Survey Computation

A Note on Standard Deviation and Root Mean Square (RMS)
Technical paper by R.E. Deakin and D.G. Kildea detailing the difference between standard deviation and RMS (6 pages)

Technical paper by R.E. Deakin, R.I. Grenfell and S.C. Bird on the definition and calculation of centroids including the determination of various centroids of Victoria.

Chi-squared distribution and Confidence Intervals of the Variance
These notes (8 pages) give an explanation of the chi-squared distribution and its use in estimating confidence intervals of the variance.  Examples are provided and the equation of the distribution is developed.
Chi-squared distribution.pdf

Horizontal Positional Accuracy from Directional Antenna
Technical paper presented at Victorian Regional Survey Conference, Traralgon, 23-25 May, 2003 (18 pages).
Positional Accuracy 2.pdf

HP35s Surveying Programs
A suite of surveying computation programs for the Hewlett Packard (HP) 35s calculator that will be useful in the field and office. Some (Closure, Radiations, Joins, Offsets) have a heritage extending back to HP desktop-computer programs from the 1970’s written by Bodo Taube of Francis O’Halloran, Surveyors. And Bodo Taube’s programs were (and are) models of efficiency. Others are more recent. Each program has a set of User Instructions, with examples and relevant formula and HP35s Program Sheets listing the program steps (that you may key into your calculator), storage registers used and program notes.
HP35s Surveying Programs.pdf

Newton-Raphson Iteration
Notes and historical discussion of this important numerical method of solving equations (27 pages).
Newton-Raphson Iteration.pdf

Shrine of Remembrance, Melbourne
One of the best known features of the Shrine of Remembrance in Melbourne is the beam of sunlight that falls on the Stone of Remembrance on Armistice day at the 11th hour of the 11th day of the 11th month each year (clouds permitting); commemorating the moment of the end of the First World War in 1918.
Each year the Shrine trustees arrange a Remembrance Day service, but since the introduction of daylight saving in the summer of 1971-72, the natural event of the beam of sunlight passing across the Stone of Remembrance occurs at 12 pm rather than at the commemoration time of 11 am.  The problem caused by daylight saving was overcome by ‘bending’ the Sun’s rays by reflections from an inclined and a horizontal mirror.  The document Bending the Beam explains Frank Johnston’s solution to the problem (Frank is a retired staff member of RMIT Surveying Department).
In 2014, The Age newspaper had a feature article on the Shrine (see below) and interviewed Frank whilst the inclined mirror was being set a few days before Remembrance Day.  The article and a video movie of 3 min duration is available below.
The Shrine Mirror Problem was a favourite assignment topic for surveying students studying Astronomy in the 1970’s and 1980’s and was reproduced for surveying students in 2010 as an exercise in spherical trigonometry.  The assignment and worked solution are shown below.  This might trigger buried memories of ‘Astro’ for those old enough to remember.

The Age Sat-08-Nov-2014.pdf
Shrine movie

Shrine Assignment.pdf

Surveyors, GPS and the World Speed Sailing Record
Technical paper by R.E. Deakin, W.N. Cameron, D.M. Silcock and K. Zhang on the surveys required for an attempt on the World Speed Sailing Record (29 pages)

Student’s t-distribution and Confidence Intervals of the Mean
These notes (10 pages) give an explanation of the t-distribution and its use in estimating confidence intervals.  Examples are provided and the equation of the distribution is developed.
t distribution.pdf

Taudistribution and testing residuals
Technical paper (17 pages) by R.E Deakin and M.N. Hunter on the tau-distribution and testing residuals for outliers.  This paper describes the original tau statistic (Thompson 1935) and a modern interpretation if this statistic by Pope (1976).  The paper defines the relationship between the tau-distribution and Student’s t-distribution and has a derivation of the probability density function of the tau distribution.  The properties of the tau-distribution are explained and tables of areas under the tau-curve are provided for statistical testing.  Computer simulations are used to verify these tabulated values and several examples are provided to help explain the use of the tau-distribution for detecting outliers in lists of observations/residuals.
Tau distribution.pdf

Total Increment Theorem
Notes on the total increment theorem (total differentials) and their practical use in some surveying applications (9 pages).
Total Increment Theorem.pdf

Traverse Analysis
Technical paper on a method of assessing traverse quality using propagation of variances (11 pages)