Subject: Space-tech Digest #84 Contents: Marc Ringuette space tethers tutorial Richard Schroeppel exotic launch technologies Marc Ringuette two-stage rotating tether Phil Fraering Re: two-stage rotating tether Hans Moravec Re: two-stage rotating tether Dani Eder Re: two-stage rotating tether Marc Ringuette Re: two-stage rotating tether Dani Eder Re: two-stage rotating tether Dani Eder Re: two-stage rotating tether Marc Ringuette Re: two-stage rotating tether Dani Eder Re: two-stage rotating tether ------------------------------------------------------------ From: Marc.Ringuette@DAISY.LEARNING.CS.CMU.EDU Some discussion follows, about space tethers. But first, it occurs to me that some people on the list won't know what we're talking about. Here are the 3 main tether ideas: Space elevator: Attach a cable to the earth, pay it out past the geosynchronous point, and attach a counterweight. It hangs there, and you can winch yourself into orbit up the cable. The cable has to be strong; stronger than current materials. But with a tapered cable (thickest in the middle where the most tension is) it's within a factor of 10-50 of current materials. Rotating tethers (pinwheels) Put a tether in low earth orbit, and spin it so that the end closest to the earth has zero relative velocity with the surface, and the far end has twice orbital velocity. It looks like the spoke of a wheel rolling around the earth in low orbit. If you grab the low end when it approaches the surface, and let go at the top, you've just been given twice orbital velocity, and will zoom out into the solar system. The strength requirements aren't as high; they're probably within the strength of some current materials. However, there are plenty of other technical problems. Non-rotating tethers in low orbit If you want to de-orbit a shuttle from a space station, you can attach a cable and pay it out, so that the shuttle hangs closer to the earth. As you pay out the cable, gravity creates tension; the station is sped up and the shuttle slowed down. The net effect is that the station is boosted into a higher orbit, and the shuttle needs less fuel to de-orbit. This is a practical idea, and is being tested right now. (Actually, there's a fourth idea about tethers interacting with the Earth's magnetic field and the diffuse plasma in low earth orbit. Ask for the excerpt on electrodynamic tethers if you're interested.) --Marc ------------------------------ Date: Thu, 6 Jun 91 16:38:22 PDT From: Richard Schroeppel To: space-tech@cs.cmu.edu Cc: eder@hsvaic.boeing.com Subject: exotic launch technologies The following material is excerpted (& edited) from messages of Dani Eder: Re: the rotating tether concept Dr. Brian Tillotson and I [Eder] invented an improvement called a two-stage rotating tether, which allows near-GEO tower capability with existing materials. The idea is to make note that the mass of a tether goes as exp(tip velocity ^2). If you put one rotating tether at the tip of a larger rotating tether, then the mass goes as (exp ( (0.5*tip velocity)^2 ))^2, which grows more slowly (in the second equation tip velocity is the sum of the two rotations. Another advantage of a two stage tether occurs when the rotation periods of the two tethers are different. The velocity vector of the tip of the second tether adds to the velocity vector of the tip of the first tether. Over time the sum of the two vectors will sweep out all the velocity/direction phase space, which means you can depart in any direction at any velocity within the range of the system. This includes a pickup at near-zero velocity at the Earth's surface with a dropoff in circular orbit without having to climb an elevator. The second rotating tether is symmetrical, tapering towards both ends, and mounted so that it's center is at the tip of the first tether. One way to look at why this gives you an advantage: In a tether you taper by a factor of e per scale length. In a rotating single tether, the local acceleration as you move from the center to the tip increases linearly. Thus the rate at which you accumulate scale lengths smoothly increases. In a more technical form: The change in tension over a length element dL is (rho)(a)(A)(dL) where rho is the material density, a is the local acceleration, and A is the cross sectional area. To maintain constant stress in the tether material, the area must increase to account for the incremental tension caused by that dL in length. So the higher the acceleration, the faster the area grows. In a two stage tether with the same tip velocity as a single stage tether, divide the tip velocities equally, but make the first stage five times longer than the second stage. Now the curve of acceleration vs. length along tether rises more slowly over the first tether,then steeply over the second tether. The integrated area under the acceleration vs. length curve is lower than the straight line for the single stage tether. ------------------------------------------------------- As far as other launch concepts: We have determined that a launch capability for a gas gun to robit orbit of 10 kg is sufficient for a useful system. For example, if you are launching propellant tanks of this size. You need a collector robot based on SDI brilliant pebbles technology to chase down and collect the tanks. The robot has to mass less than about 500 kg so that you dont use up all the propellant from one tank to chase down the next tank. Since brilliant pebbles is working in the sub-100kg regime, this should not be a problem, especially since the target will be designed to be as easy as possible to find, rather than the SDI job, where the target is un-cooperative. Lawrence Livermore Laboratory is building a gas gun to fire 2 kg to 6 km/s. A gun ten times the size, 20kg to 6 km/s, should be able to deliver 10kg payload to orbit using a solid rocket kick motor. A mechanical catapult using a falling weight can reach about Mach 4. The falling weight is connected to an axle via a rope. A large diameter wheel is attached to the same axle, being 30x the axle diameter. A second rope wind in on the large wheel as the falling weight pays out on the axle. The falling weight falls at 1/3 g, and the second rope is wound in at 10 g's (actually somewhat less after friction and drag losses). Connect your SSTO rocket to the end of the small rope, and it gets a boost to Mach 4 before going on internal propulsion. This raises an SSTO payload from 2% of takeoff weight to 9% of takeoff weight, which means you can reduce the size of the SSTO by a factor of 4-5 for the same payload to orbit. The Mach 4 limit comes from a combination of human g tolerance, physical size of the rope traverse, and rope frictional heating in the atmosphere. Even though the falling weight is measured in kilotons mass, replacing 75-80% of an SSTO rocket, aerospace grade hardware, with a civil engineering grade catapult, has to be less expensive. The overall 'how we get to space' scenario now goes like this (1) Deliver collector robot(s) to orbit. (2) Use 10 kg payload gas gun to launch propellant to LEO for use by Space Station, Space Shuttle (it can carry more payload to orbit instead of OMS propellant), and upper stages going to GEO. This brings in revenue to go on to the next stages. Investment so far on the order of $100M. Potential revenue in the $1 billion per year range (3) Intersperse 10 kg spools of tether into gas gun stream. Start building tether system. (4) Build SSTO that gets a boost from ground catapult and arrives at end of tether. Goal is 10% payload fraction, with sensible design margins. Size for manned crew of 2 or 2 tons cargo unmanned. Takeoff mass is then 20 tons. Compared to Space Shuttle mass of 2000 tons, is 100x smaller. Since aerospace harware cost scales as about 0.75 power of mass, expect cost to be 1/30 of shuttle to develop ($500 million), and build per unit ($65 million). (5) At some point upgrade to bigger gas gun for bulk cargo items, and upgrade tether so more of the velocity is done by the tether, which allows the SSTO to carry less propellant and more payload (design this capability for more payload into the SSTO) In an ideal scenarion, we are talking about 5-7 years to reach the point where 100 people per year are going up to orbit, with thousand ton per year mass flow (sufficient for tens of people per year additional living space). This is a threshold where industrialization/settlement is close to takeoff. Most of the time is in developing the collector robot and SSTO. The gas gun is funding-limited. So we need to get $100M somewhere to get started. ------------------------------------------------------- (edited & forwarded by Rich Schroeppel, rcs@la.tis.com) ------------------------------ Date: Fri, 7 Jun 1991 13:36-EDT From: Marc.Ringuette@DAISY.LEARNING.CS.CMU.EDU To: space-tech@cs.cmu.edu Subject: two-stage tether [ Regarding the suggestion of a two-stage rotating tether, with a smaller fast-rotating spoke attached to the tip of a bigger spoke ] It would seem that there's a severe whip action on the secondary tether, since its center point is undergoing acceleration. I see no particular reason to think that we can set up a stable two-tether system. As a simple case of an accelerated tether, let's think about the case of a small tether rotating in the vertical plane in a lab on the Earth's surface, undergoing uniform gravitational acceleration. The way I figure it, the outside parts of the tether would tend to fall a little behind on the "downward" arc (since the velocity picked up by the tip adds less angular velocity than the same velocity added to an inner segment of the tether), and although it will recover that velocity later, on the "upward" arc, the tip will have fallen behind the inner part of the tether after one rotation. What I conclude is that an accelerated tether can't have radial spokes. Instead, it has to have some kind of arc that bulges to the spinward direction in the middle of each spoke. The bulge provides an antispinward component of the tension force on the inner parts, and a spinward component near the tip, to counteract the effect I just described where the center gets ahead of the tips. Unfortunately, the force needed to counteract the effect is different at each point in the rotation, so this kind of tether necessarily has some sort of wobble in it. Can we set up a tether with the right wobble? If so, is it in a stable equilibrium? I have no idea. At some point we'll also have to undo my simplification of a uniform gravity field, and take into account the full double-rotation. It seems far trickier than the single tether case. Has anybody done these calculations? I would guess that the double tether is an order of magnitude harder than the single rotating tether. === However, this brings up the possibility that even one-stage rotating tethers in low earth orbit may have this kind of wobbling problem due to tidal accelerations. Hans Moravec is on this list...Hans, did you do any of these shape and stability calculations for the orbiting pinwheels? ----------------- -------------------------- -------------------------------- | Marc Ringuette | Cucumber Science Dept. | What does a blonde say when | | mnr@cs.cmu.edu | Cranberry Melon Univ. | you blow in his/her ear? __ | | 412-268-3728 | Pittsburgh, PA 15213 | "Thanks for the refill." \/ | ----------------- -------------------------- -------------------------------- ------------------------------ Date: Fri, 7 Jun 91 17:08:38 -0500 From: Fraering Philip To: mnr@cs.cmu.edu ... P.S. : Seriously, it seems that all sorts of unstable situations are controllable by computers. Could the two-stage tether be? Phil F. ------------------------------ Date: Fri, 7 Jun 1991 18:02-EDT From: Hans.Moravec@ROVER.RI.CMU.EDU To: Marc.Ringuette@DAISY.LEARNING.CS.CMU.EDU Subject: Re: two-stage tether Hi Marc, I did simple numerical simulations (recorded on film-I have a tape, maybe you'd like to see it). There were no gross lateral motions (the high tension helps), but lots of longitudinal wave action when masses are suddenly launched. Needs damped. -- Hans ------------------------------ Date: Mon, 10 Jun 91 08:11:17 CDT From: Dani Eder To: Marc.Ringuette@DAISY.LEARNING.CS.CMU.EDU Subject: Re: two-stage tether Marc, Your comments about vibrations in the two stage tether are correct, but only if people persist in thinking of a tether as a physics problem, and not as an engineering problem. If you are designing a real rotating tether (one or two stage), you have to give the structure some depth, i.e. a noodle is not stable. Instead, imagine two cones with bases connected. At the joint, which is the axis of rotation of the tether, is a structural ring that can stand compression. A typical ratio of cone height to base diameter is 8:1. The tether fibers run axially from the base to the tip. This stabilizes you against off-axis forces as long as their magnitude is less than 1/8 of the rotation-induced tension. Axial fibers, however, do not stabilize you against rotation at the tip, so the next complication is to tilt the fibers so they spiral slightly along the cone, with half spiralling clockwise and the other half spiralling counterclockwise. Make connections where they cross. Now you have "triangulated" the surface of the cone, which stabilizes it against twist. Finally, a real design has to account for induced oscillations in a single strand (harmonic pumping). This is done by mounting a shock absorber (damper) of appropriate size in line with the fibers. Finally, as for the off-center force from the second stage tether, you build it slightly assymetrical, with the lighter part having the docking port. A movable counterweight is placed on the light side to balance the tether. When a payload arrives, the counterweight is shifted towards the other side to maintain balance. Most of the time when I discuss tethers, there is enough trouble getting across the physics, so we never get into the engineering, but the engineering is not any worse than, say designing a large tower for wind loads, i.e. there are solutions that come from normal engineering of any large structure. Dani ------------------------------ Date: Mon, 10 Jun 1991 17:26-EDT From: Marc.Ringuette@DAISY.LEARNING.CS.CMU.EDU To: Dani Eder Subject: Re: two-stage tether That's interesting. I had totally ignored the possibility of "stiffening" the tether. However, I need a little convincing that it is reasonable. Presumably we have pretty ambitious strength requirements for the tether -- Kevlar or stronger. Are you really going to be able to find a material that can be compressed 1/8 as much as you're stretching the Kevlar, for 1/8 the distance, without being too heavy? I think of compression as being much, much more difficult to attain over long distances. Of course, how much stiffening you need depends on how much the tether is getting tugged around. I would need to do some calculations to get a ballpark figure on that. Have you done any of these calculations, and if so can you forward them or summarize? For instance, is 1/8 a reasonable ratio, and if so, for what ratios of primary/secondary tether radii and spin rates. It still seems to me that the two-tether system is orders of magnitude less likely to be workable than a single tether. ----------------- -------------------------- -------------------------------- | Marc Ringuette | Cucumber Science Dept. | What does a blonde say when | | mnr@cs.cmu.edu | Cranberry Melon Univ. | you blow in his/her ear? __ | | 412-268-3728 | Pittsburgh, PA 15213 | "Thanks for the refill." \/ | ----------------- -------------------------- -------------------------------- ------------------------------ Date: Tue, 11 Jun 91 10:46:49 CDT From: Dani Eder To: Marc.Ringuette@DAISY.LEARNING.CS.CMU.EDU Subject: Re: two-stage tether As far as strength ratios, Here is some data provided me by Amoco: T-40 Carbon fiber: Density 1.81 g/cc Tensile Strength 820,000 psi Modulus 42 million psi Composite (T-40 carbon fiber / ERL-1962 epoxy resin) Tensile strength along fiber axis 470,000 psi Compressive " " " " 250,000 psi Composite density approx 1.6 g/cc To calculate sideways bending forces, look at the first stage when it is at a 45 degree angle wrt Earth. The differential gravity with distance from the earth vectored with direction gives the most bending. When vertical, all the forces are along the tether, and when horizontal gravity is the same for all points on the tether, so the 45 degree case is the worst case sideways force. Then look at the centrifugal force at any point vs. the differential gravity from the center of tether mass, this force comparison tells you how wide to make the base of the tether (actually the slope of the conical surface at that point. The second stage tether in it's inner section does not generate much centrifugal force, while being at the end of the first stage generates a large radial force across the whole second stage, so it may be necessary to make the inner portion of the second stage resistant to compression so it doesn't buckle as it swings through the 'inner' part of it's rotation. Dani ------------------------------ [ Eek! I'm getting more concerned that Dani isn't being practical. Compressing that big long tether really sounds like bad news. --Marc ] ------------------------------ Date: Tue, 30 Jul 91 08:51:04 CDT From: eder@hsvaic.boeing.com (Dani Eder) To: space-tech@cs.cmu.edu Subject: Re: two-stage rotating tethers Sender: mnr@DAISY.LEARNING.CS.CMU.EDU Dear Marc, [engage gentle sarcasm] [engage little old lady voice] Upon encountering a 747 for the first time: "Oh my, will that thing really fly?" [disengage voice, sarcasm] Seriously, Marc, I myself have had a problem believing that a 747 can fly, when I was standing under the belly of one on Boeing Field in Seattle, but yet it does. I have come across a lot of other seemingly improbable engineering feats, that nonetheless have occurred. I find comments like "that doesn't look to me like it will work" don't help the discussion. If you think I've neglected something or erred in the magnitude of a value, fine, I'm happy to be corrected, but first impressions on the likelyhood of an engineering task can often be deceiving. Think about the following, if you were encountering computer technology for the first time (I assume you are actually familiar with same): Disk drive heads literally fly at 20 mph over a suface maintaining an altitude of 1/10,000 of an inch without crashing. The wires in your computer core are 1/25,000 of an inch across. Or in space technology: The power output of a Space Shuttle engine, about 50,000 times the power of a car engine, is produced in about the same volume. In a more constructive vein, I've submitted a capital request here at work to build a 'dynamics test stand', which would be a scaled version of a roating tether on a hoizontal axis. One purpose would be to prove that a two stage tether doesn't destroy itself, another would be to look at the detailed dynamics and see if it matches predictions of a dynamics code, and then extrapolating with the computer simulation to full size design. Probably Boeing won't fund this project this year, but at least I'm trying to get some real analysis done. As far as the compression ring at the base of the tether, it isn't a noodle either. Take a look at sailing ship masts (modern ones) They use guyed members to give lateral stiffness. If the payload of a tether is 10 tons, and the tether itself masses 100 tons, and the whole is under 1.5 g's average acceleration, then the radial force is 165 tons. The compression ring will then see a force of 33 tons compression (from both halves of the tether together. With a compressive strength of 120 tons/in^2, and a safety factor of 2, then you need 0.5 square inches. With a circumference of 50 km, the ring masses 30 tons, which is not out of line since the tether masses 300 tons total (for both halves. Dani ------------------------------ Date: Tue, 30 Jul 1991 16:02-EDT From: Marc.Ringuette@DAISY.LEARNING.CS.CMU.EDU To: space-tech@cs.cmu.edu Subject: Re: two-stage rotating tethers Dani, I hope I haven't stepped on your toes by being somewhat glib in my criticism. I'll see if I can find some time to be more precise. But in the meantime, I'll be glib for a while longer. You mentioned two possible needs for structural stiffness: sideways bending forces on a tensioned tether, for which you proposed a cone-shaped tether with a compression ring at the bottom; and lengthways compression of the secondary tether (which may in effect become a "tower"). Your solutions to both of these needs involve compression over long distances. The key word is "buckling". I'm very concerned with the stability of the compressed members over distances of kilometers. ===== Let me deal with the tower first since it seems most difficult. Please consider the contrast between these two statements. It is a pretty big engineering project to build a tower 1 mile high from the surface of the earth, even if there's no wind to worry about. It is trivial to hang a tapered cable a thousand miles long under 1 g, if you have some place to fasten it. I've just always considered it a given that it's far, far easier to build for tension than for compression. It has to do with the difference between a stable and unstable equilibrium. Commercially available Kevlar 29 cables have "hanging lengths" of about 200 km...meaning that a 100km cable can hold up its weight in payload. I'd like to find out the equivalent number for a tower-building material and configuration: how high can a tower of the stuff hold up an equivalent mass of payload? I'm betting the distance is a few hundred meters, because of all the stabilizing that needs to be done. Even with that number in hand, building a tower isn't the same as stringing together an exponentially growing stack of these towers, since the taller they get, the less stable they get. You need guy wires out the wazoo. ===== The tension ring at the bottom of the tether-cone has a similar problem. You mention a 0.5 square inch tension ring with a circumference of 50 km. Preventing that ring from buckling would seem to be a hellishly difficult problem, and require much more mass than the ring itself. ===== If you (or anyone else on the list) can provide a number for the maximum height of a tower to hold up its weight in payload, that would be a good start. I don't know if I can do these calculations, or if theoretical calculations are good enough, since they involve the stiffness of the compressible material, the magnitude of "jolts" to the tower, etc. --Marc ------------------------------ Date: Fri, 2 Aug 91 12:03:51 CDT From: eder@hsvaic.boeing.com (Dani Eder) To: space-tech@cs.cmu.edu Subject: Re: two-stage rotating tethers Sender: mnr@DAISY.LEARNING.CS.CMU.EDU Dear Marc: Look at the design of a Solar Power Satellite. The cross section of the thing is 5km x 400m, or 2E6 square meters. The actual filled area of structure is 2 square meters. The factor of a million comes from the structure being made up of truss bays, each of whose elements is itself a truss, each of whose elements is itself a truss, each of whose elements is formed by a 'beam builder' machine out of 1 mm thick aluminum sheet. The trick to getting stiffness without mass is 'reticulation', or dividing up your structure into elements at the extreme ends of a triangle, and doing this with sub-elements as well. The smallest compression members have to withstand buckling. You assume an eccentric load due to manufacturing tolerances (say 0.1 of the member diameter), and find the member dimensions that you have to have, dependant on strength, stiffness, and factor of safety in design. The member assumes a bent shape under this limiting load. Consider three such compression members in a triangular truss. The cross pieces have to withstand tension if the compression members are all bowed with their centers inward, and compression if the compression members are bowed outward. Given the bend angles, you can find the magnitude of the forces on the cross pieces, thus sizing them. Then you treat the triangular truss as a single element in the next larger assembly, with a moment of inertia, radius of gyration, eccentricity of load, and compressive strength based on 3 compression members. This builds up as far as necessary to get to the main structure you are trying to build. To make a 15 km diameter ring with graphite epoxy, I would use a 20:1 slenderness ratio at each stage. Thus the ring would be a triangular truss bent in a circle, with a 750 m spacing between truss elements. Each truss elemment would itself be made of smaller elements with a 37m bay size. Each of these would be made of tubes 2m long by 10cm diam by 0.5 cm thick. Thus we have 27 circumferential tubes providing compressive strength with a total cross section of 418 sqaure cm (I know this is the wrong number, I'm just showing the method). The cross peices at each stage gives 20% overhead, for a total 73% overhead, for a total area of structure of 723 square cm x so 57% of the structure is actually being used usefully. Dani ------------------------------ End of Space-tech Digest #84 *******************