Computing Area Using Planimeter

Planimeter is a mechanical instrument used for measuring area of plan. The commonly used planimeter is known as Amsler planimeter

 

The essential parts of a planimeter are:

1. Anchor: It is a heavy block with a fine anchor pin at its base. It is used to anchor the instrument at a desired point on the plan.

2. Anchor arm: It is a bar with one end attached to anchor block and the other connected to an integrating unit. Its arm length is generally fixed but some planimeters are provided with variable arm’s length also.

3. Tracing arm: It is a bar carrying a tracer point at one end connected to the integrating unit at the other end. The anchor arm and tracer arms are connected by a hinge. The length of this arm can be varied by means of fixed screw and slow motion screw.

4. Tracing point: This is a needle point connected to the end of tracer arm, which is to be moved over the out line of the area to be measured.

5. Integrating unit: It consists of a hard steel roller and a disc. The axis of roller coincides with the axis of tracer arm hence it rolls only at right angles to the tracer arm. The roller carries a concentric drum which has 100 divisions and is provided with a vernier to read tenth of roller division. A suitable gear system moves a pointer on disc by one division for every one revolution of the roller. Since the disc is provided with 10 such equal divisions, the reading on the integrating unit has four digits:

(i) Unit read on the disc

(ii) Tenth and hundredth of a unit read on the roller

(iii) Thousandth read on the vernier.

Thus if reading on disc is 2, reading on roller is 42 and vernier reads 6, then the total reading

F = 2.426

 

Method of Using Planimeter

To find the area of a plan, anchor point may be placed either outside the plan or inside the plan. It is placed outside the plan, if the plan area is small. Then on the boundary of the plan a point is marked and tracer is set on it. The planimeter reading is taken. After this tracer is carefully moved over the outline of the plan in clockwise direction till the first point is reached. Then the reading is noted. Now the area

of the plan may be found as

 

Area = M (F – I + 10 N + C) ...(18.7)

where M = A multiplying constant

F = Final reading

I = Initial reading.

N = The number of completed revolutions of disc. Plus sign to be used if the zero mark of the dial passes index mark in clockwise direction and minus sign if it passes in anticlockwise direction.

C = Constant of the instrument, which when multiplied with M, gives the area of zero circle. The constant C is added only when the anchor point is inside the area.

Multiplying constant M is equal to the area of the plan (map) per revolution of the roller i.e., area corresponding to one division of disc. Multiplying constant M and C are normally written on the planimeter. The user can verify these values by

(i) Measuring a known area (like that of a rectangle) keeping anchor point outside the area

(ii) Again measuring a known area by keeping anchor point inside a known area.

The method is explained with example. The proof of equation 18.7 is considered as beyond the scope of this book. Interested readers can see the book on surveying and levelling.

 

COMPUTATION OF VOLUMES

The following three methods are available for computation of volumes:

(i) From cross-sections

(ii) From spot levels and

(iii) From contours.

First method is useful for computing earth work involved in road/rail/canal/sewage works. Second method is useful for finding earth work in foundations of large building and the last method is useful for finding capacity of reservoirs.

Computation of Volume from Cross-sections

To compute earth work, profile levelling is carried out along the centre line of the alignment of the project and cross-sectional levels are taken at regular intervals. Then the volume of earth work can be found, if the cross-sections are determined.