Why can't buoyancy of air be used to support a mega structure as an alternative to a space elevator?

Question

The reason for asking this question stems from recent articles about large loss of strength of carbon nano tubes with even single atom movement, tested samples showing high vulnerability to space environment oxygen radical damage, as well as my understanding of almost impossible tensile strength material requirements to suspend a massive 60,000km + long cable from GEO to the surface and also away from GEO as counterweight.

Can the atmosphere not be used as a buoyant medium to support the weight of a mega structure that extends several tens of kilometres and instead act as a sort of poor substitute for what seems like impossible traditional space elevator concepts?

Is a buoyant mega structure concept like the one below feasible?

I think I am misunderstanding some basic premise of buoyancy or action and reaction here?

*** Buoyant atmospheric mega structure basic supposition ***

An outwardly smooth cone shape mega structure of 1cm thick Kevlar extends from sea level to 50 km with a small base and large 50 km diameter opening making a curved surface area of 4,398 km². π * radius * L = 4,398 km²

With a shell volume @ 1cm thick of 4.40E13 cm³ and Kevlar mass density @ 1.44g / cm³ the mega structure shell mass is 6.34E10 kg.

50% of the mega structure interior is arrayed with 20 centrifugal compression blades also of 1cm thick Kevlar, altogether equal to an additional 2.5 mega structures worth of material and total mass of 2.2E11 kg.

6.34E10 + ( 6.34E10 * 2.5 ) = 2.2E11 kg

The entire mega structure rotates such that the entire volume ~ 3.27E13 m³ of air is reduced by 20% pressure. Volume = 1/3 * π * (radius)² * height = (1/3) * π * (25km)² * 50km = 32,725 km³ = 3.27E13 m³

The buoyant force equation B = p V g assuming air pressure density @ 25km is 0.037 kg / m³ and 20% of the entire volume displaced gives 2.38E12 kg of buoyant displacement. 0.037 * (3.27E13 * 0.2) * 9.81 = 2.38E12 kg

The total mass of the structure + 2.5 additional structures of aero blade all 1cm Kevlar is 2.2E11 kg which means the tensile strength requirements of supporting it's own weight is negated by atmospheric buoyancy even at only 80% pressure differential???

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If the structure can be buoyant I tried to figure the speed required to spin the atmosphere "out" with Boyle's Law finding P2.

P2 = ( P1 * V1 ) / V2

Pressure of atmospheric air @ representative half height 25km = 256 kg / m²

P1 mega structure reduced 80% pressure air = 256 * 0.8 kg / m² = 205 kg / m² V1 mega structure total volume= 3.27E13 m³ V2 interior volume of cone @ 50% air blade volume coverage which does the compression(?) : 3.27E13m * 0.5 = 1.64E13 m³

Pressure required in centrifugal compression air blade volume P2 = ( 205 * 3.27E13 ) / ( 1.64E13 ) = 409 kg / m²

Assuming can treat as an adiabatic centrifugal compressor with very low 1% efficiency???

From https://missrifka.com/equipments/compressor/centrifugal-compressor-power-calculation.html

Centrifugal compressor power calculations require (imperial): Compressibility Factor [Z] : Air = 1 Molecular Weight [MW] : Air = 28.9647 g/mol (SI?) Gas Constant [R] : 1544/molecular weight Inlet Temperature [T1]: Average air temperature Earth : 287K = 13.85 degrees Celcius Inlet Pressure [P1] : 256 kg/m² = 0.36 psia Outlet Pressure [P2] : 409 kg / m² = 0.58 psia Heat Capacity Component [Adiabatic Component C_p/C_v] K ratio : Air @ low speeds = 1.4

Adiabatic Head = ( ( Z * R * T1 ) / ( ( K - 1 ) / K ) ) * [ ( P2 / P1 )^( ( K - 1 ) / K ) - 1 ] = 7.48E4 * 0.15 = 1.12E4 ft.lbf / lbm

Flow rate lb / minute : If assume 20% of the volume of air in the mega structure is required to be expelled to provide lifting force then assumed of every second / minute / hour that per minute is a reasonable supposition : (20% mass of air / minute ) = 1.42E13 lb / minute

( flow rate * adiabatic head ) / ( Efficiency * 33,000 ) = ( 1.42E13 * 1.12E4 ) / ( 0.01 * 33000 ) = 4.82E14 horsepower!

specificSpeed = ( rotationalSpeed * flowRate^1/2 ) / ( adiabaticHead^3/4 ) specific speed is assumed to be more similar to radial blade area pumps ~ 500 because the radial blade pumps are lower speed with larger areas and centrifugal compression as compared to higher speed axial flow pumps ~ 15,000, because the mega structure is so much bigger and not a cylinder I have chosen : 100

rotationalSpeed = ( specificSpeed * adiabaticHead^3/4 ) / ( flowRate^1/2 ) = 1.06E5 / 3.77E6 = 2.89E-2 revolutions / minute

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I then tried to figure the tensile strength requirement with the rotational speed assuming calculation for stress in rotating disk.

Stress = ( ( ( 2 * π * RevolutionsPerMinute ) / 60 )² * Radius² * Density ) / 3

Stress [Pa.N/m²] = ? RevolutionsPerMinute [revolutions/minute] = 2.89E-2 revolutions / minute Radius [m] = 25 km = 25,000m Density [kg/m³] = 1.44 g / cm³ = 1440 kg/m³

Stress = ( ( ( 2 * π * 2.89E-2 ) / 60 )² * 25,000² * 1440 ) / 3 = 9.16E-6 * 25,000² * 1440 = 8.24E6 Pa.N/m²

Maximum Tensile Strength of Kevlar @ 1m cross section = 3600 MPa = 3.6E9 Pascals Maximum Tensile Strength of Kevlar @ 1cm cross section = 3.6E9 * 0.0001 = 3.6E5 Pascals

So I believed though the Kevlar does not have sufficient tensile strength to hold together such a massive 50km mega structure from centrifugal forces it is also not as "difficult" as the tensile strength aims for a traditional space elevator concept?

**** Visual of how it works as launch system *******

Large and looming into the upper atmosphere the mega structure appears from distance like a giant mountain range that looms ever upward becoming more akin to a storm cloud as the launch train moves closer.

The top most reaches are surrounded by extensive white wisps of cloud while the environment around the launch site is drenched with perpetual moisture and rain as vast amounts of atmosphere are moved upward outward and then down from the mega structure.

Before the train dips into the tunnel the surface is viewed as bare and lacking in external features, the smooth surface does not betray the rotational movement of the entire structure.

As the train passes through a series of airlocks underneath the ground it rises into a near vertical position and is spun up within the tunnel to match the rotation of the launch mega structure, pinning the passengers to their seats.

The airlock door opens and immediately the launch tunnel atmosphere condenses in the lower pressure environment and is vented into the vast eye of a hurricane like expanse before the passengers as viewed from their screens.

The train is launched along an electric induction rail that runs along a track laid to the interior surface of the structure, slowly at first but building speed and acceleration as it climbs higher and higher.

Passing through apertures underneath the giant air blades like a toy train under skyscrapers the train accelerates assisted by centrifugal force of the structure rotation.

As the train climbs higher the trajectory flattens out before summiting the final maximum altitude and is flung out and away, the train carriage or "engine" first stage dropping away to be reused while the carried sleek "carriage" ignites a rocket motor and continues accelerating to orbit.

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Is this physically feasible?

Like a boat taking on water, once the water or higher pressure lower altitude air is "thrown out" of the top of the cone it can't come back in again? and therefore will give buoyancy?

If feasible is this easier / more reasonable than a traditional space elevator despite the lack of height?

Once spun up once could a structure like this negate some of the energy requirement as the dense sea level atmosphere once evacuated in part cannot come in again?

Can the buoyant force offset a large part of tensile strength requirements for a material to hold up it's own weight?

Answer 1

Regardless of the accuracy of your calculations, what you propose isn't useful. Space isn't high, space is fast. Getting above the atmosphere only saves a little bit of energy; you still need to get up to the 7600 m/s speed of low-Earth orbit.

The trick that makes a space elevator to geostationary orbit work is that orbital speed at geostationary altitude is 2610 m/s -- exactly the speed you need to be going to circle the Earth once per day at that height. A megastructure to any other height won't work, because the top will be moving at the wrong speed for its height: too slow for shorter structures, too fast* for taller ones.

_{*A taller structure has a use: since the top is moving too fast for its orbital height, it can be used to fling a spacecraft into a higher orbit, or into interplanetary space.}

Answer 2

Your structure isn't competing with a space elevator, it is competing with other non-rocket spacelaunch ideas of various degrees of implausibility. Your vacuum balloon can't reach to orbit altitudes (because it has no bouyancy that far up) and can't give orbital or escape velocity for "free".

The competition include StarTram, where the "Gen 2" design involves electromagnetic acceleration to >20km altitude and 8km/s velocity and then a relatively modest rocket assist for orbital insertion. The Startram launch tube is suspended by the electromagnetic repulsion of 200+km long superconducting cables.

Other include Lofstrom Loops and Space Fountains which use electromagnetic accelerators to do a momentum exchange trick and hold stuff aloft. As with the startram and your giant vacuum cone, and unlike the space elevator, you still need assistance to boost a payload to suitable velocities and do orbital insertion

Your question then becomes, "Which is the more implausible act of gonzo engineering, a self-supporting vacuum chamber covering a couple of thousand square kilometers, superconducting electromagnetic suspension systems that are hundreds of kilometers long, or a 14km/s electromagnetic machine gun that's thousands of kilometers long or high?"

I've a soft spot for the startram (and I've talked about it before on here), and even though it is an enormously expensive and technically challenging idea that I don't see anyone getting behind any time soon it doesn't require much in the way of unobtanium super scifi material science, and it is significantly smaller and lighter than your billion tonne small-country-sized behemoth and the failure modes are likely to be significantly less hazardous and somewhat easier to recover from.

So.

If feasible is this easier / more reasonable than a traditional space elevator despite the lack of height?

It is hard to think of something that's more difficult to build and more unreasonable than a space elevator on Earth. This isn't a good basis for comparison. I think your design is also an unreasonable and impractical act of gonzo megastructure engineering (and honestly, so are all the alternatives, even the ones I particularly like).

It is hard to decide on exactly what might sink your plan, but a big storm hitting your giant cone seems like it would be... difficult to protect against and withstand, even if you did solve the material and structural issues, which is a pretty big assumption.

Answer 3

From a structural point of view, pumping air out is probably not what you want to do, since you are making a vacuum balloon. So if it could be constructed, it would be providing lift to the base, but the upper cone part would in fact be getting pushed down by air pressure making it worse for making tall things already fighting gravity.

If the math checks out, instead you want to be making hovering platforms where you can use that lift to hold things up, with each 'balloon' needing to be small enough that it has vertical structural integrity - you need to stop air pressure pushing top and bottom together even if the spin part is unloading the sides. It may be interesting to re-do your math for say 100 m wide by 1 km high spinning cylinder intended to provide lift to something else. Even at this scale a 80% vacuum gets you 2.5 thousand tonnes trying to push the two end plates together.

If you reverse the fans, what you get instead is a massive inflated structure where air pressure is holding the top of it up, and the cone ares is under tension rather than compression which is much easier to work with structurally.

This makes it a larger, and possibly more structurally sound against wind loads version of Thox that was designed at 20km and claimed 200km as physically possible.

Note that with both vacuum and pressure version anything that prevents the pumps running will quickly turn into a wide area disaster, the vacuum version would appear prone to becoming a massive vacuum gun in failure, suffering a high energy implosion should it start to collapse and buckle. A positive pressure version would also have some exciting failure modes.