E-1
Appendix E.
Calculating Measurement
Error
When using a CDM-VW300 analyzer, the basic output of a measurement is
frequency (Hz) or frequency squared (Hz
2
). Vibrating-wire sensors are usually
designed with a linear relationship between wire tension and the phenomenon
being measured. Further, wire tension usually has a linear relationship to the
square of the resonant frequency (
f
2
). Manufacturers typically provide a formula
for converting frequency to an engineering unit (
U
E
) in the form,
U
E
= Kf
2
,
Eq. 1
where
K
is a constant determined from sensor specifications.
So, for a very small change in frequency,
∆f
, change in output,
∆U
E
, is given by,
∆U
E
= 2Kf∆f
Eq. 2
where Eq. 2 is obtained by taking the first derivative of Eq.1 with respect to
f
, and
f
is the present frequency on the wire.
Use Eq. 2 together with noise levels,
N
(Hz RMS), found in Table 5-3,
CDM-
VW300/305 Effective Frequency Measurement Resolution,
to calculate the
effective resolution (
R
e
) of a measurement. For a specific sample rate in Table
5-3, use the corresponding value of
N
in place of
∆f
. Eq. 2 can then be expressed
as,
R
e
= 2KfN
Eq. 3
E.1 Example Error Calculation: Geokon Strain Gauge
When using a Geokon strain gauge, constant
K
is given by,
K = GB / 1000
Where
G
is the gauge factor 4.062 or 0.391, dependent on gauge type, and
B
is a
batch factor (a number usually near 1, such as 0.97), given on the sensor
calibration sheet.
Substituting into Eq. 1 using engineering units of microstrain (
µε
):
µε = GBf
2
/ 1000,
The effective resolution,
R
e
, of the output, or
∆µε
, is:
∆µε = 2GBfN / 1000
or
∆µε = GBfN / 500,
where
N
is the noise value given in Table 5-3,
CDM-VW300/305 Effective
Frequency Measurement Resolution,
corresponding to the sample rate being used.
Summary of Contents for CDM-VW300 Series
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Page 59: ...User Manual 47 Figure 7 16 LoggerNet connect screens showing frequencies from CDM VW300 ...
Page 70: ...CDM VW300 Series Dynamic Vibrating Wire Analyzers 58 ...
Page 76: ...Appendix B SC CPI Datalogger to CPI Interface B 4 ...
Page 80: ...Appendix C CDM Devices and CPI Bus C 4 Figure C 2 Long cable lengths of a distributed CPI bus ...
Page 86: ...Appendix E Calculating Measurement Error E 4 ...
Page 116: ...Appendix G CRBasic Program Library G 26 ...
