Basics of Field Surveying

Introduction

Surveying is defined as the science of determining relative and absolute positions (both elevation and location) of points at or near the surface of the earth. It incorporates the art of presenting the results clearly and efficiently (usually on maps or cross-sections).

Surveying has applications in fields as diverse as

• geodesy (determining the shape of the earth and locating positions on it)
• topographic surveying and map making
• cadastral (legal) survey
• construction, and
• resource inventory

Principle techniques include:

1. levelling, which determines differences in elevation
2. plane surveying, which determines relative locations
3. transit surveying, which determines differences in absolute position (elevation and location)

Measurements involve:

1. angles (vertical and horizontal)
2. slope distances
3. horizontal and vertical distances

Measurements are made with precision optical instruments (transit compasses, levels, theodolites, alidades), and with tellurometers (electronic distance meters). Nowadays, tapes or chains are used to determine local detail only.

(source: GEOG 309 Field School Manual, 2004, text by M. Bovis)

Funadmentals of Levelling

Levelling is a technique whereby:

1. the differences in elevation between two or more points may be determined;
or
2. a given fixed elevation may be ranged, with negligible error, to other places (say, for building foundation work);
or
3. a topographic profile of a piece of terrain may be obtained quickly.

Here, the focus is on (1.) since this demonstrates the essential elements of using a level. Often, a survey is to made in which the absolute elevations of points within the map area must be determined. For this purpose, one or more points must be established within the map area with a known absolute elevation. To achieve this, elevations must be carried in from a benchmark (B.M.) located (usually) outside the map area. Often benchmarks (bronze hubs set in concrete) are located along major highways, along railways, on public buildings or vantage points (many in B.C. are on or near the coast for ease of ranging to islands). Bench marks are established by ultra precise methods to provide control points for the production of accurate topographic maps.

In carrying a level survey, a series of intermediate stations is set up between a bench mark and the new control point to be established. These are occupied by the stadia rod to carry the elevation from one setup to the next, and are called turning points (T.P.). Horizontal distances for the sights should be made approximately equal by pacing, by stadia measurements, by counting lengths of rails if working along a track, or by some other easy method. The effects of refraction, curvature of the earth, and lack of adjustment of the instrument, are thereby eliminated. On slopes, a zigzag path may be taken to utilize the longer rod length available on the downhill sights.

Benchmarks are described the first time used, and are thereafter referred to by noting the page number on which they are detailed. The description should give the general location first, and include enough particulars to enable a person unfamiliar with the area to find the mark readily. Bench marks are usually named for some prominent object which is nearby to aid in describing their location, one word being preferable. Examples are B.M. River, B.M. Tower, B.M. Corner, and B.M. Bridge.

Turning points are numbered consecutively along a line of levels, but need not be described, since they are merely a means to an end and often are not reoccupied. It may be useful to mark them (by chalk) if one is traversing metalled surfaces and intends to return by the same route. Reoccupation of T.P.s simplifies error location.

Reading the Reticle Lines

Once you have the stadia rod in position on the B.M. or a T.P., focus the level so that you can read the numbers on the rod and see the reticle lines clearly. Be sure that you have the vertical line aligned to the middle of the stadia rod and verify that the rod person is holding the rod vertically. You must take and record three numbers: the stadia rod reading at the upper line, the rod reading at the centre line, and the reading at the lower line. Interpolate each reading to the nearest mm when you can do so. When the rod is farther away, try to read the elevations with an precision of plus or minus 0.5 cm (i.e. to the nearest half a cm).

Recording the data

You should set up your field book to record 8 separate things:

STA (the station being surveyed),
B.S. (the back sight to a location of known elevation, E, which is the rod reading at the centre reticle),
H.I. (the height of the instrument, wherein H.I. = B.S. + E),
F.S. (a foresight to a T.P. of unknown elevation),
E (the elevation of an unknown point, wherein E = H.I. - F.S),
U (the upper reticle reading),
L (the lower reticle reading),
D (the distance from the instrument to the rod, where D = k*(U - L) + C, where k = 100 and C = 0.1 m for the Sokkia C3 levels)

HOWEVER most field books have only six columns. One trick to to record foresights and backsights in the same column, indicating backsights by adding "+" before the reading and adding "-" before the foresights. Another trick is to record the instrument height calculated during a backsight in the elevation column (e.g. HI = 101.334), as well as the control point elevations calculated during the foresights (Z = 92.961). One final trick is to put any significant notes in the table on a separate row in parentheses, crossing all of the columns. That gives us field notes that look like:

Procedure for levelling

1. Position stadia rod on B.M.
2. Determine location of next station (T.P.l)
3. Set up level midway between B.M. and T.P.l
4. Level instrument
5. Take a backsight ("plus" sight) on B.M.
6. Move rod to T.P.l
7. Rotate level. Check instrument is still within limits of self-levelling device (compensator).
8. Take a foresight ("minus" sight) on T.P.l, booking all 3 readings as before.
9. Move instrument midway between T.P.l and T.P.2. Set up and level.
10. Rotate rod on T.P.l to face instrument.
11. Take a backsight (plus sight) on T.P.l. etc.
12. Finish with a foresight on the control point (T.P. 4 in the diagram)
13. "Run back" readings to B.M., finishing with a foresight on B.M.
14. Check for acceptability of closure error. Repeat the procedure from the beginning if required.

Error Checking: before a party leaves the field, all possible note checks must be made to detect any mistakes in arithmetic. The algebraic sum of the plus and minus sights applied to the first elevation should give the last elevation. This computation checks the values of all heights and T.P.s unless compensating errors have been made. When carried out for each page of tabulations, it is termed the page check.

In single traverses, there is no check on the existence of cumulative errors. Important work is checked by leveling forward and backward between end points. The difference between the rod sum (algebraic total of plus and minus sights) on the run out, and the rod sum on the run back is called the loop closure. Specifications, or the purpose of the survey, fix the permissible loop closure.

When all calculations have been made through all stations back to B.M., it is often found that final calculated elevation of B.M.is not equal to the initial observed elevation of B.M. This is the so-called closure error.

In essence then, levelling consists of determination of an elevation difference between a known and an provision for error calculation.

Dealing with Closure Error

The polygon is defined by line segments joining the B.M. and T.P.s. the length of these line segiments (d_i is the sum of the distance associated with backsight to the point of known elevation and the foresight distance to the point of unknown elevation.

In levelling, errors are compounded with distance: therefore, total closure error is divided in proportion to lengths of shots. Suppose total error is ET metres. Then the quantity apportioned to each segment will be:

e_i = ET * d_i / D

This is assigned to TPs, of course, not to instrument stations.

Surveying Topographic Profiles

Surveying topographic profiles involves recording the horizontal location and the elevation of a series of points along the profile (which is usually a straight line of known bearing, starting at a control point estabilished by a levelling traverse). If the instrument is in line with the profile, the upper and lower reticle readings can be used to calculate distance along the profile. If the instrument cannot be positioned in-line with the profile (or even along the profile itself), then a fibreglass tape can be strung out along the ground surface of the profile. If the tape is on the ground rather than stretched taught in a horizontal line, the tape readings will give you the slope distance, not the horizontal distance, and you will have to use trigonometry to calculate the horizontal distance.

While the same proceedure is followed for recording the data, surveying profiles is much easier than conducting a levelling traverse. In the simplest case, the instrument is set up behind the starting control point in-line with the survey profile, and the rod person occupies a series of locations moving away (or towards) the survey instrument.

If there is a bench mark or control point of known elevation in view, the surveying exercise should start with a back sight to that point to determine the instrument height (HI). Then, it will be possible to calculate the absolute elevation of each foresight point, rather than just the relative elevation.

Once the instrument is set up and the instrument height has been calculated, a series of foresights are taken to various key points along the profile. It is useful to record the position of breaks-in-slope (i.e. where the topographic gradient changes), changes in land cover, and other elements of interest. Each point should be recorded using a defined code (e.g. WE = water's edge, GR = ground surface, EOV = edge of vegetation, RB = Right stream bank, etc.). Enough ground points should be taken to faithfully represent the topographic variations.

Since the instrument (ideally) remains in the same location for the duration of the survey, it is not necessary to calculate the closure error for the survey, and there is no cumulative error to distribute between the various foresights (any errors in position will affect only a single point).

Using a Theodolite

In this section, we consider the use of the theodolite (an instrument with which points can be positioned very accurately), and some fundamentals of traverse surveying - a means to set out a local network of central points. Once a secure polygonal network of control points is established, local detail can be accurately placed either by sketching or by surveying the details using the theodolite.

Two types of traverse are: (a) open, and (b) closed.

An open traverse is used in line surveys, such as highways, or where low accuracy inventories are being made in relatively unknown terrain.

Clearly, there is considerable scope for error here. The effect of small angular discrepancies is magnified, such that the position of E may be subject to considerable error. In such work, very accurate methods of measuring both angles and distances are required. A theodolite with a horizontal circle capable of reading directly to 1 second of arc is preferred.

A closed traverse is the preferable procedure, since error corrections can be made and it is best suited for mapping a compact area. First walk out the area to determine the best locations for traverse hubs (instrument positions).

Essential Features of a Theodolite

The theodolite consists of the following main parts: a fixed base with tribrach, a movable upper part, and a telescope. The base with the tribrach is screwed securely to the tripod head and is levelled up by means of its three foot screws. In simple theodolites of older construction the horizontal circle which defines the azimuthal angles (or bearings) is fixed rigidly to this base. In modern instruments the circle can be rotated independently by means of a milled knob or some other device.


On the upper part, which is rotatable about the standing (vertical) axis, two vertical pillars (called standards) are mounted that support the tilting (horizontal) axis upon which the telescope rotates and the vertical circle which defines the vertical angles.

For rough leveling-up the base has a circular bubble level mounted to the instrument. For more accurate leveling-up, the more sensitive alidade tubular level (the plate level) is used. The instrument is centred over a station point by means of a plumbob or a built-in optical plummet.

The telescope may be aimed in any desired direction in space, by means of rotations about its standing and tilting axes. Fine pointing to a particular target is achieved accurately by means of clamping and slow motion (drive) screws.

Measuring Horizontal Angles

Setting the horizontal coordinate system

The theodolite has two clamps (upper and lower) to control horizontal surveying. Turn the knurled wheel to 0°0'0" (details on vernier later). Clamp the upper movement. Set the angle exactly with the tangent screw. The angular reading will not change, if the upper tangent screw is now left alone.

The lower movement is still loose. Point the theodolite at some predefined target, which will be used to define the horizontal angular coordinate system. Then clamp the lower motion. Adjust the alignment of theodolite and the target with the lower tangent screw. Theodolite and azimuth 0°0'0" are now set on A.

Measuring the horizontal angle

Loosen the upper clamp. Rough point on the next survey point of interest, B. Clamp. Adjust the alignment of with B using the upper tangent screw. This procedure turns the theodolite over the horizontal circle, so one "turns off" and can read the angle between A and B. The effect of erroneously turning the lower tangent screw at this stage is to introduce an error into the angles.

Procedures for a Theodolite Traverse

Proceed as follows:

1. Set up at Station B; establish magnetic north.
2. Set horizontal circle to 0°0.0". Clamp lower plate.
3. Loosen upper plate. Backsight on A. Measure the horizontal distance BA by stadia. Measure angle B.
4. Determine angle A from relation A = 180 - B (supplementary). As we shall see, it is convenient to have angle A rather than angle B.
5. Record vertical angle (elevation or depression) at B. This is since, due to terrain, the shot to A may have to be inclined.
6. Sight on C from B. Read H angle, V angle, stadia
7. Move the instrument to point C. Retain the last H angle reading on the circle. Plunge the scope (i.e. turn it right over between the standards so that it is basically looking backwards). Backsight on B. Return the scope to its normal orientation. The instrument now has the same compass orientation as at B. (thinkg this procedure through geometrically and you will not go wrong.)
8. Sight on D. Read H angle, V angle, stadia.
9. Transit to D. Retain last reading. Plunge scope. Backsight on C.
10. Replunge. Foresight on A, record H angle, V angle, stadia. This completes the traverse. NOTE: there were only 3 transit stations, not four.

Calculating Distances: The slope distance depends on the difference between the upper and the lower reticle.

R' = U - L

In order to correctly calculate the slope distance, we must correct for the angle of inclination

R = R'cos Φ

where reading R would be obtained if the rod were held at 90 degrees to the line of sight, and Φ is the angle of inclination. Clearly if R' is used, stadia distance is overestimated. To compute the distance, we must know the constants in the equation

S = kR + c

where R is geometrically corrected stadia reading = (U-L), k is a multiplicative constant (or tacheometric ratio), and c is an addition constant (usually zero or 1). On the Sokkisha TS20 Theodolite, K = 100; c = 0. Thus the slope distance, S, is

S = 100 (R' cos Φ)

To compute horizontal and vertical distances, H and V, use

H = S cos Φ
V = S sin Φ

Clearly, on a map we want horizontal distances. In flattish terrain, the correction is neglibible. In steep terrain, distance could be wrong (too long) by 30% or more.

Booking Theodolite Traverse Data

Given that most fieldbooks have 6 columns only, we arrange theodoite data as follows, using the same conventions as for levelling ("-" indicates a foresight, "+" indicates a backsight, etc.).



Typically, the numerical data is recorded on the left hand page only, and the right hand page is reserved for comments such as

• description of the station to which the shot is made
• any relevant sketches
• ambient conditions (windy, etc.)
• personnel, and what tasks they were responsible for (e.g. notetaker, instrument opperator, rod person)

Reducing Traverse Data

This is normally done in the fieldbook, back at the field camp, so that original field data and reduced readings can be cross-checked readily. Elevations can be reduced as per the procedure described under levelling, except that allowance must be made for the vertical angle, but taking the sine of the vertical angle, times the properly reduce stadia slope distance.



As demonstrated in the table above, the orthongonal components of a traverse leg can be computed directly from the horizontal and vertical angles using a calculator or spreadsheet. These orthogonal components are called latitudes and departures, and they are directed orthogonal distances, which means that the sign (+ or -) of the calculated value indicates whether or not the latitude or departure should be added or subtracted from the known location (in X Y coordinates) to get the new location.

If no errors are comitted, the since the traverse returns to point A, sums of all latitudes and departures should equal zero. This is rarely the case, so that the traverse does not close.


The quantities -0.71 and +0.53 represent the components of the closure segment, as measured from the starting point A to the finishing point A' (shown above).

Closing a Theodolite Traverse

First compute the linear closure. This is the Pythagorean distance

AA' = sqrt(-0.71² + +0.53²) = 0.89

The ratio of error is:

RE = error of closure / linear distance of traverse = 0.89 / 2466 = 1 /2800

This is acceptable for our kind of work. Anything less than about 1 / 1000 is acceptable. Otherwise, a blunder is suspected, and the entire procedure may need to be repeated if the blunder cannot be found.

If the error ratio is acceptable, then you can proceed to close the traverse by distributing the total error amongst the various station locations. In this example, point A' must be brought to the north and west to effect closure. Clearly northings need to be increased, southings need to be decreased. Also, eastings need to be decreased and westings need to be increased.

Thus we need some way of (a) distributing latitude closure among northings (a latitude that is positive) and southings (a latitude that is negative), and (b) distributing departure closure among easting (a positive departure) and westings (a negative departure).

We deal with the orthogonal components of each traverse leg separately. All corrections, say to latitudes of a traverse leg, are computed proportional to the length of the leg. For example, consider segment BC, which has a segment length of 610 m on a total traverse length of 2466 m), an uncorrected latitude of -153.70 (a southing) and an uncorrected departure of +590.78 (an easting).

latitude corr. for BC = (closure in latitude / total length ) x length of segment BC
latitude corr. for BC = 0.71 / 2466 x 600 = 0.18 m

This value is subtracted from the latitude, which means the absolute value is reduced by the stated amount.

For corrections to departure, use

departure corr. for BC = (closure in departure / total length) x length of segment BC

departure corr. for BC = 0.53 / 2466 x 610 = 0.13

The new, corrected latitude is thus -153.52 (a southing) and the corrected departure is +590.65 (an easting) (see the table above for the details).

As a final check on corrections, the corrected latitudes and departures should sume to zero. These adjustments cause slight changes in the bearings of traverse segments, since latitude and departure are the orthogonal components of the travers bearing.

Plotting traverse data on the map

Clearly we could plot our polygon to scale using the measured angles and segment lengths. However, most protrators are not accurate enough for this purpose. The usual procedure is the plot by coordinates (i.e. latitudes and departures).

1. Plot the first leg AB to a convenient scale and with convenient orientation on the base map. AB is plotted by first choosing a location for A, then drawing a N-S and E-W line through A, measure the orthogonal components of B along these coordinate axes and then plot B. Before this is done, one must consider carefully what else must go on the map. One should be sure that the chosen scale will allow all the relevant control points and details to be displayed on the map.
2. Plotting C is done from the same origin at A. We do not need a new coordinate origin at B. Simply find the total departure of C (i.e. dep. B + dep. C), and the total latitude of C (i.e. lat. B + lat. C). Note: these are signed sums, not unsigned. As a check, the diagonal distance back to A can be checked by the Pythagorean formula.
3. From the reduction of the stadia rod data (provided that an initial backsight was made on a vertical control point) the absolute elevations of traverse stations can be pencilled in as the start of elevation control.

Surveying with a Transit Compass

Using a transit compass is very similar in principle to using a theodoite, but the level of accuracy is lower. In general, you proceed as follows:

• Set the magnetic declination. Nominal value in the Kananaskis area is 15.5^o E.

• Clean up the mirror and window sight with a soft cloth. Avoid paper towels.

• Most accurate bearings are obtained by using the compass in 'prismatic' mode. This involves positioning the mirror at 45^o angle with respect to compass body and aligning the object in question with both the long sight mark and the line scribed in sighting window. For elevation sights, use the long sight in a roughly vertical position and the short sight on top of mirror.

• Once alignment is approx. correct, bring the instrument to level by observing the round level in the mirror. Double check alignment and level.

• Read black not white end of compass needle as a three-digit, whole compass bearing.

• Repeat reading for best accuracy, then average. Readings should agree to within a degree but greater accuracy is usually not possible.

• Use the built-in inclinometer to sight on pole (or survey partner) at eye height . Use either percent or degrees but be consistent.

• Tape distance between stations and repeat the previous steps as needed.

• Reduction of data is identical to that of the theodolite traverse.