Question 1

Curve designation in surveying – standard definition used in practice By what is the designation of a (horizontal) curve commonly defined in classical surveying practice?

Accepted Answer

Introduction / Context:Horizontal curves are often specified by their degree of curve in roadway and railway work. While curvature and radius are fundamental properties, field-friendly definitions are historically preferred. This question asks which definition is used for the designation in classical (particularly metric/Indian) practice.Given Data / Assumptions:Degree of curve is a conventional measure related to radius.In many systems, the degree of curve is linked to a standard arc length (e.g., 30 m in metric practice).Alternative chord definitions are also used in some regions, but the question targets the classical arc-based definition.Concept / Approach:In the arc-based system, the degree of curve is the angle subtended at the center by an arc of specified standard length. This provides a direct and uniform relationship between degree and radius: larger degree corresponds to smaller radius. Although some manuals (notably in the U.S.) use the chord-based definition (angle subtended by a standard chord), the arc definition is the conventional one cited in many surveying syllabi and texts.Step-by-Step Solution:Select the standard length L (e.g., 30 m in metric).Define degree D as the central angle subtended by arc length L.Relate D and R via L = (π/180) * R * D for D in degrees.Hence, curve designation is by the angle subtended by a specified arc length.Verification / Alternative check:Worked examples equate degree of curve and radius through the arc formula; tables list R for various D assuming the standard arc length.Why Other Options Are Wrong:Chord of any length: ambiguous; the standard uses a specified arc or chord length.Radius: while fundamental, many field tables and instruments rely on degree rather than directly quoting radius.Curvature: mathematically valid (1/R) but not the traditional designation in field notes.Common Pitfalls:Mixing arc-based and chord-based systems; forgetting to use the correct standard length when converting between D and R.Final Answer:Angle subtended by an arc of specified length

Question 2

Plane table alignment – effect of cross-tilt on parallelism of line of sight and fiducial edge If the plane table is not horizontal in the direction at right angles to the alidade, the line of sight will be parallel to the fiducial edge only for whi…

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Introduction / Context:With the plane table, the alidade's fiducial edge is intended to represent the line of sight when the board is correctly leveled. However, cross-tilt (tilt at right angles to the alidade) disturbs this equivalence. Understanding when the sight line still matches the drawn ray helps avoid systematic plotting errors in hilly terrain or windy conditions.Given Data / Assumptions:Board is tilted about an axis perpendicular to the alidade.Alidade edge is used to plot rays directly on the sheet.Sights can be horizontal or inclined.Concept / Approach:When the board is perfectly horizontal, the line of sight defined by the alidade is parallel to the fiducial edge for any sight. If the board has cross-tilt, the line of sight will deviate relative to the plane of the board for inclined targets, breaking the intended parallelism. Only for truly horizontal sights does the projection remain parallel to the fiducial edge despite the cross-tilt, because the vertical component that would project differently is zero.Step-by-Step Solution:Assume a small tilt about an axis perpendicular to the alidade.For an inclined line of sight, the 3D ray does not lie in a plane parallel to the board; projected direction on the sheet differs from the fiducial edge.For a horizontal line of sight, the ray direction remains parallel to the board's plane, preserving parallelism with the fiducial edge.Therefore, parallelism holds only for horizontal sights under cross-tilt.Verification / Alternative check:A simple model using vectors shows that the component normal to the board introduced by tilt alters projected direction for inclined rays but becomes zero for horizontal rays, confirming the conclusion.Why Other Options Are Wrong:Inclined upward or downward: both create nonzero vertical components whose projections are altered by the cross-tilt.None of these: incorrect because horizontal sights are an exception where the equivalence still holds.Common Pitfalls:Assuming rough levelling is sufficient for steep sights; forgetting to re-level the board after moving; using the alidade as if the board were perfectly horizontal in windy or uneven ground conditions.Final Answer:Horizontal sights

Question 3

Terminology of curve setting – name for a chord shorter than the peg interval In laying out a curve with standard peg (stake) spacing, the chord that is smaller than the peg interval is referred to as:

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Introduction / Context:During field curve setting, stakes are usually placed at equal chainages (peg interval), creating equal standard chords. However, near the beginning or end of a curve—or where the geometry demands—one or more chords may be smaller than the regular interval. The correct term for such a chord is part of standard curve-setting vocabulary.Given Data / Assumptions:There exists a standard peg (stake) spacing along the curve.One chord is shorter than this standard spacing.Nomenclature follows conventional highway/surveying practice.Concept / Approach:The chord equal to the peg interval is termed the normal or standard chord. Any chord less than this standard length is called a sub-chord. Sub-chords commonly occur at the start (first chord) and end (last chord) of a curve to make the layout exactly fit the required tangent points.Step-by-Step Solution:Define normal chord = peg interval.Identify a chord shorter than normal → classify as sub-chord.Use sub-chords to close small residual gaps at curve ends.Adjust deflection angles for sub-chords proportionally to their chord lengths.Verification / Alternative check:Most curve-setting tables and deflection angle worksheets include a column for sub-chords with corresponding scaled deflections, confirming standard usage.Why Other Options Are Wrong:Small chord/short chord: informal phrases, not standard technical terms.Normal chord: equals peg interval, the opposite of what is described.Common Pitfalls:Forgetting to scale deflection for sub-chords; mixing up sub-chord with sub-tense or sub-tangent; using full deflection for a reduced chord leading to setting errors.Final Answer:Sub-chord

Question 4

Levelling staff graduations – counting the smallest divisions per metre On a standard levelling staff used in engineering surveys, how many subdivisions are there per metre length?

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Introduction / Context:Levelling staffs for general engineering surveys are typically metric with bold decimetre markings and centimetre subdivisions. Reading and recording staff values correctly depends on recognizing the scale of these graduations. This question asks you to identify the number of subdivisions per metre on a conventional staff.Given Data / Assumptions:Standard metric staves are considered (E-type or similar).Smallest routine graduation is 1 cm (0.01 m).We count the number of such subdivisions within 1 metre.Concept / Approach:If the smallest marked subdivision is one centimetre, each metre contains 100 equal parts. The large black–red patterning aids quick decimetre recognition, but the fine reading is at 1 cm. Vernier attachments may provide millimetre interpolation in precise levelling, yet the basic staff subdivision count remains 100 per metre.Step-by-Step Solution:Identify smallest graduation = 0.01 m.Compute number per metre = 1.00 / 0.01 = 100.Hence, 100 subdivisions per metre.Note: verniers allow readings to 1 mm but do not change base subdivisions.Verification / Alternative check:Manufacturers’ catalogues for metric levelling staffs list centimetre divisions with decimetre blocks and metre numerals, confirming 100 subdivisions per metre.Why Other Options Are Wrong:200, 500, 1000 would imply 5 mm, 2 mm, or 1 mm base divisions respectively; those are not standard base subdivisions for typical engineering staves.Common Pitfalls:Confusing basic staff graduations with vernier resolution; misreading inverted figures on E-type staffs leading to transcription errors.Final Answer:100

Question 5

Transition–circular junction geometry – offset from tangent in terms of shift For a transition curve joining a circular curve, the perpendicular offset from the tangent to the junction point (transition–circular junction) is equal to which multiple …

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Introduction / Context:Providing a transition curve between a tangent and a circular arc requires moving the circular arc slightly inward. The lateral movement is called the shift S. Field setting frequently uses simple relationships to compute offsets at key points such as the transition–circular junction. This question asks for the factor that relates the perpendicular offset from the tangent at the junction to the shift S.Given Data / Assumptions:Standard transition curve (e.g., cubic parabola/clothoid) of length L joins a circular curve of radius R.Shift S is defined as S = L^2 / (24 * R) for one transition end.Perpendicular offset y from the tangent to a point on the transition at a distance along the curve ℓ is y = (ℓ^3) / (6 * R * L); at the junction, ℓ = L.Concept / Approach:At the junction point (where the transition meets the circular arc), substitute ℓ = L into the offset expression to obtain y_junction = L^2 / (6 * R). Compare this with the definition of shift S = L^2 / (24 * R). The ratio y_junction / S then equals (L^2 / (6R)) / (L^2 / (24R)) = 4. Therefore, the perpendicular offset from the tangent to the junction point equals four times the shift.Step-by-Step Solution:Given S = L^2 / (24 * R).At junction: y_junction = L^2 / (6 * R).Compute ratio: y_junction / S = (L^2 / (6R)) / (L^2 / (24R)) = 4.Hence, y_junction = 4 * S.Verification / Alternative check:Design examples in highway engineering texts consistently derive the same relationship for standard cubic-parabola transitions; numerical checks with practical L and R values produce offsets that are exactly 4S at the junction.Why Other Options Are Wrong:Shift, twice the shift, thrice the shift: each underestimates the true junction offset, leading to an incorrect placement of the circular arc and subsequent misfit of tangency conditions.Common Pitfalls:Confusing the offset at the junction with the maximum offset within the transition; using the wrong definition of S (per end vs both ends) and mixing units for L and R.Final Answer:Four times the shift

Question 6

Surveying telescope optics – objective and diaphragm placement: Which statements correctly describe the internal arrangement of a typical surveying telescope (diaphragm location and objective lens components)?

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Introduction / Context:Surveying telescopes (in levels, theodolites, and total stations) use a compound objective and a reticle (cross-hair diaphragm) to provide a sharp, parallax-free image for precise readings on staffs and targets. Understanding where the diaphragm sits and how the objective is built improves field adjustments and troubleshooting optical issues.Given Data / Assumptions:The instrument is a Keplerian telescope with an objective that forms a real image.A cross-hair diaphragm must lie at the image plane for parallax-free viewing.Achromatic correction is achieved using crown and flint glass elements.Concept / Approach:To eliminate parallax, the diaphragm is placed at the common focal plane of the objective–eyepiece system. Practically, this lies between objective and eyepiece, closer to the eyepiece so both the image and cross hairs are in focus together. Achromats pair a crown-glass double-convex element with a flint-glass concavo-convex (meniscus) element to reduce chromatic and spherical aberrations, yielding a sharp, flat field near the optical axis for accurate stadia and levelling work.Step-by-Step Solution:Identify reticle location: between objective and eyepiece at the focal (image) plane, typically nearer the eyepiece → statements about diaphragm placement are relevant.Recall objective design: crown glass (lower dispersion) as a double-convex front element aids positive power and light gathering.Pair with flint glass (higher dispersion) as a convexo-concave element to cancel color fringing and flatten the field.Thus, each listed component/placement is a standard feature; collectively they describe the instrument correctly.Verification / Alternative check:Manufacturer exploded diagrams show the cross-hair ring just ahead of the eyepiece lens group, and achromatic objectives combining crown and flint elements with opposite dispersions to minimize secondary spectrum.Why Other Options Are Wrong:Each individual statement is correct but incomplete alone; only the combined choice fully captures the internal arrangement.Common Pitfalls:Confusing “line of sight” with the precise “line of collimation”; placing the diaphragm away from the image plane causing parallax; assuming a single-element objective is adequate for precision work.Final Answer:All of the above

Question 7

Contours and terrain interpretation: Contour lines of different elevations can meet and merge into a single line only under which special terrain condition?

Accepted Answer

Introduction / Context:Contours are the backbone of topographic interpretation in civil engineering. They represent lines of equal elevation and normally do not cross or unite. Recognizing the single exception helps avoid mapping mistakes and improves terrain reading for route location, drainage, and site planning.Given Data / Assumptions:Contours are drawn at uniform vertical intervals (e.g., 1 m, 5 m).Each contour corresponds to a unique elevation.We consider ideal, correctly drafted sheets without drafting errors.Concept / Approach:Different elevation contours cannot meet because a point cannot simultaneously have two elevations. However, at a near-vertical or truly vertical face, the horizontal distance between successive elevation levels approaches zero. On the map, successive contours then coincide, appearing to merge into one line. This is the only legitimate case of contour “meeting.” Saddles, ridges, and hilltops show contours that approach, loop, or form characteristic shapes but do not unite into a single line.Step-by-Step Solution:Recall rule: contours of different values never cross or merge under normal slopes.Consider a vertical cliff: horizontal separation between elevations becomes zero → contours coincide.Check other features: saddles show hourglass shapes; watersheds show V-shaped patterns pointing downslope; hilltops have closed concentric loops.Thus, only a vertical cliff permits apparent uniting of different elevation contours.Verification / Alternative check:Field checks on cliff faces show nearly vertical rock walls where plan distances between elevation bands are negligible, matching the map behavior.Why Other Options Are Wrong:Saddle: contours pinch but remain distinct.Watershed line: contours form V-patterns but do not merge.Hill top: contours close into separate, nested loops with decreasing area.Common Pitfalls:Misreading tightly spaced contours as crossing; mislabeling depressions as hilltops; ignoring index contour elevation labels.Final Answer:A vertical cliff (nearly vertical face)

Question 8

Triangulation quality – well-conditioned triangle: In primary/secondary triangulation, a triangle is considered well conditioned if no angle is less than what minimum value?

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Introduction / Context:The accuracy of computed sides and angles in triangulation depends strongly on the geometry of the triangles observed. “Well-conditioned” triangles minimize propagation of observational errors. A common rule-of-thumb sets bounds on the smallest and largest permissible angles.Given Data / Assumptions:Angle observations are affected by small systematic and random errors.Error magnification increases in very acute or very obtuse triangles.We target robust geometry rather than perfectly equilateral shapes.Concept / Approach:Classical practice recommends triangles with angles roughly between 30° and 120°. The lower bound of 30° avoids excessive sensitivity of computed lengths to small angle errors, while the upper bound follows from the angle sum of a triangle. Equilateral (60° each) is ideal, but rarely achievable in the field; ensuring no angle is less than 30° maintains good conditioning for network adjustment.Step-by-Step Solution:Define “well-conditioned”: geometry that limits error amplification.Apply rule: 30° ≤ angles ≤ 120°.Identify the minimum acceptable angle: 30°.Therefore, select 30° as the correct threshold.Verification / Alternative check:Condition numbers and variance–covariance analysis of angle–side computations confirm that very acute angles yield large standard deviations in derived lengths.Why Other Options Are Wrong:20°: too acute, poor conditioning.45° or 60°: desirable but unnecessarily strict; many workable triangles have smaller angles than these.Common Pitfalls:Accepting long skinny triangles for convenience; forgetting that angle misclosures increase with poor geometry; ignoring station intervisibility constraints that can be mitigated by alternate station placement.Final Answer:30°

Question 9

Tacheometry – inclined sights correction: For horizontal distance by stadia with line of sight inclined at angle θ (staff vertical), the standard horizontal-sight formula can be adapted by multiplying which constants?

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Introduction / Context:In stadia (tacheometric) surveying with a vertical staff, the familiar horizontal-sight relation is D = k * s + c, where D is horizontal distance, s is staff intercept, k is the multiplying constant, and c is the additive constant. When sights are inclined by angle θ, appropriate trigonometric factors modify these constants to recover horizontal distance directly.Given Data / Assumptions:Staff is held vertical; line of sight makes angle θ with the horizontal.k and c are instrument constants determined by focusing system and stadia interval.We seek the formula for horizontal distance (not slope distance).Concept / Approach:For inclined sights with vertical staff, the slope-distance relation is S = k * s + c. The horizontal component is D = S * cos θ, but the staff intercept seen by the inclined line of sight also projects with a cos θ factor. Combining these effects yields the well-known result D = k * s * cos^2 θ + c * cos θ, which corresponds to multiplying k by cos^2 θ and c by cos θ in the horizontal-sight formula.Step-by-Step Solution:Start from slope distance: S = k * s + c.Project to horizontal: D = S * cos θ = (k * s + c) * cos θ.Account for vertical staff intercept under inclination: effective intercept contributing to S already scales with cos θ, producing D = k * s * cos^2 θ + c * cos θ.Hence, adapt constants: k → k * cos^2 θ; c → c * cos θ.Verification / Alternative check:Textbook derivations using geometry of similar triangles for the stadia diaphragm with vertical staff confirm the cos^2 θ and cos θ factors for horizontal distance.Why Other Options Are Wrong:sin θ or sin^2 θ factors apply to vertical component computations, not horizontal distance.Using a single cos θ for both constants underestimates horizontal distance.Applying cos^2 θ to both constants overcorrects the additive part.Common Pitfalls:Confusing formulas for staff held normal to the line of sight; forgetting to distinguish slope distance from horizontal distance; mixing up the roles of k and c.Final Answer:Multiply the multiplying constant by cos^2 θ and the additive constant by cos θ

Question 10

Bearings terminology for a line AB: For two stations A and B, which statements about the fore bearing and back bearing of line AB are correct?

Accepted Answer

Introduction / Context:Consistent use of fore and back bearings is essential in traverse computations and checks. Knowing their relationship helps detect local attraction and arithmetic errors during fieldwork and plotting.Given Data / Assumptions:A reference meridian (true, magnetic, or grid) is fixed for both directions.Bearings are measured by the same system (whole-circle or quadrantal).Line AB is observed in both forward and reverse directions.Concept / Approach:The fore bearing (FB) is the direction of AB measured at A. The back bearing (BB) is the direction of the same line measured at B toward A. When using the same meridian and system, BB = FB ± 180°, adjusting to the 0°–360° or appropriate quadrantal range. This identity underpins the local-attraction test by comparing observed FB and computed BB.Step-by-Step Solution:Define FB: bearing of A→B taken at A.Define BB: bearing of B→A (i.e., BA) taken at B.Relate them: BB = FB ± 180° (normalize into range).Therefore, all listed statements are jointly correct.Verification / Alternative check:Traverse notes routinely compute a check value by FB − BB ≈ ±180°. Significant deviation flags local attraction or recording errors.Why Other Options Are Wrong:Any single statement alone is incomplete; the inclusive option reflects complete practice.Common Pitfalls:Mixing whole-circle with quadrantal bearings; forgetting to normalize to 0°–360°; using different meridians for FB and BB.Final Answer:All of the above

Question 11

Rankine’s method – deflection angle per chord: According to Rankine’s method of tangential (deflection) angles, the deflection angle in minutes for a sub-chord is obtained by multiplying the chord length by which quantity?

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Introduction / Context:Setting out circular curves by Rankine’s method uses tangential (deflection) angles from the tangent. The convenient field rule links the size of each deflection to the chord length and the degree of curve, enabling quick computation without repeatedly using radius values.Given Data / Assumptions:D = degree of curve (as per the adopted definition for the project).c = chosen chord length (sub-chord or full chord).Angles are handled in minutes for easy mental multiplication.Concept / Approach:For Rankine’s method, the tangential (deflection) angle to any chord is proportional to its length. Using the standard unit system, the deflection in minutes is obtained by multiplying the chord length by the degree of curve (with appropriate scaling if the degree is defined per a standard chord rather than an arc). This linear rule streamlines field computation and accommodates variable sub-chords near the curve ends.Step-by-Step Solution:Adopt a degree-of-curve definition (e.g., based on a standard chord).Compute deflection for a chord c: deflection (minutes) ∝ D * c.Apply proportion consistently for each successive chord from the tangent point.Thus, multiply chord length by the degree of curve to obtain the deflection angle in minutes.Verification / Alternative check:Derivations from R = K / D with K constant (based on the chosen definition) lead to linear chord–deflection relations, validating the field rule used in Rankine’s setting-out tables.Why Other Options Are Wrong:Square or inverse relationships do not match the linear geometry of deflection with chord length for small angles in Rankine’s method.“None of these” ignores the accepted field rule.Common Pitfalls:Mixing definitions of D (per arc vs per chord); forgetting scaling when sub-chords differ from standard length; accumulating rounding errors without periodic checks.Final Answer:The degree of the curve

Question 12

Chaining on slopes – choice of direction: When measuring with a chain or tape on sloping ground, along which gradient is the work generally easier and more controllable?

Accepted Answer

Introduction / Context:On sloping ground, surveyors often use the stepping method to reduce a sloped line into manageable near-horizontal segments. Practical handling of the chain, alignment, tension, and footing differs when working uphill versus downhill, influencing accuracy and speed.Given Data / Assumptions:Tape or chain is handled by two persons with pegs/arrows.The goal is to keep each segment close to horizontal to minimize slope error.Terrain can be uneven, with risk of slipping and loss of tension control.Concept / Approach:Working along the falling gradient generally allows the head chainman to sight and place marks where footing is visible ahead, while gravity helps keep the tape taut with less effort. The follower can brace above, improving stability. Shorter steps are still needed as slope increases, but the overall control of tape sag and alignment tends to be easier downhill than forcing the tape uphill against gravity, which can cause greater sag and fatigue.Step-by-Step Solution:Assess slope direction and choose downhill sequence where feasible.Use short steps on steeper gradients to maintain near-horizontal segments.Keep proper tension using gravity assist; check alignment carefully at each step.Record cumulative horizontal distance after each set of steps for the total measurement.Verification / Alternative check:Field manuals note that while either direction can be used, many crews prefer downhill chaining for control and speed, provided safety is managed and steps are shortened as slopes increase.Why Other Options Are Wrong:Uphill chaining often increases effort and sag control problems.“Equally convenient” ignores practical differences in handling and fatigue.“All of the above” cannot be true because the options are mutually exclusive.Common Pitfalls:Taking overly long steps on steep slopes; neglecting to keep the tape level; ignoring safety when working downhill on loose ground.Final Answer:Along the falling (down) gradient

Question 13

Choice of tacheometric method: Subtense tacheometry (using a fixed-length subtense bar or target) is generally preferred under which ground conditions?

Accepted Answer

Introduction / Context:Tacheometry estimates distances and elevations without chaining. The subtense method uses a target or bar of known length subtending an angle at the instrument; distance is computed from the measured angle. This approach is especially valuable where physical access to the ground line is difficult.Given Data / Assumptions:A fixed-length subtense bar or distinctive target is available.Instrument can measure angles accurately (theodolite/EDM-less setup).Lines of sight may be obstructed by relief, vegetation, or rough footing.Concept / Approach:Distance by subtense follows D = L / (2 * tan(θ/2)), where L is the known target length and θ is the subtended angle. Because no chaining is required along the ground, this technique shines on steep or rugged slopes and across ravines—typical of mountainous areas. In flat, open terrain, chaining or EDM is faster and more accurate; in deserts, long straight lines favor EDM or tape with supports rather than repeated subtense setups.Step-by-Step Solution:Set the subtense bar of known length L at the remote point.Measure the included angle θ subtended at the instrument.Compute D using D = L / (2 * tan(θ/2)) (or equivalent calibrated relations).Use vertical angle if required to obtain elevation differences.Verification / Alternative check:Comparisons with chained or EDM distances on sample lines typically show good agreement for moderate lengths when angles are observed carefully and targets are levelled/plumbed.Why Other Options Are Wrong:Flat terrain: chaining/EDM is simpler and faster.Undulating: workable, but the method is most advantageous in truly rugged terrain.Deserts: visibility is good; EDM and tapes usually outperform subtense for long, straight shots.Common Pitfalls:Mis-centring of the bar; bar not perpendicular to the line of sight; poor angle reading on shimmering hot days; neglecting vertical angle corrections for height differences.Final Answer:Mountainous (hilly) terrain with difficult access

Question 14

Angular measurement accuracy in theodolite work: If you must observe an included angle with accuracy better than what a single vernier reading provides, which observing method should you prefer?

Accepted Answer

Introduction / Context:The least count of a theodolite's vernier or digital display limits the precision of a single angle reading. Field procedures such as repetition and reiteration help surpass this limit by averaging multiple observations and cancelling systematic errors. The question asks which method directly improves the precision of one included angle beyond a single vernier read.Given Data / Assumptions:You need a single included angle with accuracy finer than one vernier read.Instrument is properly centered and leveled.Time allows multiple pointings/turns.Concept / Approach:The repetition method measures the same included angle multiple times without resetting the circle to zero, successively adding the angle on the circle and then dividing the accumulated reading by the number of repetitions. Random pointing and reading errors are reduced roughly with 1/sqrt(n), and certain index errors cancel when face-left and face-right sets are combined.Step-by-Step Solution:Set on the first line; zero or note initial reading.Turn to the second line; clamp and read angle.Without unclamping the circle, turn back to the first line and repeat the process k times so the circle carries k*angle.Compute mean angle = accumulated / k; repeat on the other face and average both faces.Verification / Alternative check:Reiteration closes a horizon by observing several angles around a station and adjusting; it is best for networks, not a single angle. Repetition targets one angle's precision directly.Why Other Options Are Wrong:Reiteration: Excellent for traverses and angular networks, not optimal for a single included angle.Double observations (one face only): Lacks face reversal and accumulation benefits.Exactness: Not a defined field method.Common Pitfalls:Poor clamping or not recording face-left/face-right sets; both degrade the expected precision gain.Final Answer:Repetition

Question 15

Error theory in chaining and traversing: Accidental (compensating) errors associated with a measured length L are generally proportional to which function of L?

Accepted Answer

Introduction / Context:In surveying measurements, accidental (random or compensating) errors arise from small, unpredictable causes such as slight pointing errors, minor tape misalignment, or reading scatter. Understanding how these random errors grow with the total length L is essential for estimating probable accuracy and for planning checks and redundancies.Given Data / Assumptions:Error sources are random and unbiased (zero-mean).Length L is made up of many similar segments or observations.Systematic errors have been corrected or are negligible in this context.Concept / Approach:By the theory of random errors, the standard deviation of a sum of many independent, identically distributed errors grows with the square root of the number of observations. If the total measured length L is built up from segments of similar length, the number of segments n is proportional to L, and hence the standard deviation (accidental error) grows as sqrt(n) ∝ sqrt(L). Thus accidental (compensating) errors scale as sqrt(L), not linearly with L.Step-by-Step Solution:Model total length as L = n * l_seg.Assume random segment errors with variance sigma^2; total variance = n * sigma^2.Standard deviation of total = sqrt(n) * sigma ∝ sqrt(L).Therefore accidental error ∝ sqrt(L).Verification / Alternative check:Traverse error of closure often follows a root-mean-square behavior, and practical specifications commonly quote tolerances proportional to sqrt(perimeter).Why Other Options Are Wrong:L: Linear growth suggests systematic bias, not random error.1/L: Implies larger lengths reduce random error, which is incorrect.L^2: Unrealistically rapid growth; not supported by error propagation theory.Constant: Ignores accumulation over multiple segments.Common Pitfalls:Confusing systematic scale/bias errors (often ∝ L) with accidental errors (∝ sqrt(L)).Final Answer:sqrt(L)

Question 16

Improving a difficult linear traverse around a large curved obstacle (e.g., a lake): When long legs are hard to obtain, which measures enhance traverse accuracy?

Accepted Answer

Introduction / Context:Traversing around a large lake or similar obstacle often forces short, awkward legs that can degrade accuracy. Good practice combines redundancy, careful measurement, and auxiliary geometry to maintain reliable coordinates and closure.Given Data / Assumptions:Obstacle prevents long, straight legs.Angles and distances can be observed, though legs are short.Subsidiary lines are feasible on nearby ground.Concept / Approach:Short legs can be used if measurements are repeated (angles and distances) to reduce random errors through averaging. A subsidiary or tie traverse can span around the obstacle or connect distant control to simulate a long chord, improving geometric strength and providing checks. Together these practices enhance precision and reveal blunders.Step-by-Step Solution:Adopt multiple sets of angle observations (face-left/right) and repeated EDM/tape distances.Introduce a subsidiary traverse to create a longer tie where direct long legs are impossible.Use least-squares or adjusted closures to distribute residuals and test for outliers.Reconcile with control points to verify positional accuracy.Verification / Alternative check:Redundant observations increase degrees of freedom; statistical adjustments (e.g., Bowditch or least squares) then yield improved, defensible results.Why Other Options Are Wrong:Each single action helps, but the best practice is the combination, hence “All of the above”.Common Pitfalls:Relying on a single short-leg traverse without redundancy; lack of checks conceals systematic errors.Final Answer:All of the above

Question 17

Plane-table resection (three-point problem) — correct sequence of operations:  Rough orientation of the plane table  The three rays form a small triangle of error  Draw back rays through the three plotted control points  Select a point within the tr…

Accepted Answer

Introduction / Context:Three-point resection fixes an unknown plane-table station by sighting three well-defined points already plotted on the sheet. Practical solutions (e.g., Lehmann’s method) refine an initial orientation until the small triangle of error collapses to a point.Given Data / Assumptions:Three control points are clearly visible and plotted.Plane table can be rotated about a trial point.Equal angular corrections concept is used to remove the triangle of error.Concept / Approach:After rough orientation, rays are drawn back from the plotted points toward the ground objects. Imperfect orientation creates a small triangle of error where the rays fail to meet. Choosing a trial point within this triangle and applying equal rotations aligns plotted and ground directions; refining this removes the triangle and fixes the true station.Step-by-Step Solution:Perform rough orientation (align approximately with previous work).From plotted control points, draw back rays toward the observed objects.Note the triangle of error formed by non-concurrent rays.Pick a point in the triangle such that each ray would need equal rotation; rotate the board accordingly.After adjustment, the three rays concur, giving the station position.Verification / Alternative check:Good geometry (well-spread controls) yields a tiny triangle and rapid convergence; poor geometry causes instability and large corrections.Why Other Options Are Wrong:They mix the order; the triangle appears only after rays are drawn, and choosing the trial point comes after recognizing the triangle.Common Pitfalls:Controls nearly collinear or acute geometry; these enlarge the triangle and degrade accuracy.Final Answer:1, 3, 2, 4, 5

Question 18

Small-angle facts and error growth in traverses: Which of the following statements are correct regarding angular/linear relations and error propagation?

Accepted Answer

Introduction / Context:Survey accuracy depends on both angular and linear measurements. Small-angle approximations and empirical error growth rules guide specifications, checking, and adjustment strategies in traversing and triangulation.Given Data / Assumptions:Using standard small-angle relations in radians.Random errors assumed independent and unbiased.Practical field conditions with conventional instruments.Concept / Approach:One radian equals about 57.3 degrees, hence 1 degree corresponds to ~1/57 rad. One arc-second equals about 1/206,265 rad, giving the 1:206,300 displacement ratio for small deflections. Random angular misclosures grow with sqrt(n) where n is the number of stations, while linear random errors tend to scale with total length measured, reflecting accumulation of many small unbiased contributions.Step-by-Step Solution:Translate degrees/seconds to radian-based displacement ratios.Relate random error accumulation to sqrt(n) growth (root-sum-square).Recognize linear error scaling with total measured length.Synthesize: each statement A–D is a standard rule of thumb; thus E is correct.Verification / Alternative check:Bowditch (compass) rule and least-squares theory corroborate sqrt(n) angular propagation and length-proportional linear behavior in typical field work.Why Other Options Are Wrong:Any single statement alone is incomplete; the bundle of all four best represents accepted surveying practice.Common Pitfalls:Confusing systematic scale errors with random errors; mixing degree–radian conversions.Final Answer:All of the above

Question 19

Chain surveying — what is the essential purpose of providing check lines (proof lines) in a chain survey of a small area?

Accepted Answer

Introduction / Context:Chain surveying relies on a framework of triangles whose sides are chain lines. Errors can creep in from chaining, ranging, or offsetting. Check (proof) lines provide independent measurements that validate the plotted framework and reveal blunders before plotting is finalized.Given Data / Assumptions:Small, relatively open area suitable for chain surveying.Well-conditioned triangles are used as the main framework.Check lines can be measured between non-adjacent points.Concept / Approach:A check line is measured across a triangle (or between distant points) and compared with its plotted length derived from the main measurements. Agreement within tolerance confirms accuracy; disagreement highlights mistakes in chaining, ranging, or plotting so they can be corrected immediately.Step-by-Step Solution:Lay out the main triangle sides and record lengths carefully.Measure an independent check line that spans across the figure.Plot and compare the measured versus computed length/position.If misfit exceeds tolerance, re-measure affected lines or offsets.Verification / Alternative check:Multiple check lines in different parts of the plan ensure robustness; agreement indicates no gross errors remain.Why Other Options Are Wrong:Plotting chain lines/offsets: Aided by field work but not the prime role of check lines.Increasing out-turn: Speed is secondary; the principal purpose is quality control.Common Pitfalls:Omitting check lines in tight schedules; this often results in distorted plots and costly rework.Final Answer:To indicate and verify the accuracy of the survey work (independent check)

Question 20

Traverse terminology — the distance between two terminal points obtained from a subsidiary traverse run between them is commonly called:

Accepted Answer

Introduction / Context:When direct measurement of a long line is impractical, surveyors often run a subsidiary (tie) traverse between the terminal points to compute the straight-line distance. The specific term for this computed connection clarifies communication in field notes and reports.Given Data / Assumptions:Two terminal points require a reliable connecting distance.A subsidiary traverse with checks is feasible.Computed distance substitutes for a direct measure.Concept / Approach:A traverse base is the straight-line distance between terminals as determined from a subsidiary traverse. It functions like a base line for subsequent work or as a control check on the main traverse. While "base" is generic, "traverse base" specifies that it was obtained via a traverse solution rather than direct chaining or EDM.Step-by-Step Solution:Run a closed or well-checked subsidiary traverse between the terminals.Adjust angles/distances and compute the straight-line chord between the terminals.Adopt this computed value as the traverse base.Use it to check or control the main survey as needed.Verification / Alternative check:Agreement with an eventual direct measurement or independent tie affirms the reliability of the traverse base.Why Other Options Are Wrong:Traverse leg: Refers to a single side of a traverse, not the computed terminal distance.A base: Too general; lacks the traverse origin specificity.All of the above: Only one term is precise.Common Pitfalls:Not distinguishing between a direct base line and a traverse-derived base; documentation should state the method.Final Answer:Traverse base

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