Chapter 6: Surveying
In the 1850s, a computer in a survey office finished a calculation that made a mountain the tallest in the world. He had never seen it. No one had measured it with a rope, and no one ever would. The mountain — Peak XV, deep in the Himalayas — had been fixed on paper from more than a hundred kilometres away.
The work belonged to the Great Trigonometrical Survey of India, begun in 1802. Its surveyors set out to map the shape of a whole subcontinent using one stubborn idea: measure a single line on the ground with extreme care, then reach every other point by measuring angles to it. From a carefully measured base line near Madras, the survey pushed northward for decades, one triangle joined to the next, up the length of India to the foot of the Himalayas.
To fix a distant peak, surveyors sighted it from both ends of a known line and read the angle at each end. Where the two lines of sight crossed, the peak stood — its position, and later its height, settled by arithmetic, not by climbing. The computer Radhanath Sikdar found that Peak XV rose higher than any other. In 1856 its height was announced as 29,002 feet.
The Survey never touched the mountain. It measured its way there. That is what surveying is: fixing where things are, on the ground and then on paper, by measurement alone.
Diagram
Fig. 6.0-1 Caption: A distant peak is fixed where the two lines of sight from a measured base line cross. Brief: A simple line diagram, not a map. Draw a short horizontal base line on the ground with its two ends labelled A and B, and mark it ‘measured length’. From A and from B, draw a dashed line of sight running up and outward to a single mountain peak in the distance, the two dashed lines meeting exactly at the peak; put an arrowhead on each line of sight pointing towards the peak. Mark the angle between the base line and the line of sight at A, and again at B. Add a note that only the base line A–B is measured directly; the peak’s position is found where the two sight-lines cross.
6.1 The Nature of Surveying
Every map begins as a set of measurements. Before a road can be aligned, a field boundary settled, or a town laid out, someone must first fix where things actually are on the ground. That patient work of measuring and recording is surveying, and everything in this chapter grows out of it.
6.1.1 Measuring to Map
Surveying is the process of measuring an area to find the relative positions of points on the earth’s surface, and then showing those points on a flat sheet of paper at a chosen scale. Its aim is not the land itself but a faithful, shrunken picture of it.
A surveyor works with two kinds of measurement, and needs both. Linear measurement is the measurement of distances — how far one point lies from another. Angular measurement is the measurement of angles or directions — which way one point lies from another. A distance alone, or a direction alone, leaves a point loose; a distance and a direction together pin it down exactly.
Notice the word ‘relative’. A survey usually fixes where each point sits in relation to the others, rather than its latitude and longitude. Once a few points are tied together correctly, the true shape of the whole area follows from them.
The ground is rarely flat, yet a map is. So surveying reduces all its measurements to a horizontal plane — an imaginary level surface — and records the plan view, as though the land were seen from straight above. A hillside and the flat field beside it both appear on paper as horizontal distances.
Because the ground is far larger than the paper, every distance is shrunk by a fixed ratio called the scale — the ratio between a distance on the map and the same distance on the ground. A scale of 1 : 50,000 means one centimetre on the map stands for 50,000 centimetres on the ground; that is 500 metres, or half a kilometre. The scale must be chosen before plotting begins, so that the whole area will fit the sheet.
Fig. 6.1-1 shows how a single distance and a single angle measured in the field become one plotted point on paper.
Diagram
Fig. 6.1-1 Caption: A distance and a direction measured on the ground become a single plotted point on paper. Brief: A two-panel line diagram. Left panel titled ‘On the ground’: a survey station at bottom left and a distant object (a small building) up and to the right; draw the straight line joining them and label its length as measured directly (‘linear measurement’); mark the angle between this line and a reference north arrow, labelled ‘angular measurement’. Right panel titled ‘On paper’: the same station plotted, the same line drawn much shorter but in the same proportion and labelled ‘reduced to scale’, the same angle preserved unchanged against a north arrow, giving the object’s plotted position. Between the panels draw a broad arrow labelled ‘plot at the chosen scale’. Emphasise that the angle is kept exactly the same while only the distance is shrunk.
6.1.2 What Surveying Is For
Surveying underlies almost every planned use of land. Any map — of a single village, a district, or a whole country — begins with survey measurements. A topographical sheet, the standard map that shows relief, drainage, roads and land use together, is built directly from survey data.
Most large construction is laid out on a survey plan before it begins. A road, a railway line, a canal, a building or a major project such as a dam is first drawn on a plan that shows exactly where each part will sit and how the land rises and falls. Engineers can then design and cost the work before a single stone is moved.
Surveying also settles boundaries. The edge of an agricultural field, the limit of a forest, the line between two land uses — each is fixed and recorded through survey. These records decide who holds which piece of land, and they are consulted whenever land is bought, sold or disputed.
Growing and new towns lean on surveying as well. Expanding an existing city, or planning a wholly new one, needs an accurate base map on which roads, plots, water lines and drains can be arranged so that they do not clash on the ground.
For most of its history surveying was slow and done entirely by hand. Advances in instruments, and more recently in satellite positioning, have made it far quicker and more accurate — a change we return to at the end of the chapter.
6.2 Kinds of Survey
Surveys are not all of one kind. The same broad task — fixing positions and mapping them — can be carried out to different standards of accuracy, for different purposes, and with different instruments. So a survey can be classified on three bases: the accuracy it aims for, the purpose it serves, and the instruments it uses. Fig. 6.2-1 sets these three schemes out together.
Flowchart
Fig. 6.2-1 Caption: Surveys are grouped three ways — by the accuracy they seek, the purpose they serve and the instrument they use. Nodes: Survey (grouped on three bases) → Basis 1, Accuracy → Triangulation (very accurate) or Traversing (quick, less accurate); Basis 2, Purpose → Topographical or Cadastral or Geological or Military; Basis 3, Instrument used → Chain-and-tape or Plane table or Prismatic compass → the plane table branch is the one this chapter follows
6.2.1 By Accuracy
By the accuracy they aim for, surveys fall into two types.
Triangulation is a very accurate survey in which the whole area is covered by a framework of connected triangles. Its accuracy rests on a simple fact of shape: a triangle is the one figure that cannot be pushed out of form once its sides are fixed — it is rigid. A four-sided frame can lean and shear without any side changing length, but a triangle cannot. A mesh of triangles therefore holds together as a stiff, self-checking framework in which errors cannot spread far.
In such a survey only one line is laid down and measured with great care; the length of every other side is then found from the angles of the triangles. This is why triangulation stays accurate even over very large areas, and why it is chosen for the control surveys on which national mapping is built.
Traversing is quicker but less accurate. Here the survey is run as a connected chain of straight lines, called legs, joining one station to the next, with the length and direction of each leg measured in turn. There is no rigid framework of triangles to hold the work together.
Because the legs simply follow one another, a small error in any leg is carried forward, and errors add up along the chain. Traversing therefore trades some accuracy for speed, and is used for ordinary maps rather than precise control work.
The two methods start from the same raw material — measured lines — but hold those lines together differently. Triangulation locks the survey into rigid triangles and stays accurate across great distances; traversing strings lines end to end and accepts a slow build-up of error in return for quicker work.
6.2.2 By Purpose
By the purpose it serves, a survey may be of four kinds.
A topographical survey maps the natural and man-made features of an area together — relief, drainage, roads, settlements and land use — and its product is the topographical sheet met in the previous section.
A cadastral survey fixes the boundaries of individual land parcels for records of ownership and land revenue. It works down at plot level and underlies the land records kept for each village.
A geological survey maps rock types, structures and mineral deposits at and below the surface, guiding the search for coal, ores and groundwater.
A military survey maps terrain for defence — the lie of the land, the routes across it, and the cover and obstacles that shape how forces can move and be placed.
The purpose decides the detail. A cadastral survey must be exact to the metre because a boundary in the wrong place moves ownership with it, while a topographical survey spreads across a wide area at a coarser scale and cannot show every plot line. What a survey records, and what it leaves out, follows from why it was made.
6.2.3 By Instrument
By the main instrument used, three types are commonly named.
In a chain-and-tape survey, distances are measured with a chain and a tape. It is the simplest and cheapest method and suits small, fairly level areas, but it fixes points by distance alone.
In a plane table survey, a drawing board is set up in the field and the map is plotted there and then, as the measurements are taken.
In a prismatic compass survey, the direction, or bearing, of each line is read off a small magnetic compass fitted with a prism, and distances are measured separately.
Of these three, the rest of this chapter follows the plane table, because it does something the others cannot: it lets the finished map take shape out in the field itself.
6.3 The Plane Table and Its Instruments
6.3.1 What Sets the Plane Table Apart
A plane table is a drawing board mounted on a tripod, on which the surveyor plots the map directly, out in the field. A plane table survey is any survey built around this instrument.
Its great advantage is that the two halves of surveying — measuring in the field and drawing the map — are done together, on the spot, rather than one after the other. In most surveys the measurements are written into a field book and the map is drawn back in the office; the plane table collapses these two steps into one.
Because the map grows as the surveyor looks at the ground, no field book is needed and the time usually spent plotting later is saved. Better still, if a detail is left out by mistake, it is noticed at once, because the surveyor can compare the growing map with the ground in front of them and correct it there and then.
6.3.2 The Instruments of the Set
A plane table survey uses a small set of instruments, each with one clear job. It is easiest to learn them by what they do rather than as a bare list. Fig. 6.3-1 shows the core of the set assembled and ready.
Diagram
Fig. 6.3-1 Caption: The plane table set up on its tripod, with the instruments that level, centre and sight it. Brief: A clean line diagram. Draw a square drawing board mounted level on a three-legged tripod stand whose feet end in iron shoes gripping the ground. On the board show a sheet of paper, an alidade (a flat ruler standing on its edge) resting on the sheet, and a small spirit level lying on the board. Clip a U-shaped plumbing fork to one edge, its plumb bob hanging on a string below the board and pointing down to a small marked station point on the ground. Label: plane table (board), tripod stand with iron shoes, alidade, spirit level, plumbing fork, plumb bob, ground station.
The Board and Its Stand
The board itself is the plane table, made of well-seasoned wood so that it does not warp. It is fixed to a tripod stand about one and a half metres tall. The three legs of the stand are what make levelling possible — a three-legged stand rests firmly on any uneven ground, where a four-legged one would rock. Iron shoes on the feet stop the legs from slipping, and a clamping screw locks the board on to the stand once it is set.
Sighting: The Alidade
The alidade is the instrument that turns a distant object into a line on the paper. It is a flat ruler, about 40 to 50 centimetres long, carrying an upright vane at each end. One end, the sight vane, holds a fine vertical thread — often a horse hair. The other, the eye vane, has a narrow slit with small eye holes through which the surveyor looks.
To use it, the surveyor lines up the eye, the slit, the thread and the object in the field all in one straight line. A line is then drawn on the sheet along the ruler’s graduated ruling edge, called the working edge (or fiducial edge). Such a drawn line, pointing from the station towards an object, is a ray, and rays are the backbone of every method that follows. The working edge lies a little to the side of the actual line of sight, but each ray drawn along it comes out parallel to that line of sight, so the offset introduces no error (Fig. 6.3-2).
Diagram
Fig. 6.3-2 Caption: Sighting along the alidade and drawing a ray along its working edge. Brief: A close-up line drawing of the alidade lying on the board. At one end an upright sight vane carrying a fine vertical thread (horse hair); at the other end an upright eye vane with a narrow vertical slit and three small eye holes (top, middle, bottom). Draw the surveyor’s line of sight as a dashed line running from an eye hole, through the slit, along the thread, out to a distant object. Along the ruler’s graduated edge draw a solid line labelled ‘ray’. Label the graduated edge ‘working (fiducial) edge’, and label the vanes, thread and eye holes. Show the solid ray and the dashed line of sight as parallel to each other, and note this.
Levelling and Centering
Two instruments make sure the board sits correctly. A spirit level — a small glass tube part-filled with spirit, leaving an air bubble — tells the surveyor when the board is level: the board is level when the bubble sits exactly in the middle of the tube.
Centering is done with a plumb bob, a pointed weight hung on a string from a U-shaped holder called the plumbing fork. The fork’s pointed tip is set on the station marked on the sheet, and the bob hangs on its string below the board. Since a hanging weight always settles on a true vertical line, shifting the board until the bob hangs exactly over the matching station on the ground places the plotted point directly above the real one.
Direction, Distance and Ground Marking
Direction is given by the trough compass, a magnetic needle set in a small box. Left free, the needle settles pointing along magnetic north, letting the surveyor mark the north direction on the sheet. It is worth remembering that this is magnetic north, which differs slightly from true (geographic) north by the local magnetic declination; but for marking direction on a plane-table sheet the magnetic north serves well.
Distances on the ground are measured with a chain and a measuring tape. The measuring tape, usually 30 metres or 15 metres long, is made of yarn woven with fine metallic wire — not pure metal — so that it stays strong and does not shrink when damp. The chain is important enough to take up on its own in the next subsection. To keep count of how many chain-lengths have been laid along a long line, iron pins called arrows, each about 35 to 45 centimetres long and pointed to drive into the ground, are planted at the end of each chain-length; a chain is usually carried with a set of ten.
Finally, ranging rods mark out the survey on the ground. These are poles two or three metres tall, painted in alternating bands about every 20 centimetres so that they stand out against any background, with a pointed iron shoe below and often a small flag on top. Planted at the survey stations, they can be seen from far off and are used to fix the lines and the limits of the survey. To all this is added the ordinary drawing material — paper, pins, pencil and rubber.
6.3.3 The Chain and Its Kinds
The chain is a line of short iron or steel wire pieces joined end to end, with a brass handle at each end so that it can be pulled taut. Each of its wire pieces is a link, and a chain is divided into exactly 100 links, each link’s ends bent into rings and joined to the next by small connecting rings.
Counting 100 links one by one would be slow, so the chain carries brass tags, called tellers, at every tenth link. The number of teeth on a tag gives its position in tens, and the tag at the very middle is round to mark 50. Because a chain can be read from either end, one tag stands for two marks — a two-toothed tag reads 20 links from one end and 80 from the other (Fig. 6.3-3).
Diagram
Fig. 6.3-3 Caption: A surveying chain, its links, and the brass tags that let distances be read at a glance. Brief: A schematic line drawing of a surveying chain laid out straight — short wire pieces joined by small connecting rings, with a brass handle at each end. Along the chain show the brass tags (tellers) at every tenth link: a one-tooth tag marked ‘10 or 90’, a two-tooth tag ‘20 or 80’, a three-tooth tag ‘30 or 70’, a four-tooth tag ‘40 or 60’, and a round tag at the middle marked ‘50’. Label ‘link’, ‘connecting rings’ and ‘brass handle’. Keep it clear and schematic.
Three kinds of chain are used, differing only in their length and the units they are built to serve. The engineer’s chain is 100 feet long with 100 links, so each link is exactly one foot, and it measures distances in feet. The Gunter’s chain is 66 feet, or 22 yards, long with 100 links, so each link is 0.66 feet (7.92 inches); its odd length is what lets it measure miles and furlongs, and areas in acres. The metric chain is 10, 20 or 30 metres long with 100 links, each link 10, 20 or 30 centimetres — this is the chain used in India after the country went over to the metric system in the late 1950s.
The 66-foot length of the Gunter’s chain looks awkward until its arithmetic is worked through.
The awkward length, then, is not awkward at all. It was chosen so that both distance and area fall out in whole units — 80 chains make a mile, and 10 square chains make an acre — letting a surveyor read acres straight off the ground without any conversion. The instrument quietly did the unit arithmetic. India’s switch to the metric chain traded this old convenience for metric neatness: a 100-link chain of 20 metres, with every link a round 20 centimetres.
6.4 Conducting a Plane Table Survey
With the instruments known, the survey itself falls into a fixed order of steps. Each one prepares the ground for the next, and skipping or rushing any of them shows up as error in the finished map. Fig. 6.4-1 lays out the whole sequence before we walk through it in detail.
Flowchart
Fig. 6.4-1 Caption: The order of steps in a plane table survey, from the first rough sketch to the finished map. Nodes: Prepare a rough sketch and plant ranging rods → Set the table at the first station (level → centre → orient) → Fix and measure the base line → Draw and label rays to each object → Measure distances and plot the points to scale → Move to the next station and re-orient (by back sighting or by trough compass) → back to ‘Draw and label rays to each object’ → continue until the survey is complete
6.4.1 Precautions Before You Begin
Good field work starts before the table is set up. The surveyor first walks the area and prepares a rough sketch of it, noting the important points and marking them, and plants ranging rods on the points that will matter. This sketch is not the map; it is a plan of attack that keeps the survey orderly.
A few precautions then guard the work. The full list of instruments is drawn up and each one checked to be in working order, because a missing plumb bob or a bent alidade in the field wastes a whole trip. The clamping screw is tightened firmly so the board cannot shift during the survey, and the two vanes of the alidade are kept upright, with care taken not to knock the board while rays are being drawn.
Two more precautions protect the drawing. The paper is fastened tightly to the board with pins, gum or tape, so it neither slips nor lifts. And the scale is chosen at the outset so that the entire area to be surveyed will fit on the sheet provided — a scale set too large will run the survey off the edge of the paper.
6.4.2 Setting the Table
Setting the table means bringing the board into exactly the right position at a station. It is done in three steps, always in the same order: levelling, then centering, then orientation.
Levelling makes the board horizontal, using the spirit level. The clamp is loosened a little and the board turned so that one of its edges lies parallel to two of the tripod’s three legs. The spirit level is placed along that edge and those two legs are adjusted until the bubble sits central. The level is then turned to the edge at right angles to the first, and the third leg alone is adjusted until the bubble is central again. The board is now level in both directions.
Centering brings the station marked on the sheet exactly over the matching station on the ground. The pointed tip of the plumbing fork is set on the plotted point, and its plumb bob hangs below the board. The whole table is shifted gently until the bob hangs directly over the ground station, so that the point on paper sits vertically above the point on the earth.
Orientation sets the board facing the right way, so that lines drawn on it run in the same directions as their real counterparts on the ground. At the very first station the length of the board is simply kept along the length of the area. At every later station the board is turned until the lines already plotted on it point along the matching lines on the ground. Levelling and centering fix where the board is; orientation fixes which way it faces, and all three are needed together.
6.4.3 The Base Line, the Rays and Re-orientation
The base line is the single line on which the whole survey rests. It is chosen by inspecting the entire area, and it is the one line measured directly and with care on the ground. A base line is well chosen if it lies fairly central to the area, runs over reasonably level ground, gives a clear view of the area from both of its ends, and reaches towards a few prominent landmarks.
Everything else in the survey then hangs off this one measured line. Once its two ends are plotted correctly to scale, any other point can be fixed by direction alone: rays are drawn to it from the two ends, and where two rays cross, the point sits. This is why a survey needs only one carefully measured line and not a distance to every object.
Drawing the rays is the next step. From the station, the alidade is sighted on each object in turn and a ray drawn along its working edge, as described earlier. Each ray is at once labelled with the name of its object, so that at the next station there is no confusion about which line points where.
When the surveyor moves from one end of the base line to the other, the board must be set facing the same way as before. Resetting the orientation at a new station is called re-orientation, and it is done in one of two ways.
The first is back sighting. Suppose the base line runs from A to B and the surveyor has moved to B. After levelling and centering there, the alidade is laid along the plotted line ba, and the board is turned until station A is seen through the alidade along that line. The board is now oriented, because the line ba on paper lies along the line BA on the ground (Fig. 6.4-2).
Diagram
Fig. 6.4-2 Caption: Re-orientation by back sighting: the board is turned until the old station is seen along its own plotted line. Brief: A line diagram. Show a base line on the ground from station A (left) to station B (right), with the plane table set up at B. On the board draw the already-plotted line b–a. Lay the alidade along b–a on the board. Draw the surveyor’s line of sight running back from the alidade at B towards A, and a curved arrow showing the whole board being rotated until A appears in that line of sight. Label station A, station B, the plotted line b–a, and add a note: ‘rotate the board until A is seen along ba; then ba on paper lies along BA on the ground’.
The second way is by trough compass. At the first station the north–south line is marked on the sheet from the trough compass. At the new station, after levelling and centering, the trough compass is laid along that same north–south line and the board turned until the needle again settles north–south. The board is then oriented to exactly the north it had before.
6.5 The Three Methods of Plane Table Survey
A plane table survey can be carried out by three methods — radiation, intersection and traverse. They differ in how many stations are used, and in how the position of each object is fixed. Which one is chosen depends on the size and shape of the area to be mapped.
6.5.1 Radiation
In the radiation method the whole survey is run from a single station. Rays radiate from that one point in every direction, to each object in turn, which is why the method carries the name.
The surveyor sets the table at a central point, marked p on the sheet, from which every object in the area can be seen. A ray is drawn along the alidade to each object — to A, B, C and the rest. The distance from the station to each object is then measured on the ground with a chain or tape, and the point marked on its ray at the chosen scale. Joining these plotted points completes the map, and the north direction is added from the trough compass (Fig. 6.5-1).
Diagram
Fig. 6.5-1 Caption: Radiation: one central station, with a ray to every object and each distance measured along its ray. Brief: A line diagram. Show a central survey station P near the middle of an irregular area, with objects A, B, C, D, E, F around its edge. On the board at P, draw rays from p out to each object. Along each ray mark the plotted point a, b, c, d, e, f at a scaled distance, and join these points to form the area’s outline. Add a north arrow from a small trough compass. Label: central station P, rays, plotted points to scale, measured distances.
Radiation works only when a single station can see the whole area, so it suits small, fairly compact plots. Within those limits it is a comparatively accurate method, because every point is fixed straight from the one station without any chain of measurements building up error.
6.5.2 Intersection
For a larger area, the intersection method is used, and its cleverness is that no distance to any object need be measured at all. A base line is laid and measured, and rays to the same object are drawn from both of its ends; the object stands exactly where the two rays cross.
The surveyor sets the table at one end of the base line, P, plots the point p, and draws rays to each object — A, B, C, D. The base line pq is drawn to scale on the sheet to fix the second end. The table is then shifted to Q and re-oriented, and rays are drawn from q to the same objects. Each new ray meets the ray already drawn from p, and the crossing point fixes the object as a, b, c, d. Joining these points completes the map (Fig. 6.5-2). It is the same idea by which a distant peak can be fixed from two ends of a measured line, without anyone ever reaching the peak.
Diagram
Fig. 6.5-2 Caption: Intersection: an object is fixed where the rays to it from both ends of the base line cross. Brief: A line diagram. Show a base line P–Q measured across the middle of an area with four objects A, B, C, D around it. From station P draw a ray to each object; from station Q draw a ray to each of the same objects; show each pair of rays crossing at a, b, c, d. Mark the base line P–Q as the only measured line. Join a, b, c, d to complete the outline. Label: base line (measured), rays from P, rays from Q, intersection points a b c d.
6.5.3 Traverse
When the area is very large, or is a long strip such as a road, a railway line, a canal, a settlement or a lake, a single base line cannot command the whole of it. The traverse method meets this by using a series of connected base lines, joined one to the next. Along each base line the nearby objects are fixed by intersection, and the surveyor then moves on to the next base line, and the next, until the area is covered.
There are two forms. In an open traverse the chain of stations runs from a start to a finish without returning — the natural choice for a road or a canal, which simply leads from one place to another. In a closed traverse the stations form a closed figure that comes back to the starting point, and there must be at least three of them; this suits an area or a lake whose whole boundary is being mapped.
In a closed traverse, check lines are drawn across the figure, between stations that are not neighbours, to test whether the survey is accurate — if a check line on the map matches its measured length on the ground, the work has held together. Sometimes, through a small personal or instrumental slip, the surveyor does not arrive back exactly at the starting point, and a gap is left between the start and the finish. This gap is the closing error, and in an accurate survey it must be removed by adjusting the work (Fig. 6.5-3).
Diagram
Fig. 6.5-3 Caption: Two kinds of traverse — an open chain that does not return, and a closed figure checked for accuracy. Brief: Two side-by-side line panels. Left panel titled ‘Open traverse’: stations A–B–C–D joined in a line that does not return, following a winding path like a road, with the plane table shown at successive stations; the plotted line a–b–c–d left open. Right panel titled ‘Closed traverse’: stations A–B–C–D–E joined in a loop that returns towards A, with dashed ‘check lines’ drawn across the figure between non-adjacent stations; show a small gap where the last line fails to meet A exactly, labelled ‘closing error’. Label both panels, the check lines and the closing error.
Seen together, the three methods answer the same need at three scales. Radiation fixes a small compact plot from one point. Intersection fixes a larger area from a single measured base line, using ray crossings instead of measured distances. Traverse strings many base lines together for an area too big, or too long, for either of the others. In every case the map is built from rays; only the number of stations, and the way the rays are made to cross, changes.
6.6 The Strengths and Limits of the Plane Table
The plane table earns its place through one central strength: the map is made out in the field, alongside the measuring, rather than back in an office afterwards. Because the plotting is done on the spot, very little laboratory work is left over, and no field book is needed to carry measurements home for drawing later.
This field-plotting brings a further gain in reliability. Since the map grows while the ground is still in view, details are unlikely to be left out, and any omission is caught at once and corrected. In the intersection and traverse methods, moreover, only the base line has to be measured — every other point is fixed by rays — so the survey moves quickly and, over modest areas, stays accurate.
The very thing that makes the plane table strong, though, is also the root of its weaknesses: it works on paper, in the open. Paper is fragile. In rain it buckles and tears, so the method is close to useless in wet weather, and a survey caught by a downpour may be lost.
There are practical burdens too. The board and its tripod are large and heavy, and awkward to carry from station to station. The method also comes with a scatter of small accessories — the alidade, spirit level, plumb bob, trough compass, arrows and ranging rods — any one of which a surveyor may leave behind, only to find it missing in the field.
The paper sets a limit on size as well. A very large area will not fit on a single sheet, so the paper must be changed again and again, which makes the plane table clumsy for big surveys — the same situation in which the traverse method’s chain of base lines is already stretched to its limit.
Weighed together, these strengths and limits point to where the plane table belongs. It is at its best on small to medium areas in fair weather, where speed and on-the-spot checking matter more than covering great distances. Its weaknesses are practical rather than errors of principle — and it is exactly these practical limits that the modern satellite methods, taken up next, set out to overcome.
6.7 Surveying by Satellite: GPS
The plane table’s limits — its bulk, its fragile paper, its need for one point to be visible from another — are exactly what satellite positioning removes. GPS, the Global Positioning System, is a way of fixing a position anywhere on the Earth’s surface from signals sent by satellites overhead, rather than by measuring across the ground.
A constellation of satellites orbits the Earth, each one continuously broadcasting two things: its own position in space and the exact time at which the signal leaves it. A GPS receiver on the ground picks up the signals from several satellites at once and measures how long each signal took to arrive. Because radio signals travel at the speed of light — about 300,000 kilometres every second — the receiver can turn each tiny travel time into a distance to that satellite.
Once it knows its distance from several satellites, the receiver can be in only one place: where all those distances agree at the same time. Fixing a position from measured distances in this way is called trilateration, and it is worth setting beside the plane table. Triangulation and intersection fix points by angles; GPS fixes them by distances. In practice, signals from at least four satellites are needed to settle a position and correct the receiver’s own clock, and the receiver then reports its latitude, longitude and height.
Diagram
Fig. 6.7-1 Caption: A receiver fixes its position where its measured distances to several satellites all agree. Brief: A schematic diagram. Show a GPS receiver at a point on the ground and four satellites at different positions in the sky above. From each satellite draw a line down to the receiver, each labelled ‘distance from signal travel time’. Suggest each distance as the radius of an arc or sphere around its satellite, and show the four arcs meeting at the receiver’s position. Label: satellites (each broadcasting its position and time), receiver, ranges, and a note ‘position fixed where the ranges meet — at least four satellites needed’.
To survey with GPS, the surveyor simply carries a receiver to each point that matters and records its coordinates, and the plan is then built up from those coordinates. There is no base line to measure, no ray to draw, and no need for one point to be seen from another — a real gain over the plane table, and one that lets the method cover large areas and rough terrain with ease.
How closely it fixes a point depends on the receiver. An ordinary handheld unit is accurate to within a few metres, which is enough for a rough plan; survey-grade receivers, using correction methods such as differential GPS, sharpen this to a few centimetres. The American GPS is the best known such system, but it is not the only one.
GPS has its own limits, and they are the mirror image of the plane table’s. It needs a clear view of the sky, because its signals are blocked indoors, under dense forest canopy, deep in narrow valleys and among tall buildings — the very places where a plane table can still be set up and used. The two, then, are less rivals than tools for different jobs: the plane table for a small, sheltered plot drawn on the spot, and satellite positioning for large or open ground that must be fixed to precise coordinates.
6.8 Summary
Surveying is the process of measuring an area to fix the relative positions of points and show them on paper at a scale. It uses linear measurement (distance) and angular measurement (direction), and reduces everything to a horizontal plane so that uneven ground can be drawn flat.
Scale is the fixed ratio between a distance on the map and the same distance on the ground; it is chosen before plotting so the whole area will fit the sheet.
Surveying underlies almost every planned use of land — topographical sheets, the layout of roads and projects, records of field and forest boundaries, and the base maps for towns.
A survey can be classified by accuracy, by purpose, or by instrument. By accuracy, triangulation covers an area with a rigid framework of triangles and stays very accurate, while traversing strings lines end to end for speed but lets error build up.
By purpose, surveys are topographical, cadastral, geological or military; by instrument, chain-and-tape, plane table or prismatic compass. This chapter follows the plane table.
A plane table is a drawing board on a tripod. Its strength is that measuring and plotting are done together in the field, so no field book is needed and a missed detail is caught on the spot.
The kit includes the alidade (which sights an object and draws a ray along its working edge), the spirit level (levelling), the plumb bob and plumbing fork (centering), the trough compass (magnetic north), the chain, tape and arrows (distance), and ranging rods (marking stations).
A chain has 100 links, with brass tags that let distances be read at a glance. The engineer’s chain is 100 feet, the Gunter’s chain 66 feet (giving miles, furlongs and acres), and the metric chain 10, 20 or 30 metres — the one used in India.
Running a survey begins with a rough sketch and a few precautions. The table is then set at each station in a fixed order: levelling, then centering, then orientation.
The base line is the single line measured directly; every other point is fixed by rays, and where two rays cross, the point sits. On moving to a new station the table is re-oriented, by back sighting or by trough compass.
There are three methods. Radiation fixes a small compact area from one central station, measuring distances along the rays. Intersection fixes a larger area from one measured base line, without measuring any object’s distance, by crossing rays from both ends.
Traverse links many base lines together for a large or long area. An open traverse does not return; a closed traverse comes back to its start, is checked with check lines, and any gap left is the closing error, which must be removed.
The plane table is quick, needs no field book and rarely omits detail, but it is useless in rain, bulky to carry, easy to lose accessories from, and limited in area by the size of the paper.
GPS fixes a position from satellite signals by trilateration — distances rather than angles — needing at least four satellites and no line of sight between ground points. It is accurate to metres for a handheld unit and to centimetres for survey-grade receivers.
Flowchart
Fig. 6.8-1 Caption: The whole chapter on one page — how a plane table survey turns ground into a map, with the satellite alternative alongside. Nodes: Classify the survey (by accuracy, purpose or instrument) → choose the plane table, so the map is made in the field → set the table at a station: level → centre → orient → fix and measure one base line → draw and label rays with the alidade → fix each object by one of three methods (radiation: one central station, distances measured; intersection: rays cross from both ends of the base line; traverse: a chain of connected base lines, open or closed) → plot to scale and join into the finished map → (modern alternative: GPS fixes points by trilateration from satellites, for large or open ground)
What This Chapter Cannot Tell You
This chapter teaches the elementary principles of surveying; it does not carry the error-adjustment mathematics by which a real survey removes its closing error or reaches survey-grade precision. A clean diagram of a method also hides the field’s difficulties — wind, an obstructed line of sight, or ground too soft or steep to level easily. And naming GPS is not the same as mastering it: the precise timing and orbit corrections behind centimetre accuracy lie well beyond an elementary account.
6.9 Key Terms
- alidade — a flat sighting ruler used to sight an object and draw a ray along its edge on the plane table.
- angular measurement — the measurement of an angle or direction between lines.
- back sighting — re-orienting the plane table at a new station by sighting back along a plotted line to the previous station.
- base line — the single line, measured directly on the ground, on which a whole survey rests.
- cadastral survey — a survey that fixes the boundaries of individual land parcels for records of ownership and land revenue.
- centering — setting the plane table so that a station marked on the sheet lies exactly above the matching station on the ground.
- chain — a measuring line of iron or steel, 100 links long, used to measure distances on the ground.
- check line — a line drawn across a closed traverse, between non-adjacent stations, to test the accuracy of the survey.
- closed traverse — a traverse whose chain of stations returns to its starting point, forming a closed figure.
- closing error — the gap left between the start and the finish of a closed traverse when the surveyor does not return exactly to the start.
- GPS — the Global Positioning System; a way of fixing a position from the signals of satellites overhead.
- horizontal plane — the imaginary level surface to which survey measurements are reduced, so that uneven ground can be drawn flat.
- intersection — a survey method that fixes an object where the rays drawn to it from both ends of a base line cross.
- levelling — making the plane table horizontal, using the spirit level.
- linear measurement — the measurement of a distance between points.
- link — one of the hundred equal parts into which a survey chain is divided.
- open traverse — a traverse whose chain of stations runs from a start to a finish without returning.
- orientation — setting the plane table so that lines drawn on it run in the same directions as their real counterparts on the ground.
- plane table — a drawing board mounted on a tripod, on which the map is plotted directly in the field.
- plumb bob — a pointed weight hung on a string, which settles on a true vertical line and is used to centre the plane table.
- prismatic compass — a magnetic compass fitted with a prism, used to read the bearings of lines in a survey.
- radiation — a survey method that maps a small area from one central station, with a ray and a measured distance to each object.
- ranging rod — a tall painted pole planted at a station to mark it and to fix the lines and limits of a survey.
- ray — a line drawn on the plane table, along the alidade’s working edge, pointing from the station towards an object.
- re-orientation — resetting the plane table’s orientation at a new station so that it faces the same way as before.
- scale — the fixed ratio between a distance on the map and the same distance on the ground.
- spirit level — a glass tube holding an air bubble in spirit, used to tell when the plane table is level.
- surveying — the process of measuring an area to fix the relative positions of points and show them on paper at a scale.
- topographical sheet — a standard map showing relief, drainage, roads and land use together, built from survey data.
- traversing — a survey run as a connected chain of measured lines; quicker than triangulation but less accurate.
- triangulation — a very accurate survey that covers an area with a rigid framework of connected triangles.
- trilateration — the fixing of a position from measured distances rather than from angles, as used in GPS.
- trough compass — a magnetic needle set in a small box, used to find and mark magnetic north on the sheet.
- working edge — the graduated ruling edge of the alidade, along which rays are drawn; also called the fiducial edge.
6.10 Points to Ponder
A plane table survey measures only one line directly and fixes everything else by direction. What is gained, and what is risked, by trusting a whole map to the accuracy of that single measured base line?
The plane table’s greatest strength — that the map is drawn out in the field — is also the root of its main weaknesses, from fragile paper to a heavy board. Can a tool’s greatest advantage always be traced back to the same feature as its greatest limitation?
Triangulation is slow but very accurate; traversing is quick but lets error build up along the chain. When is it better to be slow and certain, and when quick and roughly right — and how far does the answer depend on what the map will be used for?
If a satellite receiver can now fix any point to a few centimetres, is there still a reason to learn the plane table? Is an older method worth knowing for what it teaches about how position is fixed, even when a newer one does the job faster?
A mountain’s height was once settled by arithmetic from more than a hundred kilometres away, and a GPS position is settled by timing signals no one can see. How much of what any map tells us rests on trusting instruments and calculations we never check for ourselves?
6.11 Objective Questions
- The two kinds of measurement used in surveying are: [1 mark]
- vertical and horizontal
- linear and angular
- direct and indirect
- magnetic and true
- In a plane table survey, a ray is drawn along the: [1 mark]
- sight vane
- plumb line
- working edge of the alidade
- ranging rod
- A Gunter’s chain is: [1 mark]
- 100 feet long
- 66 feet long
- 30 metres long
- 22 feet long
- Assertion (A): In the intersection method, the distance to each object need not be measured on the ground. Reason (R): An object is fixed where the rays drawn to it from both ends of the base line cross. [1 mark]
- Both A and R are true, and R is the correct explanation of A.
- Both A and R are true, but R is not the correct explanation of A.
- A is true, but R is false.
- A is false, but R is true.
- Assertion (A): GPS can fix a point without any line of sight between one ground station and another. Reason (R): GPS uses trilateration, fixing a position from distances to satellites rather than from angles measured across the ground. [1 mark]
- Both A and R are true, and R is the correct explanation of A.
- Both A and R are true, but R is not the correct explanation of A.
- A is true, but R is false.
- A is false, but R is true.
- Match each instrument in Column A with its role in Column B. [1 mark]
| Column A | Column B |
|---|---|
| a. Alidade | i. marks a station and makes it visible from afar |
| b. Trough compass | ii. draws rays to objects |
| c. Plumb bob | iii. centres the table over a ground station |
| d. Ranging rod | iv. shows magnetic north |
- Fill in the blank: The single line, measured directly on the ground, on which an entire plane table survey rests is the ________. [1 mark]
6.12 Check Your Concepts
Define surveying, and name the two kinds of measurement it uses. [2 marks]
What is a base line, and what makes one well chosen? [2 marks]
Differentiate between triangulation and traversing. [3 marks]
Differentiate between an open traverse and a closed traverse. [3 marks]
Give reasons for the following: [3 marks]
- The tripod stand of a plane table has three legs rather than four.
- The Gunter’s chain is 66 feet long and not a round 100 feet.
Explain, in the correct order, the three steps involved in setting a plane table at a station. [4 marks]
Explain the intersection method of plane table survey with the help of a sketch. [4 marks]
‘The plane table’s greatest strength is also the source of its main weaknesses.’ Evaluate this claim. [4 marks]
Describe the full procedure of a plane table survey, from the rough sketch to the finished map, naming each step and what it achieves. [6 marks]
Compare the plane table and GPS as ways of preparing a plan of an area, and discuss where each is better suited. [6 marks]
6.13 Map, Diagram & Data Interpretation
- Study Fig. 6.3-2, the alidade. [4 marks]
- Name the parts marked sight vane, eye vane and working edge, and state the job of each.
- Explain why a ray drawn along the working edge gives the correct direction to the object, even though the working edge is not itself the line of sight.
- Look at Fig. 6.5-2, the intersection method. [4 marks]
- Which is the only line that is measured on the ground?
- Explain how the object A is fixed on the map.
- State one thing that this figure does not tell you about the survey.
- A plan is drawn at a scale of 1 : 25,000. [4 marks]
- What ground distance is represented by 4 cm measured on this plan? Show your working.
- A field is 1.5 km long. How long will it appear on the plan? Show your working.
- With reference to Fig. 6.3-3, draw a labelled sketch of a surveying chain showing the brass tags at 10 or 90, 20 or 80, 30 or 70, 40 or 60, and 50 links, and explain why a single tag can stand for two readings. [3 marks]