# Gimbal Blender Simulation with Clouds

#### Edward Current

##### Active Member
Since (as markus said), the wind can be different at different altitudes (and even with distance, although less so), just using an assumed wind of 0 is an oversimplification. However you can assume it does not change for the jet (i.e. a local wind speed of 0) then the local wind for the object and the clouds is just a component of their velocity. It's the relative speeds which are important. You can translate that to a ground speed by adding in an arbitrary jet-local wind velocity, but it won't make a huge difference. The first goal would be see what the possible relative motions are.

However we do have one datapoint of "120 knots out of the West", which is probably the jet-local wind. So you might as well use that.
The model is definitely oversimplified, because there's data we just don't have. But I assume (I have not verified) that this is a quantitative problem, not a qualitative one: With more complete data, the numbers and the plots should move, but there should still be straight-line solutions and/or constant-altitude solutions, just at different altitudes/headings/speeds. I’m happy to try out a different set of inputs to see if that’s the case, but some data will always be missing.

I'm sorry if you posted this before, but how do you know the altitude of the cloud layer? Is it an assumption? If so it seems a very important one.
Broadly speaking, the downward camera angle sets the constraints on that. The clouds in the video looked to me like stratocumulus (I have a little background in meteorology), stratocumulus being very common over water and generally the most common cloud type globally, and they typically top out at 5,000–7,000 feet. It turns out, If I point a 25,000-foot camera at a large cloud layer at 6,500, tilting the camera down by 2.22° (and keeping it there) reproduces the clouds in the FOV surprisingly well.

But that’s not the only way to do it. A “secret admirer” on Twitter did his own simulation and put the clouds at 23,000 feet (altocumulus, presumably):

If I do that in my model, the camera, anywhere between 1.5–2.5°, doesn’t see any sky at all; it just points at the clouds. I assume that my friend made the cloud layer end along a very convenient line in order to make the sky reappear. That indeed may have been the case on that day, and it changes things a lot — but it’s inventing data, and I don’t think that’s helpful or warranted.

My Twitter friend mentioned (several times!) that the range for the ATFLIR is listed at 40 NM, and the clouds in my FOV are some 90–120 NM away, while his are much closer. But the ATFLIR isn’t locked on the clouds. In my Scenario #5 and others, the object it’s locked onto is well inside that range. The camera can't help that there also happens to be stuff in the background.

#### Mick West

Staff member
My Twitter friend mentioned (several times!) that the range for the ATFLIR is listed at 40 NM, and the clouds in my FOV are some 90–120 NM away
This is a common misunderstanding. The 40 NM limit is for accurate target tracking and laser designation, not being able to see things on video. ATFLIR is a camera, and like all cameras you can essentially see any distance if the object is big enough or bright enough (with some atmospheric conditions limitations).

The obvious example being the moon.

#### jarlrmai

##### Senior Member
I gave up with my Blender simulation, there are too many variables we just don't know to make it worthwhile.
1. Cloud size/feature size, height/distance
2. The object is very likely glare so we really have no way of knowing it's size/distance/direction/speed as it's apparent size is largely based on it's brightness and distance and the camera sensitivity which is also likely a variable as it auto adjusts the gain.
3. The margins for error on measurements from the very rough numbers from a video of the ATFLIR display lead to huge margins of difference when scaled out to real world distances +/- 1 degree on the ATFLIR horizontal slant is huge when scaled out.
You end up choosing arbitrary values to make the visuals match and the variables are too great to cover all the options, change one and you change 3 more to compensate.

I think the recreation that was done in DCS is probably enough to say that it could easily have been another aircraft at a reasonable distance. Maybe one day they will make an IR model that is accurate and we can get a more close match, I think it is on the list somewhere for DCS.

Probably the best thing you can do with a Blender simulation is to assume the UFO people are right and the object is the actual shape and size it would need to be to not be glare and to be a uniformly warm but just warm enough not to glare object that is that actual size and at whatever distance if any they've decided it is and work out what that means for the cloud size/distance, but even then you are choosing between cloud distance and cloud feature size, based on no actual data.

And yeah if you think a camera can have a max range, then I think you need to go back and read the threads about these videos where we have gone over the specs/features in detail, because who knows what other incorrect assumptions you may be making in your simulation.

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#### Mick West

Staff member
the 40 NM limit is for accurate target tracking and laser designation, not being able to see things on video. ATFLIR is a camera,
It's also not a limitation for tracking an object if the tracking is passive - i.e. it's done with object tracking using the pixels in the video, as is done here. You could lock on to, and track, Venus - because you could see it in the video. So even if it was tracking the clouds, that would not put a limit on their distance.

#### markus

##### Active Member
If I do that in my model, the camera, anywhere between 1.5–2.5°, doesn’t see any sky at all; it just points at the clouds. I assume that my friend made the cloud layer end along a very convenient line in order to make the sky reappear. That indeed may have been the case on that day, and it changes things a lot — but it’s inventing data, and I don’t think that’s helpful or warranted.
Well, in all cases we're just "inventing data", right? At least as long as we're not making use of the meteorological data, like what Mick posted above (although the conclusion from that thread that the clouds top out at 7300 meters is incompatible with more robust lower bounds on the distance to the object, given the assumptions of some form of smooth motion). I believe what you're alluding to there is that the hypothesis that the clouds stop at a certain (horizontal) distance in order to give the observed horizon line is fine-tuned, and so the "infinite layer" hypothesis should be preferred. But, given any horizontal distance to the line, we would get a comparable video, from which we could infer an equivalent "infinite layer" cloud height, with respect to which the line would, in retrospect, appear "convenient"/finely tuned. Since the existence/impressive value of the video is not contingent on the exact position of the cloud layer, excluding interrupted cloud layers at higher altitudes doesn't seem warranted. The fact that stratocumulus at typical heights reproduces the observed layer reasonably well is certainly suggestive, but doesn't seem quite enough to reject alternatives.

Also worth mentioning, the TAS of the F-18 varies by some 5 kt in the course of the video, which should move the straight line trajectories a bit.

#### markus

##### Active Member
As for the quoted 40 nm range on the ATFLIR, a lot of information about military systems seems to come from bureaucrats/marketers who wanted an easily digestible number to illustrate their systems capabilities, like when the F-22 radar cross-section is compared to that of a marble even though the RCS has a complicated dependency on target aspect, and the quoted number is likely some 'best case' frontal RCS. The best case for a camera is obviously infinity, so I imagine the 40 nm figure comes with somewhat arbitrary assumptions about the intended targets and observational conditions. In the Chilean navy case, the engines were bright enough to overload the sensor even 90 nm away, so the true tracking range would be far beyond that. Worth noting that in that case the airplane was ascending, which means the engines were running at a higher power setting than they would during cruise. The effective detection range for an ascending airplane is thus higher.

Incidentally, since it appears, based on available evidence, that the pilots were able to effectively follow an intercept trajectory towards the object, the information that it was moving "against the wind", and thus to the east, is likely reliable. That would suggest we should be considering ascending trajectories rather than descending or constant-altitude ones (19k feet is a rather unusual altitude indeed).

#### Edward Current

##### Active Member
I believe what you're alluding to there is that the hypothesis that the clouds stop at a certain (horizontal) distance in order to give the observed horizon line is fine-tuned, and so the "infinite layer" hypothesis should be preferred.
We get a fairly accurate reproduction of the clouds using an infinite layer of stratocumulus at a typical height. I'm confident in the infinite layer because even the slight downward movement of the clouds in the frame over the course of the video — which once upon a time I thought meant that the object must be climbing — is reproduced. That surprised me, and I’m still not sure why this effect happens. It wasn't a fudge...it just popped out.

I agree that finite clouds can't be discarded. However, in order for finite clouds to look like they do in the video, the simulation needs to end them not only at a just-so distance, but the boundary needs to make a just-so angle with the F-18's flight path, as seen overhead. Otherwise, the clouds move up or down in the frame over time.

But as I said, this could well have been the case on 1/20/15. Perhaps I should work up a version with high finite clouds, and see what that does to scenarios?

(Note: Looking at these screenshots, the roll of my aircraft/camera is a bit off at the beginning. This is cosmetic and doesn't affect anything quantitatively.)

#### jarlrmai

##### Senior Member
As for the quoted 40 nm range on the ATFLIR, a lot of information about military systems seems to come from bureaucrats/marketers who wanted an easily digestible number to illustrate their systems capabilities, like when the F-22 radar cross-section is compared to that of a marble even though the RCS has a complicated dependency on target aspect, and the quoted number is likely some 'best case' frontal RCS. The best case for a camera is obviously infinity, so I imagine the 40 nm figure comes with somewhat arbitrary assumptions about the intended targets and observational conditions. In the Chilean navy case, the engines were bright enough to overload the sensor even 90 nm away, so the true tracking range would be far beyond that. Worth noting that in that case the airplane was ascending, which means the engines were running at a higher power setting than they would during cruise. The effective detection range for an ascending airplane is thus higher.

Incidentally, since it appears, based on available evidence, that the pilots were able to effectively follow an intercept trajectory towards the object, the information that it was moving "against the wind", and thus to the east, is likely reliable. That would suggest we should be considering ascending trajectories rather than descending or constant-altitude ones (19k feet is a rather unusual altitude indeed).
The range I think refers to the laser target designator, the ATFLIR is more than an IR camera.

#### Mendel

##### Senior Member.
the information that it was moving "against the wind", and thus to the east, is likely reliable
IIRC from the rocket thread, the clouds in that direction were not broken.

#### Mick West

Staff member
We get a fairly accurate reproduction of the clouds using an infinite layer of stratocumulus at a typical height. I'm confident in the infinite layer because even the slight downward movement of the clouds in the frame over the course of the video — which once upon a time I thought meant that the object must be climbing — is reproduced. That surprised me, and I’m still not sure why this effect happens. It wasn't a fudge...it just popped out.
The cloud "horizon" remains at a fixed distance from the jet. If the object rises up while staying at constant altitude (MSL, curved earth), then (I think) that means it's getting closer to the jet (i.e. the jet is gaining on it)

#### Edward Current

##### Active Member
The cloud "horizon" remains at a fixed distance from the jet. If the object rises up while staying at constant altitude (MSL, curved earth), then (I think) that means it's getting closer to the jet (i.e. the jet is gaining on it)
Agreed. I'm pretty sure the reason my clouds sink — coincidentally it seems, at about the same rate — is that my F-18 flight path is on the xy-plane. From its beginning point to the end point, the Earth has curved by some 0.05°. That's 1/7th of a field of view, so there you go.

I'll revise the sim by giving the flight path the correct z-curvature, and go from there. This is an important refinement, although I expect there will still be receding solutions.

#### Edward Current

##### Active Member
Version 2
I made some changes based on the above feedback.
1. In the new version, the F-18’s true airspeed starts around 347 knots, increases to about 352, then drops back down to about 349. This made the flight path slightly longer. Not surprisingly, I found that like the camera angles, the onscreen calibrated airspeed is updated only 5 times per second.
2. The F-18 “descends” from the xy-plane by about 9 feet, along a curve, to match the curvature of the Earth across the ~3.6-mile straight-line distance from the beginning to the end of its path.
3. The aircraft also “pitches down” from 0° to 0.052° (linearly) to match the curvature. As expected, this returns the clouds at the end of the simulation’s camera view to the same level in the frame as at the beginning, with the object too high in the frame.
4. The ATFLIR tilts up from –2.22° to –2.17° (linearly) to bring the object back down to the center of the frame at the end.

Results: (3) and (4) offset, resulting in no change to where the object is in the frame; (2) had no measurable effect, and (1) had very little effect. I tweaked some of the aircraft+camera yaw-angle keyframes (discussed here) by minuscule amounts, but Scenario #5, at least, remains quantitatively the same as before. For any particular scenario, the goal is to keep the object roughly centered in the frame. If the object drifts up or down the z-axis, I have to make it change altitude; if it drifts left or right continuously, I change its vector; if it drifts left or right but comes back to the center, I change its banking or distance.

Here is a new render of the simulation. I’ve added some effects, which is more Hollywood than science, but fun. I rendered the clouds and the object separately, with a FOV of 0.40° to provide some overscan. Then in After Effects, I composited the images, cropped the composite to 0.35°, and stabilized it with the object at center. Here, I’ve applied glow and directional blur to the object, reproducing the directional glare; unsharp mask, the well-established source of the “antigravity spacetime envelope”; and a gradient of gaussian blur to the clouds. I also added a "blotchiness" image made of enlarged noise, to reproduce the artifacts from the optics, at 2% opacity. Applying a rotation to the directional blur and the noise completes the picture.

Due to the lack of the flat cloud-horizon and parallax in the original (particularly at the beginning), I find myself believing less in the “infinite cloud bank” idea. So, I’ll do some experiments with truncating the clouds in the far distance in various ways. [Edit: The truncation experiments didn’t do much for me. I had to cut them off at a pretty specific distance to make the horizon line really bumpy. Perhaps a distance-dependent effect in Blender, like haze, would be better. It’s probably more of a haze effect in reality, regardless.] I’ll also try changing the altitude and movement of the cloud layer and find out how they affect the constraints from the limit case.

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#### DavidB66

##### Senior Member
I haven't followed this closely, but I'm very impressed, both by the amount of work that Edward Current has put into it, and by the rather good fit of the resulting simulation to the original Gimbal video. OK, it's not perfect, but what is? I agree with comments that there are too many variables to get a definitive solution, but that doesn't mean it is not worthwhile. At the least, it may succeed in showing that with plausible assumptions there are scenarios which replicate the movement of the object without requiring it to move in extraordinary (i.e. non-terrestrial) ways. Beyond that, it may succeed in narrowing down the 'search area' for the object to a certain range of possible distances.

Some people on Twitter have made a big deal of the speed of the actual movement of the clouds, which depends on the unknown speed of the wind where the clouds are. Taking this as 120 knots, or about 200 kmph, that would mean a speed of under 60 meters per second for the clouds, or a total movement of under 2 km in the course of the video. I guess this would only be a small proportion of the apparent movement of the clouds, which must be mainly due to parallax. That would be consistent with the fact that the apparent movement slows down and almost stops towards the end of the video, when the F18 and its camera are pointing straight at the object. But I haven't worked it out quantitatively in detail. At a distance of 150 km, the horizontal fov of 0.35 degrees would span just under a kilometer, which may seem surprisingly small, in relation to the cloud features visible, but still a lot more than 60 meters (if that is the actual movement per second of the clouds).

As usual, I apologise in advance for any blunders of logic or arithmetic.

#### Edward Current

##### Active Member
Here's an embarrassing discovery. In preparation for moving the clouds to different heights, I lowed them down close to sea level, and saw this:

The cloud layer is irregular and not curving tightly with the Earth. I realized I had made this mesh by duplicating the Earth mesh, before I had properly subdivided the latter to make it sufficiently round. This meant that the cloud layer had been made of flat segments, explaining why the above peaks and valleys were happening.

I created amore smoothly curving cloud layer. This is the resulting camera view:

The cloud-horizon is bumpy now! The irregularities in the foreground are hiding the flat cloud-horizon behind them, like in the original video. I suspect, without any added effects, this will greatly diminish or eliminate the parallax in the clouds that we have been seeing. [Edit: The measured distance to the most distant visible clouds is now 160 NM rather than 175 NM.]

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#### Edward Current

##### Active Member
Low- and high-altitude limits
The downward angle of the ATFLIR camera can be anywhere between –2.5° and –1.5°. When I fix it to –2.5°, I need to lower the clouds almost to sea level to get the clouds-and-sky look that we see at the start of the video. A more reasonable lower-altitude limit for the clouds is 2,000 feet. This corresponds to a downward camera angle of –2.4°. With this tilt, the depth of view of the clouds extends its farthest: from 110 NM to 160 NM.

In my simulation, the constant-altitude, straight-line solution under this condition (which I call Scenario #5.1) is a bit closer and slower: distance 28.4 NM, speed 365 knots, altitude 18,385 feet. The final recession velocity is 15 knots.

There are also constraints on how high the clouds can be for sky to remain visible in the shot. At a minimum camera angle of –1.5°, in my simulation I found that the cloud bank can be as high as 15,250 feet and still extend infinitely into the distance.

View attachment 49083

With the clouds at this upper limit of 15,250 feet, the constant-altitude, straight-line solution (which I call Scenario #5.2) is a bit farther and faster: distance 30.1 NM, speed 415 knots, altitude 20,775 feet. The final recession velocity is 60 knots. The depth of the clouds at this altitude is narrower, 80–110 NM.

Here are the trajectories, as seen from above:

View attachment 49081

Changing the altitude of the clouds affects the pass-through rate of the clouds in the field of view slightly. In the low-altitude limit above, the clouds run about 3% slower; in the high-altitude limit, about 4% faster. Further approximations would adjust the object trajectories accordingly.

High-altitude limit with truncation
The clouds can have a higher altitude if they are truncated in the back, to let the sky show through. (Without truncation, all we see are clouds and no sky.) I found that by setting the clouds at 16,400 feet and shaving away slices of the clouds, I could kind of recover the cloud horizon:

View attachment 49073

The depth of the clouds in this case goes from only 63–80 NM. I suppose the cloud bank could have ended just so to produce this view, but it really doesn't give us much more cloud altitude than the limit case of an infinite cloud bank at 15,250 feet and –1.5° on the camera.

To stretch things a bit further, I tried raising the clouds up to 18,800 feet. This cuts down the depth of the clouds even more, to 42–50 NM:

View attachment 49074

(The modifier creating the cloud texture was adjusted. The cloud features become much larger at high altitudes.)

The prospect of truncated clouds looks like a dead end. I think for all practical purposes, the upper limit on cloud altitude can be safely set to about 15,000 feet.

I've uploaded version 2.1 of the Blender simulation including low-altitude and high-altitude versions here, along with a read me file.

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#### jarlrmai

##### Senior Member
The ATFLIR could track a descending object from -1.5° to -2.5° without changing from showing 2°

#### Edward Current

##### Active Member
The ATFLIR could track a descending object from -1.5° to -2.5° without changing from showing 2°
But in that case, the clouds will rise up in the picture. They sink over the coarse of the video, indicating that the object is rising relative to them (from the camera’s perspective). It’s probably pretty safe to assume that the clouds at the beginning and end are at roughly the same altitude.

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#### jarlrmai

##### Senior Member
But in that case, the clouds will rise up in the picture. They sink over the coarse of the video, indicating that the object is rising relative to them (from the camera’s perspective). It’s probably pretty safe to assume that the clouds at the beginning and end are at roughly the same altitude.
Similarly it could go from -2.5 to -1.5 as well, I didn't think it required to detail the corollary.

#### Edward Current

##### Active Member
Similarly it could go from -2.5 to -1.5 as well, I didn't think it required to detail the corollary.
Unless the cloud bank slopes or changes altitude, any change in the camera pitch should result in a change in the cloud level in the frame. So, at least under the assumption of a flat cloud bank, I think we’re locked into the camera tilting up by 0.05° over the course of the video. That could be anywhere between –2.5° to –2.45° and –1.55° to –1.5°. But not –1.5° to –2.5°, or vice versa. Is that wrong?

#### jarlrmai

##### Senior Member
Probably not wrog, doesn't the actual view curve slightly because of the rotation, I seem to remember that from the video that was a corrected track of all the frames.

I saw this same effect in my limited Gimbal situation.

It would be interesting to a see a similar cloud based track for your sim

#### Edward Current

##### Active Member
It would be interesting to a see a similar cloud based track for your sim
I'm trying to figure out how I could do this. I think I could stick a very wide panoramic camera on the same bezier curve that the F-18 follows, without any rolling or panning except maybe to keep the clouds still.

I’m not sure where the curve in the above video comes from. I assumed it was just an artifact of stitching the images together.

#### jarlrmai

##### Senior Member
I'm trying to figure out how I could do this. I think I could stick a very wide panoramic camera on the same bezier curve that the F-18 follows, without any rolling or panning except maybe to keep the clouds still.

I’m not sure where the curve in the above video comes from. I assumed it was just an artifact of stitching the images together.
I noticed it in my Blender sim a very slight raising and lowering of the view as the track proceeds.

#### Edward Current

##### Active Member
I noticed it in my Blender sim a very slight raising and lowering of the view as the track proceeds.
I noticed a lowering of the clouds. But then I realized my F-18 track wasn't following the curvature of the Earth, so the view was effectively tilting up over time, relative to the surface below. When I corrected for that, the clouds stayed at the same level from beginning to end (which I then corrected for by animating the camera pitch to recover what’s seen in the original).

The smooth curvature on that stitch video has to be some kind of artifact. The video is in two parts — the clouds go down and then back up twice, in each of the white-hot and black-hot segments. The clouds in the original video don’t follow that W pattern.

#### Edward Current

##### Active Member
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:

(http://www.aerospaceweb.org/question/atmosphere/q0266.shtml)

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.

Results
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.

Discussion
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.

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#### Edward Current

##### Active Member
I finally finished up all of the outlier scenarios for the four extended cases of the Gimbal simulation (clouds at 2,000 feet, clouds at 15,250 feet, clouds moving to the right at 100 knots, and clouds moving to the left at 100 knots. All of the basic scenarios are still there; they just get shifted a bit in the plots:

These plot lines should be considered qualitative sketches. Here are the stats they derive from. The angle-of-incidence numbers in particular seem to point to a straight-and-level jet (the 5.x scenarios), regardless of the clouds.

So, that completes the simulation project. I’ll now dive into the accompanying video. I’ll touch on the object’s rotation but won’t get into details. I’ll keep it to the three lines of evidence for the rotation being local: The “flop” as the camera angle nears 0° (I’ll refer to Mick’s upcoming explainer for that); the rotation of the background with the object; and the minor rotations when the bank angle changes at :09 and :19 as seen with the picture stabilized on the horizon. I don’t really want to discuss it at all, because that wasn’t the focus of this project, but you know what’ll happen in the comments if I ignore “It’s rotating!” or, “There’s a whole fleet of ’em!”

When doing these outlier cases, I didn’t bother making the clouds both high and fast-moving — I’m sure nothing substantial would come of it, and also, higher clouds would be moving slower, not faster, relative to the F-18/object system. In the video, I will need to stress that cloud motion is relative and not absolute: the 100 knots represents the difference between the purportedly 120-knot wind at 25,000 feet and a 20-knot wind at 6,000 feet. Anyone interested in checking this last case can take it on as a challenge.

#### Mendel

##### Senior Member.
@dimebag2 regarding clouds and distance, a side-by-side video of a simulation with ~30 nm distance vs. GIMBAL is in post #52. I find it quite convincing.

#### dimebag2

##### Active Member
@Edward Current , looks like great work.

I think what would add a very valuable contribution to the discussion is whether your 3D model can retrieve what we see in the video, but with an object's trajectory as seen by the pilots : 10Nm or less, before LoS intersection, stops mid-air.

If you cannot make it work, it would be a very strong case to prove they have been fooled by the specific conditions of the event, and the trajectory they describe could not have been what they saw.

If your model does not invalidate it, then we can start discussing which of the two scenarios is the most likely. I want to start a thread on that soon.

#### Edward Current

##### Active Member
@Edward Current, looks like great work.
Thank you. It's been a long haul.

I think what would add a very valuable contribution to the discussion is whether your 3D model can retrieve what we see in the video, but with an object's trajectory as seen by the pilots : 10Nm or less, before LoS intersection, stops mid-air.

If you cannot make it work, it would be a very strong case to prove they have been fooled by the specific conditions of the event, and the trajectory they describe could not have been what they saw.

If your model does not invalidate it, then we can start discussing which of the two scenarios is the most likely. I want to start a thread on that soon.
This is what that looks like (at 2x speed). The white block is 10 NM from the starting point (and 7.1 NM from the ending point, which raises the question about how "10 NM" is defined):

The initial horizontal speed of the sightline at 10 NM is about 200 knots. Yes, an object at that distance can slow gradually to almost zero horizontal speed...but it has to steadily gain 560 feet of altitude to stay where it is in the camera view. So, at the end, it's going almost straight up at 10 knots.

I suppose it could be a coincidence that such an object slows horizontally at the exact acceleration, and climbs at the exact vertical speed, that happens to resemble (in the camera view) a straight & level trajectory 30 NM away.

#### dimebag2

##### Active Member
Thank you. It's been a long haul.

This is what that looks like (at 2x speed). The white block is 10 NM from the starting point (and 7.1 NM from the ending point, which raises the question about how "10 NM" is defined):

The initial horizontal speed of the sightline at 10 NM is about 200 knots. Yes, an object at that distance can slow gradually to almost zero horizontal speed...but it has to steadily gain 560 feet of altitude to stay where it is in the camera view. So, at the end, it's going almost straight up at 10 knots.

I suppose it could be a coincidence that such an object slows horizontally at the exact acceleration, and climbs at the exact vertical speed, that happens to resemble (in the camera view) a straight & level trajectory 30 NM away.
Thanks a lot, that's great. Don't you think any horizontal trajectory before the LoS will have a corresponding steady trajectory (or more), further away ? The vertical movement the object would need in the close scenario is new information.

#### Edward Current

##### Active Member
Thanks a lot, that's great. Don't you think any horizontal trajectory before the LoS will have a corresponding steady trajectory (or more), further away ? The vertical movement the object would need in the close scenario is new information.
Actually, the necessary altitude gain is not steady — which makes sense, as the F-18 is horizontally approaching the object slower at the beginning vs. the end. So, in addition to having a negative horizontal acceleration, an object at 10 NM needs a positive vertical acceleration in order to reproduce the camera view. The overall acceleration is negative, something like –0.3 g's. One assumes the necessary vertical acceleration applies to all changing-altitude scenarios.

Here is the side view at 4x speed:

#### dimebag2

##### Active Member
Actually, the necessary altitude gain is not steady — which makes sense, as the F-18 is horizontally approaching the object slower at the beginning vs. the end. So, in addition to having a negative horizontal acceleration, an object at 10 NM needs a positive vertical acceleration in order to reproduce the camera view. The overall acceleration is negative, something like –0.3 g's. One assumes the necessary vertical acceleration applies to all changing-altitude scenarios.

@Edward Current

I don't think we can conclude on the object having to change altitude in the close (before LoS) scenario.

I did a quick schematic with Geogebra 3D, based on these positions for Gimbal at PT1 (0'01) and PT4 (0'31). I choose this one because in this scenario the size of the object on the screen grows by ~10%, like on the screen (this is considering the object keeps the same size). But it could be a bit closer, further, this is the same.

Point 1 and Point 4

The distance from the fighter is 7.63 Nm at PT1, 6.36Nm at PT4.

Now if I put these 2 positions for Gimbal, and two positions for the fighter, in a 3D schematic, it gives that :

A leveled trajectory is absolutely possible. The elevation angles at PT1 (positive downwards in this schematic) and PT4 are -2.31deg, and -1.9deg. Which is in the range that would give -2deg on the screen.

The 2 Geogebra models :
3D : https://www.geogebra.org/3d/qdu3cabd
2D: https://www.geogebra.org/m/p4zhvaaf

#### dimebag2

##### Active Member
Based on these 3D line of sights, a leveled trajectory at 30Nm means the distant plane would have had covered 3.3Nm in 30s. That's a speed of ~400 knots, faster than the F18. Is that consistent with what you find @Edward Current ?

It's much easier to this these things directly in the 3D model, but here is the potential leveled trajectory at 30Nm

EDIT : if I'm correct, 400 Knots against a 120 Knots wind. The size of its glare is about 60ft wide. I'm no expert but this numbers seem a bit too high for a small plane.

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#### Edward Current

##### Active Member
A leveled trajectory is absolutely possible. The elevation angles at PT1 (positive downwards in this schematic) and PT4 are -2.31deg, and -1.9deg. Which is in the range that would give -2deg on the screen.
But that's an elevation difference of 0.41°, which is more than a FOV vertically. You wouldn't see any clouds at the end in that case; they'd sink out of the frame around halfway through. That's why the simulation with clouds is useful. But in your scenario, shouldn't the camera be tilting down, not up? It's approaching the object, so it should be tilting progressively more downward.

A level, close-by trajectory is absolutely possible — but in that case, the object has to be receding from the F-18, over 350 knots. Certainly that's not coming to a stop.

So, if it's close by, it can be level but not decelerating to a stop, or it can decelerate and come to a stop horizontally, but accelerate vertically. It can't come to a stop without accelerating upward.

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#### Edward Current

##### Active Member
Based on these 3D line of sights, a leveled trajectory at 30Nm means the distant plane would have had covered 3.3Nm in 30s. That's a speed of ~400 knots, faster than the F18. Is that consistent with what you find @Edward Current?
Close — I get 380 knots.

EDIT : if I'm correct, 400 Knots against a 120 Knots wind.
Airspeed is airspeed. All speed measurements are relative to the air mass, however it might be moving.

#### dimebag2

##### Active Member
Edwards
Close — I get 380 knots.

Airspeed is airspeed. All speed measurements are relative to the air mass, however it might be moving.
Cool, not too far then.

Yes you're right about the FOV. That's to consider that the clouds are perfectly flat though. All things considered I don't think the close trajectory having to climb makes a big difference, it's a trajectory that stops mid-air anyway, so it's already out of the ordinary.

Do you have a suggestion for the kind of plane that would fit the speed/glare size you retrieve ?

#### DavidB66

##### Senior Member
if I'm correct, 400 Knots against a 120 Knots wind. The size of its glare is about 60ft wide. I'm no expert but this numbers seem a bit too high for a small plane.
The glare is in the camera, not the sky. I don't think we have established any basis for a limit to the apparent size of a glare as a multiple of the angular size of the heat or light source causing it. I just looked at a bright LED street light (it is night time where I live), with the naked eye and with glasses. With the naked eye there was a 'halo' of glare at least 5 times as wide as the light itself. (This is not an atmospheric effect, as the glare disappeared when I held out a pencil to cover only the width of the street light itself. If the light were being diffused by the atmosphere, it would not be blocked beyond the width of the pencil.) With glasses, which is a fairer comparison as I am somewhat short-sighted, the central halo was a bit narrower, but there were long diffraction spikes extending far beyond the halo. (Again, they disappeared when I used the 'pencil' test.) I should probably clean my glasses.
Incidentally, 400 knots, with or without allowance for wind speed, is quite consistent with an air liner or business jet (e.g. a Bombardier Global Express, with cruise speed about 500 knots.) It is only faster than the F18 because the F18 is flying well below its maximum or even cruise speed, which Wikipedia gives as 570 knots.

#### Edward Current

##### Active Member
All things considered I don't think the close trajectory having to climb makes a big difference, it's a trajectory that stops mid-air anyway, so it's already out of the ordinary.
Agree...although it's another necessary condition that needs to be met, that does not need to be met with a straight, constant-speed trajectory at 30 NM. Then again, the 30 NM scenario has the necessary condition that Graves' account is wrong.

Do you have a suggestion for the kind of plane that would fit the speed/glare size you retrieve ?
Any small jet, I think, except for the single-engine Cirrus Vision, which is too slow (cruising speed 300 knots). It could also be a drone, although I don't know what their speeds are.

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#### dimebag2

##### Active Member
A question that bugs me : what is the probability for a plane at 25000 ft, 350 Knots, to make a coordinated turn and end up in the exact boresight of another plane at 19000ft, 380 Knots, so that the cloud motion parallax is close to 0 ?

In other words, @Edward Current , is the cloud motion coming to almost a stop very sensitive to the turn radius of the plane ? If you change the turn radius circle by a bit, does it affect cloud parallax a lot ?

#### Mendel

##### Senior Member.
A question that bugs me : what is the probability for a plane at 25000 ft, 350 Knots, to make a coordinated turn and end up in the exact boresight of another plane at 19000ft, 380 Knots, so that the cloud motion parallax is close to 0 ?
Remember that this does not occur by random chance, it's the end result of the pilot deliberately turning his aircraft towards the UAP because he has observed it.
This deliberate turn towards the UAP causes the ATFLIR to swing from looking sideways to looking straight ahead.
When the motion of the camera is in the same direction it is looking at, parallax effects are minimal, especially with a narrow field of view.

So the reduction of the cloud parallax is a necessary consequence of the pilot turning towards the UAP, and not random at all. In other words, the probability is 100%.

(Changing the turn radius would not affect this much, as long as the observer ends up pointed at the target.)

#### dimebag2

##### Active Member
So the reduction of the cloud parallax is a necessary consequence of the pilot turning towards the UAP, and not random at all. In other words, the probability is 100%.

Thanks for your reply @Mendel . Not sure you understand what I mean though. Getting roughly aligned with the object direction is different than being almost perfectly aligned. For the cloud motion parallax to stop as it does, the F18 has to be in close-to-perfect alignment with the object.

Here is an attempt to estimate this. I made a schematic to estimate parallax, for a plane (named Gimbal here) at 30Nm from the F18, and background clouds at 100Nm. That was a rough estimate of the cloud distance at some point, based on their probable height. I'm using the following equation, to calculate the apparent speed the plane would have just due to parallax effect : V2=V1*d2/d1, with d1 : distance F18-Gimbal, d2 : distance Gimbal-Clouds, V1 : horizontal component of the velocity vector that corresponds to the difference between the velocity vectors of the F18 of the unknown plane.
I start with perfect alignment between the velocity vectors of the F18 and unknown plane (Gimbal dot). I take a speed of 380 Knots for Gimbal, 350 for the F18 (this can be adjusted).

The circle at the bottom represents the mean turn radius of the F18 over the course of the video (~3.5Nm radius). The angle of the Gimbal direction and the radius of the circle can be tweaked, and it gives the correspondent parallax motion, and it also gives at how many FOV per second it corresponds by how much the clouds should move on the screen). Here the radius is such that the F18 and Gimbal velocity vector (or boresights), are perfectly aligned. No parallax motion, 0 FOV/s, we should not see background cloud motion in this configuration.

Now, check how these things are sensitive. Here I only change the angle of Gimbal by 4deg (relative to vertical axis), and I slightly reduce the radius of turn.

The vector centered on the origin is an enlargement of the difference between the velocity vectors of F18 and Gimbal, this is just to visualize how it affects the vector alignments (the F18 and Gimbal velocity vectors are tiny at this scale, and don't show up on the screen). I didn't change the turn circle by much, we barely even see the difference in the circle size of the F18.

In that slightly different configuration of the objects alignment, the parallax speed of the unknown plan relative to background should be ~100 Knots. which corresponds to ~ 0.2 FOV/s. This means here you should see the background crossing the FOV in 5sec, which is a significant speed of motion for the background. This is roughly what we see around the 0'15 mark in the video. Definitely not a configuration with non-moving clouds.

That the clouds almost come to a stop at the end means that the pilots got in quite a specific configuration of alignments with the unknown plane velocity vector. Like if they had a 3D GPS in their head and made a turn that corresponds to a circle exactly tangent to the plane direction (plane that is 6000ft below them). While watching the ATFLIR, checking the wind, and other objects on the radar (fleet of them). Also note that they keep going with their circle at the end, so it's not like they intended to "chase" the unknown plane by heading exactly behind its tail. It looks to me like they are simply going in a circle to check it out.
Did they have a trace for the plane trajectory on their instruments ? Or just a dot pointing at the direction of the unknown object on their radar ?
This looks like magic to me.

On the other hand, any F18 circle will get to zero or minimal cloud motion when targeting a non-moving object in its boresight (scenario described by the pilots).

I made this quickly so I don't guarantee my schematic here is free of errors, but you get the idea. I'd be very interested to know if Edward retrieves something similar when slightly changing the unknown plane direction and/or the F18 turn radius.
https://www.geogebra.org/geometry/wmdju36g

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