Patent Publication Number: US-8528218-B2

Title: Sundial

Description:
RELATED APPLICATIONS 
     This application is a continuation of application Ser. No. 13/347,456, filed Jan. 10, 2012 and now issued as U.S. Pat. No. 8,387,265, which is titled “Sundial” and which is a continuation of application Ser. No. 13/149,670, filed May 31, 2011 and now issued as U.S. Pat. No. 8,091,245, which is titled “Sundial” and which is a continuation of application Ser. No. 12/409,271, filed Mar. 23, 2009 and now issued as U.S. Pat. No. 7,950,159, which is titled “Sundial.” Each of the aforementioned applications and patents is incorporated herein by specific reference. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates to a sundial and, in some embodiments, to a sundial that uses a curved reflector to create a reflected image of the sun on a dial-face to indicate the time of day. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Understanding that drawings depict only certain preferred embodiments and are not therefore to be considered to be limiting in nature, the preferred embodiments will be described and explained with additional specificity and detail through the use of the accompanying drawings in which: 
         FIG. 1  is a cross-sectional view of one embodiment of a sundial according to the present disclosure. 
         FIG. 2  is a front elevation view of one embodiment of a sundial according to the present disclosure. 
         FIG. 3  is a plan view of one embodiment of a sundial according to the present disclosure. 
         FIG. 4A  and  FIG. 4B  are front elevation views of one embodiment of a sundial showing the location of a reflected image of the sun at two different times of day. 
         FIG. 5A  is a conceptual illustration of a pattern of reflection of a plane wave incident on a curved reflector. 
         FIG. 5B  is a conceptual illustration of the pattern of reflected rays from  FIG. 5A  along a focal line of a curved reflector. 
         FIG. 6  is a perspective view of an embodiment of a sundial that is configured to be self-orienting. 
         FIG. 7A  is a plan view of a radial gauge. 
         FIG. 7B  is a plan view of a radial gauge and a latitude marker. 
         FIG. 7C  is a plan view of a radial gauge and a latitude marker together with a magnet. 
     
    
    
     DETAILED DESCRIPTION 
     In the following description, numerous specific details are provided for a thorough understanding of specific preferred embodiments. However, those skilled in the art will recognize that the invention can be practiced without one or more of the specific details, or with other methods, components, materials, etc. 
     In some cases, well-known structures, materials, or operations are not shown or described in detail in order to avoid obscuring aspects of the preferred embodiments. Furthermore, the described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. 
     Disclosed are embodiments of a sundial. Various embodiments of the sundial disclosed herein may be used to determine the time of day based on the position of the sun. The sundial may utilize a curved reflector to reflect the image of the sun onto a dial-face. The curved reflector may be disposed, at least in part, behind (relative to a viewer of the sundial) the dial-face. A portion of the curved reflector may be used to reflect an image of the sun onto the back of the dial-face. Depending upon the material(s) used for the dial-face, the reflected image of the sun received on the back of the dial-face may be visible on the front of the dial-face (and/or the back of the dial-face). In some embodiments, the dial-face may be made up of one or more translucent materials, such as copper mesh, aerogel, silica gel, acrylic, glass, cloth, and/or other suitable materials. The dial-face may also have a plurality of time markings on one or both of its opposing surfaces. The position of the image of the sun on the front of the dial-face may, in some embodiments, be compared to the plurality of time markings to determine the time of day. The reflected image of the sun may exhibit optical aberration caused by the curved reflector and/or by the impact of seasonal variations in the Earth&#39;s orbit. In certain embodiments, the optical aberration may elongate the reflected image of the sun such that the reflected image may take the general appearance of a clock hand or the like. 
     In one embodiment, the curved reflector may comprise a transparent and partially-reflective sphere. The dial-face may be positioned within the sphere. In certain embodiments, the sphere may comprise acrylic or glass. In other embodiments, a latitude marker may be placed on the sphere, and may allow the sundial to be adjusted to operate at a given latitude by rotating the sphere, thereby reorienting the angle of the dial-face with respect to the angle of incidence of sunlight. 
     In embodiments not comprising a sphere, the dial-face may be reoriented in other ways, as those of ordinary skill in the art will appreciate. The latitude markings may be positioned along the sphere and may be aligned with a reference line at an appropriate marking corresponding to the user&#39;s latitude on Earth. 
     In some embodiments, a stand may be provided for the reflector or sphere. The stand may be a ring having a radius smaller than the radius of the sphere. Accordingly, the stand may hold the sphere with no fixed points of connection between the stand and the sphere, and may thus allow the sphere to be rotated with respect to the stand. 
     In certain embodiments, the sundial may include a directional indicator. When used in the Northern hemisphere, the directional indicator may be used to orient the sundial such that front side of the dial-face is oriented due north, while the back side of the dial-face is oriented toward the sun (or south). When used in the Southern hemisphere, the directional indicator may be used to orient the sundial such that the front side of the dial-face is oriented due south, while the back side of the dial-face is oriented toward the sun (or north). 
     In some embodiments, the directional indicator may include a line placed on the stand. To orient the sundial in such embodiments, the user would orient the directional line in a north-south direction. The latitude marker may then be oriented parallel to the directional line. A line perpendicular to the directional line may also be included to provide a reference for aligning the latitude markings with a user&#39;s particular latitude on Earth. 
     In certain embodiments, the sundial may be self-orienting. In one embodiment, one or more components of the sundial may be positioned within a reservoir of liquid. For example, in one embodiment, the curved reflector may float in a reservoir of water. An appropriately aligned bar magnet may be attached to the curved reflector. The magnet may, if increased accuracy is needed, be aligned with respect to the curved reflector so as to compensate for any disparity between true north and magnetic north at a particular location on Earth. In certain embodiments, a radial gauge may be used to align the magnet with respect to the curved reflector. Markings on the radial gauge may be used to offset the alignment of the magnet with respect to the curved reflector by an amount equal to the magnetic declination at the user&#39;s location. 
     More specific embodiments will now be described in greater detail with reference to the accompanying drawings. The following more detailed description of various embodiments, as represented in the accompanying drawings, is not intended to limit the scope of the present disclosure, but is merely representative of various embodiments. While various aspects of certain embodiments are presented in the drawings, the drawings are not necessarily drawn to scale. Reference numbers in the drawings are each greater than 100. Numbers in the drawings less than 100 illustrate features of various embodiments, including time markings using the numbers  5  through  12  (see  FIGS. 2 ,  4 A and  4 B), latitude markers using the numbers  0  through  90  (see  FIGS. 3 ,  7 B, and  7 C), and angle markers using the numbers  0  through  45  ( FIGS. 7A ,  7 B, and  7 C). 
       FIG. 1  is a cross-sectional view of an embodiment of a sundial  100  including a stand  106  and a curved reflector  102 . Stand  106  includes a base  108  and a support piece  109 . In some embodiments, base  108  may be a separate component from support piece  109 . Alternatively, base  108  may be integrally formed with support piece  109 . The sun  116  casts a ray of light  114  onto curved reflector  102 . Ray  114  is reflected by curved reflector  102  onto a back surface  105  of a dial-face  104 , creating a reflected image  118  of the sun. 
     As better illustrated in  FIGS. 4A and 4B , the position of reflected image  118  with respect to a plurality of time markers (reference no.  112  in  FIGS. 4A and 4B ) disposed on the front surface  103  of dial-face  104  indicates the time of day. As illustrated, reflected image  118  is reflected onto the back surface  105  of dial-face  104 . In embodiments where the face is at least partially transparent, the reflected image  118  may be viewed on the two opposing surfaces  103 ,  105  of dial face  104 . In the depicted embodiment, dial-face  104  comprises a flat material in the shape of a semicircle that fits within half of a circumference of the reflector  102 . However, a variety of other embodiments are contemplated with dial-faces having other shapes. In some embodiments, dial-face  104  may comprise a material that would permit the reflected image  118 , which is reflected onto the back surface of dial-face  104 , to be visible on the front surface  103  of dial-face  104 . In one embodiment, dial-face  104  comprises a copper mesh. In another embodiment, dial-face  104  comprises aerogel. In yet other embodiments, dial-face  104  may comprise a plastic mesh, cloth, glass, or acrylic. 
     In  FIG. 1 , curved reflector  102  is a sphere. It is contemplated that in alternative embodiments curved reflector  102  may be embodied as a portion of a sphere (e.g. a half sphere or a quarter sphere), a cylinder, or other curved geometry. The curved reflector  102  may be only partially reflective, and may also be partially transparent. In one embodiment, curved reflector  102  may be acrylic or glass. In such embodiments, curved reflector  102  may completely surround and hold dial-face  104 . In alternative embodiments, curved reflector  102  may have portions lined with a highly reflective material, so as to maximize the brightness of reflected image  118 , and to facilitate the reading of sun dial  100 . 
     Latitude marker  110  may be disposed on sphere  102  and may allow sundial  100  to be adjusted for use at a given latitude (e.g., the latitude of the location at which sundial  100  is to be used). A line  120  may be positioned directly below the center of curved reflector  102 . Line  120  may be connected to a base  108 . In some embodiments, line  120  may comprise a three-dimensional shape, such as a cylinder or rod. In other embodiments, line  120  may simply be two-dimensional, such as an acrylic transfer, a marking from a line or pen, or the like. 
     In one embodiment, sundial  100  may be adjusted to a given latitude by rotating curved reflector  102  until a line corresponding to a desired latitude of latitude marker  110  is positioned above line  120 . For purposes of illustration, a vertical reference line  126  and a horizontal reference line  124  are shown in  FIG. 1 . Horizontal reference line  124  and vertical reference line  126  bisect curved reflector  102 . An angle  122  is the angle between the dial-face and vertical reference line  126 . When positioned for a given latitude, angle  122  of the dial-face  104  with respect to vertical reference line  126  is equal to the given latitude. For example, if the latitude of a location at which sundial  100  is to be used is 30°, curved reflector  102  may be rotated such that angle  122  is equal to 30°. In certain embodiments, curved reflector  102  is able to be rotated within stand  106 , so as to allow for the adjustment of the latitude corresponding to the latitude of the location of the sundial  100 . In alternative embodiments, dial-face  104  may be pivotally connected with curved reflector  102 , and dial-face  104  may be pivoted such that angle  122  is equal to the user&#39;s latitude. In still further embodiments, latitude marker  110  may be positioned on stand  106 . 
       FIG. 2  is a front elevation view of sundial  100 . A plurality of time markings  112  are disposed on dial-face  104 . In one embodiment, base  108  includes a directional indicator  128  which is to be oriented north in the Northern Hemisphere when sundial  100  is in operation. In the Southern Hemisphere, indicator  128  would be oriented south. In the embodiment illustrated in  FIG. 2 , time markings  112  are spaced 15° apart, corresponding to the 360 degrees of rotation of the Earth in one day divided by 24 hours. Other spacings of time markings  112  are contemplated and depend on the geometry of dial-face  104  and the physical size of the sundial. For example, additional time markings may be added as the physical scale of the sun dial increases. A large sundial  100  may include time markings that correspond to every 30 minutes of a day (or less), while a small sun dial  100  may only include time markings that correspond to every hour of a day. 
     Further adjustments or refinements could be employed to compensate for a user&#39;s longitude, variations in the Earth&#39;s orbit compensated for using the equation of time, and daylight savings time. In other embodiments, a user may adjust for the variance in degrees of longitude of the user&#39;s location from the center of the user&#39;s time zone. For example Salt Lake City, Utah is approximately 7° of longitude west of Denver, Colo., which is approximately at the center of the Mountain Time Zone. The solar time indicated on the dial-face  104  of sundial  100  will be approximately 28 minutes behind standard time in Salt Lake City, Utah, unless an appropriate adjustment is made. In order to adjust sundial  100  to operate in Salt Lake City, Utah, directional indicator  128  may be rotated to the West by 7°. In an alternate method for adjusting sun dial  100 , a user may rotate face  104  such that directional indicator  128  aligns with the point on face  104  corresponding to 12:28 PM. Sun dial  100  may also be adjusted by rotating face  104  in order to compensate for seasonal variations in solar time caused by the obliquity of the Earth&#39;s rotational axis and the eccentricity of the Earth&#39;s orbit. For example, at the end of March, solar time is five minutes behind standard time. By rotating face  104  such that directional indicator  128  aligns with the point on face  104  corresponding to 12:05, the seasonal variation may be corrected. A table or chart listing adjustments between solar time and standard time at various times throughout the year may be included with sundial  100 . A user may refer to the table or chart in order to periodically adjust sundial  100 . Face  104  may also be rotated in a similar method to compensate for daylight savings time. 
       FIG. 3  is a plan view of sundial  100 . As discussed above, sundial  100  may be adjusted for a given latitude. In one embodiment, sundial  100  may be adjusted to a given latitude by rotating curved reflector  102  until a latitude marker  110  corresponding to a desired latitude is positioned above line  120 . Line  120  may be positioned on a stand (as shown in  FIG. 1 ), rather than the curved reflector  102 , while latitude marker  110  may be positioned on curved reflector  102 . Latitude marker  110  includes degree line markings in fifteen-degree increments. Of course, other increments are also contemplated. 
     Support piece  109  (shown in  FIGS. 1 and 2 ) of stand  106  may be circular, and comprise a ring having a radius that is smaller than the radius of curved reflector  102 . Curved reflector  102  may be placed on the support piece  109 , and may hold curved reflector  102  with no fixed points of connection between stand  106  and curved reflector  102 . Accordingly, curved reflector  102  may be rotated with respect to stand  106  to a desired latitude. 
     A directional line  121  (similar to reference no.  128  in  FIG. 2 ) may be placed on curved reflector  102  instead of, or in addition to, directional indicator  128 . To orient the sundial in such embodiments, directional line  121  would simply be oriented in a north-south direction. Latitude marker  110  may be generally oriented parallel to the directional line  121 . Line  120  may be perpendicular to directional line  121 . 
       FIGS. 4A and 4B  illustrate sun  116  in two different positions, and illustrate the corresponding positions of reflected image  118 . In  FIG. 4A , ray  114  is reflected by curved reflector  102  and creates reflected image  118  on dial-face  104 . Reflected image  118  is between time markers  112  corresponding to 7:00 AM and 8:00 AM, indicating that the time is approximately 7:30. In  FIG. 4B , reflected image  118  is between time markers  112  corresponding to 4:00 PM and 5:00 PM, indicating that the time is approximately 4:30. As sun  116  moves across the sky during the course of the day, reflected image  118  moves uniformly across dial-face  104  to provide an at least approximate indication of the time of day. 
     Reflected image  118  may be elongated, as shown in  FIGS. 4A and 4B , by optical aberration and/or the impact of seasonal variations in the Earth&#39;s orbit. In one embodiment, a spherical reflector is utilized, and thus reflected image  118  may exhibit spherical aberration. Spherical reflectors do not focus light to a point. Rather, spherical reflectors focus rays more tightly if they enter far from the optic axis than if they enter closer to the axis. The elongation of the reflected image  118  may be enhanced by the seasonal variation of the Earth&#39;s orbit around the sun, and the Earth&#39;s axial tilt of 23 degrees. In September and March, reflected image  118  may appear more elongated, while in June and December reflected image  118  may appear less elongated. 
       FIG. 5A  is a conceptual illustration of the pattern of reflection of a plane wave  130  incident on a cross section of a spherical reflector  132 . Plane wave  130  is comprised of a plurality of individual rays of light, the paths of which are traced after reflecting off of spherical reflector  132 . Incoming rays are shown using dashed lines, while reflected rays are shown using solid lines. The rays in plane wave  130  are not focused to a single point, but rather form a caustic. The rays are focused along a focal line, leading to an elongated reflected image.  FIG. 5B  is a close-up view of the pattern of reflected rays from  FIG. 5A  at the location indicated generally at  136 . The convergence of the plurality of individual rays may form elongated reflected image, as also illustrated on dial-face  104  in  FIGS. 4A and 4B . As illustrated in  FIG. 5B , the plurality of rays  134  may appear to be an elongated pattern, as illustrated generally at location  136 . 
     As illustrated in  FIGS. 4A and 4B , reflected image  118  is not circular. Rather, reflected image  118  is elongated by optical aberration from curved reflector  102  and/or the impact of seasonal variations in the Earth&#39;s orbit. The elongated reflected image  118  may allow a user to more precisely determine the time by providing an elongated reflection that may generally appear as a clock hand. 
       FIG. 6  illustrates one embodiment of a self-orienting sundial  100 . A sphere  102  containing a dial-face  104  may float in a reservoir  140  containing water  142 , or other suitable liquid. A magnet  144  may be attached to sphere  102 . The magnetic field of the Earth causes magnet  144  to point toward magnetic north. Magnet  144  may be aligned with respect to sphere  102  so as to compensate for any disparity between true north and magnetic north at a particular location on Earth. 
       FIGS. 7A ,  7 B, and  7 C illustrate one method for aligning magnet  144  such that sphere  102  orients to north in operation.  FIG. 7A  illustrates a radial gauge  150 . A plurality of radial markings  152  are disposed on radial gauge  150 . Radial gauge  150  may include a hole  154  disposed in the center. In most locations on Earth, the true north and the magnetic north (to which a magnet will point) are not collocated. Accordingly, the plurality of radial markings  152  on radial gage  150  may be used to adjust an angle of the magnet with respect to the sphere by an amount equal to the magnetic declination at a user&#39;s location. Information about the magnetic declination at a particular point on the globe is available from a variety of sources, including the U.S. Geological Survey, National Geomagnetism Program, Reston, Va., also available at http://geomag.usgs.gov/charts/ (last accessed Feb. 10, 2009). 
       FIGS. 7B and 7C  illustrate how radial gauge  150  may be used in conjunction with latitude marker  110  in order to adjust sundial  100  to operate at a particular latitude and a particular magnetic declination. The latitude marker  110  may be attached to sphere  102 . Radial gauge  150  has been positioned with respect to latitude marker  110  such that the latitude marker corresponding to 40° is within hole  154 . In  FIG. 7C , magnet  144  is attached along the radial gauge line labeled 15°. Accordingly, sundial  100  has been configured for use at a latitude of 40°, and a magnetic declination of 15°. In an embodiment having a transparent curved reflector, radial gauge  150  and latitude marker  110  may be configured to be viewed through the transparent curved reflector (i.e. they may be mirrored in comparison to  FIGS. 7A ,  7 B, and  7 C). 
     In operation, the weight of magnet  144  positions the dial-face  104  to receive light reflected from the sphere  102  at the user&#39;s latitude. When floating in liquid  142  in reservoir  140 , magnet  144  aligns with the magnetic field of the Earth. The adjustment of the angle of magnet  144  with respect to sphere  102  using radial gauge  150  causes dial-face  104  of sundial  100  to be oriented toward true north. 
     In an alternative embodiment, the radial gauge  150  may be embossed on, or otherwise attached to, a housing (not shown) configured to receive, hold, or connect to magnet  144 . In such an embodiment, the housing containing magnet  144  may be placed over a particular latitude, rotated until radial markings  152  on the housing equal to the magnetic declination at the user&#39;s location align with the North/South axis on the sphere  102 , then attached to the sphere. 
     The above description fully discloses preferred embodiments of a sundial. Without further elaboration, it is believed that one skilled in the art can use the preceding description to utilize the invention to its fullest extent. Therefore the examples and embodiments disclosed herein are to be construed as merely illustrative and not a limitation of the scope of the present invention in any way. 
     It will be obvious to those having skill in the art that many changes may be made to the details of the above-described embodiments without departing from the underlying principles of the invention. The scope of the present invention should, therefore, be determined only by the following claims.