Return-path: X-Andrew-Authenticated-as: 7997;andrew.cmu.edu;Ted Anderson Received: from beak.andrew.cmu.edu via trymail for +dist+/afs/andrew.cmu.edu/usr11/tm2b/space/space.dl@andrew.cmu.edu (->+dist+/afs/andrew.cmu.edu/usr11/tm2b/space/space.dl) (->ota+space.digests) ID ; Tue, 3 Apr 90 01:32:17 -0400 (EDT) Message-ID: <4a63Izq00VcJM2Zk5o@andrew.cmu.edu> Reply-To: space+@Andrew.CMU.EDU From: space-request+@Andrew.CMU.EDU To: space+@Andrew.CMU.EDU Date: Tue, 3 Apr 90 01:31:45 -0400 (EDT) Subject: SPACE Digest V11 #206 SPACE Digest Volume 11 : Issue 206 Today's Topics: Space-tech excerpt: Launch Loops ---------------------------------------------------------------------- Date: Mon, 2 Apr 1990 20:18-EDT From: Marc.Ringuette@DAISY.LEARNING.CS.CMU.EDU Subject: Space-tech excerpt: Launch Loops This is some condensed discussion from the space-tech mailing list, about the Launch Loop concept championed by Keith Lofstrom, and a variation of it we called the Hula Hoop. Beware, it's 660 lines long! \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \\\ Marc Ringuette \\\ Carnegie Mellon University, Comp. Sci. Dept. \\\ \\\ mnr@cs.cmu.edu \\\ Pittsburgh, PA 15213. Phone 412-268-3728(w) \\\ \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ Space-tech excerpt: Launch Loops [660 lines, Feb. '90] ------------------------------ From: Marc.Ringuette@DAISY.LEARNING.CS.CMU.EDU I'm sure many of you have heard of Keith Lofstrom's concept of the Launch Loop. I think it's incredibly cool, and I'll take a crack at describing what the principle of it is. 1. Kinetic Structures ===================== The physical basis of the concept is something which I call a kinetic structure. I'll explain it by example. Shoot a stream of water from a garden hose up in the air. It forms an arc. There is no need for material strength in the water: there's no tension or compression going on, but rather just the water's free-fall motion along the path prescribed by gravity. Imagine shooting a stream of water into a very high arc: it could go higher than you could build the tallest skyscraper, since it's not limited by the strengths of construction materials. Now imagine balancing a pie plate on top of the arc of water, so that it is supported by deflecting the water downwards slightly. The plate is suspended there, higher than you might have thought possible, by the force from the continuing deflection of the stream of water. 2. The Launch Loop ================== If you replace the stream of water with a segmented ribbon of iron, achieve the deflection of the stream by using magnets, and have two 'stations' suspended by the ribbon rather than a single pie plate, you have Lofstrom's launch loop. It is a structure about 2000km long and 80km high. The loop of iron runs along the earth's surface in one direction, is deflected upwards by magnets at an earth station, back parallel to the earth's surface by a station 80km high, downwards by another station, and back along the earth's surface. A --------->------------->------------->--------------- B / \ / \ / \ C ---------<----------<------------<--------------<---------- D ===============================Earth==================================== The Launch Loop. A and B are stations, 80 km high. C and D are deflector stations, 2000 km apart, on the ground. The segmented iron ribbon moves at 14 km/s. The horizontal sections, and the earth, are actually convex, not straight as shown. The whole loop of iron segments whizzes along at 14 km/s inside a vacuum sheath. The stations at A and B are held up by the force generated by magnetically deflecting the ribbon downwards; they are anchored to the ground by cables, which are needed for stability and to counteract the horizontal forces. 3. Say What? ============ I should head off your initial skepticism. This is no joke. The guy has worked out details of how you deflect the ribbon, what materials are required, how to anchor the stations, and all the other details. The idea has been reviewed by a lot of people, so if you think you see a glaring flaw, it's probably because I haven't conveyed the idea properly. The paper I have, AIAA-85-1368 (from an AIAA conference in 1985), has lots of numbers for everything. Some details that I should mention: - the iron ribbon consists of 200cm x 5cm x 1cm segments, which are slotted to fit into each other. - the ribbon undergoes no stress whatsoever; it is just a passive holder of kinetic energy. - starting up the launch loop is a difficult task, involving spinning up the ribbon while it is floating on the surface of the ocean. 4. Using the Launch Loop ======================== Once you have spun up this thing, what do you do with it? The stations themselves are useful things: they're outside the atmosphere, yet they are anchored to the surface by cables. You could put an observatory on one of them, and commute to it up and down the 80km cable. But the main use of the loop is to launch vehicles, weighing about 5 tons, including passenger vehicles. The idea is that the vehicle sits on the top section of track, and uses magnetic coupling with the moving ribbon to accelerate along the 2000km top portion until the desired velocity is reached (which could be orbital velocity or escape velocity). So to get into orbit, you winch yourself up a cable to station A, hop in a car, get accelerated up to orbital velocity on the cable, and let go. Because the loop is so massive, accelerating a vehicle doesn't decrease its velocity much; the velocity is added back in by the ground-based magnets. The result is that ground-based electrical power has been used to send a payload into orbit. 5. Practical Objections ======================= Lofstrom talks of the project as if it might be real, and even gives some guesses as to construction costs ($2 billion total). My evaluation of this whole thing is: incredibly cool physical concept, incredibly impractical engineering problem. Particularly, the ocean-based leg of the system is a 2000-km-long vacuum sheath which must be flawless. Spinning up the thing involves getting the entire 4000-km-long loop going perfectly on the first try, dealing with weather and all sorts of unpleasantness, and gradually lifting the stations up to their correct positions. 6. My preferred version: the hula hoop ====================================== I think the ground-based section of this thing is the worst part. So I propose having the loop go all the way around the earth, in low orbit. The ribbon will be moving faster than orbital velocity, so that it can be deflected by the stations to hold them up. I'd say there should be about 60 stations spaced around the equator, each of them fastened by cables to the ground. The ribbon moves in a shape somewhere between a 60-sided polygon and a circle. In between stations, it flies in free fall. It's still a really complex device, but at least it isn't in the weather. To spin up this structure, you could start with the stations in low orbit, and gradually decelerate them to a standstill as the ribbon is spun up and starts to support them. I notice that Lofstrom references some articles in the L-5 news and JBIS which discuss this idea. ------------------------------ From: Tom Neff I thought the point of the Launch Loop was that it could be powered from, and launch payloads from, the ground. The Hula Hoop might be easier to construct, but how do you power it and how does it get anything launched? ------------------------------ From: Marc.Ringuette@DAISY.LEARNING.CS.CMU.EDU This isn't a problem: the ~60 stations are all _stationary_ with respect to the ground, approximately 100km up, and are anchored by cables. You can run power lines and elevators up the cables. ------------------------------ From: dietz@cs.rochester.edu (Paul Dietz) One of my complaints with the launch loop is what happens when it fails. Should the loop break anywhere, or should the airtight jacket spring a leak, all the levitated sections fall back to earth, spread over thousands of kilometers. IMHO, the launch loop idea is more feasible on the moon. The levitation magnets can be anchored to the lunar surface, and can be externally powered. The loop provides a nice way to store energy over the lunar night. And, the required loop velocity is lower, if all you want to do is get to lunar orbit. Some work at Argonne National Labs has been inspired by the launch loop. A fellow there named Hull and some coworkers have looked into magnetically levitated rings for energy storage here on earth. The concept is nice, since (for fixed centripetal acceleration) the energy stored scales as R^2, and the energy stored per ring + magnet mass scales as R. Hull found a nifty *passively* stable attractive magnetic levitation scheme (Lofstrom used active stabilization). The idea works like this. Let o and + denote cables carrying currents into and out of the page, and let - represent the iron loop. Then, there are two positions where the magnetic field of the currents support the loop against gravity: + o + o - - In the first position, the loop is stable against vertical perturbations but unstable against lateral perturbations. In the second, the opposite is the case. Hull noticed that if you alternate sections of the two types, then the net effect, if the loop is moving in the right range of speeds, is to make it stable in *both* directions. This is the principle of Strong Focusing, which is vital to the operation of modern particle accelerators (where alternating gradient quadrupole magnets focus particle beams). ------------------------------ From: Marc.Ringuette@DAISY.LEARNING.CS.CMU.EDU I guess I'd be more interested in launch loops on the moon if I actually cared about being able to launch things from the moon. But it seems like a tidy little mass driver would be a better bet there in any case. == Paul correctly points out a really big drawback of the design, namely the fact that the thing has to work flawlessly, all the time, or the whole thing falls down. Any system which must be in continuous operation is far, far less practical than a system which just goes BANG and is done. ------------------------------ From: Jordin Kare The "full orbit" launch loop has been proposed several times. I (re)invented it in about 1980, but later found a fairly detailed analysis, I think by Hans Moravec. It is simpler than the Lofstrom loop, but takes much more material, and would be much more subject to cutting by LEO debris/meteorites. Stabilizing it is also nontrivial, although not necessarily more difficult than for the Lofstrom loop. There are serious problems starting the thing up. However, the big problem is getting the mass up there in orbit to begin with -- at least the Lofstrom Loop gets built on the ground. Jordin Kare ------------------------------ From: Lou Adornato I think a surface based loop would be a better plan for lunar colonization because of the lower materials and construction demands. Keep in mind that the size and speed of a lunar loop would be a lot lower than for a terrestrial loop. Also, for a lunar loop you wouldn't need a vacuum sheath, and there wouldn't be any concerns about weather. There are several advantages of the loop over a mass driver. According to Lofstrom, the accelerations of a terrestrial (and possibly a lunar) mass driver would be so high that it could only be used for inanimate payloads. Also, there would be a lot of problems providing the required peak energy demands. A loop would have a fairly constant energy demand, and the peak acceleration to escape velocity (at least to get to an L point or the moon) would be 3g's, and (if my understanding of the the math is correct), about 0.5g for a lunar loop. From what I understand of the design of this monster, if higher acclerations are allowed, the loop can be made smaller. ------------------------------ From: "Edward V. Wright" The Kevlar slingshot promises to be cheaper than the mass driver for launching lunar payloads. The Kevlar slingshot is just what it sounds like -- a Kevlar sling attached to a mechanical arm. Attach a payload to the end of the sling. Spin the sling until the tip reaches orbital velocity, then release the payload. The idea is almost absurdly simple, but apparently will work on the Moon. The idea was developed by Dr. Jerry Pournelle and Dr. Marvin Minsky and was mentioned by Pournelle in one of his columns. I think they gave a paper on this somewhere, but I don't have exact references. ------------------------------ From: Bob Munck The Hula Hoop (loop entirely around the earth, I assume moving faster than orbital velocity) has the obvious drawback of weighing on the order of 150,000 tons (for a 1x5 cm loop) and needing to be in orbit before it's usable. If we could put that much up, we probably wouldn't really need it. How about a 2.7 cm diameter Kevlar cable with a 1 cm iron core, breaking strength about the same as the Launch Loop (about 300T?)? That's down to a "mere" 50,000T in LEO. Does it really need that kind of strength? Would 50T be enough (cable weighs 8,000T)? That's down under 100 shuttle missions, a distinct possibility. The iron core could be discontinuous, say 1 cm pellets at 2 cm intervals. OK, where have I wandered? A 40,000 km Kevlar hoop (i cm diameter) with a (possibly discontinuous) iron core (j cm diameter) around the earth at k km altitude, traveling at x m/s. Stations at y km intervals capable of accelerating the hoop by magnetic coupling to the iron with power coming up a (superconducting) cable from the ground. Some of the stations would have an elevator capable of lifting an z ton payload and hanging it on the hoop, which would accelerate it up to orbital (or more) velocity. I like it. Possible values: i=1.5, j=0.6, k=75, x=15, y=2000, z=5. Starting up is fairly easy (but k might be low) and the broken cable mode flings cable outwards and drops stations straight down, relatively safe. What factors have I missed? How stable is it with wind and random payloads on the spokes? -- Bob Munck ------------------------------ From: Bob Munck Come on, folks, help me out. In a previous message I rambled on about a Kevlar/iron hoop around the Equator in LEO (or lower) spinning faster than orbital velocity. Stationary facilities would "ride" it magnetically (hence the iron component) with Kevlar tethers down to ground level bringing up electricity to keep the hoop spinning and payloads on the order of 5T. The payloads would couple (also magnetically) to the Hoop and, letting go of the station, be accelerated to orbital velocity and beyond. The Hoop and tethers are all on the order of 5 sq cm: the Hoop must withstand whatever strain is generated by its higher-than-orbital speed, its mass, and the weight of the stations; the tethers must support their own weight and the payloads. I *think* that the total is within reason for us to boost into orbit -- a hundred or so Shuttle launches or a lot of little mass driver shots. Start-up is easy: assemble in LEO at orbital velocity, spin it up a bit with strap-on rockets, fly up a couple of stations and reel down their tethers. If the Hoop snaps, it throws itself all over the Solar System and drops the stations straight down. (Humm. It might shotgun all our comsats.) WHAT'S WRONG WITH THIS IDEA? Does the Hoop have to be spinning so fast that it can't possibly hold together? (I haven't the foggiest how to calculate the strain on such a Hoop for a given velocity.) Is it unstable? Are the tethers beyond our current strength-of-materials capabilities? Am I orders of magnitude off on the launch mass requirement? Is the whole idea of holding up the stationary facilities crazy? (But isn't that what a Lofstrom Loop does?). HELP!! -- Bob Munck, MITRE McLean ps. I'm struck by the thought of standing on the Hoop in a 1g field with my head toward Earth, going around every 45 minutes. Hence the "Ringworld." ------------------------------ From: Marc.Ringuette@DAISY.LEARNING.CS.CMU.EDU Bob - At first, I thought you were misguided -- the Launch Loop as proposed was meant not to require any tension in the loop at all -- but now I'm starting to like this! I think we're looking at a new form for the hula hoop: use tension to hold the structure together, rather than deflector stations. Magnetic deflection is only used to hold up the launch station, and magnetic coupling is still used to launch payloads and re-accelerate the ribbon. It requires much smaller deflectors than the original scheme, and may have better reliability, since the loop can 'idle' with no deflectors operating and there's the prospect of passive or mostly-passive operation. To sum up the idea: put a Kevlar ring in low orbit, then spin it to create tension. Float a station on it as for the Lofstrom Loop, and launch vehicles using magnetic coupling with iron pellets in the cable. The tensile strength works out OK -- even with standard Kevlar like you'd use to anchor an oil rig, you can spin it to 1 km/s above orbital velocity, which is probably enough. We still need to work out the dynamic properties of the system, even if roughly, to see if we can hold up a station and succeed in launching vehicles, while staying within tension bounds and remaining dynamically stable. Here are my calculations for the tensile strength question: The tension on a spinning loop (disregarding gravity) is 2 M v F = -------- t 2 pi r ================= What's the maximum spin velocity (in excess of orbital velocity) of a loop with these parameters? .... X = tensile strength of cable Y = density of cable c = cross-sectional area of cable r = radius of loop M = total mass of cable 2 G(r) = gravitational acceleration at radius r = Vo / r Vo = orbital velocity at radius r 2 2 2 M | v | 2 pi r c Y (v - Vo ) 2 2 F = ---- |--- - G(r) | = --------------------- = c Y (v - Vo ) t 2 pi | r | 2 pi r 2 2 F = X c = c Y (v - Vo ) t max max 2 V = SQRT( X / Y + V ) max o ================= For Kevlar 29 as used for oil rigs, tensile strength = X = 2.76E9 N/m/m density = Y = 1.44E3 kg/m/m/m V = 120 m/s (in excess of orbital velocity of ~ 8.3 km/s for LEO) max This isn't too useful, but with 10-50x stronger materials, this increases to 1-3 km/s, which should be enough to hold up a deflector station and accelerate vehicles. ============== This design has the advantage that we need only one station, plus some guy cables spaced around the equator. ------------------------------ From: John Sahr Some commentary on the calculations by Marc. Summary: the Kevlar Hula hoop is likely to be very unstable if it is "anchored" and the loop travels at "reasonable" speeds. The loop must spin at "unreasonable" speed in order to become stable. For a lineal density of 1 kg/m and tension of 100T, we can calculate the speed of the transverse waves along the loop, namely v = sqrt(T/rho), ( rho = M/(2 pi r) ) = 1 km/sec. Thus, an observer on a stationary earth would observe perturbations travelling along the loop at speeds of 9.3 and 7.3 km/sec, both in the same direction of the loop. Factoring in the earth's rotation, and assuming prograde spinning of the loop in the equatorial plane, the velocities of the waves observed from the earth's surface would be 7.7 and 5.7 km/sec, still in the direction of the loop. This is a real problem, as any "stationary" perturbations (anchoring cables, suspended stations, advertising signs, and other whatnot) will be generating waves along the loop, only downstream, and none upstream. This situation is analogous to the operation of certain microwave tubes which rely upon "fast" and "slow" waves to amplify perturbations in the electron beam density. The difference is that this is a periodic problem (it is a loop, after all), and it is possible that there is a stable, noncircular, and probably (mathematically) nonlinear solution involving rather large amplitude perturbations of the loop (I'll have to think about it). A way to combat this problem is to find a way to increase the velocity of waves along the loop, so that one of the waves can travel "upstream." This can be done by increasing the T/rho ratio by a factor of about 35. From an equation above, T == F_t is proportional to the mass density, and we can write T/rho = F_t/(M/(2 pi r)) = v^2/r - G In other words, the only way to increase the wave speed is to increase loop speed. In fact, because of that pesky G, v_wave can never exceed the speed of the loop. However, the Earth is spinning with an equatorial speed of about 1600 km/hour = 450 m/s = V_e. So, the slowest loop speed V_s that will satisfy the stability condition satisfies V_w + V_e >= V_s; where V_w^2 = (V_s^2 - rG). Solving this for the minimum possible loop speed gives V_e^2 + rG V_s(min) = ------------ = 75 km/sec 2 V_e The loop must make a complete orbit every 9 minutes or less. This is a rather large velocity; it could be reduced substantially by either letting the stations drift prograde, or by spinning the Earth up so that its day was shorter, say 4 hours instead of the current 24. In the absence of a stable nonlinear large amplitude solution, or an ambitious dynamic active correction of perturbations, or a loop material which is very good at damping out transverse motions, this strikes me as a pretty fundamental limitation to this idea. note: Someone should double check the statements I have made. -john ------------------------------ From: Marc.Ringuette@DAISY.LEARNING.CS.CMU.EDU The question remains: how to make the Hula Hoop stable? John's wave calculations were very informative, and I will assume that it is necessary to damp out any waves that occur. Then the key to achieving stability is to have a means of damping out the waves downstream of the perturbation. A factor in our favor is that the main perturbation, the station, is stationary, so there can be an anchored damping mechanism downstream from it, which applies a continuous damping force to the cable. My best idea for dealing with the perturbations caused by the launch vehicle, which are not stationary, is to use a series of cables to the ground which actively damp out perturbations by adjusting their downward force. I have no idea if this will work. Can anyone fill in any details, or think of a passive way to achieve the damping? ===================== Thinking further about it, I conclude that it's important to distinguish between two separate issues. One is how to get the hoop to move in a circle: the idea of a Kevlar cable was introduced in order to achieve the desired curvature through tension rather than by using a whole lot of deflector stations. The second issue is how to aim the cable precisely where you want it. In the original loop proposals, the ribbon must be aimed at its destination with incredible precision, since there is no internal strength in the ribbon. This involves very aggressive active control. However, when we use a Kevlar cable, it is tempting to use the strength of the cable to help guide it to its destination, in order to reduce the control problem. I believe that it is these transverse guiding forces which introduce waves, and if we can't deal with the waves, we can always go back to strict active control a la Lofstrom. ===================== I'm trying to do some clearer thinking about what the shape of the hoop would look like. I've been imagining, in my weaker moments, that we just hang the station from the hoop, and that the hoop bends down in a 'U' shape. This is totally wrong! A 'U' shape would indicate that the tension of the cable is holding up the station. But unless we totally change the concept of the thing, it's magnetic deflection of the moving cable that provides the necessary force. I think a good mental picture to start from is the following. Imagine that the earth is a point mass, and that we want to support two stations 180 degrees apart, using only the iron-pellet type loop. We can do this by firing the pellets back and forth in curved paths: __-------__ -=__ O __=- ------- The faster the pellets are going, the straighter the path. If they go too fast, they run into the Earth (which isn't really a point mass after all). ====== Now, let's come back to reality. If we try this two-node solution using iron pellets around the Earth, we can't fire them very fast at all or their paths would pass through the Earth. But if we use the Kevlar hoop, the tension of the cable can pull it in a more tightly curved path, so it misses the Earth even at higher velocities. At least, I think this works. If somebody could work it out in more detail, it would be a good thing. And is a two-node setup appropriate, or more, or less? A 1-node solution is sort of asymmetrical, but perhaps a setup with 1 big node and a dozen smaller ones (cables to the ground) or something. But do we agree that any version of this will have the station supported on a 'peak' of the hoop rather than a 'valley'? I think this is right. ====== Some general reflections: I'm starting to think that we haven't really solved any fundamental problems by making the loop out of Kevlar. My feeling is that it should be able to operate in a more passive mode than the original loop, but it doesn't seem to be working out that way. ------------------------------ From: John Sahr >How about sixteen spokes anchored to the earth, one every 2500 km? >The mechanism that couples to the Hoop could include some way to pull >down harder or loosen up on the Hoop over a couple of meters of play >and with tenth-second response time. Would that do to damp the >perturbations? For a passive support system for this kinetic structure, it is possible that evenly spaced supports would be about the worst choice. Because the transverse wave speed is slower than the loop orbit speed, ordinary standing waves couldn't form; however, since the loop itself is periodic, the n=8k (n = number of wavelengths, n, k are integers, for both fast and slow waves) modes would stand between 16 spokes. A better solution would be to have aperiodic spacing such that no modes, or very few, were allowed. This could be used to filter out the long wavelength waves. In a linear world, it would be enough to have two supports, such that the ratio of the two distances between them is irrational. However, this cable is going to stretch, have nonlinear restoring forces at large amplitudes, and will be excited by the spokes them selves. With 16 suitably spaced spokes, you might be able to effectively filter out the waves of wavelength greater than a few hundred kilometers, and one or two spokes might be able to have damping mechanisms for shorter wavelengths. I could never recommend building this structure if it wasn't passively stable. I had an idea for stabilizing the loop, though, whose dynamics I have not yet had time to work out. It goes like this. The problem with the loop is that transverse waves both travel "downstream," a "negative energy mode" situation. It seems to be the case that the loop must spin terribly fast in order to allow the loop tension to be large enough to have one wave travel upstream in the frame of a rotating Earth. Notice that a retrograde loop would have the same problem, but in the opposite direction. Therefore, what would be the dynamic stability properties of two loops mechanically coupled to each other, one spinning prograde, one retrograde? To couple the two loops, they could be put side by side and connected by rungs like a ladder (probably won't work), connected like a spiralling ladder (like DNA, and probably most feasible), or connected concentrically (one inside the other; best mechanical connection, most esthetically pleasing: how to spin that inside loop, though?). Each cable separately provides one direction of wave modes; perhaps the composite structure will have 2 or 4 modes. I suspect that this structure might have very good dynamic stiffness. But it might also explode into a million tiny pieces. It may not be necessary for the retrograde loop to have the same momentum as the prograde loop. There are a few other nice properties as well; residual loop-spoke friction can be canceled (as far as the the spoke is concerned). It's just an idea. Even if this doesn't work for a launch loop, it might provide a nice frame for space structures. ------------------------------ From: Bob Gray Check out: "Orbital rings and Jacob's ladders" by Paul Birch. Vol 36, Journal of the British Interplanetary Society. pp 115-128 (1983) The article describes how to bootstrap the system by starting with a thin cable, and using that to lift the materials to build the main orbital ring. Eventual cost to orbit was estimated at $0.05/Kg. He then describes how more than one ring can be used to reach any point on the Earth's surface, and how the ring could be used in conjunction with a Lunar ring to provide a very high speed shuttle service from the Earth's surface to the Lunar surface in a few hours. ------------------------------ [ End of excerpt ] [ Space-tech is a mailing list for discussing concepts for space development, with emphasis on the technical problems and and how to solve them. Past topics have included EM launchers, orbiting tethers, and Mars missions. To join, send mail to space-tech-request@cs.cmu.edu. ] ------------------------------ End of SPACE Digest V11 #206 *******************