Boosted Orbital Tether and Orbital Runway upgrades

[LaCroix]

parasitic mass for current config contains
1 heatshield,
1 thether and hook of unknown properties,
a drone,
replacement gas bags and gas filling,
spareparts for the railgun,
fuel to provide energy for rail gun,
fuel to reorbit station,
spareparts for the pulley system and station
provisions for operating crew (?)*
Fuel/spare parts for the tug needed to brin the payload into final orbit and return to the station.
payload housing strong enough to resist initial g-forces before pulley/dampeners can help (might constrict payload types even further - satellites are fragile, some more than others )

*Additionally, it needs occasional manned missions to replace the crew. This could carry the provisions, and spare parts. Still counts as parasitic cost/mass for comparison reasons to standard spaceflight.

[Zeropoint]

I'm just wondering how you get a cloud of free-floating gas in space, without it disappearing in all directions at the speed of sound.

Well, I'm also wondering about the precision timing on the launched parts hitting the apogee of their trip at exactly the right time. There's a very small volume of space and time that will allow for a successful catch.

Another issue: the only way that two objects in orbit can remain fixed relative to each other (without continuous use of stationkeeping thrusters) is if they're on the exact same orbit, one behind the other. If they're beside each other or above/below each other, then they're on different orbits and will drift over time as the orbits diverge or converge.

[matterbeam]

I'm afraid this doesn't help very much. The fundamental question is: How do you connect the 'main' tether to the payload, so that the station can bring the payload up to speed by exerting force on the tether? This is a question that should not require four diagrams to answer- at worst, it should require a list with bullet points. Drawing pictures without a list and without captions is not very helpful.

So please, give me a list of all the steps it takes to go from:

1) Station and all parts associated with the station are at rest relative to each other, all moving at orbital velocity relative to the Earth, to


N) The tether connects to the payload.

We will be using the following components:
10 ton payload
1 ton RCS with 176m/s deltaV
0.54ton tether and drone and hook at 1000m length and 193m/s deltaV
2.1 ton safety and re-entry
Total: 13.64 tons

1kg airbag heatshield
27MJ railgun massing 28 tons

164kg+ of braking gas
850m+ of airbags
Pre-collision gas injectors
Arrestor wires and guide rails
Bolt arm

305km triplicate tether and pulleys of 431.9 tons
1080 ton flywheels and station

1) BOT station is at a 1000km orbit. Tracked from the ground and reports its own position. Velocity of all components: 7334m/s.

2) Launch booster places spacecraft on a 1000km parabolic trajectory. 450 seconds to intercept after staging. Booster must have a +/-79.2km accuracy.

3) Spacecraft manoeuvre towards an intercept with the BOT station. It must have a +/- 1km accuracy.

4) Drone is launched. It manoeuvres the hook into an intercept with the airbags, aligned with the station's railgun. The spacecraft's tether is reeled out with the drone into a position 1000m ahead of the spacecraft. The hook is permanently attached to the spacecraft's tether. It must have an accuracy of +/-0.5m/s.

5) Intercept. The drone detaches itself from the hook and spacecraft tether and flies clear. The station's railgun is activated. A 1kg heatshield is accelerated from 7334m/s to 0m/s in the direction of the airbags. The hook collides with the heatshield and is attached firmly, either using magnetics, plastic deformation of temperature-resistant glues.

6) Pre-collision gas is squirted into the space between the railgun and the airbags. The heatshield collides with this gas. Attached to it is the hook, and to the hook, the spacecraft tether. The latter suffers a 29m/s^2 gradient along its length.

7) The heatshield-hook-tether assembly slams into airbags of increasing gas density. This maintains a 3000G acceleration. The spacecraft tether has a coating of graphite to help it survive hot outgassing. It takes 0.24 seconds for the heatshield and hook to reduce their velocity relative to the station from 7334m/s to 134m/s.

In the final section of the gas brake assembly, arrestor wires and guide rails are used to stop and firmly position the hook. The heatshield is removed from the hook. A bolt arm swings down and inserts bolts through the hook's openings. These bolts connect the hook to the station's tether. The bolts must be inserted within 0.11 seconds, or else the spacecraft tether would reach maximum extension.

9) The hook is released. There is now a continuous connection between the spacecraft and the BOT station.

10) The main tether is spooled out by the spacecraft. It pulls on pulleys that expand slowly. Brakes are applied to further slow down the spool rate and to slow down the spacecraft relative to the BOT station. Simultaneously, flywheels reel in the main tether on the opposite end, at a rate of 800m/s.

11) The flywheels stop. The main tether reaches 305km in length. The pulley wheel drums are empty. The spacecraft has stopped relative to the BOT station, and it travelling at 7334m/s. relative to the ground.

Right now it seems like either your plan has "and then a miracle occurs!" somewhere between step (1) and step (N)... Or your plan is ignoring the need to accelerate a massive tether to high speed. AGAIN.

I hope the list, the images and the descriptions have cleared this misunderstanding by now.

Okay, well. Protip for future reference: If you're planning to use something as a coolant, don't use liquid hydrogen. Use a substance that doesn't vaporize at around negative 250 degrees Celsius. Use something that can absorb a lot of thermal mass without boiling. Water is nearly ideal for this purpose, so if you're actually trying to make your liquid-cooled machine work, using water as a "could this possibly work" test is much more reasonable than using liquid hydrogen.

I would have to disagree. Whether the coolant vaporizes or not, and whether it is a limitation, depends on the design of the cooling system. Regenerative cooling in rockets injects liquid hydrogen into 1000K+ channels and fully expects the coolant to continue being heated after vaporizing. A tube running alongside a hot surface, with liquid hydrogen sprinkled in and filled with hydrogen gas, can be expected to continue heating up the coolant beyond the boiling point, albeit requiring pressure vents. Many high-energy applications of water cooling fully expect it to boil, such as in nuclear reactors. I agree that it would be a decent rule of thumb in conventional engineering, where costs, pressure, temperatures and power levels are 'normal', but I was not thinking of that sort of situation.

]Hydrogen does NOT have higher heat capacity WHEN USED AS A COOLANT, because it vaporizes at around -250 degrees Celsius. A liquid coolant cannot absorb more heat than it takes to vaporize the coolant, without destroying the liquid cooling system due to vapor pockets.

Do not think in terms of a number on a table for liquid hydrogen. Think "how many joules of heat will one kilogram of this substance absorb, before it is lost to vaporization?" You didn't run those numbers, and as a result your comparisons were completely useless.

If you intend to make a long term hobby out of proposing designs for technology, I really, really hope you're studying science in mathematically rigorous courses.

Please stop with the insults.

Since the specifics are still confusing about how you expect this to work, I'm not going to comment on the detailed mechanics until you clarify the broad mechanics of how you expect this to work.

I hope the descriptions so far have been sufficient.

That doesn't answer the question.

It does. This is another design with different mechanics. This is not the skip-rope design or alternatives, but a different gas-brake design, where no tether is being accelerated.

Does the payload interact with the tether when the tether is moving at orbital velocity and the payload is (approximately) at rest relative to the Earth?

Or does the payload interact with the tether when the tether is (approximately) at rest relative to the payload and the Earth?

I created a design where neither is the case.

This is a binary question; as far as I have been able to determine from a good faith effort to listen to your increasingly complicated and messy designs, there is no way to avoid the answer being one or the other. Neither answer is a pleasant one for the purposes we have in mind.

Please stop dancing around this question.

You are the sole judge of what is in good faith, what is messy, what is complicated and whether an answer is pleasant from your end.

The problem is that you're not just competing with the parasitic mass of the rocket payload's "link to the tether" framework. You're also competing with all the costs of running the station, maintaining it, replacing any expendable parts of the system (e.g. the gas bags) and so on. It adds up rapidly.

I cannot estimate how much it would cost to run the station or how many spare parts are required. I can only set a lower limit for how many consumables are required, the set-up costs and how long it would take to become advantageous compared to modern two/three stage rockets.

For example, I know that the pressures involved in the airbags are very low, so thin plastic bags blown into the required shape in orbit are all that is needed. The system would be practical even if the entire mass of bags and gas was brought up from the ground with each launch.

[matterbeam]

parasitic mass for current config contains
1 heatshield,
1 thether and hook of unknown properties,
a drone,
replacement gas bags and gas filling,
spareparts for the railgun,
fuel to provide energy for rail gun,
fuel to reorbit station,
spareparts for the pulley system and station
provisions for operating crew (?)*
Fuel/spare parts for the tug needed to brin the payload into final orbit and return to the station.
payload housing strong enough to resist initial g-forces before pulley/dampeners can help (might constrict payload types even further - satellites are fragile, some more than others )

*Additionally, it needs occasional manned missions to replace the crew. This could carry the provisions, and spare parts. Still counts as parasitic cost/mass for comparison reasons to standard spaceflight.

The properties were described in the first post detailing this design. The hook is simple steel massing 28kg. The heatshield is 1kg, ablative or recoverable depending on how expensive we can afford the materials to be.

Gas bags and filling should mass a bit over 164kg.

Railgun spare parts... would unlikely to be required on every launch. Even the modern 64MJ railgun is expected to fire a hundred times per set of rails, and this one only requires 27MJ.

Railguns use electricity gathered from solar panels, so no fuel.

The flywheels store kinetic energy and therefore do not require the BOT to have engines or reorbiting propellants.

Why would it need a crew?

The 10 ton payload is in orbit at the end of the manoeuvre, no further propellants are required for a comparison to other launch systems.

Satellites are built to withstand 3G at a minimum during ascent. The Ariane 5's peak g-load is 4.2, for the Flacon 9 it is 4.5g, for the Mercury-Altas missions it was 8G. They are not so fragile.

[matterbeam]

I'm just wondering how you get a cloud of free-floating gas in space, without it disappearing in all directions at the speed of sound.

Well, I'm also wondering about the precision timing on the launched parts hitting the apogee of their trip at exactly the right time. There's a very small volume of space and time that will allow for a successful catch.

Another issue: the only way that two objects in orbit can remain fixed relative to each other (without continuous use of stationkeeping thrusters) is if they're on the exact same orbit, one behind the other. If they're beside each other or above/below each other, then they're on different orbits and will drift over time as the orbits diverge or converge.

The pre-collision braking gas is injected a short while before the heatshield arrives. Something like Argon at 90K expands at 237m/s (root mean square velocity). One option to minimize the amount of gas required is to inject it at much above the required density, and let it expand into the target space in time for the collision.

I do not understand the comment on orbits diverging or converging? Everything on the station is attached to each other, and the payload is on a parabolic trajectory. If you're talking about the tether, then yes, it might fall as much as 814m on the far end.

[LaCroix]

Still not getting why the railgun needs to be included.

You have a 28kg hook with drone at 0 m/s.
You have the tether end with the railgun and airbags moving at ~7300 m/s.
You fire the railgun to bring the (as you say - 1kg) heatshield to 0 m/s.
The hook and the heatshield dock at 0m/s.
Heatshield hit the airbags moving at 7300m/s.
Tether connection occurs at 7300m/s.

Other scenario:
You have a 28kg hook with 1kg heatshield (pre-assembled) and a drone at 0 m/s.
Tether end with airbags and no railgun is moving at 7300 m/s.
Heatshield hit the airbags moving at 7300m/s.
Tether connection occurs at 7300m/s.

same result, one less docking failure (hook and heatshield), one less component that can malfunction and needs servicing (railgun)

[matterbeam]

Still not getting why the railgun needs to be included.

You have a 28kg hook with drone at 0 m/s.
You have the tether end with the railgun and airbags moving at ~7300 m/s.
You fire the railgun to bring the (as you say - 1kg) heatshield to 0 m/s.
The hook and the heatshield dock at 0m/s.
Heatshield hit the airbags moving at 7300m/s.
Tether connection occurs at 7300m/s.

Other scenario:
You have a 28kg hook with 1kg heatshield (pre-assembled) and a drone at 0 m/s.
Tether end with airbags and no railgun is moving at 7300 m/s.
Heatshield hit the airbags moving at 7300m/s.
Tether connection occurs at 7300m/s.

same result, one less docking failure (hook and heatshield), one less component that can malfunction and needs servicing (railgun)

You're... right.
There is no reason for a railgun.

[Simon_Jester]

[Attempts to be patient...]

Then why... did you think you needed a railgun?

[Will respond to rest of post shortly]

[Simon_Jester]

Trimming your list of steps down to the key ones...

4) Drone is launched. It manoeuvres the hook into an intercept with the airbags, aligned with the station's railgun. The spacecraft's tether is reeled out with the drone into a position 1000m ahead of the spacecraft. The hook is permanently attached to the spacecraft's tether. It must have an accuracy of +/-0.5m/s.

To be clear, then, the drone is attached to the payload, and maneuvers end of the payload's tether (which I am henceforth calling the 'leash' for the sake of clarity). The drone pulls the end of the leash (with hook attached) to the station.

5) Intercept. The drone detaches itself from the hook and spacecraft tether and flies clear. The station's railgun is activated. A 1kg heatshield is accelerated from 7334m/s to 0m/s in the direction of the airbags. The hook collides with the heatshield and is attached firmly, either using magnetics, plastic deformation of temperature-resistant glues.

As noted by LaCroix, the railgun seems redundant and its ability to rendezvous the heatshield with the hook/drone assembly is very doubtful (trying to picture the angles involved is challenging) On the other hand, there was literally no reason whatseover you needed to do this, since you believe a one-kilogram heat shield to be sufficient to protect the hook-drone assembly as it undergoes three thousand gravity deceleration (in its own frame of reference).

If the heat shield could actually be this light (doubtful), then there is no reason NOT to just send it up with the payload and dispense with the railgun. As others have noted.

6) Pre-collision gas is squirted into the space between the railgun and the airbags. The heatshield collides with this gas. Attached to it is the hook, and to the hook, the spacecraft tether. The latter suffers a 29m/s^2 gradient along its length.

7) The heatshield-hook-tether assembly slams into airbags of increasing gas density. This maintains a 3000G acceleration. The spacecraft tether has a coating of graphite to help it survive hot outgassing. It takes 0.24 seconds for the heatshield and hook to reduce their velocity relative to the station from 7334m/s to 134m/s.

In the final section of the gas brake assembly, arrestor wires and guide rails are used to stop and firmly position the hook. The heatshield is removed from the hook. A bolt arm swings down and inserts bolts through the hook's openings. These bolts connect the hook to the station's tether. The bolts must be inserted within 0.11 seconds, or else the spacecraft tether would reach maximum extension.

Ah-HA. Here is your problem. At the end of this process, the hook is moving at seven kilometers per second relative to the payload.

So after your "0.11 seconds" are up, the payload's leash will run out, the payload leash will snap taut, and the leash will be ripped right off the payload at the mounting brackets, leaving your main tether holding haplessly onto a useless length of graphite-coated cable while the payload tumbles back to Earth in a severely damaged condition.

Alternatively, the payload will experience seven kilometers per second of delta-V in a distance shorter than the elastic limits of the leash, in which case you've probably smashed the contents of the payload into confetti in the process.

9) The hook is released. There is now a continuous connection between the spacecraft and the BOT station.

10) The main tether is spooled out by the spacecraft. It pulls on pulleys that expand slowly. Brakes are applied to further slow down the spool rate and to slow down the spacecraft relative to the BOT station. Simultaneously, flywheels reel in the main tether on the opposite end, at a rate of 800m/s.

11) The flywheels stop. The main tether reaches 305km in length. The pulley wheel drums are empty. The spacecraft has stopped relative to the BOT station, and it travelling at 7334m/s. relative to the ground.

None of this matters, because the payload isn't going to survive.

Either you lost the payload when it pulled the leash taut (the hook is at rest relative to the station, but the payload isn't). Or you lost the payload when the leash broke or ripped off its mounting point, in which case uncontrolled reentry and/or lithobraking will destroy the payload.

Right now it seems like either your plan has "and then a miracle occurs!" somewhere between step (1) and step (N)... Or your plan is ignoring the need to accelerate a massive tether to high speed. AGAIN.

I hope the list, the images and the descriptions have cleared this misunderstanding by now.

Well, now I know where you expect your miracle to occur. Specifically, you expect that decelerating a ten-to-hundred-kilo hook will automatically decelerate the payload to a comparable, comfortably low speed.

Alternatively, you think that "bolting" the hook to the tether will magically permit the combined tether-hook-leash-payload assembly to withstand the forces involved when the tether's leash snaps taut at a relative velocity of seven kilometers per second.

This is the same category of error you made when you forgot the need to accelerate the tether to seven kilometers per second so that a hook on its end could rendezvous with the payload. It's just organized differently.

Since the specifics are still confusing about how you expect this to work, I'm not going to comment on the detailed mechanics until you clarify the broad mechanics of how you expect this to work.

I hope the descriptions so far have been sufficient.

That doesn't answer the question.

It does. This is another design with different mechanics. This is not the skip-rope design or alternatives, but a different gas-brake design, where no tether is being accelerated.

Well, actually there is- the leash. Your problem now is that you have (again) created a mechanism for accelerating a tiny low-mass 'hook' and expected that to permit you to accelerate a multi-ton payload and attached cable system for free.

This is why I was confused earlier; I wasn't expecting to see this category of mistake again.

Does the payload interact with the tether when the tether is moving at orbital velocity and the payload is (approximately) at rest relative to the Earth?

Or does the payload interact with the tether when the tether is (approximately) at rest relative to the payload and the Earth?

I created a design where neither is the case.

On the contrary, you still have the basic problem of "payload and tether interact while moving at 7 km/s relative to each other." You just moved the problem, by having one component of the payload that is (theoretically) at rest relative to the tether, while the (much heavier) remainder of the payload continues to move at 7 km/s relative to it.

So that the destructive internal forces that once required a huge set of brakes to withstand... Those forces are now acting on whatever system you're using to attach the hook to the leash, the leash to the payload.

This is a binary question; as far as I have been able to determine from a good faith effort to listen to your increasingly complicated and messy designs, there is no way to avoid the answer being one or the other. Neither answer is a pleasant one for the purposes we have in mind.

Please stop dancing around this question.

You are the sole judge of what is in good faith, what is messy, what is complicated and whether an answer is pleasant from your end.

Had you recognized that you were dealing with a binary question, you would have realized the problem with this design. Like ALL designs that try to make a firm connection between an orbital-velocity tether and a payload that is still (mostly) at rest relative to the Earth, they result in very large forces exerted on (at least part of) the payload, and large releases of energy within the payload. This tends to destroy the payload, unless said payload is very heavily built and includes ablative materials of some kind... at which point you've defeated the purpose of reducing launch weight by omitting the second stage of your rocket.

The problem is that you're not just competing with the parasitic mass of the rocket payload's "link to the tether" framework. You're also competing with all the costs of running the station, maintaining it, replacing any expendable parts of the system (e.g. the gas bags) and so on. It adds up rapidly.

I cannot estimate how much it would cost to run the station or how many spare parts are required. I can only set a lower limit for how many consumables are required, the set-up costs and how long it would take to become advantageous compared to modern two/three stage rockets.

The underlined question is literally impossible to answer without knowing how much it costs to run the station. If you want realistic cost estimates, find a way to estimate the operational costs of your system. You're clever when you apply yourself- go ahead and do it!

For example, I know that the pressures involved in the airbags are very low, so thin plastic bags blown into the required shape in orbit are all that is needed. The system would be practical even if the entire mass of bags and gas was brought up from the ground with each launch.

The gas bags need to be prepositioned relative to the station and aligned to intercept the hook, when the hook itself is coming in on a not-perfectly-predictable trajectory. Any lateral or tumbling forces exerted on the hook-leash combination could easily destroy the hook or detach it from the leash, especially since the force involved is three thousand gravities, which is on par with "slam into a brick wall" or "get shot out of a cannon" accelerations.

This could be more complicated than you realize.

And even if you make it work, you still haven't solved the fundamental problem that the leash won't remain attached to an intact payload after the (still at rest) payload reaches the end of the leash that is now firmly attached to an orbital-velocity tether.

[LaCroix]

That's the part where he either wants to use the pulleys or 'spools out/brakes/flywheelthingies' the main tether to absorb the forces.

The problem is that you still have to deal with the whole 'objects in motion want to continue, objects at rest, too' problem. Before any dampening can occur, you will have a brief moment of static behaviour. On a normal earthbound system, this is something to keep in mind. At orbital velocities... Wrath of mother nature is the term to use. The forces are so gigantic tuat you most likely reach the lomits of elasticity well before the dampening system can react. (You are well beyond subsonic speed within the materials, which usually means shattering.)

You will need to design payload hull, connection to tether, tether and bolt connections so that they can withstand the forces of the payload getting acellerated to 7km/s at the blink of an eye it takes to exceed the distance given by the maximum stretch of the tether. We're looking at thousands of g, much more than the heatshield.

[LaCroix]

In a nutshell, you are still seeing the whole dynamic system as a static one.
To put my concerns into a picture:

Imagine a coil spring - it symbolizes your dampening system.
A cannonball made of glass is your payload you need to catch. If you stop it too fast, it will shatter.

If the cannonball is just dropped on it, it will be compressed and everything is fine.
Now, the ball is thrown at it. the spring needs to be bigger to slow it down before it hits the ground. Everything is fine.
Even if we fire the ball out of a cannon with 7km/s, as long as the spring is long enough (enouggh tether rope, enough pulleys, brakes, etc), we can still stop the ball safely.

But that's how a static system would work, with instant reaction in the while system.

In a dynamic sytem (aka "The real world") the bigger the spring gets, the more it starts to behave as a series of stacked springs. The ball will hit the first spring, compress it, which in turn starts compressing the next spring, etc. A wave will travel through the system.
Which will work, until you reach the critical point.

Which is when the ball compresses the first spring so quickly that it's windings smack into each other before the next spring had a chance to move. (if the speed gets even higher, it might even happen that the first WINDING of the spring is compacted before the rest of the spring can react. Ther is no upper limit - like the problem of high speed projectiles shattering if they hit armor too fast)

Still, we will still be fine as long as the speeds are low. Even the ball might survive as long as it is slowed down enough before maximum compression occurs, and the spring and ball are tough enough.

But in our case the first spring will have the windings hit each other at 7km/s. The spring will shatter, and the ball will most likely, as well.

Using your system in particular:

When the hook hists the airbags, it will be hit by a constant force of 3000g for a certain period of time, getting sped up.
Meanwhile, the first meter of payload tether is sped up at at the same rate (or slamming into the back of the heatshield with 3000g). It must survive this without exceeding it's maximum stretch capability (for the rest of the tether is still stationary at this point).
This is the first problem - it might be destroyed right there.
If it survives that, it will be now to a certain speed (determined by elasticity, which determines how fast it reacted and so on...).
The next meter of tether (still at rest) will now be acellerated to that speed plus the ongoing acelleration of the system already in motion (the hook/heatshield plus the first meter of tether). This will happen at more than 3000g, and the maximum stretching also applies. Then the next meter of tether reacts...

The whole tether will act like a whip, with an increasing "wave" of energy(gforce) being imparted on the next part, just like the real whip.

As we know, at the end, the whip cracks. For your system, that happens when the tether is pulled tout. Until this point of time, the dampening system could not react, for no force was acting on it. at this point, the last meter of tether must use it's elasticity to handle the energy that wanted to launch the payload to 7km/s instantly.
A 1000+change ton station moving at 7km/s will win this game, so you can simply take payload weight and 7km/s, in the time determined by maximum stretch distance travel, or for as long as the dampening system (if existing) needs to overcome it's internal friction to get moving.

Most likely, it will snap at this point.

If not, then the payload hull needs to undergo the same process, starting at the point the tether connects, and then for every cm of the (metal?) hull down to the bottom, which whould not get ripped off when it imparts the force to the contents. (needs a VERY strong hull and bottom)

And the payload needs to withstand that compression as well, from the bottom up to the top (direction of shockwave inverted, as this is basically another collision)

The same happens to the hook connection, and the bolts.

After this spike, the gForce will quickly taper out to your designed dampening values (I think it was 3g for the pulleys).

Still, a good portion of the system will be permanently damaged due to this (material fatigue), and will stretch less on the next capture attempt, which makes it more likely to break. To be sure, you would need to replace the tether very often.

Anyway, these spike forces can be tremendous, even if they only act for fractions of seconds. Even for something as simple as a car shock absorber and a pothole at highway speeds, they can reach double digits g loads, easily. This causes material fatigue, the main reason they break, even though they should be almost indestructible if they never encounter a pothole.

In order to make this concept work, you need to stop considering static load and start thinking dynamic. There is a huge difference. I can lift 50kg over my head and hold it there. But if you drop 50kg on me from 1 m above (even with me standing in the same position as for lifting and catching it perfectly), will most likely kill me.

[jwl]

Not sure why you are talking about gas brakes, eddy current brakes seem like they would work much better in this scenario.

[Lord Revan]

Possibly, kinetics aren't really my area of expertise (such as it is to begin with), that said even before we can even begin to discuss the viability of a system we need to get an unsimplified picture of how the picture works, dynamic systems aren't as simple as static ones and as I've stated before laws of physics apply always without mercy so simplifying something this complex into a static system makes the picture so inaccurate as to be worthless.

[Simon_Jester]

Honestly, we've been able to spot problems with each proposal so far even on a statics level, or a VERY informal dynamics level.

Problems like "accelerating one end of a rope doesn't magically accelerate the other end of the rope to the same velocity" or "the payload can't withstand the acceleration it experiences when jerked to a sudden short stop at the end of its leash." Or, earlier "given the forces involved, those brakes are going to be waaaay heavier than one ton" or "the payload has a sub-millisecond window of opportunity to latch onto the end of the tether and the centripetal accelerations involved are unreasonable."

[Lord Revan]

I'd say most of the errors I've seen would boil down to "laws of physics don't take a coffee break when you want them to" as result we have things that have incorrect or incomplete applycation of physical forces. I'm looking this from point "if I was given a task to design a system like this as a project what would I need to take into account to not get a failed grade".

[matterbeam]

[Attempts to be patient...]

Then why... did you think you needed a railgun?

[Will respond to rest of post shortly]

I didn't go back and review the entire design after adding modifications further down the line. The first design used a gun-barrel type gas brake, where compressed gasses increased in temperature. This required a much larger heatshield to survive the temperatures involved.

Such a heatshield would have been impracticable to bring up from Earth. Therefore it would have had to originate from the space station, and be accelerated up to the hook's velocity... which would be accomplished by railgun.

But then I realized that a disposable heatshield would be quite lightweight, and a lightweight shield could be thinner and still survive the forces involved, and it would have been more affordable to use high-performance materials like carbon epoxy with ablative graphite face.

To be clear, then, the drone is attached to the payload, and maneuvers end of the payload's tether (which I am henceforth calling the 'leash' for the sake of clarity). The drone pulls the end of the leash (with hook attached) to the station.

Yes. It then 'drops' the leash tip on a free-fall trajectory and flies away.

]As noted by LaCroix, the railgun seems redundant and its ability to rendezvous the heatshield with the hook/drone assembly is very doubtful (trying to picture the angles involved is challenging) On the other hand, there was literally no reason whatseover you needed to do this, since you believe a one-kilogram heat shield to be sufficient to protect the hook-drone assembly as it undergoes three thousand gravity deceleration (in its own frame of reference).

Here is a quick sketch to visualize the angles involved:

If the heat shield could actually be this light (doubtful), then there is no reason NOT to just send it up with the payload and dispense with the railgun. As others have noted.

Agreed.

Ah-HA. Here is your problem. At the end of this process, the hook is moving at seven kilometers per second relative to the payload.

So after your "0.11 seconds" are up, the payload's leash will run out, the payload leash will snap taut, and the leash will be ripped right off the payload at the mounting brackets, leaving your main tether holding haplessly onto a useless length of graphite-coated cable while the payload tumbles back to Earth in a severely damaged condition.

After being bolted to the main tether, and with the main tether free to move (wound around braked pulley wheels), the leash is supposed to pull on the main tether and the payload equally. Also, due to the acceleration gradient during braking, only the tip is at 7.33km/s, with the rest of the leash going slower the closer it gets to the tether.

Let me do some research.
[..]
Let's consider the following system:
-Main tether 431.9 tons at 0m/s relative to the payload leash
-Payload leash: 414kg at 3667m/s average velocity, relative to main tether or payload
-Payload before braking: 13.1 tons at 0m/s relative to payload leash.

The leash has a momentum of 1.51 MN.m and the payload has no momentum. The leash momentum is shared equally between the payload and the main tether. After the leash is pulled taut, the payload and the tether travel at a velocity of 55.4m/s. If the tether is firmly attached to the payload by an indestructible mount, the contents of the spaceship are pulped as the tether reaches a failure point at 2.5% maximum extension (25m) in 6.8 milliseconds and causes acceleration on the order of 830G.

The attachment point needs to be dampened, maybe down to 15G. From 0 to 55.4m/s, 15G requires a dampening length of 10.3m. The other end of the tether, attached to the main tether, travels 45.7km. This means we need a suspension system on the payload spacecraft 42.8m long and we need the main tether to spool out by 45.7km before braking begins. However, this length of main tether masses nearly 64 tons, so considering the increasing inertia of the main tether being spooled will likely reduce the spool distance of the main tether. An estimate of the main tether/leash unspooling system using a constant braking performance of 15G and a tether mass of 1.11kg/m gave a length between 2000m and 3000m.

Looking at various dampening and suspension systems, nothing is suitable. Train suspension weighs several tons but produces the necessary MN forces, while lightweight pistons have interesting performance but do not scale well. The only option would be some sort of crumple zone, built like a highway impact attenuator. This is quite appropriate, as we are considering highway speeds. The payload leash has an 'anchor' on the payload tip. This anchor starts at 0m/s and finishes at 55.4m/s. It pulls a plug through a series of collapsible water bags to slow it down at a controlled rate. Considering that actual crumple zone regulations ask for 20-40G performance on 4.5-10 ton vehicles using only mobile trailers using steel-bar collapsible structures, this problem seems solvable using modern technology.

However, this is a confusing new science to me, so I might have made gross errors in the assumptions here.

None of this matters, because the payload isn't going to survive.

Now that isn't quite constructive criticism. There are ways to solve the problem as mentioned above, and I don't think dismissing everything else is justified.

Well, now I know where you expect your miracle to occur. Specifically, you expect that decelerating a ten-to-hundred-kilo hook will automatically decelerate the payload to a comparable, comfortably low speed.

This isn't quite what is happening, as slowing down the payload is the job of the main tether and the pulley-mounted brakes.

I created a design where neither is the case.

On the contrary, you still have the basic problem of "payload and tether interact while moving at 7 km/s relative to each other." You just moved the problem, by having one component of the payload that is (theoretically) at rest relative to the tether, while the (much heavier) remainder of the payload continues to move at 7 km/s relative to it.

So that the destructive internal forces that once required a huge set of brakes to withstand... Those forces are now acting on whatever system you're using to attach the hook to the leash, the leash to the payload.[/quote]

Only half the jerk of the payload tether coming to a stop is felt by the payload, so not quite what you are describing, but it is destructive enough to require another component to be designed into the system.

Had you recognized that you were dealing with a binary question, you would have realized the problem with this design. Like ALL designs that try to make a firm connection between an orbital-velocity tether and a payload that is still (mostly) at rest relative to the Earth, they result in very large forces exerted on (at least part of) the payload, and large releases of energy within the payload. This tends to destroy the payload, unless said payload is very heavily built and includes ablative materials of some kind... at which point you've defeated the purpose of reducing launch weight by omitting the second stage of your rocket.

I am unaware of any design that attempts to do what the BOT is trying to do, not even the Rotovator or the Skyhook, so I am sceptical of that generalization. Also, the binary question you posed was unsolvable without thinking outside of the box, hence the gas brake system.

The underlined question is literally impossible to answer without knowing how much it costs to run the station. If you want realistic cost estimates, find a way to estimate the operational costs of your system. You're clever when you apply yourself- go ahead and do it!

I could, but the multiplication of assumption upon assumption squares the likelihood of my estimates being wildly wrong. So, I won't attempt it!

The gas bags need to be prepositioned relative to the station and aligned to intercept the hook, when the hook itself is coming in on a not-perfectly-predictable trajectory. Any lateral or tumbling forces exerted on the hook-leash combination could easily destroy the hook or detach it from the leash, especially since the force involved is three thousand gravities, which is on par with "slam into a brick wall" or "get shot out of a cannon" accelerations.

This could be more complicated than you realize.

A solid block of steel with holes for bolts in it is very likely to be more survivable than the excalibur artillery round that resists 40000+ g-forces. The +/-0.5m/s accuracy requirement on the drone is so that in 0.24 seconds, a 2m wide heatshield will not move outside a 12cm margin on the airbags in the 0.24 seconds it takes to brake the hook. This is half the 25cm margin that I actually implemented.

And even if you make it work, you still haven't solved the fundamental problem that the leash won't remain attached to an intact payload after the (still at rest) payload reaches the end of the leash that is now firmly attached to an orbital-velocity tether.

But if we implement a design that takes into consideration the tether jerk, based on highway crash barriers, it would work?

[matterbeam]

The forces are so gigantic tuat you most likely reach the lomits of elasticity well before the dampening system can react. (You are well beyond subsonic speed within the materials, which usually means shattering.)

You will need to design payload hull, connection to tether, tether and bolt connections so that they can withstand the forces of the payload getting acellerated to 7km/s at the blink of an eye it takes to exceed the distance given by the maximum stretch of the tether. We're looking at thousands of g, much more than the heatshield.

Something like the 'Type ISR101' train buffer stop provides 9MN of force to halt a 2200 ton train at a rate of 0.15G. The tether velocities here are much higher... but the momentum and forces are quite manageable.

Also, the speed of sound in Zylon is 12km/s.

In a nutshell, you are still seeing the whole dynamic system as a static one.

This is a confusing statement to me. If I design the system to support peak forces indefinitely, with a safety margin, using static assumptions, then what matters the dynamics of the system?

In a dynamic sytem (aka "The real world") the bigger the spring gets, the more it starts to behave as a series of stacked springs. The ball will hit the first spring, compress it, which in turn starts compressing the next spring, etc. A wave will travel through the system.
Which will work, until you reach the critical point.

Which is when the ball compresses the first spring so quickly that it's windings smack into each other before the next spring had a chance to move. (if the speed gets even higher, it might even happen that the first WINDING of the spring is compacted before the rest of the spring can react. Ther is no upper limit - like the problem of high speed projectiles shattering if they hit armor too fast)

Still, we will still be fine as long as the speeds are low. Even the ball might survive as long as it is slowed down enough before maximum compression occurs, and the spring and ball are tough enough.

But in our case the first spring will have the windings hit each other at 7km/s. The spring will shatter, and the ball will most likely, as well.

Could this be solved by using a tapered tether, where an acceleration gradient (or cascading) is converted into constant forces by varying the masses affected at each step?

Using your system in particular:

When the hook hists the airbags, it will be hit by a constant force of 3000g for a certain period of time, getting sped up.
Meanwhile, the first meter of payload tether is sped up at at the same rate (or slamming into the back of the heatshield with 3000g). It must survive this without exceeding it's maximum stretch capability (for the rest of the tether is still stationary at this point).
This is the first problem - it might be destroyed right there.

I did perform this calculation. The tether must survive a basic force of 1.27MN, to handle braking the payload. Using an acceleration gradient of 29m/s^2 per meter and a minimum tether mass of 0.369kg/m, I calculated that it required a taper of 1:1.46:1, where it is thickest halfway. The maximum forces felt by the tether during the gas braking was about 2.72MN. At the midpoint, it can survive these forces without stretching.

If it survives that, it will be now to a certain speed (determined by elasticity, which determines how fast it reacted and so on...).
The next meter of tether (still at rest) will now be acellerated to that speed plus the ongoing acelleration of the system already in motion (the hook/heatshield plus the first meter of tether). This will happen at more than 3000g, and the maximum stretching also applies. Then the next meter of tether reacts...

The whole tether will act like a whip, with an increasing "wave" of energy(gforce) being imparted on the next part, just like the real whip.

As we know, at the end, the whip cracks. For your system, that happens when the tether is pulled tout. Until this point of time, the dampening system could not react, for no force was acting on it. at this point, the last meter of tether must use it's elasticity to handle the energy that wanted to launch the payload to 7km/s instantly.
A 1000+change ton station moving at 7km/s will win this game, so you can simply take payload weight and 7km/s, in the time determined by maximum stretch distance travel, or for as long as the dampening system (if existing) needs to overcome it's internal friction to get moving.

Most likely, it will snap at this point.

Would the effects be different if we considered that the 'shockwave' or forces travel at 61% of the speed of sound within Zylon?

If not, then the payload hull needs to undergo the same process, starting at the point the tether connects, and then for every cm of the (metal?) hull down to the bottom, which whould not get ripped off when it imparts the force to the contents. (needs a VERY strong hull and bottom)

And the payload needs to withstand that compression as well, from the bottom up to the top (direction of shockwave inverted, as this is basically another collision)

The same happens to the hook connection, and the bolts.

After this spike, the gForce will quickly taper out to your designed dampening values (I think it was 3g for the pulleys).

Still, a good portion of the system will be permanently damaged due to this (material fatigue), and will stretch less on the next capture attempt, which makes it more likely to break. To be sure, you would need to replace the tether very often.

Anyway, these spike forces can be tremendous, even if they only act for fractions of seconds. Even for something as simple as a car shock absorber and a pothole at highway speeds, they can reach double digits g loads, easily. This causes material fatigue, the main reason they break, even though they should be almost indestructible if they never encounter a pothole.

In order to make this concept work, you need to stop considering static load and start thinking dynamic. There is a huge difference. I can lift 50kg over my head and hold it there. But if you drop 50kg on me from 1 m above (even with me standing in the same position as for lifting and catching it perfectly), will most likely kill me.

This has stressed the fact that yet another component has to be added to the gas brake BOT design: a dampening system based on highway crash barriers.

[matterbeam]

Honestly, we've been able to spot problems with each proposal so far even on a statics level, or a VERY informal dynamics level.
Problems like "accelerating one end of a rope doesn't magically accelerate the other end of the rope to the same velocity" or "the payload can't withstand the acceleration it experiences when jerked to a sudden short stop at the end of its leash." Or, earlier "given the forces involved, those brakes are going to be waaaay heavier than one ton" or "the payload has a sub-millisecond window of opportunity to latch onto the end of the tether and the centripetal accelerations involved are unreasonable."

I'd say most of the errors I've seen would boil down to "laws of physics don't take a coffee break when you want them to" as result we have things that have incorrect or incomplete applycation of physical forces. I'm looking this from point "if I was given a task to design a system like this as a project what would I need to take into account to not get a failed grade".

Possibly, kinetics aren't really my area of expertise (such as it is to begin with), that said even before we can even begin to discuss the viability of a system we need to get an unsimplified picture of how the picture works, dynamic systems aren't as simple as static ones and as I've stated before laws of physics apply always without mercy so simplifying something this complex into a static system makes the picture so inaccurate as to be worthless.

Do you have any suggestions that you could make? I'd appreciate help at this point, instead of repetitions of the 'no-mistakes engineering' themed criticism.

[Sea Skimmer]

Something like the 'Type ISR101' train buffer stop provides 9MN of force to halt a 2200 ton train at a rate of 0.15G. The tether velocities here are much higher... but the momentum and forces are quite manageable.

Yeah, speed matters a lot though, see aircraft carrier arrestor systems. Even with 100 people dedicated to trying to make them work we still loose planes from broke wires all the time. Those damn train buffers are never known for reliability either, and fail completely if hit above rated speed!

Your cable is not 1 piece of zylon, nor with any reasonable near term production method could it be less then thousands of them. This is why space elevator ideas always tend to involve not just carbon nanotubes, but ones at least two or three kilometers long. And why bullet proof vests are made of weaves of yarns of fibers which are further place in layers, and yet can be defeated by bullets with nothing like the speed of sound in the material. The fiber to fiber gap creates weakness, as does the very small radial diameter of each fiber compared to nearly anything else that might hit it like a shaped charge or a spacecraft at 7km/s.

Also, the speed of sound in Zylon is 12km/s.

But that only works along the long axis of a single fiber as a way to absorb energy. At 7km/s just about anything is going to be able to damage a pure Zylon cable if it hits it directly, and anything but the most trivial damage is a major durability problem in this role. Some kind of elaborate accelerating catching maneuver with a super precise ABM style booster rocket vehicle is going to be required at the least I'd think to keep the accelerating force as low as possible, several orders of magnitude better on reliability then anything existing now, though absolute accuracy won't need to be that much better. Also has to be all reuseable. I'd reckon maybe 2060 timescale we might have that, at incredible cost still. But we'll have a lot of other things too.

The problem is any screwup will break the cable, so reliability has to be crazy. You'd have to wait for military ABM tech to evolve that for you first which will take a long time. Right now the kill vehicles on say GBI sorta have a lot of the performance you'd want, and weigh a fair bit, about 150kg loaded, but they cost like 10 million dollars for the kill vehicle alone, so anything even remotely like that generation of tech is never going to be economical.

https://lh3.googleusercontent.com/-puUy ... 5GSE22.jpg

On the other hand this also could exist in a couple of years, without requiring anything new at all and not require the constant risk of unleashing a giant death cable into low orbit.

[Simon_Jester]

Ah-HA. Here is your problem. At the end of this process, the hook is moving at seven kilometers per second relative to the payload.

So after your "0.11 seconds" are up, the payload's leash will run out, the payload leash will snap taut, and the leash will be ripped right off the payload at the mounting brackets, leaving your main tether holding haplessly onto a useless length of graphite-coated cable while the payload tumbles back to Earth in a severely damaged condition.

After being bolted to the main tether, and with the main tether free to move (wound around braked pulley wheels), the leash is supposed to pull on the main tether and the payload equally.

In that case, you've got a velocity gradient wherein your leash cable is going at 7 km/s at one end and 0 km/s at the other end.

The cable snaps straight under extreme tension in a matter of moments. And when it does, something's going to break, because the cable isn't going to stretch worth a damn.

Also, due to the acceleration gradient during braking, only the tip is at 7.33km/s, with the rest of the leash going slower the closer it gets to the tether.

Different parts of the leash are a fixed length apart. Once the slack in the tether is used up (maybe even before that happens), that means that different parts of the leash will be subject to tremendous forces. Breakage or damage becomes highly likely.

The leash must fully match the tether's velocity within the time available before the leash snaps taut. Otherwise, something snaps. If one end of a taut rope is moving at high speed, while the other end is stationary, common sense tells us there HAS to be a break somewhere in the rope! Otherwise, the rope couldn't remain intact, because different points on the rope would be moving at high speed apart in opposite directions.

Furthermore, the leash and payload have negligible mass relative to the tether. This results in the leash (and payload) experiencing very high acceleration, and the tether experiencing very low acceleration. At the connection between the two, both experience equal and opposite forces- but the force that accelerates a ten ton mass at hundreds of gravities will accelerate a thousand ton tether at a single digit number of gravities.

-Payload leash: 414kg at 3667m/s average velocity, relative to main tether or payload

By the way, when you estimated braking forces on the hook at the end of the leash, did you account for the fact that you're accelerating a large fraction of the mass of the leash up to or near orbital velocity? I seem to remember you only accounting for the mass of the hook.

Let me do some research.
[..]
Let's consider the following system:
-Main tether 431.9 tons at 0m/s relative to the payload leash
-Payload leash: 414kg at 3667m/s average velocity, relative to main tether or payload
-Payload before braking: 13.1 tons at 0m/s relative to payload leash.

Uh... no. If the payload is at rest relative to the leash in some fixed frame of reference, and the tether is also at rest relative to the leash, then the payload and tether are at rest relative to each other. Which means either the entire mass of the tether has been decelerated to be at rest relative to the Earth, or the payload is already traveling at orbital velocity.

The leash has a momentum of 1.51 MN.m and the payload has no momentum. The leash momentum is shared equally between the payload and the main tether. After the leash is pulled taut, the payload and the tether travel at a velocity of 55.4m/s. If the tether is firmly attached to the payload by an indestructible mount, the contents of the spaceship are pulped as the tether reaches a failure point at 2.5% maximum extension (25m) in 6.8 milliseconds and causes acceleration on the order of 830G.

The payload isn't just getting its speed changed by 55.4 meters per second, as you well know because the entire point of this exercise is to accelerate the payload to orbital velocity.

Do it again, with the real number. It's worse than you thought. You have only begun to scratch the surface of just how bad this problem really is.

Once you've recalculated, then you can tell me with a straight face that there's some conceivable mechanical solution to this problem.

By the way, your current 'solution' seems to depend on the tether and leash being able to stretch when the payload pulls it taut. Has it occurred to you that the payload is moving at speeds on the same order of magnitude as the sound speed in the material? The tether almost certainly won't have time to stretch; it'll snap. Furthermore, if you rely on the tether's elasticity, then even if you provide enough slack in the tether to bring the payload to a stop relative to the station, you've just doomed the station.

Because, to use an analogy, you just took a 400-ton slingshot with a ten ton weight loaded in it, and pulled the ten ton weight out far enough to store enough energy in the rubber band to launch ten tons into LEO. Then, having stretched out this slingshot, you release it, with the weight coming directly back towards your station.

Even if the tether didn't snap, and I'm pretty sure it will, that just means you get the payload going 'BOING' and crashing right through the station. Because the tether won't stretch to damp out inbound velocities the way it damps outbound ones.

Looking at various dampening and suspension systems, nothing is suitable. Train suspension weighs several tons but produces the necessary MN forces, while lightweight pistons have interesting performance but do not scale well. The only option would be some sort of crumple zone, built like a highway impact attenuator. This is quite appropriate, as we are considering highway speeds.

You are not considering highway speeds. Or rather, you are, but the laws of physics applying to your problem are considering orbital speeds, because you went too far without performing a sanity check.

There is no way to cheat. An object moving at rest relative to the Earth cannot be accelerated to orbital velocity by mechanical interaction, without literally every single "at rest" part coming into contact with an "orbital velocity" part and being forced to boost up to orbital speed, somewhere at some time.

If you think you've found a way to boost your payload to orbital velocity by imparting only 55 m/s of delta-V... hint. No, no you have not. The other seven thousand and something meters per second of delta-V have to come from somewhere, and then it is the interaction between the payload and THAT part of the system that will cause the engineering problems.

None of this matters, because the payload isn't going to survive.

Now that isn't quite constructive criticism. There are ways to solve the problem as mentioned above, and I don't think dismissing everything else is justified.

The only reason you thought you'd solved the problem was because of a drastic miscalculation leading you to think you'd found a way to "cheat" and accelerate the payload to orbital velocity without ever actually imparting more than fifty-five meters per second of delta-V.

Really, matterbeam?

Well, now I know where you expect your miracle to occur. Specifically, you expect that decelerating a ten-to-hundred-kilo hook will automatically decelerate the payload to a comparable, comfortably low speed.

This isn't quite what is happening, as slowing down the payload is the job of the main tether and the pulley-mounted brakes.

In that case, the tether has to match velocity with the payload.

Again, either the payload has to reach orbital speed by interacting with an orbital-speed tether, or the tether (already having been slowed to 'at rest') has to reach orbital speed by interacting with an orbital-speed station. One or the other. There is no way to cheat around this requirement and still have a system that works without cheating on the math.

I created a design where neither is the case.

On the contrary, you still have the basic problem of "payload and tether interact while moving at 7 km/s relative to each other." You just moved the problem, by having one component of the payload that is (theoretically) at rest relative to the tether, while the (much heavier) remainder of the payload continues to move at 7 km/s relative to it.

So that the destructive internal forces that once required a huge set of brakes to withstand... Those forces are now acting on whatever system you're using to attach the hook to the leash, the leash to the payload.

Only half the jerk of the payload tether coming to a stop is felt by the payload, so not quite what you are describing, but it is destructive enough to require another component to be designed into the system.

Nope. There will still come a moment in time at which the payload, still moving at near-zero velocity relative to the Earth, is being yanked on by a tether that is trying to move at seven kilometers per second.

Because the leash probably IS strong enough, you see. So assuming your gas brakes work properly (uncertain)...

Well, the leash will snap taut. Since each part of the leash is fixed in length, it will all rapidly approach the same velocity. At docking between leash and tether there are different parts of the leash moving at different speeds, but since the leash isn't very long, that can't last for more than a few seconds, even if the leash is several kilometers long.

But the payload doesn't experience any significant acceleration until after the leash snaps taut, at which point the part of the leash nearest the payload is (by definition) moving at seven kilometers per second... but the payload is still at rest relative to the ground.

Had you recognized that you were dealing with a binary question, you would have realized the problem with this design. Like ALL designs that try to make a firm connection between an orbital-velocity tether and a payload that is still (mostly) at rest relative to the Earth, they result in very large forces exerted on (at least part of) the payload, and large releases of energy within the payload. This tends to destroy the payload, unless said payload is very heavily built and includes ablative materials of some kind... at which point you've defeated the purpose of reducing launch weight by omitting the second stage of your rocket.

I am unaware of any design that attempts to do what the BOT is trying to do, not even the Rotovator or the Skyhook, so I am sceptical of that generalization. Also, the binary question you posed was unsolvable without thinking outside of the box, hence the gas brake system.

The reason nobody tries to do what you're proposing is that, frankly, this binary question is unsolvable. The gas brake solves the problem of decelerating a tiny hook to match velocity. Although you haven't addressed issues like what keeps the leash from ablating and being damaged near the hook end, or what keeps the hook from tumbling as it passes through gas clouds at Mach twenty-something. But those don't really even matter except to illustrate the complexity of the system.

The problem is, decelerating the hook is not the same as decelerating the leash, and decelerating the leash is not the same as decelerating the payload.

You seem to have started out treating "just decelerate the hook" as a solution to the problem, as if the rest of the payload would be boosted to orbital velocity by magic if only you could decelerate a tiny part of it. This is literally exactly the same mistake you made with the idea of putting a cage on the end of the tether, only now you're applying it to the payload instead of the tether. Making this mistake for the tether just makes the system not work. Making it for the payload actively destroys the payload.

A solid block of steel with holes for bolts in it is very likely to be more survivable than the excalibur artillery round that resists 40000+ g-forces. The +/-0.5m/s accuracy requirement on the drone is so that in 0.24 seconds, a 2m wide heatshield will not move outside a 12cm margin on the airbags in the 0.24 seconds it takes to brake the hook. This is half the 25cm margin that I actually implemented.

None of this addresses the tumbling issue. Furthermore, blocks of steel can most certainly warp under heavy accelerations. Also, if this is an inert hunk of metal, what's doing the job of connecting to it. And are you seriously proposing to use threaded bolts, or was 'bolt' just a poor choice of word?

And even if you make it work, you still haven't solved the fundamental problem that the leash won't remain attached to an intact payload after the (still at rest) payload reaches the end of the leash that is now firmly attached to an orbital-velocity tether.

But if we implement a design that takes into consideration the tether jerk, based on highway crash barriers, it would work?

No, see above, you made a math error by ignoring the momentum of key parts of the system, and ignoring the fundamental reality that you cannot bring a 0 m/s payload up to 7000 m/s without imparting 7000 m/s of delta-V on it, somewhere, at some time.

[Simon_Jester]

Do you have any suggestions that you could make? I'd appreciate help at this point, instead of repetitions of the 'no-mistakes engineering' themed criticism.

Quite honestly, I first need to ask: what is your academic background? What classes have you taken in math and science? You clearly have the ability to correctly use basic algebraic formulas, and you are at least familiar with the definitions of key physics concepts. But there's a lot more to physics and engineering than that. How much of it do you know?

[Lord Revan]

Do you have any suggestions that you could make? I'd appreciate help at this point, instead of repetitions of the 'no-mistakes engineering' themed criticism.

Quite honestly, I first need to ask: what is your academic background? What classes have you taken in math and science? You clearly have the ability to correctly use basic algebraic formulas, and you are at least familiar with the definitions of key physics concepts. But there's a lot more to physics and engineering than that. How much of it do you know?

I'd second what Simon said (excuse the pun), engineering isn't something you can learn overnight and I got neither time nor the energy to try to teach it to you.