Hi Tom, Thanks for your ‘inside small sundial’ information, and for the mirror links. It’s a great idea.
I’ve found an Australian convex mirror manufacturer and have requested prices. It will be fun trying to project the beam across the room onto the far wall. Good luck with your NASS article and thanks, Roderick Wall. From: Tom Egan Sent: Thursday, February 16, 2012 5:02 PM To: R Wall ML emails ; sundial mailing list Subject: Re: A compact indoor sundial using a convex mirror on the north sideof the roof Good question. I found that a "hemispherical" (I put it in quotes because the mirror I use actually has an essentially ellipsoidal cross-section about the axis of rotation) mirror was needed to observe the entire day's travel of the sun in midsummer. There's an additional complexity: the axis must be tilted down in the amount of the site's latitude -- aligning it with the earth's spin axis -- if early a.m. and late p.m. solar az/els are to be observed. If I could have acquired a 4 pi steradian "ball" (btw, i used the word "ball" simply as shorthand for "half spheroidal mirror etc. etc.") I wouldn't have had to worry about this. But it's an easy fix to just tilt the mirror's axis. I bought a 26 inch ball from TechnologyLK http://www.technologylk.com/__74/acrylic-dome-mirrors.html It is the acrylic 360 deg. full dome detection mirror with galvanized backing. It is weatherproof. I first tried a 10 inch Victorian gazing ball from the garden, but it couldn't reflect a bright enough beam. I needed a weatherproof plane mirror, too. I found "Super #8 Nondirectional SS" a highly polished corrosion resistant stainless steel from Mirrored Stainless Solutions http://www.mirroredstainlesssolutions.com/ . The have available for nominal price a 10 x 10 inch (or larger) sample. This was large enough for my project. Enjoy! On 2/15/2012 9:17 PM, R Wall ML emails wrote: Hi Tom, Your indoor sundial is a great idea. I’m now searching the internet for convex mirrors. I note that you have used a convex ball mirror, I guess that’s needed to cover 6am to 6pm? I’ve always wondered how to do that. Thanks for a great idea, Roderick Wall. From: Tom Egan Sent: Thursday, February 16, 2012 12:54 PM To: sundial mailing list Subject: A compact indoor sundial using a convex mirror on the north sideof the roof Dave Bell, in his 2/12/2012 response (appended) to Ruben's invitation to us to view his cosmic room, discusses ways to use flat mirrors -- one being effectively a reflective pinhole aperture -- to obtain a noon line throughout the year in a living room that is well north of the equator (at 37.3 deg.). I've developed an indoor sundial that uses a large convex mirror to capture the sun's position throughout the day and year. It allows a compact dial face, if desired, that can fit on a table-top. (For development purposes, I'm using a target the size of a piece of letter paper.) I presented a slide show on it at the 2011 NASS annual conference in Seattle WA. I'll summarize the description from an article that's in preparation: A sundial system based on a three-dimensional convex mirror can overcome many of the limitations of a plane mirror. The convexity provides a wide field of view, reducing the apparent arc of the sun’s travel throughout the day and year to no more than the width of the mirror. This, in turn, permits the dial face to be compact enough to fit on a table-top. A convex mirror, while creating a compact view of the world, is a virtual view. That is, additional components are required to turn the sun’s disk into a real image of a sun spot. This is accomplished by incorporating a pinhole “camera obscura” that projects the sun’s image onto the dial face, as for example, a piece of paper with drawn hour lines and seasonal markings. When the convex mirror is mounted above a window on any side of the building – even the north side – and above the roof line, the system can deliver the sun spot to the dial face inside the building. Being above the roof line provides the mirror with a view of the sun’s travels that is least shadowed by nearby structures and vegetation. Two flat mirrors at 45 degree angles are used to change the path of light that is reflected from the convex mirror from vertical to horizontal -- allowing perpendicular entry into the building through a window to avoid distortion -- and then again re-orienting the beam to vertical to allow a convenient and easy-to-read horizontal dial face. Figure 1 (attached) illustrates the concept. The photo shows a side view of the gazebo I'm using to develop the system. The convex mirror reflects the sunlight down to a flat mirror tilted approximately 45 degrees just outside the window. This flat mirror turns the sun beam from vertical to horizontal so it can penetrate the window glass. On the inside of the window, a mask with pinhole is affixed, creating the camera obscura effect. The brightest object in the obscura image is the sun, which casts a bright spot onto the dial face after being verticalized by another 45 deg. flat mirror. This bright image of the sun indicates both time of day and season of the year, since it acts as a nodus. To lay out the hour and month lines on the dial face, I developed a math model of the system using vector notation. The smooth mirror is conceptualized as a large disco ball covered in infinitesimally small flat mirrors. This permits the use of simple relations suitable for plane mirrors. The equations turned out to be implicit ones, so I used the Solver feature of the Excel spreadsheet to perform a global step search to converge to a solution. Bob Kellogg subsequently devised an elegant least squares optimizer programmed in DeltaCad to solve the implicit equations. We're in the process of documenting this for the NASS Compendium. On 2/12/2012 5:42 PM, Dave Bell wrote: Beautiful rooms and concepts, Ruben! A wonderful teaching facility. Your low latitude is certainly a help in fitting these dial displays to an interior. After viewing your pages, I once again looked at my living room with an eye towards a noon line, as I have a roof window well situated near the South wall, but due to its height (just over 10 feet) and my latitude (37.3°), the resulting analemma doesn't fit the living room at all. It's too far from the South wall in Summer, and extends well past the open floor space in Winter. However, it did get me to thinking again, and doing some calculations. If I designed the line for a more southern location, say 9° North, the total length of the analemma was much shorter, and the Summer end would extend South of the ceiling hole, quite close to my South wall. Moving my home 28° to the South isn't very practical, but it occurred to me that I could introduce a deviation in the incoming rays, and accomplish the same result! I thought of a prism, but the geometry isn't very good; finding the right prism (apex angle and refractive index) would be difficult and/or expensive, and I would have to deal with chromatic dispersion, as well. But a pair of mirrors, even first-surface mirrors, is much easier. If the first mirror (to the north of center) was blacked-out, with a small, "pinhole" reflective aperture, inclined vertically or slightly to the North, its reflected beam could fall on the second, larger, flat a few inches to the south, inclined 14° more to the north. The 14° apex angle of the pair would introduce a 28° deviation towards the south, independent of the exact inclination of the pair. (They would have to be accurately aligned East-West, of course.) Any inaccuracies in mirror angles and orientation would be hard to allow for in plotting the Noon analemma, but I could always fall back on the ancient empirical method of driving a tack at 12:00 local solar time, once a week! Something a little like the ASCII sketch below. Assume the light enters from above and to the right... | | \ | \ \ \ Dave -----Original Message----- On Behalf Of ruben nohuitol Hi friends, please look my cosmic room, my page is www.ruben.mx --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial ------------------------------------------------------------------------------ --------------------------------------------------- ------------------------------------------------------------------------------ No virus found in this message. Checked by AVG - www.avg.com Version: 2012.0.1913 / Virus Database: 2112/4812 - Release Date: 02/15/12 ----- No virus found in this message. Checked by AVG - www.avg.com Version: 2012.0.1913 / Virus Database: 2112/4813 - Release Date: 02/16/12
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