Abstract
This paper deals with the identification of the wind profile along a flight trajectory by means of a two-dimensional kinematic approach. In this approach, the wind velocity components are computed as the difference between the inertial velocity components and the airspeed components. The airspeed profile is obtained from flight measurements. The inertial velocity profile is obtained by integration of the measured inertial acceleration. The accelerometer biases and the impact values of the inertial velocity components are determined by matching the computed flight trajectory with the measured flight trajectory, available from the digital flight data recorder and air traffic control radar. This leads to a least-square problem, which is solved analytically for both the continuous formulation and the discrete formulation.
Key to the precision of the identification process is the proper selection of the integration time. Because the measured data are noise-corrupted, unstable identification occurs if the integration time is too short. On the other hand, if the integration time is too long, the hypothesis of two-dimensional motion (flight trajectory nearly contained in a vertical plane) breaks down.
Application of the 2D-kinematic approach to the case of Flight Delta 191 shows that stable identification takes place for integration times in the range τ = 120 to 180 sec before impact. The results of the 2D-kinematic approach are close to those of the 3D-kinematic approach (Ref. 1), particularly in terms of the inertial velocity components at impact (within 1 fps) and the maximum wind velocity differences (within 2 fps).
The 2D-kinematic approach is applicable to the analysis of wind-shear accidents in take-off or landing, especially for the case of older-generation, shorter-range aircraft which do not carry the extensive instrumentation of newer-generation, longer-range aircraft.
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Abbreviations
- a b :
-
measured acceleration, ft/sec2
- a bx ,a bz :
-
measured acceleration components, body axes system, ft/sec2
- b :
-
accelerometer bias, ft/sec2
- b x ,b z :
-
accelerometer bias components, body axes system, ft/sec2
- g :
-
acceleration of gravity, ft/sec2
- h :
-
altitude above sea level, positive upward, ft
- m :
-
mass, lb sec2/ft
- p :
-
air pressure, lb/ft2
- S :
-
reference wing area, ft2
- t :
-
running time, sec
- T :
-
air temperature, °R
- V a :
-
airspeed, ft/sec
- V ax ,V az :
-
airspeed components, Earth axes system, ft/sec
- V e :
-
inertial velocity, ft/sec
- V ex ,V ez :
-
inertial velocity components, Earth axes system, ft/sec
- V ia :
-
indicated airspeed, ft/sec
- W :
-
mg=weight, lb
- W :
-
wind velocity, ft/sec
- W x ,W z :
-
wind velocity components, Earth axes system, ft/sec
- x :
-
longitudinal coordinate, positive northward, Earth axes system, ft
- z :
-
vertical coordinate, positive downward, Earth axes system, ft
- α :
-
angle of attack, rad
- γ :
-
path inclination, rad
- θ :
-
pitch angle, rad
- ϱ :
-
air density, lb sec2/ft4
- τ :
-
integration time, sec.
- b :
-
body axes system
- e :
-
Earth axes system
- h :
-
local horizon system
- w :
-
wind axes system
References
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Miele, A., Wang, T., andMelvin, W. W.,Wind Identification Along a Flight Trajectory, Part 2: 2D-Kinematic Approach, Aero-Astronautics Report No. 233, Rice University, 1989 (Revised 1991).
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This research was supported by Air Line Pilots Association (ALPA), United States Aviation Underwriters (USAU), and Texas Advanced Technology Program, Grant No. TATP-003604020. This paper is based on Ref. 2.
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Miele, A., Wang, T. & Melvin, W.W. Wind identification along a flight trajectory, part 2: 2D-kinematic approach. J Optim Theory Appl 76, 33–55 (1993). https://doi.org/10.1007/BF00952821
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DOI: https://doi.org/10.1007/BF00952821