Abstract

Citation

Researchers should cite this work as follows:

• Harwood, R. (2022). 1-005-NavigatingNumericalMethods-TechniqueNarrative. SIMIODE, QUBES Educational Resources. doi:10.25334/T2G8-2R07

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Article Context

Description

These methods are motivated by velocity field and dead reckoning navigation over two dimensions to locate a ship lost at sea.

The ship, El Perdido, was damaged during a storm which knocked out its main and backup power generators. Before the backup generator failed, Captain Miguel Gomez sent a distress call and the crew have been able to keep El Perdido afloat, but the ship is adrift in the Pacific Ocean off the coast of California. Thankfully, a US Coast Guard rescue operation is underway after receiving the distress call. The Coast Guard has El Perdido's last known position and has mapped out the surface water velocities in this area as slope fields for longitude (x) and latitude (y), which they have updated using historical data and estimated predictions. Since the search grid is small enough, this curved region on the surface of the earth is relatively flat. 

After days of failed searches, the length of time expected for El Perdido's crew to survive has expired (calculated by the standard Cold Exposure Survivability Model). Accordingly, the Coast Guard mission coordinator downgrades the rescue operation to ``Active Search Suspended, Pending Further Developments." Because the El Perdido crew had kept the ship afloat and had salvaged some of the food reserves, they are able to survive for several more days but their time is still running out.

On the fourth day adrift, El Perdido's crew is able to get a short spurt of power, in which they send another distress call and print out logs of ship velocity and acceleration from their Inertial Navigation System (INS). We join the Coast Guard rescue operation, reactivated after receiving the distress call, as they update their slope field maps and launch another search. Simultaneously, Captain Gomez now uses dead reckoning from the INS logs to estimate his own position knowing only El Perdido's previous velocities and accelerations, in hopes that he can assist the rescuers if the crew can get the power back on.

Split your group with half helping the rescuers in one numerical approach  and half helping El Perdido's captain in another numerical approach. Then compare your results. Based upon the search radius of each rescue craft and Captain Gomez's own dead reckoning, determine if El Perdido is found on this rescue attempt.