Space Elevator Dynamic Challenges
Space Elevator Dynamics Challenges
Below is a list of challenges that must be addressed in simulating space elevator dynamics simulation.
Non-Uniform Tethers
Dynamics Issue: Along the length of the Space Elevator ribbon there is a non-uniform density and load-carrying elastic cross sectional area as well as a non-uniform surface area, all varying as a function of the position along the ribbon. This must be properly simulated to accurately model the ribbon's dynamic responses to the various disturbing influences, as well as to gain an understanding of the system's dynamic nature.
GTOSS Provides simulation of non-uniform elastic cross-section, density and aerodynamic surface area. These properties can be described as arbitrary tabular data as a function of deployed ribbon length (allowing discontinuous properties), and interploated with either a linear or parabolic method.
Stable Initialization
Dynamics Issue: In its equilibrium state, the Space Elevator ribbon exhibits significantly non-uniform longitudinal strain distribution. Initializing the system with a uniform strain distribution is non-productive since such an initial strain state is not in equilibrium with gravity gradient and centripetal force along the length of the ribbon, thus the resulting motion exhibits serious artifacts that occlude dynamic attributes under investigation. A means to properly initialize all general elevator configurations with taking into account the ribbon's tapered material attributes is a necessity.
GTOSS Provides a full range of initialization options including the ability to create gravity-gradient/centripetally stable configurations consisting of "simply-connected chains" of multiple objects and tapered tethers.
Multiple Tethers/Bodies
Dynamics Issue: One envisioned initial Deployment scheme from GEO requires the simulation of at least 2 Ribbons connecting 3 Spacecraft with simultaneous deployment of the two Ribbons. In addition, the Spacecraft will be required to perform maneuvers, and complex deployment laws may be needed to dispense ribbon effectively. Dynamically speaking such a simulation calls for multiple space objects and multiple space tethers being deployed in connected fashion.
GTOSS Provides the ability to connect (arbitrary) numbers of objects and tethers connected in arbitrary fashion. The tethers can be deploying from an object, and the objects can include a variety of control features including both thrusting and attitude control; Note, some control capabilities are provided by GTOSS directly, others are easily added by the user as the GTOSS code is written with the intent of being open, understandable and modifiable.
Variable Spatial Resolution
Dynamics Issue: The extreme length of the Space Elevator drastically surpasses all engineered systems to date. Spatial Resolution of such a configuration refers to the "fineness" with which the mass and force distribution is expressed in a discrete simulation. For instance, 50 nodes distributed uniformly along a deployed ribbon's length of 100,000 km corresponds to a collocation point every (ie. resolution of) 2,000 km. The inadequacy of such resolution can be noted from the fact that the earth's gravity (that plays a significant role in the overall gravity gradient/centripetal balance) has dimished by almost half at 2000 km above the surface, and virtually all aerodynamic effects pertaining to the elevator has disappeard by an altitude of just 50 km.
GTOSS Provides up to 500 collocation points per tether (this is relaltively easly to modify if a user requires). Furthermore, since tethers can be chained together, this effectively allows two or more tethers (each with a different collocation point resolution) to be employed to span different regions with different resolutions. For example, atmospheric phenomena occur over a region no greater than 50 km, over which, spatial resolution sufficient to resolve atmospheric disturbance details is necessary and easily achievable by GTOSS resolution; now, this level of resolution is far in excess of that necessary to resolve normal dynamics response of the ribbon over the majority of the remaining length. This is solved by chaining two tethers, one 50 km in length nearest the earth (providing the high level of resolution for the atmospheric simulation), then a second tether (99,950 km) extending to the ballast mass providing appropriate resolution for that region.
Aerodynamic Response
Dynamics Issue: The low "effective end-to-end spring rate" of the elevator, combined with a significant total cross-sectional area exposed to the lower atmospheric wind environment requires a capability to simulate both the aerodynamics of the ribbon, and the earth's atmospheric environment, to determine dynamic response and loading.
GTOSS Provides a subsonic aerodynamics model based on "flat plate theory", in conjunction with an atmospheric disturbance model to produce airloads on the ribbon. The airload model assumes a section of ribbon (on the order of the collocation point resolution length) to be a flat plate with a relative wind impinging upon it. The relative wind depends upon the spatial attitude of the ribbon section combined with the local direction of the atmospheric wind (ie. local to the collocation point itself). This gives rise to flat-plate airloads that are subsequently resolved into lift and drag components. The atmospheric disturbances are programmable by the user (via data entry) to represent both Time and Altitude varying wind Speed and Direction. Transient Gusts can then be superimposed on this otherwise time-varying profile.
Non-Linarities & Free-Tether Deployment
Dynamics Issue: The dynamic effects of Crawler transit. As construction and operational payload crawlers traverse the length of the ribbon, dynamic effects will ensue resulting in both ribbon Libration and transverse "String Mode" responses. Such responses must reflect all the potentially non-linear effects related to tapered ribbon design, inverse-square gravity field, centripetal forces, coriolis effects, atmospheric disturbance, and crawling speed modulation.
GTOSS Provides the ability to simulate a crawler traversing the ribbon by means of its cability to simulate chains of multiple objects and tethers; in this case, the crawler would be an object in a "chain" with 2 adjacent tethers attached, the earth-side tether undergoing appropriate deployment, while the ballast-side tether would be undergoing retrieval. Below is an argument in behalf of this approach: Once an element of ribbon enters the "domain of the crawler" (ie. gets clenched-in and/or threaded-through rollers, etc) until it emerges, that element of ribbon is within the domain of the crawler itself, thus, not a participant in the free motion of the ribbon lying outside the crawler. It does not become so until it is emitted from the crawler; this meets all the pertinent criteria for a tether deployment/retrieval simulation. So what is true in nature is what GTOSS would do to simulate a crawler. In further support, note that the ribbon's "internal" strain states are not necessarily that of the ribbons adjacent to the crawler, as a variety of strain states can be imposed on the ribbon internally (indeed, "exceeding limit-strain" internally within the crawler may be a factor compromising the success of roller systems that "thread the ribbon thru overlapping roller schemes" to take advantage of the "capstan effect"). It is tempting to be intuitively biased because of a'priori knowledge of the "continuity of the ribbon"; however (speaking somewhat whimsically) as far as external ribbon dynamics are concerned, there could just as well be a "CNT synthesis plant" on-board the crawler that ingests ribbon from above, melts it down, makes a new ribbon, and emits it out the bottom (with deploying ribbon mass just equaling retrieved ribbon mass). This is not the only valid scheme to model crawler dynamics, but it is an existing capability within GTOSS now, and should provide valuable insight into the nature of the problems that will have to be considered in crawler design and operations.
Liftoff Dynamics
Dynamics Issue: The launching of crawlers pertain to the process of getting a payload that is stationary on the ground underway in the vertical direction, then maintaining/modulating its traversal rate. This process must address lift-off release dynamics, modulating or maintaining a chosen traversal speed scenario, and managing ribbon movement related to this process. This can be problematic because of the low "effective end-to-end spring rate" of the elevator ribbon.
GTOSS Provides the ability to study the transient dynamics of complex systems with deploying tethers attached. The above described launch problem is just such a transient situation. All salient effects including: propagation speed of longitudinal stress waves, an effective end-to-end spring rate that automatically incorporates transient effects of ribbon mass-inertia, ribbon taper, release simulation, cable management at the launch platform, etc.
Thermal Simulation
Dynamics Issue: The space elevator ribbon spends a great deal of it's time exposed to solar heating; this is because of its suptendous length. For example, the ballast mass (at 100,000 km altitude) is in the shade of the earth's shadow less than one hour per day; other sections along its length are proportionally exposed in a manner consistent with this ballast exposure and the 24 hour earth rotation period. This means that the ribbon will be subject to lengthening and shortening in response to this thermal cycle.
GTOSS Provides the ability to study thermal transient dynamics of the elevator ribbon. Heating sources include solar radiation, earth albedo, earth infrared radiation, aerodynamics, and electrical current; heat loss is through ribbon radiation.
Climber Attitude Control Response
Dynamics Issue: The climber is a 6 degree of freedom rigid body subject to control dynamics simulations, thus 6 DOF attitude simulation must be available.
GTOSS Provides the simulation of bodies as either 3 or 6 DOF objects.
