# Section 2.1 - Structural Methods

We begin our review of transport methods with the structures category. Human-made structures appear as early as 23,000 years ago [1], and the idea of building something to climb to the sky is ancient. It is only recently, however, that modern structural materials have become strong enough to perform useful space transport functions, as well as their historical uses on Earth. Since a structure only needs to be built once, but can be used multiple times, it's relative cost goes down the more often it is used, and the longer the structural life is. This is a very different economic situation than past rockets, which were only used once and then disposed of.

## Material PropertiesEdit

We want to know how useful a structural material is for space transport in and of itself, rather than as part of a vehicle with other propulsion. For that we derive measures from the material properties to compare to the job of leaving a given planet or body. These measure are relative to the body's gravity well or orbit velocity.

#### Gravity WellEdit

Conceptually, 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 the radius of the body at the 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 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 the gravitational force is $GMm/r^2$, the potential can be expressed as minus the gravitational force times r. Since generally $F = ma$, dividing by the object mass gives the gravity well per mass as $-ar$, where a is the surface gravity and r is the radius. This is a convenient form for calculations, since both surface gravity and radius are usually known.)

#### Scale LengthEdit

A vertical column or cable with a constant area has a mass

$m = DAh$

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) 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 the material can sustain before failing as

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

This is called the scale length. For example, 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, thus 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 thus a scale length of 80 km. Since the Earth's radius and equivalent gravity well depth is 6378 km, the scale length/gravity well ratio for this material is 0.0125.

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 the loads are well below the failure point. We define the Working Length as the scale length divided by the Design Factor of Safety FS. This is a factor based on experience sufficient to reduce failure probabilities to an acceptable level for the given purpose. Where 1 represents the design stress, the Factor of Safety - 1 is the Margin of Safety, the amount of strength above the expected loads to account for both known and unknown variables in loads and the actual strength of a structural element vs it's theoretical design strength.

#### Design EfficiencyEdit

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.

In a column where the weight 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 weight at the bottom, each point of the cable supports that weight, plus the cable below that point, so the cable are should increase as you go up. The amount of increase is 1/(working length) per meter, since the working length is how many meters the load increases by 100% of the allowed stress. The constant percentage increase in load per meter results in an exponential taper, by a factor of e (2.718...) per working length. In other words the area ratio AR is

$AR = \frac{A(bottom)}{A(top)} = e^{H/(h(scale)/FS)}$, where H is the total height.

Since in theory there is no limit on the area growth, you could build a structure of any height or length with any material. In practice, the exponential growth in area from a real material leads to a practical limit due to mass or cost. This is especially true for large bodies like the Earth. Where that limit falls depends on what the purpose of the structure is.

#### Tip VelocityEdit

Where the design is a system in rotation about it's center of mass, rather than vertical in a gravity well, we still have a tapered design, but the loading force is centrifugal acceleration rather than gravity. The 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 cable leads to a tapering area from center to tip, except instead of a constant gravity along the length of a vertical cable, we have a varying acceleration in the rotating cable.

We can set up a ratio of characteristic tip velocity to orbit velocity for a given rotating design and the planet or body it operates on or near. This gives us a measure of usefulness for rotating devices in that location. The characteristic tip velocity is that produced under 1 scale length of load (in average acceleration x length). You can build devices which rotate faster, but at the cost of increasing taper factor, and thus increasing mass, relative to the supported load or payload.

### Table of Material PropertiesEdit

This table includes ultimate strength and other properties of selected materials, as examples for the structural methods that follow. Strength is not the only important property for material selection. If doing a detailed design you should do a full search for available materials and also consider all design factors 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.

## A. Static StructuresEdit

Static structures have parts which are mostly fixed in relation to each other, although the structure as a whole may move with respect to the ground. 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 height 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, and fluid transfer.

Incremental winch - With tall structures, a hanging cable such as used with conventional elevators which spans the entire height ends up duplicating the loads of the supporting structure and would be quite massive. Instead this method 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 independent power for the winch. This can be by rails or wires embedded in the structure, solar arrays or other power source attached to the elevator compartment, or beamed power from an outside source

Linear Motor - 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 in the winch it needs an external power source such as 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 tower, 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 by the potential energy formula PE = 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. Large Towers (Compression Structures)Edit

Alternate Names: Skyscrapers, Megastructures

Type: Potential Energy via Mechanical Traction

Description: As noted in the 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 observation platform, a launch platform for a propulsive vehicle, or a support structure for an accelerator system. 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. If we assume a factor of safety of 2.5 and a practical limit of the tower weight is 100 times the payload weight, a carbon/epoxy tower on Earth would thus 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, so the calculation will has to account for additions of load masses 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 antenna masts or the Eiffel Tower. 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 payload masses. 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 Modulus of Elasticity is what resists this bending. To make best use of the 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. Those are only generic values, the real ratio would be determined by the designer based on actual design conditions.

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. Jacks raise the tower up by one section length. The next section down is then installed underneath. The 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. If remote controlled robots are used for construction, then the standard method of building from bottom to top can be used. To reduce wind loads in the lower 20 km, 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 oil platform, which is 1580 m ( 5200 ft) from the sea floor to the top of the surface platform. Some engineering/ architectural studies on very large towers have been done. No attempts to build anything over 1000 meters above ground are known. Versions of this concept are within current technology for structural materials, although it may require an advance in construction techniques.

Variations:

• 1a Unguyed Tower - In an unguyed tower, the base of the tower needs to be 1/10 to 1/20 of the tower height to avoid buckling (uncontrolled bending of structural elements). In the lower part of the tower, wind loads may require the base to spread at a greater slope than the upper part, which only depends on buckling for its necessary width. This approach assumes that most of the loads on the tower act vertically, as in an elevator riding up and down the tower height. If it is built as an open truss, as is likely, the spaces between the vertical structural elements can be used for other purposes.
• 1b Guyed Tower - If the loads are substantially sideways the tower may be stabilized by a set of guy wires that spread out at a 30-45 degree angle. 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.
• 1c Series of Towers - A very long, tall structure, such as a 300 km long electromagnetic accelerator, may use a series of towers of increasing height as supports, with connecting structure similar to a suspension bridge between them.

References:

#### 2. Space Elevator (Tension Structures)Edit

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

Type: Potential Energy via Mechanical Traction

Description: Konstantin Tsiolkovsky first envisioned a space elevator in 1895. This was theorized to reach from the ground all the way past geosynchronous orbit. Since geosynchronous by definition has the same orbit period as the Earth's rotation, the structure as a whole appears to be motionless, and to reach space you merely ride an elevator up. This theoretical construct is often used in popular illustrations of space elevators, but early 21st century materials are not strong enough to make full GEO space elevators practical. Smaller versions with shorter cables, however, do result in feasible designs. We will call these Partial Elevators since they only do part of the job of going from ground to orbit. If they are not connected to the ground, they are not required to be centered on a 24 hour orbit. 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 of the smaller gravity well.

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 created by the difference in gravity between it's parts, or from it's own rotation. Structural elements 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 because gravity forces increase as the square of distance. Thus 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 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.

Partial 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 the orbit velocity of the bottom end is the velocity of the center times the ratio of bottom to center's distance from the center of the body. That velocity can be further reduced if you rotate the cable such that the bottom end travels opposite the orbit direction. The design limits for this type of elevator is then governed by the mass and cost of the structure growing exponentially as you make it more capable. The structure can be used multiple times over it's design life, so the cost per use is lowered by that ratio. At some point that lower cost by multiple use is overcome by the increasing mass and cost of a larger structure no matter how many times it is used. So economics will be the limiting factor on large elevators.

Whatever velocity the bottom end has relative to the ground has to be provided by some other transport system, but that is less than is needed by a transport system without an elevator. The difficulty of building a transport system is also non-linear with velocity, like the elevator. By using both, the sum of smaller exponents is less than each exponent by itself, so the total cost and difficulty is less. The other transport system does not place itself fully in orbit, only the cargo does via the elevator, which is less total energy per delivery. The cable serves as a momentum bank to store orbital kinetic energy, which can be transferred to a payload. The kinetic energy can be stored by running an electric propulsion system, which is much more efficient than conventional rockets. So using an elevator lowers the overall difficulty of reaching orbit, and lowers 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 an elevator design vary with time. This includes arriving and departing vehicles, internal movement of cargo along the structure or deployment of extension cables, 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 planet satellite, 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 the 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.

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.

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 larger 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. Thus 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.

Status: - Hanging cables have long been used on Earth for numerous purposes. The Tethered Satellite System was an experiment to deploy a cable in orbit from the Space Shuttle but it (descibe failure).

Variations:

• 2a Orbital Vertical Elevator - The original concept, where the cable is 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.

An orbital tether system variation of potential value is the orbital slingshot. This would take advantage of the tendency of a long object to auto-rotate from horizontal to vertical orientation with the center of mass at orbital velocity, 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 reel of tether. The vehicle would be pushed out to a somewhat higher orbit, where it would fall behind the momentum bank, with tether 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 accelerate and fall outward, to be 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.

The momentum bank would lose velocity in this maneuver, but could use highly efficient solar powered thrusters (plasma, ion, magnetic) to recover that loss over an extended period. A couple of momentum banks could 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. Or the vehicle would take on fuel to circularize its orbit after being slung - the momentum bank station would be a convenient place to cache fuel for vehicles bound further out.

• 2c Orbital Rotating Elevator (Skyhook) - A more recent idea devised around 1980 where the 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 gives it the name Skyhook. 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. Again, both launch vehicle and Skyhook mass ratios are exponential in velocity, so splitting the job lowers the overall difficulty.

For example, if we assume a cable has a tip acceleration of 1 gravity, and we allow a mass ratio of e^2, or two working lengths, and the working length is 50 km, then the radius can be 200 km. From the centrifugal formula, then 10 m/^2 = (v^2)/200,000 m. Solving for v gives 1400 m/s, or about 20% of Earth orbit velocity. So a modest structural design can reach a significant fraction of orbital speed.

• 2c Atmospheric Elevator - 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 -
• Carroll, J. A. "Tether Space Propulsion", AIAA paper 86-1389, 1986.
• Penzo, P.A. and Mayer., H.L. "Tethers and Asteroids for Artificial Gravity Assist in the Solar System" Journal of Spacecraft and Rockets, Jan- Feb 1986. (Details how a spacecraft with a kevlar tether of the same mass can change its velocity by up to slightly less than 1 km/sec. if it is travelling under that velocity with respect to a suitable asteroid.)
• 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.
• Penzo, Paul A. and Ammann, Paul W. Tethers in Space Handbook, 2nd Edition, NASA Office of Advanced Program Development, 1989. (NTIS N92-19248/3)

#### 3. AerostatEdit

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 life 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 TunnelEdit

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 StructureEdit

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 StructuresEdit

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 DriverEdit

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. Launch LoopEdit

Alternate Names:

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:

References:

#### 8. Multi-Stage Space ElevatorEdit

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: