Method of Using Planimeter
Anchor point may be placed either outside the plan or inside the plan to find the area of a plan. If the plan area is small it is placed outside the plan. Then a point is marked and tracer is set on it on the boundary of the plan. The planimeter reading is taken. After this tracer is watchfully moved over the outline of the plan in clockwise direction until the first point is reached. Then the reading is noted down. Now the area of the plan may be found as following
Area = M (F - I + 10 N + C)
Where M stand for A multiplying constant &F stands for Final reading and I stand for Initial reading.
N is equal to the number of completed revolutions of disc. Plus sign to be used index mark in clockwise direction if the zero mark of the dial passes and minus sign if it passes in anticlockwise direction.
C = Constant of the instrument, which when multiplied having M, gives the area of zero circle.
Only the constant C is added when the anchor point is inside the area.
Multiplying constant M =to the area of the plan (map) per revolution of the roller for example area equivalent to one division of disc.
Normally, Multiplying constant M and C are written on the planimeter. The user can check these values by following
(i) Measuring a known area (such as rectangle) keeping anchor point outside the area
(ii) Again by keeping anchor point inside a known area measuring a known area. The method is described with example.
Example : To find out the constants of a planimeter a 20 cm × 20 cm area was measured with anchor point outside the plan area. Zero mark of disc crossed the index in clockwise direction once. The observed readings are following
Initial reading = 7.422
Final reading = 1.422
Determine the multiplying constant M.
Solution:
Now Area = M (F - I + 10 N)
Area = 20 × 20 = 400 cm2
F = 1.422, I = 7.422
∴ 400 = M (1.422 - 7.422 + 10 × 1)
∴ M = 100 cm2 Ans.