1. The Search for Azimuth An Evolution of Methodology with Technology

2. Azimuth definition noun 1. The Horizontal Angular distance from a Reference Direction, usually the Northern* Point of the horizon, to a Target Point. The measurement is made clockwise through from 0° to 360°. 2. The Horizontal Angle of the Observer's Bearing in Surveying, measured Clockwise from a Reference Direction, as from the North*. * Astronomers use the South Reference Direction

3. Why do we need Azimuth?

4. Azimuth on Cadastral Plans

5. The Need for Accurate Azimuth on Cadastral Plans

6. How do we get Azimuth? dx dy   tan -1 [dx/dy] dy ≠ 0 From Control:

7. How else do we get Azimuth? Solar Obs: Altitude Solar The Astronomical Triangle

8. What data do we need? Altitude Solar Location: , Horiz. Reading Sun & R.O. Vertical Reading Sun Approximate Time (± 1minute) Ephemeris: Sun’s Declination

9. Getting Location Before Now - GPS - Google Maps - L&S Tiles: UTM Inverse E,N → ,  Sub-second Accuracy) - Ward Sheets - Topo Maps (1’ Accuracy)

10. Getting Sun’s Declination Primary Source: Star Almanac for Land Surveyors 1989 Edition issued to N. Abdul by L&S Division Library on 14 Sept. 1988

11. Getting Sun’s Declination Star Almanac for Land Surveyors 2016 Edition Now includes a CD-ROM with tables in PDF/TXT Formats

12. Getting Sun’s Declination First Attempts to Automate the Process (1991) Fourier Coefficients a1 = 0.3631751 a2 = 4.0944611 a3 = -22.8147677 a4 = -0.224888 a5 = -0.4492882 a6 = 0.1045454 a7 = -0.2316979 a8 = 0.0251665 a9 = -0.0027951 a10 = 0.0019216 a11 = 0.0019295  = a1 + a2 sin x + a3 cos x + a4 sin 2 x + a5 cos 2 x + a6 sin 3 x + a7 cos 3 x + a8 sin 4 x + a9 cos 4 x + a10 sin 5 x + a11 cos 5 x The Fourier Equation x = 0.017 * [ days since 1990.1231 + (hr + 4 + min/60)/24 ] Available Technology The HP41CX had a function DDAYS to subtract dates to get the number of days. The HP42s did not! The Fourier Coefficients were only valid for 6 months at a time.

13. Obtaining Sun’s Declination with Fourier Series Example Date: 01 Jan 1991 Local Time 07:30 Result: -23° 01’ 22” Error* = 0” http://ephemeris.com/ Date/Time: 1991.01.01 11:30:00 UTC Declination Sun -23°01'22" Over 6 months The max. error was ±3”

14. Getting Sun’s Declination Getting Long-Term Programmable Equations from the WWW

15. Obtaining Sun’s Declination with Long-Term Equations Example Date: 01 Jan 1991 Local Time 07:30 Result: -23° 01’ 18” Error = -6” http://ephemeris.com/ Date/Time: 1991.01.01 11:30:00 UTC Declination Sun -23°01'22"

16. SDEC \<< Wait -42 SF DATE IP 'day' STO DATE FP 100 * DUP IP 'mnt' STO FP 10000 * 'year' STO TIME 2 RND 'time' STO "SUN'S DECLINATION" { { "DAY : " "ENTER DAY" 0 } { "MONTH : " "ENTER MONTH" 0 } { "YEAR : " "ENTER YEAR" 0 } { "TIME : " "ENTER LOCAL TIME" 0 } } { } DUP day mnt year time 4 \->LIST { day mnt year time } PURGE IF INFORM NOT THEN CLEAR KILL END PROC LIST\-> DROP SWAP 'year' STO 'LT' STOK 4 + HMS\-> 24 / ROT ROT STD \->STR IF DUP SIZE 2 < THEN "0" SWAP + END DUP "/" year + + "/" SWAP + 'dmy' STO SWAP \->STR DUP dmy + 'dmy' STO "." + SWAP + year + STR\-> 31.121999 SWAP DDAYS 6 FIX + 1.5 - 'd' STOK.98560028 * 357.529 + 'g' STO 280.459.98564736 d * + g SIN 1.915 * + g 2 * SIN.02 * + SIN 23.439.00000036 d * - SIN * ASIN \->HMS 4 RND 'Dec' STO "Date : " dmy + 2 FIX "Time : " LT 2 RND \->STR + IF LT 12 > THEN 1 SF "PM OBS: FLAG 1 SET" ELSE "" END 4 FIX "Sun's Declination :" Dec DMS "" "SUN [ENTER] / Quit[+]" { d g q year dmy LT } PURGE 7 dispSTK SUN \>> Major limitations with computing The Sun’s Declination on an HP Calculator were: 1.Memory (RAM) 2.The Interface (9 Lines of Text) 3.The CPU (very slow) 4.The Programming Language 5.No File System 6.Limited I/O Capability 7.No Storage Capability

17. In 2013 Android Devices caused a Paradigm Shift

18. The Computation Method for Altitude Solars became more sophisticated - Built-in GPS Chips* - Better User Interface - Powerful Multi-Core CPUs - Powerful Java Language - Better Declination Algorithm** - GBs of RAM - MS Filing System - USB/Wi-Fi/Bluetooth I/O ** From G.G. Bennett (Australian Surveyor 1980) * GPS/GLONASS on Some Models

19. The Computation Method for Altitude Solars became more sophisticated… … but the field obs. procedure was identical

20. Revisiting the Astronomical Triangle Instead of Measuring Altitude (h) we could instead Measure Time to get the Local Hour Angle (LHA)

21. Since the Earth rotates through 360° every 24 Hours (more or less) then we can compute that it rotates 15” (arc seconds) every 1 second of Time (more or less) In theory we can measure Time more accurately than we can measure the Altitude of the Sun Basis for Hour Angle Method

22. Altitude Obs. Uncertainty “…the refraction determination is to some degree an educated guess.” - Jerry L. Wahl (American Land Surveyor )

23. GPS Time Internet Time Android App “GPS Test” “Time.is” Website Android Time Certainty

24. GPS Time is based on Atomic Clocks and is never adjusted for Terrestrial Phenomena like the slowing of the Earth’s rate of rotation. Instead an offset to UT is broadcast in the GPS Signal. From the GPS Time & broadcast correction to UT, we get Accurate Universal Time. The Android OS makes the correction automatically.

25. Values of delta-T (seconds) 2014 1 1 67.2810 2014 2 1 67.3136 2014 3 1 67.3457 2014 4 1 67.3890 2014 5 1 67.4318 2014 6 1 67.4666 2014 7 1 67.4858 2014 8 1 67.4989 2014 9 1 67.5111 2014 10 1 67.5353 2014 11 1 67.5711 2014 12 1 67.6070 2015 1 1 67.6439 2015 2 1 67.6765 2015 3 1 67.7117 2015 4 1 67.7591 2015 5 1 67.8012 2015 6 1 67.8402 2015 7 1 67.8607 UT Universal Time. Defined by the Earth's rotation, formerly determined by astronomical observations but today GPS satellites are used instead. This time scale is slightly irregular. TT Terrestial Time. Was defined in 1991 to be consistent with the SI second and the General Theory of Relativity. Terrestial Time is used to Compute the Astronomical Ephemerides. We need to add delta-T to UT to get TT. TT = UT + delta-T

26. What data do we need? Hour Angle Solar Location: , Horiz. Reading Sun & R.O. Vertical Reading Sun Accurate Time (± 1second) Ephemeris: Sun’s Declination, GHA Aires, Right Ascension & Sun’s Semi-Diameter GHA Sun = GHA Aires – RA Sun LHA = GHA Sun – Longitude w

27. To compute the required Ephemerides (Right Ascension, Declination & Semi-Diameter of the Sun) to maximum accuracy, the effects of Precession & Nutation on the Earth’s position have to taken into account

28. Putting all the Required Code to process Location, Time and Ephemerides in an Android App SolarHA

29. Using realtime GPS Location & Time We can Predict the Azimuth and Grid Bearing of the Sun eliminating the need for observations then computations to orient a Total Station

30. Finally using GPS Location & Time Correction We can compute the Azimuth and Grid Bearing of the Sun at a given Time Instance to orient a Total Station.

31. Thank You!