Trajectory Simulation for Single Balloons and Networks

An understanding of the characteristics of trajectories of constant-altitude stratospheric platforms is important for scientific balloon flights because science observation sequences, safety planning, overflight negotiations, launch site selection, and recovery operations are affected by trajectory. Supported by NASA, Global Aerospace Corporation (GAC) has developed a Trajectory Simulation and Prediction System (TSPS) for NASA’s Ultra Long Duration Balloon (ULDB) Project. We identified desirable launch dates based on historical trajectory dispersion. None of the launch sites that were studied exhibits significantly less dispersion than the other launch sites. However, latitude dispersion grows with flight duration, and trajectory dispersion growth is significant from 30to 100-day flights. We also discuss work supported by the NASA Institute for Advanced Concepts (NIAC) where trajectory simulation techniques are applied to constellations of hundreds of balloons. We evaluate the prospects of managing the geometry of such constellations by using trajectory control systems. INTRODUCTION Stratospheric balloons that float at 30–40 km altitudes are an important platform for scientific and defense purposes because they fly above 99% of the atmosphere (a near-space environment), because they fly at low speeds (eliminating compression effects of sampled air), and because they float at high altitude (enabling observations of a large area of the earth). Several countries, including the United States (NASA and Air Force), France, Japan, Brazil, and others, have active stratospheric balloon programs. Recent interest in very long duration stratospheric scientific balloon flights has been stimulated by a desire to obtain high quality scientific observations from constant-altitude stratospheric platforms (Smith, 2000). Because of the predominant stratospheric circulation pattern, balloon trajectories are characterized by zonal motion. Many stratospheric science experiments require trajectories to remain in specified latitude zones. The latitudinal dispersion characteristics of the stratospheric trajectories can be an important factor in (a) selecting launch sites and launch dates, (b) preparing safety analyses, (c) planning for payload recovery operations, (d) negotiating permission for overflight, and (e) sequencing science observations. Thus, an important parameter for mission planning is the expected trajectory excursion from the launch latitude. To achieve minimum latitude excursion during stratospheric balloon flights, experience with shortduration flights has shown that polar summer circulation is the most favorable. In the summer, the polar vortex is typically unified, and the consistent, low-velocity, easterly (east-to-west) flight path yields little northward or southward motion. In the winter, the polar vortex typically fragments into two or more vortices, and significant disturbances (stratospheric warming events or stratwarms) can disrupt the prevailing westerly (west-to-east) flow. The twice-yearly reversal of the prevailing stratospheric winds is known as “turnaround.” In this paper, we explore long-duration (up to 100 days), stratospheric, constant-altitude (35 km), winddriven trajectory characteristics with spatially and temporally diverse initial conditions by calculating hundreds of trajectories from launch sites at three different latitudes and 120 launch dates using historical winds. These trajectories are studied in the context of single-balloon missions and as constellations of simultaneously-flying balloons. We begin by discussing the methods employed for trajectory simulations in this paper. Trajectory Calculations To assist calculation of stratospheric trajectories, we selected an environment data set which was created by the National Oceanic and Atmospheric Administration (NOAA) and the Goddard Space Flight Center (GSFC) because it provides daily, global, gridded, digital, stratospheric data over many years. We call it the “SC” data set because it was created by the method of “successive correction.” The SC data set provides environment information (including winds) near the balloon. The SC data is interpolated both spatially and temporally to obtain local conditions at points in the atmosphere. The SC data set is used as input data for calculating the trajectories that were analyzed in this study. Below, several aspects of the trajectory calculations are discussed. To maintain consistency with the typical balloon-borne science instrument altitude requirements and typical superpressure balloon vehicle design altitudes, we assume 35 km (~ 5 hPa) as the float altitude for all balloon trajectories simulated in this study. To simulate the horizontal trajectory of balloons, we assume that the difference between the horizontal velocity components of the wind and the horizontal velocity components of the balloon is identically zero. A typical design requirement for stratospheric superpressure balloon altitude variation is < ±1.5 km altitude excursion during the flight. This typical altitude excursion requirement is significantly less than the vertical resolution of the environmental data set, which is about 6 km at expected float altitudes (~ 35 km). Balloon trajectories are simulated by integrating stratospheric winds at the balloon location. We studied the effect of integration step size on the resulting trajectories, and selected the maximum step size for which increasing step size did not change the trajectory, about 1 hour. SINGLE-BALLOON TRAJECTORIES Using the trajectory simulation methods described above, we created a database of trajectories for various launch sites and launch dates. There are several launch sites for stratospheric balloons in the world. For the present study, we evaluated launch sites at 65° North, 24° South, and 44° South latitude, corresponding t o Fairbanks, Alaska, Alice Springs, Australia, and Christchurch, New Zealand, respectively. Launch dates were selected from a period covering the years 1981–1990. Flights originate on the first day of each month of each of the 10 years covered. The resulting trajectory database includes 360 simulated 100day trajectories. Thus, the trajectory data set consists of 360 constant-altitude (35 km geopotential), 100-day trajectories. There are 120 trajectories for each launch site, and there are 30 trajectories for each month. Although each trajectory begins and ends at 35 km, we refer to the starting point of the trajectory as the “launch site” for the remainder of this report. And, we refer to trajectories by the launch month, launch year, and launch location, omitting, for the sake of brevity, that each launch occurs on the first day of the month, that the flight altitude is 35 km geopotential, and that the integration time step is 1 hour. Dispersion Characteristics Using the trajectory database, we calculated the southernmost and northernmost excursions for every trajectory for the first 30, 60, and 100 days from launch. Figure 1 shows an example trajectory, the 100-day June 1986 Fairbanks trajectory, and Figure 2 shows the method of calculating northernmost and southernmost latitude excursions from the trajectory data. The maximum excursion for any given day is simply the greater of the extent of the northward or southward excursion. Figure 1. 100-day June 1986 Fairbanks trajectory. 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 100 N or th L at it ud e [° ] Flight Time [days] 60-day and 100-day Northernmost Excursion 30-day Northernmost