ORBITAL LOOP

An endless tether is launched in an eccentric Earth orbit. It is interspersed with winches and a segmented tube. A sounding rocket or a gun carries cargo to the tube. When the cargo enters the tube, it is accelerated by friction to the orbital velocity. Half of the orbital energy of the loop is transferred to the cargo, while the other half is wasted as heat. The orbital loop is durable but somewhat unstable. The minimum mass of a steel loop is 1000 tons.

Cargo is enclosed in a ball-shaped container. A thick coating of silicon rubber (e.g., Dow Corning 3-6077 RTV) protects the container from heat and vibration. Gas produced by ablation of the rubber generates friction which transfers the orbital energy to the cargo. The tube is tapered to compensate for the ablation. When the container has attained orbital velocity, it drops off, and is carried to its final destination by a variety of economical, low-thrust propulsion techniques.

As the loop follows the eccentric orbit, its velocity and tension undergo periodic changes, not unlike those of a pendulum or a swing. These periodic changes make it possible to restore the loop's energy without the use of propellants or electrodynamic tethers. Winches exert a periodic force on the loop which is synchronized with the orbital movement of the loop. Much like a child "pumping" a playground swing, the periodic force replenishes the energy of the loop.

BIBLIOGRAPHY

Andrew Nowicki, "Diversity," The Trumpeter, Vol. 10, No. 2, Spring 1993, pp. 65-68.

DETAILS

Orbital loop

Orbital loop

Cargo approaching the tube

Cargo approaching the tube (large image 47k)

Electromagnets can transfer momentum to the cargo with a greater efficiency than the tube, but they are massive and require more maintenance.

The gravity of the oblate Earth perturbs the loop. The perturbation results in a precession of the orbital plane, which means that the orbital plane rotates about the axis of Earth rotation. The period of precession is on the order of several months. [ref. 1]

The dynamic behavior of the orbital loop is so complex that it can be analyzed by computer simulation only. The winches can stabilize the loop [ref. 2-5], but wings interacting with the ionosphere may be more efficient.


The optimum orbit of the loop corresponds with the greatest "lineal power," which is defined as the power generated by the loop per lineal meter of the loop, per tensile strength of its tethers. If no energy is spent on maintaining the dynamic stability of the loop, its lineal power is:
p = (V1 -V2)/(V1 T)
where:
P is lineal power (power per lineal meter per tensile strength)
V1 is maximum velocity
V2 is minimum velocity
T is orbital period = 2(PI)(A3/K)0.5 [ref. 6]
K is gravitational constant times mass of the Earth = 4.0E14 m3s-2
A is semi-major axis

Length of the loop (i.e. Total length of its tethers) is: L = V1 T

Velocity at a given point along the elliptic orbit is:
V = (K(2/R-1/A))0.5 [ref. 7]

R is defined as the distance between center of the Earth and a given point along the orbit. Assuming that the perigee of the loop is 200 kilometers above the Earth's surface, the minimum value of R is R1 = 6,580,000 meters and the maximum velocity is: V1 = (K(2/R1 -1/A))0.5

At the apogee: R = R2 = A+E
where:
E = eccentricity = (A2-B2)0.5
B = semi-minor axis

The loop will collide with the Earth unless the radius of its orbit at the perigee is at least R1.
B = (R1 A)0.5, V2 = (K(2/(A+(A2-R1 A)0.5)-1/A))0.5
The results are summarized in the following chart.

Optimum orbit of the loop

Optimum orbit of the loop

Assuming that the loop has steel tethers, that the maximum tension is 2 GPa, and that half the power is spent on maintaining dynamic stability, the loop can bring its mass to a low Earth orbit in about 6 months. If the loop is integrated into a Moon-Earth momentum exchange, it can bring its mass to a low Earth orbit in 2 weeks.


The most vulnerable parts of the loop are tethers. Damage caused by meteoroids, man-made debris, and oxygen determines the minimum mass of the loop. If adjacent winches are linked by several tethers, the loop can remain operational even if some tethers are broken. In order to reduce damage, tethers should present a large surface area to meteoroids which approach from all directions.

An arcuous tether shown below is lightweight, has a large surface area, and can be flattened when it is wound up inside the winch. Suppose that the loop is composed of N = 10,000 segments, each segment consisting of two parallel, 2 centimeter wide tethers attached to the winches on each end. The distance between adjacent winches oscillates between 3.2 and 7.0 kilometers, so the average tether area exposed to meteoroids is (5.1 km)(2 cm) = 102 m2. There is an X = 0.5 probability that a given tether will be broken by meteoroids or debris in 25 years. [ref. 8] If the tether is broken, the loop must be relaxed to avoid breaking the other tether of the same segment. After the loop has been relaxed, winches slowly pull the operational tether of the damaged segment. Finally, the adjacent winches are joined, thereby eliminating the damaged segment of the loop. If both tethers of the same segment are broken, the loop ruptures, and is unable to carry cargo until it is repaired. Suppose that it takes 4 hours to bring the adjacent winches together after one tether breaks. The probability that the remaining tether breaks during the 4 hour period is Y = X/((25)(365)(6)(2)) = 5E-7. The probability that the loop ruptures in 25 years is Z = 1-(1-XY)N = 0.003.

Arcuous tether

Arcuous tether

The tube that accelerates the cargo is about 200 km long. It is tapered to compensate for the ablated rubber. The tube cannot overheat because the mass of the cargo is 2 orders of magnitude smaller than the mass of the tube. A metal tube is economical, but it may be damaged if the cargo travels faster than 5 km/s (speed of sound in the tube). If the metal tube is used, the cargo must be accelerated to 4 km/s, before it enters the tube. A glass tube reinforced with high modulus graphite fibers is expensive and difficult to assemble in space, but it has the speed of sound of about 10 km/s.

As the tube follows its elliptic orbit, it is subjected to alternating tensile and compressive forces. The compressive force is the greatest when the loop ruptures. To reduce the forces, the tube is divided into loosely fitting telescoping segments. If the cargo container is in jeopardy, the tube segments ahead of the container are moved aside, thereby letting the container out.

Shortly before the cargo is fired from the gun, the altitude of the tube is reduced to the maximum range of the gun. The loop undulates and changes its tension in order to move its tube into the path of the unguided gun projectile. Vertical undulation compromises stability, so the loop must undulate horizontally.

Undulating loop

Undulating loop (large image 30k)

A similar contraption named the electrotube is constantly immersed in the ionosphere, so it experiences a much greater aerodynamic drag and oxygen erosion. A rocket must guide cargo all the way from the Earth to the electrotube. Despite these inconveniences, the electrotube is an attractive precursor of the loop, because its minimum mass is only 100 tons.

A loop orbiting the Moon can carry its mass to a low orbit 17 times faster than a similar loop orbiting the Earth. Low gravity and the absence of atmosphere make it easy to transport containers from the Moon to the perigee of the loop. The same loop can accelerate containers bound for space and slow down containers bound for the Moon.

According to the chart the loop must be highly eccentric to generate the maximum power and carry the maximum tonnage of cargo. The vibration and precession of the loop make it difficult to use more than one independent, eccentric loop in the Earth orbit. Independent loops could either collide or force each other to operate at a reduced capacity. It seems that the best solution to this dilemma is the construction of a multitude of parallel loops attached to each other. If one loop ruptures, it can still work because of the structural support of the adjacent loops.

The orbital loop can launch satellites, stabilize them, and keep them in correct orbit. Satellites attached to the loop do not generate much drag, so the loop does not have to generate much power and does not have to be very eccentric. Several nearly circular satellite loops can coexist in equatorial orbits, with room to spare for one inclined, eccentric, Sun-synchronous loop transporting cargo to space.

REFERENCES

  1. Krafft A. Ehricke, Space Flight, Vol. II -- Dynamics, Van Nostrand, Princeton, 1962 p. 168.
  2. J. V. Breakwell, "Stability of an Orbiting Ring," presented at AIAA 18th Aerospace Sciences Meeting, Pasadena, CA, Jan 14-16, 1980, AIAA-80-0057.
  3. A. M. Fridman, A. I. Morozow, and V. L. Polyachenko, "The Destruction of a Continuous Ring Revolving Around a Gravitating Center," Astrophysics and Space Science, Vol. 103, 1984, pp. 137-142.
  4. Vladimir Vasilievich Beletskii and Evgenii M. Levin, "Dynamics of Space Tether Systems," Advances in the Astronautical Sciences Vol. 83, Univelt 1993, pp. 465-483.
  5. Vladimir Vasilievich Beletskii and Evgenii M. Levin, "Stability of a Ring of Connected Satellites," Acta Astronautica, Vol. 12, 1985, pp. 765-769.
  6. Krafft A. Ehricke, Space Flight, Vol. I -- Environment and Celestial Mechanics, Van Nostrand, Princeton, 1960, p. 266.
  7. Ibid. p. 277.
  8. William. A. Bacarat and C. L. Butner, Tethers in Space Handbook, NASA, 1986, page 4-32.