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APPENDIX D. IMPROVING THE ACCURACY OF THE CALCULATED
PRESSURE
Most vibrating wire pressure transducers are sufficiently linear (
±
0.2 % FS) 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 % FS.
This level of accuracy can be recaptured, even where the transducer is nonlinear, by the use of 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 = AR
2
+
BR
+
C
Equation 8 - Second Order Polynomial Expression
Where;
R
is the reading (digits channel B)
A
,
B
, and
C
are coefficients
Figure 18 shows a typical calibration sheet of a transducer that has fairly normal nonlinearity.
The figure under the “Linearity (%FS)” column is
Calculated Pressure-True Pressure
Full Scale Pressure
x 100%=
G
(
R
1
-R
0
)
-P
F.S.
x 100%
Equation 9 - Linearity Calculation
Note: The linearity is calculated using the regression zero for R
0
shown on the sheet.
For example when P= 420 kPa, G (R
1
– R
0
) = - 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 2.3. 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 sheet. 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.
