# Which Gimbal scenario is more likely — 30 NM or 10 NM?

#### dimebag2

##### Active Member
Entropy is very interesting, but how it is relevant to the case here, I'm not sure.

I'll note two things :

- the close trajectory was seen on SA, to go with your analogy it's like if you have an employee from the card factory telling you he's seen somebody shuffling the cards out of the machine. You can of course not trust him.

- the incredibly coincidental straight line is not incredibly straight/levelled/steady. Here it is with constant altitude in Sitrec on the left. And my reconstruction on the right, I find the same need for acceleration (from 250 to 380 Knots, average 320), to catch up with the lines of sight.

And if you want to have some sort of linear decrease in tail angle to explain the linear change in glare shape/size, it's even more difficult to find a straight line. You can of course make all kind of speculations on how a glare would or would not change linearly with tail angle.

#### Attachments

• 1660982382397.png
50.4 KB · Views: 19

#### markus

##### Active Member
Entropy is very interesting, but how it is relevant to the case here, I'm not sure.
I just explained how it's relevant. The last sentence introduced no new information, it summarized the rest of the post.
- the close trajectory was seen on SA, to go with your analogy it's like if you have an employee from the card factory telling you he's seen somebody shuffling the cards out of the machine. You can of course not trust him.
In this analogy, an employee of the card factory would be the pilot or someone otherwise involved with the piloting of the object. We obviously don't have access to that. You're also missing the point of the analogy: if someone shuffled the cards out of the machine, you agree with me the cards have been shuffled. Any of the 52! possible orderings is (roughly) equally likely after a good shuffle, so the probability it will come out in the proper order is 1/52!. So seeing the deck is in order is pretty good evidence it was intentionally placed that way. On the other hand, seeing a deck placed in some random arbitrary order like the one in my last post is not good evidence it was intentionally placed that way, because just about any of those "out of order" orderings would look equally "out of order", just like any random curved trajectory would look curved. Saying "but this is what the SA showed" is begging the question.
- the incredibly coincidental straight line is not incredibly straight/levelled/steady. Here it is with constant altitude in Sitrec on the left. And my reconstruction on the right, I find the same need for acceleration (from 250 to 380 Knots, average 320), to catch up with the lines of sight.
"I couldn't find a trajectory with these properties" != "a trajectory with these properties doesn't exist". Sitrec for example finds exact solutions for one out of constant speed, constant altitude, or straight line. This is a realistic problem with realistic uncertainties, however, and the real solution would not be an exact match for either, but would be a close match for all.

As you can see, there's some wiggle room here. What's wrong with Edward Current's original reconstruction?
And if you want to have some sort of linear decrease in tail angle to explain the linear change in glare shape/size
That's not a requirement. The change in glare size isn't even that linear to begin with.

As discussed in the other thread, this is a more complicated problem with more moving parts.

#### markus

##### Active Member
Entropy can be a confusing concept sometimes (in particular when it was a new concept - it was roundly rejected), but the closely related concept of (Kolmogorov) complexity applies equally well.
Consider the following two strings of 32 lowercase letters and digits:

abababababababababababababababab , and
4c1j5b2p0cv4w1x8rx2y39umgw5q85s7

The first string has a short English-language description, namely "write ab 16 times", which consists of 17 characters. The second one has no obvious simple description (using the same character set) other than writing down the string itself, i.e., "write 4c1j5b2p0cv4w1x8rx2y39umgw5q85s7" which has 38 characters. Hence the operation of writing the first string can be said to have "less complexity" than writing the second.
Content from External Source
-- https://en.wikipedia.org/wiki/Kolmogorov_complexity
Indeed, both concepts apply in this particular case. There is one important difference however, that entropy has a contextual character whereas Kolmogorov complexity doesn't. In the cards example, the Kolmogorov complexity of "spades diamonds clubs hearts, all A to K" is likely smaller than "A through K of Spades, A through K of Diamonds, K through A of Clubs, and K through A of Hearts", but the latter is "lower entropy" because it's the one configuration that's considered special (because it's the order manufacturers often use). By the same token, while the Kolmogorov complexity of a pure straight line is smaller than that of a curved constant altitude trajectory, in the present context the latter has smaller entropy because the statistical distribution we would define entropy with respect to, for this problem, is that of plausible aircraft trajectories.

#### FatPhil

##### Senior Member.
Indeed, both concepts apply in this particular case. There is one important difference however, that entropy has a contextual character whereas Kolmogorov complexity doesn't. In the cards example, the Kolmogorov complexity of "spades diamonds clubs hearts, all A to K" is likely smaller than "A through K of Spades, A through K of Diamonds, K through A of Clubs, and K through A of Hearts", but the latter is "lower entropy" because it's the one configuration that's considered special (because it's the order manufacturers often use). By the same token, while the Kolmogorov complexity of a pure straight line is smaller than that of a curved constant altitude trajectory, in the present context the latter has smaller entropy because the statistical distribution we would define entropy with respect to, for this problem, is that of plausible aircraft trajectories.

The latter is "new deck order" - so lower kolmogorov complexity too. Of course, everything's only defined relative to the language of known terms that is shared between the participants in the information exchange.

#### dimebag2

##### Active Member
"I couldn't find a trajectory with these properties" != "a trajectory with these properties doesn't exist". Sitrec for example finds exact solutions for one out of constant speed, constant altitude, or straight line. This is a realistic problem with realistic uncertainties, however, and the real solution would not be an exact match for either, but would be a close match for all.

We don't really see what's going on in your screenshots.

A straight trajectory of a distant plane should not be that hard to find, with all the refinements that have been made. Yet, straight-line trajectories, at 31Nm and 38Nm, look like this:

31NM 38Nm

Changes in tail angle are close to what Edward had found, but speed is all over the place. I'll repeat myself but I found the same in my reconstruction, speed is not steady for a distant straight path. No idea why Sitrec is different from Edward's model.

With constant speed :
31NM 38Nm

You can unzoom and from the top these will look more or less straight, but it looks like there are signifiant changes in heading (see video below to illutrate).

How large are these changes in heading ? I wish I could do it myself rather than suggesting Mick to do it, but I think it would be useful to have speed/altitude/heading indicated real-time along flight path. Then one should be able to share a video like mine above, showing the most plausible trajectory for the distant plane scenario, with numbers that make sense for a straight-leveled-steady trajectory. To me at this point in Sitrec, there is no incredibly coincidental straight-leveled-steady trajectory anywhere.

Next step would be to show the reconstruction to Ryan Graves, and he could pass it to the WSO who could tell us if another of their F-18 (what else?) could have been flying at 30-40Nm from them, at ~19000ft, in this direction, given the fighters from their squadron were all going back to the carrier.

#### Attachments

• 31Nm Constant Altitude.JPG
187.1 KB · Views: 18
• 31Nm Constant Speed.JPG
187.2 KB · Views: 19
• 31Nm Straight.JPG
182.5 KB · Views: 18
• 38Nm Constant Altitude.JPG
192.7 KB · Views: 20
• 38Nm Constant Speed.JPG
186.7 KB · Views: 20
• 38Nm Straight.JPG
232.9 KB · Views: 25
Last edited:

#### dimebag2

##### Active Member
I copy what I posted in another thread, the clouds are also to slow compared to the real vid. This is the problem with basing everything on how the clouds look, it's hard to see how exactly angular motion matches. But it has to be done, here looking at how many frames it takes to span one FOV, at different points of the video.

Frames per FOV crossed (left:vid ; right:sim)
from frame #0: 70 vs 85 (sim 20% slower)
from #301 : 81 vs 108 (25% slower)
from #601 : 136 vs 180 (25% slower)
from #801 (1/2FOV) : 85 vs 140 (65% slower)

This is not meant to criticize Sitrec, but hopefully help to get it more accurate. Maybe refining the angular motion will reveal a straighter line, maybe not, I don't know.

#### Mick West

Staff member
You can unzoom and from the top these will look more or less straight, but it looks like there are signifiant changes in heading (see video below to illutrate).
Something that we've observed with contrails (and some Flat Earth observation) is that it does not take much to make a path look bent when viewed from the end. I think that showing such a perspective-compressed image is rather misleading.

#### dimebag2

##### Active Member
It seems these wiggles in heading are about 4° for the 31Nm path, ~10° for the 38Nm path. A plane going straight doesn't do that.

What do you think of the cloud motion speed and do you agree with my measurements above?

#### dimebag2

##### Active Member
It seems these wiggles in heading are about 4° for the 31Nm path, ~10° for the 38Nm path. A plane going straight doesn't do that.

What do you think of the cloud motion speed and do you agree with my measurements above?
@Mick West , no comment?

A closer look at what's going on at the key moment between 26 and 30s

A small jump in the FOV, that can also be seen in this stitched panoramic view.

This would be quite a turbulence for a leveled distant plane at 30-40Nm.

#### Mick West

Staff member
I don't think you can really stitch the clouds together very well. Why is it curved? Cloud tops are flat.

#### dimebag2

##### Active Member
That's why I made the 1st image with perfecty flat clouds, to check if we see the jump there too.

#### Mick West

Staff member
That's why I made the 1st image with perfecty flat clouds, to check if we see the jump there too.
But the "flatness" of the clouds isn't the crenulated top profile, it's their direction of motion (because the camera never changes in altitude.)

#### dimebag2

##### Active Member
Just want to share here that close paths for Gimbal do not have to involve freaky or spooky physics. With wind included (roughly facing the object's direction) we can find solutions that exhibit a stop on the SA display, with no sharp vertical U-turn and moderate Gs (0.7G max).

The object needs to turn to the left at relatively low speed, decelerating under wind speed (120 Knts) as it does, making it look like a straight path that reverses direction on the SA, due to the effect of wind on the ground track. See an illustration below with the velocity vectors to visualize it (blue vector is air track, green vector is ground track).

What's unusual about that path is the climb in altitude, low speed, and of course the IR signature with no apparent means of propulsion, for an object at that distance (9Nm at the start).

Not saying it is the path, but I want to point out that a close path matching Graves' recollection does not need to involve insane physics. Which is relevant to this topic about likelihood of close versus distant paths.

Last edited:

#### Mick West

Staff member
a close path matching Graves' recollection does not need to involve insane physics.
It's still highly unusual. You've got an object that is:
1. Traveling in a straight line viewed from above
2. Slowing down with a deceleration that varies fairly linearly from 0.1 to 0.7g
3. Slowly gaining altitude at rate that's very gradually increasing
4. Coming to a dead stop along that line, while still rising vertically.
If the frame of reference of the air mass, it has to perform a weird artificial curve to maintain all these things (or just totally be ignoring wind)

To illustrate this, I've add an "air track" thin blue line that shows up when you toggle the wind display.

This shows the path the object takes in the frame of reference of the air. Since the air is all moving in the direction of the cyan arrow, then the end result its the yellow line, the ground track (which I guess I should make green).

So it has to do this weird mathematical decelerating turn to the left in order to do the weird mathematical "stop and go back" ground track.

Compare to the Gimbal (Far) scenario (with target wind at 270, so you can see it)

Since it's a straight line at a constant speed, the "air track" is just another straight line.

And, again, this all is what @Edward Current said some time ago.
The reason why the 10 NM trajectory is smooth and mathy is that it's a projection of a straight line up the sightline, not a real trajectory in space. I've used this analogy before, but long ago, it was assumed that when a planet in the sky appears to turn around and go retrograde, that's the object's actual path. In reality the object is moving along an ellipse, and the U-ey path is what happens when you view that ellipse from Earth. A random U-ey in the sky does not project to an ellipse in space, unless by sheer coincidence. But the planetary U-eys do. (I'm pretty sure that's why Kepler's ellipse model was so compelling.)

In summary: Realistic, physical trajectories don't work out to straight lines elsewhere on a sightline. Straight lines however do work out to unrealistic, un-physical trajectories elsewhere on the sightline, which is what we have at 10 NM. Or: It's not just that the 30 NM trajectory is minimal. It's that the 10 NM trajectory is a geometrical projection of a minimal trajectory — and, a rather extreme, un-physical one at that.

Last edited:

#### Mick West

Staff member
This shows the path the object takes in the frame of reference of the air. Since the air is all moving in the direction of the cyan arrow, then the end result its the yellow line, the ground track (which I guess I should make green).

Also, the "air track" moves with the air. You can think of it as being the contrail left by the craft. Contrails are almost always at an angle to the actual ground track of the plane, as they get carried along by the air moving (i.e., the wind). (This can be a little confusing)

#### dimebag2

##### Active Member
Nice to see the air track along with the ground track.

I recall Edward also proposed radar glitch at some point, to explain how the close path could have been seen by the aviators on radar. I find it difficult to defend a distant plane scenario that is completely unrelated to what's going on within 10Nm, given the coincidences it involves. With spoofing involved, I'm listening. My scenarios are for those who are unsatisfied (like me) about a scenario that leaves everything about the fleet and SA up in the air.

Replies
157
Views
16K
Replies
34
Views
4K
Replies
70
Views
4K