Application Note 21
1(2)
Rotation Angle of a Vertical Plane
OBJECTIVE
This document describes how to measure the rotational angle around a horizontal axle.
Small inclinations are possible to measure accurately with one sensor, but when exceeding 30°, two
sensors are usually required.
DESCRIPTION OF APPLICATION
As the sensor is an accelerometer, the signal is linear with respect to the horizontal component of earth’s
gravity (=acceleration 1g), and sine shaped as a function of the tilt angle. By definition, the sensitivity will
decrease when approaching 90° (fig.1.)
Angle vs. Acc.
1.50
Figure1.
Output in g as a function of
the tilt angle.
Acceleration[g]
1.00
0.50
0.00
-90
-60
-30
0
30
60
90
-0.50
-1.00
-1.50
Tilt angle [°]
Close to 0° the correlation between inclination in g and angle is nearly linear (fig.2.), thus enabling the use
of the sensors in without additional signal processing.
Nonlinearity
0.60
Figure2.
In the ±30° range
nonlinearity is 0,5°.
0.40
0.20
Linearity error [°]
-30°
-20°
0.00
-10°
0°
-0.20
10°
-0.40
-0.60
Tilt angle[°]
5 Sep 2005
VTI Technologies reserves all rights to modify this document without prior notice.
20°
30°
Application Note 21
2(2)
For linearization, the output signal needs to be transformed by the
arcsine function.
α = arcsin( x ) , where x is the inclination in g
However, the accuracy decreases the further away from 0g one is, as does the sensitivity.
RECOMMENDATION
For good inclination accuracy, a dual axis sensor should be used. The measuring axes should be
orthogonal to each other, and perpendicular to the rotation axis. By definition, the signal is linear when
calculated as follows:
x
y
α = arctan( )
,
where x and y are inclination in g
ATAN(X/Y)
90
Figure 3.
Linearized output signal by
using dual axis sensor and
arctan calculation.
Output angle [°]
60
ATAN(X/Y)
30
0
-90
-60
-30
0
30
60
90
-30
-60
-90
Angle [°]
APPLICATIONS
The above solution enables linear measurement over a wide inclination range, for example the counterand clockwise rotation of a vertical plane.
Angle
0°
0…90°
90°
90…180°
180°
180…270°
270°
X-channel
Y-channel
0g
1g
0 => 1g
1 => 0g
+1g
0g
1 => 0g
0 => -1g
0g
-1g
0 =>-1g
-1 => 0g
-1g
0g
Dir. of
gravity
Position
(module)
SUITABLE VTI PRODUCTS
All VTI dual axis products with the measuring range > 1g (90°) are suitable for this application.
Parts available in the following series are: SCA1000, SCA100T, SCA121T, SCA124T, and SCA125T.
5 Sep 2005
VTI Technologies reserves all rights to modify this document without prior notice.
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