BTEB Amin Survey Exam cheat sheet

Surveying is the art of determining relative positions of points on, above, or beneath the earth's surface; plane surveying ignores earth curvature and is valid for areas under about 250 km².

Principles: work from whole to part (fix control first, then detail), and locate a new station by at least two independent measurements from known points.

Chain units: 1 Gunter's chain = 66 ft = 100 links; 1 engineer's chain = 100 ft; 1 link = 0.66 ft = 0.2012 m; 1 m = 1.515 links.

Ranging: direct ranging by eye when both ends are intervisible; indirect ranging (reciprocal) when ends are not intervisible or the line crosses a hill.

Chain corrections: temperature Ct = L·α·(Tm − T0); pull Cp = L(P − P0)/(AE); sag Cs = −(w²l³)/(24P²) per span; slope correction = L(1 − cos θ).

Errors: positive (cumulative) errors arise from chain too long, sag-free pull too great, or slope not corrected; random errors cancel and are called compensating.

Obstacles: for a river, use similar triangles or the sine rule from a subsidiary base; for a building, offset the chain line and re-establish by equal perpendiculars.

Cross-staff, optical square, and prism square set out 90° offsets; the optical square uses two mirrors at 45° and gives a double-reflection right angle.

Field book entries: all measurements in the same units, sketches to scale, offsets recorded from the chain line with left/right indicated; never erase - score out and re-enter.

True bearing = magnetic bearing ± magnetic declination (east declination added, west subtracted); magnetic bearing = true bearing ∓ declination.

Whole-circle bearing (WCB) is measured clockwise from magnetic north, 0°–360°; reduced bearing (RB) is the acute angle from the nearer end of the meridian, 0°–90°.

Interior angle = FB of next line − FB of previous line; if negative add 360°; the sum of interior angles = (2n − 4) × 90°.

Fore bearing − back bearing = 0° if the difference is 0°, or ±180° if the difference is 180°; a difference other than 0° or 180° indicates local attraction.

Local attraction is detected by FB − BB ≠ 180°; correct by adjusting the line free from attraction first, then applying the same correction to all bearings at that station.

Theodolite: telescope transits (flips) about the horizontal axis; the vertical circle reads zenith angles or elevation; face left and face right readings average out collimation error.

Traverse closing error e = √(ΣL² + ΣD²); relative precision = e / perimeter; Bowditch (compass) rule distributes error proportional to leg length; transit rule proportional to latitude/departure.

Latitude = l·cos θ, departure = l·sin θ; ΣL and ΣD must both be zero for a closed traverse; the closing line has length e and bearing atan(ΣD/ΣL).

Angular error of a closed traverse = measured sum − (2n − 4)·90°; distribute equally with opposite sign, or by the least-squares method for precise work.

Reduced level (RL) = height of instrument (HI) − staff reading; HI = RL of benchmark + backsight reading.

Height of Collimation method: one HI per instrument setup, suitable for many intermediate sights; Rise and Fall method checks ΣBS − ΣFS = ΣRise − ΣFall = last RL − first RL.

Arithmetic check: ΣBS − ΣFS = last RL − first RL; also ΣBS − ΣFS = ΣRise − ΣFall; both must agree.

Curvature correction = 0.0785 D² m (D in km); refraction correction = −0.0112 D² m; combined correction = −0.0673 D² m, always subtractive.

Sensitiveness of a level bubble: angular sensitivity α ≈ (d/R)·206265 seconds, where d is bubble movement and R the tube radius.

Reciprocal levelling eliminates refraction, curvature, and collimation error; it is used across wide rivers or valleys.

Contour interval is the vertical distance between successive contours; it is constant on a map, while the horizontal spacing varies with slope.

Characteristics: contours of equal elevation never cross (except at an overhanging cliff), are closed loops or run to the map edge, and are closest where the ground is steepest.

Contour uses: route selection, reservoir capacity by the contour-area method, earthwork estimation, and drainage pattern interpretation (V pointing upstream in valleys).

Plane table parts: tripod, drawing board, alidade (plain or telescopic), plumbing fork with plumb bob, spirit level, and compass for orientation.

Orientation is setting the table so all lines are parallel to their ground counterparts; by backsight (tracing) or by magnetic needle when no suitable backsight exists.

Methods: radiation (from one station, rays to all points), intersection (two stations, no linear measurement), traversing (chain plus plane table), and resection (three-point problem).

Three-point problem: locate the table station from three known points; the Lehmann method uses the triangle of error; Bessel's method solves it by a graphical construction.

Two-point problem: locate a station using two known points plus a compass or a subsidiary station; used when the station is inaccessible.

The alidade's fiducial edge passes through the plotted station; sight lines are drawn along it, so the table must not be rotated after orientation.

Minor instruments: clinometer (slope angle), Abney level (slope and elevation), hand level, box sextant (angles up to 120°), and planimeter (area).

Planimeter: area = M × (final reading − initial reading); the zero circle is the area traced when the roller passes over the pole; set the index to zero before use.

Errors in plane table work: table not level, orientation error, alidade not centred, and the table not truly centred over the station.

Trapezoidal rule: A = d[(O1 + On)/2 + O2 + O3 + … + On−1]; Simpson's rule (odd number of ordinates): A = d/3[(O1 + On) + 4(sum of even ordinates) + 2(sum of odd ordinates)].

Simpson's rule requires an even number of intervals (odd number of ordinates); for an odd number of intervals, apply Simpson's to all but the last and trapezoidal to the last.

Area by coordinates (shoelace): 2A = Σ(xi·yi+1 − xi+1·yi) taken cyclically; the sign gives orientation, magnitude gives area.

Area by triangles: A = ½ab·sin C; by sides, Heron's formula A = √[s(s−a)(s−b)(s−c)] with s = (a+b+c)/2.

Prismoidal rule: V = d/3[A1 + An + 4(A2 + A4 + …) + 2(A3 + A5 + …)]; the prismoidal correction = (d/6)(A1 − A2) for a two-section prismoid.

Trapezoidal volume: V = d[(A1 + An)/2 + A2 + … + An−1]; it overestimates for convex sections, prismoidal is more accurate.

End-area method uses only the end areas; mean-area method uses the average of end areas × length; the prismoidal formula is the standard for earthwork.

Earthwork by the contour-area method: V = Σ[(A1 + A2)/2] × contour interval; used for reservoir capacity.

Cross-section area: for a level section A = h(b + sh); for a three-level section A = ½h(b + s·h) plus side triangles; side slopes s:1.

Setting out transfers design positions from drawings to the ground; horizontal control uses theodolite/total station, vertical control uses levels.

Setting out a building: establish two reference lines from a baseline, set out the first corner by coordinates, then use 3-4-5 right angles or a theodolite to fix the other corners.

Setting out a curve: by offsets from the long chord, by offsets from the tangent, by deflection angles, or by the chord-basis method; radius R = (C/2)/sin(Δ/2).

Simple circular curve: tangent length T = R·tan(Δ/2); length L = R·Δ (radians); external distance E = R[sec(Δ/2) − 1]; mid-ordinate M = R[1 − cos(Δ/2)].

Deflection angle per chord = (c/2R)·206265 seconds; the total deflection to the end of the curve equals Δ/2.

Transition curve: length Ls = V³/(CR) (C ≈ 80 for highways), or by rate of change of centrifugal acceleration; the spiral shifts the circular curve inward by shift S = Ls²/(24R).

Setting out a pipeline or sewer: use a laser level or total station; gradients set by sighting a target at the required fall, or by boning rods.

Setting out on sloping ground: use a level and staff to fix a constant height of collimation, or a clinometer for batter boards.

Checks: measure the diagonals of a set-out rectangle (they must be equal); re-observe the closing angle and compare with the design value.

Field book: bound, numbered pages, entries in hard pencil (2H–4H), no erasures; wrong entries are struck through with a single line and the correct value written above.

Chain survey field book: a sketch of the chain line and offsets to scale, with all measurements in the same unit; offsets from the chain line are recorded left or right.

Levelling field book: columns for station, backsight, intermediate sight, foresight, rise, fall, HI, and RL; arithmetic checks are recorded at the bottom of each page.

Theodolite field book: station, face (left/right), horizontal circle readings, vertical circle readings, and mean values; the mean of face left and face right eliminates collimation error.

Traverse record: station, line, length, fore bearing, back bearing, and a note of local attraction; the closing error is computed on the last line.

Plane table record: plotted sheet with station names, orientation notes, and a separate field book for radiation/intersection observations.

Permanent records: a survey report includes the benchmark list, control coordinates, datum, instrument calibration, and a signed plan.

Digital records: total station and GNSS data are downloaded daily, backed up, and the raw file kept unedited; the processed file is a separate copy.

Legal records: a plan for registration must show the datum, units, area, boundary dimensions, and the surveyor's signature and date.

Scale: representative fraction (RF) = map distance / ground distance; 1:1000 means 1 mm on the map = 1 m on the ground.

A scale is large if the RF is large (1:100), small if the RF is small (1:10,000); a diagonal scale reads to a second decimal place.

Plan versus map: a plan is a large-scale drawing (RF ≥ 1:1000) of a small area; a map is a small-scale drawing of a large area.

Contour plan conventions: contours are brown, water features blue, buildings and roads black, and the contour interval is stated in the legend.

Drawing standards: title block with project name, client, scale, date, drawing number, and surveyor's name; north arrow and legend on every plan.

Professional ethics: a surveyor must not accept work outside competence, must disclose conflicts of interest, and must keep client data confidential.

Boundary surveys: the surveyor reports measurements and discrepancies, cannot give legal title advice, and must record the datum and the method used.

Quality control: close the traverse and level loop, check with independent measurements, and keep calibration certificates for levels and total stations.

Safety and liability: surveyors are liable for negligent misstatement; professional indemnity insurance covers errors and omissions in survey reports.