To study the planimeter and computing area of an irregular figure

Theory

The planimeter is most useful in determining the area of figure plotted to scale, when the boundaries are irregular or curved such as river boundaries etc. It consists of two arms hinged at a point (pivot point). One of the arm is called the anchor arm and is of fixed length. It carries a needle point called the anchor point which is fixed in the paper and head in position by a small weight which is detachable.

The outer arm called tracing arm is of an adjustable length and carries a tracing point which is moved round the boundary of the area measured. The total normal displacement is measured by a wheel whose axis is paralled to the tracing axis. The wheel may be placed between the tracing point and the pivot point or beyond the pivot point away from the tracing point. The wheel carries a gradualed drum divided into 100 parts. The length of a part being read on the vernier.

Diagram

Use of the planimeter for computation of areas

a)  Set the index mark on the leveled edge of the side to the scale to which the figure is drown.

b)   Fix the needle or anchor point firmly in the paper. Move the tracing point in the clockwise direction ground the figure and at the same time observe the dial in order to see whether the total rotation of the wheel is in a forward or a back ward direction.

c)   Mark a definite point on the outline of the figure and set the tracing point exactly at it.

d) Read the dial and wheel and record it as the initial reading. Alternatively set the dial and wheel to zero.

e) Move the tracing point exactly around the outline always in a clockwise direction until it again reaches the starting point. Again read the dial and wheel recording it as the final reading.

f)    Note the number of times the zero mark of the dial passes fixed index mark in a clockwise or counter clockwise direction. This is done while the tracing point is moved along the outline of the figure.

The area of the figure may be obtained by the following formula

Area = M (F.R. – I.R.) +/- 10 N + C

M = the multiplier whose value is marked on the tracing arm next to the scale division

F.R. = The final reading

I.R. = The initial reading

N = The number of time the zero mark passes the fixed index mark.

C = The constant marked on the top of the tracing arm just above the scale division.

Calculation

Area = M (F.R. – I.R.) +/- 10 N + C