Experiments Using the Sun


Finding true north by methods other than a shadow at meridian crossing, or the crude wrist watch method.



 I made this cardboard equatorial ring sundial in 1988. It can be used to find north for latitude 42-29N
 once the adjustable ring is rotated to account for longitude, standard or daylight savings time, and the
 equation of time for the given day. With these set, rotate the whole until the shadow indicates clock
 time. The gnomon will lie in a north-south plane, with the ring end of it to the north. The compass
 shows that magnetic north at my location lies ~14 degrees west of geographic north.
 


 This is a Bumstead-like model that lacks a clock mechanism and uses angle measure rather than
 a 24-hour clock face. As in the Bumstead device, the rotational axis of the shadow casting pin and
 target is parallel to the earth's axis.




 Two things here.  The vertical shadow caster at the left indicates geographic north when one can
 calculate the solar azimuth for a given location and time. When it's rotated so the shadow falls on that
 azimuth, a line through 180-360 degrees is north-south, with geographic north at the 180-degree end.

 The other construction is essentially an Astro Compass MK II in cardboard disguise. It's made for
 latitude 42-29N. To use it, as in the real thing, one needs to input the declination and local hour angle
 of the celestial body to be viewed, in  this case the sun. To find geographic north once the inputs are
 made, rotate the base until the shadow of the declination pin falls in the proper place on the white target.

 (I eventually used this model, along with the realization that azimuth is measured in the horizontal plane,
 to derive an equation for azimuth by projecting the declination sight line onto a horizontal surface.
 Specifically:

 Azimuth (Zn in celestial navigation), degrees = 180 - atan [ (sin t / (sin L cos t - tan d cos L)]

 where t is the meridian angle, d is declination, and L is latitude. The atan expression differs slightly
 from that in text books because I used meridian angle--not local hour angle, LHA,-- and because I
 chose t to be positive for a body east of the local meridian.

 The common expression is atan [ sin LHA / (tan d cos L - sin L cos LHA) ]  .)
 


This is the CD sextant incarnation as of 3 March 17. Four thicknesses of neutral gray plastic glued together
 form the index shade. A piece of the same material paper-clipped to the sight vane forms the horizon
 shade. The index mirror is taped off so that it and the horizon mirror approximate the sizes given in
 antique USN specs for octants and high grade and surveying sextants. The sliver of white plastic
 inserted between the red and gray blocks supporting the horizon mirror eliminates side error.



 Different view, 3 March 17.




 3 March 17. A bris 'sextant' using three microscope slides separated by lengths of 1/4-inch diameter
 dowels. The sun shade is one layer of very dark 35 mm film. It gives a series of vertically offset
 reflections of the sun, as desired, but they appear in triplets.


 The 'back' side of the bris device. As in the CD sextant above, things are stuck together with
 double sided cellophane tape and painter's tape.


 



 This emergency navigation device, though called a bubble sextant, appears to be a 'bubble astrolabe'.
 On one side is a pair of folding sight vanes (shown folded in this photo). The other side has a folding
 mirror and a bubble level. Since the instruction booklet cover indicates it tells how to use this device to
 find latitude and longitude, this was intended to measure measure vertical angles, though it could also
 be used for horizontal angle measurement.
 





 Here are two nice images of the Pocket Bubble (or Bubble Circle) Sextant, that because of their having been
 photographed square-on, don't reveal as much as they might have. I've aligned the front (left) and back views
 as I think they'd be, using the rivet pair that attaches the bubble unit as a reference.
 
 I think the folded sight vanes in the previous image reveal how this could have been used without eye protection
 for sun sights. It appears that with the sight vanes up, a hole in one vane allows a sun spot to shine on the other.
 For other than sun sights, a notch in one vane is aligned with a projection on the other (used like open sights on
 a rifle).

13 March 17

Late in the afternoon, with a two-day snowstorm imminent, I raced to construct something akin to the Pocket Bubble
Sextant above, and try it before the sun disappeared. (I thought of doing it a week ago when I found and figured out
what was going on with that thing, but at that time there was no urgent motivation to get on with it.)

Here's what I managed in 20 minutes:



There's a bubble level taped to the back side of the protractor. Sunlight passing through a hole in the
rotatable piece projects a circle of light at the opposite end. With few options of positioning myself by
a window with a view of the sun, I managed a measurement at 1640 EDST (even with the nail
interposed between the hole and the target.) The pointer indicated an elevation of 23 degrees.

Back in the 1990's I wrote a Basic program to calculate sun data. I hurriedly ran it for today's date and
time frame of interest. This is a screen shot of the output:


The program output indicates the solar altitude at 2040 UTC (1640 EDST) to be 23.4 degrees. It may
well be a fluke that the measured angle was within a half degree of that.




 Solar menagerie at day's end. The pseudo-Bumstead sun compass shown in an earlier photo has
 been stripped and made into a model of the pseudo-astro compass for a meridian angle, t,
 of +30 degrees and declination of +23.5 degrees. The CD sextant index shade support (shown
 disconnected) has been made into an all-Lego structure since the 3 Mar 17 photo was taken.
 
To be continued when the sun returns.

15 March 17



Modified the 13 March version by moving the bubble level to the left and changing the pivot construction.





Later in the day, mounted the device to a small tripod that allowed clamping the protractor in place
once leveled. Contrast makes it difficult to see, but there's a sun spot centered at the intersection of
the horizontal and vertical lines at the left end of the alidade.



16 March 17




Taped a printed protractor to a clip board and used the corner of a Lego block to a cast a shadow.
The solar altitude (if the whole is leveled) is indicated by the intersection of the upper edge of the
shadow with the scale. Because of the way the protractor is layed out the scale value has to be
subtracted from 90 degrees (giving ~30 degrees in the photo). In the foreground the tripod structure is
not leveled and the sun spot is not quite at the intersection of the horizontal and vertical lines.





Later in the day, removed the bubble level from the protractor and taped it to the clip board protractor
sheet.



17 March 17




Took the printed protractor off the clip board and stuck it to a piece of tempered hardboard.
Mounted a circular bubble level to the board with a bolt so that it the level could be adjusted by
rotation.



18 March 17




Trying a method of using the CD sextant for making sun sights without looking at the sun. Punched a
hole in a piece of card stock and clipped it to the index mirror. Taped the bubble level to the bottom
edge of the sextant. The idea was to level the sextant using the bubble level and rotate the index disc
until the sunspot reflected from the index and horizon mirrors was centered over the back side of the
sight vane hole. (I took this photo with the camera in my left hand while trying to position things with
my right. As a result the sextant is not leveled and the spot is not centered over the sight vane hole.)



19 March 17

Did experiments with shadows from a notched gnomon 8 cm high cast on a horizontal (well, 'leveled' in
an attempt at making it horizontal) board with a 30 cm ruler taped to it. For this arrangement, the
observed altitude is the arctangent of 8 divided by the shadow length. (I'd pre-computed altitudes for
each 2 mm increment of shadow length and taped a printout of the results to the board, so that one
only needed to note the time when the shadow was at one of the calculated distances.)

This would be a great no-mirrors, no moving parts, no-looking-at-the-sun method of sun sights if shadows
were sharply delineated. Unfortunately, they are not. In addition, like every method that uses a spirit level
for a horizontal reference, the level's accuracy, and whether the bubble is truly centered, impacts the results.



 Experiments using Solar Shadows or Bright Spots to Measure the Sun's Altitude




 30 March and 2 April - Vertical member with rectangular slit 0.6" W x 0.1"H. Bottom of the slit is 8"
 above the top of the horizontal member.

30 March

  Number of measurements: 12
  Time: 1230 - 1350 UT
  Solar altitude range: 19-34 deg.
  Mean altitude error: 1.2'
  Mean absolute deviation from the mean (MAD): 4.4'
 

 Waiting for the sun to reappear.

2 April

  Number of measurements: 15
  Time: 1319 - 1425 UT
  Solar altitude range: 29-40 deg.
  Mean altitude error: -1.1'
  MAD: 4.8'
 



 3 April - replaced the slit on the vertical member with a metal shadow vane.

 Took three measurements outside, attempting to do them hand-held. A torpedo level and a watch were
 taped to the top of the horizontal member. Time window: 2039-2105 UT. First measurement was hand-held
 and was 3.9' too high. For  the second and third measurements, I attempted to steady the whole by
 supporting one end of the horizontal arm on a stake driven into the ground. Those two measurements
 were 6.0' and 10.8' too high. Mean error for the three measurements: 6.9', with MAD of 2.6'.



 9 April AM


  Number of measurements: 15
  Time: 1255 - 1407 UT
  Solar altitude range: 27-40 deg.
  Mean altitude error: -8.7'
  MAD: 3.8'
 



 
 9 April PM

  Number of measurements: 10
  Time: 1754 - 1955 UT
  Solar altitude range: 38-53 deg.
  Mean altitude error: 0.6'
  MAD: 20.6'
  




 11 April AM


  Number of measurements: 14
  Time: 1310 - 1410 UT
  Solar altitude range: 30-41 deg.
  Mean altitude error: -25.1'
  MAD: 14.3'
 



 11 April PM

 Began leveling before each measurement, and with the 'Craftsman' end of the level toward the sun each time.
 
  Number of measurements: 5
  Time: 1951 - 2012 UT
  Solar altitude range: 35-39 deg.
  Mean altitude error: 4.2'
  MAD: 2.3'
 



 14 April AM


  Number of measurements: 7
  Time: 1220 - 1256 UT
  Solar altitude range: 22-29 deg.
  Mean altitude error: -22.8'
  MAD: 1.8'
 

 14 April PM


  Number of measurements: 3
  Time: 1959 - 2010 UT
  Solar altitude range: 35-38 deg.
  Mean altitude error: -23.8'
  MAD: 1.9'
 
 Added a shim (5/64" drill bit--this is shown in the photo above) to tilt the whole ~22.7' in an attempt to
 counter the large negative error noted in the previous 10 measurements.

  Number of measurements: 3
  Time: 2017 - 2029 UT
  Solar altitude range: 32-35 deg.
  Mean altitude error: -0.7'
  MAD: 1.9'


 The shim was effective in reducing the mean error to -0.7' for three measurements. Removed the shim
 and reversed the level, putting the 'Craftsman' end away from the sun for the following three measurements.

  Number of measurements: 3
  Time: 2100 - 2120 UT
  Solar altitude range: 25-28 deg.
  Mean altitude error: -7.8'
  MAD: 0.8'
 
 15 April AM
 
 As illustrated for 14 April AM, first leveled with the 'Craftsman' end of the level away from the sun.
 

  Number of measurements: 5
  Time: 1230 - 1252 UT
  Solar altitude range: 24-29 deg.
  Mean altitude error: -5.6'
  MAD: 1.2'
 

 Then leveled with the 'Craftsman' end of the level toward the sun.
 

  Number of measurements: 5
  Time: 1308 - 1330 UT
  Solar altitude range: 31-36 deg.
  Mean altitude error: -16.7'
  MAD: 2.4'
 
 The mean error is 11.1' more positive, and the absolute mean error is 11.1' less, when leveled with the
 'Craftsman' end of the level away from the sun.


 16 April AM

 Glued three pieces of wood together to carry the shadow target atop the horizontal arm of the square,
 instead of sliding along the 'level table'. The 'level table' has been inverted so that an upward bow that it
 had acquired (or that I finally noticed) has become a slight cupping.

 Leveled with 'Craftsman' end of level toward the sun.


  Number of measurements: 5
  Time: 1254 - 1317 UT
  Solar altitude range: 29-34 deg.
  Mean altitude error: -4.4'
  MAD: 4.2'
  

 Leveled with 'Craftsman' end of level away from the sun.

  Number of measurements: 5
  Time: 1328 - 1348 UT
  Solar altitude range: 35-39 deg.
  Mean altitude error: 15.9'
  MAD: 3.1'
 

 Mean error is 19.3' more positive, and the absolute mean error is 11.5' greater, when leveled with
 the 'Craftsman' end of the level away from the sun.


 
17 April PM




 18 April PM




23 April AM




23 April AM #2




24 April AM




27, 29 and 30 April AM



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