18
APPENDIX C. USE OF SECOND ORDER POLYNOMIAL TO IMPROVE
ACCURACY
Most calibrations use linear coefficient to calculate pressure, loads strains etc. from measured
readout “digits”. If the output of the sensor is not truly linear then there will be some inaccuracy
introduced into the calculated value. Thus, even though the calibration accuracy may be 0.1% FS
(because this is the accuracy of the calibration apparatus) yet the linearity may only be 0.5% F.S.
so that the calculated value may differ from the true value by this larger amount.
To recapture the 0.1% FS accuracy inherent in the calibration data it makes sense to use a second
order polynomial to fit the calculated values to the actual calibration curve. The second order
polynomial has the following characteristics. Calculated value = AR
2
+ BR + C where R is the
observed reading on the readout box and A, B, C, are the three coefficients shown on the
calibration report. Note that, unlike the linear method, this equation does not contain the item
(R
1
– R
0
) and thus requires a different treatment for establishing zero conditions. The coefficients
shown on the calibration report are those developed under the conditions of temperature and
barometric pressure experienced at the time of the calibration and which are shown on the
calibration report. Theoretically, these could be used as is, but it is always good practice to
establish and use zero conditions at the site since the zero may have shifted slightly due to rough
handling during shipment and/or installation; and hence a slight adjustment of the “C”
coefficient may be called for. Therefor it is recommended that the value of C be determined at
the site for the conditions of temperature and barometric pressure experienced at that time.
For example, using the data from the sample calibration report shown in Appendix D:
At the site, at a temperature of T
0
= 30
°
C and a barometric pressure of 1000 mbar, the observed
zero pressure reading on a GK-404 readout (channel B) is R
1
=7420. Using the polynomial
coefficient to calculate a new value of C.
(7420)
2
x 3.303E-09 + (7420) x 0. C = O
gives C = -13.634
Note that the transducer shown is of a vented type, and hence no barometric correction is
required. However, it is essential for vented types, that the moisture trap seal screw be removed
before taking the zero reading (or any reading) so that the vent line is open to the atmosphere.
Summary of Contents for 4580
Page 2: ......
Page 4: ......
Page 25: ...19 APPENDIX D TYPICAL CALIBRATION REPORT Figure 7 Sample Model 4580 Calibration Report ...
