IMPACT OF INSERTION LOCATION ON THE LONGEVITY OF A MARS BALLOON Spaghetti plot for a balloon launch...
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IMPACT OF INSERTION LOCATION ON THE LONGEVITY OF A MARS BALLOON Spaghetti plot for a balloon launch centered in Hellas (42S, 70E) as shown above. Trajectories are calculated with 0.2 o offsets from this location extending 0.5 o from the center. The probability of following a particular trajectory is proportional to the density of the trajectories. Two solutions are most probable: one leaves Hellas and then turns northeast toward Tharsis where it terminates; the other goes poleward and completes numerous high latitude circumnavigations. Tick marks are plotted every 1.5 mars hours. Spaghetti plots for launches centered: Left: in Acidalia Planitia (45N, 30W). The dominant solution are subtropical to high latitude circumnavigations. One minor solution results in balloon flights terminating in the Tharsis region. The density of the circumnavigation trajectories indicates that all paths are roughly equally probable. However, the sharp gradients at the circumnavigation boundaries indicates that the latitude range is strongly constrained. Right: Meridiani. Nearly all the balloons meander in the launch region before ejecting toward the northwest rim of Hellas. A substantial fraction of the balloons meet their fate on the rim. A few divert around the north rim of Hellas. Some of these drift toward an eventual impact with Tharsis, and few deflect southward around Tharsis where they circumnavigate at high southern latitudes. Some of the balloons deflect southward around Hellas, avoiding Tharsis altogether and enter the circumnavigation trajectories. . Rafkin, Dept. of Space, Studies Southwest Research Institute, Boulder, CO USA, rafkin@boulder Abstract Mars is considered a planet where balloon exploration is feasible. Due to the relatively thin atmosphere, however, balloons generally need to fly at low altitudes in order to obtain sufficient buoyancy to carry the mass of the balloon system itself, a scientifically useful payload, and communication and other spacecraft systems. This presents a problem, because Mars has extreme topography, a good portion of which is not navigable by a balloon. Using output from GCM and mesoscale models, we show that a careful choice of probe insertion location can maximize the longevity of a superpressure (constant density) balloon. At the same time, improper selection can result in a very short mission lifetime. The boundaries between the two regimes are often dramatically sharp. The Tharsis plateau is the most common impact point for all balloons at low to moderate altitude, and the region is shown to draw in air over a large region. Depending on season, there are also broad regions where balloon trajectories avoid the Tharsis region and instead are caught in circumpolar circulations that permit lifetimes of many dozens of sols with many circumnavigations at middle to high latitudes. r Methodology Trajectory Dynamics The balloon trajectory is computed by integrating the balloon velocity with respect to time to obtain displacement (1) where is the position vector, and is the horizontal balloon velocity. A super-pressure balloon flies along an isopycnal (constant density) surface, and thus Eq. (1) is evaluated on a specified constant density surface. The balloon velocity is taken to be equivalent to the atmospheric velocity. Input Data •Atmospheric data from NASA ARC GCM simulation (5 o x6 o latitude by longitude). •MOLA topography re-binned to the model spacing •some peaks are understated. •the highest peaks are not of concern since the balloon would impact slopes before the peaks. •Model noromalized to Viking Lander pressure data. •The value of the balloon density surface is determined by selecting a desired flight altitude above (or below) MOLA reference zero. Then, the average global density at that altitude is determined. Trajectory Integrations Two basic types of trajectory calculations: 1) The planet is divided into a 2 o x2 o grid, and balloons are launched from each location. Statistics from each of these balloon flights are calculated and used to produce contour maps. 2) The solution stability of launching from a particular location. The initial launch location is perturbed by fractions of a degree to provide new initial locations for additional trajectory calculations. The trajectory of the balloons are plotted on the same map to provide so-called “spaghetti plots”. t t t dt t y x V r ) , , ( r V Global Trajectory Statistics Trajectory for a balloon launch centered in Hellas (42S, 70E). Every four sols is a different color. Trajectory Spaghetti Plots Time of flight and distance travelled for a balloon launched from a given any location within the northern hemisphere. Regions in white are topographic regions above the flight density surface. High latitudes within the seasonally strengthening polar vortex generally have the longest lifetimes. The boundaries between long and short flights are very strong indicating that trajectories can exhibit chaotic bifurcations.
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Transcript of IMPACT OF INSERTION LOCATION ON THE LONGEVITY OF A MARS BALLOON Spaghetti plot for a balloon launch...
IMPACT OF INSERTION LOCATION ON THE LONGEVITY OF A MARS BALLOON
Spaghetti plot for a balloon launch centered in Hellas (42S, 70E) as shown above. Trajectories are calculated with 0.2o offsets from this location extending 0.5o from the center. The probability of following a particular trajectory is proportional to the density of the trajectories. Two solutions are most probable: one leaves Hellas and then turns northeast toward Tharsis where it terminates; the other goes poleward and completes numerous high latitude circumnavigations. Tick marks are plotted every 1.5 mars hours.
Spaghetti plots for launches centered: Left: in Acidalia Planitia (45N, 30W). The dominant solution are subtropical to high latitude circumnavigations. One minor solution results in balloon flights terminating in the Tharsis region. The density of the circumnavigation trajectories indicates that all paths are roughly equally probable. However, the sharp gradients at the circumnavigation boundaries indicates that the latitude range is strongly constrained. Right: Meridiani. Nearly all the balloons meander in the launch region before ejecting toward the northwest rim of Hellas. A substantial fraction of the balloons meet their fate on the rim. A few divert around the north rim of Hellas. Some of these drift toward an eventual impact with Tharsis, and few deflect southward around Tharsis where they circumnavigate at high southern latitudes. Some of the balloons deflect southward around Hellas, avoiding Tharsis altogether and enter the circumnavigation trajectories.
Scot C. R. Rafkin, Dept. of Space, Studies Southwest Research Institute, Boulder, CO USA, [email protected]
AbstractMars is considered a planet where balloon exploration is feasible. Due to the relatively thin atmosphere, however, balloons generally need to fly at low altitudes in order to obtain sufficient buoyancy to carry the mass of the balloon system itself, a scientifically useful payload, and communication and other spacecraft systems. This presents a problem, because Mars has extreme topography, a good portion of which is not navigable by a balloon. Using output from GCM and mesoscale models, we show that a careful choice of probe insertion location can maximize the longevity of a superpressure (constant density) balloon. At the same time, improper selection can result in a very short mission lifetime. The boundaries between the two regimes are often dramatically sharp. The Tharsis plateau is the most common impact point for all balloons at low to moderate altitude, and the region is shown to draw in air over a large region. Depending on season, there are also broad regions where balloon trajectories avoid the Tharsis region and instead are caught in circumpolar circulations that permit lifetimes of many dozens of sols with many circumnavigations at middle to high latitudes.
r
MethodologyTrajectory DynamicsThe balloon trajectory is computed by integrating the balloon velocity with respect to time to obtain displacement
(1)
where is the position vector, and is the horizontal balloon velocity. A super-pressure balloon flies along an isopycnal (constant density) surface, and thus Eq. (1) is evaluated on a specified constant density surface. The balloon velocity is taken to be equivalent to the atmospheric velocity.
Input Data•Atmospheric data from NASA ARC GCM simulation (5ox6o latitude by longitude). •MOLA topography re-binned to the model spacing
•some peaks are understated. •the highest peaks are not of concern since the balloon would impact slopes before the peaks. •Model noromalized to Viking Lander pressure data.•The value of the balloon density surface is determined by selecting a desired flight altitude above (or below) MOLA reference zero. Then, the average global density at that altitude is determined.
Trajectory IntegrationsTwo basic types of trajectory calculations: 1) The planet is divided into a 2ox2o grid, and balloons are launched from each location. Statistics from each of these balloon flights are calculated and used to produce contour maps. 2) The solution stability of launching from a particular location. The initial launch location is perturbed by fractions of a degree to provide new initial locations for additional trajectory calculations. The trajectory of the balloons are plotted on the same map to provide so-called “spaghetti plots”.
tt
t
dttyxVr ),,(
r
V
Global Trajectory Statistics
Trajectory for a balloon launch centered in Hellas (42S, 70E). Every four sols is a different color.
Trajectory Spaghetti Plots
Time of flight and distance travelled for a balloon launched from a given any location within the northern hemisphere. Regions in white are topographic regions above the flight density surface. High latitudes within the seasonally strengthening polar vortex generally have the longest lifetimes. The boundaries between long and short flights are very strong indicating that trajectories can exhibit chaotic bifurcations.
