Tether System



3.2 Tether System

Anne DeLion

Nomenclature

cm Center of mass

d Distance from cm to vehicle, m

g Gravitational acceleration, 9.81 m/s2

Iz Area moment of inertia, kg m2

Mz Moment generated by thrust, Nm

p Percentage of Earth’s gravitational acceleration

t Thruster burn time, s

ΔV Delta-velocity, m/s

ω General angular velocity, rad/s

ωz Angular velocity component, rad/s

3.2.1 Introduction

When studying the feasibility of a mission to Mars, we must consider the effects of weightlessness on an astronaut crew. Astronauts spending an extended time in space often experience debilitating effects on their bodies. Their bones become brittle, their muscles atrophy, and upon return to Earth they have lost a significant amount of strength and bone mass. Interplanetary missions require long periods in space, and in a mission such as ours, the crew would spend six months in zero-gravity during Mars transit, two years on the planet’s surface at 0.38g, and over six months in zero-g during Earth return. To offset the weightless effects during the long transit times, one of our mission requirements is the production of artificial gravity to maintain the health and strength of the crew. During both the transit to Mars and the return to Earth, we will create a gravity environment of at least 0.38g. To generate this, we spin, about the center of mass, a vehicle system consisting of a manned module – a habitation module (Hab) for Mars transit and crew living quarters (ERV) for Earth return – tethered to a counterweight. This paper discusses the tether structure we need, and the methods for tether deployment, spin-up, and release for both the Hab and the ERV systems.

3.2.2 Tether Structure

Tether structure relies on several different factors. The tether material we select determines tether mass and diameter. The structure we design needs to be strong and redundant. We also need remain within constraints set by the Human Factors group and the Power group.

Material

Light weight and high strength are the two most important factors for deciding what material to use in the tethers for our mission. Some of the lightest and strongest materials available today are plastics and polyethylenes, and three materials that either have been used in tethers or were suggested as possible choices are Kevlar, Zylon, and Spectra 2000.

Table 3.2.1 Material properties

|Material |Tensile Strength (GPa) |Young’s Modulus (GPa) |Density (kg/m3) |

|Kevlar |3.6 |130 |1440 |

|Spectra 2000 |3.51 |170 |970 |

|Zylon |5.8 |280 |1580 |

To minimize cost, lower weight is more important that higher strength. To remain within that criterion, we discard Zylon first because it is the most dense, although it has the highest tensile strength. Kevlar has roughly the same tensile strength as Spectra 2000 but is 50 per cent more dense. Therefore, we choose Spectra 2000 as the material to use in our tethers1.

Tether Type

Now that we know what material to use, we need to decide what type of tether will connect our vehicles. Since the tether is mission critical, we need a tether design that is redundant to minimize the probability of failure. There are only two choices for tether structure: a single line tether or a multiline tether.

A single line tether is the simplest tether to manufacture and analyze. It is made of one braided strand of material and is easy to manufacture. However, a single line tether is a problem in a long duration mission. Assuming the possibility of losing the mission and returning the astronauts to Earth via the Earth-Mars-Venus-Earth free return, the tether could be in service for over 2 years. The possibility of a micrometeor hitting the tether grows directly with time. The damage resulting from a micrometeor impact could cause the tether to fail, therefore requiring tether redundancy. That means the single line tether needs a backup of at least one or two more single line tethers, which effectively creates a multiline tether.

Even though a multiline tether is a more complicated tether structure than a single line, it has many more advantages. A multiline is roughly the same mass as a single line; that weight is spread out over the various lines that form the tether. We examine two types of multilines: a simple multiline and a HoytetherTM. A simple multiline tether is a more massive single line tether that has been divided into any number of thinner lines. This added mass comes from the redundancy constraint that requires a minimum number of lines as well as a safety margin of redundant lines. The second type of tether we study is the tubular HoytetherTM (Hoytube). This tether is comprised of load-bearing primary lines and initially unstressed secondary lines, which will maintain the load if a primary line is severed.

[pic]

Fig. 3.2.1 Schematic drawings of a) the tubular Hoytether, b) structural detail, and c) damaged primary lines illustrating secondary line backup2.

The use of primary and secondary lines allows the tether to be impacted multiple times and still maintain its load-bearing capabilities. This feature of the Hoytether gives it a much longer lifespan than a single line tether.

Fig. 3.2.2 Survival probability of a failsafe multiline tether versus an equal-mass single line tether2.

The unreeling behavior of the Hoytether also makes it well-suited for our mission. A Hoytether is less likely to get caught in the reel winding during deployment than a single line tether, which decreases the chance of a jam in the reeling mechanism. Since the Hoytether is tubular, it also fits well with the Power group’s design to run a set of cables through the tether from the spent nuclear thermal rocket (NTR) to the HAB on the way to Mars to generate power.

After completing the analysis of the several different tether types, we decide that the Hoytether best fits the mission demands.

Tether Specifications

We need to design the tethers to meet the various requirements of both the Hab and the ERV systems. The Human Factors and the Power groups defined various constraints on each tether. The Human Factors group requires that both systems rotate at a rate of two revolutions per minute (rpm) for the Hab system to generate 0.38g during Mars transit, and the ERV system to generate 1g during the return to Earth. Using the equation for centripetal acceleration,

[pic] (3.2.1)

we find that the Hab is located at 85 meters from its system cm, and the ERV is 223 meters from its system cm (see Figs. 3.3.1 & 3.3.2). The Power group requires the Hab tether to be a tube with a three centimeter interior diameter to run electrical cables safely from the NTR to the Hab.

Along with these constraints and the masses of the manned vehicles and counterweights from various designers, we can design each tether. We find maximum tension by using Eq. 3.2.1, and we design each tether with a safety factor of five, the NASA minimum, so it can withstand five times the maximum tension before failing. Also, we assume a tether reel mechanism has roughly the same weight as a tether itself3. The Power group also finds that the cables have a mass of 350 kg, and this mass is included as part of the tether in order to estimate the Hab tether reel mechanism mass. Section 3.2 in the Appendix shows how we calculate the tether specifications.

Table 3.2.2 Tether Specifications

| |HAB |ERV |

|Total Length (m) |270.5 |912.8 |

|Maximum Nominal Tension (N) |268500 |302600 |

|Diameter (m) |.035 |.0234 |

|Mass (kg) |100.4 |381.6 |

|Stretch (m) |1.2 |3.8 |

|Power Cable Mass (kg) |350 |- |

|Deployment Reel Mass (kg) |~ 450 |~ 400 |

|Total Tether/Reel Mass (kg) |~ 900 |~ 800 |

Tether Reel Mechanism

For the purpose of this study, a reel mechanism is too complicated and is not designed. We can assume that its mass is roughly equal to that of the tether it deploys. To see an example of such a mechanism, Fig. 3.2.3 shows a schematic from the Italian satellite TSS-1.

[pic]

Fig. 3.2.3. TSS-1 tether reel and winch mechanism.

3.2.3 Deployment

To deploy a tether, we must keep it under constant tension. If a tether loses tension during deployment, it becomes slack and its resulting motion is unpredictable. Loss of tension allows such mishaps as the tether jamming inside the reel mechanism or becoming tangled as it deploys.

To keep tension on a tether during linear deployment, we need to apply constant thrust on both the manned vehicle and counterweight in anti-parallel directions along the tether line. We also need a brake along with the reel mechanism to slow the vehicles down as they approach the tether end to minimize the bobbing motion of the end bodies. However, it must be noted that the brake does not completely remove the motion, but only minimizes it.

Angular deployment is a novel method, but is an excellent way to keep tension on the tether at all times without constant thrusting. While the manned module is still docked with the spent launch rocket, we place the both vehicles onto their interplanetary trajectory. We then use reaction control system (RCS) thrusters to spin the docked system to a certain rate. We stop thrusting, undock the vehicles, and centrifugal force deploys the tether over a period of time set by the reel mechanism design. Conservation of angular momentum decreases the spin rate as the tether deploys, and when the deployment is complete the system has a very small residual spin rate that temporarily keeps tension on the tether.

To determine the deployment values, we use Euler’s equations of motion (EoMs). These equations evaluate rotational motion along the principal axes using moments, inertias, and angular velocity components. Since we assume the system rotates about only one principal axis, Euler’s EoMs reduce to

[pic] (3.2.2)

We solve this equation analytically to get

[pic] (3.2.3)

Using this equation, we determine the burn times for the deployment spin-ups.

Table 3.2.3 shows all the relevant values for both the Hab and the ERV deployments. The Hab deployment is the easiest because it needs only two burns. The maximum g-load created during the deployment is quite low. We calculate all these values using only Euler’s EoMs, conservation of angular momentum, and Eq 3.2.1.

Table 3.2.3 Deployment Values

| |HAB |ERV |

|Total Number of Burns |2 |10 |

|Burn Time (s) |165 |187 |

|Total Burn Time (s) |330 |1870 |

|Maximum g-Load |0.11 |0.47 |

|Initial Deployment Spin Rate (rad/s) |0.24 |0.96 |

|Final Deployment Spin Rate (rad/s) |0.0018 |0.0029 |

[pic]

Fig. 3.2.4 Total ERV/SMLV angular momentum increasing during incremental burn times to create enough angular momentum to deploy the tether.

Figure 3.2.4 shows the trend for the ERV deployment spin-up. Each consecutive burn produces more angular velocity than the burn before it. Because of this trend, the method of incremental burns decreases the total burn time when compared to a single long burn.

3.2.4 Spin-up

[pic]

Fig. 3.2.5 Total Hab angular velocity increasing during artificial gravity spin-up.

After tether deployment, there is a residual amount of spin in the system keeping tension on the tether. Again using Euler’s EoMs, we can find the burn times we need to spin up to .38g. Like the deployment burns, the spin-up burns will be incremental as opposed to one long continuous burn.

Spinning up using incremental burns significantly reduces the total burn time when compared to one continuous burn. The Hab spins up to 0.38g with ten burns, each lasting 200 seconds (see Fig. 3.2.5). The total burn time is 2000 seconds and this is burn time savings of over 8000 seconds.

The ERV uses a different burn scheme. To spin up to 0.38g for the first part of the return to Earth, it uses ten burns that each last 175 seconds (see Fig. 3.2.6). A few months into the return, we start a burn scheme to increase the g-load on the astronauts but 0.02g per day for 31 days. Each day, the burn time needed to create an extra 0.02g decreases. We see this trend in Fig. 3.2.7.

[pic]

Fig. 3.2.6 Total ERV angular momentum increasing during incremental burns to create 0.38g.

[pic]

Fig. 3.2.7 Total ERV angular velocity change over 31 days while increase generated gravity from .38g to 1g.

3.2.5 Tether Retrieval/Release

There are three options for tether release: cut the tether after winching it in part way to create a larger tangential velocity and therefore a larger imparted ΔV when the tether is cut; completely despin the entire system, disconnect the tether, and push the manned vehicle away from the counterweight with a small thrust; or cut the tether as the system spins at the nominal 2 rpm rate.

We believe the idea of reeling in the tether while the system is spinning is impractical. It would be helpful to generate a larger ΔV when we cut the tether, but in a space mission where low weight is extremely important, it is not reasonable to launch a heavy-duty winch strong enough to overcome the tension forces generated by such large spinning vehicles. We consider winching in the ERV tether on approach to Earth as an example. The “weight” of the ERV while spinning at 1g would be 303423 N (68212 lbf, or 34.1 tons.) A winch to reel in that much weight would have to not only generate an equal force, but an even greater one to actually pull against the centripetal force and draw in the tether. This action is comparable to a vertical lifting winch. To accomplish this, the tether would have to be made stronger, and therefore heavier, and the winching mechanism would have to be considerably larger and heavier than we want to launch.

We also do not want to de-spin the system. To despin, the spacecraft would need to carry along the fuel necessary to stop the spin, which is expensive. We would want to ensure the elimination of all spin in the system. As the spinning can be used to our advantage, we decide it is not worth the expense to carry along fuel solely dedicated to the vehicle de-spin.

After discarding the first two options as expensive we also decide not to retrieve the tether at all, only to release it. By cutting the tether during the 2rpm spin, we generate a non-propulsive ΔV. If we cut the tether on a planetary approach, we can cut the tether is such a way that the imparted ΔV will slow down the manned vehicle and speed up the counterweight. This eliminates the need for the manned vehicle to thrust away from the counterweight, and it does not cost any fuel. The Hab obtains a non-propulsive ΔV of 17.8 m/s. If for some reason the tether is cut during the ERV’s 0.38g spin, it imparts a ΔV of 28.8 m/s. As the ERV approaches Earth, we cut the tether during the 1g spin and therefore obtain 46.7 m/s.

3.2.6 Conclusion

1. Both tethers are tubular Hoytethers that are made of Spectra 2000. They have only a negligible chance of failing. The structure of the Hoytether minimizes micrometeor hazards; each tether has a designed safety factor of five to protect it from unforeseen large tension forces. We design these tethers with today’s technology and they will be effective for our mission.

2. We use the conservation of angular momentum to our advantage for tether deployment. We spin up the docked vehicles, release them, and let centrifugal force unreel the tether. The centrifugal force will keep tension on the tether at all times. Instead of a single burn for the deployment spin-up, we use an incremental burn scheme that yeilds significant total burn time savings.

3. The Hab and the ERV both use the incremental burn idea that is also employed in tether deployment. To reach the required 0.38g during Mars transit, the Hab spins to two rpm using ten 200 second burns. The ERV spins up to 0.38g after launch from Mars using ten 175 second burns. A few months into the return, we increase the artificial g-load from 0.38 to 1. The burn scheme for this manoeuver is to increase the g-load by 0.02g per day for 31 days.

4. By separating the manned modules from the tethered system while it is still spinning, we impart a ΔV that we can use as we approach a planet. The Hab gets a 17.8 m/s ΔV when we cut the tether near Mars. The ERV gets 46.7 m/s as we approach Earth on return. Cutting the tether at the right time also has the added advantage of separating a manned module its counterweight without a propulsive manoeuver.

Acknowledgements

The author thanks Dr. Robert Hoyt, of Tethers Unlimited, for the valuable information he shared about not only the HoytetherTM, but tethers in general. We also thank him for the interest he showed in our project. The author also thanks Luca Bertuccelli for his help with several parts of this paper.

References

1. Personal communication with Dr. R. Hoyt of Tethers Unlimited.

2. Hoyt, R., and Forward, R., “The HoytetherTM: A Failsafe Multiline Space Tether Structure,”

3. Kowalsky, C., and Powell, J. D., “Tethered Artificial Gravity Spacecraft Design,” Astrodynamics 1993; Proceedings of the AAS/AIAA Astrodynamics Conference, Victoria, Canada, Aug. 16-19, 1993. San Diego, CA, Univelt, Inc., 1994, p. 645-664

4. Tomlin, D. D., Mowery, D. K., Musetti, B., and Cibrario, B., “Tethered Satellite Mission 1 Flight Dynamics Anomalies,” 4th International Conference on Tethers in Space, Washington DC, April 10-14, 1995, pp. 14.

5. Palmer, K., “Dynamics of a Spinning Artificial Gravity Spacecraft” AAE 507 Project Report, Fall 2000.

6. Glaese, J., “The Dynamics of Tethers in Artificial Gravity Applications,” Space Tethers for Science in the Space Station Era; Proceedings of the Second International Conference, Venice, Italy, Oct. 4-8, 1987 (A89-43326 18-12). Bologna, Societa Italiana di Fisica, 1988, p. 388-393.

7. Tomlin, D., Faile, G., Hayashida, K., Frost, C., Wagner, C. Y., Mitchell, M., Vaughn, J., and Galuska, M., “Space Tethers: Design Criteria,” NASA TM-108537, Structures and Dynamics Laboratory, Science and Engineering Directorate. NASA Marshall Space Flight Center, AL 35812, July 1997, pp. 20.

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