Difference between revisions of "Space elevator"

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Naturally, the Space ''Tower'' would be crushed under it's own weight, so the idea of a Space ''Elevator'' was born. In 1960, Yuri N. Artsutanov,<ref>[http://en.wikipedia.org/wiki/Yuri_N._Artsutanov Wikipedia article about Yuri N. Artsutanov]</ref> a Russian engineer, conceived the possibility of using a "skyhook" where a satellite is inserted into geosynchronous orbit and a cable lowered to the Earth's surface. As the cable is lowered, a counterweight is attached to the satellite and pushed into higher and higher orbit, thus keeping the cable's center-of-mass in a constant position. Once attached, the cable would be under tension, allowing payloads to be transported into the satellite's orbit.  
 
Naturally, the Space ''Tower'' would be crushed under it's own weight, so the idea of a Space ''Elevator'' was born. In 1960, Yuri N. Artsutanov,<ref>[http://en.wikipedia.org/wiki/Yuri_N._Artsutanov Wikipedia article about Yuri N. Artsutanov]</ref> a Russian engineer, conceived the possibility of using a "skyhook" where a satellite is inserted into geosynchronous orbit and a cable lowered to the Earth's surface. As the cable is lowered, a counterweight is attached to the satellite and pushed into higher and higher orbit, thus keeping the cable's center-of-mass in a constant position. Once attached, the cable would be under tension, allowing payloads to be transported into the satellite's orbit.  
  
−
== Equations ==
+
==Equations==
 
This section is derived from a paper by P. K. Aravind Department of Physics, Worcester Polytechnic Institute<ref>http://users.wpi.edu/~paravind/Publications/PKASpace%20Elevators.pdf</ref>
 
This section is derived from a paper by P. K. Aravind Department of Physics, Worcester Polytechnic Institute<ref>http://users.wpi.edu/~paravind/Publications/PKASpace%20Elevators.pdf</ref>
  
−
Taper ratio
+
'''Calculation of taper ratio'''
  
−
Mass of cable
+
A tapered cable offers better performance than a constant section cable.  The taper ratio equation is the following:
 +
 
 +
Taper ratio=e(Rpg/2T*((R/Rg)<sup>3</sup>-3(R/RG)+2))
 +
 
 +
Where:
 +
{| class="wikitable"
 +
|
 +
|
 +
|
 +
|Mars
 +
|Earth
 +
|-
 +
|Mass of planet
 +
|M
 +
|kg
 +
|6.42E+23
 +
|5.98E+24
 +
|-
 +
|Radius of planet
 +
|R
 +
|m
 +
|3.40E+06
 +
|6.37E+06
 +
|-
 +
|Radius of geostationnary orbit
 +
|Rg
 +
|m
 +
|2.04E+07
 +
|4.22E+07
 +
|-
 +
|Gravity
 +
|g
 +
|m/s2
 +
|3.8
 +
|9.81
 +
|-
 +
|
 +
|T (GPa)
 +
|p (kg/m3)
 +
| colspan="2" rowspan="1" |Taper ratio
 +
|-
 +
|Steel
 +
|5
 +
|7900
 +
|4662520
 +
|1.74E+33
 +
|-
 +
|Zylon
 +
|5.8
 +
|1540
 +
|13
 +
|3.85E+05
 +
|-
 +
|Kevlar
 +
|3.6
 +
|1440
 +
|49
 +
|2.60E+08
 +
|-
 +
|Carbon nanotube
 +
|130
 +
|1300
 +
|1.1
 +
|1.6
 +
|}
 +
'''Calculation of cable length'''
 +
 
 +
The calculation for hte cable length, with the external cable acting as a counterweight for the internal cable, is the following:
 +
 
 +
H=R/2*(sqrt(1+8(Rg/R)<sup>3</sup>)-1)
 +
 
 +
This gives a length of 69 000 km for Mars and 159000 km for Earth.
 +
 
 +
Based on these numbers, the author finds that a counterweighted carbon nanotubes cable capable of supporting a 1000 kg lifter would mass 150 tonnes.
 +
 
 +
Based on these proportions, a similar cable on Mars would mass about 75 tonnes.  A cable made from Zylon , for the same capabilities, might mass 1000 tonnes.
 +
 
 +
The throughput of such a cable would be quite low. Supposing a velocity of 1000 km per hour travel on the cable would require 69 hours, or almost 3 days.  With a cargo of 500 kg on the climber, the yearly transfer rate would be about 120 trips per year, or about 60 tonnes.  This is clearly inadequate for a space settlement and such a structure would need to support a number of vehicles moving simultaneously, carrying higher masses and probably at higher velocities.  For 600 tonnes per year the cable might mass 10 000 tonnes, and for 6000 tonnes per year 60 000 tonnes.
  
 
==Orbit-to-surface concept==
 
==Orbit-to-surface concept==
 
For the purpose of building an [[autonomous colony]] the transportation from orbit down to the Martian surface is the main focus. For this use case a climbing technology is not necessary, and the elevator is much simpler. Only a brake needs to be installed in the cabin, preventing free falling. In this case every transport down the rope consumes a new cabin.  
 
For the purpose of building an [[autonomous colony]] the transportation from orbit down to the Martian surface is the main focus. For this use case a climbing technology is not necessary, and the elevator is much simpler. Only a brake needs to be installed in the cabin, preventing free falling. In this case every transport down the rope consumes a new cabin.  
  
−
=== Advantages ===
+
===Advantages===
  
 
*No fuel is required to be burnt. This concept might be cheaper than traditional [[rocketry]], and potentially reduces the mass to launch off Earth.
 
*No fuel is required to be burnt. This concept might be cheaper than traditional [[rocketry]], and potentially reduces the mass to launch off Earth.
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Providing the Deimos problem can be solved, a space elevator is much easier on Mars than on the Earth.  Due to the lower gravity and smaller length, a Mars elevator could be made from existing materials.
 
Providing the Deimos problem can be solved, a space elevator is much easier on Mars than on the Earth.  Due to the lower gravity and smaller length, a Mars elevator could be made from existing materials.
  
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Mars space elevator characteristics:
 
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{| class="wikitable"
 
−
|+
 
−
!
 
−
!Capacity (tonnes per day)
 
−
!Length
 
−
!Tensile strength
 
−
!Mass
 
−
!Cost to orbit
 
−
|-
 
−
|Near term
 
−
|
 
−
|
 
−
|
 
−
|
 
−
|
 
−
|-
 
−
|Mid term
 
−
|
 
−
|
 
−
|
 
−
|
 
−
|
 
−
|-
 
−
|Long term
 
−
|
 
−
|
 
−
|
 
−
|
 
−
|
 
−
|}
 
 
The space elevator uses less energy than a chemical rocket for the same service.  On Mars, propellant is produced from electricity so the costs are directly comparable.  Due to the rocket equation, a rocket necessary requires more energy than a space elevator.  However, the mass ratio to reach orbit on Mars is 3, while the mass ratio for Earth is 19.  So the advantage on Mars is less important than for the Earth.
 
The space elevator uses less energy than a chemical rocket for the same service.  On Mars, propellant is produced from electricity so the costs are directly comparable.  Due to the rocket equation, a rocket necessary requires more energy than a space elevator.  However, the mass ratio to reach orbit on Mars is 3, while the mass ratio for Earth is 19.  So the advantage on Mars is less important than for the Earth.
−
 
 
==Preliminary economical analysis==
 
==Preliminary economical analysis==
  

Revision as of 12:31, 16 May 2019

An artists impression of a "climber" ascending a space elevator from Earth. A similar model can be used on Mars.
Space elevator and radius of Martian moons.

The transport from Mars' surface to Mars' orbit and vice versa can be achieved by a Space Elevator. The idea is to install a high-tensile rope from the surface to the synchronous orbit and a certain length beyond, connected to a counter weight.

Since the gravity of Mars is lower than the gravity of Earth the requirements to the tensile strength of the rope is less, making this construction easier.

Original concept

The original concept for a "Space Tower" can be traced back to Konstantin Tsiolkovsky,[1] a Russian rocket and space pioneer. He is quoted as saying in 1895:[2]

"...on the tower, as one climbed higher and higher up it, gravity would decrease gradually; and if it were constructed on the Earth's equator and, therefore, rapidly rotated together with the earth, the gravitation would disappear not only because of the distance from the centre of the planet, but also from the centrifugal force that is increasing proportionately to that distance. The gravitational force drops... but the centrifugal force operating in the reverse direction increases. On the earth the gravity is finally eliminated at the top of the tower, at an elevation of 5.5 radii of the earth (22,300 miles)..."

Naturally, the Space Tower would be crushed under it's own weight, so the idea of a Space Elevator was born. In 1960, Yuri N. Artsutanov,[3] a Russian engineer, conceived the possibility of using a "skyhook" where a satellite is inserted into geosynchronous orbit and a cable lowered to the Earth's surface. As the cable is lowered, a counterweight is attached to the satellite and pushed into higher and higher orbit, thus keeping the cable's center-of-mass in a constant position. Once attached, the cable would be under tension, allowing payloads to be transported into the satellite's orbit.

Equations

This section is derived from a paper by P. K. Aravind Department of Physics, Worcester Polytechnic Institute[4]

Calculation of taper ratio

A tapered cable offers better performance than a constant section cable. The taper ratio equation is the following:

Taper ratio=e(Rpg/2T*((R/Rg)3-3(R/RG)+2))

Where:

Mars Earth
Mass of planet M kg 6.42E+23 5.98E+24
Radius of planet R m 3.40E+06 6.37E+06
Radius of geostationnary orbit Rg m 2.04E+07 4.22E+07
Gravity g m/s2 3.8 9.81
T (GPa) p (kg/m3) Taper ratio
Steel 5 7900 4662520 1.74E+33
Zylon 5.8 1540 13 3.85E+05
Kevlar 3.6 1440 49 2.60E+08
Carbon nanotube 130 1300 1.1 1.6

Calculation of cable length

The calculation for hte cable length, with the external cable acting as a counterweight for the internal cable, is the following:

H=R/2*(sqrt(1+8(Rg/R)3)-1)

This gives a length of 69 000 km for Mars and 159000 km for Earth.

Based on these numbers, the author finds that a counterweighted carbon nanotubes cable capable of supporting a 1000 kg lifter would mass 150 tonnes.

Based on these proportions, a similar cable on Mars would mass about 75 tonnes. A cable made from Zylon , for the same capabilities, might mass 1000 tonnes.

The throughput of such a cable would be quite low. Supposing a velocity of 1000 km per hour travel on the cable would require 69 hours, or almost 3 days. With a cargo of 500 kg on the climber, the yearly transfer rate would be about 120 trips per year, or about 60 tonnes. This is clearly inadequate for a space settlement and such a structure would need to support a number of vehicles moving simultaneously, carrying higher masses and probably at higher velocities. For 600 tonnes per year the cable might mass 10 000 tonnes, and for 6000 tonnes per year 60 000 tonnes.

Orbit-to-surface concept

For the purpose of building an autonomous colony the transportation from orbit down to the Martian surface is the main focus. For this use case a climbing technology is not necessary, and the elevator is much simpler. Only a brake needs to be installed in the cabin, preventing free falling. In this case every transport down the rope consumes a new cabin.

Advantages

  • No fuel is required to be burnt. This concept might be cheaper than traditional rocketry, and potentially reduces the mass to launch off Earth.
  • Smooth landing, suitable for fragile machinery.
  • If surface to orbit is implemented, the elevator end can serve as a launch platform, as it is moving faster than Mars escape velocity.

Challenges

The moons Phobos and Deimos are in low orbit and intersect the cable in intervals. To cope with this situation an active adjustment of the cable's position is required to avoid a collision. Bringing down Phobos would abolish part of the problem.

The Deimos problem might be solved by replacing the extension of the elevator by a counterweight located below Deimos' orbit.

Alternatively, a non equatorial space tether[5] might allow for sufficient distance from the orbit of Phobos, if such an infrastructure can be build and put in place.

Phobos elevator

A variation on the space elevator idea is the Phobos elevator[6]. This would significantly reduce the cost of lifting material from the Surface of Mars by using a suspended tether down into the martian atmosphere and an extended tether up towards space. Phobos itself would serve as source of the construction material for the elevator.

Current Technological Approach

There are already competitions to build climbing technologies, aiming to construct a machine that is able to climb a cable with a velocity of at least 1 meter per second.

Providing the Deimos problem can be solved, a space elevator is much easier on Mars than on the Earth. Due to the lower gravity and smaller length, a Mars elevator could be made from existing materials.

The space elevator uses less energy than a chemical rocket for the same service. On Mars, propellant is produced from electricity so the costs are directly comparable. Due to the rocket equation, a rocket necessary requires more energy than a space elevator. However, the mass ratio to reach orbit on Mars is 3, while the mass ratio for Earth is 19. So the advantage on Mars is less important than for the Earth.

Preliminary economical analysis

  • Landing on Mars when arriving from Earth may require very little fuel, as the atmosphere can serve to break the vehicle. Maneuvering to reach a space elevator to transfer materials may require considerable amounts of propellant. This could reduce the interest in the development of the technology.

In Science-Fiction

  • Red Mars, Green Mars, and Blue Mars by Kim Stanley Robinson (1992, 1993, 1996). Space elevators on Earth and on Mars where the cables are made of carbon nanotube which are manufactured on an asteroid. The resulting cable is then lowered into the atmosphere to be attached to the surface. An asteroid is used as a counterweight. During the Mars revolution, the Red Mars novel graphically depicts the effects of a catastrophic space elevator failure, when the cable is severed in orbit.[7]
  • In Star Trek: Voyager episode Rise the idea of a space elevator is part the story.[8]

Open issues

  • What tensile strength is required?
  • Is it possible to make a space elevator for Mars with known technology?
  • How much would it cost?
  • What negative side effects has a none-equatorial space elevator (as a possible solution to avoid intersections with the moon's orbit)?
  • For the transport from Earth to Mars using a space elevator for the landing operations on Mars: What is the mass reduction to launch off Earth compared with conventional Mars landing technology?
  • What is the financial benefit compared with conventional rocketry?

See also

External links

References

  1. ↑ Wikipedia article about Konstantin Tsiolkovsky
  2. ↑ Moon with a View: Or, What Did Arthur Know... and When Did He Know it? - Richard C. Hoagland, 2005.
  3. ↑ Wikipedia article about Yuri N. Artsutanov
  4. ↑ http://users.wpi.edu/~paravind/Publications/PKASpace%20Elevators.pdf
  5. ↑ https://gassend.net/publications/NonEquatorialUniformStressSpaceElevators.pdf
  6. ↑ https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20030065879.pdf
  7. ↑ Space Elevators in fiction.
  8. ↑ Space Elevator in Star Trek

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