In the first panel, the black contours shown are reachability front forecasts, at 6 hour intervals (with increasing line thickness for later times). The reachability front is the boundary of the largest set (the reachable set) that the glider can reach within that duration. It is computed by numerically solving our exact governing PDE for this time-optimal reachability front. The time-optimal path from the starting postion to the desired recovery position is shown by the purple curve.
In the second panel we show a zoom of the optimal path along with the reachability fronts and heading/velocity data along the optimal path. The red vectors are the optimal vehicle headings; the blue vectors, the current; and the green vectors, the resultant (sum of the current vector and propulsion vector in the heading direction).
In the third panel, the optimal heading angle (degrees, measured clockwise from true north) vs. time is shown.
Note that time is plotted on the y-axis (so the starting time is on the bottom).
In this forecast, we consider glider RU38's actual starting location of 24.1610°N, 84.5698°W on 25 Apr 1045Z. The final target point for the time-optimal path forecast is the center of the Tortugas Eddy provided by the MSEAS ocean forecast on April 30 0Z.
| Speed (cm/s) | Level Sets and Time-Optimal Path | Time-Optimal Path with Headings and Current | Optimal Headings vs. Time |
|---|---|---|---|
| Rectangular | |||
| 20 |
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| 30 |
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| 40 |
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| 50 |
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