Study of Planimeter
APPARATUS : Planimeter
A Planimeter is a mechanical integrator is used by engineer for measuring area of figure which is been plotted scale particularly when the boundaries are irregular are curved mathematically it is difficult to find the area of such irregular figures. Planimeter is largely used for finding the areas of contour in determining the capacity of storage server.
These are several types of Planimeter but the ampler polar Planimeter is in most common use & is described as-
It consists of two arms hinged at a point one is known is anchor arm & it is at fixed length. It has a needle point called the anchor point which is fixed in paper & hold in position by detachable small weight the other arm is called trussing arm. it carries a tracing point which is moved along the periphery of the figure of which the area is to be found out . Tracing arm is adjustable is length the tracing arm is set to position given by the manufacturer according to scale used the total normal displacement is measured b rolling wheel. The rolling wheel carries graduated drum divided into 100 parts. The vernier is provided to read 1/10th parts of the rolling wheel. The wheel is connected by gears is the counting disc. The counting disc measure one revolution at every 10 turns of the rolling wheel each complete reading is a figure of four digits. The zero of rolling wheel is apposite to the zero at veriner. Actually the marks of rise should be opposite to index mark due to imperfection of the wheel gear.
Instrument is equipped with magnifying lance to read vernier & a check bar or flat bar for testing the Planimeter.
Reading on Planimeter:
Each complete reading on Planimeter is a figure of digits. Let the reading be 4.375 the first digit 4 is read on the disc the second digit 3 is read on the rolling wheel (main scale) the third digit 7 is read on the falling wheel (main scale) & the last is fourth digit 5 is read on the vernier scale beside the main scale of rolling wheel position of measuring unit (setting of tracing arm) the position of tracing arm is adjustable according to given position by the manufacture for the different scalar. The position of measuring unit will be vary from instrument to the index mark on the beveled edge of the tracing arm of the figure may be obtained directly in m2 or hectors by marking use of multiplying scale factor.
Method of using Planimeter:
The Planimeter is used in determining the areas of the figure in 2 ways.
- By placing the anchor point outside the figure.
- By placing the anchor point inside the figure.
- 1Set out the index arm on the tracing arm to the given scale as per manufactures instruction exactly b using clamp & fine motion screw. Stretch the sheet making free from wrinkle ness.
- Fixed the anchor point of firmly on paper inside & for small outside keep.
- Mark the points on the boundaries of the figure & set tracing arm exactly over it.
- Now take the initial reading i.e. the reading on dial & wheel & vernier.
- Move the tracing point along the periphery of the figure & stop at the starting point.
- While tracing point is moved note the number of times the zero index mark in clockwise & anticlockwise direction. Again take the reading of on dial wheel & vernier that will be final reading.
- The calculated area (A) = m (FR-IR +10N+C)
Where, M=multiplying constant which is different scales
N=number of times the zero of dial passes the fixed index mark use the +ve sign when moves clockwise & -ve sign moves anticlockwise.
C= constant of instrument supplied by manufacture & different for different scales & it is offset when anchor point is kept inside otherwise it is taken zero if it is kept outside.
FR = Final reading
IR = Initial reading
Area of the zero circles i.e. Mc is defined as the correction circle which is defined as a circle found the circumference at which if the tracing point is moved wheel will slide without rotation in a reading. This is possible when tracing arm is placed in such a position relative to the anchor of arm that the plane of the roller passes thought the anchored point the multiply constant of Planimeter is equal to the number of unit of area per revolution of the roller.
RESULT: – Planimeter has been used to measured irregular figure.