How to write a polynomial from a set of readings from Excel:

How to write a polynomial

This is normally required for interpolating readings from a set of given readings. How to write a polynomial is mostly required during the calibration of load cells where normally only ten sets of readings are given in the calibration certification. However, during the   actual calibration of uniaxial testing machines like UTM, TTM, CTM intermittent readings may be required by engineers due to various ranges in the process.

Procedure:

 
  1. Note the set of readings in the below given box (which are in steps of 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 100%) in two adjacent columns.

    Example readings from 10kN to 100kN

    Applied Force kN

    Observed Readings kN

    10

    10.1

    20

    20.1

    30

    30.1

    40

    40.2

    50

    50.2

    60

    60.4

    70

    70.5

    80

    80.3

    90

    90.5

    100

    100.4

    2. Select the Table using the cursor / mouse

    Applied Force kN

    Observed Readings kN

    10

    10.1

    20

    20.1

    30

    30.1

    40

    40.2

    50

    50.2

    60

    60.4

    70

    70.5

    80

    80.3

    90

    90.5

    100

    100.4

3. On the selection table, right click the mouse & the insert the graph from the INSERT drag Menu.

4. Select the graph in the name of graph as scatter with smooth lines & markers.

5. With the trend line drawn, select the line. so that the points are highlighted.

6. Now using the mouse right on it. & Select add trend from the drop menu.

7. The drop-down menu is visible on the right side & you can select the polynomial of 2nd degree

8. If you scroll down the trendline menu you can find the display equation on chart option which can be selected. This gives an equation on the graph which can be put in the excel to get the X Vs Y values.

  1. With this equation every value of Y can be calculated for a given value of X.
  2. It may be necessary to know the value of X with known value of Y.
  3. IN this case the column X & Y can be interchanged in the excel so that Y Vs X can be plotted & intermittent values can be calculated.
  4. Please be informed that the readings are valid for interpolation & no extrapolation is allowed in this case.
  5. Interpolation means readings with the minimum & maximum values taken from the graph.
  6. Extrapolation means readings derived outside the linear curve of minimum & maximum readings.

 

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