Fundamentals of Surveying MSS 220 Prof. Gamal El-Fiky

Transcription

1 Fundamentals of Surveying MSS 220 Prof. Gamal l-fiky Maritime Studies Department, Faculty of Marine Science King Abdulaziz University Room 221

2 What is Surveying? Surveying is defined as the science of collecting the necessary field measurements to determine the 2-d and or 3-d positions on, above or under the earth s surface. In other words, it can be said that the surveying is a branch of science that works in determining the size and the shape of the earth. To obtain such information, some field measurements should be acquired from the field using specialized instrumentation. Slope and horizontal distances, vertical and horizontal angles, height differences, directions and bearings are the different types of observations that are collected in surveying.

3 Classification of Surveying (i) According to the earth s surface: a- Plane surveying: Surveying area is relatively small (< 50 km 2 ). All computations in any surveying process, in this type of surveying, are based on the plane as a computational surface. b-geodetic surveying: This type takes place in case of large areas (>50 km 2 ) and long distances (>15 km). Both effects of refraction and earth curvature should be taken into account. The computational surface of the earth is either sphere (50 km 2 <area>300 km 2 ), or ellipsoid (>300 km 2 ).

4 (ii) According to its uses 1- Land Surveying It is oriented towards the determination of the land boundaries. Also the preparation of maps showing the shapes and areas of land are included. 2- Cadastral Surveying It works in surveying all types of features and/or utilities such as buildings, roads, green areas, waterlines, trees, water routes, etc. It is used to produce the cadastral maps of relatively large scale. 3- Route surveying It is used to survey and prepare the maps required to design the route projects such as roads, canals, drains and railways.

5 (ii) According to its uses (Cont d) 4- Topographic surveying Where, full details to vertically control any project are obtained using the topographic surveying. Spot and grid leveling are performed using the topographic surveying to generate the topographic and the contour maps. 5- Hydrographic surveying In which, all projects in and off the shore line are controlled. In addition, the preparation of the surveying maps needed for these kinds of projects are produced.

6 (iii) According to used instrumentation 1- Chain surveying In which, mainly the linear measurements are used. 2- Compass Surveying In which, mainly angles are measured using compass. 3- Theodolite Surveying In which, mainly angles are measured using compass. 4- Total station Surveying In which, the total station is used to carry out the surveying. 5- Photogrammetric Survey A survey in which aerial photographs are used to determine the topography or the configuration of a tract. f- Satellite surveying Artificial satellites are used to carry out the surveying works.

7 Unit of Measurements Angular Measure: (i)-the degree system (sexagesimal units) of angular measurement are the degree, minute, and second. A plane angle extending completely around a point equals 360 degrees; one degree ( ) = 60 minutes ('), and one minute = 60 seconds ("), so 1 = 60' = 3600". (ii) In urope, the centesimal unit, the gon, is the angular unit; 400 gons ( g ) equal 360 ; 1 gon ( g ) = 100 centesimal minutes ( c ) = 0.9 ; 1 centesimal minutes ( c ) = 100 centesimal seconds ( cc ) = 0 00' Gons usually are expressed in decimals. xample: 100 (g) 42 (c) 88 (cc) is expressed as gons.

8 (iii) Radius System: An angle in radians is given by the ratio of the arc length, s, to the radius, r, θ = s/r Since a circle has circumference s = 2πr, the turning of a 360 circle gives θ = 360 = 2π r/r = 2π radians, or π radians = 180. Conversion from angles in degrees to radians must be done using decimal degrees. xample: is given in radians by * (π / 180) = radians.

9 Unit of Linear Measures The international unit of linear measure is the meter. The meter is subdivided into the following units: 1 decimeter (dm) = 0.1 meter (m) 1 centimeter (cm) = 0.01 meter (m) 1 millimeter (mm) = meter (m) 1 micrometer (µm) = 10-6 meter (m) 1 nanometer (dm) = 10-9 meter (m) The relationship between meter and others linear units are: 1 inch = 2.54 cm = 1/ m 1 foot = 12 inch = 3 yard = 1/ m 1 nautical mile = 1852 m

10 Coordinate systems in Surveying The coordinate system, in general, is a reference frame in which any point can be defined either in two or three dimensions. The coordinates of any point are necessary to be known in order to: Define the horizontal and/or the vertical position. Deal with different points on the earth s surface. Obtain any geometric relation between different points. Plot easily and accurately any point on the map plane, using the manual and digital tools.

11 3-D Coordinate system (Φ, λ, h): (i) Geodetic Curvilinear Coordinates System Geodetic Greenwich Meridian orth direction Z a' ha a Za Terrain φa Y λa Xa Geodetic quator X Ya Geodetic meridian of (a)

12 Geodetic curvilinear coordinates (Cont d) Geodetic curvilinear coordinates Geodetic latitude φ : is the angle measured form the equator to the point on the meridian plane of that point. φ varies from zero to 90 north or south. Geodetic longitude λ : is the angle measured from Greenwich meridian to the point on the geodetic equator anti-clockwise direction. λ varies from 0 to 360 east or form 0º to 180º east and form 0º to 180º west. Geodetic height h : Is the distance between the point and the sphere measured on the ellipsoid normal direction.

13 (ii) Geodetic Cartesian Coordinates : (X,Y,Z) Where any point may be defined within the geodetic system by three Cartesian coordinates X: The ordinates measured on the X axis direction Y: The ordinates measured on the Y axis direction Z: The ordinates measured on the Z axis direction ote that any of the above two sets of coordinates can be mathematically transformed to the other set and vice versa.

14 2- Plane coordinates system (, ): This system consists of two axes; the north axis () and the east axis (). Any point can be defined by two coordinates in this system. Calculations, in such a system, are called as two dimensional (2-D) computations. The coordinates of any point are nothing else, but the offsets to the two system axes. orthing () 1 a 1 asting ()

15 Types of north direction The north direction at a point is the tangent to the meridian passes through the point. In this case, the north direction lines at different points are not parallel and there is a convergence of all north directions towards to the orth Pole. In small area, as the case of plane surveying, such a convergence does not exist and it is assumed that all north line directions are parallel. The following are the types of the north direction: True north direction: It is the line tangent to the astronomic meridian at any point. It is measured by astronomic observations.

16 Types of north direction (Cont d) Magnetic north direction: It is the extension of the direction of the compass needle at a certain point when it is located free on the point. It is not constant and varies from point to point according to the internal metallic content of the earth at such a point. Geographic north direction: It is the tangent of the geodetic meridian at any point. It is some time called as the theoretical north direction at any point. Local north direction: In some small projects, it is possible to choose an arbitrary direction. This direction can be temporally considered as the north direction of such a project.

17 Bearing of a Line in Surveying The bearing of any line in surveying is an angle measured from a reference direction, (the north direction) to the line. The bearing of any line may be described by: (i) the whole circle bearing or (ii) the reduced bearing. (i)- The Whole Circle Bearing of a Line (WCB) (α) : It is the angle measured form the north direction to that line clockwise direction. It ranges from 0 to 360. The bearing of any line is considered as the definition of the line orientation.

18 The Whole Circle Bearing of a Line (WCB) (Cont d): The WCB of any line (α) should be measured starting from the north direction to the line clockwise direction. α ab b a α ac c

19 (ii) The Reduced Bearing (RB) (α ) The reduced bearing of any line is defined as the angle measured between the north-south line to that line under the condition that its value is ranging between 0-90 degrees. In this case the RB should be represented as a value assigned a certain symbol to show the quarter in which the line is located. H W 320 o S G = 320 o = 40 o W W F S 235 o = 235 o = S 55 o W W C S 120 o = 120 o D = S 60 o W A S 60 o B = 60 o = 60 o Fourth quarter Third quarter Second quarter First quarter

20 Transformation between WCB (α) and RB (α') WCB is preferred to be used in all surveying calculation, where the algebraic sign is considered according to the location of the side. In this case, we need usually to transform the RB (α') to WCB (α), especially in case of using a computed bearing. Values of WCB (α) Values of RB (α') o. Circle Quarter 0 ~ 90 (α ) First quarter 90 ~ 180 S (180 - α ) Second quarter 180 ~ 270 S (α ) W Third quarter 270 ~ 360 (360 - α ) W Fourth quarter H W 320 o S G = 320 o o = 40 W W F S 235 o = 235 o = S 55 o W W C S 120 o = 120 o D = S 60 o W A S 60 o B = 60 o = 60 o

21 Forward and Backward Bearing of a Line Any line is named as AB, then, automatically, a point A indicates the occupied station, while the other point b indicates the target station. In this case, the WCB (α AB ) of that line is called as the forward bearing of AB, where the bearing is named using the same sequence as the line name. If we have, then the bearing in this case is named as the backward bearing of the line AB (α BA ). We can describe the relationship between both forward and backward bearing as α AB = α BA ± 180 o where the +ve sign takes place when α AB < 180 o, and The ve sign takes place if α AB > 180 o. AB B AB 180 o BA ote that the bearing should not exceed 360 A

22 Relation Between Angles and Bearings In the shown figure, it is clear that the angle enclosed by the two lines ab and ac at point a equals the difference between the bearings of the two lines ac and ab. According to the sequence of writing the angle, it indicates which horizontal angle internal or external is required, as an example if we write, here we mean the internal angle w1 In this case, we can write bac ˆ = α ac α ab a α ab α ac b bâc=w 1 c

23 xample Given :, α ab = 45º00'00" α ad = 300º00'00", and bâc= 88º30 20" Required:, α ac, câd and dâb b Solution: d ab a bâc = α ac - α ab Then 88º30 20" = α ac - 45º00'00 ad α ac = 133º30 20 câd = α ad - α ac = 300º00'00" - 133º30 20 = 166º29 40 dâb = α ab - α ad = 45º00'00" - 300º00 00 = -255º00 00 We have to add 360 o Then, dâb = 360º - 255º00 00 = 105º c

24 Departure and Latitude Components of a Line Any line in surveying can be described relative to a specified coordinate system. The location and orientation of that line is described by the coordinates of its end points and its bearing. The line may be represented by its two end points, its length and bearing as well as the coordinates of one of its end points point, or the horizontal and vertical components of the line. This figure shows the components of the line ab. From the figure, we can mathematically write the following equations of the departure and latitude as: Δ ab = b a = l Sin ab α ab W Δ = = l Cos ab α ab b a ab === S a a b ab a l ab b b

25 Components of a Line (Cont d) The coordinates of point a are ( a, a ) The coordinates of point b are ( b, b ) The length of the line ab is l ab. The bearing of the line α ab is. The horizontal component of the line ab (departure) is Δ ab The vertical component of the line ab (latitude) is Δ ab

26 Computation of Coordinates of a Point Form the above equations of Δ ab and Δ ab, the coordinates of a point can be computed as follows. =+Δ=+lSin b a bα babaab So, in order to obtain the coordinates of an unknown point, say b, we should have the coordinates of another point, say a, as well as the observations between the unknown and known points a and b, which are the side length l ab and the side bearing (α ab ). ab=+=+lcosαδaabaababw === S a a b ab a l ab b

27 xample Calculate the coordinates of points b and c if the coordinates of point a are given as (265.38m, m ), the bearing of the line is α ab = and the horizontal angle bâc = ", the lengths of ab are m and ac m, respectively. Solution: To compute the coordinates of point b, we use the following equations: On the other hand, to obtain the coordinates of the point c, first, we have to calculate the bearing of the line ac as: then,baabaabab=+=+ SinΔlα= Sin45 13'33"= mb a l ab bâc c αab l ac baabaabab=+=+ CosΔlα= cos45 13'33"= m

28 xample (Cont d) ˆ acabbac=-ααˆacab=bac+=230 10'29"+45 13'33"=275 24'02"ααAnd then we can compute the coordinates of point c as:caacaacacocaacaacaco=+=+ Sin=Δlα Sin24'02"=64.943m275=+=+ Cos=Δlα Cos24'02"= m275

29 ΔComputations of the Length and Bearing of a Line from Coordinates Here, we have the coordinates of the points a and b and it is required to compute the length of the line ab and both forward and backward bearing of that line. Δ ab = X b -X a l ab = ( ab) + ( ab) Δ α ab = arctan 2 2 Δ Δ, Δ ab = Y b Y a bab a aba l b b Where, Δ ab and Δ ab are the departure W a a and latitude of the line ab, respectively. === S b

30 Remarks It should be mentioned here that, the resulted value of the bearing is ranging between 0º and 90º. This means that the resulted bearing is a reduced bearing and then should be assigned symbols to determine the quarter in which the line is located. To do so, we have to determine the algebraic sign of both departure and latitude, which may be one of the following four cases: If the sign of Δ is positive and Δ is positive then the line is located in the first quarter and, If the sign of Δ is negative and Δ is positive then the line is located in the second quarter and, If the sign of Δ is negative and Δ is negative then the line is located in the third quarter and, If the sign of Δ is positive and Δ is negative then the line is located in the fourth quarter. Once, the case of both departure and latitude is chosen the WCB can be computed from the reduced bearing, as discussed before. On the other hand, the backward bearing of the line ab, we can simply apply the above equations of relating both backward and forward bearings.

31 xample If the coordinates (in meter) of point P are (500,250) and the coordinates of point Q are (250W,500S), estimate the length of the line PQ and its bearing. Solution: Y Δ PQ = (500) = -750m W Δ PQ = (250) = -750 m -750Q PΔ= Tan α = Since the sign of Δ is negative and Δ is negative then the line is located in the third quarter and α= 225 o, PQ l = [(750) 2 + (750) 2 ] 1/2 = m =1Δ-750Y = 500 Q X = 250 Q S X X = 500 P L P Y = 250