Studying motion of the clouds
In my altitude study above
, I found that a 14-fold increase in the altitude of the clouds results in only a 6% change in the distance to the straight-and-level scenario, and a 14% change in its speed. It turns out, motion of the clouds has even less
of an influence on the scenarios.
I thought I would give the clouds a speed of 100 knots, in four directions (5,780 feet over 34.25 seconds). In the simulation it’s 100 knots ground speed, but we can ignore the unseen surface and instead, consider the clouds to be moving 100 knots relative to the reference frame of the F-18+object system. So, if the wind at 25,000 feet is in fact 120 knots in some direction, then the wind at the clouds’ altitude is 20 knots — which if we’re analyzing the clouds at appropriate altitudes (0–15,250 feet, as found in the altitude study) roughly accords with this graphic, plus some exaggeration for good measure:
First, I gave the clouds 100 knots of motion toward and away from the F-18,* along a line parallel to the sightline at its midpoint of travel. Neither direction had any measurable effect on the scenarios. The clouds pass through the frame at virtually the same rate (allowing for the slight angle between the sightline and cloud-motion vector toward the beginning and end). In the camera view, the clouds are not approaching or receding in any perceivable way.
Next, I gave the clouds 100 knots of motion to the left and right,* along a line perpendicular to the sightline at its midpoint of travel. I put the same animation on the “field measurers,” which are rectangles that mark out each of the nine-odd fields of clouds that pass through the frame, as well as on the “camera goal,” which is a line that moves across the field measurers at the proper rate that the camera needs to scan in order to reproduce the cloud passage through the frame.
With the clouds moving left-to-right, the camera scanned about one field too far, so I delicately reshaped the bezier curve that the F-18 follows to re-approximate the proper scan. Then I tweaked the aircraft+camera yaw animation to get the camera to stay on the camera goal. I repeated the process for the right-to-left cloud movement.
*For the toward and away cloud movement, I animated a rotation of the clouds about the center of the Earth, so that they would maintain their altitude. For the left and right movement, I animated a translation instead, since a z-axis rotation would cause distant clouds to move faster than closer ones. The latter results in an error with the clouds tilting 0.014° at one end of their travel — but since the camera is rolling anyway, I ignored this minuscule error.
We don’t know what direction the clouds were moving, if any, but if they were moving directly toward or away, for our purposes it’s effectively the same as the clouds not moving at all. The influence of cloud motion is therefore a sine function of the angle between the cloud-motion vector and the sightline.
With the clouds moving right to left at 100 knots, the straight-and-level solution becomes slightly closer: 29.1 NM, vs. 29.4 NM with fixed clouds. The object is a bit higher and slower: 18,825 feet and 350 knots (fixed clouds: 18,770 feet, 377 knots). The final recession velocity is –15 knots, and the angle of incidence goes from 20°–15° (fixed clouds: 28 knots, 14°–11°). The object takes a trajectory that’s more transverse, which is why the F-18 finishes with an approaching velocity, despite their having about the same airspeeds.
With the clouds moving left to right at 100 knots, the straight-and-level solution has about the same initial distance as with fixed clouds (29.4 NM). The object is a tiny bit lower and slower than with fixed clouds: 18,765 feet and 365 knots. The final recession velocity is 15 knots, the object taking a trajectory that’s more in line with the F-18’s at the end, and the angle of incidence goes from 11°–7°. So, this cloud motion is somewhat better for angle of incidence — the factor that makes the glare-blob start big and get larger.
One might expect the right-to-left and left-to-right cases to be symmetrical about the fixed-clouds case, but the camera is moving right to left. I certainly wouldn’t rule out measurement errors on my part, but these studies have been counterintuitive from the beginning, and the numbers are all in the same ballpark.
It was unanticipated, but there’s a simple explanation for why the original fixed-clouds, moderate-altitude findings are so robust against changes in cloud altitude and motion. The information that the Gimbal video gives us is mostly angular (camera angles and angular velocity of the clouds through the frame, which when combined with the FOV give an approximation of the flight path). The unknowns, however, are translational (altitude of the clouds, relative velocity of the clouds, exact position of the F-18 at any time). Given that the ATFLIR is locked onto a distant target, the angular quantities dominate the translational quantities. I noticed this when I needed to have the F-18 follow the Earth's curvature, even for its few miles — not because its vertical position changes, but because its downward angle changes. However, the real “aha” moment came when I scrubbed the timeline to see what 100-knot cloud movement looks like:
The angular motion overwhelms the translational motion.
I will check the corner cases, like the distant/banking scenarios, to get a better sense of how cloud altitude and motion transform the original plot. And, I will check clouds that are both high and moving. But, other than scenarios where the object changes velocities while heading in the same general direction, I believe we have exhausted the unknown variables in the Gimbal case.
There might be a question about relative winds between the F-18 and the object, but I think this would change only the (unknown/irrelevant) indicated airspeed measured by the object — the spatiotemporal relations between them remain unchanged.
I don’t think there is any room in this simulation for an object that comes to a stop and reverses direction.