HOBO® Pendant® G Data Logger (UA-004-64) White Paper: Operating Principles
HOBO® Pendant® G Data Logger (UA-004-64) White Paper: Operating Principles
HOBO® Pendant® G Data Logger (UA-004-64) White Paper: Operating Principles
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This white paper explains the operation of the HOBO Pendant G data logger (UA-004-64).
Operating Principles
The accelerometer used in the Pendant G logger is an Analog Devices ADXL330 model. Inside the accelerometer,
tethered beams are anchored at fixed locations. The beam is micro-machined with center plates that mesh in
between fixed outer plates causing a capacitance. As the beam moves, the center plate displacement causes a
change in capacitance proportional to the applied acceleration. A circuit inside the accelerometer takes advantage
of this change in capacitance and converts it to a proportional output voltage for the microprocessor. The
microprocessor uses calibration data along with a transfer function to convert the input voltage to an equivalent
acceleration value in G, where 1G = 9.8m/s².
© Analog Devices
16920-A
HOBO Pendant G White Paper
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HOBO Pendant G White Paper
Accelerometer Location
Locating the accelerometer on the printed circuit board may be useful for experiments dealing with centripetal
motion where the radius distance from the center of rotation to the accelerometer must be known. Dimensions
are from the edge of the logger and bottom of the logger to the center of the accelerometer and shown below in
inches (5/8" and 31/32").
Logging Modes
There are two logging modes: Normal and Fast. The mode is determined by the Logging Interval selected in the
Logger Launch window in HOBOware. If the Logging Interval is set to 1 second or greater, the logger will operate in
normal mode. If the Logging Interval is set to “Fast,” the logger will operate in Fast Mode (you must also select the
Hz in this mode).
Normal mode is ideally suited for tilt applications due to the low frequency of events. When in normal mode, the
logger takes one instantaneous sample every logging interval and stores it to internal memory. It does not do any
averaging or peak measurement over the logging interval.
Fast mode is better suited for dynamic acceleration events where movement, vibration, and shock need to be
captured. See the section Dynamic Acceleration: Fast Mode on page 11 for more details.
1000
Fill Time (min)
100
1 Channel
2 Channel
10 3 Channel
1
1 11 21 31 41 51 61 71 81 91
Samples/sec (Hz)
Plot A: Logger Memory Fill
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HOBO Pendant G White Paper
The logger header size will vary based on the logging parameters entered during launch. The fill time or “Logging
Duration” calculation is determined automatically by HOBOware and can be found in the Launch Logger window.
Tilt Sensing
The ability of the logger to perform tilt sensing relates to the type of accelerometer used and its construction.
Gravity acting on the mass of the beam inside the accelerometer creates a constant force that displaces the beam,
allowing it to measure the static acceleration of gravity (9.8m/s² or 1G). This is true even when the logger is sitting
motionless. As the logger orientation changes in space, gravity acts on each of the three axes, allowing it to be
used in applications to determine tilt, inclination, leveling, relative position, or orientation.
0° 0° 0°
-X Y X
Z Z Z
-Y Y
90° 90° 90°
Y X -Y
-Z -Z -Z
X -Y -X
The frame of reference for tilt angle can be either a vertical or horizontal plane and is somewhat arbitrary. We
have chosen a vertical plane since it corresponds to the vector associated with gravity.
When any of the three logger axes is pointing toward earth, for the sake of discussion using X, the measured
acceleration will be 1G with a corresponding calculated tilt angle of 180°. When in a horizontal position, a 0G
measurement corresponds to 90°. When pointing up (away from earth), a -1G measurement gives 0°.
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HOBO Pendant G White Paper
X Axis
Y Axis
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Z Axis
Absolute Positioning
Although tilt angle can be determined, rotational information cannot be obtained. In other words, its absolute
spatial orientation or absolute location in space cannot be known.
To prove this, you can position the logger in a fixed orientation and slowly rotate about the vertical axis a full 360°.
Note that none of the values change during the rotation (assuming this is done slow enough to avoid vibration or
shock). The logger cannot sense what quadrant it is in.
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HOBO Pendant G White Paper
Tilt Accuracy
The accuracy of the tilt angle varies based on the accelerometer output and temperature changes. This graph
shows the relationship between accelerometer output and tilt angle. This cosine function yields a more accurate
angle where the slope changes rapidly, occurring between 60° to 120°. Less accurate results occur as the slope
decreases in the 0° to 30° and 150° to 180° range.
Using the logger’s accuracy specification of ±0.075G (ambient) and ±0.105G (over temp), this graph quantifies the
tilt error as a function of tilt angle from 0° to 90°. This graph can be mirrored, horizontally, to determine the error
from 90° to 180°.
30.00
25.00
20.00
Tilt Error (+/- Degrees)
Error
15.00 @25C
10.00
5.00
0.00
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
Tilt Angle (Degrees)
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HOBO Pendant G White Paper
Tilt Resolution
Similar to tilt accuracy, tilt resolution varies depending on the accelerometer output. Using the logger resolution
specification of ±0.025G, this graph quantifies the tilt resolution as a function of tilt angle from 0° to 180°.
14.00
12.00
10.00
Resolution (Degrees)
8.00
6.00
4.00
2.00
0.00
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180
Tilt Angle (Degrees)
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We can see the truncation effects of the tilt formula as all values above +1G in Events 1, 3, and 4 show a
corresponding clipped tilt angle of 180°. Event 2 illustrates how data can be misinterpreted as the angle appears to
have changed from about 180° to 150° although the logger orientation remained unchanged.
1 3 4
By looking at data from the Y and Z axis, we can determine its cause. Since the Y and Z axes do not have a
corresponding change in tilt angle, we can deduce the cause as being from a dynamic acceleration event and not a
tilt event.
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HOBO Pendant G White Paper
A better approach is to devise a way of separating the static and dynamic components of accelerometer, discussed
in next section.
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Example File
The following file was generated with the logger in “Fast Mode” @ 100Hz. Each of the three axes was aligned with
the gravity vector while at the same time injecting an oscillatory vibration along the same vector.
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A “filter factor” of 0.1 is used which results in a low pass value equal to 10% of the acceleration + 90% of the
previous filtered value. The filter factor can be modified as needed.
X,lowpass Y,lowpass 2
Z,lowpass
2 2
0 0 0
1
43
85
127
169
211
253
295
337
379
43
85
1
127
169
211
253
295
337
379
1
43
85
127
169
211
253
295
337
379
-2 -2 -2
ℎ []= [ ]+ []
2 2 Y,highpass 2
X,highpass Z,highpass
0 0 0
1
48
95
142
189
236
283
330
377
1
54
107
160
213
266
319
372
48
95
1
142
189
236
283
330
377
-2 -2 -2
This leads to a decent isolation but results in high pass errors from the low pass transitions.
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Sliding Average
Another approach to filtering uses a sliding average.
1
[]= [ + ]
ℎ []= [ ]− []
0 0 0
1
48
95
142
189
236
283
330
377
1
54
107
160
213
266
319
372
1
48
95
142
189
236
283
330
377
-2 -2 -2
2 2 2 Z,highpass
X,highpass Y,highpass
0 0
1
48
95
142
189
236
283
330
377
54
1
107
160
213
266
319
372
0
-2 1 -2
Sum Vector
The sum vector is useful when working with objects in freefall. It isn’t measure by the logger but calculated by the
host software for reporting in both the data file and status window using the following formula:
Sum Vector = √(X²+Y²+Z²)
As an example, assume we start with a logger at rest measuring 1G (X). When allowed to freefall, the logger
accelerates toward earth producing a decrease in the X axis output of 1G resulting in a sum of 0G.
Note that any rotation during free fall will induce a centripetal acceleration about the axis of rotation so all axes
may not read 0G.