Operator`s manual

SECTION 7. MEASUREMENT PROGRAMMING EXAMPLES
7-9
7.13 LYSIMETER - 6 WIRE FULL
BRIDGE
When a long cable is required between a load
cell and the 21X, the resistance of the wire can
create a substantial error in the measurement if
the 4 wire full bridge (Instruction 6) is used to
excite and measure the load cell. This error
arises because the excitation voltage is lower at
the load cell than at the 21X due to voltage drop
in the cable. The 6 wire full bridge (Instruction
9) avoids this problem by measuring the
excitation voltage at the load cell. This example
shows the errors one would encounter if the
actual excitation voltage was not measured and
shows the use of a 6 wire full bridge to measure
a load cell on a weighing lysimeter (a container
buried in the ground, filled with plants and soil,
used for measuring evapotranspiration).
The lysimeter is 2 meters in diameter and 1.5
meters deep. The total weight of the lysimeter
with its container is approximately 8000 kg. The
lysimeter has a mechanically adjustable
counterbalance, and changes in weight are
measured with a 250 pound (113.6 kg) capacity
Sensotec Model 41 tension/compression load
cell. The load cell has a 4:1 mechanical
advantage on the lysimeter (i.e., a change of 4
kg in the mass of the lysimeter will change the
force on the load cell by 1 kg-force or 980 N).
FIGURE 7.13-1. Lysimeter Weighing
Mechanism
The surface area of the lysimeter is 3.1416 m
2
or 31,416 cm
2
, so 1 cm of rainfall or evaporation
results in a 31.416 kg change in mass. The load
cell can measure ±113.6 kg, a 227 kg range.
This represents a maximum change of 909 kg
(28 cm of water) in the lysimeter before the
counterbalance would have to be readjusted.
There is 1000 feet of 22 AWG cable between
the 21X and the load cell. The output of the
load cell is directly proportional to the excitation
voltage. When Instruction 6 (4 wire half bridge)
is used, the assumption is that the voltage drop
in the connecting cable is negligible. The
average resistance of 22 AWG wire is 16.5
ohms per 1000 feet. Thus, the resistance in the
excitation lead going out to the load cell added
to that in the lead coming back to ground is 33
ohms. The resistance of the bridge in the load
cell is 350 ohms. The voltage drop across the
load cell is equal to the voltage at the 21X
multiplied by the ratio of the load cell resistance,
R
s
, to the total resistance, R
T
, of the circuit. If
Instruction 6 were used to measure the load
cell, the excitation voltage actually applied to
the load cell, V
1
would be:
V
1
= V
x
R
s
/R
T
= V
x
350/(350+33) = 0.91 V
x
Where V
x
is the excitation voltage. This means
that the voltage output by the load cell would
only be 91% of that expected. If recording of
the lysimeter data was initiated with the load cell
output at 0 volts, and 100mm of
evapotranspiration had occurred, calculation of
the change with Instruction 6 would indicate that
only 91mm of water had been lost. Because the
error is a fixed percentage of the output, the
actual magnitude of the error increases with the
force applied to the load cell. If the resistance of
the wire was constant, one could correct for the
voltage drop with a fixed multiplier. However,
the resistance of copper changes 0.4% per
degree C change in temperature. Assume that
the cable between the load cell and the 21X lays
on the soil surface and undergoes a 25
o
C
diurnal temperature fluctuation. If the resistance
is 33 ohms at the maximum temperature, then at
the minimum temperature, the resistance is:
(1-25x0.004)33 ohms = 29.7 ohms
The actual excitation voltage at the load cell is:
V
1
= 350/(350+29.7) V
x
= .92 V
x
The excitation voltage has increased by 1%,
relative to the voltage applied at the 21X. In this
case, where we were recording a 91mm change
in water content, there would be a 1mm diurnal
change in the recorded water content that would
actually be due to the change in temperature.
Instruction 9 solves this problem by actually
measuring the voltage drop across the load cell
bridge. The drawbacks to using Instruction 9