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.
Sent: Thursday, February 16, 2012 12:54 PM
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...
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Dave
-----Original Message-----
On Behalf Of ruben nohuitol
Hi friends, please look my cosmic room,
my page is www.ruben.mx
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