(a) (i) Explain spot speed, running speed, space-mean speed, time-mean speed and average speed. 10
(ii) The consolidated data collected from speed and delay studies by floating car method on a stretch of urban road of length 2·5 km, running East-West

Question

(a) (i) Explain spot speed, running speed, space-mean speed, time-mean speed and average speed. 10
(ii) The consolidated data collected from speed and delay studies by floating car method on a stretch of urban road of length 2·5 km, running East-West are given below in the table. Determine the average values of volume, journey speed and running speed of the traffic stream, along either direction. 10

Mean Values of Speed and Delay

| Direction | Mean Journey Time (Minutes) | Mean Stopped Delay (Minutes) | Number of Vehicles (Mean Value) | | |
|---|---|---|---|---|---|
| | | | Overtaking | Overtaken | In Opposite Direction |
| East-West | 4·85 | 1·60 | 4·5 | 6·5 | 376 |
| West-East | 8·36 | 1·90 | 4·0 | 5·5 | 280 |

(b) (i) Two points A and B having elevations of 585 m and 250 m respectively, above datum, appear on a vertical photograph obtained with a camera of focal length of 250 mm and flying altitude of 2300 m above datum. Their correlated photographic coordinates are as follows :

Point Photographic Coordinates
x (cm) y (cm)
A + 5·65 + 3·75
B – 3·45 + 8·55

Determine the ground coordinates of points A and B and calculate the horizontal distance between points A and B. 5

(ii) The lengths, latitudes and departures of a closed traverse ABCD are as follows :

| Line | Length (m) | Latitude | Departure |
| AB | 350·8 | + 303·03 | + 176·6 |
| BC | 408·5 | – 336·7 | + 231·4 |
| CD | 285·4 | – 211·3 | – 191·9 |

Calculate the length and bearing of the line DA. 10

(c) For what specific operations are the following equipment used at construction sites ?
(i) Sheep foot roller
(ii) Bulldozer
(iii) Dragline excavator
(iv) Tower crane
(v) Hoe 15

UPSC Answer Check · Accepted Answer

This question demands clear definitions with mathematical precision for (a)(i), rigorous numerical problem-solving for (a)(ii), (b)(i) and (b)(ii), and specific operational knowledge for (c). Allocate approximately 35% time to part (a) combining theory and floating car calculations, 30% to part (b) covering photogrammetry and traverse computations, and 35% to part (c) ensuring each equipment description includes specific construction applications. Begin with definitions using standard IRC/IS formulae, proceed through step-by-step calculations with proper unit handling, and conclude with equipment functions tied to Indian construction scenarios like dam building and urban infrastructure.
- For (a)(i): Precise definitions of spot speed (instantaneous), running speed (excluding stops), space-mean speed (harmonic mean), time-mean speed (arithmetic mean), and average speed with correct mathematical expressions and distinctions per IRC standards
- For (a)(ii): Correct application of floating car method equations to compute volume, journey speed and running speed for both directions using Wardrop's formulae with proper handling of overtaking/overtaken vehicles
- For (b)(i): Accurate photogrammetric scale determination using flying height and elevation, correct ground coordinate computation using photo coordinates, and precise horizontal distance calculation using 3D coordinates
- For (b)(ii): Proper application of latitude-departure closure conditions, correct computation of DA's latitude and departure from ΣL=0 and ΣD=0, and accurate bearing conversion from trigonometric functions
- For (c)(i): Sheep foot roller - specific application to cohesive soils, clay core compaction in earth dams (e.g., Bhakra Nangal, Tehri Dam), and kneading action for high plasticity soils
- For (c)(ii-iv): Bulldozer for short haul earthmoving and site grading; Dragline for underwater excavation and canal construction; Tower crane for vertical material handling in high-rise construction
- For (c)(v): Hoe (backhoe) for trenching, foundation excavation, and loading operations with specific mention of its force characteristics (pulling action toward machine)
- Cross-cutting: Integration of IRC:106-1990 guidelines for speed studies, IS 14802 for photogrammetry, and practical Indian construction equipment deployment contexts

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	25%	12.5	For (a)(i), distinguishes all five speed types with correct mathematical formulations (harmonic vs arithmetic mean) and physical interpretations; for (a)(ii), correctly identifies Wardrop's floating car method assumptions; for (b)(i), applies correct photogrammetric scale formula accounting for terrain elevation; for (b)(ii), understands traverse closure principles; for (c), matches each equipment to its unique soil/operation suitability with no confusion between similar machines	Defines most speed types correctly but confuses space-mean and time-mean relationships; applies floating car method with minor conceptual errors; computes photogrammetric coordinates with scale errors; identifies equipment purposes generally but lacks specificity on soil types or operational constraints	Fundamental confusion between speed definitions (e.g., treats space-mean as arithmetic average); misapplies floating car formulae or ignores overtaking corrections; fails to adjust photogrammetric scale for elevation differences; describes equipment functions generically or incorrectly (e.g., confuses hoe with shovel)
Numerical accuracy	25%	12.5	For (a)(ii): volume within ±2% of correct values (EW: ~420-430 veh/h, WE: ~200-210 veh/h), journey speeds and running speeds with correct unit conversions; for (b)(i): ground coordinates accurate to 0.1m, horizontal distance within ±0.5m; for (b)(ii): DA length within ±0.5m, bearing within ±0.5°; all calculations show proper significant figures and unit discipline	Correct methodology but arithmetic errors leading to 5-10% deviation in final answers; minor unit conversion errors (km/h vs m/s); traverse computation with correct quadrant identification but approximate bearing; photogrammetric calculations with scale factor errors	Major computational errors (>15% deviation); incorrect formula application (e.g., using time-mean instead of space-mean for floating car); wrong quadrant for bearing; order-of-magnitude errors in coordinates; missing critical steps leading to incomplete solutions
Diagram quality	10%	5	For (b)(i): Clear sketch of vertical photograph geometry showing principal point, nadir, isocentre, flying height, terrain elevation, and ray geometry with proper labeling; for floating car method: schematic of test vehicle movement with overtaking/overtaken vehicle representation; for equipment: illustrative sketches showing sheep foot roller padfoot configuration, dragline boom and bucket arrangement, tower crane components	Basic diagrams present but lacking critical labels or proper proportions; photogrammetry sketch without elevation indication; equipment sketches generic without distinguishing features; floating car method described textually without visual representation	No diagrams where essential for understanding; or misleading sketches (e.g., horizontal photograph instead of vertical); confusing or unlabeled diagrams that detract from explanation; failure to illustrate 3D photogrammetric geometry
Step-by-step derivation	25%	12.5	For (a)(ii): Explicit statement of Wardrop's equations, clear substitution of values with intermediate steps shown, proper handling of (Na + Ny) terms; for (b)(i): Scale computation at each elevation, sequential coordinate transformation with clear matrix/vector representation; for (b)(ii): Closure error computation, systematic latitude-departure table, explicit tan⁻¹ calculation with quadrant analysis; all derivations logically sequenced with justification for each step	Correct final answers but with skipped intermediate steps; missing explicit statement of formulae used; adequate traverse computation but condensed photogrammetric derivation; some logical gaps in floating car calculation sequence	Final answers without derivation; or incorrect sequence leading to right answer by wrong method; missing essential steps like elevation correction in photogrammetry; no working shown for bearing calculation; disorganized presentation preventing verification
Practical interpretation	15%	7.5	For (a): Interprets speed results in urban traffic context (congestion levels, LOS per IRC); for (b)(i): Validates computed distance against typical photogrammetric accuracy; for (c): Links each equipment to specific Indian projects (sheep foot roller in Tehri Dam core, dragline in Sone canal system, tower crane in Mumbai/Delhi high-rises), mentions productivity factors, and notes equipment limitations in Indian conditions	Generic practical mentions without specific Indian context; basic equipment applications stated; acknowledges traffic congestion for speed results but no IRC reference; mentions construction sectors without project specificity	No practical interpretation; purely theoretical treatment; incorrect practical associations (e.g., sheep foot roller for granular soils); irrelevant digressions; failure to connect numerical results to engineering significance

Q3

Directive word: Explain

How this answer will be evaluated

Approach

Key points expected

Evaluation rubric

Practice this exact question

More from Civil Engineering 2024 Paper II