Planimeter - Types of planimeter, Advantages & disadvantages, Characteristics, Components and functions, Procedure, Working principle

What is planimeter in surveying?

A planimeter is a mechanical device that is used to measure the area of an irregularly shaped two-dimensional object. It consists of a flat plate that is connected to a measuring wheel by a linkage arm. To use a planimeter, the plate is placed on the surface to be measured and the measuring wheel is moved around the perimeter of the object. As the wheel rotates, the linkage arm transfers the measurement to a scale on the planimeter that indicates the area of the object in square units. Planimeters are commonly used in fields such as surveying, engineering, and architecture to measure land areas, floor plans, and other geometric shapes.

Types of planimeter: -

There are three main types of planimeters:

1. Amsler polar Planimeter - Also known as the linear planimeter, this type of planimeter measures the area enclosed by a curve. It consists of three main parts - the tracer arm, the measuring wheel, and the fixed reference point. The tracer arm follows the curve to be measured while the measuring wheel tracks the movement of the tracer arm. The enclosed area is directly read off from a calibrated scale on the planimeter.

2. Rolling Planimeter - Also known as the digital planimeter, this type of planimeter uses a digital display to measure the enclosed area. It consists of a measuring wheel that rolls along the curve to be measured. The wheel is equipped with sensors that detect the movement of the wheel and calculate the enclosed area. The measurement accuracy is generally higher than that of the polar planimeter as it eliminates manual reading errors.

3. Digital planimeter - uses digital technology to measure the area of the figure. It typically consists of a handheld device with a stylus or tracing wheel that is linked to a computer program to render the measurement results.

Advantages of Planimeter: -

1. Accurate Measurements: Planimeters provide highly accurate measurements of the area of an irregular shape or an irregularly bounded object.

2. Easy-to-Use: Planimeters are user-friendly and do not require any special skills or training to use them.

3. Time-Saving: Planimeters can measure the area of a shape in a matter of seconds, which would otherwise take a lot of time if done manually.

4. Cost-Effective: Planimeters are a cost-effective solution for measuring the area of irregular shapes as precision equipment like GPS and GIS can be prohibitively expensive.

5. Portability: Planimeters are portable, compact, and easy to carry, making them perfect for fieldwork.

Disadvantages of Planimeter: -

1. Limited Use: Planimeters can only measure the area of a 2-dimensional surface, making them unsuitable for measuring the volume of an irregular object.

2. Physical Limitations: Planimeters require a stable and flat surface to function accurately and may not work correctly on a curved or uneven surface.

3. Smaller Range: Planimeters have a limited range and may not be suitable for measuring very large areas.

4. Calibration Issues: Planimeters need to be calibrated correctly to provide accurate measurements, and calibration can be time-consuming.

5. Mechanical Malfunction: Planimeters are mechanical devices and can sometimes malfunction, leading to incorrect measurements.

 Characteristics of a planimeter: -

i. Planimeters are extremely accurate in their area calculations. They can calculate even highly irregular shapes with precision.

ii. Planimeters can be used to measure areas on a variety of surfaces, including paper, maps, and engineering drawings, making it a highly versatile instrument.

iii. Easy to use: Planimeters require minimal training and can be used by anyone to measure areas without much effort.

iv. Portable: Planimeters are quite small and can be easily carried from one place to another.

v. Planimeters are made of high-quality materials such as steel, brass, and plastic, making them durable and long-lasting.

vi. Planimeters provide consistent results when used for measuring the same shape multiple times.

vii. Planimeters can provide area measurements quickly and efficiently, making them useful in situations where time is of the essence.

viii. Planimeters have a high degree of precision and can even measure areas up to 0.1 square millimeter with accuracy.

Components of planimeter and their functions: -

The main components of a planimeter include: 

1. Tracer arm: This is the long arm of a planimeter that is used to trace the perimeter of the shape being measured. 

2. Pivot: This is a stationary point around which the planimeter rotates. The tracer arm is attached to the pivot, and it moves along the shape being measured. 

3. Roller: This is the rotating wheel that rests on the surface of the paper being measured. The roller rotates as the tracer arm moves, and it records the distances traveled by the tracer arm. 

4. Counter: This is the dial or digital display that shows the area of the shape being measured. The counter is connected to the roller and calculates the area based on the distances traveled by the tracer arm. 

5. Reset button: This allows the user to reset the planimeter to zero before starting a new measurement. 

6. Scale: This is a measuring scale that is used to calibrate the planimeter for different units of measurement. 

7. Weight and Needle Point: It is also called as anchor. A fine needle point is located at the base of heavy block. This needle point is anchored at required station on the plan.

8. Clamp: Clamp is used to fix the tracing arm in standard length without any extension.

9. Hinge: The tracing arm and anchor arm are connected by hinge to the integrating unit. With the help of this hinge the arms can rotate about their axes.

10. Tangent Screw: Tangent screw is used to extend the tracing arm up to required length.

11. Index: Index is a location where all the measuring arrangements like wheel, dial are located.

12. Wheel: Wheel is fixed in the integrating unit which helps to measure the tracing length. It is used to set zero on the scale.

13. Dial: Dial is nothing but scale which is to be set zero at the initial level using setting wheel.

14. Vernier: Vernier is attached to the wheel as rounded drum with graduations on it. It is divided into 100 parts.

How it works: -

To use a planimeter, the tracer arm is placed on the outline of the shape, and the wheel is set to zero by moving a lever or pressing a button. The tracer arm is then moved along the outline of the shape, and the wheel tracks the distance traveled. The area of the shape is calculated based on the distance traveled and the calibration of the wheel.

Planimeter procedure to measure area: -

 However, here are the steps on how to measure an area in a planimeter:

1. Set the planimeter to zero: Press the reset or zero button on the planimeter to set it to zero.

2. Place the planimeter on the drawing: Place the planimeter on the drawing paper and make sure that the starting point or the reference point is aligned with the starting point of the drawing.

3. Trace the area: Slowly trace the boundary of the area to be measured with the pointer of the planimeter. Make sure that the pointer follows the boundary accurately and is always in contact with the paper.

4. Finish tracing: Once the tracing is complete, press the finish button on the planimeter to stop the measurement.

5. Read the area: The area measurement is displayed on the planimeter. Note down or record the result. 

6. the area of the plan which boundary is traced by the planimeter is determined from the below formula.

Area = M (B – A + 10N + C)

Where, 

A = initial reading 

B = final reading 

N = no. of completed revolutions of wheel during one complete tracing. N is positive if dial passes index in clockwise, N is negative if dial rotates in anti-clock wise direction. 

M and C = constants which values are provided on the planimeter. Constant C is used only when the anchor point is placed inside the plan.

7. Reset the planimeter: Reset the planimeter to zero by pressing the reset or zero button before measuring the next area.

Note: It is important to follow the manufacturer's instructions when using a planimeter.

What is working principle of planimeter?

A planimeter works on the principle of measuring the area of a curved surface by tracing its boundary with a stylus. It consists of two arms connected by a pivot. One arm contains the tracing stylus while the other arm has a wheel attached to it. The wheel rotates as the planimeter is moved along the curve being measured. The area enclosed by the curve can be calculated based on the number of rotations of the wheel, its radius, and the scale factor of the planimeter. The working principle is based on the fact that the area enclosed by a curve is equal to the product of the average distance between the curve and the pivot point and the distance travelled by the stylus along the curve.