CE-303 Surveying - Jun 2024 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aWhat is surveying? Explain the importance of surveying in Civil Engineering.
   How to answer

   • Definition of surveying (art/science of determining relative positions)
   • Primary divisions: Plane and Geodetic surveying
   • Role in civil engineering projects (planning, design, setting out)
   • Key applications: roads, dams, bridges, town planning
2. 7 Marks
   bWrite the short notes on the following:

   1. i)True meridian and magnetic meridian
   2. ii)True bearing and magnetic bearing
   3. iii)Fore bearing and back bearing
   How to answer

   • Define True Meridian (geographical) vs Magnetic Meridian (freely suspended needle)
   • Define True Bearing vs Magnetic Bearing, magnetic declination relationship
   • Define Fore Bearing (FB) and Back Bearing (BB), and relationship $BB = FB \pm 180^\circ$
3. 7 Marks
   aExplain the geometry of theodolite with neat sketch.
   How to answer

   • Neat labelled schematic of transit theodolite showing fundamental lines
   • Vertical axis, horizontal axis (trunnion axis), line of collimation, altitude level axis, plate level axis
   • Geometric relationships and conditions between the axes
4. 7 Marks
   bWhat is trigonometric leveling? An instrument was set up at a point $200\text{ m}$ away from a transmission tower. The angle of elevation to the top of the tower was $30^\circ 42'$, whereas the angle of depression to the bottom was $2^\circ 30'$. Calculate the total height of the transmission tower.
   How to answer

   • Define trigonometric leveling (indirect leveling using vertical angles and horizontal distances)
   • Draw diagram showing instrument, horizontal line of sight, angles $\alpha_1$ and $\alpha_2$
   • Calculate height above horizontal: $h_1 = 200 \times \tan(30^\circ 42')$, where $\tan(30^\circ 42') \approx 0.5938 \Rightarrow h_1 \approx 118.75\text{ m}$
   • Calculate depth below horizontal: $h_2 = 200 \times \tan(2^\circ 30')$, where $\tan(2^\circ 30') \approx 0.04366 \Rightarrow h_2 \approx 8.73\text{ m}$
   • Total height $H = h_1 + h_2 \approx 127.48\text{ m}$
5. 7 Marks
   aA tacheometer was set up at a station A and the readings on a vertically held staff at B were $2.255$, $2.605$, and $2.955$, the line of sight being at an inclination of $+8^\circ 24'$. Another observation on the vertically held staff at B.M. gave the readings $1.640$, $1.920$ and $2.200$, the inclination of the line of sight being $+1^\circ 6'$. Calculate the horizontal distance between A and B, and the elevation of B if the R.L. of B.M. is $418.685\text{ meters}$. The constants of the instruments were $100$ and $0.3$.
   How to answer

   • Formulas for inclined sight with staff vertical: $D = k s \cos^2 \theta + c \cos \theta$, $V = \frac{1}{2} k s \sin(2\theta) + c \sin \theta$
   • For staff at B: $s = 2.955 - 2.255 = 0.700\text{ m}$, $\theta = 8^\circ 24'$. Compute $D_{AB} = 100(0.700)\cos^2(8^\circ 24') + 0.3\cos(8^\circ 24')$, and $V_B$
   • For staff at BM: $s = 2.200 - 1.640 = 0.560\text{ m}$, $\theta = 1^\circ 6'$. Compute $V_{BM}$
   • Determine R.L. of instrument axis: $\text{RL}_{inst} = \text{RL}_{BM} + h_{BM} - V_{BM}$
   • Calculate R.L. of B: $\text{RL}_B = \text{RL}_{inst} + V_B - h_B$
6. 7 Marks
   bWhat do you understand by tacheometry? State the circumstances where this type of survey is preferred.
   How to answer

   • Definition of tacheometry / tachemetry (optical distance measurement)
   • Underlying principle: isosceles triangle / stadia method
   • Circumstances preferred: rough/broken ground, steep hills, water bodies, inaccessible areas
   • Speed advantage over direct chaining/taping
7. 7 Marks
   aWhat is the degree of curve? Derive the expression between degree of curve and radius of curve.
   How to answer

   • Define degree of curve $D$ (arc definition and chord definition)
   • State relation for standard chord/arc length ($30\text{ m}$ or $20\text{ m}$)
   • Derivation: $D \text{ (radians)} = \frac{30}{R} \Rightarrow D^\circ \times \frac{\pi}{180^\circ} = \frac{30}{R}$
   • Result: $R = \frac{30 \times 180}{\pi D} = \frac{1718.87}{D} \approx \frac{1719}{D}\text{ m}$ (or for $20\text{ m}$ chain, $R = \frac{1145.9}{D}\text{ m}$)
8. 7 Marks
   bWhat are the different types of horizontal curves? Explain with neat sketch.
   How to answer

   • List types: Simple circular curve, Compound curve, Reverse (serpentine) curve, Transition curve
   • Brief explanation of each type
   • Neat sketches showing layout, radii, tangents, and points of curvature/tangency
9. 7 Marks
   aWhat is Sounding? What are the uses of taking sounding?
   How to answer

   • Definition of sounding (measuring water depth below water surface in hydrographic survey)
   • Instruments used: sounding pole, lead line, echo sounder
   • Uses: navigation charts, dredging volume calculations, harbor/port design, subaqueous construction
10. 7 Marks
    bDefine photogrammetry, its objective and application to various fields.
    How to answer

    • Definition of photogrammetry (science and technology of obtaining reliable information through photographs)
    • Primary objectives (topographic map preparation, 3D modeling, spatial analysis)
    • Applications: highway/rail alignment, urban planning, geology, archaeology, forestry, GIS databases
11. 7 Marks
    aDescribe the process of repetition and reiteration in theodolite survey.
    How to answer

    • Repetition method: measuring an angle multiple times accumulated on horizontal circle, dividing by number of repetitions
    • Errors eliminated by repetition: graduation errors, eccentricities
    • Reiteration method: measuring several angles around a single station closing the horizon
    • Step-by-step procedure for each method
12. 7 Marks
    bExplain two-point problem of plane tabling with a neat sketch.
    How to answer

    • Definition of two-point problem (locating position of instrument station given plotted positions of two known points)
    • Step-by-step field procedure using an auxiliary station
    • Neat sketch showing known points A, B, auxiliary station, and instrument station
    • Orientation and resection rays
13. 7 Marks
    aDetermine minimum number of photographs required to cover an area of $440\text{ km}^2$ from the following data:

    1. i)Size of photograph is $25\text{ cm} \times 25\text{ cm}$
    2. ii)Scale of photograph $1\text{ cm} = 90\text{ m}$
    3. iii)Longitudinal overlap $65\%$
    4. iv)Side overlap $30\%$
    How to answer

    • Ground dimension of photograph: $L_g = 25\text{ cm} \times 90\text{ m/cm} = 2250\text{ m} = 2.25\text{ km}$, $W_g = 2.25\text{ km}$
    • Net ground length covered per photograph: $L = 2.25 \times (1 - 0.65) = 0.7875\text{ km}$
    • Net ground width covered per strip: $W = 2.25 \times (1 - 0.30) = 1.575\text{ km}$
    • Net area covered per photograph: $a = L \times W = 0.7875 \times 1.575 = 1.2403\text{ km}^2$
    • Minimum number of photographs $N = \frac{440}{1.2403} \approx 354.75 \Rightarrow 355$ photographs
14. 7 Marks
    bExplain the principle of working of nautical sextant. Draw neat sketch.
    How to answer

    • Principle: When a ray of light is reflected consecutively from two plane mirrors in the same plane, the angle between the first incident ray and the last reflected ray is twice the angle between the two mirrors
    • Derivation/proof of $\theta = 2\alpha$
    • Labeled sketch of nautical sextant showing index mirror, horizon glass, index arm, and telescope
    • Application in measuring vertical and horizontal angles in navigation/hydrographic surveying
15. 7 Marks
    aThe following offsets were taken from a chain line to an irregular boundary line at an interval of $10\text{ m}$: $0.0$, $2.5$, $3.5$, $5.0$, $4.6$, $3.2$, $0.0\text{ m}$. Compute the area between the chain line and the irregular boundary line and the end offset by Trapezoidal and Simpson's rule.
    How to answer

    • Identify offsets: $O_0=0.0$, $O_1=2.5$, $O_2=3.5$, $O_3=5.0$, $O_4=4.6$, $O_5=3.2$, $O_6=0.0$; interval $d = 10\text{ m}$; number of offsets $n=7$ (even intervals, so Simpson's rule directly applies)
    • Trapezoidal Rule: $A = 10 \times [\frac{0 + 0}{2} + 2.5 + 3.5 + 5.0 + 4.6 + 3.2] = 10 \times 18.8 = 188\text{ m}^2$
    • Simpson's Rule: $A = \frac{10}{3} [ (0+0) + 4(2.5 + 5.0 + 3.2) + 2(3.5 + 4.6) ] = \frac{10}{3} [ 4(10.7) + 2(8.1) ] = \frac{10}{3} [ 42.8 + 16.2 ] = \frac{10}{3} [ 59.0 ] \approx 196.67\text{ m}^2$
16. 7 Marks
    bIn an old map, a line AB was drawn to a magnetic bearing of $5^\circ 30'$, the magnetic declination at the time being $1^\circ\text{ East}$. To what magnetic bearing should the line be set now if the present magnetic declination is $8^\circ 30'\text{ East}$.
    How to answer

    • Determine True Bearing: $\text{TB} = \text{Old MB} + \delta_{old} = 5^\circ 30' + 1^\circ 00' = 6^\circ 30'$
    • Determine Present Magnetic Bearing: $\text{New MB} = \text{TB} - \delta_{new} = 6^\circ 30' - 8^\circ 30' = -2^\circ 00'$
    • Convert negative bearing: $360^\circ - 2^\circ 00' = 358^\circ 00'$ (or $\text{N } 2^\circ\text{ W}$ in quadrantal system)