Small Tetherocket

Some years ago I posted an idea for combining tethers, rockets, and nuclear power to build an engine with very high Isp for orbital transfer operations. 750-850 seconds Isp with LH2/LO2 seemed and still seems possible. I am posting a follow on to that idea with some modifications suggested by commenters and some of my own.

 

The original post is at     http://selenianboondocks.com/2008/10/tetherocket/

spindizzy

In this cartoon, the spiderweb structure is a connected tether complex inside a pressure disk. It is powered up to 3,000 m/s by the onboard nuclear or solar power with the spin maintained by continuous power input.  The little angles on the tether tips are the throatless diverging combustion chambers. The LH2 and LO2  are sprayed into the path of the combustion chambers and both mixed and ignited by the 3,000 m/s impact. The pulse detonation burn will exit the combustion chambers at close to the 4,500 m/s characteristic of an LH2/LO2 engine in vacuum relative to the moving combustion chamber.

The small combustion chamber  expansion ratio is partially compensated by the impact heating and pulse detonation in the initial chamber. The near 4,500 m/s exhaust velocity is relative to the moving combustion chamber though and has a vehicle relative velocity of nearly 7,500 m/s. The exhaust then enters the single fixed high expansion ratio nozzle to finish expanding to as near vacuum as possible. The net exhaust velocity should be in the 8,000-8,500 m/s range.

I still see the T/W as being about 0.1 or 1 m/s acceleration with the bare engine and probably about a tenth of that including  vehicle mass. 100 cm/s would go from LEO to Lunar Transfer Orbit in about half a day using about 1/3 of IMLEO to do it.

Higher T/W than ion engines. No radioactive exhaust as in nuclear thermal and higher propellant densities to boot at similar net Isp. Switch to methane/Lox or any other bi-propellant  by changing two low pressure injector elements. Able to use inert gasses from ISRU anywhere in the solar system for Isp in the 450-500 range using the mechanical drive alone.

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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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35 Responses to Small Tetherocket

  1. Pingback: Just Space News / Small Tetherocket

  2. George Turner says:

    I’ve been thinking about this for part of the day, and I finally wondered if you could use a non-rotating thick fixed disk with slots cut into it (as if by a lathe), to which mates a thin, rotating disk with tabs that go in the slots. The tabs and slots are kept apart by magnetic levitation so that the centrifugal forces on the rotating disk don’t get to build up. Each tab only has to support the thin web down to the next tab, yet you still have a full mechanical connection between the rim and the shaft, able to transmit torque. Then I figured it would be easier to dispense with the rotating disk and just have the rockets ride like suspended maglev sleds from the non-rotating disk.

    I’ve never done maglev calculations, but the field pressure on a superconductor (in Pascals) is the square of the field strength in Teslas divided by 8π×10−7. In psi that would be B^2/25.133. A neodymium super magnet has a field strength of 1.52 Teslas, giving you 90 psi, while the highest field made by a non-superconductor is 36.2 Teslas, 75,600 psi, and the highest continuous field made in a lab is 45 Teslas, 116,800 psi. Those pressures are all well within the range of what steel can deal with, and if you know your rocket nozzle and fuel weights you can size the pad accordingly.

    I don’t think there’s an ISP limit on this thing, as long as you let your diameter increase. And of course the reaction torques and forces would just be handled by the maglev control system itself. The thickness of the fixed disk or ring is just the same as an internal pressure calculation, given the weight of the rotating thrust assemblies and the centrifugal accelerations.

  3. johnhare john hare says:

    The Isp limits are in the power inputs that are offstage in this post. Just as an ion engine doesn’t normally run at maximum possible Isp, this one wouldn’t either. With power requirements going as the square of the mechanical input to the Isp, the sweet spot for a given application could be considerably lower than what I posted here. Going for Isp=600 with tether at 1,500 m/s would quarter the power requirements and drop the tether mass enormously.

    Electromagnetic suspension is certainly an option if all other considerations work. There are still some velocity limits due to heating I believe though I don’t speak electric and can’t do the calculations. That opinion is from rail gun discussions and may apply to a totally difference problem.

    The Isp limit is still the power limit though even with electromagnetic suspension. With power requirements rising as the square of the velocity input, you could easily end up in the position of having a big block V8 supplying the power for driving the windshield wiper.

  4. George Turner says:

    I think my idea is just the cyclotron version of a linear accelerator, or a circular maglev version of a mass driver, with the addition of your rocket engine. The circle lets you retain the engine instead of launching it out the back or decelerating it. It’s so similar to a mass-driver that the prior design work on that should directly apply.

    On the power requirements, the tether sounds like it would have some of the restriction NASA faces on putting a VASIMR on the ISS, where the station can’t provide the 200 KW for continuous operation. Instead they plan to charge batteries and use it in short duration pulses. A tether system could have the ability to provide continuous thrust at lower ISP or to store power for short bursts at higher ISP.

    However, I think they’re dealing with some efficiency vs. size issues, where a more powerful VASIMR has a higher ISP than a smaller one. Where that trade off isn’t present, it would probably make sense to only make your tether system as large as the available power would support, running it continuously instead of in small bursts.

  5. Paul451 says:

    Given how little time each combustion chamber spends in the injection zone (hundredths of a second), I don’t think you want LH/LOx, I think you want ANFO or even RDX/C4.

    Also, your injection site is on the wrong side. You’d want the injection on the right, ignition near the top, giving the detonation time to propagate before the chamber is exposed to the exhaust nozzle. (Plus I would think you would inject the fuel into the centripetal disk, using the outward centrifugal force as your fuel pump.)

    And instead of separate nozzles in a spider-frame, I would think the nozzles would be a single structure with a cross-section similar to a large-toothed circular-saw blade.

    And obviously, matched pairs. This thing would just turn your ship into a catherine wheel.

  6. johnhare john hare says:

    A monopropellant would simplify things at the expense of Isp, though I don’t think an actual plastic explosive would be the ideal choice. In the original idea, the long tethers lengthened the propellant residence time to a more reasonable dwell.

    The injection point would need to be established by experiment and simulation. exhaust too early would have 7,000 m/s hot gasses eroding the interior chamber as well as losing performance to friction before entering the expansion nozzle. Using the wheel as a pump at those velocities has H2 in the 3 kilobar range with the dense propellants proportionately higher. The tubes wouldn’t handle it at the tapers required. Even pumped as gas there would be a lot of power going to pumping(compressing) and have high velocity gas heating up the necessarily thin tubing.

    The structure on a solid disk may not handle the velocities involved as even high tech tethers have substantial taper to hit 3,000 m/s. The saw tooth layout is certainly an improvement on the original.

    I believe that gimbal angles and offset thrust could keep it viable with one unit, though two would simplify things.

  7. Paul451 says:

    “though I don’t think an actual plastic explosive would be the ideal choice.”

    You’re building a pulse-detonation wheel, not a rocket engine. Short sharp bangs. Closer to Orion than SSME.

  8. Sam says:

    Wouldnt the spinning wheel simply decelerate?
    Unless the wheel weighed a massive amount, you have 3000 m/s pushing back onto it, you’d need to spin back up after just a couple of pulses..

  9. Chris says:

    We are obsessing with high Isp because it reduces the propellant mass fraction, but we forget that it also increases energy consumption. At high Isp most of the energy ends up as the kinetic energy of the exhaust. Moreover, this energy has to come from somewhere! Currently, the best option is to beam the energy. One could imagine a two stage vehicle, with first stage powered by a propellant with high density impulse (say RP-1/LOX), and second stage powered by LH2 engine powered by power beamed from a power satellite. The role of the first stage would be to boost the second stage out of the atmosphere, where it would be beamed by the solar power satellite. The satellite could be preferably in a LEO, but then we would need a bunch of them for different orbits. The externally powered LH2 engine would get easily Isp of 800s.

  10. George Turner says:

    For a continuous combustion option with a rotating ring, you could have a fixed combustion chamber mated up against the outer ring, whose inner surface is a cylinder perforated with holes that lead to individual throats and expansion nozzles. The combustion products are injected and ignited in the two regeneratively cooled chambers on the left and right, travel outwards at subsonic speeds to the rotating rim (perhaps covering an arc from the 10 o’clock to the 8 o’clock) and then entering angled holes in the rim that are passing by at supersonic speeds. The gases then get compressed and accelerated by the rim, make a 90 degree bend in the direction of travel, go sonic as they enter the throat, and then accelerate in the expansion nozzle.

    I have no idea if that would actually work, and there would be inevitable leakage between the rim and the fixed combustion chambers, but it could be tested with an existing thruster mated to high speed perforated disk. You could possibly do a proof-of-concept test with compressed air. It would hopefully sidestep the problem of start/stop transients eroding overall performance and replace them with new and different problems.

  11. Peterh says:

    Seems an unnecessary complication to mix combustion and whatever is driving the spinning vanes. The vanes themselves would seem capable of driving an arbitrary fluid to an arbitrary speed given enough power. Peripheral magnetic bearings could handle centrifugal forces. The factor I see limiting wheel speed is fluid friction heating, which should be less a problem with a larger volume/surface ratio in the driven fluid.

  12. George Turner says:

    I just thought of a way to raise a satellite’s apogee by reusing the reaction mass, which struck me as kind of bizarre, so I’ll share, even though it’s kind of impractical.

    You have a satellite with a small mass driver in a circular orbit. You fire a slug to raise or lower the opposite point in the satellite’s orbit, just as you normally would. The slug, meanwhile, goes on a different elliptical trajectory. Both slug and satellite will again pass through the same point where the slug was fired, and if you carefully pick the slug’s mass and exit velocity, you can make the slug’s elliptical orbital period an integer fraction of the satellite’s new elliptical orbital period, which means the slug and satellite will meet up once again. If you can get the slug to pass through the mass driver, you can accelerate it even further, doing the same thing over and over until the slug hits escape velocity or crashes into the atmosphere.

    Or you could have two satellites of the same mass in the same orbit, one traveling prograde and the other retrograde. They electromagnetically react with each other at perigee to increase both of their orbital velocities by equal and opposite amounts, creating an exactly equal apogee on the other side of the Earth, where they’ll meet up again. The reaction is then repeated to raise their perigees, perhaps recircularizing their orbit. Then 180 degrees around, they meet again and repeat it, raising both their orbits step by step without expending any reaction mass.

  13. George Turner says:

    I’m thinking about the previous idea, and it would be really useful for getting major payloads from low lunar orbit to low Earth orbit. You launch the payloads from the moon into opposite orbits, and the moon spins so slowly that retrograde doesn’t really have any performance penalty. There’s no atmospheric drag, so the payloads could spend months slowly pushing against each other as they pass to boost them to higher and higher lunar orbits until they’re ready for a tiny burn or bump to drop into a very high Earth orbit, one payload going retrograde and the other normal, which carries no real penalty coming from that far out.

    Then they reverse the boost process and start resisting each other as they pass, perhaps by having each generate a small magnetic field that passes through a large diameter coil on the other, or some such thing. Their initial potential energy is thus converted to electrical power twice per orbit as they slowly work their way down to LEO, expending no reaction mass in the process.

    It should let you shuffle large payloads up and down with no expenditure of fuel, which is rather hard to come by on the moon.

  14. Jeff Mauldin says:

    Read a story once where a long metallic tether hanging from a ship or station in earth orbit, moving through the earth’s magnetic field, could either be fed or drained a current resulting in a higher or lower orbit with no use of reaction mass. I think the physics was valid.

  15. johnhare John hare says:

    An orbiting momentum exchange facility would take mass and complexity off of the ships. Catch lunar suborbital and accelerate to heo. Heo to ellipse. Ellipse to Leo. Leo to reentry. And all the way back to recover all the energy. Three MEMs for translunar operations. One more in earth elliptical for deep space trajectories.

  16. born01930 says:

    I am confused…to raise orbit are you saying they each would have a mass driver and basically shoot each other to conserve momentum? Have either a solar or RTG driven railgun.

  17. George Turner says:

    Yep. A thought experiment is a space pirate (in a wooden space ship) in retrograde LEO orbit and a navy ship in normal orbit, both armed with ballistas and one bolt (big arrow). Just after they pass each other each ship fires a bolt at the other, accelerating slightly from the ballista’s recoil. Then each ship gets nailed in the stern by the other ship’s bolt, accelerating it further. That slightly raises the opposite orbital node of each ship by the energy used to crank the ballistas. Then a pirate and a seaman retrieve the bolts sticking in their respective hulls and stick it in their own ballista. The angular momentum of the system of the pair of ships and the pair of bolts remains zero at all times. Thus they can ratchet their way up from LEO without expending any fuel at all, as if they had infinite ISP. If they shoot at each other’s bows instead of each other’s sterns, they ratchet their way back down from high orbit.

    I would’ve used a cannon ball analogy but they’d run out of gunpowder. 🙂

    I’ll have to think about a dedicated momentum transfer facility because its orbit would likewise be affected, and it may have to move up and down in concert with the payload. If it does, to return to its original position it might have to transfer an equal amount of mass back up as it did coming down, whereas if two payloads worked together the process could shift mass constantly from the moon to LEO, though half would be in retrograde orbit. Perhaps if both payloads went into polar orbits, or if both payloads were destined for re-entry, that would be irrelevant.

  18. George Turner says:

    A few more thoughts.

    In the momentum transfer, the ships have to pass each other without colliding, so if they’re traveling in the X direction as they approach, one should perhaps be slightly higher than the other (viewed in the plane of the orbit) so they miss. This means their orbits will be very slightly inclined, relative to each other, with one satellite above for one pass and then below for the opposite pass. This means the momentum transfer would have a Y component (forgive the coordinate system), with one satellite getting a small +Y impulse and the other getting a -Y. So the orbital plane would get a small change in inclination with each pass, but since the satellites were going in opposite directions, the + and – Y means they’d stay in the same shared, but altered, orbital plane. You could optimize for that alone and gain the capability to both raise and lower a satellite’s orbit and do plane changes, all with no expenditure of propellant.

    For a planetary mission I would suggest having the momentum transfer system, a high ISP ion drive, and a high thrust chemical rocket. You launch the satellite pair into LEO and use momentum transfer to very slowly ratchet it up to an extremely high orbit, where the potential energy is maximized. Then they start to drop back down with a few momentum passes before firing their ion drives for a plunge past the Earth, where they fire their chemical rockets at closest approach to maximize the Oberth effect. Both then go on an interplanetary trajectory to the target, again approaching it from opposite sides, and they fire their ion drives to drop into a very high elliptical orbit. After that they use momentum transfer to ratchet themselves down into low orbit.

    That means the mass budget for an deep space mission can be reduced to two minor ion burns (for dropping out of very high Earth orbit and inserting into a high target orbit), one chemical burn for the Oberth effect, and of course the double launch to LEO (with one launch being retrograde).

    Someone’s probably written this up before. Perhaps the British Interplanetary Society. I once thought of using football shaped orbits with momentum transfer at the pointy ends to levitate a stationary structure over each poles, but they had thought of it first.

  19. Bob Steinke says:

    So the other ship becomes your reaction mass. When you pass in LEO the other ship is going to be traveling away from you at ~16km/s. I was going to say the energy efficiency is going to be terrible, but it will be about the same as an ion drive with an Isp of 1600. If you have a solar panel and plenty of time that’s okay.

  20. johnhare John hare says:

    On the other hand, a fifty ton ship in LEO with a 4 km/s rail gun could pitch and catch with a one ton ship coming in from luna with an initial ISP of 700 on the luna ship with an ISP of 400 on the LEO ship. Then the LEO ship could do the same in the other direction lifting a sub-orbital craft to LEO. All momentum conserved. The LEO ship could also pitch and catch with a craft going for escape.

    Wash, Rinse, repeat for another ship in lunar orbit.

  21. George Turner says:

    Yes, the efficiency could be very bad, depending on how you do it, but the fuel consumption is still zero, so you can keep going until the satellite wears out. 🙂

    In the case of physical mass transfer, both satellites of course have to launch a projectile on each pass. One can’t be a dedicated launcher and the other a receiver or the launcher will run out of projectiles, plus their masses would start to differ, The impulse from launching also won’t remotely match the impulse from receiving, as you can almost certainly fire a mass at high velocity a heck of a lot more safely than you can get hit by it. So perhaps ideally the muzzle velocity would be exactly the same as the closing velocity of the two satellites, or slightly biased toward a definite but slow impact so capture is guaranteed, perhaps with a giant catcher’s mitt, or by shooting metallic projectiles with a rail gun that then get sucked up by a magnetic field and floated into a railgun’s breech.

    Running some numbers to see if this could even be worthwhile:

    * Goes and builds a giant spreadsheet of orbital mechanics to analyze things shot by shot *

    A 10 tonne satellite at 170 km up firing a 4 kg projectile at 15,590 m/sec (twice orbital velocity to make the projectile mate up with the opposite satellite) would produce a recoil velocity of 6.80 m/sec, which is 15 mph, which sounds somewhat survivable with recoil absorbers. At the initial LEO it fires every 44 minutes, firing 32 shots on the first day. The shots come in pairs. The first (by both satellites) raises the orbit along a Hohmann transfer, and the second shots circularize the orbits, requiring slightly less delta V. Shot pair 1 raises the orbits by 20.9 km.

    195 days later (my time is slightly approximated to the period of the orbit prior to flying each Hohmann), on shot pair 583 (1,166 total shots per satellite) the pair reach GEO (one of course going the wrong way). The shots by then are two per day and only have a muzzle velocity of 6.13 km/sec, producing a delta V of 2.46 m/sec (5.5 mph), but each shot is also producing a very large change in altitude (124 km on the last one).

    If you went with a purely electromagnetic interaction you could have two different kinds of satellites, perhaps one being the magnet and the other the coil, or however you want to do it. Even if it’s wildly inefficient, the inefficiency would show up as heat, not lost mass or fuel, and you’d compensate with slightly larger solar arrays and batteries or capacitors (since the interaction time will be very, very brief).

    With either method, the limitation on the equivalent thrust is going to be the orbital period (two momentum transfers per orbit per opposite going satellite) and the amount of impulse the satellite can withstand during the interaction. For momentum transfer, that would be the maximum G’s and shock from the recoil. So if you had four satellites, two going in one direction and two in another, the same system should be able to climb up twice as fast. However, instead of having just one orbital plane to worry about, the slight variations required to make sure satellites don’t hit might quickly split the four up into two non-intersecting pairs. It would take some realistic design assumptions and orbital code to investigate that. Running a larger network would be very beneficial, because if two satellites can work their way up or down slowly, and twenty can make the climb or descent ten times as fast (more interactions per orbit), then the work done by the system goes up by a factor of one hundred (ten times the mass moving up or down tens times as fast). That would requiring more solar cells per satellite, obviously, but no extra energy storage because the same discharges for a two satellite system will just be happening more frequently.

    But can the orbital mechanics work for an array of satellites, could a workable reaction mechanism be built, and could satellites be controlled to the required level of precision so they don’t collide and don’t drop a ball, and can balls be fired with the precise and variable muzzle velocities required?

    And sorry about hijacking the thread. One thought led to another, as sometimes happens on interesting space propulsion topics.

  22. George Turner says:

    I went ahead and put in the correct Hohmann flight times, but it didn’t affect the above time to GEO by a whole day (still 195 days with the 15 mph recoil). But I did notice that the performance was dropping drastically the further out the pair went, taking ten years to get 75 percent of the way to the moon. Instead of firing 32 times per day as it did in LEO, at the 75 percent distance it was firing once every eight days because the crossings were so infrequent, and the delta V per firing was getting smaller and smaller because the orbital velocity kept dropping. One solution would be to fire volleys of shots, perhaps 10 spread over 10 seconds, and I was going to calculate those trajectories tomorrow to investigate the ramifications on capture, but then I realized that such a system would be designed to handle some maximum recoil energy and that I was only approaching that down in LEO. As it went higher, the system was basically idling. Since the muzzle velocity is determined by orbital parameters, the obvious solution to up the recoil was to change the weight of the shot.

    So I modified the spreadsheet to pick the heaviest shot in integer kilograms that wouldn’t result in a recoil that exceeded 7 meters per second, with an upper limit of 30 kg. I figure the shot could be disks of uniform diameter to make handling easy, resulting in a longer and longer slug. That cut the travel time to GEO in half (99 days), and had the system starting with the original 4 kg shot and working its way up to an 11 kg shot right before reaching GEO, at altitude jump number 396. The system cut the travel time to 75 percent of lunar distance by five, getting there in two years.

    If you combine that simple change with the potential for volley fire spread out over ten seconds or so, or perhaps far more (orbital math involved), such a system could perform quite nicely around any gravity well, and gravity wells are the big delta-V mass ratio sinks.

  23. George Turner says:

    * the above should read “result in a recoil that did not exceed 7 m/sec, with an upper limit of 30 kg.”

    Going down may be more technically challenging than going up with mass transfer, because to achieve the same orbital steps going down each satellite has to lob a slug without any muzzle velocity at all (the cannonball is tossed over the side), and the ball then has to precisely impact the muzzle of the opposite satellite’s ball launcher as it fires – but kind of backwards for a rail gun. The receiving blow can’t be softened without decreasing the deceleration of the receiver and accelerating the velocity of the sender. So that’s a pretty screwy hurdle to cope with. It’s a time-reversed version of going up that I didn’t foresee, but that my spreadsheet made obvious within a couple of minutes of juggling kinetic energy and momentum. A change of mental reference frame made it clear. Receiving a volley might be much more difficult than firing one, as the unfeed mechanism has to work as hitch-free as the feed mechanism. Pure electromagnetics for descent might be easier if it doesn’t turn too much of the satellite’s mass into heat sinks and radiators.

    As an aside, I was thinking how to best explain the idea to a pair of geologists on my patio earlier, and it struck me that they would understand skateboards or better yet, hoverboards, on an inclined circular track at a skate park. They are stuck going round and round and can’t speed up or slow down – unless they have a pair of footballs. If they turn backwards and throw the footballs to each other as they part, the recoil of the throw will speed them up, and they get to catch a football that’s floating right in front of them like a hand-off, so they’ve lost nothing and can keep doing it. By passing and catching as they pass and part they can speed up, working their way up the wall (but seeing slower lap times). By handing off the ball as they pass each other they can drop down and get faster lap times. Without the football and their throwing arms, they’ll be stuck in the same circles until the Sun runs out of hydrogen.

    That probably matches my Petticoat Junction proof-of-concept analogy about how to make an efficient high pressure, high volume turbopump with no moving parts and made mostly out of pipe from a hardware store. I love analogies and thought experiments like that, where you shift your mental references to sidestep an intractable problem because it was only in your head.

  24. born01930 says:

    Would doubling the number of satellites halve the time? Such that if I want to send a shipment of unobtanium I mined on the moon to reach the market on Earth in 6 months I would launch 8 satellites from the moon?

  25. johnhare John hare says:

    George,
    Given the driver tech you are postulating, one could launch cubesats retrograde to an L1 rendezvous and collect them on the way to the moon. One ship with arbitrary acceleration not tied to the counter matching orbit.

  26. George Turner says:

    borno, yes. The more satellites you use the more accel/decel interactions they can have per orbit, assuming they can all stay in-plane. Figuring out if that’s the case would take some detailed simulations, but even if it does occur they could burn very very small amounts of fuel for course corrections, as the impulse error from tossing a ball out the side at 0.1 m/sec is going to be vastly smaller than the desired impulse change from catching it at 6,000 m/sec.

    John, definitely so, assuming a workable launch/capture system can be fit to a cubesat. This system might be easier in larger sizes, depending on the technological hurdles and solutions. But you make a very interesting point. For a given mass, a constellation of 2*N cube sats can move up N times faster than a single pair of big ships that have the same mass as the fleet of cubesats – or you could reduce the required impulse per encounter to simplify the technical problems.

    This might be a great way to stage fuel depots and large pieces of equipment in high orbit or L1, from which interplanetary transfer orbits require only minor delta-V’s, massively reducing the cost and LEO-mass of major missions.

    Of course fleets of retrograde satellites would give the tracking and debris guys nightmares, so everything would have to be closely coordinated. Happily, if you abort a shot all the satellites will either stay in the elliptical orbit that was part of a Hohmann or stay in their circular orbit, and either a half-orbit or full orbit later you can try again. That might be required occasionally for debris or collision avoidance, and would undoubtedly be termed “playing Frogger” by the guys who make the call.

  27. Peterh says:

    It would seem very desirable for the satellites kicking off each other to use an electromagnetic interaction, rather than throw mass at each other. But those forces scale as 1/r^2 (electric monopole vs. monopole, difficult to maintain in the plasma of space) or worse.

  28. George Turner says:

    Yes, but tossing mass back and forth is going to be really hard, too. Earlier today I felt sad for the guy whose job would be to design a railgun that could hurl a 4 kg mass at the required velocity, having to make equipment that could deliver the kinetic energy requirement of spreadsheet cell $J$27, 470 megajoules, to fire the 4 kg ball, just so the ball can end up with the same Earth-referenced kinetic energy it had to begin with.

    I had one odd thought on coming down, which was to proceed with a forward pass at 2V, then have the opposite satellite absorb exactly half the velocity, leaving the projectile back at the same velocity as the satellite that just threw it and in very close proximity. In football parlance I guess that would be a pass deflection that’s recovered by the quarterback. It would be like letting a tiny part of each satellite have a massive electromagnetic interaction with the other.

    If you had a whole lot of satellites, a magnetic system would morph into a giant electric motor/generator that could spin its way up and down.

  29. George Turner says:

    To reduce the kinetic energy requirements on a mass transfer, the obvious answer is to go with heavy projectiles and low muzzle velocities. So I have satellite A (10,000 kg) traveling at 6000 m/sec and kicking a 100 kg projectile out the back at -100 m/sec (instead of -12,000 m/sec). That only imparts 500,000 Joules of kinetic energy relative to the launcher (which is only 139 Watt hours, trivial to recharge with solar).

    That gives satellite A a boost of 1 m/sec and leaves the projectile traveling at 5900 m/sec. Then satellite B flies past and has the projectile from A pass through a coil that tries to throw the projectile back to Satellite A, giving the shot a delta V of 102 m/sec, and a final velocity of 6002 m/sec in the same direction that it had been going previously, so that it catches back up to launcher A with a closing velocity of 1 m/sec. As a result of that kick, satellite B has also accelerated in the opposite direction of satellite A, having use the same shot with a kick in the other direction, and with only the same small velocity change, and thus the same low energy demands.

    Satellite A’s role is simple, catch and launch a 100 kg projectile at a low velocity. Satellite B’s role is difficult because it has to impart a delta V to that same projectile during an extremely brief time (2.5 milliseconds for a 30 meter coil), which means the applied force has to be very high (900,000 lbsf in his example) and very brief, almost like a kinetic impact, but the energy demands are the same as for satellite A.

    I’m not sure that actually simplifies having the satellites act directly on each other, but it sidesteps the incredibly high energy requirements and muzzle velocities in the prior stab at mass transfer.

    There are certainly a lot of other tricks to investigate, and if even one of them is practical then LEO isn’t halfway to anywhere, it’s three quarters of the way to anywhere, because satellites can ratchet up and down a gravity well for free. That makes solving the puzzles and problems more interesting.

  30. Pingback: Tether Rockets and Orbital Boosts

  31. George Turner says:

    That last method I described might be entirely feasible with an electromagnetic superconducting quench gun described here for launching payloads from the lunar surface. Such launchers store all the energy in the magnetic fields of the superconducting coils, which can be slowly charged up with solar cells without any losses.

    So the launching satellite (A) would energize the magnetic field in the projectile and launch it, and if that field doesn’t dissipate in the short time to intercept then all the quench coil on satellite B has to do is deflect it back. If four coil systems and projectiles are used per pass, and in sequence, then the satellites could get four boosts per pass within their shock/acceleration limits and also balance the torques in two planes.

  32. Bob Steinke says:

    @George Turner

    I don’t think throwing a larger mass with smaller velocity increments will save any energy. Satellite A saves energy, but Satellite B takes more energy, not less.

    Satellite A provides a local reference frame velocity change from 0 m/s to 100 m/s energy is:

    0.5 * 100 kg * 100 m/s^2 = 0.5 MJ

    Satellite B provides a local reference frame velocity change from 11,900 m/s to 12,000 m/s energy is:

    0.5 * 100 kg * (12,000 m/s^2 – 11,900 m/s^2) = 119.5 MJ

    Whereas, if you have each satellite provide a 1000 m/s velocity change to a 10 kg mass you get this:

    Satellite A 0 m/s to 1000 m/s:

    0.5 * 10 kg * 1000 m/s^2 = 5 MJ

    Satellite B 11,000 m/s to 12,000 m/s:

    0.5 * 10 kg * (12,000 m/s^2 – 11,000 m/s^2) = 115 MJ

    The total is the exact same 120 MJ. In essence, the satellites are pushing against each other, and their relative velocity determines the ratio of delta energy to delta velocity.

  33. George Turner says:

    You’re right Bob. I hadn’t gone all the way through the energy numbers on that second shot, instead assuming that since the actual delta V applied to the shot is small, the energy is probably small. To double check that it wasn’t just a KE reference frame issue I went ahead and used force, distance, and work on the second deflection and got the same numbers you did.

    So I’m back to square one with extremely high muzzle velocities and near-zero capture velocities, while assuming superconducting quench guns could achieve them.

    I’m looking at easing the close-crossing hazards by having the satellites maintain a vertical separation of about half a kilometer. Instead of trying to pass the shot between satellites immediately and directly during an extremely close pass, I’ll look at firing the shots on their own Hohmann trajectories so their apogees and the apogee of the opposite satellite will coincide half an orbit later. It adds quite a few complexities and the firing points will slowly walk (because the satellites orbital periods will never match) and it requires controlling the shot velocity and trajectory with extreme precision, but it might be workable.

    I’ll update the thread once I get something all coded and debugged, which might take a few days.

  34. George Turner says:

    Strangely enough, the above actually works. Satellite 1 is in a circular orbit at radius A and satellite B is in a retrograde orbit at radius A + S, where S is the separation distance between the two orbits, which will be kept constant. Satellite 1 fires a shot to move it to radius B, while Satellite 2 fires a shot to move from radius A + S to B + S. The shots have to fly their own Hohmann’s from (Sat 1 to Sat 2) A to B + S and from (Sat 2 to Sat 1) A + S to B. And the ratio of the shot mass to satellite mass determines the relative delta V’s of a shot and the satellite that fires it.

    When you assume that mass ratio is the same for both satellites, it means the ratios of the delta V’s are the same. So:

    sqrt(GM/A)*(sqrt(2B/(A+B))-1) / sqrt(GM / (A+S))*(sqrt(2*(B+S)/(A+B+S))-1) =
    sqrt(GM/(A+S))*(sqrt(2*(B+S)/(A+B+S))-1)/sqrt(GM/A)*(sqrt(2B)/(A+B))-1)

    All terms cancel and both satellites of equal mass fire shots of exactly equal mass, regardless of separation distance.

    Next up is figuring out why the miss distance due to the differing flight times seems to be constant (but different) for both satellites, regardless of orbital altitude, which requires one satellite to fire something like 1/8th second early and the other a quarter second late. The delay times increase with altitude, but the distance doesn’t seem to change hardly at all.

  35. Chris says:

    Speaking of momentum transfer between satellites. I had some time ago an idea for a solar powered “ion ramjet” tug in the LEO. A scoop in front of the tug could collect the gases in the thermosphere and accelerate them in an ion thurster – electrostatic, hall, MPD or a small Vasimr. As long as the exhaust velocity is larger than orbital velocity, the tug will gain energy. Without circularization thrust the orbit will become more and more elliptical, which we actually want, because the dip in the denser parts of the thermosphere is where the acceleration happens.

    No, if we put an electromagnet on the satellite, it could be used to accelerate other satellites, loosing energy itself, and getting a lower apogee orbit and recharging the kinetic energy again. Maybe a momentum exchange tether would be more efficient, and if the ion driven tug is heavy enough, it could replace a second stage of a rocket.

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