From the Earth to the Moon.

12 Liquid Propellant Charge
Alternate Names:

Type:

Description: This is similar to conventional solid propellant artillery except liquid propellants are metered into the chamber, then ignited. Liquid propellants have been studied because they produce lighter molecular weight combustion products, which leads to higher muzzle velocities, and because bulk liquids can be stored more compactly than shells, and require less handling equipment to load. Metering the propellant flow into the barrel lowers the peak pressure relative to a detonation, leading to lighter barrels.

Status:

Variations:

References:

13 Gaseous Charge
Alternate Names:

Type:

Description: A mixture of fuel and oxidizer is introduced into a chamber, and then ignited. This is similar to how automobile engines function. This method covers projectiles directly driven by the resulting high temperature gas. Indirect drive guns are covered under Light Gas Guns on the next page. The igniter is a separate device in the basic concept. An alternate version called a Scramjet Gun uses the projectile itself as a traveling igniter. It must be moving supersonic to keep the ignition front from getting ahead of it, so it needs a gas injector at the start to get it moving fast enough.

Status: Research prototypes. Methane/air mix was used as the driver for the Livermore 2 stage gas gun. The combustion drives a 1 ton piston, which in turn compresses hydrogen working gas. Research on the scramjet gun was being performed at the University of Washington under Prof. Adam Bruckner. Research gun was located in the basement of a building there.

Variations:

 * 13a Scramjet Gun (Ram Accelerator) - Fuel/oxidizer mixture present in barrel is burned as projectile travels up barrel. If projectile shape resembles two cones base to base, as in an inside-out scramjet, the gas is compressed between the projectile body and barrel wall. The combustion occurs behind the point of peak compression, and produces more pressure on the aft body than the compression on the fore-body. This pressure difference provides a net force accelerating the projectile.

One attraction of this concept is that a high acceleration launch can occur without the need for the projectile to use on-board propellants. If the projectile has a inlet/nozzle shape (hollow in the middle) it might continue accelerating in the atmosphere by injecting fuel into the air-only incoming flow, extending the performance beyond what a gun alone can do. Another attraction of this concept is the simplicity of the launcher, which is a simple tube capable of withstanding the internal pressure generated during combustion.

References:

 * A. Hertzberg, A.P. Bruckner, and D.W. Bogdanoff, "The Ram Accelerator: A New Chemical Method of Accelerating Projectiles to Ultrahigh Velocities", AIAA Journal, Vol. 26, No. 2, February, 1988. (The original scramjet gun paper)
 * P. Kaloupis and A.P. Bruckner, "The Ram Accelerator: A Chemically Driven Mass Launcher", AIAA Paper 88-2968, AIAA/ASME/SAE/ASEE 24th Joint Propulsion Conference, July 11-13, 1988, Boston, MA. (Applications to surface-to-orbit launching)
 * Breck W. Henderson, "Ram Accelerator Demonstrates Potential for Hypervelocity Research, Light Launch,", Aviation Week & Space Technology, September 30, 1991, pp. 50-51.
 * J.W. Humphreys and T.H. Sobota, "Beyond Rockets: the Scramaccelerator", Aerospace America , Vol. 29, June, 1991, pp. 18-21.

14 Rocket Fed Gun
Alternate Names:'

Type:

Description: A rocket engine is mounted at the chamber end of a gun to produce hot gas to accelerate projectile. In a conventional gun, all the gas is formed at once as the charge goes off. In this concept the gas is produced by a rocket type engine and fills the barrel with gas as the projectile runs down it. Compared to a conventional gun, the peak pressure is lower, so the barrel is lighter.

Status:

Variations:

References:
 *  NOTE: Guns and Accelerators is continued on the next page.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
Space Transport and Engineering Methods/Thermal Engines

Strictly speaking combustion engines with expansion nozzles are also thermal engines since they rely on hot gases. For discussion purposes we placed that group on the previous page, and on this one look at non-combustion thermal engines. It is possible in theory to combine both into a single device, but this is not usually considered for practical design reasons. Performance is always important, and light molecules have higher exhaust velocity at a given temperature. Therefore the tendency is to use Hydrogen if practical since it is the lightest molecule. Liquid Hydrogen requires extremely cold temperatures (14K or -435F), so storage for long periods is not practical for a small tank. Larger systems have better surface to volume ratios and can use active cooling to keep it liquid.

Electro-thermal Engines
Electro-thermal methods convert externally supplied electric power to heating of the propellant.

36 Electric-Rail Rocket
Alternate Names: Electrothermal Ramjet

Type: Heated Gas Flow by Power Line

Description: High voltage electricity supplied by rails is shorted through a tungsten heat exchanger in the engine. This heats Hydrogen carried by the vehicle traveling between the rails. The rails are assumed to be set up on an incline. Performance would be the same as a nuclear thermal rocket, about 9 km/s exhaust velocity, since both use heated Hydrogen limited by the melting point of the engine components. It requires very high power levels for large vehicles: 44 MW / ton / g acceleration. Since power is coming from outside the vehicle, it can generate enough thrust for launch from Earth. Since the Hydrogen fuel is only stored for a short period, insulation and boiloff are not major problems. This method would compete with other ground accelerator type systems such as gas guns or electromagnetic coils.

Status: Concept only at this time.

Variations:

References:

 * Wilbur, P. J.; Mitchell, C. E.; Shaw, B. D. "Electrothermal Ramjet", AIAA paper number 82-1216 presented at AIAA/SAE/ASME 18th Joint Propulsion Conference, Cleveland, OH, 21-23 June 1982.

37 Resistojet
Alternate Names:

Type: Heated Gas Flow by Photovoltaic Array

Description: In this method sunlight generates electricity, which is used to heat gas passed over or through a heating element, often after catalytic decomposition of a storable fuel to a lighter gas. In principle it is similar to the Electric rail rocket, but is used for smaller thrusters in orbit with attached solar array as power source. This limits the thrust, so it is not powerful enough to use for launch. Compared to chemical thrusters it gets about 50% better exhaust velocity

Status: This method was used to extend the operating life of communications satellites, since they had large solar arrays for their main job. The recent tendency is to use ion thrusters, which have even better performance.

Variations:

References:

 * Louviere, Allen J. et al "Water-Propellant Resistojets for Man- Tended Platforms", NASA Technical Memorandum 100110, 1987.

Photo-thermal Engines
This group uses direct electromagnetic radiation (photons) from natural or artificial sources to heat the propellant.

38 Solar-Thermal Engine
Alternate Names:

Type: Heated Gas Flow by Solar Flux

Description: In this method sunlight is concentrated by a reflector or lens, and then heats an absorber. The absorber transfers heat to a working fluid, usually Hydrogen. The Hydrogen is then expanded through a nozzle. If the absorber is in the form of pipes, the exhaust velocity is limited to about 9 km/s. If the absorber is in the form of a particle bed, which does not require mechanical strength, refractory carbides can be used. Tantalum hafnium carbide, formula Ta4HfC5, is hypothesized to have a melting point of 4488 K (7619 F) and would set an upper limit to the particle bed method. There are obvious difficulties in testing that material as no other container could hold it when melted. The bed is rotated to keep the particles from being blown out, and Hydrogen flow is from the outside in, then out a nozzle. Sunlight is focused on the inside surface which is then the hottest point. Hydrogen dissociates above 3000K to single atoms, leading to exhaust velocities slightly above 10 km/s.

Solar concentrators can be very low mass, and use all of the solar spectrum. So they can reach higher power levels than electro-thermal thrusters. They are more suited to main propulsion rather than orbit maintenance as electro-thermal typically is. The direction of the Sun is usually not the same as the direction of thrust, and changes over time. So solar-thermal systems need a way to point the concentrators. One way to handle this is to roll the vehicle about the thrust axis plus pivot the concentrators about a perpendicular axis. The concentrators are typically large, so need to be assembled or unfolded in orbit.

Status: Components have been tested by the US Air Force. Ion and plasma thrusters have become preferred because of their 3-5 times higher exhaust velocity.

Variations:

References:

 * Gartrell, C. F. "Future Solar Orbital Transfer Vehicle Concept", IEEE Transactions on Aerospace Electronic Systems, vol AES-19 no 5 pp 704-10, 1983.

39 Laser-Thermal Engine
Alternate Names:

Type: Heated Gas Flow by Laser

Description: A laser beam from an external source is passed through a window into a chamber. It is then absorbed by a heat exchanger or is focused to create a laser-sustained plasma within the gas flow. Hot gas is then expelled through a nozzle. By using a powerful energy source external to the propellant, exhaust velocity of around 10 km/s can be reached with high thrust to mass. One method of doing this on Earth is with large, ground-based lasers. Alternately the lasers can be at ground level, and a directing mirror is located on top of a large tower. A vacuum pipe connects the two. The extra height avoids atmospheric distortion and allows more distance to the horizon. Use of laser propulsion only in an upper stage would allow smaller lasers than are required for a first stage system. Even so, powerful enough lasers are not available yet, which limits the use of the method. Other methods of supplying energy to a vehicle are likely to be less expensive.

Status: Concept only at present.

Variations:

References:

 * Abe, T.; Shimada, T. "Laser Assisted Propulsion System Experiment on Space Flyer Unit", 38th International Astronautical Federation Conference paper number IAF-87-298, 1987.
 * Abe, T.; Kuriki, K. "Laser Propulsion Test Onboard Space Station", Space Solar Power Review vol 5 no 2 pp 121-5, 1985.
 * Jones, L. W.; Keefer, D. R. "NASA's Laser Propulsion Project", Astronautics and Aeronautics, v 20 no 9 pp 66-73, 1982.

40 Laser Detonation-Wave Engine
Alternate Names:

Type: Plasma via Laser

Description: In this method the propellant is a solid block with a flat bottom. A first laser pulse evaporates a layer of propellant. A second, larger, pulse creates a plasma detonation wave, which shocks and heats the propellant layer. The layer expands against the base of the solid block of remaining propellant. The pulse pattern is repeated as soon as the plasma dissipates and the laser can reach the block again. Because no fuel tank overhead or engine is needed, the vehicles are potentially very cheap, but it requires a powerful laser to function. For example, a 10 kg vehicle accelerated at 2 g's using a 20 km/s exhaust velocity plasma wave would require a pulsed laser with an average power of 2 MW, while large industrial pulsed lasers are about 600 W. Since the propellant temperature is not limited by any container, it can be hotter than other thermal methods, and so have better performance.

10 kg is a feasible size for this type of vehicle, if the laser can be kept focused on it till it reaches orbit velocity. In theory this would deliver about 6 kg to orbit. For larger payloads, such as to carry passengers, the laser would need to scale to GigaWatt power levels, which has led to the common saying within space propulsion circles of "there is nothing wrong with laser propulsion except the lack of GigaWatt lasers". Similar power levels are generally required of all launch methods carrying metric ton or larger payloads from Earth. For example, the Space Shuttle Main Engines, of which the Space Shuttle Orbiter used three, each had a power of 9.2 GW.

Status: Some detonation experiments have been carried out at small scale in a laboratory.

Variations:

References:

 * Kare, J.T. "SDIO/DARPA Workshop on Laser Propulsion, Volume 1: Executive Summary" Lawrence Livermore National Laboratory report number DE87-003254, 1987.

41 Microwave Thermal Engine
Alternate Names:

Type: Heated Gas Flow via Microwaves

Description: For this method microwaves from an external source are absorbed by a heat exchanger or concentrated by a waveguide into the engine. Hydrogen flows through the engine, absorbs the energy, and then exits by a nozzle. A large phased microwave array on the ground can focus onto a rocket-sized area over a range of hundreds of kilometers. Given a way to couple the microwave energy to a working fluid such as Hydrogen, this type of propulsion could provide significant launch vehicle velocities. High power microwave amplifiers exist in a variety of forms with efficiencies up to 75% and power levels up to one megawatt. As compared to Laser Thermal the chief advantage is the availability of high power microwave sources at relatively low cost. A disadvantage is the much larger wavelength of microwaves vs lasers, so maintaining focus over a distance is harder.

 * Design Example: 10 meter diameter receiver, 5 cm wavelength, 1 km phased array, range = 200 km.

Status: Concept only so far.

Variations:

References:

Nuclear Thermal Engines
This group use a nuclear reactor to heat the propellant. They vary in the physical state of the reactor core (solid, liquid, or gas).

42 Solid Core Nuclear Engine
Alternate Names:

Type: Heated Gas Flow by Fission Reactor

Description: Hydrogen is heated by flowing through a critical Nuclear Reactor, then expelled through a nozzle at high velocity. The low molecular weight of Hydrogen gas allows a higher exhaust velocity, about 9 km/s, than combustion rockets. Advantages include high power levels and high total stored energy.

Issues for Nuclear Thermal include:
 * For single missions the energy of the reactor has barely been tapped by the time the hydrogen is consumed, leaving a now radioactive core to work around if refueling for another mission.
 * Radiation shielding is needed for crew and cargo. To some degree that is mitigated by the need for shielding from the natural space radiation environment.
 * Any type of nuclear device raises extensive safety and environmental issues, even if not activated until in orbit, and even if not really warranted for technical reasons. One way around this issue is to mine and use the fissionable materials away from Earth. For example, parts of the Lunar surface have Thorium concentrations of 10 parts per million. If used as reactor fuel, that can provide a net energy of 350 MJ/kg of unprocessed Lunar soil, or about 7 times the energy density of gasoline on Earth. The processed fuel of course will be 100,000 times higher energy density, but the unprocessed ore energy density is an indicator of the feasibility of mining it.

In comparison to ion and plasma thrusters, nuclear thermal has about 3-5 times lower exhaust velocity, but much higher thrust levels. The near-instant burns relative to orbit time for nuclear thermal vs. constant burn for electric thrusters reduces the latter's advantage by 30%, but are still are 2.1-3.5 higher. The choice of method would depend on the importance of fuel mass, which is usually high, so today electric thrusters are usually preferred. In comparison to solar thermal it has about the same performance in terms of exhaust velocity, but higher thrust levels.

History The two major American reactor development efforts in the 1960s were KIWI and NERVA. Together with the $328 million spent on technology development, $90 million spent on the Nuclear Rocket Development Station in Nevada, and $153 million on other test facilities, almost $1.4 billion (in then-year dollars) was spent on nuclear rocket development from 1955 to 1972 (see Appendix 2:Reference Data ). Although considerable engine testing was done, the problem of solid core fuel damage at high operating temperatures, which are desirable for performance, was not solved.

Status: Nuclear rockets reached the testing stage in the 1960's under the NERVA program. Lack of actual need in a mission and rising worries about anything nuclear led to a halt in development. Since then only minor studies have been done.

Variations:

 * LOX-Augmented Nuclear Thermal Rocket Propulsion This injects Oxygen after the Hydrogen is heated by the reactor core . This increases thrust by about a factor of 3, which is useful for initial launch, then transitions to pure Hydrogen later for higher efficiency. Exhaust velocity is lowered by about 1/3 when adding Oxygen due to the higher molecular weight of the resulting exhaust.
 * Particle Bed Nuclear Engine - Although the nuclear rocket program was stopped a number of years ago, more recent work at Brookhaven National Laboratories on fluidized particle bed reactors warrants their consideration for launch vehicles. The small particle size (.3 mm) allows high heat transfer rates to the working fluid, hydrogen, and hence potentially high thrust to weight ratios. The smaller particles also potentially solves the fuel damage problem, as there is less scope for cracking in a fine powder. Exhaust velocity is increased slightly to 10 km/s.

References:

 * Thomas, Ulrich "Nuclear Ferry - Cislunar Space Transportation Option of the Future", Space Technology (Oxford) v 7 no 3 pp 227-234, 1987.
 * Holman, R.R.; Pierce, B. L. "Development of NERVA reactor for Space Nuclear Propulsion", presented at AIAA/ASME/SAE/ASEE 22nd Joint Propulsion Conference, Huntsville, Alabama, 16-18 Jun 1986, AIAA paper number 86-1582, 1986.
 * Thom, K. et al "Physics and Potentials of Fissioning Plasmas for Space Power and Propulsion", Acta Astronautica vol 3 no 7-8 pp 505-16, Jul. -Aug. 1976.
 * DiStefano, E. "Space Nuclear Propulsion - Future Applications and Technology", 2nd Symposium on Space Nuclear Power Systems, Albequerque, New Mexico, 14 January 1985, pp 331-342, 1987.

43 Liquid Core Nuclear
Alternate Names:

Type: Heated Gas Flow by Fission Reactor

Description: In order to attain higher performance than a solid core rocket, the reactor core is raised to a high enough temperature to become liquid. Hydrogen is bubbled through the liquid, then exhausted out a nozzle. The Hydrogen is first used to cool the reactor container, and so the temperature limit is governed by that rather than the melting point of the core. Expected exhaust velocity is up to 13-15 km/s, but development and testing of this type of engine will be difficult, as test failures can easily squirt the core fluid out the nozzle.

Status: Currently a concept only.

Variations:

References:

44 Gas Core Nuclear
Alternate Names:

Type: Heated Gas Flow by Fission Reactor

Description: In this version the reactor core is hot enough to be in gaseous form. The Hydrogen flow is seeded with an absorbent material to directly absorb the thermal radiation from the core. The core is kept from leaking out the nozzle either by a transparent container (nuclear light bulb), a flow vortex, which uses the density difference between uranium and hydrogen, or by magnetic separation, which uses the ionization difference between the uranium and the hydrogen. Expected performance ranges from 15-20 km/s for a quartz container, up to 30-50 km/s for a flow vortex. The latter is in the range of ion or plasma thrusters, but development and testing would be as difficult as for liquid core due to the possibility of ejecting the core during tests. A solid core reactor producing electricity for an electric thruster would have the same performance as gas core nuclear, with fewer development problems.

Status: Currently a concept only.

Variations:

References:

 * Wikipedia article: Nuclear Lighbulb


text:
Space Transport and Engineering Methods/Bulk Matter Engines

This group of propulsion methods expel solid particles as reaction mass, or accelerate cargo directly.

45 Rotary Engine
Alternate Names:

Type:

Description: A one or two stage rotary mechanism mechanically accelerates a small amount of reaction mass, then releases it. In the two stage version, top speeds of ~6 km/s are possible. The advantage is to be able to use any available material as reaction mass. The disadvantage is the relatively low ejection velocity. There is an opportunity to mechanically augment another type of thruster by having it moving backwards relative to the vehicle center when running, thus adding up to 6 km/s to whatever the native exhaust velocity is. The duty cycle of the augmented thruster would be limited to about 25%, because the rest of the time it would be moving in the wrong direction to add velocity. This raises the issue of many on-off cycles of the thruster.

Status: Centrifuges and flywheels have long been in use. Versions optimized for ejecting mass at high velocity are still in the concept stage.

Variations:

References:

46 Coilgun Engine/Launcher
Alternate Names: Mass Driver Reaction Engine

Type:

Description: This is a type of electromagnetic accelerator. A carrier, or bucket, is accelerated by interaction of magnetic fields from 'driver' coils. The carrier holds a reaction mass/cargo, which is released. The bucket is slowed down and reused. There is no theoretical limit to velocity of this type of device - particle accelerators have reached near lightspeed - but practical limits are likely to be on the order of 10 km/s. As a vehicle engine it is not dramatically different than other electric thrusters in performance, aside from the benefit of using any bulk mass as propellant. As a fixed launcher for bulk materials, a large power supply and rapid recycling of the buckets allows very high mass delivery rates to orbit velocity. Unassisted bulk material will have an orbit that intersects the launch point, so a device in orbit will have to catch the cargo lots and add some velocity to them.

Status: This method was extensively studied as part of the "Space Colony" studies of the ~1970's, and prototype parts were built and tested.

Variations:

References:

47 Railgun Engine/Launcher
Alternate Names:

Type:

Description: A railgun consists of two current-carrying rails, and a projectile that creates a short circuit between the rails. The rails create a vertical magnetic field between them, as the current goes in opposite directions in each rail. The interaction of the field with the current in the short circuit creates a Lorentz force forward that accelerates a projectile. In a large version this would be used to launch vehicles in their entirety. In a smaller version it would eject a reaction mass and function as a propulsion engine.

Status: Railguns have been under development as replacements for conventional artillery, but are not yet operational as such. For launch vehicle acceleration, a much larger power supply would be needed, and this has so far been merely a concept

Variations: