The Search for Azimuth
An Evolution of Methodology with
Technology
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
Why do weneed Azimuth?
Azimuth on Cadastral Plans
The Need for AccurateAzimuth on Cadastral Plans
How do weget Azimuth?
dx
dy
q
= q tan-1 [dx/dy]dy ≠ 0
From Control:
How elsedo we getAzimuth?
Solar Obs:
Altitude SolarThe Astronomical Triangle
What datado we need?
AltitudeSolar
Location: f,lHoriz. Reading Sun & R.O.Vertical Reading SunApproximate Time (± 1minute)Ephemeris: Sun’s Declination
Getting Location
Before Now
- GPS- Google Maps- L&S Tiles: UTM Inverse E,N → f,l (Sub-second Accuracy)
- Ward Sheets- Topo Maps(1’ Accuracy)
Getting Sun’s Declination
Primary Source:Star AlmanacforLand Surveyors
1989 Editionissued to N. Abdulby L&S Division Libraryon 14 Sept. 1988
Getting Sun’s Declination
Star AlmanacforLand Surveyors
2016 EditionNow includesa CD-ROMwith tablesin PDF/TXT Formats
Getting Sun’s Declination
First Attempts toAutomate the Process (1991)
Fourier Coefficients
a1 = 0.3631751a2 = 4.0944611a3 = -22.8147677a4 = -0.224888a5 = -0.4492882a6 = 0.1045454a7 = -0.2316979a8 = 0.0251665a9 = -0.0027951a10 = 0.0019216a11 = 0.0019295
d =
a1 + a2 sin x + a3 cos x +a4 sin 2x + a5 cos 2x +a6 sin 3x + a7 cos 3x +a8 sin 4x + a9 cos 4x +a10 sin 5x + a11 cos 5x
The Fourier Equation
x = 0.017 *[ days since 1990.1231 +(hr + 4 + min/60)/24 ]
Available Technology
The HP41CX hada function DDAYSto subtract datesto get the number ofdays.
The HP42s did not!
The Fourier Coefficientswere only valid for6 months at a time.
Obtaining Sun’s Declinationwith Fourier Series Example
Date: 01 Jan 1991Local Time 07:30
Result: -23° 01’ 22”Error* = 0”
http://ephemeris.com/
Date/Time: 1991.01.0111:30:00 UTCDeclinationSun -23°01'22"
Over 6 monthsThe max. error was ±3”
Getting Sun’s DeclinationGetting Long-Term Programmable Equations from the WWW
Obtaining Sun’s Declinationwith Long-Term Equations
Example
Date: 01 Jan 1991Local Time 07:30
Result: -23° 01’ 18”Error = -6”
http://ephemeris.com/
Date/Time: 1991.01.0111:30:00 UTCDeclinationSun -23°01'22"
SDEC \<< Wait -42 SFDATE IP 'day' STODATE FP 100 * DUPIP 'mnt' STO FP10000 * 'year' STOTIME 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 daymnt year time 4\->LIST { day mntyear time } PURGE IF INFORM NOT THEN CLEARKILL END PROCLIST\-> 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 \->STRDUP dmy + 'dmy' STO"." + SWAP + year +STR\-> 31.121999 SWAPDDAYS 6 FIX + 1.5 -'d' STOK .98560028* 357.529 + 'g' STO280.459 .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 dispSTKSUN \>>
Major limitations with computingThe Sun’s Declination on an HPCalculator were:
1. Memory (RAM)2. The Interface (9 Lines of Text)3. The CPU (very slow)4. The Programming Language5. No File System6. Limited I/O Capability7. No Storage Capability
In 2013Android Devices
caused aParadigm Shift
The ComputationMethod for
Altitude Solarsbecame moresophisticated
- 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
The ComputationMethod for
Altitude Solarsbecame more
sophisticated…
… but the fieldobs. procedurewas identical
Revisiting theAstronomical Triangle
Instead ofMeasuring Altitude (h)
we could insteadMeasure Time
to get theLocal Hour Angle
(LHA)
Since the Earth rotatesthrough 360° every 24 Hours
(more or less)
then
we can compute that itrotates 15” (arc seconds)every 1 second of Time
(more or less)
In theory we canmeasure Time
more accurately thanwe can measure theAltitude of the Sun
Basis for Hour Angle Method
Altitude Obs. Uncertainty
“…the refraction determinationis to some degree an educated guess.”
- Jerry L. Wahl (American Land Surveyor)
GPS Time Internet Time
Android App “GPS Test” “Time.is” Website
AndroidTimeCertainty
GPS Time is basedon Atomic Clocksand is never adjustedfor Terrestrial Phenomenalike the slowing of theEarth’s rate of rotation.
Instead an offset to UTis broadcast in the GPS Signal.
From the GPS Time &broadcast correction to UT,we get Accurate Universal Time.
The Android OS makes thecorrection automatically.
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
UTUniversal Time.Defined by the Earth's rotation, formerly determinedby astronomical observations but today GPS satellites are usedinstead. This time scale is slightly irregular.
TTTerrestial Time.Was defined in 1991 to beconsistent with the SI second andthe General Theory of Relativity.
Terrestial Time is used to Computethe Astronomical Ephemerides.We need to add delta-T to UT toget TT.
TT = UT + delta-T
What datado we need?
Hour AngleSolar
Location: f,lHoriz. Reading Sun & R.O.Vertical Reading SunAccurate Time (± 1second)Ephemeris: Sun’s Declination,GHAAires , Right Ascension &Sun’s Semi-Diameter
GHASun = GHAAires – RASun
LHA = GHASun – Longitudew
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
Putting all theRequired Codeto process Location,Time and Ephemeridesin an Android App
SolarHA
Using realtime GPSLocation & Time
We can Predict theAzimuth andGrid Bearingof the Suneliminating the need forobservations thencomputations to orienta Total Station
Finally using GPSLocation &Time Correction
We can compute theAzimuth andGrid Bearingof the Sunat a given Time Instanceto orient a Total Station.
Thank You!