Question 1

Traverse computation – recovering length from latitude: If the latitude of a traverse leg is known, the length of that leg can be obtained by multiplying the latitude by which trigonometric function of the reduced bearing?

Accepted Answer

Introduction / Context: In traverse calculations, each line is resolved into latitude (northing/southing) and departure (easting/westing). Sometimes, partial information is available, such as the latitude along with the reduced bearing (RB), from which the full line length must be recovered. Given Data / Assumptions: Latitude L_lat = length * cos(RB). Departure D_dep = length * sin(RB) (not directly used here). Reduced bearing is measured from the north or south towards east or west within 0° to 90°. Concept / Approach: From the fundamental relation L_lat = length * cos(RB), rearrange to length = L_lat / cos(RB) = L_lat * sec(RB). Thus, multiplying the latitude by the secant of the reduced bearing yields the traverse leg length. This is useful in missing data problems and in reconstruction of traverse elements from partial records. Step-by-Step Solution: Write the basic projection formula: latitude = length * cos(RB).Solve for length: length = latitude / cos(RB).Recognize 1 / cos(RB) = sec(RB).Therefore, length = latitude * sec(RB). Verification / Alternative check: Check with an example: if RB = 30° and latitude = 86.6 m, then length = 86.6 * sec 30° = 86.6 * 1.1547 ≈ 100 m, consistent with a 100 m line having cos 30° = 0.866. Why Other Options Are Wrong: Sine or tangent are associated with departure or departure/latitude ratio, not with recovering length from latitude alone. Cosine would give the projection, not the recovery of length. Common Pitfalls: Mixing whole-circle and reduced bearings; using the wrong quadrant sign; forgetting that secant grows large for RB near 90°, amplifying any error in latitude. Final Answer: Secant of the reduced bearing

Question 2

Fixing a point by distances from two fixed stations: In field surveying, distances AC and BC are measured from two known stations A and B (with baseline AB known), and point C is plotted by intersecting the two distance arcs. This distance–distance …

Accepted Answer

Introduction / Context: There are two classic ways to fix an unknown point using two control stations A and B whose separation AB is known: (1) angle–angle (triangulation by angles) and (2) distance–distance (trilateration). In practical chain surveying, where linear measures are primary, the point C is often fixed by measuring AC and BC and plotting with the known baseline AB. This is commonly grouped under triangulation methods as used in chain surveying frameworks. Given Data / Assumptions: AB (baseline) is known or measured accurately. Distances AC and BC are measured in the field. Angles are not necessarily observed; plotting is by intersecting arcs with radii AC and BC about A and B. Concept / Approach: With AB known, two circles of radius AC and BC centered at A and B will intersect at C (up to a mirror ambiguity resolved by sketch or reconnaissance). This is the essence of distance-based triangulation (often called trilateration). Chain surveying frequently employs such distance geometry because chains/tapes are the principal tools. Step-by-Step Solution: Measure baseline AB as accurately as possible.Measure AC and BC to the target detail point C.On the plan, draw circles with radii equal to scaled AC and BC about A and B.Mark the intersection matching the field situation as point C. Verification / Alternative check: Where possible, measure an additional tie (e.g., a third distance or an angle) to detect blunders; small triangle misfits reveal measurement issues before plotting is finalized. Why Other Options Are Wrong: Chain surveying: It is the overall method; the specific fixing technique here is distance-based triangulation within chain surveying. Traverse method: Based on successive angle and distance around a route, not two-distance intersection from a fixed baseline. None: Incorrect because the intersection method is well established in triangulation/trilateration practice. Common Pitfalls: Ambiguity between the two mathematical intersections; poor scale or plotting can shift the point. Always use checks or sketches to choose the correct intersection. Final Answer: Triangulation (distance-based fixing)

Question 3

Fundamental geometry of a theodolite: Which statements about the three principal axes and their relationships are correct? Choose the most complete option.

Accepted Answer

Introduction / Context: Theodolites measure horizontal and vertical angles precisely. Their accuracy depends on strict geometric relationships among three axes: the telescope (line of collimation) axis, the transit (trunnion) axis, and the vertical (rotation) axis. Understanding these relationships is vital for adjustments and reliable observations. Given Data / Assumptions: A properly adjusted theodolite is considered. Definitions: telescope axis (line of collimation), trunnion axis (tilt axis), and vertical axis (instrument rotation). Instrument is correctly leveled before testing the relationships. Concept / Approach: For perfect adjustment: (1) the telescope axis must be perpendicular to the trunnion axis so that elevation motion does not skew the line of sight; (2) the vertical axis must be perpendicular to the trunnion axis so that the vertical circle plane is truly vertical; and (3) all three axes intersect at the instrument’s center, ensuring consistent geometry during rotations and transits. Step-by-Step Solution: Level the instrument so the vertical axis is truly vertical.Check that the telescope axis is perpendicular to the trunnion axis using standard collimation tests.Verify that the three axes meet at a point by observing that readings are consistent upon transiting and rotating.Adjust as needed using manufacturer procedures for plate levels, crosshairs, and circles. Verification / Alternative check: Face-left and face-right readings of the same angle should agree within tolerance; discrepancies indicate axis misalignment. Why Other Options Are Wrong: Each of A–C is individually correct, but only D states the complete set required for proper theodolite geometry. Common Pitfalls: Assuming leveling alone guarantees perfect geometry; internal axial relationships still require testing and, sometimes, adjustment. Final Answer: All of the above

Question 4

Bearing conversion: A line has magnetic bearing = 32° and magnetic declination = 10° 15′ W (west is negative). What is the true bearing (from true north, clockwise)?

Accepted Answer

Introduction / Context: Converting magnetic bearings to true bearings is a frequent need when using compass observations together with maps referenced to true north. The key is handling magnetic declination with the correct sign convention: easterly declination adds, westerly declination subtracts. Given Data / Assumptions: Magnetic bearing (MB) = 32°. Magnetic declination (west) = 10° 15′ (treated as negative). True bearing (TB) is measured clockwise from true north, expressed as a single angle. Concept / Approach: For conversion: TB = MB + declination, with east positive and west negative. Since declination is westerly, subtract its magnitude. Therefore TB = 32° − 10° 15′ = 21° 45′. True bearings are typically given as a single clockwise angle without quadrant letters. Step-by-Step Solution: Write the relation: TB = MB + declination.Use sign convention: westerly = negative.Compute: 32° − 10° 15′ = 21° 45′.State the final TB: 21° 45′ (clockwise from true north). Verification / Alternative check: Graphically, rotate the magnetic meridian west of true north by 10° 15′; the true bearing must be smaller than the magnetic one by exactly that amount, confirming 21° 45′. Why Other Options Are Wrong: 42° 15′: Would imply an easterly (positive) declination. 42° 15′ W / 21° 45′ W: True bearings are not typically annotated with E/W quadrantal tags in this format. Common Pitfalls: Mixing up signs; a quick rule is “East is least? No—East adds; West subtracts” when converting MB to TB. Final Answer: 21° 45′

Question 5

Setting up a plane table at a station: Which operation is carried out first in correct field procedure before others such as levelling and orientation?

Accepted Answer

Introduction / Context: Proper setup of a plane table ensures that plotted positions correspond to ground positions. The standard sequence is important: if you level or orient before the table is actually over the station, your subsequent work is mislocated and must be redone. Given Data / Assumptions: Station point on ground is marked (peg, nail, or station mark). Plane table with plumbing fork or centering device is used. All three operations—centering, levelling, orientation—must be completed. Concept / Approach: Centering places the table exactly above the ground station so that the drawing sheet’s station point is co-vertical with the ground point. Levelling then ensures the alidade operates in a horizontal plane. Orientation matches the table's directions with the field. If you do not center first, subsequent steps are wasted because the board would have to be moved again, disturbing level and orientation. Step-by-Step Solution: Use a plumbing fork or centering device to position the board exactly over the station mark.Once centered, level the board using the spirit level (two perpendicular directions).Finally, orient the table by backsighting to a known line or using a compass if appropriate.Proceed with sighting and plotting. Verification / Alternative check: Some field crews do quick rough levelling during centering just to ease adjustments, but the formal precedence is centering → levelling → orientation. Why Other Options Are Wrong: Levelling first: You will disturb level when you later shift the board for centering. Simultaneous: Not reliable; centering must come first. Orientation first: Impossible until the board is centered and levelled. Common Pitfalls: Neglecting to re-check level after final orientation; minor rotations can throw off levelling. Final Answer: Centering the board over the station first

Question 6

Contours and landforms: At what angle does a contour line intersect a ridge line on a topographic map?

Accepted Answer

Introduction / Context: Contours are lines of equal elevation. Their patterns reveal landforms such as ridges, valleys, spurs, and saddles. Understanding how contours cross ridges and valleys enables quick, accurate terrain interpretation for route selection and drainage design. Given Data / Assumptions: A ridge line is the line of steepest descent on either side (a high line). A contour line represents constant elevation and must cross lines of maximum slope orthogonally. Map contours are sufficiently close to approximate smooth surfaces. Concept / Approach: The gradient (steepest slope) at any point is perpendicular to the contour through that point. Ridge and valley lines align with maximum slope directions. Consequently, both ridge and valley lines intersect contour lines at right angles (90°). This orthogonality also supports construction of cross-sections and computation of slopes from maps. Step-by-Step Solution: Identify the ridge line by the pattern of contours (higher values along the crest).Note that the steepest descent lines leave the ridge crest orthogonally to contours.Therefore, ridge lines intersect contours at 90°.Apply the same principle to valleys (also right angles). Verification / Alternative check: Construct a small slope triangle on a map: the gradient vector is normal to the contour; ridge direction is along the gradient on the crest—hence the intersection is right-angled. Why Other Options Are Wrong: Angles of 30°, 45°, or 60° are arbitrary and contradict the fundamental orthogonality of contours and lines of maximum slope. Common Pitfalls: Mistaking spur patterns for valley patterns; check the V/U shapes and elevation values to avoid misinterpretation. Final Answer: 90°

Question 7

Practical instrument adjustment: Which statements reflect good practice and realities when adjusting surveying instruments?

Accepted Answer

Introduction / Context: Survey instruments require periodic checks and adjustments to maintain accuracy. Field personnel must understand both the limitations of the devices and the correct use of adjustment screws to avoid over-correction, damage, or unstable results. Given Data / Assumptions: Adjustments may be iterative rather than one-and-done. Instrument condition (wear, play, looseness) affects results. Proper torque and technique for adjustment screws are assumed. Concept / Approach: Systematic errors are often minimized by iterative adjustments; a single attempt rarely eliminates them entirely. If the instrument is mechanically unstable (worn clamps, loose bearings), even correct procedures cannot hold the alignment, making satisfactory adjustment impractical. Screws must be firmly seated for repeatability, but forcing them risks thread damage and introduces stresses that later relax, reintroducing errors. Step-by-Step Solution: Diagnose using standard tests (collimation, bubble, two-peg) to quantify misalignments.Adjust incrementally; re-test after each change.Ensure mechanical stability first (tripod shoes, clamps, tribrach) before precision adjustments.Leave screws firm—no over-tightening—to preserve settings. Verification / Alternative check: Repeatability checks (face left/right) confirm whether the adjustment holds under typical instrument motions; instability shows as drifting results. Why Other Options Are Wrong: Each of A–C is correct; only D captures the full set of best practices and realities faced in the field. Common Pitfalls: Over-tightening, skipping re-tests, or attempting fine adjustments on equipment that has underlying mechanical issues. Final Answer: All of the above

Question 8

Types of errors in surveying: Which statements correctly describe mistakes, systematic errors, and accidental (random) errors in practice?

Accepted Answer

Introduction / Context: Quality in surveying depends on understanding error sources and handling them appropriately. Distinguishing between blunders (mistakes), systematic errors, and accidental (random) errors guides instrument checks, field procedures, and data adjustments. Given Data / Assumptions: Mistakes are human errors and should be detected and removed. Systematic errors have identifiable causes and consistent signs. Random errors are unbiased and reduce by averaging. Concept / Approach: Mistakes (e.g., transposed digits, wrong point sighted) are not statistical errors and must be eliminated via checks. Systematic errors (e.g., scale error, collimation error) can be modeled and corrected; otherwise they bias results consistently. Accidental errors are inherent in observation processes and are treated using statistical methods; they diminish with redundancy roughly as 1/sqrt(n). Step-by-Step Solution: Design redundancy (check lines, repeated angles) to reveal mistakes.Calibrate instruments and apply known corrections to control systematic errors.Average repeated observations and use least-squares to mitigate accidental errors.Document procedures and results to trace and rectify error sources. Verification / Alternative check: Closure checks—angular and linear—expose mistakes and systematic trends; residuals after adjustment should resemble random scatter. Why Other Options Are Wrong: All statements A–C are correct; D encompasses the full, correct classification widely taught in surveying error theory. Common Pitfalls: Attempting to “average out” mistakes or uncorrected systematic errors—averaging only reduces random components, not blunders or biases. Final Answer: All of the above

Question 9

Still water and contours: The boundary (shoreline) of a still lake on a map represents which of the following?

Accepted Answer

Introduction / Context: A still water surface is an equipotential surface of gravity, hence level. The shoreline plotted on a map is the intersection of this level surface with the ground. Understanding what that line represents helps with contour interpretation and setting reference elevations in the field. Given Data / Assumptions: The lake water is still (no wind setup or waves considered). Map shows the boundary between water and land at the same instant. Contours represent lines of equal elevation on land. Concept / Approach: Because the water surface is level, every point along the shoreline has the same elevation. Therefore the lake boundary is itself a contour line at the lake’s water level. While “level” and “horizontal” have technical distinctions, on a small area they are practically similar; however, the shoreline specifically corresponds to a contour (constant elevation) rather than a generic “horizontal surface.” Step-by-Step Solution: Recognize that a still water surface is an equipotential (level) surface.The shoreline is the intersection of this surface with the terrain.Hence, all shoreline points are at one elevation → a contour line.Map the contour value as the lake water level at the survey epoch. Verification / Alternative check: If lake level changes seasonally, new shorelines trace different contours; historic maps may show variants tied to their survey dates. Why Other Options Are Wrong: Level surface/horizontal surface: Describe the water plane itself, not the boundary line on land. Concave surface: Not applicable; large-scale curvature of Earth is negligible at map scale. Common Pitfalls: Confusing the concept of a level plane with the mapped boundary; remember the contour is the line of intersection at a single elevation. Final Answer: Contour line (single elevation)

Question 10

Slope correction in chaining: If the measured chain length along a slope of angle θ is l, what is the slope correction to reduce it to horizontal length?

Accepted Answer

Introduction / Context: Distances for plans and coordinates are horizontal. When a line is measured on a slope, a correction must be applied to obtain the equivalent horizontal length. A convenient trigonometric identity expresses this correction in terms of half-angle functions, which is especially useful with small slopes. Given Data / Assumptions: Slope angle = θ (between line and horizontal). Measured length along slope = l. Goal: compute correction to subtract from l to get horizontal projection. Concept / Approach: Horizontal length = l * cos θ. Therefore slope correction C_s = l − l * cos θ = l * (1 − cos θ). Using the identity 1 − cos θ = 2 * sin^2(θ/2), we get C_s = 2 * l * sin^2(θ/2). This quantity is subtracted from the measured sloping length to obtain the horizontal distance. Step-by-Step Solution: Write horizontal projection: L_h = l * cos θ.Compute correction: C_s = l − L_h = l * (1 − cos θ).Apply identity: 1 − cos θ = 2 * sin^2(θ/2).Hence C_s = 2 * l * sin^2(θ/2) (subtract this from l). Verification / Alternative check: For small θ, sin(θ/2) ≈ θ/2 (in radians), so C_s ≈ 2 * l * (θ^2 / 4) = l * θ^2 / 2, matching small-angle approximations used in quick estimates. Why Other Options Are Wrong: cos^2(θ/2) forms (options a, d) do not equal 1 − cos θ. tan^2(θ/2) alone does not represent the needed difference without a denominator factor. Common Pitfalls: Applying the correction with wrong sign; the sloping distance is always longer than horizontal for θ ≠ 0, so subtract C_s. Final Answer: 2 * l * sin^2(θ/2)

Question 11

Ranging in chain surveying: Ranging is primarily the operation of what activity in the field?

Accepted Answer

Introduction / Context: To measure a straight distance accurately with a chain or tape, the line between the two terminal stations must be clearly defined and kept straight. Ranging is the process used to align and mark intermediate points so that measurement proceeds along the intended straight line without lateral deviation. Given Data / Assumptions: Two terminal points are intervisible or can be connected in stages. Ranging rods or flags are available for alignment. Survey crew includes a leader and a follower for communication and sighting. Concept / Approach: In direct ranging, the observer aligns an intermediate rod so that it lies visually on the straight line joining the two terminals; in indirect ranging (hilly/obstructed terrain), reciprocal or step-by-step methods are used. Once intermediate points are fixed, chaining proceeds accurately along the straight line through these points. Step-by-Step Solution: Place ranging rods at the two terminal stations.Move the intermediate rod until it lines up with both terminal rods as seen from one end (or by reciprocal signals).Fix the intermediate point with a peg; repeat for additional points as necessary.Carry out chaining along the ranged line through these fixed points. Verification / Alternative check: Re-check alignment from the opposite terminal; small deviations appear as apparent lateral offsets of the intermediate rod, prompting fine corrections. Why Other Options Are Wrong: Reconnaissance is preliminary planning, not line alignment. Judging distance by eye is estimation, not the act of aligning. Determination of slope uses clinometers/levels and is independent of ranging. Common Pitfalls: Parallax due to not sighting with one eye; using bent or poorly painted rods; failing to check alignment from both ends. Final Answer: Establishing intermediate points in straight line between terminal stations

Question 12

Tacheometry – Variation of Staff Intercept with Distance In stadia (tacheometric) observations using a fixed-multiplying telescope, how does the staff intercept (the difference between upper and lower stadia hair readings) change as the staff is hel…

Accepted Answer

Introduction / Context: Tacheometry (stadia surveying) determines distance and elevation by reading the intercept between the upper and lower stadia hairs on a levelling staff. Understanding how the staff intercept varies with distance is fundamental to quick field checks and error spotting. This question targets the core proportionality that links staff intercept to line-of-sight distance in a fixed-multiplying stadia setup. Given Data / Assumptions: Fixed stadia hair interval in the telescope (fixed-multiplying instrument). Line of sight approximately horizontal or with known vertical angle. Standard distance formula: D = k * s + C, where D is distance along the line of sight, s is staff intercept, k is the multiplying constant, and C is the additive constant. Concept / Approach: The stadia principle forms similar triangles between the objective, stadia hairs, and staff graduations. For a fixed hair interval, the intercept on the staff increases linearly with the distance to the staff. Hence, as the staff is carried farther along the ray, the intercept grows proportionally. The additive constant C (from instrument optics) shifts the distance-origin slightly but does not change the linear growth of s with D. Step-by-Step Solution: Start from D = k * s + C.Rearrange to s = (D − C) / k.As D increases, (D − C) increases nearly linearly beyond a few metres.Therefore, s increases with distance; staff intercept is greater when the staff is held farther away. Verification / Alternative check: Field practice: doubling the line-of-sight distance approximately doubles the staff intercept for the same instrument and sighting geometry (neglecting small-angle effects). Crews routinely confirm this when selecting suitable staff ranges for clear intercepts. Why Other Options Are Wrong: 'Smaller, farther off' inverts the relation. 'Smaller, nearer' misstates the near-field behavior. 'Same, wherever' would imply k = ∞ (impossible). 'Becomes zero' is incorrect; s → 0 only if D → C, i.e., extremely near the instrument, not at long range. Common Pitfalls: Confusing the additive constant with a distance threshold where intercept stops changing; ignoring that vertical angles slightly modify the horizontal distance but not the linear dependence of s on D along the line of sight. Final Answer: Greater, the farther off the staff is held

Question 13

Tacheometric Distances – Which Corrections Apply to Horizontal Distance Derived from Stadia? When horizontal distances are computed tacheometrically from staff intercepts and vertical angle, which correction(s) are normally applied to the computed h…

Accepted Answer

Introduction / Context: Tacheometry yields distances from optical measurements rather than direct taping. The raw distance lies along the line of sight and must be converted to a horizontal distance for mapping and setting out. This question explores which corrections are normally relevant in routine tacheometric work. Given Data / Assumptions: A standard fixed-multiplying stadia instrument is used. Staff intercept s and vertical angle θ are observed. Ordinary topographic ranges (typically under a few hundred metres) are considered. Concept / Approach: The tacheometric distance computed from D = k * s + C is along the line of sight. The required plan distance is its horizontal projection. Thus, a slope reduction (multiplying by cos θ or using the appropriate formula that includes sin and cos terms) is essential. Temperature correction pertains to tape length variation and does not apply to optically derived distances. Curvature and refraction mainly influence very long sights or precise levelling; for ordinary tacheometry their effect on horizontal distance is negligible and usually ignored by specification, though vertical components may warrant atmospheric considerations in precision work. Step-by-Step Solution: Compute line-of-sight distance: D = k * s + C.Reduce to horizontal: H = D * cos θ (or use the full tacheometric reduction formula when staff is vertical).Assess other corrections: temperature (not applicable); curvature/refraction (negligible for typical stadia ranges).Therefore, apply slope reduction as the standard correction. Verification / Alternative check: Survey manuals show the horizontal component derived directly in the tacheometric equations; ancillary corrections are absent unless doing long-range geodetic-quality observations. Why Other Options Are Wrong: Temperature correction belongs to tapes and EDM scale factors, not optical stadia. Curvature/refraction corrections target vertical refraction in precise levelling; their contribution to short-range horizontal distance is minuscule. Common Pitfalls: Over-correcting tacheometric distances with tape-based formulas; forgetting to reduce the sloping line-of-sight distance to horizontal, which is the essential step. Final Answer: Slope correction (reduction from the line of sight to horizontal)

Question 14

Tangential Tacheometry – How Should the Staff Be Held for Inclined Sights? In the tangential method of tacheometry, when observing to a levelling staff on an uphill or downhill line of sight, how should the ordinary staff be held to ensure correct a…

Accepted Answer

Introduction / Context: Tangential tacheometry determines distance and elevation from two angular readings to distinct staff marks (or to the same mark with different tangent angles), without relying on stadia hairs. The geometry assumes a particular orientation of the staff. This question checks the correct field practice for holding the staff on slopes. Given Data / Assumptions: Ordinary levelling staff graduations are vertical when the staff is vertical. Tangential method uses angular measurements relative to horizontal and vertical planes. Instrument is properly levelled and centered. Concept / Approach: Whether the line of sight is upward or downward, the staff must remain vertical so that readings correspond to true vertical distances along a straight scale aligned with gravity. Tilting the staff introduces trigonometric distortions, invalidating the tangential relationships from which distances and elevations are computed. Therefore, the correct procedure is to keep the staff vertical for all observations in the tangential method, just as in stadia work with a vertical staff assumption. Step-by-Step Solution: Set up the instrument and level precisely.Instruct the staffman to plumb the staff using the circular bubble.Take angular readings to designated staff points with the staff held vertical regardless of slope direction.Compute distance and elevation using the tangential formulas that rely on a vertical staff. Verification / Alternative check: Standards for tacheometry (both stadia and tangential) consistently assume a vertical staff; any deviation requires special corrections not used in routine practice. Why Other Options Are Wrong: Tilted staff options (a), (b), and (e) corrupt the geometric basis and cause systematic errors. 'None of these' is wrong because there is a clearly correct practice. Common Pitfalls: Allowing the staff to lean on steep ground; not checking the staff bubble; attempting to 'compensate' tilt with ad-hoc adjustments instead of keeping the staff vertical. Final Answer: Kept vertical in all cases

Question 15

Precise Levelling – Recommended Limit for Probable Accidental Error (I.G.A. Standard) According to the International Geodetic Association recommendations for precise levelling, the probable accidental error (where k is the length in kilometres) shou…

Accepted Answer

Introduction / Context: Levelling specifications define acceptable random (accidental) error growth with distance to safeguard vertical control quality. The International Geodetic Association (IGA) provides widely cited limits for precise levelling. Knowing these values helps surveyors plan section lengths, balancing sight lengths and refraction to meet standards. Given Data / Assumptions: Precise levelling with matched back-sights and fore-sights to suppress systematics. k denotes total route length in kilometres. Interest is in the probable accidental error tolerance recommended by IGA. Concept / Approach: Probable accidental error scales approximately with distance because many small random effects (reading scatter, target shimmer, rod handling) accumulate. IGA guidance expresses an upper limit in millimetres as a simple function of k for specification checks. The commonly quoted allowance for probable accidental error is ±0.5 k mm for precise levelling, distinguishing it from tighter limits on systematic components and from alternative national standards that may use root-mean-square formulations with square-root distance dependence for closures. Step-by-Step Solution: Identify the specified class: precise levelling under IGA conventions.Select the probabilistic tolerance: ±0.5 k mm.Interpretation: over 40 km, allowable probable error ≈ ±20 mm.Apply during planning to distribute instrument set-ups and observation repetition. Verification / Alternative check: Comparative specifications (e.g., national mapping agencies) provide similar magnitude limits, with some adopting closure rules based on square-root of distance; the stated IGA figure fits within that family for precise work and is a standard exam recall value. Why Other Options Are Wrong: ±0.1 k mm is more typical of systematic-error guidance (stricter but not for accidental errors). The higher values (±1 k, ±2 k, ±5 k mm) are too permissive for precise levelling and would not meet control standards. Common Pitfalls: Confusing accidental error limits with misclosure limits or with systematic error allowances; forgetting to report the unit as millimetres per kilometre, not per setup. Final Answer: ± 0.5 k mm

Question 16

Transition Curve (Cubic Parabola) – Maximum Perpendicular Offset from the Tangent A transition curve of length L = 90 m is inserted between a straight and a circular curve of radius R = 500 m. For a standard cubic parabola transition, what is the ma…

Accepted Answer

Introduction / Context: Transition curves provide gradual change from zero curvature on the tangent to the full curvature of a circular arc, improving riding comfort and safety for highways and railways. Designers commonly use the cubic parabola, for which several handy formulas exist. One such quantity is the maximum perpendicular offset (also called shift) produced by the transition relative to the original tangent alignment. Given Data / Assumptions: Transition type: cubic parabola connecting tangent to a circular arc. Length of transition L = 90 m. Circular radius R = 500 m. Standard formula for shift (maximum perpendicular offset) applies. Concept / Approach: For a cubic parabola transition, the shift S (maximum perpendicular offset from the tangent to accommodate the transition) is given by the widely used relation S = L^2 / (24 * R). This small lateral movement of the circular curve ensures a smooth curvature ramp while preserving the external geometry. It is independent of speed but depends on L and R. Step-by-Step Solution: Use S = L^2 / (24 * R).Compute L^2 = 90^2 = 8100.Compute denominator 24 * R = 24 * 500 = 12000.S = 8100 / 12000 = 0.675 m ≈ 0.70 m. Verification / Alternative check: Cross-check order of magnitude: for L/R ≈ 0.18, a sub-metre shift is expected. If L doubled, shift grows with L^2, highlighting sensitivity to transition length selection. Why Other Options Are Wrong: 1.70 m, 2.70 m, 3.70 m, and 4.70 m exceed the computed shift by large margins and would correspond to much longer transitions or much smaller radii, inconsistent with the data. Common Pitfalls: Confusing shift with mid-ordinate of the circular curve or with the offset y at a partial length; applying a wrong constant (e.g., 6 or 12 instead of 24) in the denominator leads to significant overestimation. Final Answer: 0.70 m

Question 17

Traverse Fundamentals – Recognizing Types of Traverses and Their Control Which of the following statements correctly describe traverse systems and terminology used in engineering surveying?

Accepted Answer

Introduction / Context: Traversing establishes horizontal control by measuring directions and distances along a connected framework of lines. Correct terminology helps in planning, computation, and specifications. This question tests recognition of standard definitions for various traverse types and control conditions. Given Data / Assumptions: Distance and direction measurements are of adequate precision for the task. Control points may be existing (geodetic, cadastral) or newly established. Closures and adjustments follow standard practice (Bowditch, transit rule, or least squares). Concept / Approach: A traverse is the backbone of many surveys. A closed traverse returns to its start, enabling strong closure checks on both angles and coordinates. A controlled traverse ties into known points at each end, fixing scale, orientation, and position robustly. A fly traverse lacks adequate external control and is primarily used for reconnaissance or to reach control, with weaker checks until closure is made later. Understanding these categories guides how errors are detected and corrected. Step-by-Step Solution: Identify the network of lines with measured lengths and directions → traverse.Check whether the path returns to the start → closed traverse if yes.Confirm ties to known control at both ends → controlled traverse.If run without such ties → fly traverse. Verification / Alternative check: Most surveying texts define these exactly; computational routines for closures depend on whether the traverse is closed or controlled. Why Other Options Are Wrong: Since each statement accurately captures a standard definition, choosing anything other than 'All of the above' would omit correct information. Common Pitfalls: Confusing 'closed traverse' (returns to start) with 'link traverse' (joins two known points); assuming a fly traverse is necessarily inaccurate—its weakness is lack of external checks until closure. Final Answer: All of the above

Question 18

Optical Principles – Basic Construction of a Refracting Telescope for Surveying Which of the following statements correctly describe the optical construction of a refracting telescope as used in theodolites and levels?

Accepted Answer

Introduction / Context: Survey instruments use compact refracting telescopes to form clear, magnified images of distant targets (staff graduations, targets, prisms). Understanding the basic lens arrangement aids in diagnosing focus, parallax, and aberration issues during fieldwork and maintenance. Given Data / Assumptions: Simple refracting telescope (no mirrors) with an objective and an eyepiece. Cross-hair diaphragm placed near the focal plane. Optical axis alignment is properly adjusted at the factory. Concept / Approach: The objective, a convex lens, collects light from the target and forms a real, inverted image near the focal plane where the cross-hairs lie. The eyepiece then magnifies this image for the observer. Both lenses are coaxial, ensuring that the line of sight is centered and that vignetting or off-axis aberrations are minimized. This configuration is the foundation for more advanced designs (e.g., achromatic objectives, Ramsden eyepieces) but the essential two-lens description remains valid. Step-by-Step Solution: Identify the two-lens structure: objective (front) and eyepiece (rear).Confirm coaxial alignment to maintain image quality and mechanical centering.Assign functions: objective forms real image; eyepiece magnifies it for the eye.Therefore, all listed statements are correct. Verification / Alternative check: Manufacturer diagrams show a convex objective and composite eyepiece (often two lenses acting as a system), all centered on a single optical axis with the reticle at or near the focal plane. Why Other Options Are Wrong: Because (a)–(d) are all correct, any option denying one of them would misrepresent the telescope’s basic design. Common Pitfalls: Confusing refracting telescopes with reflecting designs (mirrors); assuming the eyepiece is a single simple lens—while conceptually true, in practice it is a compound pair arranged as a unit. Final Answer: All of the above

Question 19

Controlling Aberrations – Practical Measures in Survey Telescopes Which of the following statements correctly describe methods used to control spherical and chromatic aberrations in the optics of surveying instruments?

Accepted Answer

Introduction / Context: Aberrations degrade image sharpness and color fidelity. Survey telescopes must deliver crisp cross-hair coincidence on fine targets, so designers employ simple yet effective optical strategies to control spherical and chromatic aberrations while keeping instruments rugged and compact. Given Data / Assumptions: Standard refracting telescope architecture (objective + eyepiece). Desire to limit spherical blur and chromatic fringing. Use of classical eyepiece designs compatible with reticles. Concept / Approach: Spherical aberration arises when peripheral rays focus at different points than paraxial rays. Narrowing the aperture cuts peripheral rays (option a) and helps immediately. More powerfully, using a compound lens system (option b) allows designers to balance ray paths. Objectives are typically achromats—a convex lens cemented to a concave lens of different glass types—to reduce both spherical and chromatic errors (option c). Eyepieces like Huygens and Ramsden employ two plano-convex elements separated by a small gap, arranged to minimize aberrations while accommodating a reticle (option d). Step-by-Step Solution: Relate aberration type → mitigation: aperture control for spherical; doublets for spherical + chromatic.Note objective design: convex–concave achromat.Note eyepiece design: two plano-convex lenses, orientation and spacing per design.Conclude all statements are valid and collectively describe standard practice. Verification / Alternative check: Optics texts and instrument manuals illustrate these exact configurations for survey telescopes to achieve adequate field performance with modest complexity. Why Other Options Are Wrong: Each statement is accurate; therefore, none of them should be rejected individually, making 'All of the above' correct. Common Pitfalls: Assuming eyepieces are single lenses; overlooking that aperture reduction also reduces brightness—designs balance sharpness and light. Final Answer: All of the above

Question 20

Instrument Geometry – Definition of Line of Sight / Collimation in Survey Telescopes In a surveying telescope, the imaginary straight line passing through the intersection of the cross-hairs and the optical center of the objective is called what?

Accepted Answer

Introduction / Context: Precise angle and level readings depend on a well-defined reference line within the telescope. Surveying terminology distinguishes between the line of sight (a general viewing direction) and the exact geometric line used for measurements, called the line of collimation. This question clarifies the correct definition used in instrument adjustment and observations. Given Data / Assumptions: A telescope contains a cross-hair diaphragm and an objective lens. The cross-hair intersection defines the measurement reference point. Instrument is properly focused to place the image in the cross-hair plane. Concept / Approach: The line of collimation is rigorously defined as the straight line joining the optical center of the objective lens to the intersection of the cross-hairs. This is the line along which the instrument points for measurements. While some texts use 'line of sight' loosely as a synonym, in strict surveying adjustment procedures, 'line of collimation' is preferred for the exact reference used in collimation error tests and two-peg tests. Step-by-Step Solution: Identify the cross-hair intersection in the focal plane.Join this with the objective’s optical center—this defines the measurement line.Recall that adjustments (collimation test) aim to align this line correctly to instrument axes.Therefore, the correct term is 'line of collimation'. Verification / Alternative check: Adjustment procedures (e.g., for theodolites) explicitly reference the line of collimation being perpendicular to the trunnion axis and coincident with the target direction when correctly adjusted. Why Other Options Are Wrong: 'Axis of the telescope' often refers to the mechanical axis, not the optical measurement line. 'Principal focal ray' is not standard survey terminology. 'None of these' is invalid because a precise term exists. Common Pitfalls: Using 'line of sight' ambiguously; neglecting that small collimation errors cause systematic pointing bias unless eliminated by reversal or adjustment. Final Answer: Line of collimation

Surveying Questions