Tethered Rings, Launch Loops, Space Fountains, and The Space Elevator

This article continues the exploration of Space Transit Systems from the previous article Chapter Three: The Gravity Well, and expands into space transit infrastructures such as tethered rings, launch loops, space fountains, space elevators and The SkyHook.

Tethered Rings

A tethered ring is an interesting, somewhat counterintuitive design. The ring is built on the ground or in the ocean. Its construction is somewhat similar to that of a closed orbital ring, except it uses a particle beam instead of a cable for momentum. This is probably because it would be very hard to get a cable moving when it is lying inside its casing on the ground for many thousands of miles.

Assuming that issue is resolved and the particle beam is moving at a velocity somewhat akin to that of the cable in an orbital ring, it constitutes an incredibly elegant design. The idea is that the force provided by the particle beam makes the ring’s circumference, which is somewhere in the vicinity of 30,000 km (18,600 miles), rigid. Since the ring is lying on a spherical segment of the earth, when it is pulled inwards from all directions, it rises. The Graviton Media channel on YouTube made a very nice video that demonstrates this effect. Just ignore the part about orbital rings; I will debunk all that later. You can also find all the details at project-atlantis.com.

From The Graviton Media channel on YouTube https://youtu.be/7EgYDzX5Eo8

One advantage a tethered ring has over an orbital ring is that it is built at sea level. Another significant advantage is that it can be placed in various locations since it is set on a spherical segment plane, not a great-circle plane (a great-circle plane goes through the center of the sphere, cutting it in half, while a segment plane does not pass through the sphere’s center). Additionally, a tethered ring does not have a lower parking altitude limit like an orbital ring does, as the particle beam is enclosed in a vacuum before it is set in motion. Therefore, a tethered ring could theoretically exist as low as a few kilometers above Earth’s surface, whereas an orbital ring would need to be placed at an altitude of at least 100 kilometers (62 miles).

A tethered ring and an orbital ring are very similar in capacity. However, an orbital ring is capable of achieving higher launch velocities since its centripetal force is aligned with the great-circle plane of Earth. An astronaut sitting upside down would not feel 1 g of force until the centrifugal force reaches 2 g, as the first g would merely cancel out Earth’s gravity for the upside-down occupant. The tethered ring, on the other hand, can vary drastically in size and can be placed in many different locations.

There are two significant issues that are likely to be showstoppers for the tethered ring. The first is that the particle beam inside the tube will be much harder to implement than manufacturing a cable at orbital speed. As you will learn in the section on building the orbital ring (in the book Orbital Ring Engineering), creating the cable for the orbital ring is a straightforward process. While it’s challenging due to the sheer volume of it, it is something we know how to do.

Producing a particle beam with the amount of energy required by the tethered ring is a showstopper. This is especially true given the fact that the beam needs to be aligned with the center of the containment tube while laying on the ground. The startup process will be very difficult. Additionally, if even a minuscule amount of the particle beam contacts any part of the wall, the structure will disintegrate. The second issue is that the stiffness required for the tethered ring to behave as predicted seems unrealistic, even with the force distribution achieved by bifurcating the tether lines to help distribute the forces.

A tethered ring on a segment plane is constructed on the planet’s surface. The particle beam running through the tube is then spun up to a velocity high enough to rigidize the ring. Subsequently, all the tethers are pulled towards the center simultaneously. This pulling action lifts the rigid ring from the surface of the planet to the desired altitude. The segment does not need to be in any particular plane, so there could be one around the Pacific Ocean, the Atlantic Ocean, and the North and South Poles, for example.

An orbital ring, on the other hand, must be placed in a great-circle plane. It can theoretically be in any great-circle plane, but in practice, the equatorial great-circle plane is by far the best. These images show the difference between an orbital ring in a great-circle plane and a tethered ring in a segment plane.

From The Graviton Media channel on YouTube https://youtu.be/7EgYDzX5Eo8

Launch Loops (Lofstrom Loop)

A Launch Loop, also known as a Lofstrom Loop, was first proposed by Keith Lofstrom in 1984. Its basic design is similar to a section of an orbital loop, with the cable looping back to the start and continuing round and round continuously.

The cable path resembles that of a ski lift cable. The bulk of the cable runs in close proximity in opposite directions. At each end, it follows a wide teardrop-shaped path, ensuring that the bend radius does not overstrain the cable.

This rapid change in direction is what delivers the force, driving the cable upward as the upward section facilitates the acceleration of the cable around its bend to return to the beginning.

This means that the entire cable is supported by its upward end. The downward end is anchored in such a way that the pull of the upward end creates tension between the two ends, thereby increasing the radius of the sagging cable’s bend towards the ground. This radius determines the maximum velocity of the launch vehicle based on the maximum g-force load of its cargo. The overall length is another potential limit on the launch vehicle’s velocity since the length determines how long the maximum amount of acceleration can be applied. That length is measured in the thousands of kilometers (or miles).

Launch loops are often envisioned with active supports to help reduce the arch at the upper end of the loop. An active support is a structure from which a particle beam is shot upward from the base to impart momentum on the upward sections of the structure, supporting it with that upward thrust. More on active support structures will be discussed later in the book chapter. The launch loop then uses a vacuum tube-enclosed maglev launch sled to launch its cargo.

The launch loop suffers from the same issues as the tethered ring. If the structure is constructed on the ground, it would be nearly impossible to initiate the motion of the cable. Then, assuming they overcome this obstacle, the stress on the ends of the cable will be enormous due to the relatively rapid change in velocity. The challenges of building a launch loop, therefore, far outweigh the challenges of constructing a far more functional orbital ring structure.

There are several similar designs that skip the looping cable and rely on active support instead. These include the StarTram and the Hyperloop to Space. If active support becomes a viable technology, those designs would be simpler to build and more likely to be pursued than a Lofstrom Loop. The big issue is that active support would consume enormous amounts of energy for little benefit when a far simpler and much more functional orbital loop could be built, which would deliver power rather than consume it—something I will explain in later chapters.

Space Fountains

While on the topic of active support, a space fountain is an active support structure. A space fountain is a theoretical structure designed to provide continuous access to space by suspending a tower or platform high above the Earth’s surface using a stream of high-velocity projectiles or plasma circulating within the system.

Unlike space elevators, which rely on tethers extending from geostationary orbit, a space fountain is supported dynamically by the kinetic energy of its internal components.

The basic idea involves a continuous loop of projectiles or plasma particles launched vertically from the Earth’s surface at high speeds. These projectiles travel up a hollow column or guideway and are redirected back to the surface by electromagnetic or mechanical means at the top of the fountain. As the projectiles descend, their momentum is transferred to the structure, supporting the weight of the column and any platforms attached to it.

A space fountain is envisioned to extend up to several hundred kilometers above the surface of the Earth. Although the platform at the top of the space fountain would be above the bulk of the atmosphere, it would only marginally reduce the energy needed to launch into space since it is stationary relative to the ground. It would, therefore, make much more sense to use the space fountain as active support for one of the other launch systems such as a Lofstrom Loop.

Other issues with this type of structure include the incredible amount of energy it would consume to maintain its upper platform. A loss of power would also mean that the upper platform would immediately begin a free fall toward the surface. Additionally, there is the tremendous amount of heat that would need to be dissipated in a near vacuum at the top of the structure.

Now, back to space elevators. The idea is to place a platform at the geosynchronous orbit location mentioned above. This platform functions as a counterweight. A very strong lightweight cable is then lowered from that platform. As the cable is lowered, the platform is moved upwards so that the combined center of mass of the platform and the cable remains at that exact geosynchronous location. Once the cable reaches the surface of the Earth, it is anchored to the Earth. The platform is now at a new distance from the surface of the Earth, somewhat further out but directly above the geosynchronous location from which it started.

At that orbit, the cable prevents the platform from flying away into space. It is interesting to note that if a station were built into that platform, it would need to be upside down relative to the orientation of observers on Earth. For someone in that station looking up, they would see the Earth. This is because the centrifugal force is greater than the force of gravity at that point and at that orbital velocity. Stated another way, the cable absorbs the centripetal force created by the station, which would be felt as a centrifugal force by the observer in the platform station. This is, in essence, artificial gravity.

I am going into these details so that you have a realistic understanding of the issues. Each section of the cable experiences both the pull of gravity and the upward lift from the centrifugal force.

Centrifugal force is determined by ω²r, where ω is the angular velocity of the satellite and r is the distance from the satellite to the center of the Earth. For clarity, ω = 2π / (the orbital period of the satellite in seconds). We will discuss this in more detail later when we address the challenges faced by the space elevator design.

Another important point is that a space elevator can only exist on the equator. All other great-circle orbital planes would result in the point on the surface below the platform migrating back and forth across the equator in a figure-eight pattern called an analemma. This would occur once every 24 hours. The combined center of mass of the cable and platform would still need to be at an altitude of about 35,786 km (22,236.4 miles) above sea level. By the way, the crucial number is actually 42,164 km (26,199.5 miles), which is the distance from the gravitational center of the Earth to the geosynchronous location in space.

Now let’s say the platform winds up at an altitude above the equator of 40,000 km (24,855 miles). Trolley cars would need to move up and down along the cable to bring people, cargo, and launch vehicles up from the surface. At 200 km/h (125 mph), the journey would take 8.33 days each way! Even if the trolley could move at 500 km/h (310 mph), the trip would still take 3.33 days each way.

Another issue is that cars probably won’t be able to pass each other since they would likely need to wrap around the cable to gain traction. This means all the trolleys would need to go up for 3.33 to 8.33 days and stack up underneath each other at the bottom of the platform. Let’s say there are 48 trolleys, and it takes 30 minutes to load each one. This adds another 24 hours. Therefore, the cycle time would be between 8 and 19 days before another set of loads can go up. Having multiple cables could significantly improve this situation; however, it is clear that the capacity is relatively low compared to many of the other space transit systems examined so far.

Now, let’s look at feasibility. The limiting factor is the breaking length of the cable. The material with the highest strength-to-weight ratio known at this time is graphene. In fact, it isn’t even close. Graphene has a tensile strength of between 100 and 130 GPa. For comparison, the strongest steels have a tensile strength of about 0.4 GPa. Additionally, graphene is much lighter than steel, with a density of approximately ρ = 2,260 kg/m³, whereas steel has a density of about ρ = 7,850 kg/m³. To provide some perspective, the natural breaking length of a graphene cable is more than 900 times that of a steel cable!

To determine the breaking length of graphene, we need to take into account that gravity decreases as altitude increases. We also need to consider the centrifugal force. Both of these factors work in our favor in this case. If gravity were constant, the breaking length would be approximately 5,866 km. Accounting for the variability of gravity and the centrifugal force increases the breaking length of the graphene cable to 12,006 km. This is impressive, but it is still well short of the 40,000 km breaking length required to construct the space elevator.

Furthermore, these figures are based on the optimistic tensile strength value of 130 GPa, without any safety margin. This means there can be no defects in the 40,000 km sheet of rolled-up graphene—no splices and no atoms out of place. Additionally, for human-rated cables, a safety factor of 15 to 1 is added, which would reduce the allowable length to only 800 km. Even if we used the absolute minimum safety factor of 5 to 1, the allowable working length would still be only 2,400 km. That is a far cry from the 40,000 km needed, even with no safety factor at all! Tapering the cable could help, but it is highly doubtful that a cable could be made to reach anything close to the 40,000 km required. It’s not even close.

Other issues include the fact that the tether would pass through regions of orbital debris, posing significant risks of collision and severance. Active debris mitigation strategies and tether shielding would be necessary. Additionally, there are the Van Allen belts, with their charged particles zipping back and forth between Earth’s poles. Cosmic rays and the solar wind will flow through and past the cable, causing wear and defects in the cable. The upper atmosphere is also fraught with other hazards, such as ozone and monatomic oxygen. The lower portion of the tether would experience wind, lightning, and weather events, requiring active stabilization systems and advanced materials capable of withstanding environmental stresses.

The climber trolleys would also require energy to travel long distances. Concepts for laser power beaming and solar arrays are under development to address this, but constructing the 40,000 km space elevator would be a major challenge, to say the least.

Other candidate materials include carbon nanotubes and boron nitride nanotubes (BNNTs). Although the characteristics of these materials are very impressive, graphene is slightly better, which is why I have mentioned only graphene so far. Graphene, carbon nanotubes, and BNNTs all face the same manufacturing difficulties; however, these are engineering challenges that will likely be resolved in the future. The strength-to-weight ratio and breaking length issues, on the other hand, present a different story—one that is likely not solvable.

History of The Space Elevator

The concept of a space elevator has captivated scientists, engineers, and science fiction writers for over a century. Though no space elevator exists today, the idea continues to inspire technological advancements and exploration into alternative space transportation methods.

The Russian scientist Konstantin Tsiolkovsky, often regarded as the father of astronautics, first conceptualized the space elevator in 1895.

Inspired by the Eiffel Tower, Konstantin Tsiolkovsky imagined a tower reaching into geostationary orbit (36,000 km above Earth). He proposed that a structure at this height could allow objects to be “dropped” into orbit without the need for rockets. Although Konstantin Tsiolkovsky‘s vision was limited by the technological constraints of his time, his work laid the groundwork for future space tether concepts.

In the 1920s, a contemporary of Konstantin Tsiolkovsky, Friedrich Zander, expanded on the idea, proposing a tether extending from Earth to orbit. His work focused more on space stations and orbital mechanics but contributed to the broader discourse on space transportation.

In the 1960s, A Soviet engineer, Yuri Artsutanov revitalized the space elevator concept in a 1960 article. Unlike Konstantin Tsiolkovsky‘s stationary tower, Artsutanov proposed a tensile structure suspended from orbit downward to Earth, supported by counterweights above geostationary orbit. This approach avoided the need for constructing from the ground up and instead focused on deploying the tether from space. Artsutanov’s work introduced the concept of dynamic stability and balance of forces that remains central to modern space elevator designs.

In the 1970s Jerome Pearson, an American engineer working with NASA, independently proposed a space elevator concept in 1975. His design closely mirrored Artsutanov’s but with a deeper focus on the engineering challenges and the need for ultra-strong materials. Pearson introduced the notion of advanced composite materials that could withstand the immense tensile forces required for such a structure.

Space Elevators have featured prominently in science fiction literature, films, and video games. In his 1979 book, The Fountains of Paradise, Arthur C. Clarke popularized the space elevator concept for the general public. The book imagines the construction of a space elevator on a fictional Earth-like planet, detailing the technological and political challenges involved. Clarke consulted with Pearson, incorporating realistic engineering concepts into his narrative. Clarke famously stated, “The space elevator will be built about 50 years after everyone stops laughing.“

In 1992 Kim Stanley Robinson wrote about space elevators in his book Red Mars. The Mars Trilogy featured space elevators as essential infrastructure for colonizing Mars. His depiction included Martian elevators, which are more feasible due to Mars’ lower gravity and reduced atmospheric drag.

The discovery of carbon nanotubes by Sumio Iijima sparked renewed interest in space elevators. Carbon nanotubes, with their extraordinary tensile strength and low density, emerged as the most promising candidate for tether material. However, the challenge of producing them in large, defect-free quantities remains unresolved.

Conclusion

Why people think a space elevator is a good idea confounds me! Maybe it would make sense on a lower-mass, faster-spinning body where the length of the cable would be much shorter.

Even then, a space elevator would only make sense if there is an atmosphere. On planets with no atmosphere, it would make much more sense to use a mass driver or another launch system directly from the surface. Sure, the idea of a space elevator sounds cool, but give me a break! There are better ideas out there.

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