Inertial type inclinometers measure tilt by sensing the component of the earth gravity vector along their sensitive axis, as shown in the open loop sensor in figure 1.
FIGURE 1 An open-loop mass/spring inclinometer
In figure 1, a tilt angle results in a gravity induced force F=mgsin on the mass m, and a deflection x of the suspension spring x=F/k=(mg/k)sin, where k is spring stiffness. A pickoff converts the deflection x into an output value Vp=kpx=(kp/k)mgsin, and the final output after a gain kv amplifier is: Vo=(kpkv/k) mgsin (figure 2).
FIGURE 2 Block diagram of the open-loop inclinometer
Each of the elements in the open loop sensor contributes to the total measurement error. Both the spring coefficient k and the pickoff scale factor kp change with deflection, temperature and time producing non-linearity and repeatability errors, and the amplifier contributes other errors of electrical character.
Another limitation of an open loop sensor is the trade-off between sensitivity and response speed, a measure of which is the natural frequency Tn= (k/m). Reducing k to obtain a sizeable sensitivity results in a reduction of the response speed.