Stephen Speicher

Archimedes and the siege of Syracuse

38 posts in this topic

The thought also occurs to me that this might have also made some kind of "terror weapon" to demoralize enemy troops trying to attack a fortified walled city in the daytime (subject to the sun being in the right position to make it possible.) A couple of hundred guys manning the walls, aiming their polished metal rectangles at the same spot in a crowd of enemy troops would probably cause panic as they began to get burned. The target wouldn't have to just be ships at sea.  In fact, it would be a very logical way to systematically pick off officers, subject to the effective range of the mirrors as the reflected light spread out over distance.

Couldn't we do that with today's technology? How about some cutting, burning, or vaporizing lasers like the ones they use in surgery -- only much more powerful -- mounted on a remote controlled plane like the ones they use for reconnaissance. An operator hundreds of miles away could sit at a computer console and pick off a few dozen Warlords or Ayatollahs. :)

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Couldn't we do that with today's technology?  How about some cutting, burning, or vaporizing lasers like the ones they use in surgery -- only much more powerful -- mounted on a remote controlled plane like the ones they use for reconnaissance.  An operator hundreds of miles away could sit at a computer console and pick off a few dozen Warlords or Ayatollahs.  :)

The problem with that is not can we do it. America can, but we won't. :)

~Aurelia

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The main problem with this weapon, and why it wasn't used much in antiquity, is that it required what in ancient times was tantamount to a mathematical genius to get all the foci properly, and the angles with which the polished surfaces were inclined. That's the only way I can explain why such an absolutely terrifying weapon was not used constantly.

The energy delivered is roughly inversely proportional to the distance squared, so its usefulness as a weapon is restricted to relatively close distances.

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A productive methodology I somtimes apply for questions like this is to ask myself if there are examples of this technology in the animal kingdom.

Given lifes amazing propensity for discovering things like sonar, etc... then it isn't unreasonable to conclude that mirrors are probably not an effective weapon, as life has not converged on this strategy. It's not proof, but I think it's a worthwhile strategy when first "peeling the onion" on such questions.

Another element of such thinking, is to try and imagine a series of small incremental steps that each have survival value leading up to the "mirror based weapon". (it's not a requirement that each step be useful as a mirror-based weapon, it just has to be useful for something)

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... ask myself if there are examples of this technology in the animal kingdom.

Reminds me of the classic Arthur C Clarke short story, "A Meeting with Medusa," about the first manned probe into Jupiter's atmosphere ... Flying sharks swim through the methane, feeding on miles-wide jellyfish ... until the jellyfish strike back, electronically!

A marvelous story (except for one morally depraved touch, the name Clarke gives to a ship).

As for Betsy's idea ... I prefer my Ayatollahs well done ... actually, burned to a crisp! :)

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Couldn't we do that with today's technology?  How about some cutting, burning, or vaporizing lasers like the ones they use in surgery -- only much more powerful -- mounted on a remote controlled plane like the ones they use for reconnaissance.  An operator hundreds of miles away could sit at a computer console and pick off a few dozen Warlords or Ayatollahs.  :)

Reminds me of one of my favorite movies, Real Genius :)

Actually I have heard of the development, by the U.S. Air Force, of very powerful chemically powered lasers designed to be carried onboard a jet with a computer controlled mirror/targeting system, but I think the goal there is to shoot down enemy missiles or planes.

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The energy delivered is roughly inversely proportional to the distance squared, so its usefulness as a weapon is restricted to relatively close distances.

But wouldn't the reflected light from a flat mirror, not disperse by inverse square as does a single, simple point light source? A mirror reflecting 1 kilowatt of solar light (say as the final reflected power), vs. a light bulb emitting 1 kilowatt of light, will spread the energy in a very different way. The mirror is directed - but the light from the bulb is dispersing in an expanding spherical way to get the inverse square relationship. Each "ray" hitting the surface of the mirror is already basically parallel to the other rays due to the distance of the sun, so a, say, 1 square meter flat mirror will project sunlight in a roughly parallel way.

At say 100 meters away, the kilowatt light bulb would be projecting that kilowatt basically evenly over the surface of a sphere of radius 100 meters, or dispersed over about 125,664 square meters - but 100 meters away, the rectangle of light projected by the mirror wouldn't be much larger than 1 square meter. (Would it?) Which is far more highly concentrated.

Or am I missing something? :)

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Reminds me of one of my favorite movies, Real Genius :)

Yes, that movie (among other things) really inspired me to go into physics.

Actually I have heard of the development, by the U.S. Air Force, of very powerful chemically powered lasers designed to be carried onboard a jet with a computer controlled mirror/targeting system, but I think the goal there is to shoot down enemy missiles or planes.

Like this? :)

Another neat idea:

"ADVANCED TACTICAL LASER (ATL) AND RELAY MIRRORS (ARMS)

In the high-energy laser market, Boeing’s Laser and Electro Optical Systems (L&EOS) is under contract to build a prototype ATL to target precise ground targets from the air. The ongoing ATL advanced concept technology demonstration program will provide a transition to a deployable ultra-precision strike capability. L&EOS also has started studies and is working with the government to demonstrate an Advanced Relay Mirror System (ARMS) concept by 2006.

As envisioned, ARMS would offer a range extension to a variety of high-energy laser platforms. One proposed deployment scheme would entail a “constellation” of as many as two dozen orbiting mirrors that would allow 24/7 coverage of every corner of the globe. When activated, the constellation would enable a directed energy response to critical trouble spots anywhere."

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But wouldn't the reflected light from a flat mirror...
Aren't you assuming that the mirror Archimedes used was flat? Whereas both in descriptions of his device, and in the modern re-enactments, a curved reflective surface was used. Even if the individual 'component' surfaces were flat in some instances, the composite superstructure was curved.

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But wouldn't the reflected light from a flat mirror, not disperse by inverse square as does a single, simple point light source?

...

Or am I missing something? :)

To maximize the concentration of light on the target, you'd want to shape the mirror such that its focus was on the target. For example, if your light source was "at infinity" (i.e., the incoming light rays are parallel) and your target was a kilometer away, the radius of curvature should be R = f/2 = 500m for a spherical mirror. (While a parabolic mirror would actually be better, I think the manufacturing process back then would have been prohibitive.)

This would be fine if the sun is low in the sky and in roughly the same direction as the target, so that the angle between the sun and target was small. But as the angle increases (e.g., the sun rises or the ship moves across the horizon), the mirror has to tilt to keep the light on the ship. In addition, optical aberrations known as "coma" and "astigmatism" would gradually increase the size of the focus, so that the smallest possible spot of light you can make with the mirror becomes asymmetric and larger. As the size of the spot increases, the power in the spot drops as the inverse square of the circle's radius.

One way to mitigate this (though I can't believe it would have been done way back then) would be to use flat relay mirrors to reflect the sun's light on to the curved mirror. This would require picking up and moving at least one flat mirror to continually re-align the optical system. If it doesn't take too long to set the ship afire, though, you could set up the system to where the ship will be and just wait for the ship to cross that point.

Another way would be to use an elliptical mirror with a different light source (say a burning torch or, these days, a laser) at the near focus and set the far focus to be the target's location. But this, too, would have been difficult to manufacture.

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To maximize the concentration of light on the target, you'd want to shape the mirror such that its focus was on the target.  <snip>

No, flat mirrors alone are sufficient. If you keep piling on multiple suns in the same spot, it *will* get hot enough. In fact some fellow has done just this:

http://www.solardeathray.com/

He glued 112 flat mirrors on to a flat board, angled to converge on a focus point. It's certainly enough to burn up quite a few things with a net power of 112 suns (minus losses due to imperfect reflection.) You need not focus *each* mirror to a tiny point - the "active" area around the focus should be roughly the size of the individual mirrors.

He has a FAQ here, where he mentions the Mythbusters episode on Discovery channel that (I think) Bill Bucko brought up:

http://www.solardeathray.com/FAQ.html

I don't think he's right in his explanation though. A central point, for me, is that a human being acting as an individual dynamic controller of the mirror is acting, in effect, as a very powerful aiming system, in computational terms. I seriously doubt that the ancients would have attempted an elaborate mechanical system.

Also, there is no particular reason why the mirrors have to be spread out in a 2D arrangement. I think 200 men lined up alone a coastline (or standing on the wall of a fortification), in an essentially 1D arrangement, each dynamically aiming the sun from their mirrors onto a common spot, would achieve essentially the same results: 200 suns worth of power (minus reflective imperfections) at the common spot, or focus, with a focal spot roughly the size of the individual mirrors.

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Here, MIT guys have also replicated the feat, on a smaller scale:

http://web.mit.edu/2.009/www/lectures/10_A...edesResult.html

Pretty small (flat) mirrors too. I would guesstimate that 1 large polished flat shield = 16 of their mirrors, so a small army of men trained and practiced under a central commander to dynamically focus on a given spot should do even better. Even with some unsteadiness, hundreds of large polished shields reflecting to about the same place would create some serious heat.

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