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Comment by ajnin | Hacker News Reader

Pretty interesting read. I'd like to know the answer to the 3rd question at the end as well, microwave manufacturers must have known about this all along since the doors embed a chunky piece of metal with small holes and not a lightweight grid of thin wire as one might expect with the "traditional" understanding of the Fraday cage effect.

So did they figure out the theory independently ? Did they design the screens based on measurements ? Maybe there's a patent somewhere that may shed some light on this.

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Radio propagation is quite a bit like magic, and if you're an engineer making a microwave, you probably really don't care that much about the theoretical underpinnings. The thought process goes something like this:

I have a loud radio source I want to keep contained in a box. I want people to be able to see into that box while it's on. I know that radio waves are blocked as long as the holes are smaller than some multiple or fraction of the wavelength of the radio source.

So what do I do? I think about what's easy and cheap to manufacture while being reliable. I try out a few things and measure the radio leakage. I pick the best solution out of the few I tried.

None of that really has anything to do with the subtleties of theory, the practice is you want something good at shielding that's good for the guys building it.

That's probably a pretty good guess for what happened early on when designing microwave doors. And 99% of what's happened since is "the existing design is effective and cheap, so I'm not gonna try to fix what ain't broken."

Your post is a great description of the phenomenon that Tableb describes in his book Antifragility, as "Lecturing Birds how to fly" [1] Essentially the argument is: we learn by doing and formalize that knowledge in research. Birds don't need to be lectured on fluid mechanics(drag,lift,etc) to understand how to fly.

[1]http://www.yourparttimehrmanager.com/lecturing-birds-to-fly-...

And it seems to me a trivial step to then say that formalized knowledge churned through the science leads us to things that are impossible for birds.

The counterpoint to that is people that have read a book on what a certain organism is supposed to do / usually does and then extrapolate that to all organisms of that variety in all situations. They usually forget that said organism hasn't read that book and will do whatever it damn well pleases given the physical constraints it finds itself under.

Many theoretical and experimental studies were done. One example from the early 70s is http://ipnpr.jpl.nasa.gov/progress_report2/II/IIO.PDF

Wow! :) A quick read seems to indicate that the case where the "metal plate with holes in it" approaches a wire mesh (holes are large compared to spacing) is treated in "Reflectors for a Microwave Fabry-Perot Interferometer" published by W. Culshaw in 1959 [1].

It's still locked up behind a paywall though, some 57 years later! :( Anybody have access (or can afford the $13 / $33 to buy it)? I checked if I could access it through DeepDyve but, no.

(Perhaps this is the answer to Q1, that it really hasn't "remained unanalyzed for 180 years", but that our broken way of archiving scientific knowledge has hid the analysis?)

1. http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=112468...

Here it is: http://sci-hub.cc/10.1109/tmtt.1959.1124685#

Thanks! :)

To me it seems not entirely implausible that both the OPs main conclusions can be derived from Culshaw's 1959 paper:

1. "First of all, the radius of the wires matters. As r→0, the shielding goes away. This, we now realize, must be why your microwave oven door has so much metal in it, and is not just a sheet of glass with a thin wire grid."

This conclusion could possibly be derivable from Eq 26 in Culshaw's paper. There's a clear dependence on r there. It's not completely obvious (to me) though, as it seems Culshaw is studying a more general case with a 3D structure of rods/wires.

2. "Secondly, the shielding is linear in the gap size, not exponential."

This conclusion too could possibly be derivable from Eq 26; there's a linear dependence on a there. But for the same reasons as above it's not entirely obvious (to me).

Seems to me that Trefethen should at the very least read Culshaw's paper though, if he hasn't already. :P

Can anyone with some electrical field theory knowledge/experience make a better comparison? :)

> but that our broken way of archiving scientific knowledge has hid the analysis?

A thousand times this.

What we need is a wikipedia of academic science where edits are peer-reviewed.

Perhaps it was determined by trial and error! Or maybe the earlier oven iterations happened to get lucky. We don't know that embedding a flyscreen on the door of the food chamber was necessarily the look that people would have gone for!

Now of course there are statutory "radiation leakage" limits in most markets. One might easily imagine that engineers would take a few goes at implementing the Ezy-Look-Into oven sketched by the folks over at industrial design, measure the emissions levels with thinner wire screens, and shrug it back with several binders full of readings. When experiment and theory are in disagreement, the product manager is unlikely to fund too much research into picking apart Maxwell's Other Equations. Given the known configurations for "good enough" microwave shielding, presumably the design team gets to sign off on a suitable colour instead of insisting on mechanically-etched glass impregnated with nanowires.

Engineers solve problems all the time either through experiment or applied science. Their goal is to make progress on the immediate project. Writing about it would be a sidetrack.

A company making microwave ovens is not an academic. They could have had an intern figure it out. Without a reason to share such knowledge (aka financial incentive) a company will usually not.

Or perhaps it was just easier and cheaper to fabricate a sheet-metal box with one side die-punched with a grid of holes.

I can totally see how making a cage of wires might use less material, but be magnitudes harder to fabricate correctly (electrically, mechanically, and aesthetically) and get right without any leaks.

I also wonder about shielding in cellphones. I'm guessing that it's designed more-or-less empirically, based more on accepted practices than on theory.

all of this shielding (including microwaves) is checked ... we all have to pass FCC emissions checks (very expensive) if we make consumer equipment, be it microwaves, cell phones or kid's toys

Right. I was also thinking of the need to shield modules from each other. All this stuff, packed closely together, with interconnections.

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