In this paper, we present a method for determining the area in which an airplane that has feared
... more In this paper, we present a method for determining the area in which an airplane that has feared to crash in open waters can be found. We then utilize our models to help plan for future aircraft disasters by finding areas of high search priority so that we can optimize search flight formations. Our models first take a continuous approach to solve for the differential equations that describe the motion of the plane as it crashes. Then, to account for the ocean's surface currents, a discrete method is used to track the motion of the wreckage after crashing at a location near the plane's loss of signal. With both combined, our model takes advantage of fundamental theorems in both Physics and Calculus in order to find areas of high search priority. Specifically, we use the Fundamental Theorem of Calculus to assess that solving the problem at its bounds will give us a solution within the bounds. Our physical crash model finds that the area of uncertainty for a plane crash is proportional to the time between the lost signal and the crash multiplied by the difference in its maximum and minimum velocities. This means that the more we know about when a crash takes place, the less the area of uncertainty. We show results of different areas of uncertainty for different aircraft. The ocean current model used in this paper attempts to emulate circulatory currents, called gyre currents. We find that the closer a crash is to the center of a gyre, the more likely it is for the crash debris to drift outward radially. We also find that the further a crash site is from the gyre center, the likelier it is to spread out along a curve. Our ocean current model has the capability to resemble an arbitrary surface current, and to potentially represent real-time surface currents from ocean sensors and be expanded for underwater currents. We combine the data to determine areas of search priority and search patrol. A test comparison case is presented with the Air France flight 447 crash as the leading example. With this, we construct a plan to aid in future search and rescue missions with a primary emphasis on ensuring the safety of possible survivors.
In this paper, we present a method for determining the area in which an airplane that has feared
... more In this paper, we present a method for determining the area in which an airplane that has feared to crash in open waters can be found. We then utilize our models to help plan for future aircraft disasters by finding areas of high search priority so that we can optimize search flight formations. Our models first take a continuous approach to solve for the differential equations that describe the motion of the plane as it crashes. Then, to account for the ocean's surface currents, a discrete method is used to track the motion of the wreckage after crashing at a location near the plane's loss of signal. With both combined, our model takes advantage of fundamental theorems in both Physics and Calculus in order to find areas of high search priority. Specifically, we use the Fundamental Theorem of Calculus to assess that solving the problem at its bounds will give us a solution within the bounds. Our physical crash model finds that the area of uncertainty for a plane crash is proportional to the time between the lost signal and the crash multiplied by the difference in its maximum and minimum velocities. This means that the more we know about when a crash takes place, the less the area of uncertainty. We show results of different areas of uncertainty for different aircraft. The ocean current model used in this paper attempts to emulate circulatory currents, called gyre currents. We find that the closer a crash is to the center of a gyre, the more likely it is for the crash debris to drift outward radially. We also find that the further a crash site is from the gyre center, the likelier it is to spread out along a curve. Our ocean current model has the capability to resemble an arbitrary surface current, and to potentially represent real-time surface currents from ocean sensors and be expanded for underwater currents. We combine the data to determine areas of search priority and search patrol. A test comparison case is presented with the Air France flight 447 crash as the leading example. With this, we construct a plan to aid in future search and rescue missions with a primary emphasis on ensuring the safety of possible survivors.
Uploads
Papers by Jacob Hempel
to crash in open waters can be found. We then utilize our models to help plan for future aircraft
disasters by finding areas of high search priority so that we can optimize search flight
formations. Our models first take a continuous approach to solve for the differential equations
that describe the motion of the plane as it crashes. Then, to account for the ocean's surface
currents, a discrete method is used to track the motion of the wreckage after crashing at a
location near the plane's loss of signal. With both combined, our model takes advantage of
fundamental theorems in both Physics and Calculus in order to find areas of high search priority.
Specifically, we use the Fundamental Theorem of Calculus to assess that solving the problem at
its bounds will give us a solution within the bounds.
Our physical crash model finds that the area of uncertainty for a plane crash is proportional to the
time between the lost signal and the crash multiplied by the difference in its maximum and
minimum velocities. This means that the more we know about when a crash takes place, the less
the area of uncertainty. We show results of different areas of uncertainty for different aircraft.
The ocean current model used in this paper attempts to emulate circulatory currents, called gyre
currents. We find that the closer a crash is to the center of a gyre, the more likely it is for the
crash debris to drift outward radially. We also find that the further a crash site is from the gyre
center, the likelier it is to spread out along a curve. Our ocean current model has the capability to
resemble an arbitrary surface current, and to potentially represent real-time surface currents from
ocean sensors and be expanded for underwater currents.
We combine the data to determine areas of search priority and search patrol. A test comparison
case is presented with the Air France flight 447 crash as the leading example. With this, we
construct a plan to aid in future search and rescue missions with a primary emphasis on ensuring
the safety of possible survivors.
to crash in open waters can be found. We then utilize our models to help plan for future aircraft
disasters by finding areas of high search priority so that we can optimize search flight
formations. Our models first take a continuous approach to solve for the differential equations
that describe the motion of the plane as it crashes. Then, to account for the ocean's surface
currents, a discrete method is used to track the motion of the wreckage after crashing at a
location near the plane's loss of signal. With both combined, our model takes advantage of
fundamental theorems in both Physics and Calculus in order to find areas of high search priority.
Specifically, we use the Fundamental Theorem of Calculus to assess that solving the problem at
its bounds will give us a solution within the bounds.
Our physical crash model finds that the area of uncertainty for a plane crash is proportional to the
time between the lost signal and the crash multiplied by the difference in its maximum and
minimum velocities. This means that the more we know about when a crash takes place, the less
the area of uncertainty. We show results of different areas of uncertainty for different aircraft.
The ocean current model used in this paper attempts to emulate circulatory currents, called gyre
currents. We find that the closer a crash is to the center of a gyre, the more likely it is for the
crash debris to drift outward radially. We also find that the further a crash site is from the gyre
center, the likelier it is to spread out along a curve. Our ocean current model has the capability to
resemble an arbitrary surface current, and to potentially represent real-time surface currents from
ocean sensors and be expanded for underwater currents.
We combine the data to determine areas of search priority and search patrol. A test comparison
case is presented with the Air France flight 447 crash as the leading example. With this, we
construct a plan to aid in future search and rescue missions with a primary emphasis on ensuring
the safety of possible survivors.