Recreating the math behind the first stealth aircraft

https://www.pramit.gg/post/remaking-echo-1-stealth-physics

by pmazumder • 6 days ago

66 29 6 days ago

xbar• 23 hours ago

Thanks. I needed that reminder to sometimes NOT just solve a matrix of 3000 * 3000 equations and merely make an assumption and take an integral, metaphorically.

dmwood• 23 hours ago

Not an average software engineer--beautiful page (imperfect spelling)! Why does detection scale as the 4th root of the RCS? Nice problem for the radiation theory part of a graduate electrodynamics class.

HNisCIS2• 22 hours ago

It's a 4th power because you're doing the inverse square law twice, once for the outbound pulse and once for the reflection.

MalbertKerman2• 22 hours ago

Why does detection scale as the 4th root of the RCS?

Because the power returned to the antenna scales as the -4th power of the distance to the target, and detection depends on that power being greater than some threshold. If the fourth power (rather than the square) is surprising, think of the reflection as re-transmitting the power that arrived at the target. The incident power on the target goes as RCS/r^2, and the power that makes it back to the original antenna gets another factor of 1/r^2, so the return scales as RCS/r^4.

ahartmetz• 18 hours ago

This -4th power also makes stealth very difficult. Reducing the RCS by a factor of 1000 reduces detection range by a factor of 5.75.

brandmeyer• 21 hours ago

It shouldn't, under the assumptions they are opening up with. Inverse square law twice is appropriate for an approximation that the reflection is entirely diffuse because you assume that the diffuse reflection is uniform in all directions away from the illuminated surface. A single inverse square law is appropriate (with both distances added to each other before squaring) under the approximation that the reflection is specular.

tonyarkles2• 19 hours ago

I’m guessing it’s because the detector is then working with power, not amplitude. The whole 10 log vs 20 log thing with dB.

MalbertKerman2• 18 hours ago

That only holds in the near field of the reflecting surface, which is roughly (it's a fuzzy boundary so who cares about a 2 pi here or there) where the ratio of distance to width of the surface is less than the ratio of the width of the surface to the wavelength. For wavelengths around 10^-2 m and surfaces around 10^0 m, that means distances within 10^2 m. Much further than that and the reflected wave is spreading out and falling off as 1/r^2. A radar working at ranges of tens or hundreds of kilometers is firmly in the far field.

There's still a strong angular dependence in the reflection amplitude; 1/r^2 fall-off does not imply isotropic distribution.

elictronic• 23 hours ago

The instant I realize it's an LLM generated piece. I'm out. Thanks for adding all the animations to make it abundantly obvious.

changadera• 23 hours ago

What animations ?

purplecats• 23 hours ago

background

robofanatic• 23 hours ago

the footer says "made by hand, mostly." not sure what that means, though!

readthenotes1• 22 hours ago

"All visualizations were drawn/generated by me and code can be found in this project's github repo"

Also, I feel it's not who the generator is that should concern you--it's the quality of the text.

I would much rather read something that is clear, concise, and consistent regardless of the source.

fwip• 21 hours ago

The text is low quality because it is un-proofread LLM output.

dariusxxs• 23 hours ago

where RR is the distance from the target (imagine the radar being very far away) en.wikipedia.org . This formula might look intimidating, so let's break it down:

You didn't even read your own slop. Why should anybody else?

MinimalAction• 22 hours ago

A random professor's academic website is usually barebones, no CSS, only HTML, mostly text. But the value one finds there is incredible.

As opposed to this, vibe coded slop which neither explains the stuff that's already there, nor is pedagogical. Why use AI for this?

King-Aaron2• 21 hours ago

It makes me sad, and to some extent offended, that so many people want to use AI to replace the human element in art. It dilutes what makes art impressive.

ButlerianJihad• 21 hours ago

In certain ways, A.I. has been welcomed because cost of content had become a true obstacle.

Ask any teacher who’s designed a PowerPoint lecture, or any marketer who just needed some anodyne ad copy and stock photography. They were procuring licenses at $$$ cost, and this licensing takes a lot of effort and a lot of legal counsel to get it right.

It is far more expedient to simple AI-generate the stuff you need, guaranteed royalty-free, unencumbered.

Ordinary computer users can just get a nice wallpaper, or icons we like, without signing up to a sleazy “Free Clipart” site.

This new normal is not born from a hatred of the human element, but I would say it’s because of the naked greed and unforgiving legal pitfalls of intellectual property today.

King-Aaron2• 20 hours ago

So I don't disagree that this is all a result of runaway capitalism. But also, and I know this is going to sound extremely anal retentive of me - but I wasn't born with an ability to create art - I learned.

Then when I was doing teaching (broad career, lol) I didn't find it too difficult to product my own content. Additionally I was also working in advertising for ages, and often created my own art. If I didn't want to create my own things, then I wouldn't be in a career where I was creating my own things.

I just don't know man. I was a creative once. I changed course, but I still feel so torn that I'm watching the entire creative process be taken over by non-creatives and then being argued out of the room that it's better.

(Edit, I would like to add that I'm no AI luddite, I just don't like the way it's being utilised)

quanto2• 19 hours ago

The whole mirror analogy for angular facets breaks down when you realize airplane is a moving object and at some point in its trajectory, one of the facets is likely to be facing the radar (maximum cross section).

If I remember from my numerical analysis days, it was the ease of numerical computing that necessitated the facets. Think 3D graphics from the 90s. All polygons.

rich_sasha• 18 hours ago

3d graphics is still mostly polygons, just much smaller?

Anyway, I'd imagine the part that is an integral over the surface becomes a finite sum, the post doesn't say but it seems like a reasonable guess.

hingler36• 18 hours ago

My understanding is that this more of a tactical consideration than a technical one. When these planes were used in the Gulf war, they were absolutely detected by Iraqi radars; they were just detected too late to do anything about them. While these planes were approaching the radar stations, they were oriented in one relative direction so the radar waves could be scattered away from the source consistently. Source is the Ben Rich Skunkworks book.

quanto2• 14 hours ago

Your answer shows why flat surfaces were acceptable for a bomber (with an asterisk) given the constraints.

Then, the question becomes why is the B-2 bomber (and latest stealth fighter jets) not angular like F 117.

Scientific computing has come a long way since the days of F-117. We do not need flat surfaces to scatter the beams away. Finding optimal curved surfaces that scatter the beams away is just a harder math problem.

bob1029• 15 hours ago

The primary design goal of the stealth mechanism is to get to the target undetected. By the time a radar signature shows up, the aircraft have ideally already dropped their bombs.

Being detected too late might as well be the same as not being detected at all in most practical scenarios.

pmazumder• 18 hours ago

I'm very surprised honestly that this has picked up as much as it has, and have been mulling over the polarized responses to it.

few things I'd like to clarify: - yes, I do use claude quite a bit. I don't have much background in frontend design or do it for work (which is mostly low level perception and controls, ironically something I'm seldom able to use AI for), so it makes tasks for me way more accessible. I try, as much as possible, to use LLM content to increase the creativity of a human behind it as much as possible (all the drawings on the site are drawn by visitors, for example, and I actually storyboarded the site's design by hand before implementing it).

- for writing, it is for better or worse mostly me, but I'm starting to see the parts that unravel. I've always been known to be rather verbose, and I tried to use LLMs to suggest strategies to make my drafts more palatable to a reader. I feel in retrospect that these attempts may have added a synthetic tinge. Mostly everything I write about is something I first make code for and investigate in my own time, without any expectation of explaining; there is a lot of real effort that's disproportionately put there over packaging.

This article was genuinely my first time making something educational of the sort, and I had my physics major friends checking in and auditing, and was gleefully showing progress wherever I could. I used manim for the first time to make those very shitty looking animations as well. I did not want to nor claim to look like an expert on this. I just wanted to show an exploration I did in my free time earlier, to maybe spark a little bit of interest in one of my random discord peers regarding the subject matter. I can say that for the close group of people around me in real life who this article was originally intended for, that I was successful. tl;dr I'm now somewhat embarassed that I've immortalized and publicized my lackluster first attempt at making educational content

HNisCIS2• 3 hours ago

FWIW I quite liked it but I'm from the RF world so maybe I'm biased.

Recreating the math behind the first stealth aircraft

Related Stories