Post on 25-Nov-2021
Surveying by the Stars, Part II: Solar Observation (Hour-Angle Method) and
Polaris Observation
Please obtain written permission from author/compiler Wayne Twigg, (copyright 2017 A.D.) before using for educational and instructional exercises.
We Surveyors today record our measurements to [a supposed] accuracy
of one second of arc.
Facts: Earth’s radius = 3,961± miles. At this place on the Earth’s surface, 1 second of
Latitude = 101’±;1 second of Longitude = 78’±
In fact, one second of arc subtends
the width of a human hair at……..
“He must be blind who does not at once see, from the best and wisest structure of things, the infinite wisdom and goodness of their almighty Creator; and he must be mad who refuses to acknowledge them.”
….preface to the 2nd Edition of Sir Isaac Newton’s The Principia by Roger Cotes, Plumian Professor of Astronomy, Cambridge, England, 12 May 1713
Radio Station WWV broadcasts UTC time scale (Coordinated Universal Time).
Available over shortwave radio at 2.5, 5, 10, 15 and 20 MHz.
WWV telephone (303)499-7111. There is a time announcement delay of less than 30 ms (“land line”) and up to 150 ms (cell phone).
To convert to UT1 (Survey Time), apply DUT correction in 0.1 seconds, which is encoded in the voice announcement as the number of double-ticks during the first 16 seconds of each minute; positive sign in seconds 1 – 8; negative sign in seconds 9 – 16.
The Equator is
perpendicular to the
Poles.
The Horizon is
perpendicular to the
Observer’s Zenith.
Complementary
angles: Latitude
and Co-Latitude;
Altitude and Zenith;
Declination and
Polar Distance.
Angle Z is the
angle west (or east)
from the N. Pole.
By definition, all
meridians pass
through both Poles.
The “t” (a.k.a.
meridian) angle is
formed at the Pole.
If LHA is < 180°
(as shown), then “t”
and LHA are =.
In other words,
Local Hour Angle (t)
= Greenwich Hour
Angle – West
Longitude.
Here is a star chart to help locate the Sun in the sky.
(Only teasing! Every-one can find the Sun).
Accuracy to 5 seconds of arc
Minimum of 3 observations (but you can easily get 5)
Needs both Latitude and Longitude
Must be timed using Precise Time, such as tuning to Station WWV with a shortwave radio.
Does not need Vertical or Co-Vertical (a.k.a. Zenith) Angles
Instrument leveling must be very precise; use a striding level if you can get one.
Use Hour Angle Method when observing (1) between ½ hour after sunrise and 9:00 a.m. Local Standard Time, and (2) between 3:00 p.m. and ½ hour before sunset Local Standard Time. The closer it is to noontime, the faster the Sun moves and the steeper it is in the sky. Then you can’t see it through your scope anyway without a right angle eyepiece.
Accuracy of time is critical.
Here is a recommended D&R sequence for sighting the Sun.
The Surveyor acquires the Sun’s image on a white card. He focuses both image and cross-hairs.
He puts Sun’s image on the proper side of the vertical cross-hair (as shown). The instant the Sun “leads” onto the vertical hair’s point-of-tangency, he hits “lap” button.
½ hour after sunrise to 9:00 a.m.; 3:00 p.m. to ½ hour before sunset
DIRECT
REVERSE
Let’s practice with the
stopwatch.
✓ Contact Station WWV by shortwave radio or cell phone (303)499-7111, but remember that switching
may cause delay of 150 msec. Start stopwatch at exact minute (may need more than one call).
✓ Two-man crew: Instrumentman/Observer sets up instrument and acquires backsight Direct on Zero;
then he turns to the sun, gets the white card ready and notifies Notekeeper when he has acquired the
sun’s image and is ready to start readings.
✓ Notekeeper writes start time as hour and exact minute. He will record “lap” time for each observation.
At end, he checks stopwatch against WWV and notes DUT as well as synchronous correction, if any.
✓ During the observation session, the Observer calls “Rea-a-a-a-d-y-y-y” “TICK” when sun’s image
becomes tangent to the vertical crosshair. He reads the horizontal angle aloud to the Notekeeper.
✓ Immediately at “TICK”, the Notekeeper hits “lap” button and afterward writes the minutes, seconds and
tenths of seconds. Subsequently he records the horizontal angle as he heard it from the Observer.
✓ Observer re-acquires sun’s image and again calls “TICK” at tangency. At “TICK”, the Notekeeper hits
“lap” button, records minutes, seconds and tenths of seconds; he hits “lap” button again to continue
stopwatch and again records the horizontal angle as he heard it from the Observer.
✓ Repeat for eight more observations (or at least, sufficient for three complete D&R sets).
✓ Notekeeper stops stopwatch at moment of final observation and records last set of minutes and
seconds. He then notes the daily hourly time and makes sure that the subtraction of his start time and his
ending time equals the duration of the session’s set of minutes and seconds. Observer makes a Reverse
backsight check.
Field Notes: Hour-Angle Sunshot
This Observer has made 3 D-R sets on the sun. He also noted the DUT correction as well as a stopwatch correction.
Back in the office, both corrections are applied and the angle sets averaged. Note the Lat/Long of the observation station, also the magnetic bearing to the backsight.
This poor
survey schlupp
who observed in
the field then
computed his
own sun shots
in the office. He
decided to
compute each
field observation
separately and
then average
the results.
Notice that the
angle right is the
same as the first
angle right from
the field notes.
Having an
HP-41 at the
time, he then
keyed EKSI’s
program into it
and used it to
calculate all
six observa-
tions.
This sheet
represents the
calculations
for Observa-
tion No. 1,
with average
of the six
shown below.
First, you have to find it! (Also,
remember compass and co-latitude).
Polaris, a circumpolar star, traces a 1°± arc around the North Pole.
During its counter-clockwise circumpolar path, it is directly aligned with True North at “Upper Culmination” and at “Lower Culmination” when it is exactly on line between the Surveyor’s Zenith (Meridian) and the North Pole. Then all the Surveyor has to do is sight it.
However, it is moving quickly then, being at Culmination only for an instant. It is easier for the Surveyor to track it when it is near Eastern or Western Elongation (90° from Culmination).
It crosses every Meridian once during each Sidereal Day.
The distance around the circle from the Surveyor’s Meridian to Polaris is called the Local Hour Angle (LHA).
The distance around the circle from the Greenwich (or Prime) Meridian to Polaris is called the Greenwich Hour Angle (GHA). This is the angle that is/was published in the EKSI Ephemeris.
We are here at 39°29’± North Latitude. The Co-Altitude (90° minus angle up from Horizon) to Polaris is approximately 50°41’.
…is the conical wobbling movement of Earth’s axis that causes a 23.4º circle (the angle of the Ecliptic) to be scribed onto the Celestial Sphere.
Astronomers theorize that precession has a period of 26,000 years. If any of you are still surveying in the Year 27985 A.D., you will have to sight the star Vega (in the constellation Lyra) as the North Pole, instead of Polaris.
Here in 2017 A.D., wasn’t it considerate of God to give us Land Surveyors here in the Northern Hemisphere the star Polaris to aim at?
Professor Porter W. McDonnell, Jr. from his 1975 class on Celestial Observations at Penn State Mont Alto.
Note that he has this form set up for the use of
a short-wave radio.
He also wants two sets D&R, with first B.S. from close to 0°and the second B.S. from close to 90°.
This is one
of the
computation
sheets from
the
Appalachian
Chapter’s
Polaris
observation
of 2003.
This sheet
not only
computes
the North
bearing to
the
backsight….
…it notes the
Local
Magnetic
Declination
and also
computes
the Mapping
Angle for
conversion
of the True
North
Azimuth to
MD Grid Azimuth.
Here’s one possibility:
https://celnav.de/longterm.htm
This long term almanac calculates Greenwich Hour Angle (GHA) and Declination for the Sun and Polaris.
However, you need to calculate DT by the formula DT = 32.183 sec. + (TAI-UTC) – DUT1
For this, use the USNO Multiyear Interactive Computer Almanac (MICA) or consult the USNO website
Any other questions or comments?
of grateful indebtedness to the following Land
Surveying giants for the use of their instructions,
programs and data
Robert E. Angle, LS Professor Porter McDonnell, Penn State University, Mont
Alto Campus Professor Jim Mask, Catonsville Community College Dr. R. Ben Buckner, Ohio State University Drs. Elgin, Knowles & Senne (EKSI) for their Celestial
Observation Handbook and Ephemeris U.S. Naval Observatory (USNO)
Our profession of Land Surveying is intimately connected with the sky’s
celestial bodies and their movements.
There is very much that we have not mentioned in these presentations, but what
we have seen should be enough to challenge you to perform your own
celestial measurements from this constantly moving, constantly changing platform of observation we call “Earth”.
Now let’s all go
outside and perform
a sun shot!