polar applications
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Geography
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Dec 6, 2023
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docx
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Uploaded by MasterReindeerPerson314
Anika Kothari and Uma Yaga
Precalculus Honors
Sybertz
28 May 2023
Applications of Polar Graphs in Radar Navigation
Polar Graphs are a circular representation of the traditional rectangular plane, but instead
of defining (x,y) points using the horizontal and vertical distance, polar coordinates, indicated by
(r, θ), represent the distance from origin and angle measured from the x-axis. By using polar
coordinates to represent spatial information, radar systems can detect, track, and navigate
through objects in the environment around them.
Radar systems work by emitting radio waves from an antenna. When the waves hit an
object, asignal gets reflected back to the antenna, which then provides the range and bearing of
the object in its relative location from the antenna.
In converting the received measurements into
polar coordinates, operators can use radar and polar graphs to easily analyze the position, speed,
and trajectory of a target object. The use of polar graphs is best utilized with navigation, since the
natural measurements of range and bearing that are given by the radar easily correspond to the
distance and angle measurements that define polar coordinates. In radar navigation objects are
depicted in a circular arrangement, with the radar antenna located at the origin of the coordinate
system, therefore resembling the circular shape of polar graphs.
In both maritime and air travel radar systems, polar graphs help ensure safety. On boats
and ships, polar graphs play a crucial role in detecting vessels, obstacles, and landmasses. With
radar systems equipped with polar displays, ships can safely navigate through congested waters
and difficult weather conditions. Similarly, polar graphs are vital in aviation radar systems,
providing key information for air traffic controllers and pilots. The use of polar coordinates in
radar displays assists in maintaining safe distances between aircraft, managing air traffic flow,
and facilitating precision landing approaches.
In conclusion, the utilization of polar graphs in radar navigation, with their circular
representation and the ability to accurately depict angular information, promotes safety and
efficiency in both the maritime and aviation industries, assisting operators in detecting, tracking,
and navigating objects effectively.
Works Cited
Britannica, The Editors of Encyclopaedia. "polar coordinates." Encyclopedia Britannica, 2 Jun.
2022, https://www.britannica.com/science/polar-coordinates. Accessed 28 May 2023.
Collins, Danielle. "Motion basics: Difference between Cartesian and polar coordinate systems."
Linear Motion
, 22 Oct. 2019, www.linearmotiontips.com/motion-basics-difference-
between-cartesian-and-polar-coordinate-systems/#:~:text=A%20key%20difference
%20when%20using,sets%20to%20describe%20any%20point. Accessed 28 May 2023.
"Polar (Radar) chart."
HighCharts
, www.highcharts.com/docs/chart-and-series-types/polar-chart.
Accessed 28 May 2023.
Skolnik, Merrill I.. "radar." Encyclopedia Britannica, 20 May. 2023,
https://www.britannica.com/technology/radar. Accessed 28 May 2023
.
Websites used for conversion:
à
Rectangular form to polar form
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https://keisan.casio.com/exec/system/1223526375
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https://www.emathhelp.net/en/calculators/calculus-2/polar-rectangular-equation-calculator/?
f=%5Cfrac%7B%5Cleft%28%5Cleft%28x-3%5Cright%29%5E%7B2%7D%2B%5Cleft
%28y%2B4%5Cright%29%5E%7B2%7D%5Cright%29%7D%7B20%7D%3D1
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