Tetherocket

guest blogger john hare

Once a vehicle is in orbit, a high thrust to weight engine becomes a convenience rather than a necessity. For orbital transfer, Isp becomes far more important due to the cost of delivering propellant to orbit. Nuclear thermal seems like a good compromise between thrust to weight and Isp except for the political problems with getting it developed. All of the electrical propulsion system suffer from excessive weight when the power generation requirements are considered. Solar sails will be better for deep space work if they are ever developed and get appropriate markets.

There is at least one credible plan out there to deliver propulsion modules to orbit for $100.00 per pound of propellant. If this happens, then the propulsion for even a mars mission becomes economical enough that all the numbers change. If the modular propulsion modules become available at that price, then 5,000 tons of propellant with tanks and engines would cost one billion dollars delivered to orbit. That would put over a thousand tons of  people, consumables, and gear  in mars orbit for a fraction of one year of the NASA manned spaceflight budget.

Until some of the above items start delivery, a high Isp engine with relatively high thrust to weight compared to ion and other electric thrusters will be very attractive. I propose a 750+ second orbital transfer engine with an estimated T/W of 0.1. Or one meter per second acceleration of the tetherocket system mass with no propellant or payload. It is a mix of tether and rocket technology with some nuclear or beamed energy in the mix. I believe it could be done for an investment that would be economical compared to most of the alternates I am aware of. I believe the performance compromises would be favorable compared to most proposed systems.

Current tether technology can easily get 3,000 meter per second tip speeds on a rotating tether in vacuum. Current hydrogen oxygen rockets can easily get 4,500 meter per second exhaust velocities in vacuum. If an axle anchors the center of the tether to the vehicle with rockets at the spinning tips, then the rockets can pulse during the 10% of the rotation when the vectors line up. When the rockets pulse, the 4,500 meters per second exhaust velocity is added to the 3,000 meters per second tether velocity to give a total exhaust  velocity of 7,500 meters per second relative to the vehicle.

The catch (you know there is one) is that the tether must be powered to reach and keep the 3,000 meter per second tip velocity. It also must transfer the momentum of the rocket pulses to the ship to turn them into propulsion. This will take a considerable amount of power. Nuclear engines would be a good choice with nuclear steam driving the tether. The hydrogen and oxygen could provide the cooling cycle for the nuclear engine before injection into the pulsed thrusters. The nuclear engine would be regeneratively cooled this way with the waste heat providing propulsion gain.

If this propulsion system can be built, it would be somewhat useful for geosats and lunar missions. It would be very useful for NEO, mars, and farther missions. For a lunar mission, it would cut the mass ratio from ~2.4 down to ~1.7 starting in LEO and ending in LLO. For asteroid and mars missions, it could cut travel time by more than  half, or increase the available mass to the destination.

In the sketch above, blue represents the tether being spun  counterclockwise with thrusters only burning from the 10 o’clock to the 8 o’clock position. Yellow is the clockwise tether with a burn from the 2 o’clock to the 4 o’clock positions. With the start and stop transients, true thrust is about a 10% duty cycle. Direction of ship travel is up the page.

I’ve read that current 3,000 m/s tethers can handle tip loads of 1% of their own mass without problems. Each tether has two thrusters firing a total of 20% of the time. A 100 lb tether can hold two 1 lb mass thrusters. A 1 lb mass thruster can have a thrust to weight of 100. Each 102 lbs of tether and thruster will average 20 lbs of thrust. The nuclear or beamed energy engine that drives the tethers should mass about the same. A bare engine would accelerate at about 1 m/s^2. If the engine mass is 10% of the total ship mass, then acceleration is about 100 cm/s^2. It would take half a day to reach escape velocity from LEO. There would be some gravity losses taking this much time to leave orbit. This thing would be more useful in longer range operations.

Feeding and igniting the thrusters seems more difficult than it actually is. If a fine propellant mixture is sprayed in front of each thruster as it approaches the pulse point, the propellants will impact the thruster chamber at 3,000 m/s. The impact will heat the mixed propellants well past the temperature of ignition. The heat generated by the impact boosts the thruster Isp by increasing the mix start temperature. The reaction is that of a pulse detonation engine. Ignoring the performance claims of pulse detonation engine advocates, the hydrogen/oxygen thruster can reach 4,500 m/s exhaust velocities plus some gain from the very high pressure and high expansion ratio possible here. If this reaction can be brought to service, I believe it quite possible that net Isp will be in the 850 range with system thrust to weight double what I am suggesting here.

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johnhare

johnhare

I do construction for a living and aerospace as an occasional hobby. I am an inventor and a bit of an entrepreneur. I've been self employed since the 1980s and working in concrete since the 1970s. When I grow up, I want to work with rockets and spacecraft. I did a stupid rocket trick a few decades back and decided not to try another hot fire without adult supervision. Haven't located much of that as we are all big kids when working with our passions.
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18 Responses to Tetherocket

  1. Tim says:

    1) Exactly how long are the tethers? I’m thinking they might act as a pretty powerful centrifugal pump if you’re going to run fuel lines down them.

    2) I got to thinking about how you could differentiate the torque on each tether to control the yaw (like a great big reaction wheel). Then I realised that since the mass ditribution on each tether is going to change (from transfering and then burning the fuel), there’s going to be some pretty weird dynamics going on. There’ll be some coriolis effects, but thrusting on one side will complicate matters. I’d be more specific, but I barely understand it myself. You can probably learn something from more useful helicopter text book, since the main rotor does a lot more than just spin around.

  2. jsuros says:

    I’m enjoying these thought experiments very much.

    I have to say that the mass involved in delivering fuel to the tether tips and the amount of energy needed to keep the tethers spun up to speed look like the fatal flaws of this design.

    Just how fast can you speed up a light tether, anyway? Would you have enough time to get the tether back up to speed for the next pulse?

  3. john hare says:

    Tim,

    1) Exactly how long are the tethers? I’m thinking they might act as a pretty powerful centrifugal pump if you’re going to run fuel lines down them.

    The tether length would be determined by a bunch of variables. They could be from ten meters to a thousand in practice depending on total thrust to be delivered, size of vehicle involved, pulse rate effects on the tether, and so on. Realized pressures would be insane as a centrifugal pump with tip speeds five times that of a high performance hydrogen impeller. And with pressure rising as the square of tip speed, you are well into the kilobar scale. And tens of kilobars pressure with the LOX.

    Timing the pulses with the pump action would be really tough, and valving those pressures even tougher. If it could work though, expansion ratios of a thousand would make sense.

    2) I got to thinking about how you could differentiate the torque on each tether to control the yaw (like a great big reaction wheel). Then I realised that since the mass ditribution on each tether is going to change (from transfering and then burning the fuel), there’s going to be some pretty weird dynamics going on. There’ll be some coriolis effects, but thrusting on one side will complicate matters. I’d be more specific, but I barely understand it myself. You can probably learn something from more useful helicopter text book, since the main rotor does a lot more than just spin around.

    Changing the orientation of the vehicle with torque would be fairly easy. It’s a reaction wheel sort of thing. Changing the direction of flight would only involve retiming the pulses if sideways thust is acceptable.

  4. john hare says:

    Jsuros,

    I’m enjoying these thought experiments very much.

    Thank you. I think of these as serious fun. It’s just fun unless I see a route to taking it to serious use, then it would be even more fun.

    I have to say that the mass involved in delivering fuel to the tether tips and the amount of energy needed to keep the tethers spun up to speed look like the fatal flaws of this design.

    It could be either one of them that dooms this idea. I’m reasonably certain that the muzzle loading pulses could be made to work without high pump pressures. The energy of the propellant impact in the thrust chamber would be recovered as heat just as the energy pumping the propellant down the tether would be recovered as pressure. The impact method for sufficiently short pulses would have the benefits (if any) of the pulse detonation engines only with more power. The energy of keeping the tethers spun up to speed would take some serious engineering work. For this application, a nuclear steam engine seems like the first choice.

    Just how fast can you speed up a light tether, anyway? Would you have enough time to get the tether back up to speed for the next pulse?

    The 3,000 m/s tether tip speed I suggested is supposed to be well within state of the art. The tethers will have to be tapered though. If you look hard you can find people recommending much higher velocities for rotovators. The time to return to full speed has not been answered that I know of, and I don’t know quite how to tackle that issue.

    I’ve thrown this idea out a few times to tether people with them showing interest. The interest seemed to be tied to the possibility of research funding though. So I don’t know whether the idea intrigued them technically, or just as a lever for research grants.

  5. Roger Strong says:

    If I understand this correctly, you could make the cables tens of kilometers long, rotating at lower rpm. This would make the timing and valving less critical.

    At that length you might be able to also use it as an electrodynamic tether – both for propulsion and for power to supply the rotation torque.

    I have this mental image of one a couple hundred kilometers long acting as a rotovator, picking up fuel or swapping engines from a hypersonic aircraft in the upper atmosphere. (Or from one of JP Aerospace’s Ascenders or Dark Sky Stations?) Then it switches to electrodynamic tether mode to gain altitude, then to tetherocket mode.

  6. john hare says:

    Roger,

    It’s going to take me a while to get my mind around that one. Interesting but confusing ideas there.

  7. Bob Steinke says:

    When I first thought about it, the muzzle loading pulses seemed like they wouldn’t work because the cloud of propellant would expand in vacuum and not all of it might get scooped up into the engine chamber. If any got away it would hurt Isp and high Isp is the only reason to use this design.

    But now that I think about it, maybe two relatively large drops of liquid, one fuel, one oxidizer, or two solid pellets could be lobbed into the rocket throat without boiling or subliming too much outside the chamber.

  8. David C. Neal says:

    Maybe I am missing something… from the 10:00 to 8:00
    burn is 4500+3000=7500…BUT… from the 4:00 to the
    2:00 position actually is 4500 MINUS 3000=1500… thus
    the average EV is (7500+1500)/2=4500, for a net increase
    over the existing engines exhaust velocity of zip.
    Throwing in the added mass/complexity of the tether system
    in effect degrades the performance of the system as a whole.
    Also, the thrust vectors of the two engines must balance, otherwise
    all you will do is create rotation.
    For this to correctly work, the Ev of the 4:00/2:00 engine would have to be (7500+3000)=10500, and if you had such an engine, you wouldn’t need the tether anyway.

  9. Tim says:

    @David C. Neal
    There are supposed to be two tether/engines. The burn between 2:00 and 4:00 is done by the yellow tether in the picture, which is turning clockwise, so the vectors add up. The blue tether is turning anticlockwise and burns from 10:00 to 8:00 for the same effect. Each engine only burns once a rotation.

  10. David C. Neal says:

    Tim,
    That’s what I get for not looking at the picture close
    enough… this is actually a pretty cool idea, and should
    be fairly easy to prove out experimentally.

  11. Eric Collins says:

    This is an interesting concept. When I first read this post, I suddenly had this mental picture of a space craft doing the breast stroke.

    My first thought was that you are going to be dealing with very high rotation rates. For a tether radius of 100 meters, you would need to rotate at 1800 rpms (30 Hz) in order to generate a tip speed of 3000 m/s. For a one kilometer tether, you are still looking at 180 rpms (3 Hz). The time in which you would have to perform your propulsive burn is (1/6)(1/(f Hz)). For the 100 m tether, that would be 1/180 of a second and 1/18 of a second for the km tether. During that time all of the following must occur: a) the fuel/oxidizer enters the chamber, b) rise to a combustible temperature and pressure, c) combustion products expand and exit the chamber, d) thus providing a forward impulse to the chamber. I guess this is not unheard of. You’d basically have to come up with an engine cycle similar to that of an internal combustion engine.

    The reason I do not mention longer tethers is because of my second thought. We’re no longer talking about rigid bodies, but rather vibrating strings. Your thrust events are going to be generating oscillations on the tether perpendicular to their length. Think of a rope tied to a wall and you sending wave trains down it by shaking the end. The thing you would like to avoid is resonant behavior where the amplitude of the oscillations grow. If possible, you’d like to extract as much energy from theses pulses to move the spacecraft forward. These wave pulses will move with a velocity of v = sqrt(F/mu) where F is the tension in the tether and mu is the linear mass density (m/L). Resonance will occur when the time it takes a wave pulse to travel down the tether and reflect back to the source is some multiple of the time between pulses. My concern is not that you will have trouble keeping the tethers spun up. You must somehow be able to extract forward thrust from them while simultaneously trying to prevent the whole thing from shaking apart. It’s possible that, with clever engineering and careful analysis, these forces could be put to effective use for propulsion, but from my first instincts, I’m not entirely certain that it would be possible at all.

  12. john hare says:

    Eric,

    It’s definitely not certain, just possibly very useful if it works. The oscillations are a major biggie. The very fast reaction would be basically a thrust chamber flying backward into a cloud of mixed propellant at 3,000 m/s. The impact should handle the mix and ignition in under a millisecond.

    A by product of the system is that it could use any liquid for propellant including martian CO2 and lunar LOX without burning it. Impact vaporization would heat it into almost respectable rocket temps with system Isp in the 450-500 range.

  13. john hare says:

    Roger,

    I had to chew on your idea a while. I’m of a first impression that we may be talking at cross purposes. One problem being that I don’t speak electricity or electronics.

    My current understanding of electrodynamic tethers is that you can add power to raise the altitude or collect power at the expense of drag and altitude loss, but not both at once. The rapidly rotating tether/rotovator would only be in position to use the earths’ magnetic field for propulsion/power supply about 20% of each revolution in two 10% segments. The rest of the time the tethers would be too far out of alignment to work effectively. If I said this wrong, I would appreciate correction from anyone that speaks fluent electrodynamic tether.

    It does seem possible that enough electricity could be harvested to run the tetherocket as a lower Isp/higher mass propulsion device.

    It would be interesting to see how a motorized rotovator could be made to work by your description. It seems possible that the tether could be spun up with the torque engine and the stored energy used to help raise the orbit after a catch. Could get interesting.

  14. Eric Collins says:

    As a potentially useful modification to your design, one could easily envision six arms for each rotating tether. That way there is always one arm (on each side) in the “thrusting position”.

    The electromagnetic tether idea is an interesting in itself. I think that it actually does end up looking a bit like an electric motor. This motor would effectively have two stators (i.e. positions where the maximum amount of torque may be generated). However, the number of rotors may be greater, and it would probably be possible to figure out the optimal configuration for a given amount of power available. As with an electric motor, the key is to switch the current in the rotors at precisely the right time to generate a push/pull in the desired direction.

    The electrodynamic tether would even seem to help mitigate the vibrating string problem (mentioned in my previous comment), since the Lorentz force would be applied to the entire length of the tether simultaneously, thus avoiding or at least diminishing the difficulty of managing traveling wave-pulses along the length of the tether.

    The more I think about it, the more I like this idea. If anyone can think of a show-stopper for the em-tether-drive please chime in.

  15. john hare says:

    Eric,

    As a potentially useful modification to your design, one could easily envision six arms for each rotating tether. That way there is always one arm (on each side) in the “thrusting position”.

    You gave me this visual of a spider web with the arms providing mutual support to smooth and carry the load.

  16. John,

    A 100 pound rocket exhaust at the end of an e.g. 1000 foot tether produces a ridiculous amount (100,000 ft-pounds) of torque, which will slow the tether’s rotation rate. You need to put torque back into the tether to keep the rotation going.

    If you have a 100 pound rocket going at 10% duty cycle, then you’ll need to put in 10,000 ft-pounds of torque continuously. You can do it by connecting the tethers to the spacecraft by an offset bell crank. The mechanical power going through this bell crank is huge, because that’s how you are imparting the extra kinetic energy to your exhaust propellants. If you’ve increased Ve from 4500 m/s to 6500 m/s, for instance, more of your energy is going through the crank motor than is coming from the propellant chemical reaction.

    Yes, nuclear is one way to get a lot of power, but if you’re not in a hurry photovoltaics can do the job too. Once you are getting the majority of your rocket power from photovoltaics you can assume you’ll be thrusting for a month or so.

    Note that the idea of launching the propellants in front of a ramjet-type engine at the tether tip does not work to improve Isp. The propellants aren’t starting with the tether tip’s velocity, so they don’t benefit.

  17. john hare says:

    Iain,

    A 100 pound rocket exhaust at the end of an e.g. 1000 foot tether produces a ridiculous amount (100,000 ft-pounds) of torque, which will slow the tether’s rotation rate. You need to put torque back into the tether to keep the rotation going.

    If you have a 100 pound rocket going at 10% duty cycle, then you’ll need to put in 10,000 ft-pounds of torque continuously. You can do it by connecting the tethers to the spacecraft by an offset bell crank. The mechanical power going through this bell crank is huge, because that’s how you are imparting the extra kinetic energy to your exhaust propellants. If you’ve increased Ve from 4500 m/s to 6500 m/s, for instance, more of your energy is going through the crank motor than is coming from the propellant chemical reaction.

    I agree the power used here is huge. It is one of the largest potential show stoppers. If anybody decided to develop this thing, I would hope that they would spend a week or three on a feasibility study of this exact issue before spending another nickle. While I was thinking of a shaft drive from the nuke, the crank is in the drive train on some methods. On a short enough unit, it might be turbine direct.

    Yes, nuclear is one way to get a lot of power, but if you’re not in a hurry photovoltaics can do the job too. Once you are getting the majority of your rocket power from photovoltaics you can assume you’ll be thrusting for a month or so.

    If you are taking your time, ion or Hall thrusters might offer enough advantage to make this concept redundant. In either case, microwave or laser beamed energy is worth looking into, possibly as a supplement to solar.

    Note that the idea of launching the propellants in front of a ramjet-type engine at the tether tip does not work to improve Isp. The propellants aren’t starting with the tether tip’s velocity, so they don’t benefit.

    Sooner or later I will learn to express myself clearly. 🙂 A ramjet compresses air in a forward intake, combusts it in the middle, and expands in through a nozzle. This unit would be a thrust chamber moving backwards at 3,000 m/s into a cloud of gaseous propellant. The propellant will be accelerated to the 3,000 m/s of the chamber in a small fraction of a millisecond as it impacted the chamber. The 3,000 m/s impact would vaporise and heat the propellants to a very high temperature disregarding any combustion energy. With the propellants beginning combustion well mixed and very hot, the final combustion temperature would be considerably higher than that of propellants that started from liquid. The rocket Isp would be higher regardless of tether velocity addition.

    Another view is a fast pitch baseball hitting the bat vs hitting the same ball from a stationary tee with the same bat velocity. The pitcher is adding to the distance it is possible to hit the baseball with the increased impact energy. This is the reasoning I use for the in situ fuel claim of 450-500 Isp without combustion.

  18. Eric Collins says:

    You gave me this visual of a spider web with the arms providing mutual support to smooth and carry the load.

    Actually, the spiderweb layout might be a good way to help damp out the tether oscillations.

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