Planimeter: Meaning, types, usage and accuracy

Johann Martin Hermann, a surveyor by trade, devised the planimeter in 1818, a device that follows the boundary curve with a pointed needle connected to a measuring wheel that alters the length of the boundary up to the desired capacity. Jacob Amsler-Laffon built the first practical, feasible and advanced planimeter in 1854.

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A planimeter is a basic tool for precisely measuring any shape’s areas of planar figures. To calculate an area, trace the shape of the figure clockwise with the tracing lens’s centre point (inside the ring) and read out the result on the scales.

The planimeter comprises three parts: the tracing arm, the roller housing, the polearm and the pole plate. In this case, the three sections are bundled separately. The polearm is a straightforward beam. A ball is attached to either end, one for fitting into the roller housing and the other onto the pole plate. The roller housing is supported by three elements: a tracing lens, a measuring roller and a supporting ball.

Planimeter: Types of planimeter

The following are the five primary types:

Polar planimeter

A polar planimeter is a mechanical device that measures the size of a region by tracing its perimeter. The instrument is made up of three basic parts- a polearm, a tracer arm, and a measurement wheel. The polearm spins around the pole, a pivot joint connects the tracer arm to the free end of the polearm and the measuring wheel is linked with its axis parallel to the tracer arm.

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A linear planimeter

The linear planimeter is a variant of the polar planimeter that measures the areas of long, slender zones.

Amsler polar planimeter

The Amsler polar planimeter comes in help for measuring an uneven or self-assertive shaped region. This device tracks the shape’s border keeping in mind the origin. The measurement is shown on the wheel at the hinge.

Digital planimeter

A digital planimeter is a sophisticated device with a built-in nickel-cadmium storage battery. Mechanical planimeters now use a turning encoder instead of an integrating wheel. An electrical circuit calculates the beats of the rotating encoder, and the area is displayed in digital form on the display screen.

Prytz’s planimeter

In 1875, this innovation was produced. It is a very simple device consisting of a rod with its ends bent at right angles. Prytz called it a ‘stang planimeter’, which means ‘rod’ in Danish.

Planimeter: How to use it?

Using the clamp and movement screw, precisely position the record arm on the tracing arm at the necessary scale.
For accuracy, avoid using wrinkled sheets.
Keep the anchor point constant on paper inside the border for little external maintenance.
Set focus points on the plan’s exterior boundary line and precisely place the tracing arm over it.
Take the first readings for the dial, wheel, and Vernier. Continue tracing the point along the plan’s boundary until you reach the starting point.
Note zero rotations clockwise and anticlockwise as the tracing arm moves.
Repeat examining readings on the dial, wheel, and Vernier before perusing.

Planimeter: Things that affect its accuracy

The gadget’s precision

To test the device’s accuracy, create an ellipse of 100 sq. cm. Follow the steps to compute the ellipse’s area. Reading is proper if the roller completes a rotation from 0 (start point) to 0 (endpoint). It is equivalent to 1000 Vernier units multiplied by 0.1 to equal 100 cm². After running the test, we determined that it would produce an inaccuracy of 0.1 in each reading.

Environmental aspects

External circumstances also have an impact on accuracy. If the paper on which it is drawn is wrinkled or ripped, accurate results cannot be expected. The correct temperature is 20º Celsius (68º Fahrenheit).

Human mistakes

Trained individuals outperform others, so attention and patience are essential while tracing. Daylight and a comfortable working position also affect results.

Area dimensions

While tracing a square with side lengths of 1 inch each and an inaccuracy of 0.01 inch results in a value of 1.04 sq. inch, which equals a 4% error instead of 1 sq. inch. If we repeat the error with squares with two sides, the result is 4.08 sq. inch, which equals a 2% error. The result for a 10-inch square is 100.4 sq. inch, which equals a 0.4% error. The greater the area, the higher the rate of error.

FAQs

What is a planimeter, and what are its applications?

A planimeter is a tabletop equipment used to measure areas, often the areas of irregular regions on a map or image. They were previously common but have since been supplanted mainly by digital technologies.

What's the distinction between a mechanical and a digital planimeter?

Digital planimeters function similarly to mechanical ones but feature a digital readout of measurements. A digital planimeter also allows you to pick your map scale and unit of measurement to receive a direct output in multiple quantities, such as km2, removing the need to convert measurements.

What are the different types of linear measuring instruments?

Linear measuring instruments are classified based on their precision. Non-precision instruments and precision instruments are divided into two groups. Steel rules, calliper dividers, and telescopic gauges are non-precision tools used to measure rule line graduations.

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