1. Direct Measurement of Distance

 

Lecture-1 Direct Measurement of Distance One of the fundamental operations involved in surveying is to find out distance (on the surface of the earth). In plane surveying distance means spatial separation of points projected on a horizontal plane.

Introduction The horizontal distance between points, projected onto a horizontal plane, is required to be measured in order to prepare plan or o r map of the area surveyed.

Methods of measurement In surveying there are several methods for measurement of distance. These are 1.  Direct methods; 2.  Optical methods; and 3.  Electronic method. In any work, the choice of a method depends on many factors like field condition, accuracy required, availability of resources (instruments, time, skill, fund etc).  etc).  Table 8.1 8.1   summarizes the  principal methods, instrument required, precision, precision, use, errors of measure measurement ment of distance.

Table 8.1 Salient Methods of Measuring Distance Instrument Relative Method  Use  Required Precision (A) Direct Measurement of distance d istance Tape, pegs, plumb 1  / 3000 to 1  / Traverse for land surveys and topographic surveys Taping  bob 5000 and during combustion. (B) Optical Measurement of distance d istance 1  / 300 to 1  /  Location of detail for topographic mapping, rough Stadia Tacheometer 2000 traverse, checkingmore amount measurement. (C) Electromagnetic measurement of Distance Traverse, Triangulation and trilateration for control 0.2 mm ± 1 surveys of all relative precision is defend as the ratio EDM EDM Equipment  ppm of the type anf for allowed stand and deviations to the distance type and for contraction surveys.

 

Direct Measurement When the distance between points  / stations are measured directly, usually by using tape, is known as direct method. Ranging When the distance to be measured is more than a tape length, a straight line is required to be laid between the points/ stations along which measurements are to be carried out. The process of laying out a straight straight line between points po ints is known as ranging.    

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Direct Ranging  Ranging  Indirect Ranging  Ranging 

Direct Ranging When the end stations are inter visible, ranging is being carried out directly. The intermediate  points are placed at distances having interval less than one ttape ape length. The intermediate points are found by moving a ranging pole in transverse direction and thus, points are selected in such a way that the end points and the intermediate points lie in a straight line ( Figure 8.1) 8.1). In this method, two flags, one ranging pole and a bunch of pegs are required in a team of at least one surveyor and one assistant.

Indirect Ranging When the end stations between which a straight line is to be laid, are not inter visible, indirect method of ranging is being adopted. It is being carried out either by reciprocal method or by random line method. 1.  Reciprocal Ranging  Ranging   Method   2.  Random Line Method

 

Reciprocal Ranging 8.2  shows the field operations involved in reciprocal ranging. Let A and B are the two Figure 8.2  end points whose distance is required to be found and are not inter visible. To fix the intermediate points in a straight line between these points, two more points say C and D are chosen in such a way that D & B are visible from C and C & A from D. Then, direct ranging is  being carried out o ut alternatively along DCA and CDB for a number of o f times so that ACDB lie in a straight line.

 

 

 

 

Ranging by Random Line Method

 

In this method, (Figure 8.3) 8.3) a random line such as BQ is being laid such that R is visible from Q. A perpendicular QR is being erected at Q and measure its distance. Then the desired distance BR is being calculated using distance formula.

In laying the line BR, intermediate points are established first. These are laid by taking offset from the random line at distances calculated by b y using the method of similar triangle such as

After locating the intermediate points on the line BR, the obstructions get cleared to make the end points intervisible. Then, direct ranging is being carried out to obtain an extended continous straight line.

 

  Taping Taping involves measurement of the distance with tapes (steel/linen), either by placing it on the ground or sometimes by getting it suspended between points. Additional equipments employed during taping are plumb bob, the hand level, pegs/ pins and range pole (or flag or ranging rod) etc. The precision of distance measured with tapes depends upon the degree of refinement with which measurements are taken.

Field Problems During measurement of distance, various obstacles may be encountered in the field. Depending upon the type of obstacle, a suitable geometrical figure has to be framed and an equivalent distance has to be measured or computed. Obstacles encountered in the field can be divided into three broad categories. Type I : Ranging along obstacle is possible but not measurement such as pond, river etc

 

Fig 8.4 a. Measurement of Obstructed Ranging round the obstacle. To carry measurement along the type of obstacles where measurement round the obstacle is possible,  perpendicular  perpendic ular offsets are drawn from the line one at each side of the obstacle obstacle,, as shown in Figure 8.4(a).  Then, a parallel distance equivalent to distance along the obstacle is measured. In some cases, the distance is being calculated either adopting basic principle of geometry and/or trigonometric relations Figure 8.4(b) 

When measurement round an obstacle is not possible, similar triangles are established as shown in Figure 8.5(a),, Figure 8.5(b). The unknown distance is calculated by solving similar triangles. 8.5(a)

 

 

 

 

Ex8-1 During measurement of distance, a pond had been come across the path. Let P and Q are the stations selected on the opposite side of the pond. A line PC = 900 m, was set out on one side of PQ, and a line PD =1100m was set out on the other side, such that CQD was in a straight line. The length of the lines CQ and QD are 500m and 600m respectively. Determine the desired distance PQ.

 

  Figure Ex8-1 Solution : Refer Figure for Ex8-1

Ex8-2 A survey line AB crosses a river. A line AP is run perpendicular to the survey line having length 200m. Another line PB is set at right angle to QP such that the point Q lies on the survey line at the extension of BA and at a distance of 50m from A. Compute the distance AB.

 

  Figure Ex8-2 Solution : Refer Figure for Ex8-2

Type II : Measurement along obstacle is possible but not ranging such as bush etc.

In this case, either of method of reciprocal ranging or ranging by random line method is being adopted to range a line between stations and subsequently measurement of distance is being carried out. Type III : Both ranging and measurement along a long the obstacle is not possible such as building.

In this case, two perpendicular offsets of equal length are erected from the line before the obstacle and a parallel line is ranged, as shown in Figure 8.6 . The parallel line is extended and two perpendicular offsets, of same length as before, beyond the obstacle, are dropped from the line beyond the obstacle. Equivalent distance along a line parallel to ranged line is then measured to get the distance. However, depending on field condition surveyor can apply suitable geometrical /trigonometric concepts to find the unknown distance

 

  Mistakes in Taping During taping, mistakes generally made by individuals individua ls (usually inexperienced) are: 1.  2.  3.  4.  5. 

Adding or dropping a full length of tape Adding or dropping a part of o f the length of tape Other points incorrectly taken as 0 or 30 meter marks on tape Reading numbers incorrectly Calling numbers incorrectly or not clearly

Exercise 8 Ex.8-1  Describe how you would range a survey line between two stations which are not inter visible? Ex.8-2 A survey line AB crosses a river obliquely. P and Q are two points selected on the line one at each end of the river. Another line EPF is run parallel to the centre line of the river and  point E is such that angle QEP is right r ight angle and a nd EP = PF = 100 m. A third point G is set at a distance of 150 m from P such that angle GFP is also right angle. Compute the distance PQ

Answers For Exercise 8 M3-Ex.8-2 180.278 m