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MAHALAKSHMI ENGINEERING COLLEGE TIRUCHIRAPALLI-621213

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QUESTION BANK CE2254 SURVEYING - II UNIT 5 – HYDROGRAPHIC AND ADVANCE SURVEYING PART A What do you understand by parallax? (AUC Nov/Dec 2012) (AUC Apr/May 2010) Parallax is defined as the apparent displacement of an object due to the real displacement of the observer. For example the apparent movement of the stars is due to the real displacement of the observer from one position to another upon the earth’s orbit. Distinguish between crab and drift. (AUC Apr/May 2010) Crab: The angle formed between the flight line and the edges of the photograph in the direction of flight is designated by a term called crab. The crab is caused in the photograph when the focal plane of the camera is not square with the direction of flight. Drift: Drift is caused by the failure of the photograph to stay on the predetermined flight line. If an aircraft is allowed to go on its course without allowance for wind velocity, it will drift. What do you mean by sounding? (AUC Nov/Dec 2010) (AUC Apr/May 2011) The measurements of depths below the water surface are called soundings. It is to find the depth measurement in land with reference to a datum. Distinguish between ‘terrestrial photogrammetry’ and ‘aerial photogrammetry’. (AUC Apr/May 2011) Terrestrial photogrammetry: Photographs taken from a fixed position on or near the ground and the branch deals on such aspects are called terrestrial photogrammetry. Aerial photogrammetry: Aerial photogrammetry is the other branch wherein the photograph are taken by cameras mounted on an aircraft flying over the area. What is meant by scale of a photograph? (AUC May/June 2009) Scale of photograph is obtained from the ratio of the distance of any two points on the photograph and the distance between the corresponding points on the ground. The two points chosen for scaling should lie nearly equidistant on either side of the principal point. Write the concept of map – marking in cartography? (AUC May/June 2009) While there are many steps involved in the map making process, they can be grouped into three main stages: data collection, organization, and manipulation; map design and artwork preparation; and map reproduction. What is a fathometer? (AUC May/June 2012) A fathometer is used for measuring depth of large rivers and seas with depth more than 10 m. by this instrument the depth of water is obtained by sending a sound impulse from the surface of water towards the bottom of the river or sea bed.

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IV Semester Civil CE2254-Surveying II by M.Dinagar A.P / Civil

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8. Differentiate between ‘tilted photograph’ and ‘oblique photograph’. (AUC May/June 2012) Tilted photograph: A tilted photograph is an aerial photograph made with the camera axis unintentionally. The tilt from the vertical axis is usually less than 3O. Oblique photograph: An oblique photograph is the one made in an aerial photograph intentionally between the horizontal and the vertical. 9. Define hydrographic surveying. (AUC Nov/Dec 2010) (AUC May/June 2013) Hydrographic surveying is that branch of surveying connected with all the observations and measurements concerned with bodies of water. These observations and measurements are needed for the design of marine structures, hydraulic structures and other cross-drainage works. 10. Define EDM. (AUC May/June 2013) Electro-magnetic distance measurement is a general term used collectively in the measurement of distances applying electronic methods. Basically the EDM method is based on generation, propagation, reflection and subsequent reception of electromagnetic waves. 11. What are the equipments used for sounding? (AUC Nov/Dec 2012) i) Sounding rods or poles. ii) Lead lines or sounding cables. iii) Fathometer. 12. What is meant by three point problem in hydrographic surveying? If a sounding is located by two angles from the boat by observations to three known points on the shore, the plotting can be done adopting three-point problem. The three point problem may be solved by mechanical, graphical or analytical methods. 13. Explain the term ‘Cartography’. Cartography: Cartography has always been closely associated with Geography and Surveying. Its recognition as a distinct discipline is relatively recent. Scientific journals dealing with Cartography began to appear in the middle of the twentieth century. Numerous definitions of Cartography have appeared in the literature. Earlier definitions tend to emphasize map making while more recent definitions also include map use within the scope of Cartography. 14. What are lunar and solar tides? Lunar tides: The periodical variations in natural water level are called as tides. The resultant force between the earth and moon causes lunar tides. Solar tides: The production of solar tides is due to force of attraction between earth and sun which is similar to the lunar tides. 15. What is meant by photo-theodolite? Photo-theodolite is a combination of a camera and a theodolite. It is used to take photographs and measuring angles. 16. Define tilt displacement. Tilt displacement: Tilt distortion or tilt displacement is defined as the difference between the distance of the image of a point on the tilted photograph from the isocentre and the distance of the image of the same point on the photograph from the isocentre if there had been no tilt. IV Semester Civil CE2254-Surveying II by M.Dinagar A.P / Civil

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17. Name the different methods for soundings.  By cross rope  By range and time intervals  By range and one angle from the shore  By range and one angle from boat  By two angles from the shore  By two angles from the boat  By one angle from shore and one angle from boat  By intersecting ranges  By tacheometry 18. Give the significance of trilateration. There is no angular measurement is made. The three sides of triangles are measured precisely using the EDM equipment. This technique is useful when angular measurement is difficult or impossible due to any reason. 19. Define cadastral surveying. Cadastral surveying is the one which is conducted in order to determine the boundaries of fields, estates, houses, etc. 20. What are the uses of photogrammetry?  Construction of planimetric and topographic maps.  Mountainous and hilly areas with less number of trees can be very satisfactorily surveyed.  Aerial surveying is most suitable for reconnaissance.  Acquisition of military intelligence.  Interpretation of geology and soil details.  Largely used for the surveys of buildings. PART B 1. Explain Direction and velocity of current by floats using three methods.

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(AUC Nov/Dec 2010)

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IV Semester Civil CE2254-Surveying II by M.Dinagar A.P / Civil

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2. Explain the location of floats with two theodolite method.

(AUC Nov/Dec 2010)

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In this method, a point is fixed independent of the range by angular observations from two points on the shore. The method is generally used to locate some isolated points. If this method is used on an extensive survey, the boat should be run on a series of approximate ranges. Two instruments and two instrument men are required. The position of instrument is selected in such a way that a strong fix is obtained. New instrument stations should be chosen when the intersection angle (θ) falls below 30°.

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Thus A and B are the two instrument stations. The distance d between them is very accuarately measured. The instrument stations A and B are precisely connected to the ground traverse or triangulation, and their positions on plan are known. With both the plates clamped to zero, the instrument man at A bisects B ; similarly with both the plates clamped to zero, the instrument man at B bisects A. Both the instrument men then direct the line of sight of the telescope towards the leadsman and continuously follow it as the boat moves. The surveyor on the boat holds a flag for a few seconds, and on the fall of the flag the sounding and the angles are observed simultaneously. The co-ordinates of the position P of the sounding may be computed from the relations: d tanβ d tan α tanβ x = ; y = tan α + tanβ tan α + tanβ

(AUC May/June 2013) (AUC Nov/Dec 2010)

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Advantages:  The preliminary work of setting out and erecting range signals is eliminated.  It is useful when there are strong currents due to which it is difficult to row the boat along the range line. 3. Explain Tilt distortion with neat sketch in photographic method.

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4. Write in detail about the methods of locating soundings. (AUC May/June 2009) (AUC Apr/May 2011) (AUC Apr/May 2010) The methods of locating soundings:

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i) By cross rope. ii) By range and time intervals. iii) By range and one angle from the shore. iv) By range and one angle from the boat. v) By two angles from the shore. vi) By two angles from the boat. vii) By one angle from shore and one from boat. viii) By intersecting ranges. ix) By tacheometry. Location by Cross-Rope:

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This is the most accurate method of locating the soundings and may be used for rivers, narrow lakes and harbours. It is also used to determine the quantity of materials removed by dredging the soundings being taken before and after the dredging work is done. A single wire or rope is stretched across the channel etc. and is marked by metal tags at appropriate known distance along the wire from a reference point or zero station on shore. The soundings are then taken by a weighted pole. The position of the pole during a sounding is given by the graduated rope or line. ii) By range and time intervals: In this method, the boat is kept in range with the two signals on the shore and is rowed along it at constant speed. Soundings are taken at different time intervals. Knowing the constant speed and the total time elapsed at the instant of sounding, the distance of the total point can be known along the range. The method is used when the width of channel is small and when great degree of accuracy is not required. However, the method is used in

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conjunction with other methods, in which case the first and the last soundings along a range are located by angles from the shore and the intermediate soundings are located by interpolation according to time intervals. iii) By range and one angle from the shore: In this method, the boat is ranged in line with the two shore signals and rowed along the ranges. The point where sounding is taken is fixed on the range by observation of the angle from the shore. As the boat proceeds along the shore, other soundings are also fixed by the observations of angles from the shore. Thus B is the instrument station, A 1 A2 is the range along which the boat is rowed and α 1, α2, α3 etc., are the angles measured at B from points 1, 2, 3 etc. To fix a point by observations from the shore, the instrument man at B orients his line of sight towards a shore signal or any other prominent point (known on the plan) when the reading is zero. He then directs the telescope towards the leadsman or the bow of the boat, and is kept continually pointing towards the boat as it moves. The surveyor on the boat holds a flag for a few seconds and on the fall of the flag, the sounding and the angle are observed simultaneously.

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The angles are generally observed to the nearest 5 minutes. The time at which the flag falls is also recorded both by the instrument man as well as on the boat. In order to avoid acute intersections, the lines of soundings are previously drawn on the plan and suitable instrument stations are selected. iv) By range and one angle from the boat:

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The method is exactly similar to the previous one except that the angular fix is made by angular observation from the boat. The boat is kept in range with the two shore signals and is rowed along it. At the instant the sounding is taken, the angle, subtended at the point between the range and some prominent point B on the sore is measured with the help of sextant. The telescope is directed on the range signals, and the side object is brought into coincidence at the instant the sounding is taken. The accuracy and ease of plotting is the same as obtained in the previous method. Generally, the first and the last soundings, and some of the intermediate soundings are located by angular observations and the rest of the soundings are located by time intervals.

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As compared to the previous methods, this method has the following advantages:  Since all the observations are taken from the boat, the surveyor has better control over the operations.  The mistakes in booking are reduced since the recorder books the readings directly as they are measured.  On important fixes, check may be obtained by measuring a second angle towards some other signal on the shore.  Obtain good intersections throughout; different shore objects may be used for reference to measure the angles. v) By two angles from the shore:

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In this method, a point is fixed independent of the range by angular observations from two points on the shore. The method is generally used to locate some isolated points. If this method is used on an extensive survey, the boat should be run on a series of approximate ranges. Two instruments and two instrument men are required. The position of instrument is selected in such a way that a strong fix is obtained. New instrument stations should be chosen when the intersection angle (θ) falls below 30°.

Thus A and B are the two instrument stations. The distance d between them is very accuarately measured. The instrument stations A and B are precisely connected to the ground traverse or triangulation, and their positions on plan are known. With both the plates

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clamped to zero, the instrument man at A bisects B ; similarly with both the plates clamped to zero, the instrument man at B bisects A. Both the instrument men then direct the line of sight of the telescope towards the leadsman and continuously follow it as the boat moves. The surveyor on the boat holds a flag for a few seconds, and on the fall of the flag the sounding and the angles are observed simultaneously. The co-ordinates of the position P of the sounding may be computed from the relations: d tanβ d tan α tanβ x = ; y = tan α + tanβ tan α + tanβ

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Advantages:  The preliminary work of setting out and erecting range signals is eliminated.  It is useful when there are strong currents due to which it is difficult to row the boat along the range line. vi) By two angles from the boat:

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In this method, the position of the boat can be located by the solution of the threepoint problem by observing the two angles subtended at the boat by three suitable shore objects of known position. The three-shore points should be well-defined and clearly visible. Prominent natural objects such as church spire, lighthouse, flagstaff, buoys etc., are selected for this purpose. If such points are not available, range poles or shore signals may be taken.

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Thus A, B and C are the shore objects and P is the position of the boat from which the angles α and β are measured. Both the angles should be observed simultaneously with the help of two sextants; at the instant the sounding is taken. If both the angles are observed by surveyor alone, very little time should be lost in taking the observation. The angles on the circle are read afterwards. The method is used to take the soundings at isolated points. The surveyor has better control on the operations since the survey party is concentrated in one boat. Advantages:  Preliminary work setting out and erecting range signals is eliminated.  The position of the boat is located by the solution of the three point problem either analytically or graphically.

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vii) By one angle from shore and one from boat:

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This method is the combination of methods 5 and 6 described above and is used to locate the isolated points where soundings are taken. Two points A and B are chosen on the shore, one of the points (say A) is the instrument station where a theodolite is set up, and the other (say B) is a shore signal or any other prominent object. At the instant the sounding is taken at P, the angle α at A is measured with the help of a sextant. Knowing the distance d between the two points A and B by ground survey, the position of P can be located by calculating the two co-ordinates x and y. viii) By intersecting ranges:

This method is used when it is required to determine by periodical sounding at the same points, the rate at which silting or scouring is taking place. This is very essential on the harbors and reservoirs. The position of sounding is located by the intersection of two

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ranges, thus completely avoiding the angular observations. Suitable signals are erected at the shore. The boat is rowed along a range perpendicular to the shore and soundings are taken at the points in which inclined ranges intersect the range, as illustrated in figure. However, in order to avoid the confusion, a definite system of flagging the range poles is necessary. The position of the range poles is determined very accurately by ground survey. ix) By tacheometry:

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The method is very much useful in smooth waters. The position of the boat is located by tacheometric observations from the shore on a staff kept vertically on the boat. Observing the staff intercept s at the instant the sounding is taken, the horizontal distance between the instrument stations and the boat is calculated.

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The direction of the boat (P) is established by observing the angle (α) at the instrument station B with reference to any prominent object A The transit station should be near the water level so that there will be no need to read vertical angles. The method is unsuitable when soundings are taken far from shore. 5. Derive the parallax equation for determining the height from a pair of vertical photographs. (AUC Apr/May 2010)

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6. Explain the following: i) Scale of a vertical photograph. ii) Relief displacement on a vertical photograph. Scale of a vertical photograph:

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(AUC Apr/May 2011)

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ii) Relief displacement on a vertical photograph:

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7. A section line AB appears to be 10.16 cm on a photograph for which the focal length is 16 cm. The corresponding line measures 2.54 cm on a map which is to a scale 1/50,000. The terrain has an average elevation of 200 m above mean sea level, Calculate the flying altitude of the aircraft, above mean sea level, when the photograph was taken. (AUC Apr/May 2011)

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Solution: The relation between photo scale and map scale is given by Photo scale Photo distance = Map scale Map distance

1 50000 1 Photo scale = n

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1 n

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Again, S200 =

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1 f = n H - h ( 16 / 100 ) H - 200

H = 2200 m IV Semester Civil CE2254-Surveying II by M.Dinagar A.P / Civil

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8. What is a three point problem in hydrographic surveying? What are the various solutions for the problem? Explain in detail. (AUC May/June 2009) Given the three shore signals A, B and C, and the angles α and β subtended by AP, BP and CP at the boat P, it is required to plot the position of P. 1. Mechanical Solution (i) By Tracing Paper Protract angles α and β between three radiating lines from any point on a piece of tracing paper. Plot the positions of signals A, B, C on the plan. Applying the tracing paper to the plan, move it about until all the three rays simultaneously pass through A, B and C. The apex of the angles is then the position of P which can be pricked through.

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(ii) By Station Pointer: The station pointer is a three-armed protractor and consists of a graduated circle with fixed arm and two movable arms to the either side of the fixed arm. All the three arms have beveled or fiducial edges. The fiducial edge of the central fixed arm corresponds to the zero of the circle. The fiducial edges of the two moving arms can be set to any desired reading and can be clamped in position. They are also provided with verniers and slow motion screws to set the angle very precisely. To plot position of P, the movable arms are clamped to read the angles α and β very precisely. The station pointer is then moved on the plan till the three fiducial edges simultaneously touch A, B and C. The centre of the pointer then represents the position of P which can be recorded by a prick mark.

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2. Graphical Solutions (a) First Method:

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Let a, b and c be the plotted positions of the shore signals A, B and C respectively and let α and β be the angles subtended at the boat. The point p of the boat position p can be obtained as under:  Join a and c.  At a, draw ad making an angle β with ac. At c, draw cd making an angle α with ca. Let both these lines meet at d.  Draw a circle passing through the points a, d and c.  Join d and b, and prolong it to meet the circle at the point p which is the required position of the boat.

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Proof: From the properties of a circle, apd = acd = α and cpd = cad = β which is the required condition for the solution. (b) Second Method:

 Join ab and bc.  From a and b, draw lines ao1 and bo1 each making an angle (90° - α) with ab on the side towards p. Let them intersect at 01.  Similarly, from b and c, draw lines each making an angle (90° - β) with ab on the side towards p. Let them intersect.

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 With – as the centre, draw a circle to pass through a and b. Similarly, with – as the centre draw a circle to pass through b and c. Let both the circles intersect each other at a point p. p is then the required position of the boat. ao1b = 180° - 2 (90° - α) = 2α apb = ½ ao1b = α Similarly, bo2c = 180° - 2 (90° - β) = 2β and bpc = ½ bo2c = β. The above method is sometimes known as the method of two intersecting circles. (c) Third Method:

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Proof:

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 Join ab and bc.  At a and c, erect perpendiculars ad and ce.  At b, draw a line bd subtending angle (90° - α) with ba, to meet the perpendicular through a in d.  Similarly, draw a line be subtending an angle (90° - β) with bc, to meet the perpendicular through c in e.  Join d and e.  Drop a perpendicular on de from b. The foot of the perpendicular (i.e. p) is then the required position of the boat. 9. Explain briefly the different methods of prediction of tides. (AUC May/June 2009) i) Age of tide ii) Lunitidal interval iii) Mean establishment iv) Vulgar establishment i) Age of tide: This condition is fulfilled only in southern ocean extending southwards from about 40 O S latitude. It is the only portion of ocean where equilibrium figure may be developed. Primary tide waves are generated and secondary waves are propagated into pacific, Atlantic and Indian oceans. The velocity of wave travel may exceed 1000 km per hour, though it is less in shallow water. The amplitude of vertical range from crest to trough is not more than 60 to 90 cm. due to direction of propagation of tide wave, high or low water occurs at different times at various places on the same meridian. “The time which elapse between the generation of spring tide and its arrival at the place is called Age of tide”. ii) Lunitidal interval: “It is the time interval that elapses between the moon’s transits and occurrence of next high water”. The value is found to vary because of existence of priming and lagging. The IV Semester Civil CE2254-Surveying II by M.Dinagar A.P / Civil

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Correction in minutes

0

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values can be observed and plotted for a fortnight against the times of moon’s transits, a curve is obtained. A curve has approximately same for each fortnight and used for rough prediction of time of tide. The time of transit of moon at Greenwich is given in nautical almanac. The time of transit can be derived by adding 2 m for every hour of west longitude and subtracting 2 m for every hour of east longitude. iii) Mean establishment: The average value of Lunitidal at a place is known as mean establishment as shown by dotted line. If the value is known and Lunitidal interval and the time of high water can be estimated. The procedure of determination are  Find from charts, the age of tide and mean establishment for the place.  Knowing the hour of moon’s transit, determine the time of moon’s transit on the day of generation of tide. Day of generation = day in question – age of tide  Corresponding to time of transit of moon on the day of generation of tide, find out the amount of priming or lagging correction.  Add the priming or lagging correction to mean establishment to get Lunitidal interval for day in question.  Add the Lunitidal interval to the time of moon’s transit on the day in question to get approximate time of high water. Hour of moon’s transit 0 1 2 3 4 5 6 7 8 9 10 11 12 -16

-31 -41

-44

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iv) Vulgar establishment: “It is defined as the value of Lunitidal interval on the day of full moon or change of moon”. Its value is always more than establishment since lagging correction in second or fourth quadrant is positive. The difference between vulgar establishment and mean establishment depends upon age of tide. The value of vulgar establishment is approximately equal to clock time at which high water occurs on day of full moon or change of moon. Mean establishment = vulgar establishment – lagging correction Height of tide: The approximate height of tide of known rise at any time between high and low water can be expressed 1 H = h + r cos θ 2 H = required height of tide above datum h = height of mean tide level above datum

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θ =

interval from high water X 180O interval between high and low water

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10. The scale of an aerial photograph is 1 cm = 100 m. the photograph size is 20 cm x 20 cm. determine the number of photographs required to cover an area of 100 sq.km, if the longitudinal overlap is 60% and the side lap is 30%. (AUC May/June 2012) Solution: Scale, S = 100 Width of photograph, W p = 20 cm = 0.2 m Length of photograph, Lp = 20 cm = 0.2 m Percentage longitudinal overlap, Ol = 60% = 0.60

S Lp (1 Ol ) 100 x 0.2 ( 1 8m

Wg

S Wp (1 Ow )

Ap

100 x 0.2 ( 1 14 m Lg x Wg

0.6 )

0.3 )

8 x 14 112 sq.m

Ag

Ap

100 x 10002 = 892857.14 112

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Percentage of side overlap, Ow = 30% = 0.30 Area of track to be photographed, A g = 100 sq.km Net ground distance,

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11. Explain the principle underlying “Electronic Distance Measurement”. Write a note on errors in EDM. (AUC May/June 2013) (AUC May/June 2012) Principle: Electronic Distance Measurement (EDM) is a general term used collectively in the measurement of distances applying electronic methods. Basically the EDM method is based on generation, propagation, reflection and subsequent reception of electromagnetic waves. Every EDM equipment should perform the following functions:  Generation of carrier wave and measuring wave frequencies.  Modulation and demodulation of the carrier wave.  Measurement of the phase difference between the transmitted and received measuring waves.  Display, in some form, the result of this measurement.

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Scale Error: Scale error is proportional to the length of the line measured and is caused by:  internal frequency errors, including those caused by external temperature and instrument "warm up" effects;  errors of measured temperature, pressure and humidity which affect the velocity of the signal; and  non-homogeneous emissions/reception patterns from the emitting and receiving diodes (phase in-homogeneities).

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R

The scale expressed as R.F. if given by

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Cyclic Error The precision of an EDM instrument is dependent on the precision of the internal phase measurement. Unwanted interference either through electronic/optical cross talk or multi-path effects of the transmitted signal onto the received signal causes cyclic error. The major form of the cyclic error is sinusoidal with a wavelength equal to the unit length of the instrument. The unit length is the scale on which the EDM instrument measures the distance, and is derived from the fine measuring frequency. Unit length is equal to one half of the modulation wavelength. The magnitude of the cyclic error can be of the order of 5 - 10 mm, but it will vary depending on the actual length measured. 12. A camera having focal length of 20cm is used to take a vertical photograph of a terrain having an average elevation of 1500m. What is the height above sea level at which an aircraft must fly in order to get the scale of 1:8000? (AUC May/June 2012) Solution:

1 8000 H

f

H

f

0.2 H 1500 3100 m above m.s.l.

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13. Given the three shore signals A, B and C and the angles α and β subtended by AP, BP and CP at the boat P, it is required to plot the position of P (refer figure below). How will you obtain the position of P using a station pointer? (AUC May/June 2012)

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Solution to three-point problem is also obtained using mechanical devices. Most usual solution is obtained by use of one such machine named as station-pointer. This instrument consists of three arms, the fiducial edges of which radiate to a common centre. The middle arm is fixed, while the two outer arms are capable of rotation about the centre of the instrument. These two arms are fitted with verniers reading to 1 minute and with clamp and tangent screw arrangements for accurate adjustment. In order to use the instrument the arms are so set by means of the verniers a to include the observed angles 1 and 2 . The instrument is moved over the paper until the fiducial edges pass simultaneously through the three points a, b, c on the chart. The centre is then marked with a hard pencil or pricker or rays drawn along the edges of the arms which are produced to intersect and the point P is thus obtained.

IV Semester Civil CE2254-Surveying II by M.Dinagar A.P / Civil

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14. write short notes on i) Aerial photograph ii) Stereoscopy. i) Aerial photograph:

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(AUC Nov/Dec 2012)

IV Semester Civil CE2254-Surveying II by M.Dinagar A.P / Civil

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ii) Stereoscopy:

(AUC Nov/Dec 2012)

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15. How to measure angles with the sextant?

IV Semester Civil CE2254-Surveying II by M.Dinagar A.P / Civil

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16. Explain the procedure to use fathometer in ocean sounding.

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A Fathometer is used in ocean sounding where the depth of water is too much, and to make a continuous and accurate record of the depth of water below the boat or ship at which it is installed. It is an echo-sounding instrument in which water depths are obtained be determining the time required for the sound waves to travel from a point near the surface of the water to the bottom and back. It is adjusted to read depth on accordance with the velocity of sound in the type of water in which it is being used. A fathometer may indicate the depth visually or indicate graphically on a roll which continuously goes on revolving and provide a virtual profile of the lake or sea.

IV Semester Civil CE2254-Surveying II by M.Dinagar A.P / Civil

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17. Explain the different types of tides in detail. Tides: All celestial bodies exert a gravitational force on each other. These forces of attraction between earth and other celestial bodies (mainly moon and sun) cause periodical variations in the level of a water surface, commonly known as tides. Types of tides: i) Lunar tides ii) Solar tides iii) Spring and neap tide (combined effect) iv) Other effects i) Lunar tides: The figure shows the earth and the moon, with their centres of masses O1 and O2 respectively. Since moon is very near to the earth, it is the major tide producing force. To start with, we will ignore the daily rotation of the earth on its axis. Both earth and moon attract each other, and the force of attraction would act along O1 O2. Let O be the common centre of gravity of earth and moon. The earth and moon revolve monthly about O, and due to this revolution their separate positions are maintained. The distribution of force is not uniform, but it is more for the points facing the moon and less for remote points. Due to the revolution of earth about the common centre of gravity O, centrifugal force of uniform intensity is exerted on all the particles of the earth. The direction of this centrifugal force is parallel to O1O2 and acts outward. Thus, the total force of attraction due to moon is counter-balanced by the total centrifugal force, and the earth maintains its position relative to the moon. However, since the fore of attraction is not uniform, the resultant force will very all along. The resultant forces are the tide producing forces. Assuming that water has no inertia and viscosity, the ocean enveloping the earth’s surface will adjust itself to the unbalanced resultant forces, giving rise to the equilibrium. Thus, there are two lunar tides at A and B, and two low water positions at C and D. The tide at A is called the superior lunar tide or tide of moon’s upper transit, while tide at B is called inferior or antilunar tide.

Now let us consider the earth’s rotation on its axis. Assuming the moon to remain stationary, the major axis of lunar tidal equilibrium figure would maintain a constant position. Due to rotation of earth about its axis from west to east, once in 24 hours, point A would occupy successive position C, B and D at intervals of 6 h. Thus, point A would experience regular variation in the level of water. It will experience high water (tide) at intervals of 12 h and

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low water midway between. This interval of 6 h variation is true only if moon is assumed stationary. However, in a lunation of 29.53 days the moon makes one revolution relative to sun from the new moon to new moon. This revolution is in the same direction as the diurnal rotation of earth, and hence there are 29.53 transits of moon across a meridian in 29.53 mean solar days. This is on the assumption that the moon does this revolution in a plane passing through the equator. Thus, the interval between successive transits of moon or any meridian will be 24 h, 50.5 m. Thus, the average interval between successive high waters would be about 12 h 25 m. The interval of 24 h 50.5 m between two successive transits of moon over a meridian is called the tidal day. ii) Solar tides: The phenomenon of production of tides due to force of attraction between earth and sun is similar to the lunar tides. Thus, there will be superior solar tide and an inferior or antisolar tide. However, sun is at a large distance from the earth and hence the tide producing force due to sun is much less. Solar tide = 0.458 Lunar tide

iii) Spring and neap tides: Solar tide = 0.458 Lunar tide. Above equation shows that the solar tide force is less than half the lunar tide force. However, their combined effect is important, especially at the new moon when both the sun and moon have the same celestial longitude, they cross a meridian at the same instant.

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Assuming that both the sun and moon lie in the same horizontal plane passing through the equator, the effects of both the tides are added, giving rise to maximum or spring tide of new moon. The term ‘spring’ does not refer to the season, but to the springing or waxing of the moon. After the new moon, the moon falls behind the sun and crosses each meridian 50 minutes later each day. In after 7 ½ days, the difference between longitude of the moon and that of sun becomes 90°, and the moon is in quadrature. The crest of moon tide coincides with the trough of the solar tide, giving rise to the neap tide of the first quarter. During the neap tide, the high water level is below the average while the low water level is above the average. After about 15 days of the start of lunation, when full moon occurs, the difference between moon’s longitude and of sun’s longitude is 180°, and the moon is in opposition. However, the crests of both the tides coincide, giving rise to spring tide of full moon. In about 22 days after the start of lunation, the difference in longitudes of the moon and the sun becomes 270° and neap tide of third quarter is formed. Finally, when the moon reaches to its new moon position, after about 29 ½ days of the previous new moon, both of them have the same celestial longitude and the spring tide of new moon is again formed making the beginning of another cycle of spring and neap tides. iv) Other effects: The length of the tidal day, assumed to be 24 hours and 50.5 minutes is not constant because of (i) varying relative positions of the sun and moon, (ii) Relative attraction of the sun and moon, (iii) Ellipticity of the orbit of the moon (assumed circular earlier) and earth, (iv) Declination (or deviation from the plane of equator) of the sun and the moon, (v) Effects of the land masses and (vi) Deviation of the shape of the earth from the spheroid. Due to these, the high water at a place may not occur exactly at the moon’s upper or lower transit. The effect of varying relative positions of the sun and moon gives rise to what are known as priming of tide and lagging of tide. At the new moon position, the crest of the composite tide is under the moon and normal tide is formed. For the positions of the moon between new moon and first quarter, the high water at any place occurs before the moon’s transit, the interval between successive high water is less than the average of 12 hours 25 minutes and the tide is said to prime. For positions of moon between the first quarter and the full moon, the high water at any place occurs after the moon transits, the interval between successive high water is more than the average, and tide is said to lag. Similarly, between full moon and 3rd quarter position, the tide primes while between the 3rd quarter and full moon position, the tide lags. At first quarter, full moon and third quarter position of moon, normal tide occurs. Due to the several assumptions made in the equilibrium theory, and due to several other factors affecting the magnitude and period of tides, close agreement between the results of the theory, and the actual field observations is not available. Due to obstruction of land masses, tide may be heaped up at some places. Due to inertia and viscosity of sea water, equilibrium figure is not achieved instantaneously. Hence prediction of the tides at a place must be based largely on observations.

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18. Explain the method of plotting of plain metric maps by radial method.

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## UNIT 5- BY Civildatas.blogspot.in.pdf

chosen for scaling should lie nearly equidistant on either side of the principal point. 6. Write the concept of map â marking in cartography? (AUC May/June 2009).

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