12 minute tutorial and challenge
How to Aim Your Death Ray:
Assuming you plan on building your own Death Ray, how do you target the device using only the aiming mirror? As explained in the video, the mirror is oriented in three dimensions. Normally, people are familiar with the three Cartesian dimensions, like "X, Y and Z" or "1250 Ave of the Americas, 6th floor, NYC". In the case of the Stealth Archimedes Death Ray, the dimensions are "pan, forward tilt and horizontal tilt". These three angular motions are related to the Euler coordinate system-- the bane of physics students everywhere, and somewhat difficult to visualize. But, in this particular case, a simple method emerges:
All the soldiers agree to align their virtual image of the sun (as viewed through the small aiming mirror) to a pre-arranged target just above the section of the boat you plan on engulfing in flames. Say the horizontal spar's intersection with the main mast. Rotate the PAN axis until the virtual image is in a vertical line below the target. Then adjust the HORIZONTAL TILT controls to bring the virtual image directly atop the target intersection. Finally, swing the FORWARD TILT up while observing the gnomon's shadow on the arm holding the aiming mirror. When the gnomon's shadow is parallel to the bottom of the aiming mirror, the death ray mirror's reflection will lay just below the target intersection.
Since the sun (and perhaps the target) move with time, the aiming mirror must be adjusted dynamically during the attack. Assuming the boat can only move horizontally, the PAN direction is most important.
A few practical concerns. Make sure all three axis are mutually perpendicular and move smoothly and precisely. The aiming mirror will reflect bright sunlight, which is painful and possibly dangerous to observe for more than a few seconds. So it is important to dull the mirror's surface while still retaining its specular nature. A torch and a bit of oil will darken the surface of the brass mirror, or a dark matte translucent stain can be applied to the glass.
The BEST approach is not as intuitive, but more effective and easier to construct. In this case, the observer moves to the OPPOSITE side of the aiming "mirror", and views a VIRTUAL image of the boat against a dim image of the sun. In this case, the aiming mirror is a dark glass filter:
|For safety, the viewer looks through a dark glass filter. For example, a welding glass. Less than 0.01% of the sunlight makes it through the filter, but this is still bright enough to clearly locate the ACTUAL image of the sun through the glass
||Glass, even dark glass, still reflects around 4% of the incident light. So the welding filter acts like a two-way mirror, and a weak VIRTUAL image of the boat appears aligned to the actual image of the sun.
Experts recommend a welding filter with a shade number of #12 (0.002% visible light transmission) to view solar eclipses, though I use a #10 (0.01% transmission) for brief periods. Other alternatives, such as a stack of CDs, or two-way mirrors, can be effective with the advantage of a brighter virtual image, but when in doubt, choose the welding filter.
The apparatus is also simplified. Instead of a rigid gnomon that can bend or kink, I use an elastic cord stretched over the aiming mirror arm. The welding filter is set into a tight dado, and after the rig is assembled, a marker line is drawn on the mirror arm to indicate the perpendicular shadow position for the gnomon
Note this principle is related to the "signaling mirror" (ESM/1 and ESM/2) concept developed during WWII to help soldiers communicate across long distances, or to attract attention during search and rescue operations. But our stealth death ray mechanism is much easier to orient and precisely align than simply pointing a very large signaling mirror at a Roman ship, while simultaneously trying to peer through a narrow cross.
A wonderful contemporary instructional video from WWII for the ESM can be found here, and even today you can still buy signaling mirrors for hiking that employ similar principles. I expect, given the number of people (including myself) who independently discovered the concept of a partial reflection to orient a virtual image, that the same approach was known by the ancient Greeks.