1. direct measurement of distance

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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 bemeasured in order to prepare plan or 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; and3. 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).Table 8.1summarizes theprincipal methods, instrument required, precision, use, errors of measurement of distance.

Table 8.1 Salient Methods of Measuring Distance

MethodInstrumentRequired

RelativePrecision

Use

(A) Direct Measurement of distance

TapingTape, pegs, plumbbob

1 / 3000 to 1 /5000

Traverse for land surveys and topographic surveysand during combustion.

(B) Optical Measurement of distance

Stadia Tacheometer1 / 300 to 1 /2000

Location of detail for topographic mapping, roughtraverse, checkingmore amount measurement.

(C) Electromagnetic measurement of Distance

EDM EDM Equipment0.2 mm 1

ppm

Traverse, Triangulation and trilateration for controlsurveys of all relative precision is defend as the ratio

of the type anf for allowed stand and deviations tothe distance type and for contraction surveys.
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Direct Measurement

When the distance between points / stations are measured directly, usually by using tape, isknown as direct method.

Ranging

When the distance to be measured is more than a tape length, a straight line is required to belaid between the points/ stations along which measurements are to be carried out. The process

of laying out a straight line between points is known as ranging.

Direct Ranging

Indirect 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 tape length. The intermediate points

are found by moving a ranging pole in transverse direction and thus, points are selected in sucha way that the end points and the intermediate points lie in a straight line (Figure 8.1). In thismethod, 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, indirectmethod of ranging is being adopted. It is being carried out either by reciprocal method or by

random line method.

1. Reciprocal Ranging2. Random Line Method
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Reciprocal Ranging

Figure 8.2shows the field operations involved in reciprocal ranging. Let A and B are the twoend 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 arechosen in such a way that D & B are visible from C and C & A from D. Then, direct ranging is

being carried out alternatively along DCA and CDB for a number of times so that ACDB lie ina straight line.
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Ranging by Random Line Method


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In this method, (Figure 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 BRis being calculated using distance formula.

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

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

straight line.
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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 withwhich 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 equivalentdistance 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


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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 offsets are drawn from the line one at each side of the 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 Figure8.4(b)

When measurement round an obstacle is not possible, similar triangles are established as shown in Figure8.5(a), Figure 8.5(b).The unknown distance is calculated by solving similar triangles.
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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 sideof 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 desireddistance PQ.


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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 surveyline at the extension of BA and at a distance of 50m from A. Compute the distance AB.


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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 beingadopted to range a line between stations and subsequently measurement of distance is being

carried out.

Type III : Both ranging and measurement along 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 andtwo 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 measuredto get the distance. However, depending on field condition surveyor can apply suitable

geometrical /trigonometric concepts to find the unknown distance
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Mistakes in Taping

During taping, mistakes generally made by individuals (usually inexperienced) are:

1. Adding or dropping a full length of tape2. Adding or dropping a part of the length of tape

3. Other points incorrectly taken as 0 or 30 meter marks on tape4. Reading numbers incorrectly

5. Calling numbers incorrectly or not clearly

Exercise 8Ex.8-1Describe how you would range a survey line between two stations which are not inter

visible?

Ex.8-2A survey line AB crosses a river obliquely. P and Q are two points selected on the lineone 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 angle and EP = PF = 100 m. A third point G is set at adistance 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

1. direct measurement of distance

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