Boosted Orbital Tether and Orbital Runway upgrades

[matterbeam]

Hi!

I've come up with four ideas for cheap access to space, involving orbital tethers.

The first has already been thought up of: the orbital tether pulls a suborbital tether into orbit. However, my variant has the tether station itself being used as a platform which can change its orbit to increase or decrease rendezvous velocity.

The second involves a tether being used as a 'runway': the tether trails behind a space station. A spacecraft latches onto the tether and starts braking. This speeds up the spacecraft and slows down the space station, effectively pulling the spacecraft from a suborbital trajectory into orbit.

The third involves flywheels. The runway is attached to flywheels spinning in the opposite direction. When the spacecraft brakes, it pulls on the flywheels and slows them down, instead of slowing down the space station. The flywheels are kinetic energy reserves that allow for propellantless operation.

The fourth involves replacing the tether with a series of pulleys. The relative velocity between the spacecraft and the tether can be very high in a simple runway, making braking hard. With the pulleys, the tether 'expands' like a bungee cord. The relative speed between spacecraft and tether is divided by the number of pulleys for easy braking.

These ideas and designs are described and illustrated with calculated examples here:

http://toughsf.blogspot.com/2017/01/boo ... ne-in.html
http://toughsf.blogspot.com/2017/01/the ... ments.html

[Simon_Jester]

Hi!

I've come up with four ideas for cheap access to space, involving orbital tethers.

The first has already been thought up of: the orbital tether pulls a suborbital tether into orbit. However, my variant has the tether station itself being used as a platform which can change its orbit to increase or decrease rendezvous velocity.

The second involves a tether being used as a 'runway': the tether trails behind a space station. A spacecraft latches onto the tether and starts braking. This speeds up the spacecraft and slows down the space station, effectively pulling the spacecraft from a suborbital trajectory into orbit.

The third involves flywheels. The runway is attached to flywheels spinning in the opposite direction. When the spacecraft brakes, it pulls on the flywheels and slows them down, instead of slowing down the space station. The flywheels are kinetic energy reserves that allow for propellantless operation.

My big question with these three ideas is, where are you getting the kinetic energy from? If you slow a space station down enough, it de-orbits and crashes into the atmosphere. And the total amount of delta-V it takes to deorbit a space station is fairly small compared to the delta-V it took to put the thing in orbit in the first place.

This isn't going to be a very efficient system for accelerating things to orbital velocity, because you'll have to keep launching fuel to enable the station to accelerate itself back up to speed. Sure, you can use thruster systems with high specific impulse, but your options are basically nuclear or ion propulsion. Ion propulsion is really low thrust, so it will take an extremely long time to accelerate a massive station back up to speed, and you cannot use any single station this way very often. Nuclear propulsion is problematic because the only really good propellant for a nuclear rocket is hydrogen, and hydrogen isn't easy to store for prolonged periods in orbit. You can't just keep a big tank farm of liquid hydrogen up there indefinitely and use it 'whenever.'

Also, the flywheel system in has a problem where you appear to have forgotten about conservation of angular momentum. The problem here is making the flywheels spin, as opposed to making the station around them spin (and gradually wrap the tether around itself). How do you resolve that? Remember that orbiting spacecraft routinely use flywheels to store angular momentum- in order to turn the craft. Reaction wheels are great for that purpose, but when you spin the reaction wheel in one direction, the spacecraft will turn the other way!

I suppose you could have TWO sets of flywheels spinning in opposite directions, storing up opposite angular momentum, so that there is no net change in angular momentum for the station as you spin them up. But then the satellite starts slowing one set of wheels by grabbing the tether... which means that some part of the system, probably the station, will suddenly be experiencing a torque from its interaction with the slowing reaction wheels.

Where does the angular momentum go, and what is the consequence?

The fourth involves replacing the tether with a series of pulleys. The relative velocity between the spacecraft and the tether can be very high in a simple runway, making braking hard. With the pulleys, the tether 'expands' like a bungee cord. The relative speed between spacecraft and tether is divided by the number of pulleys for easy braking.

In the pulley system, the pulleys are being subjected to very large forces that start and stop very suddenly, and the cables are moving at speeds of thousands of meters per second relative to the pulleys.

I think you're confusing the rate at which the pulleys move apart (which can be quite low) with the rate at which the cable itself is moving (which is much higher). A block and tackle

[matterbeam]

Thank you for answering! I was not expecting this much.

I mentioned in the blog post that the station, the simple version that uses its own kinetic energy, does slow down and does drop its apoapsis. A 1000 ton station at a 1000km orbit (7350m/s) catching a 10 ton spaceship loses 270.1GJ and 36.8m/s orbital velocity. Its apoapsis drops from 1000km to about 855km.

It can do so about 6 times before it drops to a dangerously low 150k orbit.

This isn't going to be a very efficient system for accelerating things to orbital velocity, because you'll have to keep launching fuel to enable the station to accelerate itself back up to speed.

In the example I gave above, I used a 100km/s exhaust velocity thruster that only needs about 360kg of propellant to push the 1000 ton station back into its original orbit. Placing the 10 ton spacecraft up to 7350m/s using chemical thrusters requires about 85 tons of propellant depending on non-payload dry mass. The net gain is huge, even if it takes 39 hours to complete the manoeuvre.

Even more realistic 50km/s or 30km/s thrusters only require up to 1.23 tons of propellant.

You can scale up the propulsive power for lower delays between rocket launches. With such a small propellant fraction, most of the station can be dedicated to other utilities, such as electric engines with terrible specific power.

But then the satellite starts slowing one set of wheels by grabbing the tether... which means that some part of the system, probably the station, will suddenly be experiencing a torque from its interaction with the slowing reaction wheels.

The tether is strung around all flywheels, like a wire spooling from several coils. The evenly distributes angular momentum.

In the pulley system, the pulleys are being subjected to very large forces that start and stop very suddenly, and the cables are moving at speeds of thousands of meters per second relative to the pulleys

Not to my understanding! The pulleys are subject to large forces... in total. The force is distributed between all wheels. For a 74-segment system, that's a minimum division of the forces by 148. If you want a 10 ton craft to decelerate at 3G, you need to apply 2.94MN, or 5.9MN for realistic brakes and a safety brakes. This is 38kN per set of brakes. That's less than an F1 car!

Also, each set of wheels is moving away from each other at 50m/s. The wires strung around them moves at 100m/s due to mechanical advantage. 74*100 gives us the full expansion velocity of the entire train of pulleys, or about the relative velocity the spacecraft on the other end is achieving.

I think your comment cut off at the end.

[Simon_Jester]

Thank you for answering! I was not expecting this much.

I mentioned in the blog post that the station, the simple version that uses its own kinetic energy, does slow down and does drop its apoapsis. A 1000 ton station at a 1000km orbit (7350m/s) catching a 10 ton spaceship loses 270.1GJ and 36.8m/s orbital velocity. Its apoapsis drops from 1000km to about 855km.

It can do so about 6 times before it drops to a dangerously low 150k orbit...

In the example I gave above, I used a 100km/s exhaust velocity thruster that only needs about 360kg of propellant to push the 1000 ton station back into its original orbit. Placing the 10 ton spacecraft up to 7350m/s using chemical thrusters requires about 85 tons of propellant depending on non-payload dry mass. The net gain is huge, even if it takes 39 hours to complete the manoeuvre.

Even more realistic 50km/s or 30km/s thrusters only require up to 1.23 tons of propellant.

The problem is that you have to deliver the propellant to the station, and you have to orbit the thousand-ton station in the first place. This adds a lot of cost to setting up the system, and considerable ongoing cost. The kinetic energy of the station and its resources isn't "free."

Also... Hey, wait a minute... how did you get your payload up to where it will rendezvous with the space station in the first place? Presumably you had to loft it on a suborbital trajectory, which would still require a significant amount of fuel- not as much as reaching orbit, but nontrivial. And if the payload is on a suborbital trajectory moving at several kilometers per second relative to the station, there are some serious problems with the plan:

1) The requirements for a precision rendezvous are extremely tight. It's not impossible to make an object on a suborbital trajectory collide with an orbiting object; that's the performance requirement for a successful ASAT weapon. But it's not something that works 100% of the time. And here, if you miss your 'catch,' the payload is going to be coming back down to Earth as a meteor. At best.

2) One very plausible failure mode of the system is a collision between the payload and the station, or harmful collision between the payload and the tether, at several kilometers per second! A collision will destroy both station and payload and very possibly create enough debris in orbit to trigger a Kessler cascade scenario. Even a tether-like cable could still "whip-crack" its way right through the payload if the angle of impact is wrong; I don't know if you've ever seen what can happen when things like antenna guy wires and other steel cables under tension snap, but the results can be grisly. You won't lose the station in that case, probably, but you assuredly lose the payload.

In theory you can armor the payload to at least protect it against the tether, maybe, but such a mass of armor may well and several tons of parasitic mass to the payload. At which point you're launching ten tons of payload plus armor on a suborbital trajectory, which requires a launcher that might very well be able to just put the payload itself straight into orbit if you weren't mucking around with the armor!

3) Even if you succeed in grabbing the tether, slight errors in the angles involved, or millisecond errors in timing, will correspond to significant deviations from the planned maneuver. Which could be hazardous to the station, the payload, or both.

You can scale up the propulsive power for lower delays between rocket launches. With such a small propellant fraction, most of the station can be dedicated to other utilities, such as electric engines with terrible specific power.

What is "specific power?" That is not a term I have ever heard used in the context of rocket science before.

Found it.

Well, as noted, you CAN gradually and laboriously use ion thrusters or the like to boost yourself back up to the proper orbit. But the electrical generating machinery is going to add further mass to the station, which has to be orbited by conventional means before you can begin doing this.

Another cost to consider is the cost of maintaining the station. All its machinery will need to be regularly inspected and in perfect working order, because a stuck pulley, a jammed RCS thruster, a misaligned radar that measures the approach of the payloads at orbital speed... Any breakdown can destroy the entire expensive apparatus!

The inspections will be particularly complicated and expensive because it would be suicidal to put a permanent human crew on this station, and reckless in the extreme to even put a crew in the same orbit as something that might be shattered into thousands of tons of space debris by a collision.

But then the satellite starts slowing one set of wheels by grabbing the tether... which means that some part of the system, probably the station, will suddenly be experiencing a torque from its interaction with the slowing reaction wheels.

The tether is strung around all flywheels, like a wire spooling from several coils. The evenly distributes angular momentum.

If the flywheels are rapidly spinning AND the tether is being yanked at a speed of multiple kilometers per second... I'm honestly having trouble imagining materials that can withstand these stresses regularly. And if anything breaks under tension, or due to cumulative fatigue, at best you lose the payload and at worst your station blows itself apart in a storm of exploding flywheels.

I will also note that you didn't actually address the conservation of angular momentum problem associated with the flywheel system. How do you spin up a huge battery of flywheels to store billions of joules of kinetic energy, without also exerting enough torque to set your space station to spinning around so that it wraps itself up in its own tether like a yo-yo?

In the pulley system, the pulleys are being subjected to very large forces that start and stop very suddenly, and the cables are moving at speeds of thousands of meters per second relative to the pulleys

Not to my understanding! The pulleys are subject to large forces... in total. The force is distributed between all wheels. For a 74-segment system, that's a minimum division of the forces by 148. If you want a 10 ton craft to decelerate at 3G, you need to apply 2.94MN, or 5.9MN for realistic brakes and a safety brakes. This is 38kN per set of brakes. That's less than an F1 car!

The problem is that rearranging the force doesn't mean that the full force isn't exerted on the cable, or on the brackets holding the "block and tackle" system in place. Or that the cable is moving slowly relative to the pulleys.

Also, each set of wheels is moving away from each other at 50m/s. The wires strung around them moves at 100m/s due to mechanical advantage. 74*100 gives us the full expansion velocity of the entire train of pulleys, or about the relative velocity the spacecraft on the other end is achieving.

Stop and consider what happens at the last pulley in the system. The one that you encounter last if you follow the path of the tether out from the station to where the payload will be latching on.

That specific pulley has to "pay out" several kilometers of tether per second. Because all your cleverness with the block and tackle hasn't actually changed the fact that when the payload latches on, abruptly it's going to be taking several kilometers of tether every second as it slows down. So that specific pulley is still experiencing friction with a cable that is moving at 7 km/s relative to the pulley, regardless of how fast or slow the rest of the pulleys are moving relative to each other. This simply isn't optional, because if the pulley doesn't see a cable moving past it at seven kilometers a second, then the payload isn't getting enough cable to slow itself down, in which case the payload just 'jerked' off the end of the tether and is headed back down to Earth.

Likewise, the next pulley in the system is experiencing friction due to having to 'pay out' 6.95 km of cable per second, and 6.9 km for the one after that, and so on. Tweaking the layout of the pulleys might change those numbers, but it doesn't really matter. The point is, even if the pulleys are moving away from each other at low speeds, the cable itself is still moving very fast relative to the pulleys.

...

Incidentally, I'm also having trouble imagining a tether strong enough to handle these kinds of dynamic loads, long enough that it can play "catch" successfully, and light enough to be practical to space-launch. You propose three-gravity deceleration to impart a delta-V of 7350 m/s. Rounding off g to ten meters per second squared, that means that the deceleration maneuver will require 245 seconds. During which time the payload will travel (relative to the station) a distance of nine hundred kilometers.

So you need a cable that can withstand a tension force on the order of several million newtons, nine hundred kilometers in length... One that can stand being repeatedly grabbed at immense speeds, subjected to immense friction forces, and reeled back in, under deep-space conditions where temperature varies wildly.

Building a space elevator is hard enough, but at least those are static loads! These are dynamic loads, and the engineering of dynamic loads tends to be far, far more challenging.

[LaCroix]

Wouldn't it be much easier to invest in a Lofstrom launch loop? Instead of 39 hours for 6 launches of your proposed 10t vehicle, you would get between 35 and 80 5 ton lauches a day. And you would exchange the need for a booster to get into suborbital (the most fuel expensive part) with the need for a booster to get into orbit from the loop disconnect in suborbit. Your vehicle will need a drive to change orbit to final, anyway, so putting an initial 1.6km/s delta-v in to reach GEO (or a 100 plus change m/s for LEO) is not too bad.

That loop would reduce delta-v cost by a factor of ten, and would strip the two bottom stages of most modern launch configurations. Depending on how much power generation you invest initially to increase launch frequency, you would end up in ranges of a few hundred to only a few $ per kg (best case) to orit.

It also doesn't need a space-elevator rated cable, and is safer. Instead of a 1000t space station deorbiting in case of failure, we do have a worst case of the "cable" falling to earth, which could be slowed down by parachutes or such, and would fall to a rather predictable location (over the ocean, for example).
There are technological problems with the loop, but in comparison to an elevator or this tether station and cable, they are relatively trivial, for the whole system is assembled on earth, and the most problematic points of failure (end turns) are permalocated on earth and easily accessible. It can also be brought back to earth for repairs by "simply" turning the power off, plus a recovery system (parachutes) that is needed for emergencies, anyway.

[matterbeam]

The problem is that you have to deliver the propellant to the station, and you have to orbit the thousand-ton station in the first place. This adds a lot of cost to setting up the system, and considerable ongoing cost. The kinetic energy of the station and its resources isn't "free."

I agree. However, it is interesting relative to alternative solutions. A space elevator is massively more difficult to make, requiring technology we do not have available and ludicrous masses to put into orbit. A rotovator is useful and realizable, but very restricted in what it can do. A skyhook has heating difficulties that requires heat resistant materials, making it heavier than it should be....

...and all of those are dwarved by the long term costs of rocket flight using chemical propulsion. The Boosted Orbital Tether is a halfway measure: smaller, rocket, smaller tether.

Also... Hey, wait a minute... how did you get your payload up to where it will rendezvous with the space station in the first place? Presumably you had to loft it on a suborbital trajectory, which would still require a significant amount of fuel- not as much as reaching orbit, but nontrivial. And if the payload is on a suborbital trajectory moving at several kilometers per second relative to the station, there are some serious problems with the plan:

The 'boosted' part of boosted orbital tether is the initial rocket launch that provides 4500m/s of deltaV, going straight up. It can be achieved with a relatively cheap Kerlolox rocket with 350 average Isp and a mass ratio of only 3.8

1) The requirements for a precision rendezvous are extremely tight. It's not impossible to make an object on a suborbital trajectory collide with an orbiting object; that's the performance requirement for a successful ASAT weapon. But it's not something that works 100% of the time. And here, if you miss your 'catch,' the payload is going to be coming back down to Earth as a meteor. At best.

I'm sure that by the time we need regular 10 ton payloads in orbit, precision rendezvous will be more reliable. Also, a mass ratio of only 3.8 means that the initial rocket booster can accommodate increased safety features such as a heatshield for a half-speed re-entry and big parachutes and retro-boosters on landing.

2) One very plausible failure mode of the system is a collision between the payload and the station, or harmful collision between the payload and the tether, at several kilometers per second! A collision will destroy both station and payload and very possibly create enough debris in orbit to trigger a Kessler cascade scenario. Even a tether-like cable could still "whip-crack" its way right through the payload if the angle of impact is wrong; I don't know if you've ever seen what can happen when things like antenna guy wires and other steel cables under tension snap, but the results can be grisly. You won't lose the station in that case, probably, but you assuredly lose the payload.

Quite right. But the Shuttle exploded, a space elevator can fall to the ground and a laser launch system cut right through the payload at the wrong angle. I don't think it is inherently more risky than other launch options. If the cable does smack against the side of the spacecraft, its very low mass per meter means that collision energy is quite low (about 1.3kg/m for the Zylon). That is with a 10x safety margin, as in the cable can withstand 10x the regular tension load.

In theory you can armor the payload to at least protect it against the tether, maybe, but such a mass of armor may well and several tons of parasitic mass to the payload. At which point you're launching ten tons of payload plus armor on a suborbital trajectory, which requires a launcher that might very well be able to just put the payload itself straight into orbit if you weren't mucking around with the armor!

I doubt armor requirements are 85 tons or more per 10 ton of payload!

3) Even if you succeed in grabbing the tether, slight errors in the angles involved, or millisecond errors in timing, will correspond to significant deviations from the planned maneuver. Which could be hazardous to the station, the payload, or both.

If you grab the tether, the center of pressure, the braking point, is far behind the center of mass. It's an autocorrecting system, like a pendulum. With the pulley train configuration, you can use differential braking to offset an unequal pull on the tether.

Well, as noted, you CAN gradually and laboriously use ion thrusters or the like to boost yourself back up to the proper orbit. But the electrical generating machinery is going to add further mass to the station, which has to be orbited by conventional means before you can begin doing this.

Electrically generating machinery is the mass of the station. The more mass you have, the better. I see the first station's mass as majoritarily being ISRU propellants hauled in from the Moon. It can serve as a propellant depot for incoming and outgoing craft....

Another cost to consider is the cost of maintaining the station. All its machinery will need to be regularly inspected and in perfect working order, because a stuck pulley, a jammed RCS thruster, a misaligned radar that measures the approach of the payloads at orbital speed... Any breakdown can destroy the entire expensive apparatus!

The pulley design has lots of built-in redundancy. The remaining failure points, other than the spacecraft's breaks not working or the tether snapping, are no different than the ISS during a rendezvous with a Soyuz pod, except with higher energies involved!

If the flywheels are rapidly spinning AND the tether is being yanked at a speed of multiple kilometers per second... I'm honestly having trouble imagining materials that can withstand these stresses regularly. And if anything breaks under tension, or due to cumulative fatigue, at best you lose the payload and at worst your station blows itself apart in a storm of exploding flywheels.

The flywheels are spinning at about 3500 RPM. The hoop stresses on the wheels is 200MPa, less than the yield strength of commonly made A36 steel and far less than that of exotic materials such as carbon flywheels already being used in power stations at 10000RPM+.

I will also note that you didn't actually address the conservation of angular momentum problem associated with the flywheel system. How do you spin up a huge battery of flywheels to store billions of joules of kinetic energy, without also exerting enough torque to set your space station to spinning around so that it wraps itself up in its own tether like a yo-yo?

The same way a Chinook helicopter doesn't twist itself to death. Spin one set of flywheels one way, spin the other set the other way, and they cancel each other out.

The problem is that rearranging the force doesn't mean that the full force isn't exerted on the cable, or on the brackets holding the "block and tackle" system in place. Or that the cable is moving slowly relative to the pulleys.

Yes. That's why an 11mm cable of Kevlar can handle 10 times the maximum tensile stress expected from the braking maneuver. A Zylon tether can be even thinner, with the same safety margin. The slow moving cable relative to the pulley wheels is an exercise in minimizing braking requirements.

Stop and consider what happens at the last pulley in the system. The one that you encounter last if you follow the path of the tether out from the station to where the payload will be latching on.

Imagine pulling on a bungee cord. Or any elastic object with a speed of sound far above the speed you're pulling it at.

Does only the end bit stretch? No. It stretches uniformly. The part closest to your finger stretches as much, and at the same rate, as the part furthest from your finger.

Incidentally, I'm also having trouble imagining a tether strong enough to handle these kinds of dynamic loads, long enough that it can play "catch" successfully, and light enough to be practical to space-launch. You propose three-gravity deceleration to impart a delta-V of 7350 m/s. Rounding off g to ten meters per second squared, that means that the deceleration maneuver will require 245 seconds. During which time the payload will travel (relative to the station) a distance of nine hundred kilometers.

Kevlar! Zylon! The latter even has negative thermal expansion! And unless we're talking about the simplest runway design, they can be held in shielded spools for most of their life.

[matterbeam]

Wouldn't it be much easier to invest in a Lofstrom launch loop? Instead of 39 hours for 6 launches of your proposed 10t vehicle, you would get between 35 and 80 5 ton lauches a day.

6 launches is the number of catches a 1000 ton station can make before orbit drops too low.
39 hours is the time it takes a 400MW, 100km/s exhaust velocity engine to push a 1000 ton station back into orbit.

If we use a heavier station, we can perform more 'sacrificial' launches. If we use a lower exhaust velocity, or higher power engine, we can perform 'sacrificial' launches more often. A 20km/s hall effect thruster can perform the same manoeuvre in 7.8 hours.

If we use the proposed upgrades, such as the flywheels, we can perform an unlimited number of launches. It takes 11.25 minutes for a 400MW power supply to refill the 270GJ needed to catch a 10 ton payload at 1000km altitude. A 43MW power source can do it once per 1000km orbit.

And you would exchange the need for a booster to get into suborbital (the most fuel expensive part) with the need for a booster to get into orbit from the loop disconnect in suborbit. Your vehicle will need a drive to change orbit to final, anyway, so putting an initial 1.6km/s delta-v in to reach GEO (or a 100 plus change m/s for LEO) is not too bad.

The recoverable Falcon 9 has demonstrated that an initial boost into space is not so expensive.

The main problem with the Loftrom launch loop is the massive masses involved, the 4000km loop length, the 17GW power supply that cannot be turned off, the temperature limits, and all for putting 5 tons into orbit, minus the 1.6km/s deltaV requirement.

[Simon_Jester]

I would just like to point out that the problem with this design, at its heart, is that the extreme forces involved are dynamic rather than static. Anyone with a little engineering background will know the problem caused by that.

A launch loop is under static forces and can be spun up gradually, as I understand it. Much simpler even if it's much bigger.

The problem is that you have to deliver the propellant to the station, and you have to orbit the thousand-ton station in the first place. This adds a lot of cost to setting up the system, and considerable ongoing cost. The kinetic energy of the station and its resources isn't "free."

I agree. However, it is interesting relative to alternative solutions. A space elevator is massively more difficult to make, requiring technology we do not have available and ludicrous masses to put into orbit. A rotovator is useful and realizable, but very restricted in what it can do. A skyhook has heating difficulties that requires heat resistant materials, making it heavier than it should be....

...and all of those are dwarved by the long term costs of rocket flight using chemical propulsion. The Boosted Orbital Tether is a halfway measure: smaller, rocket, smaller tether.

As noted, there are a huge number of other possible technologies

Your problem is that you're starting from "we must do something about launch costs," imagining a particular system, and saying "this is something... therefore we must do it." That's backwards from an engineering standpoint; what you need to do is find the best system. And the best system is the one with the fewest random associated hazards (like triggering a Kessler cascade the first time anyone goes 'oops').

Also... Hey, wait a minute... how did you get your payload up to where it will rendezvous with the space station in the first place? Presumably you had to loft it on a suborbital trajectory, which would still require a significant amount of fuel- not as much as reaching orbit, but nontrivial. And if the payload is on a suborbital trajectory moving at several kilometers per second relative to the station, there are some serious problems with the plan:

The 'boosted' part of boosted orbital tether is the initial rocket launch that provides 4500m/s of deltaV, going straight up. It can be achieved with a relatively cheap Kerlolox rocket with 350 average Isp and a mass ratio of only 3.8

Yes, but the same rocket that can loft a ten-ton payload to 1000 km straight up could probably also loft a significant payload to LEO.

And you're going to have a lot of parasitic mass on your "tetherball" payloads from the weight of armor and grabbing equipment that makes it possible for the payload to survive being snagged by the tether.

It's entirely possible that the amount of useful payload you can orbit in this system will turn out to be only, say, a ton or so... In which case you'd have done better to just put the payload on the rocket booster in the first place.

I mean heck, think about the grabbing mechanism you need in order to make sure the cable doesn't just slip through your payload's "fingers," when the cable starts at a relative velocity of seven kilometers per second compared to the grabber. And when you need the cable to be made out of some very smooth material so that it doesn't burn or carve its way through all those pulleys you're using.

I'm not sure you have a good intuitive grasp of just how high these speeds really are. You're doing some of the calculations, but you don't seem to realize just what these numbers mean.

1) The requirements for a precision rendezvous are extremely tight. It's not impossible to make an object on a suborbital trajectory collide with an orbiting object; that's the performance requirement for a successful ASAT weapon. But it's not something that works 100% of the time. And here, if you miss your 'catch,' the payload is going to be coming back down to Earth as a meteor. At best.

I'm sure that by the time we need regular 10 ton payloads in orbit, precision rendezvous will be more reliable. Also, a mass ratio of only 3.8 means that the initial rocket booster can accommodate increased safety features such as a heatshield for a half-speed re-entry and big parachutes and retro-boosters on landing.

Now you're adding MORE parasitic mass. At what point could you just take the same booster rocket, the same useful payload, and boost the payload straight to orbit by taking that parasitic mass of armor/grabber/parachutes/whatever and replacing it with a high-impulse upper stage like a Centaur?

2) One very plausible failure mode of the system is a collision between the payload and the station, or harmful collision between the payload and the tether, at several kilometers per second! A collision will destroy both station and payload and very possibly create enough debris in orbit to trigger a Kessler cascade scenario. Even a tether-like cable could still "whip-crack" its way right through the payload if the angle of impact is wrong; I don't know if you've ever seen what can happen when things like antenna guy wires and other steel cables under tension snap, but the results can be grisly. You won't lose the station in that case, probably, but you assuredly lose the payload.

Quite right. But the Shuttle exploded, a space elevator can fall to the ground and a laser launch system cut right through the payload at the wrong angle. I don't think it is inherently more risky than other launch options. If the cable does smack against the side of the spacecraft, its very low mass per meter means that collision energy is quite low (about 1.3kg/m for the Zylon). That is with a 10x safety margin, as in the cable can withstand 10x the regular tension load.

OHHH, your cable weighs 1.3 kilograms per meter? So nine hundred kilometers of the stuff masses, what, 1.3*900000 is 1170 tons?

This station is going to have to be bigger than you thought, and the forces are more significant than you thought. Because in the station's frame of reference, the pulley system has to exert not only enough force to change the velocity of the payload, but of the cable.

By the way, how is this cable launched? A thousand ton cable spool isn't going up on one rocket, or if it is, you've got Big Dumb Booster technology so cheap it may well reduce costs to LEO to a few hundred dollars per kilo all by itself. So how do you attach each cable segment to the next? Square knots?

Also, my point is that it seems as though you haven't evaluated the risks in any mathematically rigorous sense. You've simply dismissed them.

I mean, I don't want to discourage you from thinking outside the box here, but quite frankly the box exists for a reason, and as soon as you step outside it, you're in unfamiliar territory. Rational cost-benefit analysis is key to success for someone trying to pioneer a new idea. Especially one that involves tens or hundreds of billions of dollars of infrastructure, as this likely would.

In theory you can armor the payload to at least protect it against the tether, maybe, but such a mass of armor may well and several tons of parasitic mass to the payload. At which point you're launching ten tons of payload plus armor on a suborbital trajectory, which requires a launcher that might very well be able to just put the payload itself straight into orbit if you weren't mucking around with the armor!

I doubt armor requirements are 85 tons or more per 10 ton of payload!

Remember, you're talking about accelerating a ten-ton total package here. All your calculations are based on that. Don't move the goalposts. The question is, of those ten tons, how much is real payload (the thing you want in space), and how much is random useless crud you threw into orbit to protect the payload from being destroyed by its own launch system?

There's going to be a practical minimum size for this system. Because a mechanism capable of grabbing onto a rope that is moving at seven kilometers per second, and latching onto the rope firmly enough to be accelerated at three gravities but NOT to be subjected to destructive, instantaneous jerk that wrecks the payload, and that WON'T get fried by frictional heating as the rope slides through its "fingers" at several kilometers per second...

This system is not going to be small or light. That grabber unit is going to have to be very tough, and that means it's going to have to be heavy.

So if you're talking about a ten-ton "payload" lofted by your booster rocket, you're actually talking about a multi-ton "grabber unit" mated to a (much smaller) mass that is the real payload of the system. It's entirely possible that this will end up looking like a two-ton payload on an eight-ton grabber.

And a rocket that can loft two-plus-eight tons up to one thousand kilometers can ALSO loft two tons of payload plus eight tons of upper stage on the same trajectory. At which point if you used a gravity turn like a sensible person, you might very well be able to get into orbit.

Now, in the part of your post I quoted, I think you accidentally tried to move the goalposts by talking about how the ten tons of payload were actually ALL real, beneficial payload, with the mass of armor and so on being 'extra.'

Trouble is, if that's ten tons of payload plus protection and a grabber unit, including (according to you) a heat shield and parachutes that you won't even use if this goes right... Now we're talking about a mass that is going to be way more than ten tons total. How much depends on the engineering of the grabber unit (which you haven't even discussed) and the armor required to prevent damage to the payload from an accidental tether strike (which you haven't discussed in detail, except to dismiss the problem).

And, again, a rocket that can lift all THAT to 1000 km on a ballistic trajectory is quite capable of boosting a considerable payload straight to orbit, with the provision of an upper stage of the rocket that might well weigh less and be easier to build than the grabber unit!

3) Even if you succeed in grabbing the tether, slight errors in the angles involved, or millisecond errors in timing, will correspond to significant deviations from the planned maneuver. Which could be hazardous to the station, the payload, or both.

If you grab the tether, the center of pressure, the braking point, is far behind the center of mass. It's an autocorrecting system, like a pendulum. With the pulley train configuration, you can use differential braking to offset an unequal pull on the tether.

If you assume all the parts of the system are invulnerable, yes. The problem is, as I mentioned in my last post, that dynamic loads are much harder to cope with than static loads. It's not just about making sure the static forces are in equilibrium, it's about what happens when a large number of moving parts suddenly start moving very quickly, from a standing start.

That's the part which makes the system very sensitive to small errors. Because if those forces are not exerted in the way that was planned for, the whole thing is likely to fall apart.

Well, as noted, you CAN gradually and laboriously use ion thrusters or the like to boost yourself back up to the proper orbit. But the electrical generating machinery is going to add further mass to the station, which has to be orbited by conventional means before you can begin doing this.

Electrically generating machinery is the mass of the station. The more mass you have, the better. I see the first station's mass as majoritarily being ISRU propellants hauled in from the Moon. It can serve as a propellant depot for incoming and outgoing craft....

You still have to put the station itself into orbit. And you still have the problem

Another cost to consider is the cost of maintaining the station. All its machinery will need to be regularly inspected and in perfect working order, because a stuck pulley, a jammed RCS thruster, a misaligned radar that measures the approach of the payloads at orbital speed... Any breakdown can destroy the entire expensive apparatus!

The pulley design has lots of built-in redundancy. The remaining failure points, other than the spacecraft's breaks not working or the tether snapping, are no different than the ISS during a rendezvous with a Soyuz pod, except with higher energies involved!

If you throw a five-pound iron weight at me, I catch it and say "oof."

If you take the same five pound weight and shoot it out of a railgun at Mach 8 at me, they'll have to clean what's left of me off the walls with a mop and bucket.

And yet, the remaining failure points of the "me getting shot with a railgun" system were "no different than those during me catching an iron weight, except with higher energies involved."

Seriously, during a Soyuz rendezvous, spacecraft handle the final approach with each other at speeds on the order of one meter per second. Less, for final docking. It is done very carefully, using reaction thrusters that have more than enough delta-V to bring the maneuvering craft to a full and complete stop if anything goes wrong.

Here, by contrast, spacecraft handle final approach at speeds on the order of several thousand meters per second. It cannot possibly be done carefully, because there is only one chance to get it right, no way to abort the process if something goes wrong. The payload might have some minimal maneuvering capability, but not nearly enough to stop or even slow down significantly in case of a problem.

That's faster than a bullet. It's even faster than that railgun I was just talking about.

Ever heard of the "bullet catch" magic trick? Well here, you're performing it for real- you're firing a bullet at a space station, a hypervelocity bullet, and expecting the station to catch the bullet successfully without harm.

That's not a harder version of the same problem as an ISS docking. That is a completely different problem. And any mechanical failure in the system will result in disaster, because of the sheer amount of energy being released. Materials are GOING to break, bend, and deform when exposed to that much force and that much energy in that short of an amount of time.

If the flywheels are rapidly spinning AND the tether is being yanked at a speed of multiple kilometers per second... I'm honestly having trouble imagining materials that can withstand these stresses regularly. And if anything breaks under tension, or due to cumulative fatigue, at best you lose the payload and at worst your station blows itself apart in a storm of exploding flywheels.

The flywheels are spinning at about 3500 RPM. The hoop stresses on the wheels is 200MPa, less than the yield strength of commonly made A36 steel and far less than that of exotic materials such as carbon flywheels already being used in power stations at 10000RPM+.

And they're getting spun down regularly and quickly. How fast do power stations spin their flywheels down?

I will also note that you didn't actually address the conservation of angular momentum problem associated with the flywheel system. How do you spin up a huge battery of flywheels to store billions of joules of kinetic energy, without also exerting enough torque to set your space station to spinning around so that it wraps itself up in its own tether like a yo-yo?

The same way a Chinook helicopter doesn't twist itself to death. Spin one set of flywheels one way, spin the other set the other way, and they cancel each other out.

I suppose you actually could rig that one to work, with care. The problem is, again, that this only works if the loads in question are in perfect balance so that all the flywheels can be spun down rapidly, at the same time, during a capture maneuver. If there's asymmetry in which flywheels are being spun down or by how much, your station starts trying to impersonate a yo-yo.

The problem is that rearranging the force doesn't mean that the full force isn't exerted on the cable, or on the brackets holding the "block and tackle" system in place. Or that the cable is moving slowly relative to the pulleys.

Yes. That's why an 11mm cable of Kevlar can handle 10 times the maximum tensile stress expected from the braking maneuver. A Zylon tether can be even thinner, with the same safety margin. The slow moving cable relative to the pulley wheels is an exercise in minimizing braking requirements.

Stop and consider what happens at the last pulley in the system. The one that you encounter last if you follow the path of the tether out from the station to where the payload will be latching on.

Imagine pulling on a bungee cord. Or any elastic object with a speed of sound far above the speed you're pulling it at.

Does only the end bit stretch? No. It stretches uniformly. The part closest to your finger stretches as much, and at the same rate, as the part furthest from your finger.

Does your tether stretch like a bungee cord? Not if it's made out of kevlar, it doesn't. Or of Zylon.

Remember that if you're trying to make this realistic, you have to give each part of the system internally consistent material properties. The tether cannot be very elastic AND very strong at the same time. It can't have tensile strength greater than steel AND the ability to stretch out to several times its original length without breaking. You can weave the tether out of many very strong fibers like a bungee cord, and maybe (I doubt it) get stretchiness out of it that way... but then you have to worry about the tether fraying when it's running through pulleys and grabber units at a relative velocity of several kilometers per second.

Because if you have to replace a thousand ton tether every few dozen launches, you've just lost all the advantages of this system.

[qutoe]

Incidentally, I'm also having trouble imagining a tether strong enough to handle these kinds of dynamic loads, long enough that it can play "catch" successfully, and light enough to be practical to space-launch. You propose three-gravity deceleration to impart a delta-V of 7350 m/s. Rounding off g to ten meters per second squared, that means that the deceleration maneuver will require 245 seconds. During which time the payload will travel (relative to the station) a distance of nine hundred kilometers.

Kevlar! Zylon! The latter even has negative thermal expansion! And unless we're talking about the simplest runway design, they can be held in shielded spools for most of their life.[/quote]Your aforementioned Zylon tether needs to weigh 1170 tons, remember.

Incidentally, that means that when you're performing the 'catch' maneuver, you're not just exerting acceleration forces on the payload. You're exerting acceleration forces on the tether. Towards the end of the cable run, that involves accelerating several hundred tons of cable at (you told me) three gravities. Which is a very different order of problem than just accelerating a ten ton payload. For every action there is an equal and opposite reaction. If you're exerting (say) ten meganewtons of force to accelerate (say) 340 tons of your 1170-ton tether... where else in the system are those forces acting on? Are you braced to withstand THOSE forces, as well as the comparatively small forces required to accelerate the payload?

[Sea Skimmer]

The problem with all cable based ideas is they depend on keeping precise control of tension on the cable, with no gravity as an aid, and the cable can tangle. And if that happens your going to need some really awesome robots, or in the near future realistically actual people in suits to have any chance of getting it working again. Theoretical engineering meets practical, again. It may not be impossible, but the shear amount of work it would take, in space, at extremely high cost to perfect is discouraging to say the least. The sort of technology we'll perfect after we've gotten other low cost to orbit methods working. With a sustained presence in space cable experiments become easy, right now if you needed a different pully machined in space were talking about spending 10 billion dollars to add another module to the ISS to make that happen. Because they could have an entire lathe in that module, and then avoid the need to wait 9 months for the next supply launch.

Since you need a low cost reusable launch system to make a tether catch work out in the first place that just enormously favors relying purely on pure rocket in any near term scenario. Cheaper access to space is not likely to be accomplish by throwing a huge number of added moving parts into orbit. Rocket fuel itself is not a major cost.

Electrostatic thrust though probably has a place in the future for raising orbits of payloads already in a stable LEO position. But all kinds of ideas will work for orbital tugs, a nuke-ion engine one was the intended partner of the shuttle. Its just waiting for cheaper enough launch to orbit to justify it since orbital tugs would take along time to pay for themselves at present launch rates. Too much of a reliability problem at that point.

[matterbeam]

Let me stop using the 'spherical cow' of ten ton payload and 1000 ton station. I think it will be benefitcial for a more realistic view of the masses and forces involved.

9G Pulley train + Flywheel kinetic sink + Booster orbital tether system
Components:
-Spacecraft
10 ton payload. Contains structure and avionics. Shaped like a 4x2m cylinder.
500kg 1cm steel faceplate.
1 ton RCS for 200m/s deltaV
1 ton suspension and brake system with effective 50kN braking force
1 ton heatshield (max re-entry velocity is 4.5km/s, so about 1/4 the heating of regular re-entry)
100kg parachute, 10% of Shuttle SRB
100kg retro-engine with 750 kg hypergolic fuels for 150m/s deltaV
Total: 14.45 tons

-Booster
5 ton structure and mass and engines.
74 ton Kerolox propellant for 4500m.s deltaV
Total with spacecraft on top: 88.4 tons

-Pulley train
1 ton wheels, suspension and bracing
100kg 15kN set of brakes with cooling system
x85: 93.5 tons

-Flywheels
100 ton spinning mass, 5x5m cylinder at 900m/s or 3500RPM.
10 ton set of electric engines for 10MW propulsive or braking force
x8: 880 tons

-Station:
100 tons of bracing and structural support
100 tons of 100MW solar panels
Total: 200 tons

-Tether:
305km Zylon stops 8450m/s spacecraft in 95 seconds
The spacecraft adds 122MN.m of momentum to the system. To be removed in 95 seconds, 1.28MN of force is required.
17.37mm wire, 0.369kg/m, 112.8 tons
x3: 338.4 tons

Total orbiting mass: 1511.9 tons

Performance:

Can catch 10 tons into 1000km orbit. Recovery time 45 minutes. Flywheels contain 58% of total mass. Kevlar materials for the flywheels increase catch to 180 tons. Zero propellant required.

I would just like to point out that the problem with this design, at its heart, is that the extreme forces involved are dynamic rather than static. Anyone with a little engineering background will know the problem caused by that.

I'm considering the dynamic forces as a static system with peak forces involved. As soon as the spacecraft hits the brakes, forces and velocities become lower and lower.

Your problem is that you're starting from "we must do something about launch costs," imagining a particular system, and saying "this is something... therefore we must do it." That's backwards from an engineering standpoint; what you need to do is find the best system. And the best system is the one with the fewest random associated hazards (like triggering a Kessler cascade the first time anyone goes 'oops').

Not quite. I'm starting from 'is there something smaller than a space elevator but better than a rotovator?' and going through with 'how do we minimize the difficulties involved with the Boosted Orbital Tether design?'. Feasibility, economic sense, practicality are of secondary concern to making it work with current-day technology. One thing I can say though... is that you can build a 10 times smaller BOT for 1.4 tons spacecraft, and so on, with each BOT launching the components of a bigger version of itself into space.

The smallest version I can conceive of is a 15.1 ton OBT launched in one go, flinging 100kg satellites into orbit.

Yes, but the same rocket that can loft a ten-ton payload to 1000 km straight up could probably also loft a significant payload to LEO.

4500m/s deltaV takes a 3.8 mass ratio spacecraft straight up to 1000km. You need another 4500m/s deltaV to reach a circular orbit at 200km, requiring a mass ratio of 10-15+.

And you're going to have a lot of parasitic mass on your "tetherball" payloads from the weight of armor and grabbing equipment that makes it possible for the payload to survive being snagged by the tether.

It's entirely possible that the amount of useful payload you can orbit in this system will turn out to be only, say, a ton or so... In which case you'd have done better to just put the payload on the rocket booster in the first place.

I mean heck, think about the grabbing mechanism you need in order to make sure the cable doesn't just slip through your payload's "fingers," when the cable starts at a relative velocity of seven kilometers per second compared to the grabber. And when you need the cable to be made out of some very smooth material so that it doesn't burn or carve its way through all those pulleys you're using.

I'm not sure you have a good intuitive grasp of just how high these speeds really are. You're doing some of the calculations, but you don't seem to realize just what these numbers mean.

Maths adds up.

The last loop of wire can in fact be an array of wires gradually curving gently into various possible positions the spacecraft will take upon rendezvous. The gentle curve means relative lateral velocity remains low.

By the way, how is this cable launched? A thousand ton cable spool isn't going up on one rocket, or if it is, you've got Big Dumb Booster technology so cheap it may well reduce costs to LEO to a few hundred dollars per kilo all by itself. So how do you attach each cable segment to the next? Square knots?

Launched by smaller versions of itself.
Segments are attached by twisting them over each other for several km. Friction, especially static friction, can work wonders. It doesn't matter much if them move under tension. Bracing stops them from unwinding, and 'joint brakes' can increase the pressure and friction during peak load, like clamps.

Does your tether stretch like a bungee cord? Not if it's made out of kevlar, it doesn't. Or of Zylon.

I was trying to compare the pulley train as a whole to something we encounter every day. I wasn't saying that the zylon had elastic properties.

[matterbeam]

The problem with all cable based ideas is they depend on keeping precise control of tension on the cable, with no gravity as an aid, and the cable can tangle.

Then split the thick cable into a dozen thin wires. Arrange in a circle. Add actuators to the wires to compensate for lateral forces. With wire guide rings keeping the configuration straight.

And if that happens your going to need some really awesome robots, or in the near future realistically actual people in suits to have any chance of getting it working again. Theoretical engineering meets practical, again. It may not be impossible, but the shear amount of work it would take, in space, at extremely high cost to perfect is discouraging to say the least. The sort of technology we'll perfect after we've gotten other low cost to orbit methods working.

My personal dream is laser launch to orbit. However, that requires multi-gigawatt power installations with several dowzen km laser ranges. Until then, a 15 ton boosted orbital tether punting 100kg satellites into orbit is quite useful.

With a sustained presence in space cable experiments become easy, right now if you needed a different pully machined in space were talking about spending 10 billion dollars to add another module to the ISS to make that happen. Because they could have an entire lathe in that module, and then avoid the need to wait 9 months for the next supply launch.

Since you need a low cost reusable launch system to make a tether catch work out in the first place that just enormously favors relying purely on pure rocket in any near term scenario. Cheaper access to space is not likely to be accomplish by throwing a huge number of added moving parts into orbit. Rocket fuel itself is not a major cost.

10 tons of fuel on the ground is cheap. 10 tons of fuel in orbit costs 100 tons of fuel on the ground plus engines, tanks, avionics and so on. It is quite expensive once you get it where you need it. With BOTs able to fling components of bigger BOTs into orbit, to be assembled in space, at the cost of fuel on the ground and no fuel in space, the cheap access to space network can be accomplished.

Electrostatic thrust though probably has a place in the future for raising orbits of payloads already in a stable LEO position. But all kinds of ideas will work for orbital tugs, a nuke-ion engine one was the intended partner of the shuttle. Its just waiting for cheaper enough launch to orbit to justify it since orbital tugs would take along time to pay for themselves at present launch rates. Too much of a reliability problem at that point.

I dislike the simple design of an orbital platform performing 'sacrificial' catches. It forces it to have a propellant supply in space. This can be drawn from the payload it catches, but that cuts into useful payload. Relying on an extraterrestrial ISRU fuel depot system to pop up without cheap access to space beforehand might be ill advised.

[Simon_Jester]

Let me stop using the 'spherical cow' of ten ton payload and 1000 ton station. I think it will be benefitcial for a more realistic view of the masses and forces involved.

9G Pulley train + Flywheel kinetic sink + Booster orbital tether system
Components:
-Spacecraft
10 ton payload. Contains structure and avionics. Shaped like a 4x2m cylinder.
500kg 1cm steel faceplate.
1 ton RCS for 200m/s deltaV
1 ton suspension and brake system with effective 50kN braking force
1 ton heatshield (max re-entry velocity is 4.5km/s, so about 1/4 the heating of regular re-entry)
100kg parachute, 10% of Shuttle SRB
100kg retro-engine with 750 kg hypergolic fuels for 150m/s deltaV
Total: 14.45 tons

The big question on my mind is, how confident are you that one ton of suspension and brakes will be enough to handle the load of fourteen tons accelerating at nine gravities? Without failing as the cable slides through the brake system at seven kilometers per second? Come to think of it, your math doesn't add up now, because a 50 kN braking force isn't enough to impart a 9g acceleration. More like 0.35g. You're off by a factor of 25 to 30.

You need well over a meganewton of braking force, and you need the brakes to withstand that force (imparted in the form of friction) for a period of one to two minutes. I'm not at all confident one ton is enough.

And if the suspension/brake system can't be made to weigh one ton, and instead has to weigh five or ten tons, it drastically reduces the desirability and effectiveness of this system.

-Booster
5 ton structure and mass and engines.
74 ton Kerolox propellant for 4500m.s deltaV
Total with spacecraft on top: 88.4 tons

Right. You're launching a 14.5 ton satellite. And this satellite has a ten-ton useful payload of mass that isn't purely parasitic once you reach orbit. The satellite has to be built to withstand nine gravities for a minute and a half or so without wrecking anything.

Suppose, with a similar design, you replace the entire payload structure with an upper stage of similar design to the lower stage and identical mass ratio. Instead of 88.4 tons of rocket to loft 14.5 tons of payload, the upper stage would mass 14.5 tons and accelerate about 2.5 tons to orbital velocity. More, if you use a more efficient propellant for the upper stage (as with Centaur), but there you are.

So I can at least comprehend why you think this is a good idea. You increase the mass of useful material that gets to orbit by a factor of four.

But the advantages of this system become a lot less apparent if:
1) You don't assume the brakes need to mass only one ton- and so far that is an unsupported claim on your part.
2) You factor in the extremely large initial investment of launch capability to get the station up into orbit in the first place and assemble it- assemble it out of many small pieces if we use your notion of having the station be built out of components launched by smaller versions of the same station.
3) You factor in the risk of simply losing the payload if the game of "catch an object moving at Mach 22" does not go according to plan, or the risk of having the whole station completely obliterated in the worst-case scenario of a collision.

Furthermore, you're getting something like a factor of four out of this (ten tons of useful payload instead of 2.5), not a massive order of magnitude improvement. The grabber units you're talking about are, IF they perform as you advertise, a cost-effective alternative to the second stage of a rocket. But that's about all they are, and replacing the second stages of rockets with something more efficient only gets you so far.

I would just like to point out that the problem with this design, at its heart, is that the extreme forces involved are dynamic rather than static. Anyone with a little engineering background will know the problem caused by that.

I'm considering the dynamic forces as a static system with peak forces involved. As soon as the spacecraft hits the brakes, forces and velocities become lower and lower.

That generally isn't a sufficient model for how dynamic loads behave. Have you heard of jerk? It is a thing. Objects that would perform well under a static load that increases gradually perform poorly under a dynamic load that increases abruptly, even if the force exerted by the dynamic load is not greater.

That's especially true when things like material fatigue are factored in.

Yes, but the same rocket that can loft a ten-ton payload to 1000 km straight up could probably also loft a significant payload to LEO.

4500m/s deltaV takes a 3.8 mass ratio spacecraft straight up to 1000km. You need another 4500m/s deltaV to reach a circular orbit at 200km, requiring a mass ratio of 10-15+.

Which, as noted, gets you a 2.5 ton payload to orbit. You're proposing a very complex and expensive system, and very possibly making unjustified generous assumptions about the low mass of the grabber units the system required, to decrease cost to orbit by a factor of four.

There are a lot of ways we could decrease cost to orbit by a factor of four just by being more efficient about existing conventional rocket designs. And they don't have anything like the same up-front investment cost.

And you're going to have a lot of parasitic mass on your "tetherball" payloads from the weight of armor and grabbing equipment that makes it possible for the payload to survive being snagged by the tether.

It's entirely possible that the amount of useful payload you can orbit in this system will turn out to be only, say, a ton or so... In which case you'd have done better to just put the payload on the rocket booster in the first place.

I mean heck, think about the grabbing mechanism you need in order to make sure the cable doesn't just slip through your payload's "fingers," when the cable starts at a relative velocity of seven kilometers per second compared to the grabber. And when you need the cable to be made out of some very smooth material so that it doesn't burn or carve its way through all those pulleys you're using.

I'm not sure you have a good intuitive grasp of just how high these speeds really are. You're doing some of the calculations, but you don't seem to realize just what these numbers mean.

Maths adds up.

The last loop of wire can in fact be an array of wires gradually curving gently into various possible positions the spacecraft will take upon rendezvous. The gentle curve means relative lateral velocity remains low.

This does not address my point.

What precedent or baseline do you have, for thinking that you can design a one-ton set of brakes, designed to slow a fourteen-ton vehicle at roughly ninety meters per second squared (that's "speed of sound to zero in four seconds") by gripping a cable that is moving at seven kilometers per second, and keep doing this for a full minute and a half or so?

I'd consider it a miracle if a mechanism capable of doing that massed only one ton.

By the way, how is this cable launched? A thousand ton cable spool isn't going up on one rocket, or if it is, you've got Big Dumb Booster technology so cheap it may well reduce costs to LEO to a few hundred dollars per kilo all by itself. So how do you attach each cable segment to the next? Square knots?

Launched by smaller versions of itself.
Segments are attached by twisting them over each other for several km. Friction, especially static friction, can work wonders. It doesn't matter much if them move under tension. Bracing stops them from unwinding, and 'joint brakes' can increase the pressure and friction during peak load, like clamps.

If the segments are braided together, that impacts how they interact with the pulleys (they're not smooth cables). It also means you need more cable per unit length, which means you need more mass of cable, which means drastically more force exerted on the anchoring system attaching the cable to the station. And more launches to get this whole thing up and running.

Does your tether stretch like a bungee cord? Not if it's made out of kevlar, it doesn't. Or of Zylon.

I was trying to compare the pulley train as a whole to something we encounter every day. I wasn't saying that the zylon had elastic properties.

Then be careful with your analogies.

Because you're still dodging my point. The relative velocity of the moving cable compared to the last pulley in the system still has to be approximately seven kilometers per second. Because that last pulley is at rest or nearly at rest compared to the station... but the cable has to be moving along with the spacecraft and paying out at high speed.

Because the cable can't be pre-deployed as a "runway" for the satellite, it has to unspool from within the structure of the station itself. Or were you moving the goalposts when you said that the cable would be mostly protected from exposure to space conditions (i.e. radiation and temperature changes)?

[matterbeam]

The big question on my mind is, how confident are you that one ton of suspension and brakes will be enough to handle the load of fourteen tons accelerating at nine gravities? Without failing as the cable slides through the brake system at seven kilometers per second? Come to think of it, your math doesn't add up now, because a 50 kN braking force isn't enough to impart a 9g acceleration. More like 0.35g. You're off by a factor of 25 to 30.

You need well over a meganewton of braking force, and you need the brakes to withstand that force (imparted in the form of friction) for a period of one to two minutes. I'm not at all confident one ton is enough.

And if the suspension/brake system can't be made to weigh one ton, and instead has to weigh five or ten tons, it drastically reduces the desirability and effectiveness of this system.

The braking force is divided by the number of wheels in the pulley train. Just like today an 18 wheeler doesn't use a single big brake on the front wheels, the braking force can be divided across a large number of pulleys.

50kN*85: 4.25MN
Braking force required to decelerate 14.45 tons at 9G: 1.27MN

Also, 50kN is less than the peak braking force of an F1 car, and they achieve it with the whole car weighing less than a ton. The suspension is active, and is suppose to dampen vibrations and absorb sideways motion.

Right. You're launching a 14.5 ton satellite. And this satellite has a ten-ton useful payload of mass that isn't purely parasitic once you reach orbit. The satellite has to be built to withstand nine gravities for a minute and a half or so without wrecking anything.

Suppose, with a similar design, you replace the entire payload structure with an upper stage of similar design to the lower stage and identical mass ratio. Instead of 88.4 tons of rocket to loft 14.5 tons of payload, the upper stage would mass 14.5 tons and accelerate about 2.5 tons to orbital velocity. More, if you use a more efficient propellant for the upper stage (as with Centaur), but there you are.

So I can at least comprehend why you think this is a good idea. You increase the mass of useful material that gets to orbit by a factor of four.

That's not quite a fair comparison. The 2.5 ton is with none of the safety and return features I included in the pod design. If we include those in your alternative, the payload would have to include a multi-ton heatshield to deal with 8km/s re-entry speeds, and either a ton of parachutes or a ton of retro-thrusters to land safely.

On the other hand, if I only included the bare essentials for a we-can-afford-to-lose-it design, then we'd only need 1.5 tons of 'parasitic mass' for 10 ton payload. The benefits are higher than you suppose.

But the advantages of this system become a lot less apparent if:
1) You don't assume the brakes need to mass only one ton- and so far that is an unsupported claim on your part.
2) You factor in the extremely large initial investment of launch capability to get the station up into orbit in the first place and assemble it- assemble it out of many small pieces if we use your notion of having the station be built out of components launched by smaller versions of the same station.
3) You factor in the risk of simply losing the payload if the game of "catch an object moving at Mach 22" does not go according to plan, or the risk of having the whole station completely obliterated in the worst-case scenario of a collision.

Furthermore, you're getting something like a factor of four out of this (ten tons of useful payload instead of 2.5), not a massive order of magnitude improvement. The grabber units you're talking about are, IF they perform as you advertise, a cost-effective alternative to the second stage of a rocket. But that's about all they are, and replacing the second stages of rockets with something more efficient only gets you so far.

The 'realistic' design is built using very conservative materials to minimize cost. If we must consider its value based on whether or not it can be built by rocket launch instead of being built in orbit from ISRU materials, then including more expensive materials such as several hundred tons of carbon fibre wheels instead of simple steel, or high strength pulleys instead of 1 ton versions becomes only a small fraction of the price.

Such mass-optimized designs might require only 48 tons of flywheels (Kevlar) and only 51 tons of pulleys. You can replace the 500kg steel faceplate with a 100kg bumper zeone of whipple shields. Replace 100 tons of solar panels with 1 tons thin-film panels at the cost of 4 hours instead of 45 minute recovery times. Bring everything down to about 550 tons.

If we use a 5.5 ton BOT to pull the components of the 550 ton BOT into orbit, you need half the deltaV to put them into orbit compared to a regular launch. The today-equivalent cost of putting the 550 tons BOT into orbit would be 5.5 tons for the initial BOT plus 110 equivalent tons in orbit.

What do you mean by 'gets you so far'?

If the segments are braided together, that impacts how they interact with the pulleys (they're not smooth cables). It also means you need more cable per unit length, which means you need more mass of cable, which means drastically more force exerted on the anchoring system attaching the cable to the station. And more launches to get this whole thing up and running.

Not really. As they are only turning around the pulley wheels at 100m/s, then the braided sections can roll around them without adverse effects. Also, we don't really have to use Zylon on Zylon. Grip pads can be used with 1.00 static friction coefficients.

'More force' due to a heavier cable violates the conservation of energy, as I understand it. If the cable is heavier, then the spacecraft pulls it to lower velocities. The spacecraft is the external energy input, so the total sum of energy in the system cannot be higher at any point than the initial input, so the wires can never be pulled harder than as if they were connected directly to the spacecraft...

Then be careful with your analogies.

Because you're still dodging my point. The relative velocity of the moving cable compared to the last pulley in the system still has to be approximately seven kilometers per second. Because that last pulley is at rest or nearly at rest compared to the station... but the cable has to be moving along with the spacecraft and paying out at high speed.

No, no. The relative velocity at capture of the last segment of tether is 7.35km/s relative to the station... but only 100m/s relative to the spacecraft and 100m/s relative to the last set of wheels of the last pulley. The tether segment halfway up is 3675m/s relative to the station but 100m/s to its own pulley. The whole point of the pulley system is to never have a single segment of tether experience high velocities, but for their sum total motion to match that of the spacecraft.

Because the cable can't be pre-deployed as a "runway" for the satellite, it has to unspool from within the structure of the station itself. Or were you moving the goalposts when you said that the cable would be mostly protected from exposure to space conditions (i.e. radiation and temperature changes)?

I don't understand this problem.
The tether is spooled around the pulley wheels initially. Those wheels can be shielded. When the catch happens, the tether is pulled out and exposed. Afterwards, it is wound back into cover.

[Simon_Jester]

The big question on my mind is, how confident are you that one ton of suspension and brakes will be enough to handle the load of fourteen tons accelerating at nine gravities? Without failing as the cable slides through the brake system at seven kilometers per second? Come to think of it, your math doesn't add up now, because a 50 kN braking force isn't enough to impart a 9g acceleration. More like 0.35g. You're off by a factor of 25 to 30.

You need well over a meganewton of braking force, and you need the brakes to withstand that force (imparted in the form of friction) for a period of one to two minutes. I'm not at all confident one ton is enough.

And if the suspension/brake system can't be made to weigh one ton, and instead has to weigh five or ten tons, it drastically reduces the desirability and effectiveness of this system.

The braking force is divided by the number of wheels in the pulley train. Just like today an 18 wheeler doesn't use a single big brake on the front wheels, the braking force can be divided across a large number of pulleys.

50kN*85: 4.25MN
Braking force required to decelerate 14.45 tons at 9G: 1.27MN

Also, 50kN is less than the peak braking force of an F1 car, and they achieve it with the whole car weighing less than a ton. The suspension is active, and is suppose to dampen vibrations and absorb sideways motion.

The problem isn't the braking system on the station, which can be as heavy as it needs to be. In principle, assuming you're willing to launch enough tons, and assuming material science permits you to make the system out of stuff that can survive hundreds of "catches" without needing replacement, you could build the station's brakes. Now, both those issues are very serious and you have not even begun to address them adequately, but they're totally separate from the problem I'm actually talking about.

The problem here is the braking system on the payload. The payload needs to be small, compact, and cannot be too heavily built or the parasitic weight makes the whole system pointless because you're replacing X tons of second stage rocket with X tons of cable-grabbing machinery.

But the braking system on the payload also has to be up to the task of grabbing a cable which you described as less than an inch thick, exerting enough friction force to accelerate the payload at nine gravities, and doing so without melting or snapping or exerting uneven acceleration that causes the payload to get shaken up and damaged.

Moreover, all this force MUST be exerted by one or a very few massive clamps on the payload, because there simply is not room on the payload itself to have an elaborate system of pulleys and dozens of braking systems working in parallel, each with racecar level performance.

...

Now, by comparison, the maximum legal weight of a loaded tractor-trailer in the US is forty short tons or (rounding up to be generous) 36 metric tons. Truck brakes typically slow the truck enough that (looking at information on auto accidents) a truck can decelerate from 65 mph to zero in a distance of roughly 525 feet. That's in the context of avoiding a car accident, so we can assume it's close to the truck's maximum braking force. Assuming the truck brakes apply constant force (if they don't they could probably be designed to, it would just cost more money)...

From 95 ft/s to zero, in a distance of 525 feet, break out some basic kinematic equations...

525 ft = (0 ft) + [.5(0+95 ft/s)(t)] => the truck takes 11 seconds to stop... implying a deceleration of about nine feet per second squared, or about 0.3 gravities. This is consistent with our physical experience in motor vehicles- if slamming on the brakes in a car could decelerate you at one gravity, you would feel an "eyeballs out" force pushing you against your seatbelt as intense as your own weight force. That is not the case, speaking as one who has occasionally slammed on the brakes.

Now, 0.3 gravities of acceleration imparted to a 36-tonne truck would translate to 0.75 gravities of acceleration imparted to your 14.5-tonne payload with its one-tonne brakes. Nine gravities of deceleration will in turn require brakes twelve times as powerful as those found on a semi tractor-trailer.

Moreover, said brakes have to fit in a compact, single package that will be gripping a cable in a small number of locations no more than a few meters apart. The station's brakes can be as elaborate as you want, but the payload's brakes have to fit inside a rocket fairing and be able to start working instantly as soon as the payload clamps onto the tether. There is no time to thread the cable (which is moving at 25000 kilometers per hour or more) through an elaborate structure of pulleys (which are stationary) to disprese the load of the braking!

I strongly, strongly suspect that a brake and suspension system for this payload, which must exert twelve times the force of a semi tractor-trailer's brakes, will NOT weigh only one ton. I would be pleasantly surprised if it weighs less than ten tons.

Oh, one more thing! While some ablative damage to the 'catcher' is to be expected because it is expendable (in effect, it's the second stage of your rocket)... The intense braking force exerted at only a few points must not damage, scuff, or unravel the cable that is being gripped! Because if we have to refurbish the cable every few launches, or replace it... there is no possible way for this system to be profitable. All the fixed infrastructure for this system, the stuff that weighs a thousand tons or more (like the cable spool) has to last through hundreds of launches. Otherwise, you end up in the foolish position of launching, say, 1000 tons into LEO, in order to save yourself the expense of launching 75 tons into LEO (numbers are an example).

Right. You're launching a 14.5 ton satellite. And this satellite has a ten-ton useful payload of mass that isn't purely parasitic once you reach orbit. The satellite has to be built to withstand nine gravities for a minute and a half or so without wrecking anything.

Suppose, with a similar design, you replace the entire payload structure with an upper stage of similar design to the lower stage and identical mass ratio. Instead of 88.4 tons of rocket to loft 14.5 tons of payload, the upper stage would mass 14.5 tons and accelerate about 2.5 tons to orbital velocity. More, if you use a more efficient propellant for the upper stage (as with Centaur), but there you are.

So I can at least comprehend why you think this is a good idea. You increase the mass of useful material that gets to orbit by a factor of four.

That's not quite a fair comparison. The 2.5 ton is with none of the safety and return features I included in the pod design. If we include those in your alternative, the payload would have to include a multi-ton heatshield to deal with 8km/s re-entry speeds, and either a ton of parachutes or a ton of retro-thrusters to land safely.

No, it wouldn't. Because if I launch the payload to orbit on a conventional rocket, the payload isn't coming back down. Most of the time, with commercial launch vehicles, the payload goes into orbit. The other 2-5% of the time, the problem is either rocket booster failure (which would wreck your payload in any event) or some kind of guidance failure (which would ALSO wreck your payload).

All of those extra features are redundant parasitic weight that you had to add on in order to recover the payload for a risk associated only with the tether system. Namely, the risk in case your "catcher" fumbles and the payload follows a ballistic suborbital path back to the ground.

Or were you proposing to bring back the mass of the grabber unit itself for reuse? Because if so, then you don't need a four kilometer per second heat shield. That grabber will have been accelerated to orbital velocity, after all! Also, I for one would not be comfortable reusing the grabbers, because they experience a lot of friction heating and intense mechanical stress very quickly, and according to you, they aren't all that bulky. If so, they almost certainly won't come back down in any shape to be used again without (in effect) completely rebuilding them.

So we're still back to a 14.5 tonne payload... or more likely more than that...

On the other hand, if I only included the bare essentials for a we-can-afford-to-lose-it design, then we'd only need 1.5 tons of 'parasitic mass' for 10 ton payload. The benefits are higher than you suppose.

Because those brakes are very likely to mass more than one ton.

But the advantages of this system become a lot less apparent if:
1) You don't assume the brakes need to mass only one ton- and so far that is an unsupported claim on your part.
2) You factor in the extremely large initial investment of launch capability to get the station up into orbit in the first place and assemble it- assemble it out of many small pieces if we use your notion of having the station be built out of components launched by smaller versions of the same station.
3) You factor in the risk of simply losing the payload if the game of "catch an object moving at Mach 22" does not go according to plan, or the risk of having the whole station completely obliterated in the worst-case scenario of a collision.

Furthermore, you're getting something like a factor of four out of this (ten tons of useful payload instead of 2.5), not a massive order of magnitude improvement. The grabber units you're talking about are, IF they perform as you advertise, a cost-effective alternative to the second stage of a rocket. But that's about all they are, and replacing the second stages of rockets with something more efficient only gets you so far.

The 'realistic' design is built using very conservative materials to minimize cost. If we must consider its value based on whether or not it can be built by rocket launch instead of being built in orbit from ISRU materials, then including more expensive materials such as several hundred tons of carbon fibre wheels instead of simple steel, or high strength pulleys instead of 1 ton versions becomes only a small fraction of the price.

If you don't make this thing out of high quality materials, it's going to break. Machines break. Their parts require replacement. If you don't use the best materials available, a system like this is going to require constant maintenance and inspections between each launch.

The system isn't going to pay if you have to orbit five tons of spare parts to replace station parts that are worn out, for every ten ton payload you orbit. Especially since you cannot use the station itself to catch the spare parts payload because the tether isn't functional until you replace the worn-out parts!

Such mass-optimized designs might require only 48 tons of flywheels (Kevlar) and only 51 tons of pulleys. You can replace the 500kg steel faceplate with a 100kg bumper zeone of whipple shields.

By the way, what is that armor for? It can't save the payload from a collision with the tether because the tether is under tension and moving at 25000 kilometers per hour. Either it'll carve right through on an extended collision, or the payload will break the tether and then you have a really expensive accident on your hand.

If we use a 5.5 ton BOT to pull the components of the 550 ton BOT into orbit, you need half the deltaV to put them into orbit compared to a regular launch. The today-equivalent cost of putting the 550 tons BOT into orbit would be 5.5 tons for the initial BOT plus 110 equivalent tons in orbit.

What do you mean by 'gets you so far'?

Part of your problem is that you're ignoring the fact that this system still requires expendable mass to be orbited in order to accelerate the payload. The difference is that the "second stage" of your system is a grabber unit (plus the 'insurance' system intended to permit the payload to survive reentry, plus the bracing required to permit the payload to not be destroyed by the forces exerted while interacting with the tether) instead of a rocket.

The more extra weight you pile onto this system, the more marginal it becomes compared to conventional rockets. Remember your 88.5-ton rocket launching a 14.5-ton grabber/payload combo? And how we could just put a second stage on the rocket to orbit a (roughly) 2.5 ton payload directly?

Well, if you have to add a couple of extra tons onto the brake system that grips the tether, in order to ensure it grabs the tether successfully... your rocket first stage didn't get bigger. The total mass of the system remains the same, which means its mass fraction drops off dramatically.

Your starting assumption was a ten ton payload. Realistically, some fraction of those ten tons is further parasitic weight imposed by the need to brace the payload to survive a 9g acceleration for one and a half minutes, which is much more acceleration than second stages usually exert on their payloads. But let's be generous and assume that what you really have for your grabber/payload combo is, say, 9.75 tons of useful payload, plus about 4.7 tons of extraneous stuff that ceases to be useful after you attain orbit.

Now, suppose your brakes don't weigh only one ton- because gee, it turns out they need to be twelve times as powerful as the combined brakes of a semi tractor-trailer, in order to accelerate the payload from zero to Mach 22 in about ninety seconds. Suppose you need three tons of brakes to grab the cable safely and reliably enough, without damaging the cable, which I think is quite optimistic.

If so, then that comes directly out of your payload mass. Now you're orbiting 7.75 tons of useful payload instead of 9.75 or 10. Now you're only actually orbiting about three times as much mass as a perfectly ordinary, bog-standard rocket stage could do using the same first stage booster rocket.

And this is before we even count the many, many costs associated with maintaining the orbiting station per launch, in particular inspections of the elaborate stationside pulley systems, the hundreds of kilometers of cable tether, and replacements of any worn or damaged parts.

That's what I mean by "only gets you so far." If this thing were reducing launch costs by a factor of 10 or 100, it would be considerably more practical, because you'd have more margin to cover all the extra expenses associated with the system. But you don't have that, which is going to make it a lot harder for you to convince people that this system is worth the bother compared to just using a two-stage rocket and economizing on payload mass, or using a bigger two-stage rocket and launching the same payload.

Because you're dealing with a lot of issues- the cost of inspection and maintenance, the percentage of payloads that just plain miss the catch and have to be salvaged after reentry, refurbished, and re-launched, the insurance costs associated with the station itself because of the risk of catastrophic damage wrecking the whole multibillion dollar investment...

It's going to be very hard for you to squeeze out enough of an improvement on marginal costs to orbit for this system to be worth the very large startup cost.

If the segments are braided together, that impacts how they interact with the pulleys (they're not smooth cables). It also means you need more cable per unit length, which means you need more mass of cable, which means drastically more force exerted on the anchoring system attaching the cable to the station. And more launches to get this whole thing up and running.

Not really. As they are only turning around the pulley wheels at 100m/s, then the braided sections can roll around them without adverse effects. Also, we don't really have to use Zylon on Zylon. Grip pads can be used with 1.00 static friction coefficients.

'More force' due to a heavier cable violates the conservation of energy, as I understand it. If the cable is heavier, then the spacecraft pulls it to lower velocities. The spacecraft is the external energy input, so the total sum of energy in the system cannot be higher at any point than the initial input, so the wires can never be pulled harder than as if they were connected directly to the spacecraft...

To be fair, the acceleration of the cable is significantly less than the acceleration imparted to the payload, as are the velocities the pulleys need to handle- not because of the forces involved, but because of how stupidly massive the tether is compared to the payload grabbing it. So thinking about it further, your real problems remain on the payload end.

Of course, for this to work, you need a 300 or 900 km cable trailing your station while awaiting the launches, at which point my concerns about exposing the cable to space conditions over the long term come back into play.

Then be careful with your analogies.

Because you're still dodging my point. The relative velocity of the moving cable compared to the last pulley in the system still has to be approximately seven kilometers per second. Because that last pulley is at rest or nearly at rest compared to the station... but the cable has to be moving along with the spacecraft and paying out at high speed.

No, no. The relative velocity at capture of the last segment of tether is 7.35km/s relative to the station... but only 100m/s relative to the spacecraft and 100m/s relative to the last set of wheels of the last pulley. The tether segment halfway up is 3675m/s relative to the station but 100m/s to its own pulley. The whole point of the pulley system is to never have a single segment of tether experience high velocities, but for their sum total motion to match that of the spacecraft.

To be fair, on further consideration I have realized you are correct about this specific point. The mechanical problems here

Because the cable can't be pre-deployed as a "runway" for the satellite, it has to unspool from within the structure of the station itself. Or were you moving the goalposts when you said that the cable would be mostly protected from exposure to space conditions (i.e. radiation and temperature changes)?

I don't understand this problem.
The tether is spooled around the pulley wheels initially. Those wheels can be shielded. When the catch happens, the tether is pulled out and exposed. Afterwards, it is wound back into cover.

Remember that the payload doesn't stop moving relative to the tether, until it has been 'tugged' up to orbital velocity, by your own statements.

Consider the situation in the station's frame of reference. The payload has been lofted on a ballistic trajectory, and is presumably near the top of that trajectory when it encounters the station. From the station's point of view, the payload is a 14.5 sixteen or more ton mass drifting lazily into the station's path... laterally speaking. In terms of relative velocity the payload is approaching from ahead at 25000 kilometers per hour. It hurtles past, hopefully missing the station, and latches onto the tether.

Now the fun starts! The point where the payload latches onto the tether is hopefully several kilometers away from the station itself, to minimize collision hazards. And the payload duly seizes the cable in its iron fingers (soon to be glowing white-hot with friction heat), and starts accelerating at nine gravities, while the cable continues to slide through its 'fingers' at a speed of seven kilometers per second (soon to be six, soon to be five).

Here's the problem. Even after the catch is made, the cable is STILL moving at multiple kilometers per second relative to the payload, at least until the payload has nearly slowed to a stop relative to the station. It will need to remain in contact with the tether for hundreds of kilometers before coming to a stop!

And therefore, those hundreds of kilometers of tether must already be there, before the payload arrives. If that length of tether isn't already in place, then the payload will duly grip the tether, start accelerating... then hit the end of the tether and slide right off, still on a suborbital trajectory and headed back to the ground.

You can't keep the cable "spooled up" and just "unreel" it during the course of the capture like paying out fishing line. Or rather if you did do that, you'd have to unreel the cable at a rate of several kilometers per second. In which case all my objections about needing ridiculously durable pulley systems on the station side apply.

My initial assumption that you'd need pulleys capable of paying out your line at a rate of seven kilometers per second were based on assuming the tether wouldn't already be there waiting for the payload to decelerate along it. Since it had appeared, at the time, that you were making the same assumption, in order to keep the tether protected aboard the station instead of dangling out in deep space.

[matterbeam]

No, you're right. I forgot about that issue. The payload must be braked against the initial loop of tether, and at the full 9G, so massive brakes are needed.

This got me thinking. There is a solution. Have the payload rendezvous not with the wire itself, but with a cage. The cage must be accelerated to catch up with the spacecraft. At rendezvous, no braking. The cage latches onto the payload firmly, maybe with bolts the slide into slots on the spacecraft's structure.

The cage holds the spacecraft during acceleration. Forces are transmitted to the tether holding the cage.

This removes the need for the payload spacecraft to need any brakes or suspension, further improving the ratio between BOT launch and conventional rocket payload mass in orbit.

The downside is that the cage needs some sort of element that handles compressive forces, and another for shear stress in the bolts. If the payload is 2m wide, we need at least 8kg of vanadium steel or 3.5kg of beryllium. If the bolts are 30cm long, we need at least 3.6kg. With 3x margin, we have a cage mass of about 12kg. To accelerate it to meet the spacecraft, we need 313MJ, or quite a massive railgun massing about 330 tons based on modern estimates for a 64MJ railgun. Or the cage can be rocket-fuelled. If we manage to fit a thruster and avionics system under 10kg, we'll need 174kg of propellant to obtain 7350m/s plus 150m/s for manoeuvring.

The 174kg will have to come out of the payload, but will be a major improvement over several tons of brakes.

From 95 ft/s to zero, in a distance of 525 feet, break out some basic kinematic equations...

525 ft = (0 ft) + [.5(0+95 ft/s)(t)] => the truck takes 11 seconds to stop... implying a deceleration of about nine feet per second squared, or about 0.3 gravities.

Feet per second squared?

Right. You're launching a 14.5 ton satellite. And this satellite has a ten-ton useful payload of mass that isn't purely parasitic once you reach orbit. The satellite has to be built to withstand nine gravities for a minute and a half or so without wrecking anything.

That's the design constraints on modern jet airliners. Do-able.

The system isn't going to pay if you have to orbit five tons of spare parts to replace station parts that are worn out, for every ten ton payload you orbit. Especially since you cannot use the station itself to catch the spare parts payload because the tether isn't functional until you replace the worn-out parts!

I can't really comment on these, or even start to estimate them. Will these like an internal combustion engine, where dozens of working parts only need an inspection every few months? Or will it be like the Space shuttle, where weeks of inspection are refitting are needed per launch?

By the way, what is that armor for? It can't save the payload from a collision with the tether because the tether is under tension and moving at 25000 kilometers per hour. Either it'll carve right through on an extended collision, or the payload will break the tether and then you have a really expensive accident on your hand.

If it strikes a section of tether head-on, we can get away by considering only the kinetic energy of the intersecting segment (about 2m long and massive 0.7kg. The tether snaps from shear stress.

Part of your problem is that you're ignoring the fact that this system still requires expendable mass to be orbited in order to accelerate the payload. The difference is that the "second stage" of your system is a grabber unit (plus the 'insurance' system intended to permit the payload to survive reentry, plus the bracing required to permit the payload to not be destroyed by the forces exerted while interacting with the tether) instead of a rocket.

The more extra weight you pile onto this system, the more marginal it becomes compared to conventional rockets. Remember your 88.5-ton rocket launching a 14.5-ton grabber/payload combo? And how we could just put a second stage on the rocket to orbit a (roughly) 2.5 ton payload directly?

Well, if you have to add a couple of extra tons onto the brake system that grips the tether, in order to ensure it grabs the tether successfully... your rocket first stage didn't get bigger. The total mass of the system remains the same, which means its mass fraction drops off dramatically.

Your starting assumption was a ten ton payload. Realistically, some fraction of those ten tons is further parasitic weight imposed by the need to brace the payload to survive a 9g acceleration for one and a half minutes, which is much more acceleration than second stages usually exert on their payloads. But let's be generous and assume that what you really have for your grabber/payload combo is, say, 9.75 tons of useful payload, plus about 4.7 tons of extraneous stuff that ceases to be useful after you attain orbit.

If we use the cage, the expendable mass in orbit is 173kg of rocket fuel. The parasitic mass is 3.5 tons or less. If the parasitic mass is de-orbited and re-used by flywheel ejection, we'd have wasted only 173kg in to put 9.827 tons in orbit. Flywheel ejection is when you spin the flywheels in the opposite direction to pull a tether in retrograde direction.

Of course, for this to work, you need a 300 or 900 km cable trailing your station while awaiting the launches, at which point my concerns about exposing the cable to space conditions over the long term come back into play.

The tether only needs to be exposed for less than half an hour per catch. It will accumulate, but it will have a very long lifetime compared to how much it is saving in propellant.

The mechanical problems here

Cut off?

And therefore, those hundreds of kilometers of tether must already be there, before the payload arrives. If that length of tether isn't already in place, then the payload will duly grip the tether, start accelerating... then hit the end of the tether and slide right off, still on a suborbital trajectory and headed back to the ground.

I don't agree with this, but since we have a cage now that is at zero relative velocity to the payload, there are no complications or confusions regarding the payload's own braking. The cage catches and holds the payload. The tether it is attached to is spooled out in advance to allow the cage time and room to accelerate. This section of tether pulls on the pulley train. The pulley train expands rapidly, at 9G, with each pulley only expanding slowly up to a maximum of 100m/s then back down to zero. It is only during this expansion phase that the majority of the tether's length is exposed to space. And even then, if we accept the mass penalty, the tether can be dragged through shielded tunnels. [/quote]

[Simon_Jester]

No, you're right. I forgot about that issue. The payload must be braked against the initial loop of tether, and at the full 9G, so massive brakes are needed.

This got me thinking. There is a solution. Have the payload rendezvous not with the wire itself, but with a cage. The cage must be accelerated to catch up with the spacecraft. At rendezvous, no braking. The cage latches onto the payload firmly, maybe with bolts the slide into slots on the spacecraft's structure.

The cage holds the spacecraft during acceleration. Forces are transmitted to the tether holding the cage.

This removes the need for the payload spacecraft to need any brakes or suspension, further improving the ratio between BOT launch and conventional rocket payload mass in orbit.

The downside is that the cage needs some sort of element that handles compressive forces, and another for shear stress in the bolts. If the payload is 2m wide, we need at least 8kg of vanadium steel or 3.5kg of beryllium. If the bolts are 30cm long, we need at least 3.6kg. With 3x margin, we have a cage mass of about 12kg. To accelerate it to meet the spacecraft, we need 313MJ, or quite a massive railgun massing about 330 tons based on modern estimates for a 64MJ railgun. Or the cage can be rocket-fuelled. If we manage to fit a thruster and avionics system under 10kg, we'll need 174kg of propellant to obtain 7350m/s plus 150m/s for manoeuvring.

The 174kg will have to come out of the payload, but will be a major improvement over several tons of brakes.

Uh... It sounds like you've taken a system that would work if you had magical materials to build it with, and replaced it with a system that isn't even physically coherent or describable.

Exactly how does the cage NOT need brakes to catch the tether, again? Did you just abandon the idea of having a tether at all? Is the cage supposed to be trailing the tether like the hook on a fishing line? How does this work, physically?

Is the plan to shoot the cage out of a cannon and somehow have it rendezvous perfectly with the payload over a distance of hundreds of kilometers? Or is the plan to somehow build a rocket with a dry weight of ten kilograms to impart 7500 m/s of delta-V to the cage?

And once the cage has reached rendezvous with the payload (that is, nearly stationary relative to the Earth), how do you boost it back up to orbital velocity again? It's holding a 10-15 ton mass inside, remember, so that ten-kilogram thruster pack isn't going to do the job anymore.

From 95 ft/s to zero, in a distance of 525 feet, break out some basic kinematic equations...

525 ft = (0 ft) + [.5(0+95 ft/s)(t)] => the truck takes 11 seconds to stop... implying a deceleration of about nine feet per second squared, or about 0.3 gravities.

Feet per second squared?

Oh, I'm sorry, did you think the laws of physics care what units you use? They don't magically stop working because you're using distances in feet pulled off an insurance company's website. Do you actually have a refutation of my math?

Right. You're launching a 14.5 ton satellite. And this satellite has a ten-ton useful payload of mass that isn't purely parasitic once you reach orbit. The satellite has to be built to withstand nine gravities for a minute and a half or so without wrecking anything.

That's the design constraints on modern jet airliners. Do-able.

Citation needed for the part where this means you can build a one-ton set of brakes adequate to the task you have outlined. If you can't back this claim up, please stop to reconsider the idea.

Remember, the fact that you have had a cool idea does not mean the idea is magic, or that valid problems with the idea should be ignored.

The system isn't going to pay if you have to orbit five tons of spare parts to replace station parts that are worn out, for every ten ton payload you orbit. Especially since you cannot use the station itself to catch the spare parts payload because the tether isn't functional until you replace the worn-out parts!

I can't really comment on these, or even start to estimate them. Will these like an internal combustion engine, where dozens of working parts only need an inspection every few months? Or will it be like the Space shuttle, where weeks of inspection are refitting are needed per launch?

Well, that's something you should probably start to look into, yes?

By the way, what is that armor for? It can't save the payload from a collision with the tether because the tether is under tension and moving at 25000 kilometers per hour. Either it'll carve right through on an extended collision, or the payload will break the tether and then you have a really expensive accident on your hand.

If it strikes a section of tether head-on, we can get away by considering only the kinetic energy of the intersecting segment (about 2m long and massive 0.7kg. The tether snaps from shear stress.

If the tether snaps, you're going to have to loft a LOT of heavy cable and a service mission. Especially since, of necessity, the cable must already be deployed before the payload grabs it, based on your own description of the mission profile. If the payload hits the tether and snaps it, you've just lost several hundred tons of tether. The loss of the payload is a fairly small deal by comparison.

Oh, by the way, you do remember that the profile for the "catch" maneuver has the payload coming at the station from ahead in the station's frame of reference and having to pass it to catch the tether, right? That's a significant issue- how do you ensure that a failure in control doesn't result in a head-on collision?

Part of your problem is that you're ignoring the fact that this system still requires expendable mass to be orbited in order to accelerate the payload. The difference is that the "second stage" of your system is a grabber unit (plus the 'insurance' system intended to permit the payload to survive reentry, plus the bracing required to permit the payload to not be destroyed by the forces exerted while interacting with the tether) instead of a rocket.

The more extra weight you pile onto this system, the more marginal it becomes compared to conventional rockets. Remember your 88.5-ton rocket launching a 14.5-ton grabber/payload combo? And how we could just put a second stage on the rocket to orbit a (roughly) 2.5 ton payload directly?

Well, if you have to add a couple of extra tons onto the brake system that grips the tether, in order to ensure it grabs the tether successfully... your rocket first stage didn't get bigger. The total mass of the system remains the same, which means its mass fraction drops off dramatically.

Your starting assumption was a ten ton payload. Realistically, some fraction of those ten tons is further parasitic weight imposed by the need to brace the payload to survive a 9g acceleration for one and a half minutes, which is much more acceleration than second stages usually exert on their payloads. But let's be generous and assume that what you really have for your grabber/payload combo is, say, 9.75 tons of useful payload, plus about 4.7 tons of extraneous stuff that ceases to be useful after you attain orbit.

If we use the cage, the expendable mass in orbit is 173kg of rocket fuel. The parasitic mass is 3.5 tons or less. If the parasitic mass is de-orbited and re-used by flywheel ejection, we'd have wasted only 173kg in to put 9.827 tons in orbit. Flywheel ejection is when you spin the flywheels in the opposite direction to pull a tether in retrograde direction.

The cage still has to grab the tether! Now your brake system needs to be attached to the cage. You haven't solved the problem, you've just moved it. Especially since the brake system attached to the cage is very likely to be damaged or experience massive wear and tear during each operation

[Incidentally, this also means that your '173kg of rocket fuel' figure is absolutely ridiculous. You're not accelerating a lightweight cage massing no more than a few dozen kilos. You're accelerating a braking system that will likely weigh several tons. If it started out in orbit, you need to impart 25000 kilometers per hour of delta-V, falling out of orbit in the process, THEN have the cage intercept the payload (potential for collision is high, precision needs to be perfect down to a few centimeters over immense distances and speeds), THEN have the combined payload/cage combination catch the tether.

So there's a step here where you need to take a "cage plus brakes" system massing several tons and impart 7350 m/s or whatever of delta-V. This is exactly what you were trying to avoid, with this whole system, in the first place! Exactly how much effort it will require is going to depend on the mass of the cage and the specific impulse of the cage's thrusters. But it seems very unlikely that you are providing net savings at this point.

Of course, for this to work, you need a 300 or 900 km cable trailing your station while awaiting the launches, at which point my concerns about exposing the cable to space conditions over the long term come back into play.

The tether only needs to be exposed for less than half an hour per catch. It will accumulate, but it will have a very long lifetime compared to how much it is saving in propellant.

I'm concerned that reeling the 300-900 km cable in and out over and over will increase the risk of mechanical breakdowns. I'm also suspicious of the claim that it can be done in less than half an hour.

The mechanical problems here

Cut off?

Meant to read "the mechanical problems here are mostly at the payload end."

And therefore, those hundreds of kilometers of tether must already be there, before the payload arrives. If that length of tether isn't already in place, then the payload will duly grip the tether, start accelerating... then hit the end of the tether and slide right off, still on a suborbital trajectory and headed back to the ground.

I don't agree with this, but since we have a cage now that is at zero relative velocity to the payload, there are no complications or confusions regarding the payload's own braking. The cage catches and holds the payload. The tether it is attached to is spooled out in advance to allow the cage time and room to accelerate. This section of tether pulls on the pulley train. The pulley train expands rapidly, at 9G, with each pulley only expanding slowly up to a maximum of 100m/s then back down to zero. It is only during this expansion phase that the majority of the tether's length is exposed to space. And even then, if we accept the mass penalty, the tether can be dragged through shielded tunnels.

Here are the problems with what you're saying in the order that they arise. Bluntly, any one of these issues is enough to completely cripple your plan and make it so that only a complete idiot would ever want to launch anything to your station, even if you had it already built. You need to address all these issues, individually and separately, to make your proposal work. Each set of issues is under an underlined heading.

1) The cage has to undergo a very large velocity change to intercept the payload.

1a) And now, a small guidance error in either the cage or the payload results in losing both. You need precision timing, literally to the millisecond and the centimeter, for this to work. This is literally like trying to hit a bullet with another bullet from tens of kilometers away. I'm not sure you grasp just how hard a requirement this is in real life.
1b) This rendezvous operation is totally unlike any real life orbital rendezvous, because it is being done very quickly and must happen perfectly. Real spacecraft that dock with one another take extended periods of time and approach each other at low relative velocities. They have the luxury of doing so because they are in stable orbits. The cage and the payload are not- they have to get it perfect, they can't slow down, and they only get one chance.

2) Somewhere in here you seem to have waved a magic wand and made the brakes disappear. As described, your system no longer has a mechanism to grip the tether and accelerate to orbital velocity. Therefore, your system no longer works.

2a) Assuming you didn't mean to leave out the brakes... You have told me that those brakes are no longer attached to the payload. Therefore, they are attached to the cage, because the cage is the part of the system that directly interacts with the payload. Is that correct?
2b) Because if that is correct, then you are now accelerating the mass of the cage from orbital velocity, to a state of rest relative to the Earth, before the rendezvous. And since the mass of the cage includes the mass of the brakes, you are accelerating a mass of several tons.
2c) Therefore, no it is NOT just a matter of losing "174 kg of propellant." Far more than that will be required to impart seven thousand meters per second of delta-V to a multi-ton braking system. You will need a rocket stage comparable to what you WOULD have needed for the second stage of the booster rocket launching your payload into orbit! Remember, this entire system exists for the sole purpose of avoiding the necessity of imparting about four kilometers per second of delta-V to a massive payload. If, in order for the system to work, you must impart seven kilometers of second of delta-V to a mass of comparable size, then this isn't going to work at all.

Furthermore, the cage and brakes will not be reusable.

3a) Any plausible materials are going to experience massive heating, abrasion, and damage in the process. Well designed brakes will hopefully absorb this damage rather than either failing or passing it on to the payload. But you'd have to be a complete idiot to reuse the same brakes, without an extremely expensive refurbishing.
3b) This refurbishing will have to be completed in orbit, and is therefore going to be extremely expensive. Or it will involve reentry and relaunch of the cage, which will also be extremely expensive. Either way, it massively eats into the cost savings of this system compared to the much simpler and more robust "just use a two stage rocket, making the first stage bulkier if necessary."

Even if the cage is attached to the end of the tether, which WOULD allow you to dispense with the brakes, but which is NOT what you have said in a clear or consistent fashion, you still have a problem.

I will elaborate further on this last problem, IF AND ONLY IF you clearly state that the cage is attached to the end of the tether. Because I don't want YOU to accuse ME of being inconsistent by pointing out all the problems with two separate versions of your proposal, even if both of them are problematic.

[matterbeam]

Uh... It sounds like you've taken a system that would work if you had magical materials to build it with, and replaced it with a system that isn't even physically coherent or describable.

Exactly how does the cage NOT need brakes to catch the tether, again? Did you just abandon the idea of having a tether at all? Is the cage supposed to be trailing the tether like the hook on a fishing line? How does this work, physically?

Is the plan to shoot the cage out of a cannon and somehow have it rendezvous perfectly with the payload over a distance of hundreds of kilometers? Or is the plan to somehow build a rocket with a dry weight of ten kilograms to impart 7500 m/s of delta-V to the cage?

And once the cage has reached rendezvous with the payload (that is, nearly stationary relative to the Earth), how do you boost it back up to orbital velocity again? It's holding a 10-15 ton mass inside, remember, so that ten-kilogram thruster pack isn't going to do the job anymore.

You're correct, I didn't account for a few elements.

The cage is already attached to the tether the same way the tether is attached to the station. I need to add propellant to have the tether section being pulled along to reach 7350m/s. I did some calculations and it becomes evident that higher acceleration of the cage reduces the tether length requires and the propellant mass required.

Payload is the cage, at 22kg. It looks like a steel basket. It docks with the spacecraft at zero relative velocity and latches on.

Rocket engine mass X producing Y newtons of thrust per kg. Isp 350.

Tether mass is 0.369kg*D with D the distance required to accelerate to 7350m/s in meters. It masses M kg.

Propellant mass P is 7.9 times the dry mass B. Total mass is T, burnout mass is B with A the average mass between launch and burnout. A= B+P/2, or A= 4.45B

D= 0.5*(A/XY)*(7350/(A/XY))^2

Burnout mass, called dry mass, is equal to 22kg plus X kg engine mass plus M kg tether mass. Something like the AJ10-118K engines produce up to 500N/kg. Y=500.
A= 4.45(22+X+M)= 97.9+4.45X+4.45M = 97.9+4.45X+ 1.64205D
A/XY= (97.9+4.45X+1.64205D)/500X = 0.1958/X + 0.089 + 0.0032841D/X
and D= 0.5*(0.1958/X + 0.089 + 0.0032841D/X)*(7350/(0.1958/X + 0.089 + 0.0032841D/X))^2
D= (0.0979/X + 0.0445 + 0.00164205D/X)*(7350/(0.1958/X + 0.089 + 0.0032841D/X))^2

Let's replace '0.1958/X + 0.089 + 0.0032841D/X' with 'H'.

D=0.5*H*(7350/H)^2
D=0.5*H*7350^2/H^2= 0.5*7350^2/H = 27011250/H
D= 27011250/(0.1958/X + 0.089 + 0.0032841D/X) or 0.1958D/X + 0.089D + 0.0032841D^2/X -27011250= 0
I don't know how to solve that and neither can wolfram alpha, so I must experiment with some numbers.

If we add 10kg of engines, tether distance is 286.625km and propellant mass is 835 tons. If we add 0.1kg of engines, tether distance is 28647m and propellant mass is 10.59 tons. So this entire solution is unfeasable. Of course, not factoring in the tether becoming longer over time instead of being a fixed mass floating in space might have a significant impact.

Now that I'm burnt out on equations, I can safely say mission accomplished. The pulleys work, the flywheels allow for propellantless capture of payloads into orbit. I can't find those ideas on the internet, so I'm happy to have come up with something original.

I've dutifully answered branching questions on how to implement a detailed BOT station, tried working out various capture mechanics, but there's a reason I don't have the skills of a Mechanical engineering Masters.

Oh, I'm sorry, did you think the laws of physics care what units you use? They don't magically stop working because you're using distances in feet pulled off an insurance company's website. Do you actually have a refutation of my math?

No, but you can't take an imperial/S.I. joke without going straight for the acid attack.

That's the design constraints on modern jet airliners. Do-able.

Citation needed for the part where this means you can build a one-ton set of brakes adequate to the task you have outlined. If you can't back this claim up, please stop to reconsider the idea.[/quote]

Wings on the A380 are supposed to withstand 3.8G*1.5: 5.7G, and the interior is rated to 16G to survive a crash. The F-16 can pull 9.8G, requiring a structural check, but it can support 14.7G loads even if the pilot can't.

Well, that's something you should probably start to look into, yes?

There is absolutely no way to estimate reliability until we start building test models in space. Until the, it would be baseless speculation.

If the tether snaps, you're going to have to loft a LOT of heavy cable and a service mission. Especially since, of necessity, the cable must already be deployed before the payload grabs it, based on your own description of the mission profile. If the payload hits the tether and snaps it, you've just lost several hundred tons of tether. The loss of the payload is a fairly small deal by comparison.

If the spacecraft strikes the tether due to a rendezvous gone wrong, then it is only snapping off the last loop of wire. If it somehow strikes it close to the orbital platform and removes most of it.... the tether would drift away at walking speeds.It can be captured and the segment repaired or replaced without having to haul up 300km of new wire from the ground.

Oh, by the way, you do remember that the profile for the "catch" maneuver has the payload coming at the station from ahead in the station's frame of reference and having to pass it to catch the tether, right? That's a significant issue- how do you ensure that a failure in control doesn't result in a head-on collision?

The tether can be extended 'down', towards the earth. The spacecraft would appear to be approaching sideways. The catch will impart a lateral and longitudinal force on the tether. The flywheel absorbs both forces and the station won't rotate. If it is the simple hook and line design, the station will rotate.

The cage still has to grab the tether! Now your brake system needs to be attached to the cage. You haven't solved the problem, you've just moved it. Especially since the brake system attached to the cage is very likely to be damaged or experience massive wear and tear during each operation

The cage idea doesn't work if a rocket has to accelerate the cage plus a long length of tether. It will if it is designed with a massive railgun and huge energy sinks, but that might as well be upgraded to a full-on reverse-mass-driver considering the sunk costs.

I'll have to come up with another idea that brakes the payload without requiring a lot of onboard mass, but without accelerating several tons of tether either.

For now, I have this design:

O.................I__¦uv¦__I.................O

The Os are flywheels separated by about 10km. The dots are pulleys with the tether spooled up. The Is are skip-rope-stations that spin lengths of cord in space, around in a circle. The _s are exposed lengths of tether. . The ¦s are two sides of a cage with brakes. The v is the spacecraft.

The skip-rope stations turn a 10km radius loop of tether at 513RPM using electric motors. A counterweight of equal momentum is needed. The tip speed is 7350m/s. The skip-rope tether is stressed to 3% of maximum load. At the tip is a small cage. The spacecraft is caught in the cage, and the bolts are locked into place. Once the capture is confirmed, the skip-rope stations release the rotating length of tether. The skip-rope section of tether with the spacecraft at its end breaks orbit and flies off on an extended arc. It pulls on the pulleys and their brakes, and on the flywheels on either end.

I took some elements from the design of a traditional rotovator. I don't believe I can do any better than this.

I'm concerned that reeling the 300-900 km cable in and out over and over will increase the risk of mechanical breakdowns. I'm also suspicious of the claim that it can be done in less than half an hour.

The braking process is completed in under two minutes. Reeling back in the tether using 10MW electric engines is as simple as winding the flywheels back up, then using the brakes to slow down. If the tether and pulleys and spacecraft mass 445 tons, a 10MW engine accelerates them at a gentle 6.7m/s^2. 300km crossed in 300 seconds. If we reasonably want to stop the tether before it hits the station, and only use as much braking force as would be applied in normal operation (1.27MN), it takes a 60/40 split of accelerating and deceleration plus braking.

Here are the problems with what you're saying in the order that they arise. Bluntly, any one of these issues is enough to completely cripple your plan and make it so that only a complete idiot would ever want to launch anything to your station, even if you had it already built. You need to address all these issues, individually and separately, to make your proposal work. Each set of issues is under an underlined heading.

Okay.

1) The cage has to undergo a very large velocity change to intercept the payload.

The skip-rope small-scale rotovator might solve this.

2) Somewhere in here you seem to have waved a magic wand and made the brakes disappear. As described, your system no longer has a mechanism to grip the tether and accelerate to orbital velocity. Therefore, your system no longer works.

Having the cage already attached to the tether might solve this.

Furthermore, the cage and brakes will not be reusable.[/agreed]

If the cage is latched on, it suffers far less stress than it is designed to handle. it does have a limit on useable life, but it is as reusable as any other machine.

Even if the cage is attached to the end of the tether, which WOULD allow you to dispense with the brakes, but which is NOT what you have said in a clear or consistent fashion, you still have a problem.

Excuse my communication skills.

[Simon_Jester]

You're correct, I didn't account for a few elements.

The cage is already attached to the tether the same way the tether is attached to the station. I need to add propellant to have the tether section being pulled along to reach 7350m/s. I did some calculations and it becomes evident that higher acceleration of the cage reduces the tether length requires and the propellant mass required.

To summarize the extremely foreseeable problem with your idea...

In the process of accelerating the cage, you also have to accelerate the tether, which is rigidly connected to it in a single long strand. Which means you're not hitting a few dozen kilograms with enough delta-V to boost it to orbital velocity. You're hitting a few hundred tons with that amount.

All to avoid accelerating, oh, ten tons to orbital velocity.

REREADING THE BOTTOM OF YOUR POST, IT BECOMES CLEAR THAT YOU FIGURED THIS OUT ON YOUR OWN. MY COMPLIMENTS; MY ESTIMATE OF YOUR IQ JUST WENT UP ABOUT 15-20 POINTS.

Payload is the cage, at 22kg. It looks like a steel basket. It docks with the spacecraft at zero relative velocity and latches on.

Rocket engine mass X producing Y newtons of thrust per kg. Isp 350.

Tether mass is 0.369kg*D with D the distance required to accelerate to 7350m/s in meters. It masses M kg.

Propellant mass P is 7.9 times the dry mass B. Total mass is T, burnout mass is B with A the average mass between launch and burnout. A= B+P/2, or A= 4.45B

D= 0.5*(A/XY)*(7350/(A/XY))^2

Burnout mass, called dry mass, is equal to 22kg plus X kg engine mass plus M kg tether mass. Something like the AJ10-118K engines produce up to 500N/kg. Y=500.
A= 4.45(22+X+M)= 97.9+4.45X+4.45M = 97.9+4.45X+ 1.64205D
A/XY= (97.9+4.45X+1.64205D)/500X = 0.1958/X + 0.089 + 0.0032841D/X
and D= 0.5*(0.1958/X + 0.089 + 0.0032841D/X)*(7350/(0.1958/X + 0.089 + 0.0032841D/X))^2
D= (0.0979/X + 0.0445 + 0.00164205D/X)*(7350/(0.1958/X + 0.089 + 0.0032841D/X))^2

Let's replace '0.1958/X + 0.089 + 0.0032841D/X' with 'H'.

D=0.5*H*(7350/H)^2
D=0.5*H*7350^2/H^2= 0.5*7350^2/H = 27011250/H
D= 27011250/(0.1958/X + 0.089 + 0.0032841D/X) or
0.1958D/X + 0.089D + 0.0032841D^2/X -27011250= 0
I don't know how to solve that and neither can wolfram alpha, so I must experiment with some numbers.

It would be rather helpful to know what equation you started with or what you were originally planning to solve for; as it stands you have enough steps that I could check your algebra, but not enough to check your physics.

If we add 10kg of engines, tether distance is 286.625km and propellant mass is 835 tons. If we add 0.1kg of engines, tether distance is 28647m and propellant mass is 10.59 tons. So this entire solution is unfeasable. Of course, not factoring in the tether becoming longer over time instead of being a fixed mass floating in space might have a significant impact.

I rather suspect that it wouldn't, because the actual cable has to move at the same velocity all along its length; it doesn't stretch. Even if it did stretch, the actual speed of the moving cable (subject to the limit of the sound speed) would be linearly proportionate to how far along the length of the cable you go, so you might save a factor of two or something here.

[snip something you figured out for yourself; the rest of this may not be relevant now that you've figured out the crux of the problem with the idea of running out the end of the tether to match velocities with the suborbital-trajectory payload]

Another problem is that the tether has to slow back down after rendezvousing with the payload, so you actually need drastically more cable than you realize.

And yet another problem is that if you're running that tether out by tying a big rocket engine onto one end, then the time required to accelerate the tether becomes an issue. If the rocket is a little beastie like the AJ-110 series you described tends to be, then it can't exert nearly enough force to get hundreds of tons of mass up to orbital speed quickly... which means it has to travel a longer distance, which means a longer tether, which means more mass... et cetera.

Now that I'm burnt out on equations, I can safely say mission accomplished. The pulleys work, the flywheels allow for propellantless capture of payloads into orbit. I can't find those ideas on the internet, so I'm happy to have come up with something original.

...The pulleys work, the flywheels work, but the capture of payloads into orbit doesn't work. And your attempt to solve the problem wound up making important aspects of it worse, to the point where a plan that used to work "if everything goes perfectly and we have magically advanced material science" becomes a plan that doesn't work at all.

This is not a good time to declare "MISSION ACCOMPLISHED" and go home.

To your credit, you appear to have realized that the mission is not accomplished, later on

---

I've dutifully answered branching questions on how to implement a detailed BOT station, tried working out various capture mechanics, but there's a reason I don't have the skills of a Mechanical engineering Masters.

While I have an M.S. in physics, I haven't had to use anything here other than freshman physics, a bit of experience talking to engineers casually, and basic common sense.

Spotting the problems here literally doesn't take a rocket scientist. Just a bit more care and caution and thinking about how you'd actually deal with the forces involved.

Oh, I'm sorry, did you think the laws of physics care what units you use? They don't magically stop working because you're using distances in feet pulled off an insurance company's website. Do you actually have a refutation of my math?

No, but you can't take an imperial/S.I. joke without going straight for the acid attack.

If I felt like you were handling this the way someone I consider a peer would, I would have been less acidic. My apologies for that; my respect for you went up a tick when you noticed the problem caused by having to accelerate the mass of the cable.

That's the design constraints on modern jet airliners. Do-able.

Citation needed for the part where this means you can build a one-ton set of brakes adequate to the task you have outlined. If you can't back this claim up, please stop to reconsider the idea.

Wings on the A380 are supposed to withstand 3.8G*1.5: 5.7G, and the interior is rated to 16G to survive a crash. The F-16 can pull 9.8G, requiring a structural check, but it can support 14.7G loads even if the pilot can't.[/quote]The fact that an airliner can survive these accelerations without having the wings rip off proves nothing relevant to the problem. None of this indicates that you can build a one-ton set of brakes adequate for decelerating a 15-ton mass at nine gravities for ninety seconds.

Which is unfortunate, because you're stuck with the brakes as per our previous discussion.

Also, an airliner might have to survive sixteen gravities in a plane crash, for a few seconds, because decelerating at around 147 meters per second squared means that a subsonic airliner has run out of forward speed within less than two seconds even in the worst case scenario.

Well, that's something you should probably start to look into, yes?

There is absolutely no way to estimate reliability until we start building test models in space. Until the, it would be baseless speculation.

A real engineer could make some estimates, though they might turn out to be wrong. Then again, applying real engineering to this project would result in a lot of changes.

If the tether snaps, you're going to have to loft a LOT of heavy cable and a service mission. Especially since, of necessity, the cable must already be deployed before the payload grabs it, based on your own description of the mission profile. If the payload hits the tether and snaps it, you've just lost several hundred tons of tether. The loss of the payload is a fairly small deal by comparison.

If the spacecraft strikes the tether due to a rendezvous gone wrong, then it is only snapping off the last loop of wire. If it somehow strikes it close to the orbital platform and removes most of it.... the tether would drift away at walking speeds.It can be captured and the segment repaired or replaced without having to haul up 300km of new wire from the ground.

Hm. To be fair, the cable won't necessarily be ruined by this process- though the dynamics of a 300km rope in middling-low Earth orbit, that isn't anchored at either endpoint, could be problematic. I suspect you'd end up with a tangled cat's cradle of cable, or with a situation where the cable tends to tumble due to transverse forces and one end isn't moving at the same velocity as the other when viewed in three dimensions.

Oh, by the way, did I mention that being 1000 km up means your astronauts doing the work on this thing are being exposed to the Van Allen Belts? That could be an issue with doing much work on the station. Then again, 'discharging' the Van Allen belts with tether-based systems is actually a MUCH more viable thing to do with tethers, so it's not really that big of a problem. Anyone who could even think about building this station, let alone making it work, would have little trouble getting rid of the threat of the Van Allen belts.

Oh, by the way, you do remember that the profile for the "catch" maneuver has the payload coming at the station from ahead in the station's frame of reference and having to pass it to catch the tether, right? That's a significant issue- how do you ensure that a failure in control doesn't result in a head-on collision?

The tether can be extended 'down', towards the earth. The spacecraft would appear to be approaching sideways. The catch will impart a lateral and longitudinal force on the tether. The flywheel absorbs both forces and the station won't rotate. If it is the simple hook and line design, the station will rotate.

The tether is long enough that orbital velocity isn't the same all along its length. It's strong enough to handle the resulting longitudinal stress, of course, but I'm pretty sure that dangling it "down" from the station in a hurry would require a rocket engine on the end of the cable, which in turn creates a lot of the problems above that are associated with trying to perform the catch using a cage on the end of your tether.

The cage still has to grab the tether! Now your brake system needs to be attached to the cage. You haven't solved the problem, you've just moved it. Especially since the brake system attached to the cage is very likely to be damaged or experience massive wear and tear during each operation

The cage idea doesn't work if a rocket has to accelerate the cage plus a long length of tether. It will if it is designed with a massive railgun and huge energy sinks, but that might as well be upgraded to a full-on reverse-mass-driver considering the sunk costs.

Okay, now it becomes clear that you understand this... As noted above, you just gained about 15 IQ points in my eyes.

---

ON YOUR SKIP-ROPE-ROTOVATOR-THING

For now, I have this design:

O.................I__¦uv¦__I.................O

The Os are flywheels separated by about 10km. The dots are pulleys with the tether spooled up. The Is are skip-rope-stations that spin lengths of cord in space, around in a circle. The _s are exposed lengths of tether. . The ¦s are two sides of a cage with brakes. The v is the spacecraft.

The skip-rope stations turn a 10km radius loop of tether at 513RPM using electric motors. A counterweight of equal momentum is needed. The tip speed is 7350m/s. The skip-rope tether is stressed to 3% of maximum load. At the tip is a small cage. The spacecraft is caught in the cage, and the bolts are locked into place. Once the capture is confirmed, the skip-rope stations release the rotating length of tether. The skip-rope section of tether with the spacecraft at its end breaks orbit and flies off on an extended arc. It pulls on the pulleys and their brakes, and on the flywheels on either end.

I took some elements from the design of a traditional rotovator. I don't believe I can do any better than this.

Let me ask you a few generic questions:

1) At what moment does your (firmly suborbital) payload make contact with an object intended to accelerate it to orbital velocity?
2) What is the object in question?
3) What forces are exerted on the object, in the process of boosting the payload to orbital velocity?
4) What parts of the system need to be made unusually rugged, in order to withstand those forces?

Answering those questions makes it a lot easier to spot engineering issues with the system.

I'm concerned that reeling the 300-900 km cable in and out over and over will increase the risk of mechanical breakdowns. I'm also suspicious of the claim that it can be done in less than half an hour.

The braking process is completed in under two minutes. Reeling back in the tether using 10MW electric engines is as simple as winding the flywheels back up, then using the brakes to slow down. If the tether and pulleys and spacecraft mass 445 tons, a 10MW engine accelerates them at a gentle 6.7m/s^2. 300km crossed in 300 seconds. If we reasonably want to stop the tether before it hits the station, and only use as much braking force as would be applied in normal operation (1.27MN), it takes a 60/40 split of accelerating and deceleration plus braking.

The problem isn't reeling the tether IN, the problem is reeling the tether OUT. As you saw. It's heavy, it doesn't want to move. Having the tether not all be at the same orbital altitude might help a bit, because you may be able to come up with a solution in which the tether "falls" under its own weight. My concern then is that the tether will tend to "swing" back and forth relative to the station, which could cause some problems with the overall system that are not obvious when we imagine the tether moving in one dimension.

[Sea Skimmer]

Then split the thick cable into a dozen thin wires. Arrange in a circle. Add actuators to the wires to compensate for lateral forces. With wire guide rings keeping the configuration straight.

And you think a solution like that, with 12 instead of 1 cable to tension, and vast increase in the parts count, is going to still go smoothly and easily over your pulley rig? Any time a 'solution' is hideously more complicated then what you started with your heading for trouble. 12 small wires will have much greater problems then one cable. What your going to need is a very exotic cable composition, and a great deal of full scale testing.

My personal dream is laser launch to orbit. However, that requires multi-gigawatt power installations with several dowzen km laser ranges. Until then, a 15 ton boosted orbital tether punting 100kg satellites into orbit is quite useful.

Not if it has a high failure rate due to its own complexity, and a very high initial cost to develop, as well as requiring multiple orbital platforms for different orbits. And You still need a major investment in rockets to make this idea work, at which point it has to compete against other high complexity ideas like an air launch plane, which is complex as hell on the plane end, but all of that is operated and maintained from the ground. In space again, you need near flawless operation for anything you intend to use.

LIke I said, its not something that's going to happen easily, and your engineering 'solutions' only point exactly towards that. Past this I really don't care, nor expect it to be used, if you only want to launch 100kg at a time then what will win long term is some kind of electromagnetic gun. Acceleration is no problem for launching raw materials into space, and you'll get a lot of shots out of the gun before its scrap. Much more I expect then the lifetime of your teather and pully system, though again notionally, if we had a major manned presence in space replacing a teather is far less of a concern then it is today.

10 tons of fuel on the ground is cheap. 10 tons of fuel in orbit costs 100 tons of fuel on the ground plus engines, tanks, avionics and so on. It is quite expensive once you get it where you need it.

Na, seriously 100 tons of hydrogen is still only about 400,000 dollars, and that's with cost of delivery when you reformulate it from natural gas and barge it to your rocket launch site. The tonnage is really never a relevant cost, not by any standard of modern space launching at least. The avonics ect.... can be reusable.

That's a key part of a orbital teather idea making any real sense, but you still need a pretty big reusable rocket to lob the payload high enough. At that point a reusable rocket direct to orbit is very appealing for simply being lower risk of failure, and much more flexible. An orbital teather requires that the ground launch and orbit be coordinated in a narrow window, making it weather sensitive among other problems.

I dislike the simple design of an orbital platform performing 'sacrificial' catches. It forces it to have a propellant supply in space. This can be drawn from the payload it catches, but that cuts into useful payload. Relying on an extraterrestrial ISRU fuel depot system to pop up without cheap access to space beforehand might be ill advised.

That's why the desired NASA tug had a nuclear ion engine. It needed propellent sure, but far less then liquid engine rockets.

Importantly the tug concept accomplished something people tend to forget about, which is it handles space debris. If a satellite dies the tug infrastructure can go retrive it and drag it back to a recovery or scrapping point, or simply force it into reentry. Thus we avoid a massive long term orbital problem. This is also a problem in general with all plans to spam orbit with satellites at anything but very low altitudes.

[Lord Revan]

I while I'm still just a student, there's a few things I've learned about engineering first off when trying to solve a problem of this level of complexity you start with the realistic "worst case scenario" you can think of, work how to solve that then work down from there. Everytime your plan has "if this works flawlessly" in it you're heading for a disaster and you should rethink your plan so it doesn't assume parts of it have work perfectly all the time.

According to my brother who actually worked on such nuclear power plants have plans of emergencies that 1 in 1000000 change of happening in fact working on those security systems was my brother's first job after graduating from the place I'm studying atm. This station is gonna need the same level (if not higher) of redundency though for a different reason and those redundant systems add weight that needs to be taken into account.

when designing stuff that needs to be sent into space complexity is something you want to keep as low as realistically possible, that's why chemical rockets are really the best we can do atm. Also ISS is running 386 (or was it 486) processors even though civilian market hasn't used those in decades using modern quad core processors would add a possible point of failure since those aren't rated for space (yet) and more potential points of failure your plan has the worse it will be (especially if those points are something that have a high chance of happening).

[matterbeam]

It would be rather helpful to know what equation you started with or what you were originally planning to solve for; as it stands you have enough steps that I could check your algebra, but not enough to check your physics.

I started with the formula for rocket mass ratio, and tried adding the mass of the tether to the dry mass. That mass depended on the acceleration of the rocket, which depended on the the engine mass.

I rather suspect that it wouldn't, because the actual cable has to move at the same velocity all along its length; it doesn't stretch. Even if it did stretch, the actual speed of the moving cable (subject to the limit of the sound speed) would be linearly proportionate to how far along the length of the cable you go, so you might save a factor of two or something here.

My follow-up idea to solve this was to use ultra-light cable that would suffice to hold the cage+spaceship while the main tether holds back up, but you're going to have to get the kinetic energy to accelerate the main cable anyways.

If I felt like you were handling this the way someone I consider a peer would, I would have been less acidic. My apologies for that; my respect for you went up a tick when you noticed the problem caused by having to accelerate the mass of the cable.

Well, we're all here discussing problems with a theoretical design. I'm very grateful for all the time you've put in, even SeaSkimmer's contributions. It gives me hope that many of the other designs on my ToughSF blog could get a fresh pair of eyes to look at them.

The fact that an airliner can survive these accelerations without having the wings rip off proves nothing relevant to the problem. None of this indicates that you can build a one-ton set of brakes adequate for decelerating a 15-ton mass at nine gravities for ninety seconds.

I was just trying to prove that building something to support 9G would not require so much structural support that it cuts significantly like a payload. A jet fighter is mostly empty space for equipment and fuel, and it can handle several 9G+ turns in a row. for dozens of total minutes in a single mission.

A real engineer could make some estimates, though they might turn out to be wrong. Then again, applying real engineering to this project would result in a lot of changes.

Ideally, the tethers and pulleys are no more or less reliable than an elevator shaft.

Hm. To be fair, the cable won't necessarily be ruined by this process- though the dynamics of a 300km rope in middling-low Earth orbit, that isn't anchored at either endpoint, could be problematic. I suspect you'd end up with a tangled cat's cradle of cable, or with a situation where the cable tends to tumble due to transverse forces and one end isn't moving at the same velocity as the other when viewed in three dimensions.

If it is not moving when the impact happens, I think it'll slowly wind into a U-shape then snap at the other end and tangle. In the most extreme position, straight up from Earth between 1000 and 700km, the difference between the ends is 150m/s. It will make a full 'U' in 33 minutes. If the cable is moving, then the pulley wheels are spinning. This nearly 100 tons of gyroscope-like masses will keep it straight while it expands. I'm assuming the brakes can be remotely controlled to keep it straight for longer by differential braking.

Oh, by the way, did I mention that being 1000 km up means your astronauts doing the work on this thing are being exposed to the Van Allen Belts? That could be an issue with doing much work on the station. Then again, 'discharging' the Van Allen belts with tether-based systems is actually a MUCH more viable thing to do with tethers, so it's not really that big of a problem. Anyone who could even think about building this station, let alone making it work, would have little trouble getting rid of the threat of the Van Allen belts.

1000km is just a nice round figure to use as a reference. If the various rendezvous problems are solved, I can easily see a 200km altitude version working to catch 7784m/s payloads instead of 7334m/s payloads. Of course, G-forces have to be quite higher so we don't have a cable trailing down into the atmosphere and dragging the whole platform down with it. 50G inert payloads would only need a 62km tether. The best thing is that you only need 2000m/s deltaV after losses to reach a 200km altitude. It would be the perfect first step towards placing a lot of rocket fuel, cheaply, in orbit.

A flywheel+pulley platform can work in reverse. Spin up the flywheel, hook them up to the tether with pulleys to spread out the velocity gradient between payload and flywheel rim, and you can get a free 900m/s boost in any direction. A serious attempt at free boosts while already in orbit would require a flywheel at regular intervals down the tether. Their 100m/s rim velocities would add up to incredible speeds, but they'd waste quite a bit of energy accelerating themselves.

If we go further down this route, I can see a bow-and-arrow configuration being possible. Flywheels on either ends of the virtual bow, with the tether between them. The payload is the arrow. If the flywheels have 10x the mass of both the payload and the tether, they can launch the 'arrow' to 10x the flywheel rim velocity.

The tether is long enough that orbital velocity isn't the same all along its length. It's strong enough to handle the resulting longitudinal stress, of course, but I'm pretty sure that dangling it "down" from the station in a hurry would require a rocket engine on the end of the cable, which in turn creates a lot of the problems above that are associated with trying to perform the catch using a cage on the end of your tether.

The fast method is a momentum exchange between the tether, a flywheel and the station. Spin the flywheel up slowly and leave it spinning. This rotates the station and the tether. Centripetal forces keep the tether straight. To stop rotating, apply brakes to the flywheel.

Okay, now it becomes clear that you understand this... As noted above, you just gained about 15 IQ points in my eyes.

High praise.

Let me ask you a few generic questions:

1) At what moment does your (firmly suborbital) payload make contact with an object intended to accelerate it to orbital velocity?
2) What is the object in question?
3) What forces are exerted on the object, in the process of boosting the payload to orbital velocity?
4) What parts of the system need to be made unusually rugged, in order to withstand those forces?

Answering those questions makes it a lot easier to spot engineering issues with the system.

Okay then.
1) The payload is caught at the tip of its trajectory, where vertical velocity is near-zero and can be cancelled just before rendezvous by RCS.
2) It is a spacecraft containing a g-hardened payload, strong RCS systems, guide rails for the cage and arrestor hook backups for docking with the cage.
3) An initial jerk from instantaneously spinning up the first set of pulley wheels. A series of smaller to indistinguishable bumps from the forces being transmitted down the tether. Maybe some wobble from un-compensated-for lateral movement. A gradually increasing force as brakes are applies down the tether. 9G peak is held for nearly a minute and a half. The force gradually dies down to zero, then a final bump as the flywheel brakes are applied for a complete stop of the tether.
4) The tether must have a large safety margin in case emergency braking is required. The brakes must be able to handle several times the regular acceleration and tether speed to compensate for failure of other brakes and prevent a cascade failure. The flywheel should handle its own centripetal forces plus forces during a rapid spin-down. If the cage bolts fail, the payload must be able to re-activate its RCS and prepare for re-entry at close to orbital velocity.

The problem isn't reeling the tether IN, the problem is reeling the tether OUT. As you saw. It's heavy, it doesn't want to move. Having the tether not all be at the same orbital altitude might help a bit, because you may be able to come up with a solution in which the tether "falls" under its own weight. My concern then is that the tether will tend to "swing" back and forth relative to the station, which could cause some problems with the overall system that are not obvious when we imagine the tether moving in one dimension.

Rotating at a tip velocity of 10m/s applies 150N of force to the tether. Is that enough to hold it straight?

I think there is an unclarified point on how the tether looks like just before catching the payload. I see it as being a 2km length or so, like a string of beads, with the tether wound around pulley wheels, that are all reeled up tip to tip.

Each pulley contains about 3-6km of tether around each wheel, depending on the safety tolerances. They are unwound until the tether reaches 305km.

[matterbeam]

Not if it has a high failure rate due to its own complexity, and a very high initial cost to develop, as well as requiring multiple orbital platforms for different orbits. And You still need a major investment in rockets to make this idea work, at which point it has to compete against other high complexity ideas like an air launch plane, which is complex as hell on the plane end, but all of that is operated and maintained from the ground. In space again, you need near flawless operation for anything you intend to use.

I see about in the single-cable version, about 733 moving parts if we count things like 'brake hydraulics' and 'suspension system' as one part each. The 12 cable version increases this to 1654. An F1 car has 80000, so I don't think the number of part simply gives an estimate of reliability.

LIke I said, its not something that's going to happen easily, and your engineering 'solutions' only point exactly towards that. Past this I really don't care, nor expect it to be used, if you only want to launch 100kg at a time then what will win long term is some kind of electromagnetic gun. Acceleration is no problem for launching raw materials into space, and you'll get a lot of shots out of the gun before its scrap. Much more I expect then the lifetime of your teather and pully system, though again notionally, if we had a major manned presence in space replacing a teather is far less of a concern then it is today.

The 100kg to orbit version is the smallest possible BOT I see as being possible, with the objective of being placed into orbit in a single launch. The 100kg it sends can be the lucrative micro-satellite market or components of a larger BOT. I mentioned above, if we are catching raw materials, then 50G decelerations in low 200km orbit are doable, with only 2000m/s initial boost required. That's something achievable by today's versions of non-rocket launch platforms, like conventional railguns.

Na, seriously 100 tons of hydrogen is still only about 400,000 dollars, and that's with cost of delivery when you reformulate it from natural gas and barge it to your rocket launch site. The tonnage is really never a relevant cost, not by any standard of modern space launching at least. The avonics ect.... can be reusable.

What I'm saying is that the 100 tons, once in orbit, cost the entire mission price tag divided by the amount in orbit. It doesn't matter if its cost on the ground is $1/kg or $4000/ton.

That's a key part of a orbital teather idea making any real sense, but you still need a pretty big reusable rocket to lob the payload high enough. At that point a reusable rocket direct to orbit is very appealing for simply being lower risk of failure, and much more flexible. An orbital teather requires that the ground launch and orbit be coordinated in a narrow window, making it weather sensitive among other problems.

Big rocket is relative. The 1000km BOT requires just the first stage of most rockets. The 200km version can do without a rocket.

That's why the desired NASA tug had a nuclear ion engine. It needed propellent sure, but far less then liquid engine rockets.

The initial BOT, the simple 'runway' design, was based on this trade too. A 6000isp electric rocket only needed 612kg of propellant to recover the orbit of a 1000 ton station catching a 10 ton payload at 1000km, compared to a chemical engine needing 27115kg to push a 10 ton payload into orbit from 1000km altitude.

However, a flywheel is completely free and more flexible.

Importantly the tug concept accomplished something people tend to forget about, which is it handles space debris. If a satellite dies the tug infrastructure can go retrive it and drag it back to a recovery or scrapping point, or simply force it into reentry. Thus we avoid a massive long term orbital problem. This is also a problem in general with all plans to spam orbit with satellites at anything but very low altitudes.

[matterbeam]

I while I'm still just a student, there's a few things I've learned about engineering first off when trying to solve a problem of this level of complexity you start with the realistic "worst case scenario" you can think of, work how to solve that then work down from there. Everytime your plan has "if this works flawlessly" in it you're heading for a disaster and you should rethink your plan so it doesn't assume parts of it have work perfectly all the time.

According to my brother who actually worked on such nuclear power plants have plans of emergencies that 1 in 1000000 change of happening in fact working on those security systems was my brother's first job after graduating from the place I'm studying atm. This station is gonna need the same level (if not higher) of redundency though for a different reason and those redundant systems add weight that needs to be taken into account.

when designing stuff that needs to be sent into space complexity is something you want to keep as low as realistically possible, that's why chemical rockets are really the best we can do atm. Also ISS is running 386 (or was it 486) processors even though civilian market hasn't used those in decades using modern quad core processors would add a possible point of failure since those aren't rated for space (yet) and more potential points of failure your plan has the worse it will be (especially if those points are something that have a high chance of happening).

Realistic worst case scenario? The payload misreports is altitude, suddenly accelerates in the wrong direction at th last moment, and collides with the orbital platform itself. Big explosion, everything is lost, and a cloud of big to small items is all that remains.

Solution?

A thin plate of aluminium with a massive stack of styrofoam plates trailing the orbital platform. The highest velocity particles released by the collision would vaporise upon collision with the aluminium, and the styrofoam collects the debris. Lower velocity particles that survive the passage through the aluminium and styrofoam enter elliptic orbits that do not reach the more populated altitudes.

[Lord Revan]

My specialization is energy technology so I'll leave it to others to discribe why that's not so simple. however you're still assuming your highly complex pulley system works perfectly, remember Murphy's law what can fail, will fail. For a realistic discussion you cannot have any assumption of perfect performance in any mechnical parts because that just doesn't happen.

If you ask me a correct "worst case scenario" would be the breaking system malfunction during intercept causing failure of both the station and the payload.

[LaCroix]

I'm not sure if I'm getting it right, but did you change the proposal from "sub-orbital rocket clamps onto a multi-km long super-rope dangling in space with a 7km/s perpendicular relative speed" to "Suborbital rocket flies into a multi-ton docking clamp/holding cage that is moving perpendicular at 7km/s relative speed"?

The first one is at least moderately possible, for you grab hold on an (at least in one direction) quite big target, and can adjust your aim and slowly tighten that hold while the rope flys by for a few seconds.
The second one means if you succeed with the rendevouz, you are hit by an object of roughly equal mass traveling at 7km/s relatively to you. That's not docking, that's crashing.