Appendix C.Improving the Accuracy of the Calculated Pressure
Most vibrating wire pressure transducers are sufficiently linear (±0.2% F.S.) that the use of the linear calibration factor satisfies normal requirements. However, it should be noted that the accuracy of the calibration data, which is dictated by the accuracy of the calibration apparatus, is always ±0.1% F.S.
This level of accuracy can be recaptured, even where the transducer is nonlinear, using a second order polynomial expression, which gives a better fit to the data then does a straight line.
The polynomial expression has the form:
Pressure = AR2 + BR + C
equation 8: Second Order Polynomial Expression
Where:
R is the reading (digits channel B)
A, B, and C are coefficients
Appendix D shows a typical calibration report of a transducer that has fairly normal nonlinearity. The figure under the "Linearity (%F.S.)" column is
|
Calculated Pressure − True Pressure |
x 100% = |
G(R1 − R0) − P |
x 100% |
|
Full Scale Pressure |
F.S. |
equation 9: Linearity Calculation
Note: The linearity is calculated using the regression zero for R0 shown on the calibration report.
For example, when P= 420 kPa, G (R1 – R0) = –0.1795(6749-9082), gives a calculated pressure of 418.8 kPa. The error is 1.2 kPa equal to 122 mm of water.
Whereas the polynomial expression gives a calculated pressure of A (6749)2 + B (6749) + 1595.7 = 420.02 kPa and the actual error is only 0.02 kPa or two millimeters of water.
Note: If the polynomial equation is used it is important that the value of C be taken in the field following the procedures described in Section 3.2. The field value of C is calculated by inserting the initial field zero reading into the polynomial equation with the pressure, P, set to zero.
If the field zero reading is not available, the value of C can be calculated by using the zero-pressure reading on the calibration report. In the above example the value of C would be derived from the equation: 0 = A(9074)2 + B(9074) from which C = 1595.7
It should be noted that where changes of water levels are being monitored it makes little difference whether the linear coefficient or the polynomial expression is used.