The PS-2136 PASPORT 3-Axis Acceleration/Altimeter Sensor and PS-2154A PASPORT Weather Sensor, use a barometer to determine relative altitude (height). Barometric altimeters give reasonably accurate (+/- 3%) relative altitudes without calibration; however, uncalibrated absolute altitudes may differ by as much as +/- 100 meters from published values. Fortunately, the barometric altimeter can be easily calibrated to yield more accurate altitudes.
Principle of Operation
The PASCO altimeter calculates the absolute altitude, h, from the pressure exerted by the air mass above it:
h = A ln (P0/P)
, where A = 8428 m, P is the measured local atmospheric pressure, and P0 = 101.32 kPa (the standard atmospheric pressure at sea level). The coefficient A corresponds to the scale factor for dry air (molar mass = 28.97) at a temperature T of 287.825 K and standard atmospheric pressure (P0= 101.32 kPa at sea level.):
A = kb T / m/ g
where m is the molar mass * 1.66e-27 kg and g is the gravitational acceleration near the surface of the Earth (9.8 m s-2).
From this equation, it is obvious that a change in the temperature of the air column will result in a determination of the relative altitude. For absolute altitude determinations, which involves the integrated density of air from sensor level up to the stratosphere, atmospheric density profiles are predominantly the result of a superposition of atmospheric tides.
The PS-2136 PASPORT 3-Axis Acceleration/Altimeter Sensor was designed for roller coasters for which relative changes in altitude are important, but absolute altitude is much less important.
Fortunately, the standard deviation in the relative altitude inaccuracy is only +/- 3% (corresponding to a standard deviation of +/- 3 m for the world's tallest (100 m) roller coaster) and can be reduced to +/- 1% with calibration.
Correction for Firmware Miscalculation
The datasheet of the PS-2136 PASPORT 3-Axis Acceleration/Altimeter Sensor , which is included with DataStudio 1.9.0 has value of A that is off by 1.2, leading to incorrect altitude data. If you are using a version of DataStudio prior to 1.9.1, please upgrade. If you are using a portable data logger, please connect it to a USB port of a computer running DataStudio 1.9.1 or later. Connect a sensor to the interface and collect a few data points to be sure that it is working.
The following corrections should be done within an hour of the measurements because atmospheric conditions change rapidly:
Calibration Using the Published Elevation Change of the Roller Coaster
(+/-1 % relative error)
Amusement parks almost always publish the maximum elevation change for their roller coasters on their websites. If you cannot locate this information from their website, you may be able to determine the peak height using a hollow sighting tube, a measuring tape and a protractor. (height = distance between observer and base * tan( angle_between_base_and_sight) ). One can use this value as a calibration point for the altimeter:
Check that you have the latest datasheet update as mentioned in the Correction for Firmware Miscalculation section.
Use the calculator to multiply your results by the ratio of the published maximum change in elevation to the measured change in elevation:
CorrectedRelativeAltitude = R * MeasuredAltitude,
R = PublishedMaximumElevationChange/MeasuredMaximumElevationChange .
Correction for the Actual Temperature (+/-2 % relative error)
Alternatively, you may find it easier to correct the altitude readings by measuring the ambient temperature:
Make sure that you have the latest datasheet update as mentioned in the Correction for Firmware Miscalculation section.
Multiply the value of the altimeter by the ratio of the temperature measured at the base of the roller coaster in Kelvin (T) to 287.825 K. (This reduces the 3% error in the relative altitude to 2% (2 m for the roller coaster). ) This correction should be done within an hour of the measurements because atmospheric conditions can change rapidly.
Obtaining Absolute Altitudes (+/-1 % absolute error)
Once you have corrected the relative altitude to your satisfaction, your results may still differ from the actual altitudes relative to sea level by +/- 100 m. You can obtain accurate absolute altitudes, provided that you know the actual base altitude from a published source. Simply enter the following equations in the calculator:
ActualAltitude = CorrectedRelativeAltitude + h0
h0 = PublishedBaseAltitude - CorrectedRelativeAltitude(z =h0) .
Note: In the sensor dialog the "zero sensor automatically on start" only applies to the acceleration, not the altitude.