A GEOMETRIC ANALYSIS TO PROTECT MANNED ... ... AAS 13-360 A GEOMETRIC ANALYSIS TO PROTECT MANNED...
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A GEOMETRIC ANALYSIS TO PROTECT MANNED ASSETS FROM NEWLY LAUNCHED OBJECTS- COLA GAP ANALYSIS
Mark E. Hametz* and Brian A. Beavert
A safety risk was identified for the International Space Station (ISS) by The Aerospace Corporation, where the ISS would be unable to react to a conjunction with a newly launched object following the end of the launch Collision Avoid- ance (COLA) process. Once an object is launched, there is a finite period of time required to track, catalog, and evaluate that new object as part of standard on- orbit COLA screening processes. Additionally, should a conjunction be identi- fied, there is an additional period of time required to plan and execute a collision avoidance maneuver. While the computed prelaunch probability of collision with any object is extremely low, NASA/JSC has requested that all US launches take additional steps to protect the ISS during this "COLA gap" period. This pa- per details a geometric-based COLA gap analysis method developed by the NASA Launch Services Program to determine if launch window cutouts are re- quired to mitigate this risk. Additionally, this paper presents the results of sev- eral missions where this process has been used operationally.
A safety risk for the International Space Station (ISS) was identified by The Aerospace Corpo- ration as early as 2006, but awareness heightened following the launch of GPS IIR-20 (March 24, 2009), when the spent upper stage of the launch vehicle unexpectedly crossed inside the ISS noti- fication box shortly after launch (Reference 1). This event highlighted a 56-hour vulnerability period following the end of the launch Collision A voidance (COLA) process where the ISS would be unable to react to a conjunction with a newly launched object (typically the spent upper stage). Current launch COLA processes screen each launched object across the launch window to determine if an object's nominal trajectory is predicted to pass within 200 Jan of the ISS (or any other manned/mannable object), resulting in a launch window closure. These launch COLA screens are performed from launch through separation plus 100 minutes. Once the objects are in orbit, they are cataloged and evaluated as part of routine on-orbit conjunction assessment pro- cesses. However, as the GPS IIR-20 scenario illustrated, a vulnerability period exists between the end of launch COLA coverage and the beginning of standard on-orbit COLA assessment activi- ties. The gap between existing launch and on-orbit COLA processes is driven by the time re- quired to track and catalog a launched object, identify a conjunction, and plan and execute a colli- sion avoidance maneuver. For the ISS, the total time needed to accomplish all of these steps is 56
• Senior Engineer, Launch Services Division, a.i. solutions, Inc., 8910 Astronaut Blvd., Suite 120, Cape Canaveral, FL 32920 t Flight Analysis Branch Chief, Launch Services Program, Mail Code VA-HI , Kennedy Space Center, FL 32899
hours. To protect human lives, NASNJSC has requested that all US launches take additional steps to protect the ISS during this "COLA gap" period.
DERIVATION OF THE WORST -CASE COLLISION PROBABILITY
The uncertainty in the state of a spent upper stage can be quite large after all bums are com- plete and all remaining propellants are expelled to safe the stage. Simply extending the launch COLA process an additional 56 hours is not a viable option as the 3-sigma position uncertainty would far exceed the 200 km miss-distance criterion. Additionally, performing a probability of collision cPc) analysis over this period is also impractical due to the limiting effects of these large orbit state uncertainties. The remainder of this section details the results of a worst-case Pc esti- mation for a typical spent upper stage nominally aligned for a direct broadside collision with the ISS.
From Reference 2, the probability of collision, assuming a nominal predicted miss distance of zero, can be estimated using the following relationship:
A* = effective collision area OT = combined 1 sigma position error in x Veqv = combined 1 sigma position error in y Pc = probability of collision
A complete definition of the variables and Relative Motion Coordinate System (RMCS) used in this equation, as well as its derivation, can be found in Reference 2.
The effective collision area, A*, is calculated form the following formula (Reference 2):
A* = effective collision area A 1 = area of body 1 A2 = area of body 2 k1 = ratio of length/width for body 1 k2 = ratio of length/width for body 2
Using dimensions of the ISS and launch vehicle upper stages, the estimated upper bound on A* is 9301 m2 for a conjunction between the Atlas V/Centaur upper stage and ISS, and 8672 m2
for the Delta II second stage. These values assume that both the upper stage and ISS are projected into the collision plane as the largest possible rectangles (i.e. , composed of each object's two largest dimensions). This is the most conservative size characterization. The lower bound on A*,
which assumes an edge-on approach to ISS and a frontal cross section for the upper stage, is 1773 m2 for Delta II and 1798 m2 for Centaur.
The other information necessary for calculating Pc is the uncertainty in the launch vehicle po- sition. For conservatism, this bounding assessment assumes zero uncertainty in ISS state knowledge. The size and shape of the launch vehicle position dispersion distribution is vehicle and mission-dependent, and will also vary as a function of time and location in the orbit. Analyti- cally determined launch vehicle position uncertainties at the end of launch COLA screens gener- ally range from tens of kilometers to 100 kilometers or more, and will only grow with time over the COLA gap period. These analytical results have been shown to correlate well with flight data (Reference 3).
Figure 1 illustrates the probability of collision , assuming the upper bound A* value of 9301 m2
and a nominal predicted direct hit (zero miss distance) between the ISS and the upper stage, as a function of 1-sigma position uncertainties (in meters) in the conjunction plane as defined in Ref- erence 2. Comparison of analytical results for flight missions to the trends observed in this plot indicates that upper stage dispersions during the COLA gap period generally exceed the values necessary to result in probabilities of collision greater than the 10·6 order of magnitude.
90 Probability of Collision
- 1.00E-06 c 0 80 ·,p ~
- 1.00E-05 .. i5 70
1.00E-04 _!-.. ] o- 60 .. .I:. .. " Jll "' :I 0 .!II li. 50 'tl c. c< Ill . c. ..
i ~ 40 >.2 c!: -~ 0 30
~ c :) 20 t:) ...
0 0 10 20 30 40 50 60 70 80 90 100
la Uncertainty in the Direction of Closest Approach (km)
Figure 1. Probability of Collision as a Function of Launch Vehicle Position Uncertainties for Zero Miss Distance
Based on these bounding results, it is seen that even under very conservative assumptions (a pre-flight predicted zero miss distance between the ISS and a Centaur upper stage and worst case broadside approach for both objects), uncertainties associated with the upper stage state alone result in an estimated probability of collision on the order of 10·6 or less for all but the tightest possible uncertainties, which are themselves very unlikely to occur. When one factors in the like-
lihood of the two conservative assumptions outlined above actually coming to pass, it is apparent that attempts to screen for conjunctions during the COLA gap period using standard techniques will yield probabilities that essentially never exceed the existing screening threshold for manned objects (10-6). This issue, along with the desire to perform this analysis in-house at NASA KSC, led to the development of the geometric-based approach outlined in this paper.
GEOMETRIC-BASED ANALYSIS APPROACH
Given the limitations of the launch COLA evaluation techniques for the COLA gap problem, a geometry-based methodology may be used to determine if launch opportunities pose a threat to the ISS during the COLA gap period. The NASA Launch Services Program (LSP) at Kennedy Space Center has developed this COLA gap analysis method and has employed it for four NASA missions to identify potential ISS conjunctions and corresponding launch window closures during the 56-hour at-risk period. In each of these cases, the potential conjuncting object has been the spent upper stage of the launch vehicle.
In the analysis, for each launch opportunity, the nominal trajectory of the spent upper stage and the orbit state of the ISS are propagated simultaneously over the 56 hour period. Each time the upper stage crosses the ISS orbital plane, the only location where a collision could occur (cross-track= 0), the relative radial and argument of latitude separations are calculated (Figure 1). The argument of latitude is the sum of the argument of perigee and true anomaly and represents the angle in the plane of the orbit from the ascending node, measured in the direction of the ob- ject's motion.
In Figure 2, the green disk is the orbital plane of the ISS and the actual propagated location is shown with the ISS graphic in the foreground. The red trajectory is the path of the upper stage and at this time, the simulation has been paused at an instance where the upper stage inter