There are usually objects at the ends of the tether which are more massive than the tether itself. An introductory handbook on tethers is available Carroll , and many prospective tether applications are described by Carroll A tether in orbit will experience a gravity gradient force orienting it toward the local vertical. In LEO this force is about 4 x 10 -4 gravities per kilometer from the center of mass of the tethered system.
The tether may oscillate about the local vertical. These oscillations can be broken into components parallel and perpendicular to the plane of orbital motion. The out-of-plane potential function is symmetrical with respect to position and velocity. The in-plane potential function is not symmetrical. Tension is greater for a swing in the direction of orbital motion posigrade than it is for a swing contrary to the direction of orbital motion retrograde.
Since the tether exerts a net force on the mass at either end of it, the path the mass follows is not a free orbit. If an object is released by a hanging tether of length , the orbits of the two end masses will be separated by at that point and by about 7 half an orbit later. If release is from the top or bottom of the swing of a widely swinging tether, the initial separation will again be and the separation half an orbit later will be about A current-carrying tether in orbit around a body with a significant magnetic field such as Earth or Jupiter, but not the Moon or Mars experiences a JxB magnetic force perpendicular to both the tether and the magnetic field.
This is the force that results when an electric current of density J is passed through a magnetic field of inductance B. The tether will usually be held close to the local vertical by gravity gradient forces, so the direction of thrust is not arbitrarily selectable and it will generally have an out-of-plane component which varies with time. Appropriate current control strategies will be necessary to allow use of electrodynamic tethers as efficient thrusters. Reasonable estimates of power per thrust are 2 to 8 kilowatts per newton, depending on the orbital inclination.
For Earth, the lower power consumption is at high inclinations, where fewer lines of the magnetic field are crossed. One would expect the best electrodynamic tether material to be that with the highest specific conductivity- lithium or sodium. However, these high specific conductivity materials are not very dense and therefore have a low areal conductivity. That is, wire made of lithium or sodium is larger in diameter than wire with the same conductivity but made of a more dense material, such as copper.
Typical electrodynamic tethers operating at kilovolt potentials must be insulated against current loss. Because insulation is of roughly the same thickness whether it is applied to small-or-large-diameter wire, the less dense conducting wires require more massive insulation. Tradeoffs between high specific conductivity and high areal conductivity must therefore be studied for each application. Tether materials are subject to degradation in the space environment.follow site
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High-strength plastics will be degraded by ultraviolet and ionizing radiation and by atomic oxygen in LEO. The effects of these degradational influences and the utility of protective coatings must be studied. Although tethers are typically quite thin, their great length gives them a large impact area. Thus, they have a significant chance of failure due to micrometeoroid impact. This chance is conservatively estimated to be 1 cut per kilometer-year of exposure of a heavily loaded 1-millimeter-thick tether in LEO. The risk of system failure can be reduced by using multiple independent strands or a tape.
While a tape would be hit more often, a micrometeoroid would only punch a hole in it and not sever it, as it might a single strand. However, additional insulation would be required for multiple strands or a tape. Tether Propulsion Basics The simplest operation with a tether is to raise or lower an object and release it from a hanging tether. Since a tethered object is not in a free orbit the tether exerts a net force on it , this method can be used to change velocity without using rocketry.
Even in this nominally hanging case, there will be some libration of the tether. By controlling the tether tension and thus mechanically pumping energy into these librations like a child pumping a swing , the tether can be made to swing. The characteristic velocity, V c , of a tether can be defined as the square root of its specific strength that is, its tensile strength divided by its density : where s is the tensile strength that is, force per unit area which the tether can withstand without breaking and p is the density.
These characteristic velocities incorporate an adequate safety factor to account for manufacturing variations in the material and for degradation in use. The higher the effective V c , the lower the tether mass for a given operation. The characteristic velocity just defined is for a spinning tether. The effective characteristic velocity depends on the type of tether operation. To convert Vc for a spinning tether to V c for some other operation, multiply by the factor given below. Thus, to impart a velocity change much less than V c to a unit payload mass, the ratios of required tether mass to that of a spinning tether are as follows: The velocity that a tether imparts to a payload depends on the orbital velocity of the tether, the speed at which it is swinging or spinning, and the length of the tether.
The tether can be lighter than its tip mass if the desired velocity change is much lower than the characteristic velocity. As the desired velocity approaches V c , the mass of the tether becomes appreciable. A number of other materials obtain 10 to 20 GPa in some samples on the nano scale, but translating such strengths to the macro scale has been challenging so far, with, as of , CNT-based ropes being an order of magnitude less strong, not yet stronger than more conventional carbon fiber on that scale.
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Electrodynamic tethers, such as the one used on TSS-1R, [ clarification needed ] may use thin copper wires for high conductivity see EDT. There are design equations for certain applications that may be used to aid designers in identifying typical quantities that drive material selection.
Space elevator equations typically use a "characteristic length", L c , which is also known as its "self-support length" and is the length of untapered cable it can support in a constant 1 g gravity field. Hypersonic skyhook equations use the material's "specific velocity" which is equal to the maximum tangential velocity a spinning hoop can attain without breaking:. These values are used in equations similar to the rocket equation and are analogous to specific impulse or exhaust velocity.
The higher these values are, the more efficient and lighter the tether can be in relation to the payloads that they can carry. Eventually however, the mass of the tether propulsion system will be limited at the low end by other factors such as momentum storage. Proposed materials include Kevlar , ultra high molecular weight polyethylene , [ citation needed ] carbon nanotubes and M5 fiber.
M5 is a synthetic fiber that is lighter than Kevlar or Spectra. For gravity stabilised tethers, to exceed the self-support length the tether material can be tapered so that the cross-sectional area varies with the total load at each point along the length of the cable. In practice this means that the central tether structure needs to be thicker than the tips.
Correct tapering ensures that the tensile stress at every point in the cable is exactly the same. For very demanding applications, such as an Earth space elevator, the tapering can reduce the excessive ratios of cable weight to payload weight. For rotating tethers not significantly affected by gravity, the thickness also varies, and it can be shown that the area, A, is given as a function of r the distance from the centre as follows: .
This equation can be compared with the rocket equation , which is proportional to a simple exponent on a velocity, rather than a velocity squared. This difference effectively limits the delta-v that can be obtained from a single tether. In addition the cable shape must be constructed to withstand micrometeorites and space junk.
This can be achieved with the use of redundant cables, such as the Hoytether ; redundancy can ensure that it is very unlikely that multiple redundant cables would be damaged near the same point on the cable, and hence a very large amount of total damage can occur over different parts of the cable before failure occurs.
Beanstalks and rotovators are currently limited by the strengths of available materials. Although ultra-high strength plastic fibers Kevlar and Spectra permit rotovators to pluck masses from the surface of the Moon and Mars, a rotovator from these materials cannot lift from the surface of the Earth.
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In theory, high flying, supersonic or hypersonic aircraft could deliver a payload to a rotovator that dipped into Earth's upper atmosphere briefly at predictable locations throughout the tropic and temperate zone of Earth. As of May , all mechanical tethers orbital and elevators are on hold until stronger materials are available.
Cargo capture for rotovators is nontrivial, and failure to capture can cause problems. Several systems have been proposed, such as shooting nets at the cargo, but all add weight, complexity, and another failure mode. At least one lab scale demonstration of a working grapple system has been achieved however. Currently, the strongest materials in tension are plastics that require a coating for protection from UV radiation and depending on the orbit erosion by atomic oxygen. Disposal of waste heat is difficult in a vacuum , so overheating may cause tether failures or damage.
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Electrodynamic tethers deployed along the local vertical 'hanging tethers' may suffer from dynamical instability. Pendular motion causes the tether vibration amplitude to build up under the action of electromagnetic interaction. As the mission time increases, this behavior can compromise the performance of the system. Over a few weeks, electrodynamic tethers in Earth orbit might build up vibrations in many modes, as their orbit interacts with irregularities in magnetic and gravitational fields.
One plan to control the vibrations is to actively vary the tether current to counteract the growth of the vibrations. Electrodynamic tethers can be stabilized by reducing their current when it would feed the oscillations, and increasing it when it opposes oscillations. Simulations have demonstrated that this can control tether vibration. Another proposed method is to use spinning electrodynamic tethers instead of hanging tethers. The gyroscopic effect provides passive stabilisation, avoiding the instability. As mentioned earlier, conductive tethers have failed from unexpected current surges.
Unexpected electrostatic discharges have cut tethers e. It may be that the Earth's magnetic field is not as homogeneous as some engineers have believed. Mechanical tether-handling equipment is often surprisingly heavy, with complex controls to damp vibrations. The one ton climber proposed by Dr.
Brad Edwards for his Space Elevator may detect and suppress most vibrations by changing speed and direction.
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The climber can also repair or augment a tether by spinning more strands. The vibration modes that may be a problem include skipping rope, transverse, longitudinal, and pendulum. Tethers are nearly always tapered, and this can greatly amplify the movement at the thinnest tip in whip-like ways. A tether is not a spherical object, and has significant extent. This means that as an extended object, it is not directly modelable as a point source, and this means that the center of mass and center of gravity are not usually colocated. Thus the inverse square law does not apply except at large distances, to the overall behaviour of a tether.
Hence the orbits are not completely Keplerian, and in some cases they are actually chaotic. With bolus designs, rotation of the cable interacting with the non-linear gravity fields found in elliptical orbits can cause exchange of orbital angular momentum and rotation angular momentum.
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