Moon & Mars Orbiting Spinning Tether Transport - Tethers Unlimited

Rapid Interplanetary Tether Transport SystemsIAF-99-A.5.10MERITT ModelingCalculations of the MERITT systemperformance were performed using the mathematicalmodeling software package ÒTK SolverÓwhich allows the user to type in the relevantequations and get results without having to solvethe model algebraically or structure it as aprocedure, as long as the number of independentrelationships equals the number of variables.This is very useful in a complex system when onemay wish to constrain various variables forwhich it would be difficult, if not impossible, tosolve and to perform numerical experiments toinvestigate the behavior of the system.Two versions of a tether based interplanetarytransfer system are being worked on, one fortether-only transfers and the other incorporatingan aerobraking pass at the destination body toaid in capture and rotation of the line of apsides.It should be emphasized that the resultspresented here are very preliminary and muchremains to be done with the software. Because ofthe ongoing work and the growing number ofvariables and lines of code, we will not try to gothrough this line by line here. Questionsconcerning the code should be referred to GeraldNordley at the above address.The general architecture of the models issequential. A payload is picked up from atrajectory at the origin planet, and added to arotating tether in a highly elliptical orbitaround the origin planet. The pickup isaccomplished by matching the position andvelocity of the grapple end of the unloadedrotating tether to payload position and velocity.This addition of the payload mass to one endof the tether shifts the center of mass of thetether toward the payload. The tether used inthese examples is modeled as a rigid line withtwo arms, a grapple, a counterweight and acentral mass. The tether is assumed to bedesigned for a payload with a given mass and a"safety factor" of two, as described in Hoyt andForward 18 and to be dynamically symmetricalwith a payload of that mass attached.The mass distribution in the arms of thetether was determined by dividing the tetherinto ten segments, each massive enough to supportthe mass outward from its center; this was notneeded for the loaded symmetric tether casespresented here, but will be useful in dealing withasymmetric counterweighted tethers. The totalmass of each tether arm was determined fromEqn. (1). The continuously tapered mass definedby Eqn. (1) was found to differ by only a fewpercent from the summed segment mass of the 10segment tether model used in the analysis, andthe segment masses were adjusted accordinglyuntil the summed mass fit the equation. Thesmall size of this adjustment, incidentally, can betaken as independent confirmation of Eqn. (1).We ended up designing many candidates forthe EarthWhip and MarsWhip tethers, fromsome with very large central station masses thatwere almost unaffected by the pickup or toss of apayload, to those that were so light that the tossof an outgoing payload caused their orbits to shiftenough that the tether tip hit the planetaryatmospheres, or the catch of an incoming payloadsent the tether (and payload) into an escapetrajectory from the planet. After many trials, wefound some examples of tethers that weremassive enough that they could toss and catchpayloads without shifting into undesirableorbits, but didn't mass too much more than thepayloads they could handle. The tethers areassumed to be made of Spectra ª 2000 materialbraided into a Hoytube ª structure with a safetyfactor of 2. The tether design consists of a largecentral station with a solar array power supply,winches, and control systems, plus any ballastmass needed to bring the mass of the total systemup to the desired final mass value. From thetether central station is extended two similartethers, with a taper and mass determined byEqn. (1) according to the loaded tip velocitydesired. At the end of the tethers are grapplesthat each mass 20% of the payloads to behandled. To simplify this initial analysis, weassumed that one grapple is holding a dummypayload with a mass equal to the activepayload, so that after the grapple on the activearm captures a payload, the tether system issymmetrically balanced. Later, more complex,analyses will probably determine that a one armtether system will do the job equally well andcost less.20