Page 143 - Lehrbuch Neigungsmessung deutsch 2018.indd

COMPENDIUM INCLINATION MEASUREMENT
WYLER AG, WINTERTHUR / SWITZERLAND

APPENDIX

INFLUENCE OF GRAVITY ON THE MEASURED INCLINATION
Gravitational force is known to be fairly constant all over the world. This is the foundation of the
measuring principle applied in WYLER sensors. However, gravitational force does vary by up to 0.5%.
To utilize the full precision of the sensors, which are among the most accurate inclinometers, the local
gravity must be taken into account. The measured values have to be interpreted accordingly.
The electronic sensors use a capacitive measuring system as shown in Fig. 1. A friction-free supported
disc is placed in between two electrodes, forming a differential capacitor. Rotational symmetric springs
hold the disc in the middle of the gap. When the sensor is inclined, the gravitational force moves the disc
to the lower side, reducing the distance to one electrode, whereas on the other side the distance to the
other electrode increases. This leads to an increase of the capacitance on the lower and to a decrease on
the upper side. From these changes, the electronics in the sensor calculate the angle of the inclination.
The equilibrium of the resilient and the gravitational force can be described as follows:
cx = mg sin () (1)
where
x displacement of the disc
c spring constant
m mass of the disc
g gravity
 inclination angle

Fig. 1 Schematic representation of
the capacitive measuring system

This measuring principle relies on gravity to be constant. However, gravitational force varies by about
0.5% around the Earth‘s surface. Because the Earth is rotating and its shape is not a perfectly uniform
sphere, the strength of Earth‘s gravity changes with latitude, altitude, local topography and geology. The
International Union of Geodesy and Geophysics (IUGG) defined the international gravity formula, which
relies on the reference ellipsoid, a mathematically-defined surface. It describes gravity sufficiently accura-
tely:

(2)
where
 latitude
h altitude

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