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Keywords: Zero circle, circle of correction, planimeter, area computation using planimeter
We already discussed the instrumental method for area computation i.e., the planimeter method. If you want to freshen your knowledge then read it here.
Zero circle or the circle of correction, is the circle around whose circumference if the tracing point is moved but no rotation of the wheel will be caused.the wheel will slide on the paper without causing any change in the reading.
This condition is obtained when the tracing arm is maintained in such a position with reference to the anchor arm that the plane of the wheel will always pass through the anchor point (i.e. this is by making sure that the line joining to the anchor point of the wheel should be at right angles to the line joining the tracing point to the wheel). The anchor point is defined as the center of the zero circle. The line joining the anchor point with the tracing point is termed as its radius.
In these cases, the area of the zero circle is to be added to the recorded result. Because when the anchor point is placed inside the plot figure, the planimeter usually records the total area of the annular space between the given figure and the zero circle.
Methods for the determination of the area of zero circle
The different methods by which the area of the zero circle can be determined are:
(a) Using the planimeter
The stepwise procedure is given below:
1) Find the area of the figure of known area by the planimeter with the anchor point inside the figure. The relevant equation is
A = M (FR – IR±10N+C)
A, M, FR, IR and N are known.
M= the multiplier
FR= final reading
IR= initial reading
N= it is the number of times the zero mark of the dial passes the fixed index mark
C= a constant
Then solve for C
2. When the tracing arm moves along the circumference of the zero circle,
IR=0, FR=0, N=0 therefore, A= MC
Substitute M=100 and the value of C from step 1 to get the area of the zero circle.
(b) If the area of the figure is not known, find its area by the planimeter with anchor point OUTSIDE the figure for which
A= M (FR-IR ± 10 N), Since C=0
Now apply the method (a) and find the area of the zero circle.
(c) By measuring the radius of the zero circle
The stepwise procedure is
(i) Draw two lines AW and TW at right angles to each other intersecting at W
(ii) Place the tracing point at T, the anchor point at A and the wheel at W. Measuring the distance AT between the anchor point and the tracing point, which gives the radius R of the zero circle.
Then the area of the zero circle is given by= πR2
If you have a query, you can ask a question here.