Space Towers and Skyhooks

JoshNH4H · 2018-09-09 22:27:17

Rockets are a good way to get into space that has served us well for a long time, but I think they're too complex and precise to get prices down far enough.

In this thread, I want to talk about a couple possible technologies that I think have a lot of promise: Inflatable Space Towers (IST) and Hypersonic Rotating Skyhooks (HRS). Each of the two has a lot of potential by itself, and even more potential when taken together.

Inflatable Space Towers first: These towers are tensile structures supported by internal gas pressures that are higher than the external atmospheric pressure. They are flat on top, with any loads supported by the difference between the gas pressure inside and outside, and then increase in diameter as you go down towards the bottom. They are similar to the space elevator insofar as the "Taper Ratio" is the figure of merit, because you can hypothetically build a tower that is arbitrarily tall as long as you have an infinite area on which to build it. The towers will probably be held in place by stay cables, much like tall communications towers.

These towers can come in two varieties: Filled with a gas with a similar molecular weight as the atmosphere (either air or nitrogen) or filled with a lighter gas (Presumably Hydrogen, because Helium is quite expensive and is also heavier than Hydrogen).

I've derived an equation which will give the change in radius between the top and the bottom. I can post it if anyone is interested but the results can be found in the two tables below. Different columns represent different values for the pressure at the base of the tower, presented in atmospheres. Different rows represent different heights of the tower, in kilometers.

For a given height, the taper ratio (base area per top area) is a function only of the material used. This is on the column labeled "R". Then for each base pressure and tower height, a number is given for the top loading (the amount of mass which the tower can support), measured in kg/m^2.

The following table applies if the tower is filled with air:

The following table applies if the tower is filled with Hydrogen:

These figures are predicated on the following assumptions: Gases are assumed to be ideal; changes in gravity are not substantial over the length of the tower; The curvature of the Earth does not have a substantial effect on the design of the tower; gases inside and outside the tower exist at a constant temperature of 260 K; The base of the tower is at sea level; The tower is constructed from a material with a strength of 3 GPa, a density of 1000 kg/m^3, and a safety factor of 4, or a material that is proportionally stronger in relation to its density. Bending forces and buckling are ignored.

I recognize it's a lot of numbers to throw at you, so here's the tl;dr: For a material of this strength or stronger, even 200 km tall towers have totally reasonable taper ratios. Towers inflated with Nitrogen can't bear substantial loads at heights above the 25-50 km tall range depending on the base pressure. Towers inflated with Hydrogen can bear substantial loads all the way up to 200 km even with atmospheric pressure at the bottom.

Even in conjunction with traditional rockets, such a tall tower would make it way easier to get into orbit. You could use a simple elevator to get to the top, and you will achieve full vacuum Isp from the moment of launch, plus have less gravity drag to fight against. Given the exponential nature of the rocket equation, this will actually make a big difference.

Another possibility is some kind of lofstrom launch loop, angled up and supported by subsidiary towers, which accelerates payloads to orbital velocity or some fraction thereof. How you might actually accelerate these payloads to those speeds is a more difficult problem which has not been solved, but building really tall towers is a subsidiary but still important part.

Anyway, I'm tired and going to leave it here for tonight. More tomorrow!

kbd512 · 2018-09-10 00:05:18

The principle problem with achieving orbit is the velocity delta. Gravitational losses (a few hundred meters per second at most) are substantially more significant than drag losses (by a factor of ten or more, roughly speaking) in well designed rockets, which we already have, and those still pale in comparison to the required velocity delta (when your initial / starting velocity is still zero, there's little gain from starting higher up in the atmosphere). If initial vehicle tonnage, therefore cost, is a significant factor, then I would take a rocket launched at sea level with an initial / starting velocity of Mach 2 over one in a vacuum at zero relative velocity any day of the week since I'd need far less fuel to attain orbital velocity with a given payload mass. A hypersonic skyhook is a far more attractive proposition from this standpoint than any sort of exceptionally tall inflatable structure that does almost nothing to decrease the required dV increment.

For a tower to be so tall that it nears a low orbital altitude, it has to be made of materials so strong and/or so light that we don't presently have anything that meets the strength-to-weight ratio requirements. Dependent upon how it was designed, a practical Skyhook could be constructed from existing materials and is probably a more fruitful topic for discussion if we're doing more than debating science fiction.

Incidentally, some people have done reasonably detailed work on what a practical high altitude launch assist system would entail using existing materials science and I've posted a link to one of those below:

A Low-Cost Launch Assistance System for Orbital Launch Vehicles by Oleg Nizhnik

Again, I'm not sure how much such a balloon system actually buys us without nearly eliminating the requirement for propellant by combining its use with some kind of Skyhook. We don't need a few percentage points of improvement over existing solutions. We can get that through better rockets at substantially lower cost since the science behind the rockets is so well developed and understood.

The other major problem with these non-propulsive systems is that if anything fails catastrophically, all that suspended mass is going somewhere and you have no control over it. In relative terms, even a truly massive rocket like Saturn V or BFR is quite small compared to a 100km tall tower or an even longer cable attached to a Skyhook system.

The most practical system I can think of is an electromagnetic sled that accelerates a comparatively smaller rocket to hypervelocity over a few kilometers. With an evacuated tunnel, a vehicle could achieve orbital velocity before leaving the surface of the Earth, at which point fantastically tall structures and hypersonic vehicle captures are no longer required. We've already built large pipelines far longer than what would be required for such a system to work.

Terraformer · 2018-09-10 04:42:55

Most of what we need to be sending into space is bulk mass - water, propellent, food, construction materials. Squishy humans and other fragile cargo is a small fraction of that. A launch gun, whether gas or electric, should be able to massively reduce launch costs for bulk cargo.

JoshNH4H · 2018-09-10 20:06:07

Hey kbd512,

I see your point, that reducing the delta-V from (perhaps) 9.5 km/s to 8.5-9 km/s is a small reduction compared to the overall difficulty of getting to orbit, but the exponential nature of the rocket equation means that small changes of this kind have magnified effects upon the design of the whole system. This is even more true when you consider the difference between vacuum and sea level/trajectory-averaged exhaust velocity.

Let's consider two hypothetical SSTOs, the first fueled with H2/LOX and the second fueled with kerolox.

The first, if launched from sea level, will have a trajectory-averaged exhaust velocity of perhaps 4 km/s, and a required delta-V of 9.5 km/s. This works out to a mass ratio of 10.8 and a dry mass fraction of 9.3% of liftoff mass.

The second, if launched from sea level, will have a trajectory-averaged exhaust velocity of perhaps 3 km/s, and a required delta-V of 9.5 km/s. This works out to a mass ratio of 23.7 and a dry mass fraction of 4.2%.

Now consider some very similar rockets, launched from the top of a 200 km tower, achieving their full vacuum exhaust velocity for the entire launch. H2/LOX has a vacuum exhaust velocity around 4.4 km/s, and kerolox around 3.3 km/s. With a delta-V around 8.75 km/s, the first rocket now has a mass ratio of 7.3 and a dry mass fraction of 13.7%, an increase of 47%. The second has a mass ratio of 14.2 and a dry mass fraction of 7.1%, an increase of 69%.

Though a fully reusable, airline style SSTO is somewhat beyond the technologies and materials available to us today, I believe that given this additional mass budget it becomes much more practical.

The material I have specified for this structure has a tensile strength of 3 GPa and a density of 1000 kg/m^3, which puts it somewhat below the range of the better carbon fibers out there in specific strength. I have furthermore specified a fairly robust safety factor of 4, meaning that such a structure could realistically be built from such a material.

A structure of this kind would have additional value as a communications and weather observation tower (also, perhaps, military value?), and for power generation purposes (a substantial source of the unpredictability of solar power comes from weather, which does not exist above the main part of the atmosphere. Building this kind of tower would therefore be a potential replacement for the additional required storage to even out unpredictable weather events. Night of course will still exist, but on a schedule that can be predicted literally thousands of years in advance.

You're basically correct that all things considered this system would not be wholly transformative, but it could make a pretty big, incremental difference to rocket launch as it exists.

Terraformer,

I can't speak to electromagnetic systems, but I've recently had a bit of experience with gas guns. It is my understanding that a gas gun that can launch a 10 gram projectile at 8 km/s is roughly 15 m long, 5000 kg, and costs roughly $1,000 to fire. I don't mean to propose that this will scale precisely but that works out to $100,000/kg.

kbd512 · 2018-09-11 00:02:51

Josh,

A tower is theoretically possible, but a 4.4% increase in payload probably isn't worth the substantial construction costs and dangers associated with maintaining a structure that tall. If it was in the middle of nowhere, which would substantially increase launch costs by virtue of being located away from major population centers, then it might be worth experimenting with just to characterize feasibility. The Skyhook system requires far less propellant and looks like a more realistic application of incredibly strong composite fibers to fling payloads into orbit. I want more info about the Skyhook concept since that seems closer to feasibility and likely less dangerous to use.

elderflower · 2018-09-11 03:46:16

I've been kicking the inflatable tower idea around my head for years. I can't see a way of making it safe in the face of earth weather and Professor Murphy.

louis · 2018-09-11 06:16:31

I definitely agree with the initial premise that we need to do better than existing chemical rockets if we are eventually to become a space-faring species. For one, thing if you had a thousand BFR launches a day you would be seriously contributing to pollutant levels, certainly in localised spaceport areas.

I seem to recall looking into eletro-magnetic gun launch...I think it's feasible but does require a huge energy input over a very short period of time... I can't remember precisely but it was huge - like say 25% of UK grid power output.

Laser and microwave beam launches have both been shown to work in principle. I could imagine that becoming a brilliant way of sending supplies to space stations and crews in orbit getting ready for Mars missions.

One idea I had, inspired by Space X's original launch in a tropical Pacific site (where you could see the water droplets running down the rocket). I'm reading it takes about 9 Kwhs of energy to get 1 Kg to orbit. A solar power satellite could beam power to the rocket, so the water vapour can then be super-heated to create the steam jet. Maybe you could use compressed air as well for the initial launch from the launch site.

Terraformer · 2018-09-11 11:51:58

louis,

I don't think a high power requirement is a showstopper. Lot's of things have power demands far exceeding the capacity of the grid. The usual solution is to use flywheels and capacitors.

louis · 2018-09-11 12:13:54

I see - noted.

Terraformer wrote:

louis,
I don't think a high power requirement is a showstopper. Lot's of things have power demands far exceeding the capacity of the grid. The usual solution is to use flywheels and capacitors.

kbd512 · 2018-09-11 12:31:48

I believe EMALS uses super capacitors, but flywheels could also work. A launch system for a much heavier rocket would be proportionally larger, but the basic technology is sound and proven to work. Expensive? You bet, but so are launch vehicles. The difference is how much of the dV increment you want allocated to the rocket, which affects the mass of the rocket, versus how much of the dV increment is provided by a ground based system without any significant mass restrictions. Aerospace vehicle prices go up exponentially as a function of mass. All outsized aerospace vehicles, especially exceptionally fast vehicles, get really expensive, really fast.

If we could design a ballistic cargo carrier launched into the upper atmosphere with EMALS and a Skyhook that provides the rest of the dV increment to attain orbital velocity, that'd be ideal. That pretty much does away with fantastic aerospace vehicle performance requirements. No evacuated tube for a hypervelocity launch, no super high power microwave or laser array, no multi-staged rocket, and just enough propellant to circularize the orbit.

JoshNH4H · 2018-09-11 13:09:03

kbd512-

I agree with you in broad strokes, but I have a sort-of-important quibble with one thing you said in your last post:

kbd512 wrote:

[...]a 4.4% increase in payload[...]

While this is technically an accurate statement of the numbers in my previous post, I think it's profoundly misleading. The implication is that this space tower would reduce launch costs by 4.4%. To be clear: I don't believe that you think this, just that stating my numbers in this way fails to recognize the true value of a space tower.

A typical orbital rocket is between 0.5% and 5% payload at launch. The Falcon rockets are at the high end of this, and shuttle at the low end. One would expect a single-stage rocket to be somewhere at the low end, and to make up for the reduced amount of payload with a longer lifespan and cheaper launch operations (In the ideal case, a SSTO could be refueled and put on the launch pad and relaunched with inspections and refurbishment every so often). All things considered, I think the percent increase of dry mass fraction (47% and 69%) is a better estimate for the amount by which payload would increase, resulting in a 32% and 41% reduction in launch costs per kilogram, respectively. Call it a third, if you like. I believe the structure can be built relatively cheaply because it consists of a simple structure, little more than fabric, and is quite similar along its length. If launch rates are high it's a good investment. I would call it a substantial change (rather than a rounding error, as a 4.4% decrease in cost would be) but not a transformative one.

Fundamentally, I do agree that the hypersonic rotating skyhook has a more transformative potential and I'm working on that post now. The analysis there is taking a little more work: For the space tower, I was able to derive a simple formula for the taper ratio and the loading capacity, and then copy-paste the formula into different spreadsheet cells to do a parametric analysis. The hypersonic skyhook is a more complicated structure and I'm working on a matlab script that can analyze and optimize it for me.

Louis-

As I'm sure you know, most Nuclear Thermal Rocket proposals use liquid Hydrogen as propellant. The reason for this is that exhaust velocity will be roughly inversely proportional to the square root of the molar mass of the propellant gas at the same temperature and pressure. Basically, this means that Hydrogen will give you a 3x higher exhaust velocity than water. Using beamed propulsion doesn't change things very much, because the beam generally needs to make contact with a solid object to transfer its energy to the propellant. Given that chemical, H2/LOX rockets generally operate near this maximum temperature anyway, beamed propulsion acting on water is unlikely to provide a substantially better performance.

Compressed air, being at both lower pressure and temperature while having a higher molar mass (29 vs 18 for water and 2 for Hydrogen) will have even lower exhaust velocities. Operating in a vacuum, these "cold gas thrusters" generally have specific impulses around 90 seconds (900 m/s).

kbd512 · 2018-09-11 15:45:25

Josh,

You're correct. My statement about the increased payload mass fraction was misleading without context. The context was how massive a rocket you could potentially hoist to the top of that tower without imparting structural loads that would topple the tower or fatigue the materials so quickly that substantial reuse was not possible without substantial maintenance. I just don't think it'd be any better than what we could achieve with a sea level electromagnetically accelerated supersonic launch. You're talking about building something roughly 100 times taller than the tallest structure we've ever erected. It might be possible, but how practical would it be? Someone had better give that some consideration as well.

JoshNH4H · 2018-09-11 23:18:01

OK, Hypersonic Rotating Skyhooks, let's go:

This is not an original idea from me, but I think it's a very interesting one. The idea is similar to a space elevator: An orbiting tensile structure makes it easier for a payload to get into orbit. The important difference between the space elevator and the skyhook is that the skyhook is orbiting while it rotates, in such a way as the bottom part of the tether has a slower speed than it were if it were simply orbiting naturally.

A simple model balances gravitational and tensile forces in a rotating coordinate system. My model is for an un-tapered tether and is based on Newtonian gravitation and mechanics. I disregard gravitational effects of any body other than Earth.

Based on my calculations, the orbital height that minimizes the required tensile strength is 2400 km. At this height, for an un-tapered tether with a density of 1000 kg/m^2, the required tensile strength is 16 GPa. The tether has a velocity relative to the Earth's surface of 0 m/s at a height of 100 km. The structure diameter is 4600 km.

The g-force at the base of the tether is 14.5 m/s^2, around 1.5 gs.

This tether requires a material that is roughly 4 times less strong as the material required for a full space elevator. I have said in the past that I don't see a problem with taper ratios of 100 or more, which is good, because such a taper ratio might be necessary to build this sort of structure with existing materials.

So, here's how the process might look: A suborbital rocketplane takes off from the surface of the earth, rockets up to a height of 100 km (delta-V is around 1.4 km/s, a mass ratio of about 1.6 with kerolox), and docks with the tip of the tether. I envision this as being like a plane landing on a runway at an airport. I believe that this should be within the abilities of human pilots, especially with various kinds of digital/robotic assistance that are available.

From there, the payload will ride an elevator up to the centerpoint of the tether or beyond, which will be in orbit or even faster than orbit, allowing it to leave the cable at speeds faster than escape velocity on paths across the solar system. In doing so, the tether will transfer some of its momentum to the payload. In order to counterbalance this, the cable will need either to have counterbalancing payloads going down, or use solar-powered ion drives to keep its momentum.

I have not yet modeled this (indeed, I'm not sure I know how, or if my relatively low-powered computer could do it in a reasonable amount of time), but I suspect that a single rotating tether would be destroyed due to dynamic effects of the Earth, Sun, and Moon upon it. My intuition suggests (and if you all are interested this is something I can work to model) that rigidity is key and that a wheel, with a larger number of tethers cross-linked and cross-stabilized, would be less likely to be wrecked by dynamic/tidal forces. This wheel would also have many times more docking points than a simple tether.

An additional benefit to this kind of system? You can build cities at varying gravity levels embedded in the web. 1 full G is available, as well as partial gravity levels all the way down to 0. These may be the factory/port cities of the future, located as they are in places where lots of energy is available from the Sun, and exchange of resources, people, and machines is commonplace.

If you'd like, you can replace the suborbital rocketplane with your suborbital transportation system of choice. If you're starting from a space tower which is already 90 km tall, it really is quite easy to get to the docking point.

kbd512 · 2018-09-12 22:32:56

Josh,

I'd like to know what your ballpark IMLEO figure is to get the required tonnage of hardware up there. Instead of using spinning masses of solid materials, what about using liquids to translate the forces involved and make the tethers substantially shorter?

Basically, I'm thinking about how a centrifugal hydraulic clutch operates and combining it with a weighted tether on the other end so that when the payload is accelerated to orbital velocity, throws the weighted tether in the opposite direction. I know that wasn't a very good explanation. I think I'd have to provide a visual example of how that would work. In simple terms, there's a heavy spinning fluid inside a donut that slings a counterweight in the other direction so as not to slow the slingatron's (that's what I'm calling it) orbital velocity so greatly that it reenters.

Spaniard · 2018-09-13 02:37:49

I don't know if hydrogen baloons could push a cargo so high that at high delta-v could move without important drag.

A horizontal tether could be used to launch a cargo very fast. The limit are g and tether resistance.

Using https://www.artificial-gravity.com/sw/SpinCalc/

With a cable with 250km radius (500 for both sides) at 4 g we could reach 11273 k/h. Not enough for LEO but a reasonable first stage equivalent.

So, with a balloon you put your spaceship into a tether with a equivalent weight in the other side and begin to rotate at 1g at first and accelerating. Like a gigant carousel or like a sling.

250km is a very long radius, taller than the balloon height so cable would need to be extended in the process being rolled at first and unwinded as the speed become faster and faster.

The tension of the cable should be close to magnitudes of a gravity elevator but the shorter longitud could make things easier.

SpaceNut · 2018-09-13 16:28:45

Any tower rise from a planet or planetoid surface will always suffer from gravity and atmospheric pressure on the structure in the stresses of mass of the materials used as it rises in hieght above the surface. The base will always be of a great size when compared to the top of the tower. Sure we can change materials from heavy to lighter as it rises but its still a compression of mass that the lower section will feel. Then we would want to move a mass up to the top only makes the stresses greater on that section.

JoshNH4H · 2018-09-13 17:57:09

kbd512 wrote:

I'd like to know what your ballpark IMLEO figure is to get the required tonnage of hardware up there. Instead of using spinning masses of solid materials, what about using liquids to translate the forces involved and make the tethers substantially shorter?

As a ballpark, if the tether is to come from Earth the launched mass would be somewhere between "prohibitively high" and "absurd". As a figure for comparison, a tether with an area of 1 square centimeter (1e-4 m^2), a density of 1000 kg/m^3, and a length of 4600 km would have a mass of 460 tonnes (which is less than I thought it would be, actually--I would not consider 500 T to be either prohibitively large or absurd as long as it wouldn't need to be launched in one go). Any real system will likely be substantially higher than that.

My suggestion would be to acquire the material from elsewhere. The elevator will presumably be made from some sort of Carbon fiber, and carbon is common in the universe. The design and development of this kind of system will be tremendously expensive, which suggests that there will be a substantial demand for orbital launch services already, itself implying a substantial human presence in space.

In any case, this calculations assumes a tether with no taper and specifies neither specific strength nor the maximum amount of mass you'd like to hang off the end. You could fill in values for these numbers

I think I am going to work on the taper calculations, which will give a better number for the total mass. I'd like to put the results online somewhere as a calculator, but that may be a bit above my ability (particularly because no website that I know of runs on matlab). If anyone wants to use my code or has a particular scenario they would like to see modeled I'd be glad to make that happen.

If you're looking for me to give a guess for what the minimum mass is, assuming a single tapered rotating tether is dynamically stable and made from advanced (but currently-existing) carbon fiber with a real world (let's say roughly 4) safety factor I would guess somewhere in the 10,000-100,000 tonne range. But this really is a guess, I don't put any faith in it and neither should you.

Basically, I'm thinking about how a centrifugal hydraulic clutch operates and combining it with a weighted tether on the other end so that when the payload is accelerated to orbital velocity, throws the weighted tether in the opposite direction. I know that wasn't a very good explanation. I think I'd have to provide a visual example of how that would work. In simple terms, there's a heavy spinning fluid inside a donut that slings a counterweight in the other direction so as not to slow the slingatron's (that's what I'm calling it) orbital velocity so greatly that it reenters.

I tried to figure out how the system you're describing would work or exactly what it was but I couldn't, could you provide some kind of schematic, drawing, or reference to help me out?

Spaniard and Spacenut-

Per my original post, Hydrogen-inflated space towers using advanced, but existing materials are strong enough to get to extreme heights with reasonable taper ratios, around 15 to 100 km and under 200 for 200 km; I will post the equations when I get home and would be happy to go into the derivation if you're interested.

SpaceNut · 2018-09-13 18:46:39

Is the tower sectioned to allow for different pressures and even helium use so that we can heat to cause espansion in the chambers to increase vertical strength under launch or load of the item to orbit.

JoshNH4H · 2018-09-13 19:21:43

It turns out that doing that doesn't get you any advantage because of the weight/downwards air pressure of the gas in the tower

elderflower · 2018-09-14 03:20:59

Sectioned buoyancy chambers for the tower could be designed to allow for failure of some parts. This would be a bit more safe. You have to address the question of response to adverse weather conditions, one of which would be icing, so heating would be necessary. A lot of heating!

kbd512 · 2018-09-14 03:21:52

Josh,

That mass figure looks doable using a few BFS flights.

How big would this thing be when packaged for launch and could it be transferred in multiple loads?

Hydraulic Torque Converter Concept (the Yo-Yo / Weed Whacker Trimmer Line Skyhook):

If you've ever seen how a hydraulic clutch works, it uses hydraulic pressure to lock up under load to transfer torque. I want the torque transferred from the payload being flung into orbit, through the torque converter, to the suspended counterweight on the other end. It's an application of the same system Christian von Koenigsegg's company created for their Regera sports car to transfer torque from the series hybrid motor without using a geared transmission. The only difference is what the torque converter is transferring the load to and what is actuating the converter to cause it to lock up and transfer torque. The force generated from the payload pulling on the snare line / hook is causing the hydraulic unit to lock up and transfer the torque to the counterweight.

248 MPH Without A Gearbox: Direct Drive -- /INSIDE KOENIGSEGG

This is just an oversized Yo-Yo / Weed Whacker Trimmer Line head. One line with a hook snags the payload while the counterweighted line, which is also connected to a torque converter in the middle, is used to limit / adjust the rate of transfer to reduce the shock loading on the lines, thereby controlling the acceleration rate. The distance from the counterweight to the body of the Yo-Yo is adjustable for the exact payload mass. Prior to operation, the tethers are spun up to speed. During operation, the clutch allows some slip in the counterweight tether to dynamically transfer load when the payload is initially snared. In that regard, it's also somewhat like the arresting gear found aboard an aircraft carrier. The power source is a small Hydrazine APU that spins the device up to speed prior to operations.

JoshNH4H · 2018-09-14 22:57:12

Spacenut and Spaniard,

The equations I have used to calculate taper ratios are as follows:

R=exp(2gh/S)

Where:

R is the area taper ratio, the area of the bottom of the tower divided by the area of the top of the tower
g is Earth's gravity, 9.8 m/s^2
h is the height of the tower, in meters
S is the effective specific strength of the material. This can be calculated with the equation:

S=Sy/df

Where:

Sy is the tensile yield strength of the material
d is the density of the material
f is the factor of safety; I recommend 4

Now, in order to determine how much area the tower will take up you need to know what the area on top is. You can calculate this as follows:

A=mg/(Pi-Po)

Where:

A is the surface area of the top of the tower
m is the total mass you are looking to support, including the mass of any support on top of the tower (You will want some sort of "floor" as otherwise the top of the tower will be a surface similar to a bouncy house). In designing a tower for practical purposes you will need to be able to support not just the liftoff weight of the rocket itself but also various launch support facilities that mass many times more than the rocket.
Pi and Po are the internal and external pressure at the height of the top of the tower, respectively

Pi and Po can be calculated using the barometric formula:

Ph=Po*exp(-gMh/RT)

Where:

Ph and Po are the absolute pressures at height h and sea level, respectively
g is Earth's gravity, 9.8 m/s^2
M is the molar mass of the gas whose pressure you are calculating, 0.029 kg/mol for air and 0.002 kg/mol for Hydrogen
h is the height of the tower, in meters
R is the universal gas constant, 8.314 J/molK
T is the temperature. This equation assumes a uniform temperature; I have been using 260 K as an approximation.

These four equations will allow you to calculate most of the important characteristics for an idealized, tapered tensile tower of your choosing.

kbd512-

That mass figure looks doable using a few BFS flights.
How big would this thing be when packaged for launch and could it be transferred in multiple loads?

A reasonable estimate would be that if you spool up the cable you might get a density half that of the material itself. Having said that, I don't think 500 T is a good estimate for total mass because I don't regard a 1 square centimeter untapered tether (made from unobtanium, no less!) as being a genuine possibility.

A real, functional system is more likely in my opinion to be a disc composed of tethers which split and recombine in a highly complex manner for 6-dimensional stabilization at each point in the lattice. I'm not sure how exactly one would configure the joints between tether sections, but they will presumably be positioned at the point of splitting. In any case if for whatever reason people want to ship 100,000+ tonnes of cable up in separate rockets instead of making it in space that should be possible.

I'm still not sure I understand what your idea is. Is this right?

You're proposing a skyhook that has a much smaller size than the one I've been talking about, but instead of being a fairly static structure involves a tether rotating around a counterweight that acts as a sort of variable-friction bearing.

What I don't understand is...why? The factor that dominates the stresses on the cable is the rotation speed. Ignoring the effects of gravity, the following equation holds for any rotating tether:

s/d=v^2/2

Where s is the max tensile strength (for an untapered tether), d is the material density, and v is the velocity of the end of the tether relative to the center. So for comparison, the orbital velocity for the tether I've found to be optimum in length is 6741 m/s. Using this equation you would predict a required tensile strength (for a tether with no taper and a density of 1000 kg/m^3, and subtracting Earth's rotational velocity of 465 m/s) of 19.7 GPa. The actual (calculated) value is 16.0 GPa.

In my calculation, the equilibrium comes from a balance between increasing tidal stresses and decreasing velocity as the orbit height increases.

I don't fully understand how the system you're proposing works, but I also don't understand what problems you believe it solves.

SpaceNut · 2018-09-15 08:43:41

Thanks as its always better to talk about a subject with more than a gut feeling about how stuff works and general knowledge.

The Hypersonic Rotating Skyhooks (HRS) seems interesting in that you are looking to use uplift to counter the mass of the towering unit with a counter mass in orbit that is greater than that to which is in the atmopsphere.

kbd512 · 2018-09-15 20:13:33

Josh,

My concept is just a variation on the HASTOL concept proposed by Boeing. Remember that study they published around 2000? I was thinking about the problems they found with simply using a tether attached to a rotating counterweight. The incredible mass of the total solution was driven primarily by the requirement to keep the station from reentering after tossing the payload.

The Boeing / Tethers Unlimited / University of Maryland study proposed to put a facility in 610km by 700km equatorial orbit and use a 600km long tether. A fictional reusable hypersonic spaceplane would deliver the payload to the Skyhook at a 100km+ altitude at Mach 10 to Mach 19. The tip speed of their tether was around 3.5km/s. Their tether material was Spectra (UHMWPE) and last 20km of the tether was Zylon for heat resistance. Target payload mass was 14t. The 600km long tapered "HoyTether" would weigh an estimated 1,360t and the counterweight / station would weigh 1,650t. Eventually, they proposed increasing the intercept altitude from 100km to 150km and the intercept velocity from 3.5km/s to between 5km/s and 6km/s. IIRC, that reduced the tether mass to about a third of what the Phase I study proposed and mandated the use of a reusable rocket stage. SpaceX has a reusable booster stage. The general idea was that the reusable spaceplane, or booster rocket, would provide about 50% of the dV increment, with the Skyhook providing the other 50%.

Here's the link:

HYPERSONIC AIRPLANE SPACE TETHER ORBITAL LAUNCH (HASTOL) ARCHITECTURE STUDY PHASE II: FINAL REPORT

Proposed Changes to the Concept To Solve Problems

I'm trying to limit the total mass and the peak acceleration from shorter tethers using a hydraulic or an electro-mechanical momentum transfer mechanism. I looked at hydraulic torque converters and thought about how they could be applied to a system that limits peak acceleration. The flywheel, which is essentially part of the torque converter in this application, is used to limit peak acceleration associated with the shorter tether and also used to prevent inertia from causing the Skyhook to reenter after the toss.

Here's what problems the proposed solution would solve:

From the study:

"...We need to find methods of operating the Boost Facility so that it picks up the payload and tosses the payload at CM orbit positions that are not at perigee or apogee, and tether rotation angles that are not at zenith or nadir. We also need to find methods to change the tether length, rotation rate, and orbital parameters of the Boost Facility before, during, and after the payload interaction to achieve a desired final payload velocity at a minimum value of maximum tether stress, so as to minimize the tether mass and thus the total facility mass."

1. lower mass - acceleration is achieved using a variable-length counterweighted-tether attached to the torque converter / flywheel, rather than simply using the mass of the counterweight to provide the acceleration

2. lower peak acceleration - the flywheel and torque converter smooth out the acceleration curve

3. shorter and less complex tether geometries - system simply contends with a faster acceleration at the point of payload grapple

4. after the toss, the flywheel retracts the tether to prevent inertia from causing reentry and the counterweight on the other tether also assists with this

5. rather than contend with tether material degradation from atomic Oxygen by continually swinging the tether in open space, the tether is retracted after the toss

JoshNH4H · 2018-09-25 21:50:45

Hey kbd512,

I was not familiar with the HASTOL topic, it's very interesting. It seems like the big difference between what they're talking about and what I'm talking about is that their rotation speed is dramatically lower, and their required rocket delta-V is consequently dramatically higher. The system they discuss is way less ambitious, but also way more doable in the short term. Your suggestion seems like it would work well with it.

I'm interested in something that's on a bigger scale and with more significant effects. I should have some time this week to work on my taper calculator so hopefully I'll have some results to share soon

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