SpaceShaft
Encyclopedia
A SpaceShaft is a proposed atmospherically levitating
structure that would serve as an elevator
system to near-space
altitudes. It will support multiple platforms distributed at several elevations that would provide habitation facilities
for long term human operations throughout the mid-atmosphere and near-space altitudes. A SpaceShaft is also a candidate of the technologies cataloged for non-rocket spacelaunch
.
A SpaceShaft is comparable to a maritime oil spar platform
. Although a SpaceShaft is also described as a structure
, it is not a space tower because it does not stand on foundations in contact with the surface of the planet as to support compressive forces (see image of mode 3 stretching and compression) caused by weight. On the contrary, it is a very dynamic system since it would be constantly moving upwards. A SpaceShaft is not an orbital insertion system, as is assumed to intrinsically be the case with the proposed centrifugally extended carbon-nanotube tether Space Elevator
. However, from a platform at the top of a SpaceShaft either spaceplane
s or spacecraft
s with built-in propulsion
systems could be launched.
Because of the orbital insertion
incapability of the SpaceShaft, some people do not regard a SpaceShaft as a true space elevator.
The SpaceShaft was originally proposed at the 2nd Eurospaceward Conference on December 2008 in Luxembourg as part of a possible transportation method for the CNT
tether spools that the popular ISEC space elevator system will need for its deployment from space.
system behaving as a typical oceanic spar-buoy
or spar type oil platform
; instead of being "mostly submerged in water and partially rising into the atmosphere", it is "mostly submerged in the planet’s atmosphere and partially rising out into the fringes of Space".
Because of the large volumes of displaced air-mass
resulting from the diameters of its multiple concentrically aligned, telescopic cylinders (stabilization shafts) and their different heights, thousands of tons of buoyancy would be harnessed, making it theoretically possible to support several permanent platforms at the top of each of the stabilization shafts on the outer rims and thousands of tonnes of upthrust on the cylinders at the core of the telescopic system (transportation shafts). The type of shafts and their intended uses are discussed later.
Within the conduit at the innermost transportation shaft (i.e. the flue
), which would extend from near sea-level
to the highest elevation, where a platform will be located, a special shuttling
-cab(s), comparable to a vertically oriented air-ship
, will travel up and down the system quickly carrying personnel and light cargo, first by means of buoyancy
and afterward by electromechanical systems.
The location of the individual platforms, except for the one at the summit of the highest shaft, are mostly distributed at altitudes below the Mesosphere
, and so allowing for long term human activities never before possible throughout the mid-atmosphere of our planet. The reason for the distribution is that the platforms (also known as mooring platforms) also serve as the attaching points for guy-lines
similar to those used with sailing masts
and guyed mast antennae
.
The platform at the top of the innermost shaft, i.e. the one within the core of the telescopic system, will be able to reach altitudes around 100 km, and perhaps above depending on the intended operation, and so potentially provide the needed support for facilities to exercise important non-orbital space operations. The platform could even provide the facilities for initiating the “assisted launch” of a typical second stage rocket or spaceplane (see Rockoon and balloon-launched self-stabilized rocket).
Besides its capability of supporting multiple platforms throughout the atmosphere, a SpaceShaft will also serve to house a more traditional elevator system consisting of a special shuttling-cab traveling through the flue of the core shaft. It is however important to note that this elevator system can be considered as just the secondary elevator system that a SpaceShaft can provide for reasons that will be explained later in the Deployment section.
system that consists of highly customized atmospherically buoyant building blocks and a specialized method of assembly by which a structure can be built and which the developers describe as "a combined and simultaneous method of construction and transportation". As a consequence of the deployment
method, the structure is also capable of simultaneously transporting cargo during its ascent; this simultaneous transport is done by placing the payload
within some of the building blocks, in a vertical and unidirectional FIFO sequence
, which ultimately creates a large upwards-moving structure capable of constant delivery of a high tonnage of cargo contained within selected building blocks.
As said, the SpaceShaft is assembled using atmospherically buoyant building blocks. These building blocks consist of specifically engineered buoyant pressure vessels. Some of which are designed for high buoyancy and ballasting
, while others are engineered for more specific structural purposes. However, all of these building blocks are characterized by being buoyant and having internal skeletons made from composite materials, and so making these units very strong, very light, modular, and maintainable, even when they have already been integrated into the buoyant structure and have reached high atmospheric altitudes. One interesting property of such a buoyant structure is that in the event of an accident only limited amounts of debris will fall back to the ground since most of the building blocks will remain atmospherically buoyant.
Other components of the system are not as buoyant or may not be buoyant at all, (e.g. anchor lines
, winches, deck equipment, etc.). The design goal of the SpaceShaft is to construct a structure that is; "atmospherically buoyant from sea level up to altitudes of 50km". Higher altitudes are attained by transferring excess weight as compressive loads down the SpaceShaft.
The SpaceShaft will have net positive buoyancy which will necessitate anchoring it to the ground. Additionally, since the lower portion of the SpaceShaft is subject to atmospheric winds will therefore require mooring lines. To quickly differentiate the functionality of the systems; the anchoring system is to keep the SpaceShaft from freely flying away, while the mooring system is to counteract lateral wind forces that could toss around the structure. More about the combined effects of wind loads and upthrust is discussed later, under the section of "Heave and roll behavior" which would describe the similar of a spar-buoy on a waterway
and on the section "Wind force and Coriolis
", likewise for bending and deflection on the structure. Beside the two mentioned external control systems there is an electronically controlled, self sufficient, ballasting system incorporated into every one of the buoyant building blocks.
As the SpaceShaft is constructed, the sum total of the buoyant forces of all the component rings is available to support the weight(s) of the elevated (elevating) platform(s) and payloads. Thus, as you add more component rings, you increase the load carrying capacity of the SpaceShaft.
The SpaceShaft structure is constructed with a larger number of concentric rings at the lower levels. The SpaceShaft structure is wider at the base, narrower at the top. The appearance of which resembles a telescoping device. Some of the SpaceShaft structures may resemble an elongated version of the Burj Khalifa, currently the tallest building at 828 m (2,717 ft).
While the total volume of the Burj Khalifa is not listed, the floor area is listed as 309,473 square meters. If we approximate floor height as averaging 3 meters then the volume is 928,419 cubic meters. At the bottom of the Burj Khalifa (sea level) the density of air is approximately 1.2 kilograms per cubic meter. At the top of the Burj Khalifa (828 meters) the density of air is approximately 1.1 kilograms per cubic meter. With a total displacement of 928,419 cubic meters, and considering the majority of the displacement is at the bottom, using 1.175 kg/m³ average density of displaced air, the available buoyancy is approximately 1,090 metric tons (less the mass of the SpaceShaft components). While the average density of the SpaceShaft components is unknown at this time, targeted values are in the range of 0.1 to 0.2 kg/m³. Using the higher density, a sea level based SpaceShaft of the size and shape of the Burj Khalifa could lift 905 metric tons. The Burj Khalifa represents a structure that is approximately 1% the size (height and volume) of a SpaceShaft.
where the altitude is defined as with the distance of the Earth's center and the Earth's radius.
The net vertical upthrust per unit length acting upon the SpaceShaft at a given altitude , is composed of:
The net vertical upthrust per unit length becomes then: . The different composing forces are detailed below.
per unit length of the SpaceShaft at a given altitude is computed as
in which is the air density and the gravitational acceleration
defined by:
due to the Earth's rotation is computed as:
in which is the constant Earth's rotation speed given by:
in which is the duration of a day on Earth in seconds.
an altitude is then given by the integration of the vertical upthrust over the SpaceShaft's length:
or, using the expressions for the respective upthrust components given above:
Considering a SpaceShaft that is in a neutral floating state , the above expression in which is replaced by any altitude between and gives the vertical buckling force
the upper parts of the SpaceShaft exert on the lower parts of the SpaceShaft at that altitude. This allows to evaluate the vertical stresses in the internal of the SpaceShaft and, hence, to choose the appropriate materials and design to cope with these stresses.
In case the SpaceShaft is not in a neutral floating state , the SpaceShaft must be anchored as discussed above. The anchoring force will then equal for the SpaceShaft to be in mechanical equilibrium
. This force can then be used to evaluate the stresses in the anchoring system.
The cross sectional variation of the SpaceShaft in this example study is given by the following formula:
in which is the minimum remaining cross sectional area at the top of the SpaceShaft,
is the cross sectional area of a perfect cylindrical SpaceShaft having the same total
volume as the current SpaceShaft, the case of . All studied SpaceShafts will have the same total volume and, hence, will represent approximately the same material cost.
The computations are done using and and . The different shapes of the studied SpaceShaft corresponding to different values of is shown below.
The total internal vertical forces along the SpaceShaft for the different shapes and the corresponding internal vertical stresses are depicted below:
In the case of the cubic shape , the internal force reaches a maximum of 185,000 kN (about 18,500 tons) at an altitude of about 15 km while the maximum vertical stresses read 73 kN/m (about 7.3 tons per m) at an altitude of about 23 km.
Lateral forces=
To cope with different lateral forces such as wind and Coriolis
forces (for instance, when a shuttle is moving rapidly upward within the Spaceshaft), a number of stabilization techniques are envisaged that can be categorized in two main categories:
It is important to investigate how a SpaceShaft can remain in equilibrium under the effect of lateral forces in order to design appropriately the different aforementioned stabilization techniques. Mechanical equilibrium
of the SpaceShaft is reached if the sum of all forces and the sum of all moments around some reference point (in this case the anchor point at the bottom of the SpaceShaft) are zero. In absence of any active stabilization technique, the SpaceShaft will no longer a straight vertical artefact but will have to lean against the side forces that are then compensation by the SpaceShaft's own weight force.
To model the mechanical static equilibrium of a SpaceShaft, the different acting forces and moments are listed below:
The overall mechanical static equilibrium of a SpaceShaft undergoing lateral forces is then expressed by the following two equations:
The subsequent subsections will address each of the individual terms in these equations in more detail.
packages that have the capability to model correctly the full shape of the SpaceShaft. These packages use the three dimensional Navier-Stokes equations augmented with a decent turbulence model. Furthermore, the air flow around the SpaceShaft will in most cases be inherently unsteady as a so called von Karman vortex street
may occur at certain altitudes with certain wind speeds. To cope with such unsteadiness, the SpaceShaft must have enough internal damping to avoid mechanical resonance
effects.
However, for overall engineering purposes, one can use the aerodynamic drag coefficient
at different altitudes to evaluate the overall side wind force
:
in which the aerodynamic drag coefficient , the wind speed vector
, the atmospheric air density 
and the reference aerodynamic cross sectional length 
are all dependent on the position along the SpaceShaft. Note that does not exactly equals the altitude as the SpaceShaft may be bending and not take an exact vertical position when in a static mechanical equilibrium state. represents the total axial length of the SpaceShaft.
Assuming a SpaceShaft with a circular horizontal cross sectional shape, the value of the aerodynamic drag coefficient will be about 0.5 if the wind direction is horizontal too. In case the wind is not purely horizontal, the SpaceShaft will present an elliptical shape with a lower value of the aerodynamic drag coefficient.
The total moment
around the anchor point due to wind forces is given by (while using the vectorproduct operator 
):
in which
denotes the actual position vector along the axis of the SpaceShaft relative to its anchor point on the Earth’s surface.
in which the radial distance from the Earth's center becomes now a function of the position along the (most probably bended) SpaceShaft.
The weight force moment $\vec{M}_G$ relative to the SpaceShaft's anchor point is computed as follows:
representing the bending magnitude and the axis of rotation of the bending. This assumption is valid as long as the deformation is within the range of elastic deformation. We use as the proportionality factor whose actual value is depending on the designed shape of the SpaceShaft and the used materials and my vary along the SpaceShaft's axis. The total moment 
relative to the SpaceShaft's anchor point due to internal stiffness moments is then given by:
where will generate a total moment around the SpaceShaft's anchor point that is given by:
in the mooring point or the propeller nacelle location
where is the known length along the SpaceShaft's axis. However the actual position 
will depend on the amount of bending.
We shall assume in the subsequent development that the mooring forces
are only non-zero when moving the predicted equilibrium position. The modelling of this process requires a more complex dynamic equilibrium model that also accounts for the acceleration forces. For now, we are only interested in predicting the static equilibrium position of the SpaceShaft whereby all mooring forces 
are equal to the null vector.
, to above set of equations describing the static mechanical equilibrium of the SpaceShaft can be solved for the three dimensional space coordinates of the end points of the one-dimensional Finite Elements.
In principle, the set of mechanical equilibrium equations are non-linear in the sense that for instance the aerodynamic drag coefficient is dependent on the local bending of the SpaceShaft and that the radial distance is a non-linear function of the length along the axis of the (bended) SpaceShaft. Hence, some kind of iterative Newton-Raphson technique will have to be used to solve the equations.
Nonetheless, the equations can be linearized under the assumption that the SpaceShaft is only bending a little and that it has no internal stiffness: . Under these assumptions, the aerodynamic drag coefficient can be considered independent on the SpaceShaft's position and the length along the axis of the SpaceShaft is approximately equal to and, hence, the differentials and will be identical. Also, the radial distance becomes a purely linear function.
In the case of a SpaceShaft, Coriolis forces can occur in two cases:
The vertical speed during the deployment and FIFO delivery will be very slow and in the order of 0.1 m/s. However, the mass of the SpaceShaft as such can be very large. A SpaceShaft that is 50 km tall with a constant cross sectional area of will represent a mass of about kg.
Placed at the equator, a SpaceShaft will undergo a global Coriolis force of about 300 N towards the west. This force can be considered negligible to other lateral forces.
If a nacelle with a mass of 5000 kg is moving upward within the SpaceShaft (placed at the equator) at a speed of 40 m/s (or 144 km/h), it will generate a coriolis force on the SpaceShaft of about 30 N, which, again, is a very small force compared to other lateral forces that may act upon the SpaceShaft.
Relation to Space Elevator=
A Space Elevator is a tethered satellite
(counterweight
) located at an altitude of ~100,000 km. The tether of Space Elevator offers a purchase point for an electrically driven elevator. The advantage of a Space Elevator is that the climbers have an altitude range of 0 to 100,000 km as opposed to the SpaceShaft operating in an altitude range of 0 to 100 km, and potentially 0 to 300 km. The disadvantages of the Space Elevator (as of the time of this writing) are:
The SpaceShaft can be located at latitudes away from the equator. Although the altitudes reached by the SpaceShaft are significantly lower than that of the Space Elevator, many of the envisioned missions of the space elevator (listed at the top of this article) can easily be provided by a SpaceShaft. Therefore, the two distinct advantages the SpaceShaft has are:
Levitation
Levitation is the process by which an object is suspended by a physical force against gravity, in a stable position without solid physical contact...
structure that would serve as an elevator
Elevator
An elevator is a type of vertical transport equipment that efficiently moves people or goods between floors of a building, vessel or other structures...
system to near-space
Near space
Near space is the region of Earth's atmosphere that lies between 65,000 and 325,000–350,000 feet above sea level, encompassing the stratosphere, mesosphere, and thermosphere. A more understandable definition would be above where a commercial airliner flies but below the realm of an orbiting...
altitudes. It will support multiple platforms distributed at several elevations that would provide habitation facilities
Habitation Module
thumb|right|250px|ISS Habitation moduleThe Habitation Module for the International Space Station was intended to be the Station's main living quarters designed with galley, toilet, shower, sleep stations and medical facilities. About the size of a bus, the module was canceled after its pressurized...
for long term human operations throughout the mid-atmosphere and near-space altitudes. A SpaceShaft is also a candidate of the technologies cataloged for non-rocket spacelaunch
Non-rocket spacelaunch
Non-rocket space launch is a launch into space where some or all needed speed and altitude is provided by non-rocket means, rather than simply using conventional chemical rockets from the ground. A number of alternatives to rockets have been proposed...
.
A SpaceShaft is comparable to a maritime oil spar platform
SPAR (platform)
A spar, named for logs used as buoys in shipping and moored in place vertically, is a type of floating oil platform typically used in very deep waters. Spar production platforms have been developed as an alternative to conventional platforms...
. Although a SpaceShaft is also described as a structure
Architectural structure
An architectural structure is a free-standing, immobile outdoor constructed element. The structure may be temporary or permanent.Structures include buildings and nonbuilding structures . Examples of building structures include houses, town halls, libraries, and skyscrapers...
, it is not a space tower because it does not stand on foundations in contact with the surface of the planet as to support compressive forces (see image of mode 3 stretching and compression) caused by weight. On the contrary, it is a very dynamic system since it would be constantly moving upwards. A SpaceShaft is not an orbital insertion system, as is assumed to intrinsically be the case with the proposed centrifugally extended carbon-nanotube tether Space Elevator
Space elevator
A space elevator, also known as a geostationary orbital tether or a beanstalk, is a proposed non-rocket spacelaunch structure...
. However, from a platform at the top of a SpaceShaft either spaceplane
Spaceplane
A spaceplane is a vehicle that operates as an aircraft in Earth's atmosphere, as well as a spacecraft when it is in space. It combines features of an aircraft and a spacecraft, which can be thought of as an aircraft that can endure and maneuver in the vacuum of space or likewise a spacecraft that...
s or spacecraft
Spacecraft
A spacecraft or spaceship is a craft or machine designed for spaceflight. Spacecraft are used for a variety of purposes, including communications, earth observation, meteorology, navigation, planetary exploration and transportation of humans and cargo....
s with built-in propulsion
Spacecraft propulsion
Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. There are many different methods. Each method has drawbacks and advantages, and spacecraft propulsion is an active area of research. However, most spacecraft today are propelled by forcing a gas from the...
systems could be launched.
Because of the orbital insertion
Orbit insertion
Orbit insertion is the spaceflight operation of adjusting a spacecraft’s momentum to allow for entry into a stable orbit around a planet, moon, or other celestial body...
incapability of the SpaceShaft, some people do not regard a SpaceShaft as a true space elevator.
The SpaceShaft was originally proposed at the 2nd Eurospaceward Conference on December 2008 in Luxembourg as part of a possible transportation method for the CNT
Carbon nanotube
Carbon nanotubes are allotropes of carbon with a cylindrical nanostructure. Nanotubes have been constructed with length-to-diameter ratio of up to 132,000,000:1, significantly larger than for any other material...
tether spools that the popular ISEC space elevator system will need for its deployment from space.
General appearance and arrangement
The general structural appearance of a SpaceShaft is that of an upright standing telescopicTelescoping (mechanics)
Telescoping in mechanics describes the movement of one part sliding out from another, lengthening an object from its rest state. In modern equipment, this is often done by hydraulics....
system behaving as a typical oceanic spar-buoy
Spar buoy
A spar buoy is a tall, thin buoy that floats upright in the water and is characterized by a small water plane area and a large mass. Because they tend to be stable ocean platforms, spar buoys are popular for making oceanographic measurements. Adjustment of the water plane area and the mass allows...
or spar type oil platform
Oil platform
An oil platform, also referred to as an offshore platform or, somewhat incorrectly, oil rig, is a lаrge structure with facilities to drill wells, to extract and process oil and natural gas, and to temporarily store product until it can be brought to shore for refining and marketing...
; instead of being "mostly submerged in water and partially rising into the atmosphere", it is "mostly submerged in the planet’s atmosphere and partially rising out into the fringes of Space".
Because of the large volumes of displaced air-mass
Air mass
In meteorology, an air mass is a volume of air defined by its temperature and water vapor content. Air masses cover many hundreds or thousands of square miles, and adopt the characteristics of the surface below them. They are classified according to latitude and their continental or maritime...
resulting from the diameters of its multiple concentrically aligned, telescopic cylinders (stabilization shafts) and their different heights, thousands of tons of buoyancy would be harnessed, making it theoretically possible to support several permanent platforms at the top of each of the stabilization shafts on the outer rims and thousands of tonnes of upthrust on the cylinders at the core of the telescopic system (transportation shafts). The type of shafts and their intended uses are discussed later.
Within the conduit at the innermost transportation shaft (i.e. the flue
Flue
A flue is a duct, pipe, or chimney for conveying exhaust gases from a fireplace, furnace, water heater, boiler, or generator to the outdoors. In the United States, they are also known as vents and for boilers as breeching for water heaters and modern furnaces...
), which would extend from near sea-level
Sea level
Mean sea level is a measure of the average height of the ocean's surface ; used as a standard in reckoning land elevation...
to the highest elevation, where a platform will be located, a special shuttling
Shuttle (weaving)
A shuttle is a tool designed to neatly and compactly store weft yarn while weaving. Shuttles are thrown or passed back and forth through the shed, between the yarn threads of the warp in order to weave in the weft....
-cab(s), comparable to a vertically oriented air-ship
Airship
An airship or dirigible is a type of aerostat or "lighter-than-air aircraft" that can be steered and propelled through the air using rudders and propellers or other thrust mechanisms...
, will travel up and down the system quickly carrying personnel and light cargo, first by means of buoyancy
Buoyancy
In physics, buoyancy is a force exerted by a fluid that opposes an object's weight. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the...
and afterward by electromechanical systems.
The location of the individual platforms, except for the one at the summit of the highest shaft, are mostly distributed at altitudes below the Mesosphere
Mesosphere
The mesosphere is the layer of the Earth's atmosphere that is directly above the stratosphere and directly below the thermosphere. In the mesosphere temperature decreases with increasing height. The upper boundary of the mesosphere is the mesopause, which can be the coldest naturally occurring...
, and so allowing for long term human activities never before possible throughout the mid-atmosphere of our planet. The reason for the distribution is that the platforms (also known as mooring platforms) also serve as the attaching points for guy-lines
Guy-wire
A guy-wire or guy-rope, also known as simply a guy, is a tensioned cable designed to add stability to structures . One end of the cable is attached to the structure, and the other is anchored to the ground at a distance from the structure's base...
similar to those used with sailing masts
Mast (sailing)
The mast of a sailing vessel is a tall, vertical, or near vertical, spar, or arrangement of spars, which supports the sails. Large ships have several masts, with the size and configuration depending on the style of ship...
and guyed mast antennae
Radio masts and towers
Radio masts and towers are, typically, tall structures designed to support antennas for telecommunications and broadcasting, including television. They are among the tallest man-made structures...
.
The platform at the top of the innermost shaft, i.e. the one within the core of the telescopic system, will be able to reach altitudes around 100 km, and perhaps above depending on the intended operation, and so potentially provide the needed support for facilities to exercise important non-orbital space operations. The platform could even provide the facilities for initiating the “assisted launch” of a typical second stage rocket or spaceplane (see Rockoon and balloon-launched self-stabilized rocket).
Besides its capability of supporting multiple platforms throughout the atmosphere, a SpaceShaft will also serve to house a more traditional elevator system consisting of a special shuttling-cab traveling through the flue of the core shaft. It is however important to note that this elevator system can be considered as just the secondary elevator system that a SpaceShaft can provide for reasons that will be explained later in the Deployment section.
Possible uses of a SpaceShaft
- Tourism destination with spectacular view
- Atmospheric observation station
- Communications platform
- The ultimate BASE jumpingBASE jumpingBASE jumping, also sometimes written as B.A.S.E jumping, is an activity that employs an initially packed parachute to jump from fixed objects...
experience - Solar power generation
Background regarding the concept
A SpaceShaft is one of many applications of a foundationless scaffoldingScaffolding
Scaffolding is a temporary structure used to support people and material in the construction or repair of buildings and other large structures. It is usually a modular system of metal pipes or tubes, although it can be from other materials...
system that consists of highly customized atmospherically buoyant building blocks and a specialized method of assembly by which a structure can be built and which the developers describe as "a combined and simultaneous method of construction and transportation". As a consequence of the deployment
System deployment
The deployment of a mechanical device, electrical system, computer program, etc., is its assembly or transformation from a packaged form to an operational working state....
method, the structure is also capable of simultaneously transporting cargo during its ascent; this simultaneous transport is done by placing the payload
Cargo
Cargo is goods or produce transported, generally for commercial gain, by ship, aircraft, train, van or truck. In modern times, containers are used in most intermodal long-haul cargo transport.-Marine:...
within some of the building blocks, in a vertical and unidirectional FIFO sequence
FIFO and LIFO accounting
FIFO and LIFO Methods are accounting techniques used in managing inventory and financial matters involving the amount of money a company has tied up within inventory of produced goods, raw materials, parts, components, or feed stocks....
, which ultimately creates a large upwards-moving structure capable of constant delivery of a high tonnage of cargo contained within selected building blocks.
Deployment and FIFO delivery
The FIFO deployment sequence is as follows; having one of the buoyant building blocks already anchored; some slack is then given to the anchor lines as to let it further rise, i.e.; in a controlled fashion and for a limited height, as much as to allow for enough space being made as to insert a new buoyant building block right underneath the first one. These building blocks are then firmly attached to each other and so becoming a unit with the understandably incremented buoyancy. The process is then repeated for as many times as is necessary, such that: when both the desired carrying capacity and desired altitude are achieved for the building block at the top of the stack, with whatever payload is contained, is then submitted for their relocations. And so is the FIFO sequence completed.As said, the SpaceShaft is assembled using atmospherically buoyant building blocks. These building blocks consist of specifically engineered buoyant pressure vessels. Some of which are designed for high buoyancy and ballasting
Ballast tank
A ballast tank is a compartment within a boat, ship or other floating structure that holds water.-History:The basic concept behind the ballast tank can be seen in many forms of aquatic life, such as the blowfish or argonaut octopus, and the concept has been invented and reinvented many times by...
, while others are engineered for more specific structural purposes. However, all of these building blocks are characterized by being buoyant and having internal skeletons made from composite materials, and so making these units very strong, very light, modular, and maintainable, even when they have already been integrated into the buoyant structure and have reached high atmospheric altitudes. One interesting property of such a buoyant structure is that in the event of an accident only limited amounts of debris will fall back to the ground since most of the building blocks will remain atmospherically buoyant.
Other components of the system are not as buoyant or may not be buoyant at all, (e.g. anchor lines
Anchor windlass
A "windlass" is a machine used on ships that is used to let-out and heave-up equipment such as for example a ship's anchor or a fishing trawl.An anchor windlass is a machine that restrains and manipulates the anchor chain and/or rope on a boat, allowing the anchor to be raised and lowered. A...
, winches, deck equipment, etc.). The design goal of the SpaceShaft is to construct a structure that is; "atmospherically buoyant from sea level up to altitudes of 50km". Higher altitudes are attained by transferring excess weight as compressive loads down the SpaceShaft.
The SpaceShaft will have net positive buoyancy which will necessitate anchoring it to the ground. Additionally, since the lower portion of the SpaceShaft is subject to atmospheric winds will therefore require mooring lines. To quickly differentiate the functionality of the systems; the anchoring system is to keep the SpaceShaft from freely flying away, while the mooring system is to counteract lateral wind forces that could toss around the structure. More about the combined effects of wind loads and upthrust is discussed later, under the section of "Heave and roll behavior" which would describe the similar of a spar-buoy on a waterway
Waterway
A waterway is any navigable body of water. Waterways can include rivers, lakes, seas, oceans, and canals. In order for a waterway to be navigable, it must meet several criteria:...
and on the section "Wind force and Coriolis
Coriolis effect
In physics, the Coriolis effect is a deflection of moving objects when they are viewed in a rotating reference frame. In a reference frame with clockwise rotation, the deflection is to the left of the motion of the object; in one with counter-clockwise rotation, the deflection is to the right...
", likewise for bending and deflection on the structure. Beside the two mentioned external control systems there is an electronically controlled, self sufficient, ballasting system incorporated into every one of the buoyant building blocks.
As the SpaceShaft is constructed, the sum total of the buoyant forces of all the component rings is available to support the weight(s) of the elevated (elevating) platform(s) and payloads. Thus, as you add more component rings, you increase the load carrying capacity of the SpaceShaft.
The SpaceShaft structure is constructed with a larger number of concentric rings at the lower levels. The SpaceShaft structure is wider at the base, narrower at the top. The appearance of which resembles a telescoping device. Some of the SpaceShaft structures may resemble an elongated version of the Burj Khalifa, currently the tallest building at 828 m (2,717 ft).
While the total volume of the Burj Khalifa is not listed, the floor area is listed as 309,473 square meters. If we approximate floor height as averaging 3 meters then the volume is 928,419 cubic meters. At the bottom of the Burj Khalifa (sea level) the density of air is approximately 1.2 kilograms per cubic meter. At the top of the Burj Khalifa (828 meters) the density of air is approximately 1.1 kilograms per cubic meter. With a total displacement of 928,419 cubic meters, and considering the majority of the displacement is at the bottom, using 1.175 kg/m³ average density of displaced air, the available buoyancy is approximately 1,090 metric tons (less the mass of the SpaceShaft components). While the average density of the SpaceShaft components is unknown at this time, targeted values are in the range of 0.1 to 0.2 kg/m³. Using the higher density, a sea level based SpaceShaft of the size and shape of the Burj Khalifa could lift 905 metric tons. The Burj Khalifa represents a structure that is approximately 1% the size (height and volume) of a SpaceShaft.
Buoyancy and upthrust
Buoyancy is a force that exists because of a potential difference due to the density differences between at least two fluids. This potential difference reaches a point of equilibrium when the weight of the two fluids is equalized. What this means is that a vessel, with a shell of negligible mass, containing a lighter fluid than that of the environment in which it is submerged will have a higher buoyancy value at a larger depth than the value it will have when close to the surface of the containing fluid. Assuming an imaginary column of such vessels, the summation of the buoyancy harnessed from the stacked vessels at a depth larger than at the point of zero buoyancy, i.e. with respect to the surface of the surrounding liquid, is what is informally called by the developers of the SpaceShaft the upthrust of the system.The upthrust formula
The total upthrust of a SpaceShaft equals the payload that it can carry at its top while still being in a neutral floating state. The total upthrust is computed assuming that:- the SpaceShaft’s cross sectional area may vary in function of the altitude :
- the SpaceShaft’s mass per unit length (i.e. the consolidated mass of its structure) may vary in function of the altitude:
where the altitude is defined as with the distance of the Earth's center and the Earth's radius.
The net vertical upthrust per unit length acting upon the SpaceShaft at a given altitude , is composed of:
- the upward buoyancy force ;
- the upward centrifugal force due to the Earth's rotation;
- the downward weight force .
The net vertical upthrust per unit length becomes then: . The different composing forces are detailed below.
Upward buoyancy force
The buoyancy forceBuoyancy
In physics, buoyancy is a force exerted by a fluid that opposes an object's weight. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the...
per unit length of the SpaceShaft at a given altitude is computed as
in which is the air density and the gravitational acceleration
Gravitational acceleration
In physics, gravitational acceleration is the acceleration on an object caused by gravity. Neglecting friction such as air resistance, all small bodies accelerate in a gravitational field at the same rate relative to the center of mass....
defined by:
Upward centrifugal force
The centrifugal forceCentrifugal force
Centrifugal force can generally be any force directed outward relative to some origin. More particularly, in classical mechanics, the centrifugal force is an outward force which arises when describing the motion of objects in a rotating reference frame...
due to the Earth's rotation is computed as:
in which is the constant Earth's rotation speed given by:
in which is the duration of a day on Earth in seconds.
Downward weight force
The downward weight force per unit length is simply computed as:The total upthrust
The total upthrust for a SpaceShaft with bottom section at an altitude and top section atan altitude is then given by the integration of the vertical upthrust over the SpaceShaft's length:
or, using the expressions for the respective upthrust components given above:
Considering a SpaceShaft that is in a neutral floating state , the above expression in which is replaced by any altitude between and gives the vertical buckling force
Buckling
In science, buckling is a mathematical instability, leading to a failure mode.Theoretically, buckling is caused by a bifurcation in the solution to the equations of static equilibrium...
the upper parts of the SpaceShaft exert on the lower parts of the SpaceShaft at that altitude. This allows to evaluate the vertical stresses in the internal of the SpaceShaft and, hence, to choose the appropriate materials and design to cope with these stresses.
In case the SpaceShaft is not in a neutral floating state , the SpaceShaft must be anchored as discussed above. The anchoring force will then equal for the SpaceShaft to be in mechanical equilibrium
Mechanical equilibrium
A standard definition of static equilibrium is:This is a strict definition, and often the term "static equilibrium" is used in a more relaxed manner interchangeably with "mechanical equilibrium", as defined next....
. This force can then be used to evaluate the stresses in the anchoring system.
Simplification
In many cases the weight per unit length of the SpaceShaft will be proportional to its cross sectional area: where is the SpaceShaft's own density. The total upthrust now becomes:Practical Example
Using the simplified global upthrust formula above, computations can be carried out for different shapes of a SpaceShaft placed at the equator and starting at an altitude of and reaching up to . SpaceShafts with different cross sectional variations and at equilibrium with no payload (zero global upthrust) are studied while the SpaceShaft’s proper material density is computed inversely to obtain a zero global upthrust.The cross sectional variation of the SpaceShaft in this example study is given by the following formula:
in which is the minimum remaining cross sectional area at the top of the SpaceShaft,
is the cross sectional area of a perfect cylindrical SpaceShaft having the same total
volume as the current SpaceShaft, the case of . All studied SpaceShafts will have the same total volume and, hence, will represent approximately the same material cost.
The computations are done using and and . The different shapes of the studied SpaceShaft corresponding to different values of is shown below.
The total internal vertical forces along the SpaceShaft for the different shapes and the corresponding internal vertical stresses are depicted below:
In the case of the cubic shape , the internal force reaches a maximum of 185,000 kN (about 18,500 tons) at an altitude of about 15 km while the maximum vertical stresses read 73 kN/m (about 7.3 tons per m) at an altitude of about 23 km.
Lateral forces=
To cope with different lateral forces such as wind and Coriolis
Coriolis
Coriolis may refer to:* Gaspard-Gustave Coriolis , French mathematician, mechanical engineer and scientist* Coriolis effect, the apparent deflection of moving objects from a straight path when viewed from a rotating frame of reference...
forces (for instance, when a shuttle is moving rapidly upward within the Spaceshaft), a number of stabilization techniques are envisaged that can be categorized in two main categories:
- Passive techniques:
- application of lightweight tensegrityTensegrityTensegrity, tensional integrity or floating compression, is a structural principle based on the use of isolated components in compression inside a net of continuous tension, in such a way that the compressed members do not touch each other and the prestressed tensioned members delineate the...
like structures to enhance the stiffness of the SpaceShaft artefact
- application of lightweight tensegrity
- Active techniques:
- spoke-like mooring systems at different altitudes (much like antenna-masts)
- computer-controlled propellerPropeller (aircraft)Aircraft propellers or airscrews convert rotary motion from piston engines or turboprops to provide propulsive force. They may be fixed or variable pitch. Early aircraft propellers were carved by hand from solid or laminated wood with later propellers being constructed from metal...
nacelles at different altitudes to combat side winds
It is important to investigate how a SpaceShaft can remain in equilibrium under the effect of lateral forces in order to design appropriately the different aforementioned stabilization techniques. Mechanical equilibrium
Mechanical equilibrium
A standard definition of static equilibrium is:This is a strict definition, and often the term "static equilibrium" is used in a more relaxed manner interchangeably with "mechanical equilibrium", as defined next....
of the SpaceShaft is reached if the sum of all forces and the sum of all moments around some reference point (in this case the anchor point at the bottom of the SpaceShaft) are zero. In absence of any active stabilization technique, the SpaceShaft will no longer a straight vertical artefact but will have to lean against the side forces that are then compensation by the SpaceShaft's own weight force.
To model the mechanical static equilibrium of a SpaceShaft, the different acting forces and moments are listed below:
- the external forces
: wind forces, Coriolis forces,... - the SpaceShaft's own weight force
- the SpaceShaft's anchor force
- mooring forces and/or propeller forces at discrete altitudes
where with the number of mooring stations or propeller nacelles; altitude increases with the index ; - the moment
generated by the external forces; - the moment
generated by the SpaceShaft's own weight; - the moments
generated by the mooring stations and propeller nacelles where with the number of mooring stations or propeller nacelles; - the moment
caused by any possible bending of the SpaceShaft whose stiffness is resisting to such bending.
The overall mechanical static equilibrium of a SpaceShaft undergoing lateral forces is then expressed by the following two equations:
The subsequent subsections will address each of the individual terms in these equations in more detail.
Wind forces and moments
A very precise prediction of the wind forces with a given wind profile at different altitudes can only be done using full-blown three-dimensional CFDComputational fluid dynamics
Computational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with...
packages that have the capability to model correctly the full shape of the SpaceShaft. These packages use the three dimensional Navier-Stokes equations augmented with a decent turbulence model. Furthermore, the air flow around the SpaceShaft will in most cases be inherently unsteady as a so called von Karman vortex street
Von Kármán vortex street
A Kármán vortex street is a term in fluid dynamics for a repeating pattern of swirling vortices caused by the unsteady separation of flow of a fluid over bluff bodies...
may occur at certain altitudes with certain wind speeds. To cope with such unsteadiness, the SpaceShaft must have enough internal damping to avoid mechanical resonance
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
effects.
However, for overall engineering purposes, one can use the aerodynamic drag coefficient
Drag coefficient
In fluid dynamics, the drag coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment such as air or water. It is used in the drag equation, where a lower drag coefficient indicates the object will have less aerodynamic or...
at different altitudes to evaluate the overall side wind force
:in which the aerodynamic drag coefficient , the wind speed vector
, the atmospheric air density and the reference aerodynamic cross sectional length are all dependent on the position along the SpaceShaft. Note that does not exactly equals the altitude as the SpaceShaft may be bending and not take an exact vertical position when in a static mechanical equilibrium state. represents the total axial length of the SpaceShaft.Assuming a SpaceShaft with a circular horizontal cross sectional shape, the value of the aerodynamic drag coefficient will be about 0.5 if the wind direction is horizontal too. In case the wind is not purely horizontal, the SpaceShaft will present an elliptical shape with a lower value of the aerodynamic drag coefficient.
The total moment
around the anchor point due to wind forces is given by (while using the vectorproduct operator ):in which
denotes the actual position vector along the axis of the SpaceShaft relative to its anchor point on the Earth’s surface.Weight forces and moments
The weight force due to gravitation is computed using the expression for the simplified upthrust:in which the radial distance from the Earth's center becomes now a function of the position along the (most probably bended) SpaceShaft.
The weight force moment $\vec{M}_G$ relative to the SpaceShaft's anchor point is computed as follows:
Internal stiffness moments
The SpaceShaft will resist to being bended by generating an internal stiffness moment that is assumed to be linear with the local bending vector representing the bending magnitude and the axis of rotation of the bending. This assumption is valid as long as the deformation is within the range of elastic deformation. We use as the proportionality factor whose actual value is depending on the designed shape of the SpaceShaft and the used materials and my vary along the SpaceShaft's axis. The total moment relative to the SpaceShaft's anchor point due to internal stiffness moments is then given by:Mooring forces and moments
The mooring forces where will generate a total moment around the SpaceShaft's anchor point that is given by:in the mooring point or the propeller nacelle location
where is the known length along the SpaceShaft's axis. However the actual position will depend on the amount of bending.We shall assume in the subsequent development that the mooring forces
are only non-zero when moving the predicted equilibrium position. The modelling of this process requires a more complex dynamic equilibrium model that also accounts for the acceleration forces. For now, we are only interested in predicting the static equilibrium position of the SpaceShaft whereby all mooring forces are equal to the null vector.Numerically predicting the equilibrium position
Using one-dimensional linear Finite Elements placed in the three dimensional space and using the appropriate and well-known Finite Element techniquesFinite element method
The finite element method is a numerical technique for finding approximate solutions of partial differential equations as well as integral equations...
, to above set of equations describing the static mechanical equilibrium of the SpaceShaft can be solved for the three dimensional space coordinates of the end points of the one-dimensional Finite Elements.
In principle, the set of mechanical equilibrium equations are non-linear in the sense that for instance the aerodynamic drag coefficient is dependent on the local bending of the SpaceShaft and that the radial distance is a non-linear function of the length along the axis of the (bended) SpaceShaft. Hence, some kind of iterative Newton-Raphson technique will have to be used to solve the equations.
Nonetheless, the equations can be linearized under the assumption that the SpaceShaft is only bending a little and that it has no internal stiffness: . Under these assumptions, the aerodynamic drag coefficient can be considered independent on the SpaceShaft's position and the length along the axis of the SpaceShaft is approximately equal to and, hence, the differentials and will be identical. Also, the radial distance becomes a purely linear function.
Coriolis forces
Any moving object that follows a path whereby the distance to the axis of rotation of the Earth is changing, will undergo the so called Coriolis force.In the case of a SpaceShaft, Coriolis forces can occur in two cases:
- during deployment and FIFO delivery of the SpaceShaft whereby the SpaceShaft is intermittently moving upward
- a nacelle is moving quickly up- or downwards within the SpaceShaft
The vertical speed during the deployment and FIFO delivery will be very slow and in the order of 0.1 m/s. However, the mass of the SpaceShaft as such can be very large. A SpaceShaft that is 50 km tall with a constant cross sectional area of will represent a mass of about kg.
Placed at the equator, a SpaceShaft will undergo a global Coriolis force of about 300 N towards the west. This force can be considered negligible to other lateral forces.
If a nacelle with a mass of 5000 kg is moving upward within the SpaceShaft (placed at the equator) at a speed of 40 m/s (or 144 km/h), it will generate a coriolis force on the SpaceShaft of about 30 N, which, again, is a very small force compared to other lateral forces that may act upon the SpaceShaft.
Relation to Space Elevator=
A Space Elevator is a tethered satellite
Satellite
In the context of spaceflight, a satellite is an object which has been placed into orbit by human endeavour. Such objects are sometimes called artificial satellites to distinguish them from natural satellites such as the Moon....
(counterweight
Counterweight
A counterweight is an equivalent counterbalancing weight that balances a load.-Uses:A counterweight is often used in traction lifts , cranes and funfair rides...
) located at an altitude of ~100,000 km. The tether of Space Elevator offers a purchase point for an electrically driven elevator. The advantage of a Space Elevator is that the climbers have an altitude range of 0 to 100,000 km as opposed to the SpaceShaft operating in an altitude range of 0 to 100 km, and potentially 0 to 300 km. The disadvantages of the Space Elevator (as of the time of this writing) are:
- a) it will require a Carbon Nano-Tube (CNT) tether, which exceeds our current manufacturing knowledge, and,
- b) it will require being located at or near the equator.
The SpaceShaft can be located at latitudes away from the equator. Although the altitudes reached by the SpaceShaft are significantly lower than that of the Space Elevator, many of the envisioned missions of the space elevator (listed at the top of this article) can easily be provided by a SpaceShaft. Therefore, the two distinct advantages the SpaceShaft has are:
- a) it can be built with current knowledge of materials science, and
- b) it can be located near populated areas.