1.4: Types of surveying : Divided according to the type of work

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1 Part Introduction Surveying: It is that art and science who specializes holding measure distances and angles and represent the measurements values on the paper in form of, map, section or chart in order to set the relative positions of horizontal and vertical points are located on the surface of the land or to compute areas and volumes. Surveying include the following acts : ( data - gathering measurements ) 1- Assign the horizontal locations for points located on the surface of the earth. 2- Find points levels relative to the known level surface (Datum), such as sea level. 3- Determine the form of terrain. 4- Set the orientation and lengths of lines. 5- Assign the border lines of the land plots. 6- Compute the areas of land plot and the quantities of cutting and filling materials 1.2 Plane surveying: It's the surveying which assumes that the earth's surface is a flat surface ( neglect the convexity of the earth ). This type is common in medium sized areas. 1.3 Geodetic surveying : It's the surveying which take into consideration the convexity of the earth, This type is common in very large sized areas and very long distance. 1.4: Types of surveying : Divided according to the type of work 1.4.1: UCadastral surveying U is the sub-field of surveying that specializes in the establishment and reestablishment of real property boundaries. It is an important component of the legal creation of properties. A cadastral surveyor must apply both the spatialmeasurement principles of general surveying and legal principles such as respect of neighboring titles : UTopographic surveying U Topographic Surveys are used to identify and map the contours of the ground and existing features on the surface of the earth or slightly above or below the earth's surface (i.e. trees, buildings, streets, walkways, manholes, utility poles, retaining walls, etc.). If the purpose of the survey is to serve as a base map for the design of a residence or building of some type, or design a road or 1

2 driveway, it may be necessary to show perimeter boundary lines and the lines of easements on or crossing the property being surveyed, in order for a designer to accurately show zoning and other agency required setbacks. Topographic Surveys require "bench marks" to which ground contours are related, information regarding surface and underground utilities, determination of required setbacks, etc : URoute surveying U Route surveying is comprised of all survey operations required for design and construction of engineering works such as highways, pipelines, canals, or railroads. At Caltrans a route surveying system is generally associated with highway design and construction : UPhotogrammetry surveying is the science of making measurements from photographs, especially for recovering the exact positions of surface points. Moreover, it may be used to recover the motion pathways of designated reference points located on any moving object, on its components and in the immediately adjacent environment : UHydrographic survey U is the science of measurement and description of features which affect maritime navigation, marine construction, dredging, offshore oil exploration/offshore oil drilling and related activities. Strong emphasis is placed on soundings, shorelines, tides, currents, seabed and submerged obstructions that relate to the previously mentioned activities : UCity surveying U It specializes in planning the streets and set up and extend sewage pipelines : UMine surveying U It includes a ground survey and below it : Units of measurement U Many different units of length, width, height, depth, and distance have been used around the world. The main units in modern use are U.S. customary units in the United Statesand the Metric system elsewhere. British Imperial units are still used for some purposes in the United Kingdom and some other countries. 2

3 U lecture U1.5.1 : Units of length and area Metric System In the metric system, each basic type of measurement (length, weight, capacity) has one basic unit of measure (meter, gram, liter). Conversions are quickly made by multiplying or dividing by factors of 10. UEnglish System The basic unit of length is the yard (yd); fractions of the yard are the inch (1/36 yd) and the foot (1/3 yd), and commonly used multiples are the rod (51/2 yd), the furlong (220 yd), and the mile (1,760 yd). The acre, equal to 4,840 square yards or 160 square rods, is used for measuring land area. 1 foot = inch = yard = 3 feet 1 foot = 12 inch 1 mile = 5280 feet U1.5.2 : Units of angles Sexagesimal system In sexagesimal divided circle from its position point to 360 section and each section is called degree and has the symbol ( ) and the degree divided into 60 minutes and symbolized by the symbol (') and every minute to 60 seconds and symbolized by the symbol (") ex : '17" Centesimal system In centesimal divided circle from its position point to 400 section and each section is called (grad) and has the symbol (g) and the grad divided into 100 section and called ( centigrade ) and symbolized by the symbol (c) and every centigrade to 100section and symbolized by the symbol (c c) and called (cent centigrade) ex : 82 g 46 c 91 cc 3

4 is lecture Radial system In radial system divided circle into (2π) of the radial angles and the Uradial angle U the angle at which the central arch that correspond to long, equal to the radius of the circle. 1.6 : UErrors and Mistakes U 400 g =360 =2π radians 1.6.1: Why Errors in Surveying Take Place And Types of Error That Occurs During Survey. The values of distances and angles measured in the field can never be equal to the true values, but by accident!!!, but the measured values may be equal to the true values if the amount of errors, mistakes was very small. Error in any quantity is the difference between the measured value and the true, if the measured value is greater than the measured true, the error is positive, and vice versa. Errors in surveying may arise from three main sources: 1. Instrumental: Surveying error may arise due to imperfection or faulty adjustment of the instrument with which measurement is being taken. For example, a tape may be too long or an angle measuring instrument may be out of adjustment. 2. Personal: Personal errors caused by the inability of the individual to make exact observations due to the limitations of human sight, touch and hearing. 3. Natural: Error in surveying may also be due to variations in natural phenomena such as temperature, humidity, gravity, wind, refraction and magnetic declination. If they are not properly observed while taking measurements, the results will be incorrect. For example, a tape may be 20 meters at 20 0 C but its length will change if the field temperature is different. 4

5 1.6.2 :Types of Surveying Errors: Ordinary errors in surveying met with in all classes of survey work may be classified as: 1. Mistakes 2. Accidental errors 3. Systematic or cumulative errors 4. Compensating errors Mistakes: Mistakes are errors which arise from inattention, inexperience, carelessness and poor judgment or confusion in the mind of the observer. They do not follow any mathematical rule (law of probability) and may be large or small, positive or negative. They cannot be measured. However, they can be detected by repeating the whole operation. If a mistake is undetected, it produces a serious effect upon the final result. Hence, every value to be recorded in the field must be checked by some independent field observation. The following are the examples of mistakes: 1-Erroneous recording, e.g. writing 69 in place of 96 2-Forgetting once chain length 3-Making mistakes in using a calculator Accidental Errors: Surveying errors can occur due to unavoidable circumstances like variations in atmospheric conditions which are entirely beyond the control of the observer. Errors in surveying due to imperfection in measuring instruments and even imperfection of eyesight fall in this category. They may be positive and may change sign. Systematic or Cumulative Errors: A systematic or cumulative error is an error that, under the same conditions, will always be of the same size and sign. A systematic error always follows some definite mathematical or physical law and correction can be determined and applied. Such errors are of constant character and are regarded as positive or negative according as they make the result great or small. Their effect is, therefore, cumulative. For example, if a tape is P cm short and if it is stretched N times, the total error in the measurement of the length will be P N cm. 5

6 The systematic errors may arise due to (i) variations of temperature, humidity, pressure, current velocity, curvature, refraction, etc. and (ii) faulty setting or improper leveling of any instrument and personal vision of an individual. The following are the examples: 1. Faulty alignment of a line 2. An instrument is not leveled properly 3. An instrument is not adjusted properly If undetected, systematic errors are very serious. Therefore, (1) all surveying equipment must be designed and used so that, whenever possible, systematic errors will be automatically eliminated, and (2) all systematic errors that cannot be surely eliminated by this means must be evaluated and their relationship to the conditions that cause them must be determined. Compensating Errors: This type or surveying error tends to occur in both directions, i.e. the error may sometimes tend to be positive and sometimes negative thereby compensating each other. They tend sometimes in on direction and sometimes in the other, i.e. they are equally likely to make the apparent result large or small. 6

7 Part measuring distance 1- direct method 2- indirect method The most direct way is the way in which uses a measuring tape. Tachometry considering as indirect method. 2.2 Tapes Tapes are used in surveying for measuring Horizontal, vertical or slope distances. Tapes are issued in various lengths and widths and graduated in variety of ways. The measuring tapes used for surveying purposes are classified in 4 types according to the material from which they are manufactured: 1. Linen or Cloth Tape. It is made of linen cloth with brass handle at zero end whose length is included in the tape length. It is very light and handy, but cannot withstand much wear and tear. So it cannot be used for accurate work. It is little used in surveying except for taking subsidiary measurements like offsets. 2. Metallic Tape. The tape is reinforced with copper wires to prevent stretching or twisting of fibers and is then called as metallic tape. They are available in many lengths but tapes of 20 m and 30 m are more commonly used. 3. Steel Tape. It is made of steel ribbon varying in width from 6 mm to 16 mm. It is available in lengths of 1, 2, 10, 30 and 50 meters. It cannot withstand rough usage and therefore it should be used with great care. 4.Invar Tape. It is made of an alloy of steel (64%) and nickel (36%). It is 6 mm wide and is available in lengths of 30 m, 50 m and 100 m. The singular advantage of such tapes is that they have a negligible coefficient of expansion compared with steel, and hence temperature variations are not critical. Their disadvantages are that the metal is soft and weak, whilst the price is more than ten times that of steel tapes 2.3 Range Poles : Ranging poles (see Fig. 2.1) are used to mark areas and to set out straight lines on the field. They are also used to mark points which 7

8 must be seen from a distance, in which case a flag may be attached to improve the visibility. Fig Pins or Arrows: Arrows are made of tempered steel wire of diameter 4mm, Its overall length is 400mm Fig

9 2.5 Pegs: Pegs (see Fig. 2.3) are used when certain points on the field require more permanent marking. Pegs are generally made of wood; sometimes pieces of tree-branches, properly sharpened, are good enough. The size of the pegs (40 to 60 cm) depends on the type of survey work they are used for and the type of soil they have to be driven in. The pegs should be driven vertically into the soil and the top should be clearly visible. Fig Plumb Bob: A plumb bob is used to check if objects are vertical. A plumb bob consists of a piece of metal (called a bob) pointing downwards, which is attached to a cord (see Fig.2.4). When the plumb bob is hanging free and not moving, the cord is vertical. Fig

10 2.7 Hand level: is used to check if objects are horizontal or vertical. Within a level there are one or more curved glass tubes, called level tubes : Setting out Straight Lines 2.8.1: Setting out straight lines over a short distance Step 1 As shown in Figure 2.5a, pole (B) is clearly visible for the observer standing close to pole (A). The observer stands 1 or 2 meters behind pole (A), closes one eye, places himself in such a position that pole (B) is completely hidden behind pole (A) (see Fig. 2.5a). Step 2 The observer remains in the same position and any pole (C in Fig. 2.5b) placed by the assistant in between (A) and (B), which is hidden behind pole (A), is on the straight line connecting (A) and (B) (see Fig. 2.5b). Step 3 The observer remains in the same position and any pole (D in Fig. 2.5c) placed behind (B), which is hidden behind poles (A), (B) and (C), is on the extension of the straight line connecting (A) and (B) (see Fig. 2.5c). Fig

11 2.8.2: Setting out straight lines over a long distance As shown in Fig. 2.6, ranging pole (B) is at quite a distance from pole (A) and it is hard to see pole (B) clearly. A flag is attached to ranging pole (B) to make it more visible Fig. 2.6 Step 1 Pole (C) is approximately set in line with (A) and (B) at about one third of the distance between (A) and (B), closer to (A) (see Fig. 2.6a). Fig.2.6a 11

12 Step 2 The observer moves to pole (C) and pole (D) is set in line with (C) and (B) (see Fig. 2.6b) Step 3 Fig.2.6b The observer moves Co pole (D) and pole (C) is reset in line with (D) and (A) (see Fig. 2.6c). 12

13 Fig.2.6c Step 4 The observer moves back to pole (C) and pole (D) is reset in line with (C) and (B) (see Fig. 2.6d). Step 5 Fig. 2.6d Continue until poles (C) and (D) do not require resetting anymore, which means that all poles (A), (B), (C) and (D) are in line (see Fig. 2.6e). Fig. 2.6e 13

14 Intermediate poles can now easily be set in line with (A) and (C), (C) and (D), or (D) and (B) Setting out straight lines over a ridge or a hill Sometimes, a straight line has to be set out between two points (A and B) which are one on each side of a hill, dyke or any other high obstacle (see Fig. 2.7); standing at point A it is impossible to see point B. A procedure by trial and error is used, which requires two observers and one, or preferably two, assistants. Step 1 Fig. 2.7 First, poles (C) and (D) are placed on top of the hill, as accurately as possible in line with (A) and (B), and in such a way that both (C) and (D) can be seen by the observers standing near pole (A) and pole (B) (see Fig. 2.7a). 14

15 Fig. 2.7a Step 2 At the indication of the observer at pole (A), pole (C) is set in line with (A) and (D); in other words pole (C) is moved from position C1, (the original position) to position C2(see Fig. 2.7b). Step 3 Fig. 2.7b 15

16 At the indication of the observer at pole (B), pole (D) is set in line with (B) and (C); in other words, pole (D) is moved from position D1, (the original position) to position D2.) (see Fig. 2.7c). Step 4 Fig. 2.7c The procedure is repeated: pole (C) is reset in line with (A) and (D) and pole (D) is reset in line with (B) and (C). Continue until no more correction is required, which means that the four poles (A), (B), (C) and (D) are in line (see Fig. 2.7d). Fig. 2.7d 16

17 2.9: Measuring Distances 2.9.1: Measuring Short Distances The following procedure is used when measuring a distance which does not exceed the total length of the chain or the tape. Step 1 Pegs are placed to mark the beginning and the end of the distance to be measured. Step 2 The back man holds the zero point of the chain (or tape) at the centre of the starting peg. The front man drags his end of the chain (or tape) in the direction of the second peg. Before measuring, the chain (or tape) is pulled straight (see Fig. 2.8). Step 3 Fig. 2.8 When using a measuring tape, the distance between the two pegs can be read directly on the tape by the front man : Measuring Long Distances Very often, the distance to be measured is longer than the length of the chain or the tape. The front man is then provided with short metal pins, called 17

18 arrows. The arrows are held together by a carrying ring. These arrows are used to mark the position of the end of the chain (or tape) each time it is laid down. Step 1 The procedure to follow when measuring long distances is: Pegs are placed (A and B) to mark the beginning and the end of the distance to be measured, and ranging poles are set in line with A and B. Step 2 The back man holds the zero point at the centre of the starting peg (A). The front mar drags his end of the chain (or tape) in the direction of peg (B). Directed by the back man, he stretches the chain, in line with the ranging poles. Then he plants an arrow to mark the end of the chain (or tape) (see Fig. 2.9a). Step 3 Fig. 2.9a Both men move forward with the chain (or tape) and the procedure is repeated, the back man starting this time from the arrow the front man has just planted (see Fig. 2.9b). Step 4 Fig. 2.9b 18

19 The procedure is repeated until the remaining distance between the last arrow and the peg (B) is less than one chain (or tape) length (see Fig. 2.9c). Step 5 Fig. 2.9c The remaining distance is measured using the procedure as described in section The number of arrows used during the procedure represents the number of times the full length of the chain (or tape) has been laid out. The total distance measured is then calculated by the formula: Total distance= number of arrows used x length of the chain (or tape) + distance between the last arrow and peg B EXAMPLE The distance between two pegs (A) and (B) has been chained. When reaching peg (B), the back man has used 7 arrows. 23 links have been counted between the last arrow and peg (B), What is the total distance between peg (A) and peg (B)? Given number of arrows used by the back man = 7 length of the chain = 20 m number of links between the last arrow and peg (B) = 23 length of one link = 20 cm = 0.20 m Answer Distance between the last arrow and peg (B) = number of links x length of one link = 23 x 0.2 = 4.6 m Total distance = (number of used arrows x chain length) + (distance between last arrow and peg B) = (7 x 20 m) m = m 2.9.3:Measuring Distances in Tall Vegetation 19

20 Distances may have to be measured in a field where a tall crop or tall grass is cultivated. The measuring tape (a chain would be too heavy) must then be stretched horizontally by the two men above the crop. When measuring distances it is important to keep the tape horizontal. Push two arrows or two pegs into the soil to mark the distance to be measured (see Fig. 2.10). Plumb bobs can be used to check if the measuring tape is indeed horizontal. If horizontal, the free hanging plumb bobs (immediately above the arrows) are perpendicular to the measuring tape. In other words, the measuring tape and the plumb bobs form right angles. Fig

21 2.10: Correction & Errors of measurement by TAPES :Error in length of tapes (standardization correction) Due to manufacturing defects the actual length of the tape may be different from its designated or nominal length. Also with use the tape may stretch causing change in the length and it is imperative that the tape is regularly checked under standard conditions to determine its absolute length. The correction for absolute length or standardization is given by C s or L =ll ff ll ss (when the measured distance is equal one standard length of the tape ) C s or L =( ll ff -ll ss )* LL ll ss (when the measured distance is more than one standard length of the tape ) L=L*(ll ff /ll ss ) - L (The general form) C s or L =Correction in meters L' = corrected distance needed L= Field distance measured in meters. ll ff = Actual length (field length). ll ss = Nominal length (standard length). Ex: Assuming that the nominal length of the tape was 30meters, and its true length was meters,and the measured distance was 195 meters. compute : 1- The correction in the length of the tape. 2- The total correction in measured distance. 3- The true measured distance. 21

22 Ans: (1) L=ll ff ll ss C s = = m (2) L =(ll ff -ll ss )* LL ll ss or L=L*(ll ff /ll ss ) - L *(195/30)= m L'=L- L (3) = m :Error due to change in temperature The real lengths tapes be equal to the nominal total length in standard conditions of temperature and pressure, when the temperature of the tape be different from the standard temperature, the tape shrinks or expands, which requires a necessary correction. CC tt =correction in meter. L= Field distance measured in meters. CC tt = LLαα (TT ff TT ss ) α= Coefficient of thermal expansion of the material of the tape. TT ff = Temperature during the measurement. TT ss = (standard temperature) : Error due to Pull or Tension Tension introduces error when the tape is pulled at a tension which differs from the standard tension used at standardization. The tape will stretch less than its standard length when a tension less than the standard tension is applied, making the tape too short. 22

23 The correction due to tension is given by: CC p = correction in meter. CC p = PP ff PP ss LL AAAA PP ff = Tensile hanging on the tape in (Newton's) N. PP ss = Standard tensile in Newton's N. L= measured distance in meters. A= cross sectional area of the tape in (m 2 ). E= Modulus of elasticity of the tape in (kg/m 2 ) : Error due to sagging The difference between the straight distance and overhanging distance is equal to correction due to sagging, and it's always (-) negative. The correction due to sag must be calculated separately for each unsupported stretch and is given by: When a tape is suspended between two measuring heads, A and B, both at the same level, the shape it takes up is a catenary (Figure above). If C is the lowest point on the curve, then on length CB there are three forces acting, namely the tension T at B, T0=Pf at C and the weight of portion CB, where w is the weight per unit length and s is the arc length CB. Thus CB must be in equilibrium under the action of these three forces. Hence For a small increment of the tape Fy=0 Fx=0 T sin θ = ws T cos θ = P f tan θ= w s/ Pf 23

24 For a small increment of the tape dx/ds= cos θ = [1 + tan2 θ] 1/2 =[1+ ww 2 SS 2 x= [1 ww2 SS 2 x=s - ww2 SS 3 2PP ff 2 ]ds 6PP ff 2 + k When x = 0, s = 0, K = 0, x=s - ww2 SS 3 6PP ff 2 PP ff 2 ] 1/2 =[1- ww 2 SS 2 2PP ff 2 ](Tylor sires ) The sag correction for the whole span ACB = C sag = 2(s x)=2[ ww 2 SS 3 6PP ff 2 ] but s = l/2 A) for L ll ss L= C sag = ww 2 ll 3 24PP ff 2 Where : w = weight per unit length (kg/m) P f = tension applied (kg) l = hanged recorded length between the two ends (m) C s = correction (m) As w = W/l s, where W is the total weight of the tape B) for L>ll ss L=C sag =n WW2 ll ss 24PP ff 2 Where: W= Total length of the tape (m) so: W=w *ll ss 24

25 2.10.5: Correction due to slope When distances are measured along the slope, the equivalent horizontal distance may be determined by applying a slope correction. The vertical slope angle of the length measured must be measured. (see Fig 2.11) fig 2.11 S=d+CC h CC h =S-d d=s.cosθ CC h =S-S.cosθ C h = the correction of measured slope distance due to slope; =the angle between the measured slope line and horizontal line; S = the measured slope distance. The correction C h is subtracted from S to obtain the equivalent horizontal distance on the slope line: LL = L ±C s ±CC tt ±CC p -C sag

26 Example2: A steel tape its length equal to 20m, its measure at flat land was 20.11m at 15 0 c, the tape hanged under a tension equal to 6 kg at 25 0 c to measure a distance equal to m, what was the true length of distance?, known that the total weight of the tape was 2.15 kg and the coefficient of the thermal expansion of the tape material was solution 1- standardization correction L>ll ss C s or L =( ll ff -ll ss )* LL ll ss =( )* = m 2- correction for temperature CC tt = LLαα (TT ff TT ss ) =253.6 ( )(25-15) = m 3- correction for sagging L>ll ss n= LL ll ss = n= *20=13.6m SO WE HAVE 2 CASES for L ll ss for L ll ss L=C sag = 2 ll 3 24PP 2 = = ff L= C sag =nn WW2 ll ss 24PP ff 2 =12 (2.15) = LL = L ±C s ±CC tt ±CC p -C sag LL = ( )= m 26

27 Example 3: A 20 m steel tape with a cross-sectional area of 5 mm 2 and 1.5kg weight, while it is hanged under a tension force of 50.1 N, this tape is used to measure a distance equal to 506m at 40 0 c, its actual length is 19.95m and α= m/ 0 c and this tape has been made under a tension force of 24.6 N and 20 0 c, calculate the correct distance, E = 10 6 kg/cm 2 sol: l s =20m, l f =19.95m, A=5mm 2, T f =40 0 c, T s =20 0 c,p f =50.1N, P s =24.6N, L=506m, α= m/ 0 c A=5mm 2 x(1 m 2 / mm 2 ) = 5x10-6 m 2 P f =50.1N = 50.1/9.81=5.107 kg P s =24.6N= 24.6/9.81= kg 1) correction for standardization (L> l s ) C s =(ll ff -ll ss )* LL ll ss C s = ( ) * (506/20) = m 2) correction for temperature CC tt = LLLL (TT ff TT ss ) CC tt = 506x x( 40-20)= m 3) correction due to pull CC p = PP ff PP ss LL AAAA = ( )x506/( 5x10-6 m 2 x kg/m 2 ) = m 4) correction due to sagging for L > l s n=l/ l s = 506/20=25.3 n= 25 C sag = n WW2 ll ss 24PP ff 2 = 25 * ( 1.52 xx20 24x ) = 1.797m to fine the L < l s so *6 = 6m C sag = ww 2 ll 3 24PP2 = = m ff 24xx L / = ( )= m 27

28 2.11: Setting Out Right Angles And Perpendicular Lines : Setting out Right Angles: the Method To set out right angles in the field, a measuring tape, two ranging poles, pegs and three persons are required. The first person holds together, between thumb and finger, the zero mark and the 12 meter mark of the tape. The second person holds between thumb and finger the 3 meter mark of the tape and the third person holds the 8 meter mark. When all sides of the tape are stretched, a triangle with lengths of 3 m, 4 m and 5 m is formed (see Fig. 2.11), and the angle near person 1 is a right angle. 28

29 Fig NOTE: Instead of 3 m, 4 m and 5 m a multiple can be chosen: e.g. 6 m, 8 m and 10 m or e.g. 9 m, 12 m and 15 m. EXAMPLE: Setting out a right angle Step 1 In Fig. 2.12a, the base line is defined by the poles (A) and (B) and a right angle has to be set out from peg (C). Peg (C) is on the base line. 29

30 Fig. 2.12a Step 2 Three persons hold the tape the way it has been explained above. The first person holds the zero mark of the tape together with the 12 m mark on top of peg (C). The second person holds the 3 m mark in line with pole (A) and peg (C), on the base line. The third person holds the 8 m mark and, after stretching the tape, he places a peg at point (D). The angle between the line connecting peg (C) and peg (D) and the base line is a right angle (see Fig. 2.12b). Line CD can be extended by sighting ranging poles. Fig. 2.12b : Setting out Perpendicular Lines: the Rope Method A line has to be set out perpendicular to the base line from peg (A). Peg (A) is not on the base line. 30

31 A long rope with a loop at both ends and a measuring tape are used. The rope should be a few meters longer than the distance from peg (A) to the base line. Step 1 One loop of the rope is placed around peg (A). Put a peg through the other loop of the rope and make a circle on the ground while keeping the rope straight. This circle crosses the base line twice (see Fig. 2.13a). Pegs (B) and (C) are placed where the circle crosses the base line. Step 2 Fig. 2.13a Peg (D) is placed exactly half way in between pegs (B) and (C). Use a measuring tape to determine the position of peg (D). Pegs (D) and (A) form the line perpendicular to the base line and the angle between the line CD and the base line is a right angle (see Fig. 2.13b). 31

32 Fig. 2.13b : shortest distance method to get a right angle from a point to a known line : using intersection of two equal radius. 32

33 2.12: Measure distances encountered by obstacles : Obstruction hide the vision but don't block the measurement: like Ground high or hill : Obstruction don't hide the vision but block the measurement: 1-we can pass out the obstruction like lakes and huge pits 2- we cannot pass out the obstruction like a wide river 33

34 : Obstruction hide the vision and block the measurement: like a building 34

35 Part 3 3.1Chain Surveying Chain surveying the simplest method of surveying in which only linear measurements are made and no angular measurements are taken. The area to be surveyed is divided into a number of triangles and the sides of the triangles are directly measured in the field. Since the triangle is a simple plane geometrical figure, it can be plotted from the measured length of its sides alone. In chain surveying, a NETWORK of TRIANGLES is preferred. Preferably all the sides of a triangle should be nearly equal having each angle nearly 60 o to ensure minimum distortion due to errors in measurement of sides and plotting. Generally such an ideal condition is not practical always. Usually attempt should be made to have WELL CONDITIONED TRIANGLES in which no angle is smaller than 30 o and no angle is greater than 120 o. The arrangement of triangles to be adopted in the field depends on the shape, topography and the natural or artificial OBSTACLES met with. 3.2Chain surveying is suitable for the following cases: Ground fairly level and open with simple details Large scale plans (1 cm = 10 m) Extent of the area comparatively small 3.3 Chain surveying is unsuitable for the following cases: Area crowded with many details Wooded countries 35

36 Undulating areas Extent of large area 3.4 Metric surveying chains: Length of chain: 20 m or 30 m Number of links per meter length : 5 Length of each link : 20 cm Tallies are provided at every 5 m Small brass rings are provided at every meter except where tallies are provided. 36

37 37

38 Part Leveling According to science Leveling is a branch of surveying which deals with the measurement of relative heights of different points on, above or below the surface of the earth. Thus in leveling, the measurements (elevations) are taken in the vertical plane. Simple Definition Leveling is the process used to determine a difference in elevation between two points. 4.2 Definitions fig 4.1 Difference in elevation between two points. Station:- A point where the levelling staff is kept. Height of instrument:- It is the elevation of the plane of sight with respect to assumed datum. It is also known as plane of collimation. Datum line ( M.S.L. ) :- Is the level (line) which are attributed to it points levels on the surface of the Earth. Which is the average sea level. Reduced level ( R.L) :- Is the high point from datum line. 38

39 Benchmark (B.M ) :- Are fixed points information site and attributed placed in different places until you start racing them when conducting settlement. fig4.2 Benchmark Back sight ( B.S.) :- Is the first reading taken after placing the device in any position so that we see the greatest possible number of points required to find the elevation. Fore sight (F.S) :- Is the last reading taken before the transfer device. Change point(cp) or turning point(tp): The point at which both BS and FS are taken. Intermediate sight ( I.S.) :- Is reading taken between the back sight and fore sight reading. Elevation of line of sight ( H.I) :- Is the imaginary vertical level determined by the line of sight to the amount of increase or decrease for sea level. Tripod stand :- is a portable three-legged frame, used as a platform for supporting the weight and maintaining the stability of some other object 39

40 fig 4.3 Tripod stand Leveling Staff :-Is a wooden or metal ruler one side runway to meters and centimeters. And is a ruler of solid wood 2, 3, 4, 5 meters in length and usually 4 meters 4.3Leveling of the instrument fig 4.4 leveling staff It is achieved by carrying out the following steps: Step 1: The level tube is brought parallel to any two of the foot screws, by rotating the upper part of the instrument. 40

41 Step 2: The bubble is brought to the centre of the level tube by rotating both the foot screws either inward or outward. (The bubble moves in the same direction as the left thumb.) Step 3: The level tube is then brought over the third foot screw again by rotating the upper part of the instrument. Step 4: The bubble is then again brought to the centre of the level tube by rotating the third foot screw either inward or outward. Step 5: By rotating the upper part of the instrument through 180, the level tube is brought parallel to first two foot screws in reverse order. The bubble will remain in the centre if the instrument is in permanent adjustment. fig4.5 level instrument 4.4 Types of levelling 1] Simple levelling When the difference in the elevation of two nearby points is required then simple levelling is performed. 41

42 2] Differential levelling Performed when the first point is very far from the final point. 42

43 3] Fly levelling Performed when the work site is very far away from the bench mark. The surveyor starts by taking BS at BM and proceed towards worksite till he finds a suitable place for temporary BM. All works are done with respect to temporary BM. At the end of the day the surveyor comes back to original BM. This is called fly levelling. 4] Profile levelling Profile levelling, which yields elevations at definite points along a reference line, provides the needed data for designing facilities such as highways, railroads, transmission lines.reduced levels at various points at regular interval along the line is calculated. After getting the RL of various points the profile is drawn. Normally vertical scale is much larger than horizontal scale for the clear view of the profile. 43

44 5] Reciprocal levelling When levelling across river is required then this method is applied to get rid of various errors. 4.5Methods for obtaining the elevations at different points: There are two methods for obtaining the elevations at different points: 1] Height of instrument (or plane of collimation) method. 2] Rise and fall method. 44

45 1] Height of Instrument method The basic equations are Height of instrument for the first setting H.I=Elev. of BM + BS(at BM) Subtract the I.F.S and F.S from H.I to get Elev. of intermediate stations and change points. Elev. of a point =H.I-F.S Elev. of a point =H.I-I.F.S Checking: ΣBS -ΣFS = Last Elev. First Elev. 45

46 Example: In Surveying process took the following readings starting from a point A which represent B.M which had an elevation equal to m to point J, and the readings was : 1.237, 1.315,2.28,1.953,0.87,1.42,2.213, 2.104, 1.313, 0.976, 1.512, 1.915,0.854,1.506m note; the position of leveling instrument was changed by the surveyor after the 4th, 7th, 9th,12th readings, find the elevation of all stations from A to J 46

47 solution1: by using high of instrument method point B.S I.F.S F.S H.I Elevations Remark M M M M M A B.M B C D T.P1 E F T.P2 G T.P3 H I T.P4 J ΣBS=6.041 ΣFS=8.9 FOR Checking: 1- no. of BS = no. of FS = 5 2-( no. of readings = 14 ) = (no. of points = 10 ) + ( no. of TP = 4 ) ΣBS -ΣFS = Last Elev. First Elev = = O.K ] Rise and fall method. The difference in elevation between A & B = the vertical distance AC = RA -RB = = 1.63 m. 47

48 positive value means Rise The difference in elevation between A & B = the vertical distance BC = RA -RB = = m. Negative value means Fall In this method, the difference of level between two consecutive points for each setting of the instrument is obtained by comparing their staff readings. The difference between their staff readings indicates a rise if back sight is more than foresight and a fall if it is less than foresight. The Rise and Fall worked out for all the points given the vertical distances of each point relative to the proceeding one. If the RL of the Back staff point is known, then RL of the following staff point may be obtained by adding its rise or subtracting fall from the RL of preceding point. Elevation Difference = first reading at A second reading at B Elevation of B ( RL ) = elevation of A + Rise or- Fall Example: In Surveying process took the following readings starting from a point A which represent B.M which had an elevation equal to m to point J, and the readings was : 1.237, 1.315,2.28,1.953,0.87,1.42,2.213, 2.104, 1.313, 0.976, 1.512, 1.915,0.854,1.506m note; the position of leveling instrument was changed by the surveyor after the 4th, 7th, 9th,12th readings, find the elevation of all stations from A to J solution2: by using rise and fall method point B.S M I.F.S M F.S M Rise Fall R.L M Rema rk 48

49 A B.M B C D T.P1 E F T.P2 G T.P3 H I T.P4 J sum Checks: 1- no. of BS = no. of FS = 5 2-( no. of readings = 14 ) = (no. of points = 10 ) + ( no. of TP = 4 ) 3- ( BS - FS) = ( ) = ( R - F) = ( ) = ( RL last - RL1st ) = ( ) = so 3=4= Inverted reading staff An inverted staff reading can be used to determine the reduced level of a point above the line of sight of the instrument such as a ceiling, 49

50 underside of a bridge, balcony etc. As the name suggests, the staff is simply turned upside down, the bottom placed against the point that the level is required, and then read. An important difference between inverted staff readings and other types is that they are treated as negative quantities, both in the booking of the readings and the reduction of the levels. BACK INTER- FORE H.P.C. REDUCED COMMENTS SIGHT MEDIATE SIGHT LEVEL OBM (=33.550) point A Point B - c.p. -[1.603] -[3.890] Point C - Bridge Soffit Inverted staff - c.p Point D - c.p. -[2.192] Point E - Balcony Inverted staff ΣBS ΣFS Last - First BS - FS Check sums: arithmetic OK

51 4.7 Sources of Errors and mistakes in leveling Instrumental errors: (1) The main source of error is the residual collimation error of the instrument. From the two-peg test it should be apparent that this error would be eliminated by equalizing the lengths of the BS and FS. (2) Parallax error has already been described. (3) Staff graduation errors may result from wear and tear or repairs and the staffs should be checked against a steel tape. Zero error of the staff, caused by excessive wear of the base, will cancel out on backsight and foresight differences. However, if two staffs are used, errors will result unless calibration corrections are applied. (4) In the case of the tripod, loose fixings will cause twisting and movement of the tripod head. Overtight fixings make it difficult to open out the tripod correctly. Loose tripod shoes will also result in unstable set-ups Observational errors (1) Levelling involves vertical measurements relative to a horizontal plane so it is important to ensure that the staff is held strictly vertical. (2) There may be errors in reading the staff, particularly when using a tilting level which gives an inverted image. These errors may result from inexperience, poor observation conditions or overlong sights. Limit the length of sight to about m, to ensure the graduations are clearly defined. (3) Ensure that the staff is correctly extended or assembled. (4) Avoid settlement of the tripod, which may alter the height of collimation between sights or tilt the line of sight. Set up on firm ground, with the tripod feet firmly thrust well into the ground. On pavements, locate the tripod shoes in existing cracks or joins. In precise levelling, the use of two staffs helps to reduce this effect. 51

52 (5) Booking errors can, of course, ruin good field work. Neat, clear, correct booking of field data is essential in any surveying operation. Typical booking errors in levelling are entering the values in the wrong columns or on the wrong lines, transposing figures such as to and making arithmetical errors in the reduction process. Very often, the use of pocket calculators simply enables the booker to make the errors quicker Natural errors (1) Curvature and refraction have already been dealt with. Their effects are minimized by equal observation distances to backsight and foresight at each set-up and readings more than 0.5 m above the ground. (2) Wind can cause instrument vibration and make the staff difficult to hold in a steady position. Precise levelling is impossible in strong winds. In tertiary levelling keep the staff to its shortest length and use a wind break to shelter the instrument. (3) Heat shimmer can make the staff reading difficult if not impossible and may make it necessary to delay the work to an overcast day. In hot sunny climes, carry out the work early in the morning or in the evening TWO-PEG TEST From the two-peg test we can calculate the error due to residual collimation and its can be done by two steps and three approaches : step 1 Set the instrument level in the middle of a distance subjected with two pegs as shown in the fig below 52

53 0BStaff on point A 1BDescription 2BStaff on point B 3BDescription 4Ba 5BFalse reading with 6Bb 7BFalse reading with error error 8Be 9BThe error 10Be 11BThe error 12Ba' 16Ba'=a-e 13BTrue reading with out error 14Bb' 17Bb'=b-e 15BTrue reading with out error step 2 Set the instrument level at a distance equal to ll far way from point B for example as shown in fig below 53

54 18BStaff on point A 19BDescription 20BStaff on point B 21BDescription 22Bd 23BFalse reading with error 24Bc 25BFalse reading with error 26Be3 27BThe error 28Be1 29BThe error 30Bd' 31BTrue reading with 32Bc' out error 34Bd'=d-e2 35Be2=e3+e1 36Bc'=c-e1 33BTrue reading with out error To make sure the there is no error in the instrument level, we have to achieve that by : H1= H2 And mathematically can be done by three approaches: First approach : to find αα where : e3=(b-a)-(c-d). L= distance between the pegs. 1 ee3 α = tttttt LL α= slope angle of sight collimator. - the collimator is sloped to the bottom of the line sight so must added 0 there is no errer + the collimator is sloped to the top of the line sight so must subtract 54

55 corrected reading = false reading - D tan αα D = distance in( m) between the instrument level and the staff at a certain point ========================================================== Second approach : from the first step of two peg test we can find the true difference of readings : reading at point A - reading at point B = True difference from the second step of two peg test we can find the actual difference of readings: reading at point A - reading at point B = Actual difference Actual difference - True difference=error for distance between the pegs A.d-T.d=e True difference Actual difference the collimator is sloped to the bottom of the line sight True difference Actual difference the collimator is sloped to the top of the line sight True difference Actual difference there is no error 55

56 corrected reading = false reading ± D. e' D = distance in( m) between the instrument level and the staff at a certain point e'= error for one meter

57 Area: The amount of space inside the boundary of a flat (2-dimensional) object such as a triangle or circle. Areas of Regular Figures The following is a summary of the most important formula Areas bounded by straight lines 1.Triangle (a) (Area) A = half the base x the perpendicular height i.e. A = 1/2 b.h (b) A = half the product of any two sides x the sine of the included angle i.e. A = 1/2 a.b sin C = 1/2 a.c sin B = 1/2 b.c sin A (c) A = s(s a)(s b)(s c) where S= 1/2(a + b+c). 57

58 2.Quadrilateral (a) Square, A = side 2 or 1/2 (diagonal 2 ) (b) Rectangle, A = length x breadth (c) Parallelogram (Fig. 9.2) (i) A = a.h (ii) A = a.b.sin(a) (d) Trapezium (Fig. 9.3) A =( half the sum of the parallel sides) x( the perpendicular height) i.e. A = 1/2 (a + b)h (e) Irregular quadrilateral (Fig. 9.4) (i) The figure is subdivided into 2 triangles, A = 1/2 (AC x Bb) + 1/(AC x Dd) 58

59 = 1/2AC(Bb + Dd) 59

60 Areas involving circular corves Circle 60

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64 The mean ordinate rule (Fig. 9.26) The figure is divided into a number of strips of equal width and the lengths of the ordinates o1, o2, o3 etc. measured. (N.B. If the beginning or end of the figure is a point the ordinate is included as oo nn = zero.) 64

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