Saturday, February 22, 2014

How to find out the area using Planimeter


Planimeter is a Surveying instrument which can be used to find out the area of a map or plan.  A Swiss mathematician Jacob Amsler Laffon built first modern planimeter in 1854. Many developments followed Amsler's famous Planimeter including the electronic planimeter.

A Polar Planimeter (source: wikipedia)
We have three mechanical types of Planimeters:

  1. Polar 
  2. Linear
  3. Hatchet Planimeter
All Planimeter work on the same principle.
There is a linkage, at one end is a pointer and the other is fixed for a polar planimeter and is restricted for a linear.The pointer is traced along the perimeter of the area of the shape is indicated on a scale.

There is a wheel attached to planimeter which rolls when the movement of the pointer is perpendicular to the axis of the wheel so, this movement is recorded.
It will skid when the movement of the wheel is parallel to the axis so, this movement is ignored.
Linear Planimeter (Source : Wikipedia)
That means that planimeter measures the distance which is traveled by the rolling of the wheel. Area of the shape is proportional to the nos. of turns through which the measuring wheel turns.

The area calculations can be proved by using Green's Theorem.

Please visit wikipedia for detailed study.

In order to find out the area, all you have to do is to trace the perimeter of the area on the map, and note down the reading.

To get more accurate results one should be skilled in tracing the exact perimeter of the shape.
You can convert the area to the field area using the scale of the map.
These days digital planimeters are in the market which are more easy to use.

Thanks for visit!


Solved Example-Distance of a Point from a Line, whose end Co-ordinates are given.

Hi, Problem: The X and Y co-ordinates(in meters) of station Shore are 246.87 and 659.46 respectively, and those for station Rock are 437...

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