The New Zealand Railways Magazine, Volume 5, Issue 9 (April 1, 1931)
The Purpose Of Surveying
The Purpose Of Surveying.
Members of the Railway Department have no doubt observed surveyors on Railway property taking innumerable measurements, with strange instruments, have seen them waving their arms, driving pegs, placing coloured flags in position, and have no doubt wondered what purpose the various operations were intended to serve.
I will endeavour to take the reader along by easy stages from the more simple to the more advanced surveying methods, avoiding, as far as possible, technicalities.
For a better understanding of the subject, rough diagrams are given. Any dimensions shewn on these diagrams are, with a view to simplicity, in approximate figures only. (See page 13.)
Surveying may be described as ascertaining by measurement the shape and size of any portion of the earth's surface and representing the same, on a reduced scale, in a conventional manner, so as to bring the whole under the eye at once.
The Unit of Measurement.
Engineering surveying is a supplementary branch dealing more particularly with the configuration of the earth's surface and the subsequent location of lines, curves, grades, levels, angles, etc., of all works and structures included in the profession of Civil Engineering. The unit of measurement is the link and 100 of these go to the chain. A chain also equals 66 feet, so that a link is approximately eight inches. The one chain measure is divided into 100 links, and in accurate measuring the links are further divided into tenths. The colonial practice is to have a steel band 6 or 11 chains in length and about one-eighth inch wide. This band is wound upon a drum. The end length of the steel band, for a distance of one chain is marked in links by brass studs, and each chain by a numbered disc. This length of measuring band permits of a rough surface to be spanned in one operation, correction being made from standard tables, for the sag in the band, and varying expansion through temperature.
The unit of area is an acre, which equals 10 square chains, or 100,000 square links, practically a metric system. The area of any rectangular section can be found by multiplying the frontage by the depth in links and taking off five places of decimals thus: 100 links frontage by 250 links depth = 250 × 100 = 25,000, and with five places of decimals off = .25 or quarter of an acre. (In surveying, all measurements and areas are the horizontal equivalent.)
If you reside on a property with a natural slope, you have a surface beyond that shewn on your title deeds, but you could not place a larger building upon page 11 it, grow more trees vertically, or catch more rainfall than on a similar area on flat ground. (See Fig. No. 1.)
Let us first consider a survey made with the chain measure only, and without the use of an instrument (theodolite). (Such a survey can be undertaken by any layman and will be approximately correct.)
In figure No. 2 is shewn an irregular shaped field. Each of the four sides is measured on the ground, and diagonals as check lines. Having these measurements and deciding upon a suitable scale, the various measurements are taken, one at a time, on a pair of compasses and arcs drawn, the points of intersections of the arcs being the corners of the field. If the ground is on a slope, the measurements are taken on the horizontal, and a “plumbob” used to mark this length on the slope. (See Fig. No. 3.)
The width of a river, too wide to be spanned by direct measurement, may be ascertained by proceeding as shewn in figure No. 4. At C, in the line AB, a line CD, is laid off close to the river bank and at right angles to AB. The line CD is halved at E, and the line DF laid off parallel to CA. As soon as the point F comes into line with BE then DF equals CB. Deducting the distances of B and C from the actual river bank, the width of water is given. In laying off the right angle a triangle with sides measuring 3, 4 and 5, or any multiple thereof is set out with the chain. (See Fig. No. 5.)
A survey of a stream meandering through a field may be completed with the use of a chain only, as shewn in Fig. No. 6. Check measurements or tie lines across the angles, as shewn by line ABC, ensure the accuracy of the survey. The distance of the stream bank from the adjoining survey line is observed and noted at each chain, when measuring along the lines.
Description of a Theodolite.
For accurate surveying an instrument of great precision, called a theodolite, is used.
Though to the uninitiated this instrument appears extremely complicated, its manipulation is simple. The theodolite is used only for measuring angles, both vertical and horizontal, and for placing marks, or stations, in a straight line in any desired direction. It is not used for the purpose of making calculations, as it is popularly supposed.
There is a story of a bush surveyor buying a dead pig for camp meat from a Maori. The price agreed upon was 3d. a pound. The Maori was told to hang the pig on a tree. The surveyor had a look at it through the theodolite. He estimated the pig would weigh 100lbs., so he told the Maori the instrument gave the weight as 60lbs., which at 3d. a pound, the instrument calculated as 12s. 6d. The Maori accepted this sum with bad grace, but returned the next day with a battered ready reckoner wherein 60lbs. at 3d. a pound was correctly shewn as 15s. The surveyor asked to have a look at the book, and then informed the Maori that the book was no good as it was last year's and out of date, so the Maori was quite satisfied, being convinced of the calculating powers of the theodolite.
The instrument is mounted on three strong legs to give rigidity, and is set up directly over a mark, or station, by a “plumbob” hanging from the instrument. The machine is levelled up true by thumb screws operating a spirit bubble, similar to that on a carpenter's level. For horizontal angles two flat circular plates, about six inches in diameter and half an inch thick, move one above the other. The edge of the lower plate is graduated with great precision shewing degrees and half degrees, and on the upper plate is a scale shewing further graduations in minutes. The moving of one plate on the other permits of any angle through which the plates have moved being read. A magnifying glass is used for accurate reading. For vertical angles two similar plates with the graduated markings are mounted vertically on the machine. The complete circle is divided into 360 degrees, each further divided by the upper scale into 60 minutes, and further divided into 60 seconds. The circle is thus divided into no less than 1,296,000 parts. In practice it is only possible to read to one- page 12 third of a minute with the small theodolite in general use, and this gives a range of 64,800 different angles.
Mounted on the horizontal axis of the instrument is a small telescope, in the eye-piece of which fine cross lines at right angles fix the central point in the line of sight.
Making Observations with a Theodolite.
To observe any angle, either horizontal or vertical, made by two objects with the position occupied by the instrument, all that is required is to bring one object into focus with the telescope centre, clamp the lower plate in that position, read the bearing or angle made by the adjoining plate, and swing the telescope to the second object. The top plate turns with the telescope, and on reading the bearing now made by the two plates, the angle traversed by turning the telescope from one object to the other may be read off the scale.
To place a number of marks or stations in any given direction the horizontal plates are clamped together, the telescope pointed in the desired direction and then moved vertically and focussed on each mark as required. This is a brief and very elementary description of a theodolite and its use.
The Uses of Trigonometry.
Varying in accordance with their magnitude, the angles and sides of triangles have certain relationships to one another. This relationship is called trigonometry and books of tables giving this information are used. When certain sides and angles of a triangle are known, the remaining sides or angles are readily found. I have shown in figure No. 7 the various cases, with known sides or angles in full lines, from which the remaining sides and angles are obtainable. It will be seen that practically all contingencies are met.
It is advisable to make a special note that the sum of the three angles in any triangle equal two right angles or 180 degrees, and that the adjoining angles made by a straight line meeting another straight line also equal two right angles or 180 degrees. I also bring particularly under notice the relationship of the sides of a right angled triangle i.e., a triangle having one of its angles a right angle, or 90 degrees, as this will be referred to again. This relationship is that the longer side multiplied by itself equals the sum of the two other sides when multiplied by themselves. (See Fig. No. 8.) It is interesting to note the figures 3, 4 and 5 make a right angled triangle, and should you desire to set out a right angle, such as for marking out a tennis court, these figures are easily memorised.
I mentioned previously that all measurements are horizontal, and if taken on the slope are reduced to the horizontal equivalent. In figure No. 9 is shewn an inclined measurement, and the method of arriving at the horizontal distance. The angle A of slope is observed at the instrument, the angle B is known to be a right angle, and as the sum of the angles of a triangle equal two right angles, the angle at C must be the difference between a right angle and the angle at A. We thus have a triangle ABC with all angles known, and also the side AC. The tables are looked up for the side AB, and the horizontal measurement AB is given.
In figures No. 10 and 10a are shewn the methods of ascertaining the height of inaccessible points. The observed measurements are in full lines. It will be seen the inaccessible angle and sides are computed. In arriving at the height of the mountain peak in figure 10a the side BC in the triangle ABC is first found. Then in the triangle BCD the angle BCD is known, as it equals 180 degrees less angle ACB. The angle D is a right angle, therefore the angle CBD equals a right angle less angle BCD, as the sum of the angles must equal two right angles. The height of the mountain can now be computed.
Surveying New Zealand.
I will now deal with surveying in its general application, and take the period when New Zealand was a virgin country, as far as surveys were concerned.
Surveying in Relation to Railway Engineering.
Particulars explanatory of the above drawings are given in the accompanying letterpress.
The first operation is to locate a base line some 10 to 12 miles long on level country. This line is measured with great accuracy many times, and the mean measurement adopted. Extreme care is taken in this measurement, and allowance is made for the expansion of the measuring band through changes of temperature. Permanent monuments are placed at the terminals, and the bearing of the line in relation to true North is obtained by repeated theodolite observations of the sun by day and certain stars by night, the true bearing being found from astronomical tables. The base measurement and its bearing having been fixed, the horizontal angles to some distant prominent major mountain peak, or hilltop, are observed from each end of the base line, and the angles made with the base line are recorded. (See ABC in Fig. No. 11.)
A triangle is thus obtained with the base as the known side, two angles known and the third computed, being the difference of the sum of the two known angles and 180 degrees. The unknown sides are then computed. These sides are then used for bases of other triangles, without actual measurement, and observations are made from these sides to other major points, and the process is carried on ad infinitum. Minor triangulation is a further breaking up of the major triangulation to provide points of ready accessibility for surveyors.
It will be seen that the whole of New Zealand can thus be surveyed with the taking of only one actual measurement, i.e., the original base line, all other measurements being computed. Cook Strait could be spanned by observations to prominent landmarks on each side. There is no possibility of error provided the original base line and angles are correctly observed, as each subsequent triangle in the triangulation automatically checks itself with the adjoining triangles. Minor triangulation is further subdivided in town areas into a standard survey for the town, and standard blocks or stations are placed permanently at street intersections. These are placed with great accuracy as the value of the adjoining property is high and any discrepancy would be costly.
An instance of this may serve to lighten this somewhat serious subject. An ingenious person once “raised the wind” by obtaining the loan of a decrepit theodolite, and planting it in the main street of a small town, spent most of the day making great pretence of taking observations and measurements to the hotel on the corner. Later in the day he waited upon the publican and informed him he regretted that he found the hotel encroached about two feet on the public street. The publican was very disturbed, and gave the man £10 to say nothing about it.
Methods of Procedure.
Surveyors use standard blocks when surveying (usually at daylight) in town areas, so as to avoid interruption from street traffic, and have probably been seen doing so by many persons. All surveys are connected by measurement to the nearest trig station in the country, and to a standard block in a town. This permits of any survey being subsequently reproduced with great accuracy from the trig or standard block.
We will assume it is desired to survey an estate for subdivision. The surveyor proceeds to a convenient trig in the vicinity, takes an. observation to an adjacent trig, the bearing and distance of which is recorded on the triangulation maps. Survey lines are then run around the boundaries of the estate, the bearing of each line and its accurate horizontal measurement being recorded, and so back to the starting point at the trig. If the work has been well done the distance travelled north will equal the distance travelled south, and the distance travelled page 15 east will equal the distance travelled west, or at least within the limits of error allowable, which are very small. In Fig. No, 12 is shewn such a survey. The survey is plotted on a plan to scale, the bearings as they deviate from north-south and east-west being calculated. Thus if a line 20 chains long has a bearing of 15 degrees from true north the line has proceeded a certain distance north and also a little to the east. We have a triangle shewn in Fig. 12a, and the northing and easting are computed by the same methods as previously explained for solving the unknown measurements of triangles.
The plan having been completed, the subdivision lines are decided upon, and these are reproduced on the ground, using the points of the original survey for check purposes. If it is desired to subdivide a piece of land of unknown area the survey is made and the area is computed from the plan. On the other hand, if it is desired to subdivide a given area the subdivision is computed from the plan and reproduced on the ground.
Surveys are made of all mine workings underground, for it is by this means all material that can be safely removed is brought to the surface. The only method of ascertaining the proximity of adjoining headings and galleries is by accurate survey and plotting on plans.
(To be continued.)