AARO GoFast Case Resolution and Methodology

UNCLASSIFIED
10
UNCLASSIFIED
= [
7408 ∙ cos(−29°) + 0 ∙ 0 + 0 ∙ sin (−29°)
7408 ∙ 0 + 0 ∙ 1 + 0 ∙ 0
7408 ∙ −sin(−29°) + 0 ∙ 0 + 0 ∙ cos (−29°)
] (4𝑐)
= [
6479
0
3591
] (4𝑑)
Next, the vector result from (4d) was rotated about the z-axis by the sensor azimuth, γ. Note that
the sensor is pointing 49° to the left (designated by the “L”), which is a negative angle in the
defined coordinate system. These calculations are provided in (5a-d):
𝑅𝑧(𝛾) ∙ 𝑣𝐿𝑂𝑆 = [
cos (𝛾) −sin (𝛾) 0
sin (𝛾) cos(𝛾) 0
0 0 1
] [
6479
0
3591
] (5𝑎)
= [
cos (−49°) −sin (−49°) 0
sin (−49°) cos(−49°) 0
0 0 1
] [
6479
0
3591
] (5𝑏)
= [
6479 ∙ cos(−49°) + 0 ∙ − sin(−49°) + 3591 ∙ 0
6479 ∙ sin(−49°) + 0 ∙ cos (−49°) + 3591 ∙ 0
6479 ∙ 0 + 0 ∙ 0 + 3591 ∙ 1
] (5𝑐)
= [
4251
−4890
3591
] (5𝑑)
The resulting vector m means that the UAP was located 4,251 m ahead,
4,890 m to the left (the y-coordinate is negative), and 3,591 m below (the +z-axis is pointing
down) the F/A-18. At 3,591 m below the F/A-18 the UAP was at an altitude of 4,029 m (13,219
ft).
Location of UAP at t2
To find the UAP location at t2, the F/A-18 location had to be estimated based upon the known
flight dynamics. Because the aircraft was banking at 14° between t1 and t2, it was turning in a
curved path while moving at an average speed of 190 m/s. As it turned it also changed heading
away from the +x-axis. This rotation away from the axis can be represented as a yaw angle of φ
relative to its orientation at t1, as depicted in Figure 4.
The curved path of the F/A-18 is essentially part of a circle. The radius of that circle, or radius
of curvature, was found from (6).
𝑅𝑐 = 𝑣𝐹𝐴182
𝑔 ∙ tan(𝜃𝐵) (6)