1. Introduction
Basic principles for determination of the three-dimensional wind vector from airborne platforms are well established (e.g., Lenschow 1986), and research groups worldwide are developing and operating wind measurement systems on aircraft (e.g., MacPherson 1990; Bögel and Baumann 1991; Lenschow et al. 1991; Tjernström and Friehe 1991; Crawford and Dobosy 1992; Whitmore et al. 1992). The enormous range in accuracy, complexity, and sophistication of individual installations is necessarily linked to performance and budgetary requirements, with systems designed for accurate high-resolution meteorological turbulence and flux measurements being among the most demanding. In recent years, this field has benefited from dramatic progress in aircraft position and motion sensing technology (e.g., Dobosy and Crawford 1996), sophisticated correction procedures for aircraft position and motion measurements (e.g., Shaw 1988; Leach and MacPherson 1991, 1994; Masters and Leise 1993), and new air motion sensing systems (e.g., Brown et al. 1983; Whitmore et al. 1992;Crawford and Dobosy 1992).
Although the calibration of airborne wind measurement systems is practically a “science in itself,” detailed critical discussions of such procedures appear only rarely in the literature (e.g., Bögel and Baumann 1991; Tjernström and Friehe 1991; Haering 1992). Central to this issue is the treatment of flow distortion effects (e.g., MacPherson and Baumgardner 1987; Cooper and Rogers 1991; MacPherson 1993; Crawford et al. 1996). Failure to compensate for the effects of flow distortion can lead to very significant errors in Reynolds stress and scalar flux measurements from aircraft (Wyngaard et al. 1985; Wyngaard 1991).
Many of the difficulties experienced in obtaining satisfactory and reliable results from wind calibrations may be attributable to the following interrelated characteristics of the measurement and calibration process.
The wind vector cannot be measured directly but must be inferred via a complex nonlinear combination of more directly measurable components, all of which are subject to uncertainty in varying degrees.
Many of the parameters required to “connect” these components are dependent upon properties of the distorted airflow in the direct vicinity of the measuring instruments during flight. Such parameters therefore are determinable only from carefully designed dedicated flight maneuvers and may lose their applicability outside a strict range of operating parameters or if the instrumentation is modified or relocated. (An obvious example is the upwash correction to angle of attack, which depends critically upon instrument location.)
Flight maneuvers used for these purposes sometimes incorporate periods of rapidly varying motion, such as high-frequency pitches and yaws. Such maneuvers may not be appropriate for obtaining calibration parameters for use during steady flight, unless the calibration models consider possible variations in aircraft flow patterns during periods of significantly nonzero accelerations and angular rates.
Commonly used calibration models and procedures are nonideal in their treatment of the interrelationships between essential components. They often require that raw (uncorrected) estimates of important quantities be used in the estimation of calibration parameters. Although such undesirable procedures are not completely avoidable (due to the highly nonlinear nature of the process), their use and effects can be minimized by careful design of the calibration analysis.
This paper details a calibration procedure that enables the calculation of winds of sufficient accuracy for use in boundary layer turbulence work from data obtained via measurement systems mounted on a Convair 580 (C580) twin-engine turboprop aircraft. The Flight Research Laboratory (FRL) of the Canadian National Research Council (NRC), which operates this aircraft primarily for cloud physics and aeromagnetics studies, has recently augmented its capabilities to include eddy correlation equipment for the measurement of fluxes of heat, moisture, momentum, and CO2 in the atmospheric boundary layer, in a vein similar to that of the well-known Twin Otter aircraft, also operated by the FRL. Given that the NRC Convair mission flights usually have multiple objectives, it is often tempting to gather wind data during maneuvers that would normally be regarded as marginal in terms of data accuracy. Such maneuvers include spiraling ascents and descents, low-frequency “porpoising” (used to profile cloud layers), and steeply banked turns. Therefore, there is an interest to know which kinds of flight maneuvers can be executed without compromising the data accuracy significantly, as well as an interest to investigate the possibilities for data correction methods that may help to extend these boundaries.
As is often the case with multipurpose airborne research facilities, it is sometimes necessary to mount an instrument in a position that is not optimum. Such is the case with the C580 air motion measurement system, an extended Rosemount-858AJ pressure probe (for attack–sideslip angles, and static and dynamic pressure) mounted in one of four Particle Measuring Systems (PMS) canisters on a pod that is located 12.4 m, spanwise, along the wing, with its tip positioned only 0.52 m ahead of and 0.84 m below the leading edge of the wing (see Fig. 1). To minimize flow distortion effects, air-motion measurements are commonly made on booms ahead of the nose of an aircraft (as with the NRC Twin Otter), or from the holes in the nose of an aircraft (as in the radome system) (Brown et al. 1983; Tjernström and Friehe 1991). Such a configuration is not currently used by the C580, as the nose of the aircraft houses a“spotlight” synthetic aperture radar. As the analysis to follow will show, however, despite this nonideal configuration, it is possible to derive winds that remain accurate even during certain types of rapid maneuvers, provided that special attention is given to the variable effects of flow distortion in the calibration procedure. An important aspect of the current study is a method that allows explicit determination of the effects of flow perturbations induced during flight periods when accelerations and rotation rates are significantly nonzero. This greatly simplifies the process by which such effects can be characterized in terms of measured quantities.
2. Wind measurements using the NRC Convair 580
The aircraft-based coordinate system coincides with that of the LTN-91 Inertial Navigation System (INS), mounted at the Convair center of mass. The variable G is provided in real time directly by the INS, or it may be obtained in postflight reanalysis to an improved accuracy by combining high-frequency velocity components from the INS with low-frequency components from the NovAtel Global Positioning System (GPS), thereby eliminating low-frequency INS velocity errors (order of 1–2 m s−1) associated with the Schuler Oscillation (Shaw 1988). The variable Ω and the attitude angles (used in calculating
Incorporated into the calibrations of the four basic pressure-related quantities (static and dynamic pressure, and the angles of attack and sideslip) are flow-distortion corrections for both steady and rapidly varying flight, the latter being denoted ɛx. For the purposes of this study, the term “rapidly varying” refers to periods in which aircraft accelerations and/or angular rates are significantly nonzero. The exact form of the corrections will be left undefined for the present. The major task of the subsequent sections is to assign empirical forms to these terms. We continue with the derivation of τ using the corrected quantities.
Atmospheric static pressure at the altitude of the pressure probe ppp is best estimated by correcting measurements made on the fuselage
Note that the above equations for Pγ, TT, and τ can be derived easily from expressions in standard texts (e.g., Lenschow 1986).
3. Estimation of calibration parameters from flight tests
a. Calibration philosophy
In designing a calibration procedure for airborne wind measurements within the restrictions of a given installation, the general objective is to identify suitable submodels for the various components, and then to calibrate and combine them in such a way that errors in the final calculated winds are minimized over the widest possible range of operating conditions. Clearly, the ideal calibration model is one in which all components are calibrated completely independently, and the resultant quantities are combined in exact equations to compute the wind vector. In such a model, residual errors can be tracked back directly to deficiencies in one or more of the individual calibration submodels. Such ideality is unreachable in practice (because of the complexity of airborne wind computations), and the best calibration procedure is one that minimizes the effects of component interrelationships (which lead to a need for intermediate approximations and an iterative evaluation of the parameter values between the submodels) and that maximizes the clarity with which residual errors can be related to deficiencies in specific contributing submodels.
In the current study, temperature and static pressure are calibrated independently using directly measured quantities. The steady part of the dynamic pressure and angle-of-attack calibrations are then obtained from measured quantities and from the corrected temperature and static pressure. The remaining quantities to be obtained are the sideslip-angle calibration for steady flight and any corrections to be applied to q, α, and β to account for the effects of rapidly varying motion. The analysis proceeds by recognizing that enough quantities are known accurately at this stage to invert the wind equation using a sensible guess for the ambient wind and to obtain the values of q, α, and β required to return that wind. These can now be used as reference quantities, first to calibrate the β during steady flight and then to investigate the residual error in the computed q, α, and β resulting from flow perturbations during rapidly varying motion. In terms of the dataset used, this technique does not differ from an iterative calculation of parameters in the submodel equations for β and ɛx, based on a requirement to minimize the final wind error. (The input “guess” for the ambient wind in our technique is the same as the assumed ambient wind used as a benchmark for such a minimization.) However, the current method has the very significant advantage that since the errors in q, α, and β are explicitly calculated, the process of identifying flow-distortion problems, and then formulating and calibrating revisions to the submodels for each of these quantities, can be performed directly and independently.
b. Temperature
The derivation of the temperature recovery factor from test flight maneuvers is performed traditionally from gradual speed variations in straight-and-level flight, for which it can be shown that a plot of
Since it can be shown that 
In order for Eq. (8) to be valid, we note that the following three conditions must be satisfied for the two racetrack maneuvers, (i) wind speed and direction must be the same on all four legs, (ii) the four legs must be parallel and aligned with the assumed constant wind direction, and (iii) the true airspeed must be the same on the two legs of each racetrack. Although in practice a combination of precision piloting and careful choice of location and ambient meteorological conditions tends to keep the associated errors to an acceptable minimum, it is nevertheless important that racetrack maneuvers be repeated on independent occasions, in order to check the robustness of the derived effective recovery factor.
A value of rpp = 0.94 was obtained for the Rosemount temperature probe mounted near the pressure probe on the Convair. This is slightly smaller than the value of 0.975 quoted by Rosemount for this probe type [verified in wind tunnel tests of a similar probe by MacPherson (1978)], indicating that the local flow velocity at the probe position is slightly reduced relative to the overall aircraft airspeed. To a fair approximation, 
c. Static pressure
Here, and in subsequent sections, symbols of the form
Quadratic forms are chosen in Eqs. (9) and (10), as some of the dependencies are expected to be nonlinear:for example, lateral and normal acceleration dependencies may be symmetric about zero. The form for ɛp is based upon the reasoning that during accelerated motion the pressure distribution about the fuselage of the aircraft will be perturbed relative to the steady-flight distribution. Note that the correction functions above are expected to be valid only over the range of airspeeds used during the flight maneuvers. In particular, application of Eq. (9) with the aircraft stationary on the ground (i.e., the case of
The q and alon dependencies of static pressure (
A quadratic component is apparent in the dynamic pressure correction term for static pressure “position” error on the Convair (Fig. 3a). Determinations of
We note that, strictly speaking, the q and alon dependencies should be investigated separately, in order to explore possible effects due to variations in the form of the q-dependency curve upon the value of alon. This could be accomplished for the case of alon = 0 only by flying a series of straight-and-level runs at a range of constant speeds. Such a dataset was not available from the test flights used for this study, as the strong alon dependency was not foreseen.
For static pressure position error upon a Sabreliner aircraft, Tjernström and Friehe (1991) also reported a need to depart from a linear model in q, finding instead that a combination of 2 third-order polynomials (each valid over a different range of dynamic pressure) was required to cover the very large range of airspeeds treated in their study. Even after this rather complex correction, they found a residual hysteresis in their corrected pressures, which they attributed to varying flow regimes around the fuselage for accelerating and decelerating motion. It is clear that the flow around the Convair fuselage is similarly affected by accelerations. Tjernström and Friehe (1991) go on to suggest that such variations in flow regimes about the fuselage of their twin-engine jet may be explained by the change in role of the engines, which are acting more or less as air brakes when idling during decelerations. In the case of the Convair, it has been speculated that the large pressure drop across the propeller disks required to achieve a longitudinal acceleration could be the direct cause of the variations in the pressure distribution at the fuselage static pressure port (only a few meters away), rather than the accelerations themselves. However, the data do not appear to support this hypothesis. For each of the two halves of the acceleration–deceleration maneuver, engine power was held at a near-constant value (this was confirmed postflight, as horsepower and propeller rotation rate were recorded variables), whereas the resultant alon varied much more gradually. As horsepower and alon were therefore not closely correlated, we would expect to see a marked hysteresis in the alon-dependency plot (Fig. 3b), the absence of which appears to indicate that the observed pressure distribution variations are more directly related to changes in alon itself rather than to engine power.
Bögel and Baumann (1991) also reported variations in static pressure position error during pitching and yawing maneuvers with the DLR Falcon aircraft, which Bögel and Baumann corrected empirically as functions of α and β. It is possible that these variations were equivalent to the errors corrected using normal and lateral acceleration components in the current study.
d. Dynamic pressure—Steady flight
The error in computed true airspeed thus can be estimated as Gave − τ. The variable
e. Attack angle—Steady flight
The wind tunnel analysis of MacPherson (1985) has shown that the geometry of the extended canister-mounted probe alters the theoretical flow about the nose of the probe only very marginally. In particular, the α/β sensitivity factor f is reduced from 0.0785 to 0.0780. The value of
f. Reference quantities for sideslip angle and rapidly varying maneuvers
As introduced in section 3a, we now describe a general technique used for the derivation of reference values for dynamic pressure and attack/sideslip angles to be used in the determination of both the steady sideslip angle corrections and the remaining correction terms for rapidly varying motion. This technique requires an a priori estimate for the mean ambient wand vector Uest during the period of the maneuver. A good method for providing this estimate in the absence of independent data is to compute “best-guess” winds using the aircraft data, with the corrected values of static and dynamic pressure and angle of attack derived above but assuming that βpp = βl and that the remaining rapidly varying correction terms are zero. The reference winds thus obtained will contain spurious variations resulting from the neglect of these terms, but their mean (or slowly varying) values provide an adequate guess for the ambient wind vector for current purposes.
The true airspeed vector τrev required to produce Uest can be computed by inverting the wind equation, (1): τrev =
α′ =
Cα0 Cαα1 D′ = (1 + tan2α′ + tan2β′)1/2
τrev = −τlonD′, αrev = tan−1(−τnrmD′/τrev), βrev = tan−1(−τlatD′/τrev) (Eq. 2)
α′ = αrev, β′ = βrev
Iterate back to step 2, until τrev, αrev, and βrev are constant to desired accuracy
The dynamic pressure and attack/sideslip angles qrev, αrev, and βrev, computed as above, will be referred to as “reverse reference” quantities in the subsequent analysis.
g. Sideslip angle—Steady flight
The use of Eqs. (16) is already a very crude approximation in the case of steady motion, and application to rapidly varying yawing maneuvers can lead to very scattered results. Tjernström and Friehe (1991) calibrated
Under an aircraft wing, particularly near the wing tip, a sidewash (along wing) circulation occurs that may change with the angle of attack. The present results (
The possibility that the flow angle offsets
h. Corrections to q, α, and β for rapidly varying motion
Once values for
In addition to the three aircraft accelerations (alon, alat, anrm) used in the analysis of the fuselage static pressure measurements, it was considered that an investigation of flow distortion effects in the vicinity of the pressure probe during rapidly varying motions should also include the three body rates (Ωlon, Ωlat, Ωnrm) and the flow angles themselves (α, β). Nonzero angular rates can produce significant additional accelerations at the position of the probe (because of its location far from the aircraft’s center of gravity) and, along with variations in the flow angles, can alter the form of flow over and along the wing. The differences Δq, Δα, and Δβ were thus investigated relative to all of these quantities, once again using multiple regression analysis techniques.
Errors in all three air data quantities derived from the pressure probe are evident during pitching motions and can be reduced substantially via corrections based on pitch rate (Ωlat) and normal acceleration (anrm). Note that Ωlat and anrm are 90° out of phase during a pitching maneuver and therefore are uncorrelated, excluding the possibility of spurious correlations. Nonzero normal accelerations and pitch rates produce sudden vertical displacements and rotations (respectively) of the wing, which the oncoming airflow must adjust to over a finite time period. The effect upon q and attack angle can be explained as a delay in the adjustment of the oncoming flow vector to the movements of the wing, whereas variations in sideslip angle are likely to be attributable to adjustments in the pattern/strength of the along-wing (sidewash) circulation.
During yawing motions, both slow and fast, all three air data quantities again exhibited errors. In the case of Δβ (Fig. 10), these were corrected partially using lateral acceleration (alat). Although a dependence on alat seems understandable in terms of delayed adjustment of the oncoming flow to sideways wing movement while the aircraft is yawing, this correction is not entirely satisfactory as it overcorrects during fast yaws and undercorrects during slow yaws, leading to substantial residual errors (Fig. 10). A possible explanation is that distortion of the sidewash circulation pattern becomes more severe as the yawing frequency increases. Similar errors found in wind data from the NOAA P3 aircraft during high-frequency yawing maneuvers have also been attributed to variable time lags in air data quantities caused by such effects (J. Masters 1998, personal communication). In any case, the corrected sideslip angle (β) subsequently was used fairly successfully to correct errors in both Δq and Δα during yawing motions (Figs. 9 and 11).
During rolls, errors appear in Δq and Δβ (Figs. 9 and 10) that are corrected partially by the alat and β dependencies discussed above. In addition, however, Δα is correctable as a function of roll rate Ωlon (Fig. 11), which is likely due to the additional vertical accelerations of the wing in the vicinity of the probe, induced by the roll rotation.
4. Discussion
In the absence of a sound physical description of flow around and along the Convair wing and fuselage during steady and rapidly varying motion, this study has been necessarily empirical in nature. Although attempts are occasionally made in the literature to derive relationships between aircraft motion parameters and airframe flow distortion fields on a more physical basis (Wyngaard et al. 1985; Crawford et al. 1996), the complexity and variability of such fields (both from aircraft to aircraft and as a function of location on any given aircraft) makes generalization of such relationships difficult. Although another approach is sophisticated numerical modeling of the flow about the wing, such studies still require empirical fitting of real flight data to model results.
In any case, it appears that our approach is effective. Figure 12 demonstrates the effects of the corrections derived above for rapidly varying motion upon the final computed wind vector. Errors associated with the violent pitch/yaw/roll maneuvers have been reduced substantially, with peak-to-trough values now being around ±0.6 m s−1 for the horizontal components over a wide range of flying conditions (substantially less during steady flight). The vertical component of wind velocity Uz (critically important for meteorological turbulence and flux measurements) is in particularly good health, with errors during pitch maneuvers almost completely removed and errors during yaws and rolls reduced to around ±0.4 m s−1 (peak to trough). In the horizontal wind components (Ux and Uy), the largest remaining errors appear during yawing maneuvers, probably attributable to complex adjustments in sidewash circulation patterns as β is varied, which remain uncompensated for. In addition to further flow distortion effects and possible influences of variations in flap settings, residual errors may be attributable at least partially to latencies and inaccuracies in the attitude and ground speed components obtained from the inertial navigation system (Bögel and Baumann 1991; Tjernstrom and Friehe 1991), which potentially could be removed in the future by Kalman filtering techniques (Leach and MacPherson 1991, 1994) or by the implementation of modern attitude differential GPS technology (Dobosy and Crawford 1996).
Acknowledgments
Alastair Williams wishes to recognize the extensive help and support provided by Dr. Ian MacPherson during Williams’s time at the NRC Flight Research Laboratory in Ottawa. Thanks go to Jeffrey Masters, of the University of Michigan, for granting permission to use some concepts from his unpublished 1991 report that he prepared with James Leise. Patient technical assistance was provided by George Hoftyzer, Wilmer Budarick, and other members of the Convair crew. Piloting was performed by Captains John Aitken and John Croll. While in Canada, Dr. Williams was funded by the Natural Sciences and Engineering Research Council (NSERC) as a Visiting Fellow in a Canadian Government Laboratory.
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APPENDIX A
Flow Angles and q at the Pressure Probe
The Rosemount-858 probe mounted in the FRL PMS canister (MacPherson 1985) consists of a conventional array of five pressure holes drilled into a hemispheric nose, with an additional static pressure measurement made via a ring of smaller holes drilled in a circle around the cylindrical housing, 3 in. back from the nose. The probe is plumbed/configured to supply the following outputs:
pppmeas Δ
Pppα Δ
Pppβ Δ
Pppq pppmeas
Elsewhere in this paper, static pressure at the probe altitude (ppp) is derived using the fuselage static sensor
APPENDIX B
Notation
Subscripts–superscripts
Geodetic coordinates: x is east, y is north, and z is up.
Aircraft coordinates: lon is longitudinal, lat is lateral, and nrm is normal.
Others: meas is measured, l is local, fus is fuselage, pp is pressure probe, ref–rev is reference–“reverse”-reference quantities (for calibration), +/− is with-wind/into-wind, prt is pitch rate, and rrt is roll rate.
Parameters
Regression coefficients:
Cυwn
r Effective recovery factor for temperature probe
CL Lift coefficient
fα/β sensitivity factor
λ Angle between central and any other port on pressure probe
r Vector position of pressure probe (aircraft coordinates)
Variables
a Aircraft acceleration vector (aircraft coordinates)
α, β Effective aircraft angles of attack and sideslip
cp, cυ Specific heats for moist air at constant pressure and volume
D Derived term containing airflow angles
ΔPx Differential pressures measured at the pressure probe (x = q, α, β)
ɛx Correction terms for rapidly varying motion (x = p, q, α, β)
G Aircraft ground-speed vector (geodetic coordinates)
γ Ratio of specific heats (cp/cυ)
M Mach number
M̃ Ω Vector of angular “body” rates about the aircraft axes (aircraft coordinates)
p Static pressure
Pγ Pressure term defining static-to-total temperature ratio in adiabatic process
q Dynamic pressure
T Static temperature
TT Total temperature
Tmir Dewpoint mirror temperature
τ Effective aircraft relative wind vector (aircraft coordinates)
τ True airspeed (magnitude of τ)
U Wind vector (geodetic coordinates)
u Wind speed (magnitude of U)
θ, ϕ, ϕ Aircraft pitch, roll, and true heading angles
Δα, Δβ, Δq Errors in α, β, q due to rapidly varying motion (Δ is the “reverse”-reference quantity minus the steady-motion estimate).
NRC Convair 580, showing positions of air data sensors during this study. (a) Overview. (b) Close-up of wing, showing extended Rosemount-858AJ pressure probe mounted in lower outboard PMS canister (foreground), and showing Rosemount temperature probe mounted on underside of a separate boom farther inboard (background).
Citation: Journal of Atmospheric and Oceanic Technology 17, 6; 10.1175/1520-0426(2000)017<0795:WMOAMT>2.0.CO;2
Racetrack maneuver (see text for definition of symbols).
Citation: Journal of Atmospheric and Oceanic Technology 17, 6; 10.1175/1520-0426(2000)017<0795:WMOAMT>2.0.CO;2
Static pressure “position” error during a straight-and-level gradual acceleration–deceleration maneuver. (a) Dynamic pressure dependency and residuals. (b) Longitudinal acceleration dependency and residuals. (c) Contribution of various terms (upper panel) and final correction (lower panel): Δp = mean(
Citation: Journal of Atmospheric and Oceanic Technology 17, 6; 10.1175/1520-0426(2000)017<0795:WMOAMT>2.0.CO;2
Static-pressure rapidly varying corrections (ɛp) during pitch/yaw maneuvers. Upper panel: contribution of various terms. (For clarity, αlat term is offset as indicated.) Lower panel: final correction. Here Δp = mean(
Citation: Journal of Atmospheric and Oceanic Technology 17, 6; 10.1175/1520-0426(2000)017<0795:WMOAMT>2.0.CO;2
True airspeed error as a function of the steady-flight dynamic pressure correction parameter
Citation: Journal of Atmospheric and Oceanic Technology 17, 6; 10.1175/1520-0426(2000)017<0795:WMOAMT>2.0.CO;2
Reference free-stream attack angle (αref) vs α at the pressure probe (αl) for gradual acceleration–deceleration maneuver (dots) and racetracks (triangles). Here
Citation: Journal of Atmospheric and Oceanic Technology 17, 6; 10.1175/1520-0426(2000)017<0795:WMOAMT>2.0.CO;2
Computed reverse-reference sideslip angle (βrev) vs sideslip angle at the pressure probe (βl) for slow yawing maneuver. Here
Citation: Journal of Atmospheric and Oceanic Technology 17, 6; 10.1175/1520-0426(2000)017<0795:WMOAMT>2.0.CO;2
Time series of computed quantities during pitch/yaw/roll maneuvers. Top three panels: wind components (m s−1) uncorrected for rapidly varying motion, superimposed with linear regression lines used for the reference winds. Bottom three panels: Δq (hPa), Δα, and Δβ (°) (“reverse”-reference minus steady-motion estimates).
Citation: Journal of Atmospheric and Oceanic Technology 17, 6; 10.1175/1520-0426(2000)017<0795:WMOAMT>2.0.CO;2
Dynamic pressure rapidly varying corrections (ɛq) during pitch/yaw/roll maneuvers. Upper panel: contribution of various terms (for clarity, some are offset as indicated). Lower panel: final correction. Here Δq = qrev − q(slow).
Citation: Journal of Atmospheric and Oceanic Technology 17, 6; 10.1175/1520-0426(2000)017<0795:WMOAMT>2.0.CO;2
Sideslip angle rapidly varying corrections (ɛβ) during pitch/yaw/roll maneuvers. Upper panel: contribution of various terms. (For clarity, some are offset as indicated.) Lower panel: final correction. Here Δβ = βrev − β(slow).
Citation: Journal of Atmospheric and Oceanic Technology 17, 6; 10.1175/1520-0426(2000)017<0795:WMOAMT>2.0.CO;2
Attack angle rapidly varying corrections (ɛα) during pitch/yaw/roll maneuvers. Upper panel: contribution of various terms. (For clarity, some are offset as indicated.) Lower panel: final correction. Here Δα = αrev − α(slow).
Citation: Journal of Atmospheric and Oceanic Technology 17, 6; 10.1175/1520-0426(2000)017<0795:WMOAMT>2.0.CO;2
Time series of computed quantities during pitch/yaw/roll maneuvers. Top two panels: east (x) wind component (m s−1), uncorrected (upper) and corrected (lower) for rapidly varying motion; superimposed with linear regression line used for the “reference” wind. Middle two panels: north (y) wind component. Bottom two panels: vertical (z) wind component.
Citation: Journal of Atmospheric and Oceanic Technology 17, 6; 10.1175/1520-0426(2000)017<0795:WMOAMT>2.0.CO;2
Measured air data quantities onboard the NRC Convair 580 aircraft. Superscripts/subscripts fus, pp, meas, and mir refer to“fuselage,” “pressure probe,” “measured,” and “mirror,” respectively.
Derived model calibration parameters. Note that the stated parameters are valid for accelerations measured in meters per second squared, rates measured in degrees per second, and angles in degrees.
