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Plots of Polar Coordinates

Points as distance from the origin and angle from an axis.

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How NOT To Get Lost At Sea

Polar Coordinate System in Navigation

Recall that the polar coordinate system is just another way to plot points versus the rectangular coordinate system. To graph in the polar system, you plot points in the form (r,ϴ) such that ϴ describes an angle and r determines the distance away from the origin.

Credit: Thorsten Pohl
Source: http://commons.wikimedia.org/wiki/File:ShipNorway.JPG
License: CC BY-NC 3.0

Ship Norway anchoring in Bremerhaven, Germany [Figure1]

Navigating ships or aircraft is very different than driving a car. For starters, cars are dependent on rigid roads to guide them to the places they would like to go. You can think of navigation in driving as being on a rectangular coordinate system: go two blocks to the right, and three blocks up. Well as for the ships in the open sea,  their captains do not have to adhere to the same navigational rules as drivers have with roads and rectangular coordinates. Instead captains and pilots use a variation of the polar coordinate to help them navigate through open territory. In math, a polar coordinate has 0 degrees set on right axes of the coordinate system and has angles increasing counter-clockwise, but in navigation, 0 degrees is set at top axes or “north” and angles increase as one moves clockwise about the system. Instead of 4 miles right and 3 miles up, captains would call for 5 miles in a direction of 53.13 degrees which is more efficient and direct.

Creative Applications

1. A pilot is traveling 2°N and wants to turn to the 270°E. In what direction should he turn and in how many degrees?

2. If a ship is traveling in a direction of 180°S and receives instruction to travel 2 miles in a direction of 30°E of its current location, convert the final destination point to rectangular coordinates.

3. Could we apply the polar system to driving on roads?

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Image Attributions

  1. [1]^ Credit: Thorsten Pohl; Source: http://commons.wikimedia.org/wiki/File:ShipNorway.JPG; License: CC BY-NC 3.0

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