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!