The New Zealand Railways Magazine, Volume 6, Issue 1 (May 1, 1931)
Surveying in Relation to Railway Engineering
The following is the concluding instalment of Mr. Kent's non-technical explanation of surveying, surveying instruments, and the methods employed in their use, more especially in relation to railway engineering.
Surveying as Applied to Civil Engineering.
We now come to the question of surveying as applied to Civil Engineering, a branch of surveying usually demanding extreme accuracy.
In figure No. 13 is shown a survey for a tunnel through an inaccessible mountain range (except by the Pass followed by the survey). Proceeding from the point A, a survey is made to the point B, with great care and checking. In computing this survey it is found that the point B is 35 chains north, and 55 chains east, of the point A. We now have the triangle A B C of which two sides are known, and also the angle at C. The angles at A and B and the length of the side A B can now be computed, as previously explained, giving the length of the straight—included in which is the tunnel and also the bearing of the tunnel in relation to true north. In the diagram the dotted lines are computed and the full lines observed and measured. The grade of the tunnel is fixed by ascertaining the relative height of the points A and B. This will be dealt with when explaining levelling practice. The figures above the line are the measured distances, and below the line the bearing or angle to true north.
Location and Setting out of Curves.
In railway engineering the location and setting out of curves enters into surveying practice. All true curves bear certain relationships according to their magnitude or radii to the angle of intersection of the straight lines which they join up, i.e., the length of the starting and finishing points of the curve from such intersection. The length of the curve is also known, the distance in a straight line across the curve and joining the curve ends, and the angle a chord of any length makes with the straights when drawn across any portion of the curve from the starting point or end of a curve (see figure No. 14). This information is given in books of tables for any curve for any angle of intersection of the straights and the calculations are reproduced on the ground with a theodolite.
There are several types of curves as shown in figure No. 15 and their characteristics are as follows:—
A true curve is one of even curvature throughout its length. The radius is decided upon to meet, economically, the configuration of the country with a minimum of construction work in the placing or the removal of earthwork. The present allowable minimum curvature is 7 ½ chains radius, but this is only adopted in very rough country and easier curves are provided if at all practicable, even with increased construction costs.
Reverse curves are provided in rough country to meet local conditions, but are not good practice as the opposing elevations of the outer rails of each curve give a rolling motion to vehicles at the junction of the curves. A compound curve is a curve made up of two or more true radii page 42 and is sometimes used in following along a river bank with a limited location between the river and the adjacent hill. The entrance to sharp curves gives rough transit to rolling stock and necessitates reduction in speed. To overcome to some extent, this disability, the ends of the true curve are flattened by easy approaches running from the straight track with gradually increasing curvature, until the true curve is reached. This is known as a transition curve. At the intersection of steep grades vertical curves are provided to eliminate discomfort in running from one grade to another.
How Levels are Taken.
Intimately associated with engineering surveying is the necessity for accurate levels to determine heights, fix gradients and earthwork quantities. This work is carried out with an instrument known as the dumpy level. The instrument comprises a telescope mounted on three rigid legs and fitted with a very sensitive spirit bubble parallel to the telescope. The telescope and levelling bubble revolve freely, horizontally. The eye-piece of the telescope is fitted with two fine vertical cross lines and one horizontal crossing at right angles. The instrument is fitted with thumb screws on the top of the leg mounting to bring the telescope into a horizontal position in any direction. The telescope has considerable magnification for distances up to 300 yards and onehundredth of a foot can be observed at 100 yards distance. A graduated staff about 14 feet long and three inches wide, marked in feet, tenths and hundredths of feet, is employed in observing the heights of various points in relation to the line of sight through the level telescope.
In figure No. 16 is shown the method of taking a series of levels with the dumpy level. In the first series of readings A B C D and E it will be seen the readings are 12, 3, 11, 7 and 5 respectively. That is to say B is 9 feet higher than A, C is 1 foot higher than A or 6 feet lower than E and so on. The instrument is then moved from station 1 to station 2 and a back sight taken on the last reading from station 1 at E. This connects the second series with the first series—a procedure repeated again and again until the area to be covered is completed. As a check, levels are taken on the completion of the work back to the starting point as at A, and if the work has been well done the same level is arrived at, or at least within allowable limits. The levels of each reading are then tabulated, the original level being related to mean sea-level by connection to fixed monuments known as bench marks (much the same as surveying trigs), and available throughout the country. When thus tabulated the varying heights of each point of observation above mean sea-level are shown, and any one point can be compared with any other point as to their relative heights.
Railway Location Methods.
Surveying in Relation to Railway Engineering.
(See accompanying letterpress for explanatory particulars.)
The modern practice is to compensate railway grades for curvature, i.e. to provide a slightly easier gradient on sharp curves to balance the resistance of wheel flanges on the rails on such curves.
Railway location in rough country calls for considerable investigation and trial lines. To reach a given elevation by a direct route is often impracticable as the gradient would be prohibitive. The only alternative to get a working gradient is to cover distance, called development. The Raurimu Spiral is an example of this. It is frequently remarked by railway passengers, when proceeding up a valley and they see the river well below them, that they cannot understand the mentality of the engineers in leaving the river flats where the gradient is so easy. They overlook the fact that in the lower part of the valley the river has an easy gradient, but higher up the valley it begins to rise until finally it may be as steep as 1 in 10. The railway leaves the level of the river at the lower entrance of the valley and following a workable grade throughout eventually again joins the river level at its source and passes over the summit to the adjoining watershed. This is illustrated in figure No. 18.
In past years it was the practice to go in for cheap construction, the alignment and grades following the contour of the country. This gave heavy gradients and sharp curves, but light banks and cuttings. The Lawrence Branch is a typical example. This practice is economically unsound. Though the initial cost is light, the limitation of loads, speeds and the heavy wear to track and rolling stock is perpetuated and this expense would more than pay for a better and more costly location in the first instance. When traffic demands make it imperative to improve the old location by grade and curve easements, the money expended on the original location may for the most part be written off as a dead loss. In locating and grading a line, the likely trend of heavy loading should be investigated. To have an average falling gradient over many miles in the direction of heavy loading, with a steep opposing gradient for a short distance at some point in this area is bad practice. The opposing grade limits all loads on the down gradients to that of the up gradients.
The Lighter Side of the Subject.
Surveying has its humorous incidents, and I give one or two of my experiences in an endeavour to detract from the heaviness of this subject.
I once sent a man down a high embankment to measure the size of a large square culvert and gave him a three foot rule to do so. He returned and said it was as high as the rule and three widths of his hand. On investigating personally I found it 4 feet high. He had overlooked the using of the rule for the additional measurement beyond its length!
After placing a number of pegs to the exact level with considerable care I instructed the ganger to see they were not disturbed. He met me later looking very pleased with himself and informed me he had knocked them all in to level with the ground so they would not be disturbed!
When surveying a water catchment area on the Bluff Hill I was unable to page 45 pick up an observation on to a white flag at a peg on an adjoining ridge owing to the blooming of white clematis on the scrub surrounding the peg. I told my amateur chainman to proceed to the ridge and stand alongside the flag so I could take a shot at it. I went on with other observations and on again looking at the adjoining ridge was surprised at the ease with which the flag could be seen and to observe also my chainman sitting alongside, having a smoke. I took an observation and on plotting the survey found it hopelessly wrong. It later transpired that the chainman had lifted the flag from alongside the peg, walked with it to an adjacent knob where he could plainly see me, stuck the flag in the ground and sat down alongside it. He said he thought I wanted to have a look at the flag!
When transferring camp from Turakina to Otahuhu on grade easement surveys I wrote the Auckland Office to engage for me a chainman-cook for the camp. I intended a man capable of either work. My request was evidently only casually read as they replied, “What did I want a Chinaman cook for? Was not a white man good enough?”
In conclusion I may state that surveying is a very satisfactory following as there is no guess work, all work automatically checks itself and one knows definitely the margin of error. In this respect the final computations give as much satisfaction as solving a problem does to a mathematician, or a balance to an accountant.
I trust that my explanations have been sufficiently lucid to be followed by an attentive reader and that some may have found interest in this subject which is an important branch of railway work.page 46