Inertial sensors are often categorized as accelerometers and inclinometers. Fundamentally, they follow the same design and largely operate the same way however they differ in that an accelerometer’s output will correspond to dynamic, higher frequency input forces; compared to an inclinometer, where the output signal will reflect static to the measured environment expressed as a tilt angle.
Read on to learn a little more about how an inclinometer output is interpreted, and how unwanted acceleration can add error to the sensor output:
Jewell Instruments’ analog inertial sensors output their signals scaled to g’s (local acceleration due to Earth’s gravity). To determine the angle measured by an analog inclinometer, the user needs to first convert the VDC or current output to g’s by dividing the measured output signal by the unit’s scale factor; and then convert the output in g’s to degrees by using the trigonometric arcsine function:
gout = (Vout)/(Scale factor)
θ = sin-1(gout)
Note: Scale factor units will vary depending on the product and its configuration. For example, an LSOX Force Balance Inclinometer configured for voltage output, will have a scale factor in units of V/g since it outputs DC voltage, and an SMIC-L would have a scale factor of mA/g, since it outputs 4-20mA.
A force-balance or MEMS inclinometer will also respond to both earth’s gravity and any acceleration applied to the sensor. To further elaborate the sensors output includes the following inertial components:
- Acceleration effects due to local gravity, which represents the tilt observed by the inclinometer: asin(gtruetilt).
- Plus centripetal due to rotational motion of customer’s system: gc
- Plus any changes in velocity (acceleration) if the measured object increases or decreases its velocity linearly along the sensing axis: Δg
Below is an approximate equation demonstrating the relationship between these factors and the sensors output. Note that these factors may be expressed as negative values in the case of a negative tilt, or deceleration as opposed to positive acceleration.
θtotal output = asin(gtruetilt) + asin(gc) + asin(Δg)
There is no singular sensor which can distinguish or compartmentalize these three inertial inputs, so measurement errors can occur when a number of these elements are present; however, there are options to mitigate them.
As an example, one customer uses a dual-axis inclinometer, such as the JDHI-200 dual axis MEMS inclinometer to measure the tilt of an antenna pedestal in all 4 horizontal quadrants which rotated at 10°/minute. The inclinometer is output will respond to acceleration due to local gravity but will also measure the effects of centripetal acceleration during rotational motion. To calculate this error, we need to know the radius of rotation where the sensor will be mounted along with the platform’s angular velocity, which would need to be measured in real time. The centripetal acceleration can then be calculated simply using the αc = v2/r formula where v is the tangential velocity of the platform in real time, and r is the radial distance between the sensor and the center of rotation.
Note: For more details on the effects of local gravity on the sensor and how to compensate, check out our article on Gravity.
An additional issue could occur if the antenna itself tilts as the user tries to measure the angular position of the rotating platform. In this case, the inclinometer output could display a sinusoidal like output signal as the sensor moves through a series of shifting angles, as the platform rotates about the tilted antenna: this is particularly evident in dynamic situations where wind or other phenomenon may lead to periodic swaying of the antenna. A solution to this is the implementation of a second inclinometer installed onto the antenna itself to monitor its verticality this data could then be used to normalize the measured data of the rotating stage and remove the sinusoidal output, revealing the tilted angle of the platform.
Other sources of error can come from thermal drift caused by changes in the operating environment’s temperature. Thermal drift can cause shifts in the zero-degree output and linearity. At Jewell’s factory located in Manchester NH, USA, we characterize these errors using precision industrial thermal test chambers. The resulting calibration report – shipped with each unit – contains thermal calibration data which the user can take advantage of to compensate for this thermal drift during operation. For demanding applications where accuracy across temperature is a critical feature, Jewell also offers additional thermal characterization options.