Pressure Measurements
Instrumentation
The BAe-146 E3001-ARA (G-LUXE) is fitted with a Reduced Vertical Separation Minimum (RVSM) certified altitude keeping system [D. N. Ferguson, 2004, Ferguson, 2000, Ferguson, 2004], providing altitude and airspeed measurements for both pilot and co-pilot independently, and an emergency backup. It is this system that provides the static and dynamic pressure measurements used in post processing for data collected on the aircraft. Data is sent to the rear core console via the ARINC 429 data bus at approximately 20 Hz, and is interpolated to 32 Hz.
Data Processing
(See p_rio_rvsm.py, p_rvsm.py, p_dry_mach.py and p_wet_mach.py)
Although the RVSM system is fundamentally a set of static and dynamic pressure measurements, the data is sent as a pressure altitude and indicated airspeed. The pressure altitude is converted (back) to static pressure, parameter PS_RVSM, using the ICAO standard atmosphere. That static pressure and the indicated airspeed are converted to Mach number, using the equation:
where \(V_0 = 340.294\) m/s, \(P_0 = 1013.25\) mb, \(P\) is the static pressure and \(V_{IAS}\) is the indicated air speed. Mach and static pressure are then used to find the dynamic pressure, parameter Q_RVSM:
In post processing v004 [FAAM, n.d.], the Mach number used was that calculated using equation (1). In post processing v005 [FAAM, n.d.], the humidity-dependent equation for Mach was introduced as follows:
where \(c_p\) is the specific heat capacity at constant pressure of moist air, \(c_v`\) is the specific heat capacity at constant volume of moist air, \(R_a\) is the specific gas constant of moist air, \(P\) is the static pressure from the RVSM system and \(Q\) is the dynamic pressure from the RVSM system. \(c_p\), \(c_v\) and \(R_a\) are calculated as described in Appendix 1 of Khelif et al. 1998 [D. Khelif, 1998]. Specific humidity, \(q_h\), is calculated using the calibrated volume mixing ratio measurement from the flush-mounted WVSS-II (see section Water Vapour Measurements), as follows:
where \(M_w\) is the molar mass of water, 18.01528 g/mol, \(M_d\) is the molar mass of dry air, 28.9644 g/mol, and \(w\) is the calibrated WVSS-II water vapour mixing ratio in ppm (parameter WVSS2_VMR_C).
The specific heat capacity at constant pressure, \(c_p\), and constant volume, \(c_v\), are given by:
where \(R_d\) is the specific gas constant for dry air, 287.058 Jkg \(^{-1}\text{K}^{-1}\), and the moist air gas constant, \(R_a=c_p-c_v\). In the rare case that humidity data is not available, post processing v005 reverts to calculating the Mach number using equation (1).
Uncertainties
Neither of the RVSM pressure measurements could be described as calibrated in a scientific sense since their main purpose is for aviation. They are maintained by aircraft engineers, and checked regularly for compliance with aviation regulations [Authority, n.d., Ferguson, 2000], but they do not have calibrations applied which are traceable to national scientific standards.
The measurement of static pressure at a static port on an aircraft is always subject to systematic error related to the position of the static port on the aircraft body [Ferguson, 2000]. This position error can be quantified by experiment, and BAE have determined a velocity-dependent position error correction, named the -903 Law, for AVRO 146-RJ aircraft. The BAe-146 E3001-ARA (G-LUXE) is sufficiently aerodynamically similar to the 146-RJ aircraft that the -903 law can be used for its RVSM certification. Residual errors exist, and were measured for some flight conditions in the early 2000s by comparison with a trailing cone (a free stream measurement of static pressure achieved by trailing a cone behind the aircraft [D. N. Ferguson, 2004]). Those measured residual errors were found to be a function of velocity, altitude and, to lesser extent at science speed, aircraft weight. Since those trailing cone flights, G-LUXE’s nose cone has been replaced, and additional science instrumentation fitted. No residual error correction is applied in the FAAM post processing, so there remains a systematic error. That error is small enough to disregard for RVSM certification, but nevertheless results a small bias in the pressure measurements.
An intercomparison flight with the DLR HALO aircraft (which has a very well characterised static pressure measurement, [A. Giez and Mallaun, 2019]) in July 2017 shows that FAAM’s RVSM static pressure error could be 1-2 mb below 10 kft, with no data available above 10 kft. Applying a correction for the residual position error according to the data collected during trailing cone flights in the early 2000s does not improve agreement with HALO.
Despite their deficiencies, the static and dynamic pressures derived from the RVSM system are the best pressure measurements currently available on the FAAM aircraft, so an estimate of their uncertainties is required in order to determine the uncertainties in other measurements made downstream. Using the intercomparison flights with HALO as our current best source of comparison data, we estimate an uncertainty in the RVSM static pressure measurement, PS_RVSM, of 2 mb. The BAe146 Series 300 Certificate of Airworthiness Report No. 126 [Poole, 1988] shows that there is a residual Mach number correction of up to 0.005 for a science speed of 210 kts, and in the absence of a more thorough uncertainty analysis we take this as an estimate of uncertainty in Mach from the RVSM system.
The uncertainty contribution from the water vapour measurement used in the calculation of moist Mach in equation (2) was calculated by propagation of uncertainties through equation (2), and can be approximated by
where \(w\) is the calibrated volume mixing ratio from the WVSS-II in ppm. Combining with ‘uncertainty’ associated with the residual Mach number correction, \(M_{res}\) of 0.005:
The uncertainty in moist Mach due to the uncertainty in the water vapour measurement, \(u(M_{humidity})\), is orders of magnitude smaller than the ‘uncertainty’ associated with the residual Mach number correction, but has been included for completeness.
Future work
Since the HALO intercomparison flight in summer 2017, a new science static pressure measurement has been fitted to the FAAM aircraft at port S10, but its static position error has not yet been characterised. To quantify the static position error requires further trailing cone flights, comparison with a pacer aircraft with a well-characterised static pressure measurement, tower fly-bys, height monitoring unit overflights, or some combination of these. It is hoped that characterisation work will soon be undertaken so that a position error correction can be applied to the static pressure measurement at S10 and the dynamic pressure measurement at P0 and S10. This will then provide traceable static and dynamic pressure measurements, and subsequently Mach, for use in post processing.