Hypervelocity Tether Rockets
Rotating tethers can reach incredible velocities when they are built out of high strength materials. With some design features, they can greatly surpass the exhaust velocities of chemical or even nuclear rockets. They can become propulsion systems with impressive performance... and might look like the classic 'saucer' spaceship. How would they work? What performance could they achieve? Rotating Tethers Rotating tethers are a fascinating topic that have been treated in depth by previous posts on ToughSF, such as using them to extract energy from planetary motion or make space travel much shorter. In summary, a tether made of high strength-to-weight ratio material can withstand enormous forces while remaining lightweight. If spun in a circle, usually many kilometers wide, it can support a load on one end as long as it is supported by a counter-weight on the opposite side. The tip velocity achievable before the tether breaks from centrifugal force will reach several kilometers per second. It can be boosted even further if the tether is tapered: wider at the base and thinner towards the tip. With this technique, tethers made of mass-produced materials like Kevlar can cover a significant fraction of orbital velocity, making it good enough to be used to build a skyhook. The important factor here is how heavy of a tether we need to handle a certain payload mass spinning at a certain velocity. First we need to work out the characteristic velocity of a tether, which depends on its material properties: tensile strength and density. Characteristic velocity in m/s Tensile Strength in Pascals Density in kg/m^3 For Kevlar, the values we have are 3,620,000,000 Pa and 1,440 kg/m^3. Kevlar’s characteristic velocity is 2242 m/s Then we need to find the ratio between the tether’s tip velocity and the characteristic velocity, which we’ll simply call the Velocity Ratio VR. If our tether is spinning at 3300 m/s, then the VR is 3300/2442 = 1.351 Finally we get to the Tether Mass Ratio. It is the ratio between the tether mass and the payload mass it can handle. A tether with a VR of 1.351 will have a Tether Mass Ratio of 1.772 * 1.351 * e^(1.351^2) = 14.85. It means that a 1485 kg Kevlar tether can handle a 100 kg payload at its tip while spinning at 3300 m/s. The Tether Mass Ratio is square-exponential. It climbs extremely rapidly with increasing VR. Doubling the tip velocity to 6600 m/s, for example, raises the Tether Mass Ratio of a Kevlar tether to 7122. Now a 712.2 ton tether is needed for the same 100 kg payload; a nearly 48x increase. As a consequence of this scaling relationship, large rotating tethers are optimized for velocities only slightly above their material’s characteristic velocity. Then some safety margin has to be added on top. It is not practical to have a 10 ton capsule matched with a tether of several thousand tons. Hundreds of launches would be needed to justify the presence of the tether. Large tethers also have some additional complications limiting their performance, such as the need to add multiple redundancy against micro-meteorite strikes and shielding against solar radiation that would otherwise degrade their materials. All of these measures cut into the mass actually dedicated to supporting a payload. Higher Velocities It is possible to imagine much smaller tethers, perhaps a few meters across, spinning at much higher velocities. They would be completely enclosed in a protective container. The idea of a smaller, faster tether launching objects is not new. In fact, it is being worked on at full scale by alternative launch companies like SpinLaunch today. The idea is that we can increase tether velocity to many kilometers per second, then release small masses from the tether tips. This can be water or dust grains or whatever can flow down the tether’s length. Their release generates recoil in the opposite direction: that’s thrust. Momentum is lost with each release, though it can be regenerated by an electric motor that spins the tether. If we mount a tether like this on a spacecraft, it can be used as a rocket engine as propellant exiting in one direction and thrust produced in the opposite direction. As long as two counter-rotating tethers are used, there is no torque. Essentially, they become an electric thruster with an ‘exhaust velocity’ equal to the tether tip velocity. There are many advantages. The tethers can use nearly any propellant they can pipe to their tips. Whether it is dust gathered from an asteroid’s surface, nitrogen scooped up from the edge of Earth’s atmosphere or water derived from a lunar mining operation, it can all go in the propellant tanks with minimal processing. That means there is no need to haul a chemical factory with you to every landing site in the Solar System. The tether itself should be practically frictionless and have nearly 100% efficiency. It operates mechanically (no electric currents or coolant flows) so it should produce negligible heat even at extreme power outputs, which are in turn limited only by its RPM. A tether rocket compares favourably in many ways to existing technology like Hall effect thrusters or MPD thrusters. They do not have to pay the energy penalty to ionize their propellant, nor do they have the pulsed energy storage concerns of mass drivers (railguns, coilguns). Further advantages will be described later in this post. These tethers can be spun to very high velocities at the expense of impressive mass ratios. The g-forces exerted at their tips would be immense, but it is acceptable as their payloads won’t be fragile spacecraft. Also, since they are on a much smaller scale, it becomes much more affordable to build them out of the best materials available. For example, Toray’s polyacrylonitrile fiber T1100G with a characteristic velocity of 2,796 m/s or new UHMWPE fibres (Dyneema) being tested to a characteristic velocity of 2900 m/s. These may seem like tiny gains over the characteristic velocity of widely available Kevlar, but remember that the Tether Mass Ratio is square-exponential. Small improvements lead to huge decreases in tether mass. Here is a table of the performance we can get: All of these materials make it possible to achieve tether tip velocities exceeding the best performance of chemical rockets (460s Isp or 4512 m/s) with a moderate mass ratio. Kevlar struggles when going faster than that. T1100G or UHMWPE can get us 7500 m/s exhaust velocity with a Tether Mass Ratio in the thousands. An exhaust velocity exceeding that of nuclear thermal rockets (1000s Isp or 9810 m/s) is achieved with T1100G at TMR 2.27 million and UHMWPE at TMR 0.89 million. A Tether Mass Ratio in the millions sounds extreme but consider it in these terms: a tether of 1 ton mass would be handling 1 gram of propellant at its tip. If it is 1 meter in radius, and the tip velocity is 10,000 m/s, then it makes a complete rotation 1591 times a second 95,460 RPM). It is not so extreme: commercial hard-drive disks spin at 7200 RPM and ultracentrifuges manage 100,000 RPM. We could compare at them to uranium gas centrifuges spinning at 90,000 RPM. If this 1m long tether releases a 1 gram drop of water every time it completes a rotation, it will have a mass flow rate of 1.59 kg per second. Thrust is propellant flow rate times exhaust velocity, so multiplying that figure by 10,000 m/s gives us a thrust of 15.9 kN. Thrust power is equal to half the thrust times exhaust velocity, which in this case is 0.5 * 15,900 * 10,000 = 79.5 MegaWatts! Let’s try to design two realistic Hypervelocity Tether Rockets, one with T1100G aiming for an exhaust velocity of 6000 m/s which is ideal for travel between the Earth and Moon, and another using slightly more advanced UHMWPE aiming for 10,000 m/s which is better for interplanetary travel. The g-forces at the tether tips will exceed 1,000,000g, which is troublesome as there would have to be some moving part that controls the flow of propellant that can open and close thousands of times a second. Putting as many components as possible on the external container (control electronics, magnetic actuators) rather than on the moving tip could help. Lunar Tether Rocket The Toray T1100G material is selected because you can order spools of it right now. The individual fibres have a tensile strength of 7000 MPa and a density of 1790 kg/m^3. With its characteristic velocity, 6000 m/s tip velocity means a Tether Mass Ratio of 380. Why 6000 m/s? Because it allows a rocket to make the 8400m m/s deltaV trip from Low Earth Orbit to Low Lunar Orbit and back with a propellant mass ratio of 4 (that’s 3 kg of propellant for each 1 kg of empty rocket). That is modest for an upper stage of a launch vehicle, let alone a lunar transfer stage. The tether here can have a length of 3.67 m. It would rotate at 15,607 RPM. If it aims to shoot off 10 grams of water with each rotation, then it will have a mass flow rate of 2.6 kg/s. The tether itself will mass 3.8 kg but we can bump that up to 5.7 kg to add a 50% safety margin. A counter-weight doubles that value to 11.4 kg. It will feel 60 Newtons of recoil with each release, which seems like it can easily be handled by a suspension mechanism. To counter torque effects, we must add a second tether rotating in the opposite direction, which adds another 11.4 kg for a total of 22.8 kg. Average thrust from both tethers is 31.2 kN. Thrust power is 93.6 MW. This power can be delivered by a high power density megawatt-scale electric motor. An example of this today would be the H3X HPDM-3000 that manages 2.8 MW of output with a power density of 12.7 kW/kg. It is already meant to be stacked in multiple units. 93.6 MW of power would need to be delivered by 7370 kg of these electric motors. The motors are 94% efficient, so there’s 5.97 MW of waste heat to consider. The motors operate at 60°C, so 4282 m^2 of double-sided radiator panels are needed to handle their waste heat. This may need 4282 kg of 1 kg/m^2 radiator panels based on carbon fibre heat pipe technology. In total, this propulsion system masses 11,675 kg. If we add a 10% mass margin for equipment like water pumps, tether container walls, coolant pipes, we arrive at a total mass of 12,843 kg. The tethers are by far the smallest component, representing only 0.178% of the mass total. Toray T1100G Tether Rocket Performance Tip velocity = 6000 m/s Total Mass = 12,843 kg Thrust = 31.2 kN Thrust-to-weight ratio = 0.247 Average power density = 7.3 kW/kg If you add a power supply, propellant tanks, structural components and a payload, you get the rough draft of an Earth-Moon spaceship. The Hypervelocity Tether Rocket here far exceeds the performance of most electric propulsion systems you could slot into its place on such a spaceship. Aerojet Rocketdyne’s Hall thrusters struggle to reach 0.26 kW/kg. NASA’s more advanced electric thrusters aim for up to 4 kW/kg, but at a reduced efficiency of 60 to 85%. They are superior in terms of specific impulse, but that is not particularly needed in cis-lunar space. Interplanetary Tether Rocket Now we look at a 10,000 m/s UHMWPE tether. It will be more advanced but still within the realm of ‘near future technology’. Tether Mass Ratio is 891,437. The tether is short: 0.95 m in radius. It spins at 100,000 RPM. The amount of propellant released with each rotation is 1 gram. That means a tether mass of 891.4 kg and a mass flow rate of 1.67 kg/s. With counter-weights and a second counter-rotating tether, the tether assembly adds up to 3566 kg. We bump this up to 5349 kg for a 50% safety margin. The average thrust produced from the two tethers is 33.4 kN. Thrust power is 167 MW. At this power level, it is sensible to switch superconducting devices. NASA’s 2035 goals for turboelectric propulsion on aircraft uses high temperature superconductors to achieve 40 kW/kg at 99.99% efficiency. The electric motor mass would only need to be 4175 kg. The waste heat produced at 65 Kelvin would be 16.7 kW. A 201 kW Stirling cryocooler of 300 W/kg, would raise the temperature to 300 Kelvin (30% of Carnot efficiency) and 670 kg of equipment. The radiators to handle the final heat load (16.7 + 201 * 0.7 = 157.4 kW) add another 171 kg. In total, this propulsion system masses 10,365 kg. If we add a 10% mass margin as before, we arrive at a total mass of 11,401 kg. UHMWPE Tether Rocket Performance Tip velocity = 10,000 m/s Total Mass = 11,401 kg Thrust = 33.4 kN Thrust-to-weight ratio = 0.298 Average power density = 14.65 kW/kg This design has even higher performance and better specific impulse. It is well suited for missions to Mars. Its performance is somewhat comparable to a solid-core nuclear thermal rocket using liquid hydrogen, as it has the same exhaust velocity but it does not need bulky cryogenic propellant tanks or a full electrolyzing ISRU plant to refuel it. If solar or beamed power is available, it could do away with nuclear technology altogether and still achieve comparable performance. Neither of these designs are optimized. There could be further performance gains to be had from selecting a better tip velocity or cooling solution. For example, the propellant water could first be used to cool the electric motors to save on the mass of radiators needed. Or, we could employ several tethers to multiply the thrust the engine could produce without having to also increase RPM or tip velocity. Staging tethers on tethers Rockets get around the problem of exponential mass ratio by using staging. Tethers can employ the same strategy. Instead of placing a payload on the tip of a tether, another smaller tether can be attached. Each tether would spin independently of each other, and at the right moment, their tip velocities would add up. Here is an example with Kevlar: We want a tip velocity of 10,000 m/s. As we calculated previously, this would require an impractical tether with a Tether Mass Ratio of over 139.1 million. If we instead break it down into tethers of 5,000 m/s velocity, and stage them tip-to-tip, we would obtain stages with a mass ratio of 240. Two stages would add their tip velocities to 10,000 m/s and multiply their mass ratios to 240 x 240 = 57,600. This is obviously much lower than one huge tether. There is very little literature available on this idea. The closest concept is the Tillotson Two-Tier Tether, as depicted here. There will be challenges to designing a two-stage tether for use as a rocket. There’s the issue of transferring propellant between the tethers, which could be very troublesome if you want solid particles as propellant. Designing a rotating joint that can work smoothly when under high g-forces can’t be easy. Then there’s the difficulty of restoring momentum to the second-stage tether. A second-stage tether also needs its own counter-weight, which could double the overall mass ratio. But, if all these challenges can be solved, then we would get much more impressive tether rockets. Here is a table for two-stage performance: The same material selection as in the previous section is given a second stage so that the total Tether Mass Ratio for both stages reaches 500, 50,000 and then 500,000. The final ratio is doubled to account for the second stage tether’s counterweight. In this arrangement, even Kevlar exceeds 11 km/s tip velocity. UHWPE manages 13.1 km/s with a final tether ratio of 1 million. Let’s update the two tether rocket designs with staged tethers: Toray T1100G Two-Stage Tether Rocket Performance Tip velocity = 7430 m/s Total Mass = 12,843 kg Thrust = 25.2 kN Thrust-to-weight ratio = 0.2 Average power density = 7.3 kW/kg We maintained the 380 final tether mass ratio from the Toray 1100G tether rocket. However, with two stages, we get an exhaust velocity of 7.43 km/s. Thrust power from the electric motor is identical so the thrust-to-weight ratio has to fall to 0.2. UHMWPE Two-Stage Tether Rocket Performance Tip velocity = 10,000 m/s Total Mass = 6095 kg Thrust = 33.4 kN Thrust-to-weight ratio = 0.56 Average power density = 27.4 kW/kg The UHMWPE tether rocket aims for the same tip velocity, but with two stages the final Tether Mass Ratio (x2) can fall from 891,437 to just 7128. The tether assembly is reduced from 5349 kg to 42.7 kg, raising the overall thrust-to-weight ratio and average power density significantly. Note that for both of these designs, we are only calculating the mass of the engine - the part that converts electrical power to thrust. A complete spaceship would have to include an electrical generator, be it an onboard reactor, solar panels or a laser-photovoltaic receiver. In a realistic study, you will find that high engine power densities means the average power density of the propulsion module of a spaceship approaches that of the power generating section alone. The overall performance of a spaceship won’t improve much if you have a terrible power generator (0.2 kW/kg solar panels) but excellent engines (20 kW/kg). Two-stage tether tip velocities means we obtain a propulsion system that can make shorter interplanetary trips. 1200 seconds of specific impulse means that a spaceship that’s 75% water (a mass ratio of 4) has 16.3 km/s of deltaV. It can start in Low Earth Orbit and arrive in Low Mars Orbit in 88 days, or complete a trip to Io’s orbit around Jupiter in 1.73 years instead of the usual Hohmann transfer of 2.73 years. This is without the assistance of aerobraking and with the ability to quickly load up on propellant at the destination for the return trip. Theoretically, a third tether stage is possible. It would push the potential performance of tether rockets well into the domain of electric thrusters (2016s Isp with UHMWPE) while retaining the upper hand in thrust-to-weight and power density. However, the problems mentioned above would all be exacerbated. Carbon extraordinaire So far we have restricted ourselves to materials available in bulk today. Better materials exist; we only need to learn how to manufacture them in large quantities. The most promising of these are carbon nanomaterials: nanotubes and graphene. Carbon nanotubes are being grown right now, up to lengths of 50 centimeters. Graphene flakes are regularly added to epoxy resins and nanocomposite materials to enhance their strength. In the future, we could see them being produced in much larger quantities, enough to use for tethers. In order of difficulty of manufacture, we have multi-walled carbon nanotubes, single-walled carbon nanotubes and then graphene. Here are their ‘perfect’ properties: The characteristic velocity of these materials can exceed 10 km/s. When used in a tether with a Tether Mass Ratio (TMR) of 100, they can achieve tip velocities approaching 20 km/s. In a TMR 10,000 tether, they approach 30 km/s and they can push beyond 60 km/s with a TMR of 1 million. That’s better than what most electric thrusters are capable of today. Of course, it is unlikely we will be able to form tethers of several meters in length with zero defects, errors or safety margins using these materials in the near future. The strength of a single perfect fibre is reduced when it has to be bundled with many other fibres, bringing down the ‘engineering strength’ to about half of the maximum with no other factors involved. If we assume that a half of the theoretical maximum could be achieved in bulk quantities, the tip velocities we would actually achieve would be reduced by 42%. Then, we could apply staging. A two-stage hypervelocity tether rocket with specific impulse of 2000 to 4800s seems achievable with these materials. The overall power density of the rocket is difficult to estimate because access to carbon nanomaterials would also affect the weight of components like electric motors or radiator panels. The final design could easily exceed 100 kW/kg. It does mean that the performance of the power generating source becomes critical to good overall performance. Even a nuclear reactor with radiators and a turbine that we consider excellent today at 10 kW/kg would become a performance bottleneck when paired with a 100 kW/kg carbon nanotube tether rocket. Mechanical Rocketry What’s it like to use hypervelocity tether rocket engines? They can simply be mounted on spacecraft and used to travel by throwing propellant out. It would look rather weird: they have no nozzles, only need small propellant tanks and their most distinguishing feature might look like a wheel... or if the tethers are placed internally, the whole spaceship might be configured like a disk. Meaning, your diamond hard science fiction can have fully justified 'flying saucers' roaming the Solar System. The tethers can thrust in different directions by selecting a different firing port for their exhaust. A disk-shaped spaceship with firing ports along its rim can accelerate in any direction. It just has to take care not to aim its exhaust at nearby objects. Water can drill holes through asteroids, space stations and other spacecraft when shot out at 10 km/s. Over long distances, it would disperse into harmless mist but at short distances it would be dangerous. Dust or other solid particle propellant would not disperse and would remain dangerous forever. Their use in the Outer Solar System or between asteroids might be justified by the vast distances involved, but not in cluttered low planetary orbits, especially if exhaust velocity is less than escape velocity (the dust would circle back around). Spaceship pilots might need to pay attention to how long it takes for their tethers to reach operational RPM. Thrust would not be instantaneous, which makes delicate or urgent manoeuvres troublesome. Thrust levels can be adjusted by firing more or less frequently. Theoretically, the tether can be spun down to a lower tip velocity to allow for more propellant to be fired with each rotation. The potential thrust would increase exponentially as the tether velocity is decreased. However, the other critical component in a tether rocket is the electric motor. Its output is tied to its RPM, so spinning slower might also mean less watts from the motor. The solution to this is a gearbox… but the practical details of building a MW-scale 100,000 RPM set of gears are best left to people in the future. It should be noted that electric motor power does not have to exactly match the thrust power of a tether rocket. The spinning mass of a tether can be considered a type of flywheel, so it can store energy. Energy can be accumulated gradually by a small motor (which enables some mass savings), then released quickly from the tether. This is most useful for spacecraft that aim to raise their orbit via multiple short burns at the periapsis of their orbit. It maximizes the contribution of the Oberth effect and was used by Rocketlab’s Photon stage for the CAPSTONE lunar mission. It’s possible to rely on rotating energy storage alone for propulsion. An asteroid mining spacecraft could land on a target, hollow it out for raw materials, build flywheels-tethers out of the leftovers and spin them up before leaving. Those tethers would then eject pieces of asteroid dust for propulsion until their energy ran out. RAMA proposed this architecture but with a different way of converting stored energy into thrust (using catapult sling arms). In fact, asteroid mining is one of the best applications of tether rockets. The ability to use any propellant, the decent exhaust velocity (for an electric rocket) and the ability to store energy then release it quickly combine to make tether rockets ideal for asteroid hopping spacecraft. The deltaV for travelling between asteroids can be very low, which suits the tether rocket perfectly. Sunlight may be too weak to keep a powerful motor running continuously in the asteroid belt, so slowly accumulating energy into a flywheel is a good option to have. Being able to use asteroid dust as propellant means the mining ships can hop to very ‘dry’ targets without worrying about the availability of water to refuel themselves. The tether itself could be made of locally sourced materials, such as glass or basalt fibres that exhibit ‘good-enough’ characteristic velocities of 1.5 km/s to 2 km/s. Glass fibre tethers would be larger and heavier than carbon nanotubes, but that’s actually an advantage if they double as energy storage flywheels. This creates a ‘low performance’ niche for tether rockets. They could excel here as well as they do in the ‘high performance’ role with super-materials and extreme tip velocities. Other Applications Beyond simple use as rockets, hypervelocity tethers can have a variety of further applications. Drilling and excavation A series of high velocity impacts concentrated onto a small area can serve as an efficient drill. Water or dust at 10 km/s can overcome the mechanical strength of practically any material, so what the target is made of does not matter. The impacts can be tuned to bore a hole through a target, or create shockwaves that fracture it into smaller pieces for easy excavation. One idea is to have the spinning tether first serve as a rocket to bring a spaceship close to an asteroid, then become part of mining equipment to dig into the asteroid’s surface and expose the dense core potentially loaded with precious metals. Just make sure to anchor the tether well! Mass Streams The hypervelocity tether can be used as a mass driver to shoot a series of projectiles to propel other spacecraft. This is known as mass stream propulsion. The spacecraft riding these mass streams only need a device to catch the projectiles - it can be as simple as an ablative pusher plate or as complex as a magnetic nozzle that drops solid targets into the path of the mass streams and pushes off the resulting plasma explosions. Either way, the riders are unburdened by propellant, reactors or radiators, so they can have fantastic acceleration. Mass drivers are usually fixed structures that do not have to worry about their weight, so the tethers can aim for extreme mass ratios. A two-stage T1100G tether with a TMR of 100,000 per stage would have a tip velocity of 17.5 km/s. Spacecraft riding these mass streams could achieve a good fraction of this velocity, perhaps 16 km/s. More mass streams headed in the opposite direction would be waiting for them at their destination for braking. Together, they enable fast interplanetary travel. Railguns or coilguns could also be used as mass drivers, but they are usually much less efficient and take up a lot more room than tethers. Stealth Drive You might imagine that a hypervelocity tether would make for a good weapon. It could drill through any target and its firing rate would allow for enough shots to ensure hits at long range. However, this is unlikely. Hypervelocity tethers have no barrel, so they are inaccurate. It would be difficult to put them in a turret. Their large rotating mass means they act like a gyroscope that resists turning. The way the tether mass scales with projectile mass means that only the smallest projectiles are possible. That removes the option of using ‘smart’ guided projectiles with sensors and RCS thrusters to track a target as these may have a minimum mass of several hundred grams. Worse, they would be extremely vulnerable to battle damage. A small cut on the tether might lead to it completely disintegrating… inside your spaceship. So spinning tethers are a bad weapon. Does that mean they have no military use? There is one final advantage that comes into play. The exhaust of a tether rocket can be cryogenically cold. The entire launch process does not release any heat. Even the electric motor can be of a superconducting design bathed in liquid helium at <4 Kelvin. So long as you have access to electrical power, the tether rocket can be a completely stealthy propulsion system. 
But that is not the only way to use tethers. We can design them for an entirely different role..png)
Counter-rotating tethers ejecting water for propulsion. 
Rows of uranium gas ultracentrifuges. 
Fully superconducting electric motors can reach astounding kW/kg values 
Solar-electric spacecraft with football fields of photovoltaic panels might not benefit much. 
A relatively quick trip from Earth to Jupiter. .png)
The radiators are tapered to fit inside the reactor's shadow shield, with the water tanks serving as extra shielding. 
Not aliens, a spaceship with equatorial tether-rockets (and fancy lighting)! 
Docking might have to be done entirely using secondary propulsion (RCS thrusters). 
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A high pressure water drill. .png)
Dark, non-radiating and doesn't even leave a trail of hydrogen behind it.