The post Problems in Ranging and Chaining of a Line | Chain Surveying | Surveying appeared first on Engineering Notes India.

]]>It can be done by forming a right angled triangle by taking three sides of a triangle in the proportion of 3, 4 and 5. Let AB be the chain line and C a point on it at which it is desired to erect a perpendicular (Fig. 3.29). Measure CE = 40 units (chain links or decimetres).

Pin zero end of the tape at C and 80th unit at E, the remaining portion of the tape hanging free. Hold 30th unit and pull the tape until both segments DC and DE are taut. Fix an arrow at D. CD will then be the required perpendicular.

**There may be two cases:**

(i) When the point is accessible, and

(ii) When the point is inaccessible.

**(i) When the point is accessible: **

Let AB be the chain line and C a given point out side it (Fig. 3.30). With C as centre and any convenient length of the tape as radius, describe an arc EF cutting the chain line at E and F. Fix arrows at E and F Measure EF and bisect it at D. CD will then be the required perpendicular.

**(ii) When the point is inaccessible: **

In fig. 3.31, let C be the inaccessible point. Choose suitable points D and E on the chain line and set out EG and DF perpendiculars to CD and CE respectively and mark H, the intersection point. Locate the point K in line with H and C or alternatively, from H, drop perpendicular UK on AB. CK is then the required perpendicular.

**There may be two cases:**

(i) When the point is accessible, and

(ii) When the point is inaccessible.

**(i) ****When the point is accessible: **

Let AB be the given line and C the point through which a parallel is to be run (Fig. 3.32), From C. drop a perpendicular CD on AB and measure it. Select another point E on AB and erect a perpendicular EF equal in length to CD. CF is then the required parallel.

**(ii) ****When the point is inaccessible: **

In fig. 3.32, let C be the inaccessible point. Locate the foot D of the perpendicular CD on the line AB by the method explained above in 2 (ii) and “find the obstructed perpendicular distance CD as described in the obstacles in chaining” [3. 10(2)].

Choose another point E on AB and erect a perpendicular EF equal in length to CD.CF is then the required parallel.

In fig. 3.33, let AB be the given inaccessible line and C the given point. Fix a point D in line with AC. Fix another point E. Through C, run a parallel CF to AE. cutting DE at F. Through F, run a parallel FG to EB, intersecting DB at G. Then CG is the required parallel to AB.

Let any two lines AO and BO intersect in the lake at O. On the line AO, take any two points X and Y and on the line BO, take a point P. Join YP and produce it to Y_{1} making PY_{1} = PY. Similarly, join XP and produce it to X_{1} making PX_{1} = PX. Join X_{1}Y_{1} and range a rod O_{1} in the direction of X_{1}Y_{1} meeting BO at O_{1}. Then Δs XOP and X_{1}O_{1}P are congruent.

.** ^{.}**. PO = PO

**There may be two cases: **

(i) When the base is accessible, and

(ii) When the base is inaccessible.

**(i) When the base is accessible (Refer to fig, 3.35). **

Take two rods AB and CD of unequal lengths and range their tops A and C in line with the top T of the tower. Comparing Δs ACD and ATQ, we find that these are similar.

Take two rods AB and CD of unequal length and their tops A and C in line with the top T of the tower. Comparing ∆s ACD and ATQ, we find that these are similar.

**(ii) When the base is inaccessible (Refer to fig. 3.36.): **

Take four rods AB, CD, EF and GH; each pair having equal lengths i.e. AB = EF and CD = GH. Fix two rods AB and CD in such a way that their tops A and C are in line with the top T of the tower. Fix the other two rods EF and GH ranging their tops E and G again in line with T. Cut off FD’ = BD and erect a perpendicular D’C’. Join EC. ∆s GTC and GEC’ are evidently similar.

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]]>The post Limiting the Length of an Offset in Chain Survey | Chain Surveying |Surveying appeared first on Engineering Notes India.

]]>**However, the length of offset mainly depends upon:**

(i) The scale of the plan

(ii) The accuracy desired

(iii) The maximum permissible error in eye judgement in laying out the direction of the offset and

(iv) The error in chaining.

In fig. 3.5 let AB be the chain line and P the point upto which the offset is to be measured. D is the correct position of the foot of the perpendicular from P and PD is the correct length of the offset. But while laying, CP is considered to be the direction of the α^{0}. C being the foot of the perpendicular CP is the measured length of offset (say l).

While plotting, the measured length of the offset (l), is set out at right angles to AB at C, so that the point P is displaced to P’ and the amount of displacement PP’ is approximately equal l sin α to I sin α on the ground and on the paper, where s m to 1 cm is the scale of the paper. The length of the offset should be limited to such an amount that this displacement should not be appreciable on the paper. It is assumed that the smallest distance on the paper which can be distinguished while plotting is 0.025 cm.

= 0.025 cm (Eqn. 3.1)

**The displacement of the point in a direction perpendicular to the chain line: **

= CP’ – PD = I-I cos α

=l (1- cos α) on the ground

This is very small and hence negligible.

Putting the values of α (the angular error) and s (the scale) in the above equations, the limiting length of the offset (l) can be found out.

**Errors in Length and Direction Combined: **

Sometimes the error in measuring the length of the offset also occurs. In that case, referring to the Fig. 3.6.

If CP= the true length of the offset

CP’=I= the measured length of the offset.

CP’’=I= the length of the offset as plotted on paper

α= the angular error in direction

Putting the value of n, α and s, the limiting length of the offset (I) can be found out.

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]]>The post Scale of Map: Construction and Classification | Chain Surveying | Surveying appeared first on Engineering Notes India.

]]>In plotting a survey, often an object to be represented on paper is so large that it would be inconvenient to make a full sized drawing of it. The drawing or map is then made to a reduced size, the operation being called **“drawing to scale “.** The Scale of a drawing or a map is the fixed proportion which the length of a line on the drawing or map bears to the corresponding distance on the ground.

Thus if a line one cm long represents 10 m on the ground, the drawing is said to be drawn to a scale of 10 m to a cm. It is usually written as 1 cm = 10m. It is evident that every line on this drawing is 1/1000th part of the corresponding line on the ground.

This fraction which represents the proportion of the drawing distance to the corresponding ground distance is called the Representative Fraction (R.F.) It is, therefore, the ratio of one cm map distance to the corresponding distance on the round converted into centimetres. It may be noted that in finding R.F., the numerator must always be one and denominator will be reduced to the same unit as the numerator.

**For example, if the scale is 10 m to a cm, the R.F. of the scale is:**

The scale should be shown near the title of the drawing or map either graphically or by numerical relation. Scales are generally 15 cm to 25 cm long and never more than 30 cm. The right end of the extreme left division of the scale is invariably marked with 0; the secondary subdivisions starting from that point are marked from right to the left and the primary divisions from left to the right.

**Scales may be classified as: **

A. Plain Scales.

B. Diagonal Scales.

C. Comparative or Corresponding Scales.

D. Vernier Scales.

E. Scales of Chords.

**A. Plain Scale: **

It is used to read in two dimensions only such as units and tenths and hundredths, kilometres and hectometres, metres and decimetres etc.

The scale consists of two lines about 3 mm apart, the bottom one being thicker than the top one. The whole length is divided into suitable number of equal parts or units, the first of which is further sub-divided into smaller parts or sub-units of the main unit. The primary and the secondary divisions are drawn perpendicular to the two lines and are made about 1.5 mm projecting above the top line.

For convenience in reading, it should not involve any arithmetic calculation in measuring distance on the map. The main division should, therefore, represent one, the or hundred units etc.

**Example 1:**

Construct a scale 1 cm = 3 m to read to a metre and show on it 37 metres.

**Solution:**

Draw a line 20 cm long which represents 20 x 3= 60 m length. Divide it into 6 equal parts each representing 10 m length. Subdivide the extreme left division into ten equal parts, each sub-division reading 1 m. Place 0 at the right end of the extreme left division and mark the figures, counting from 0, in both the directions as shown in fig. 3.37. To read 37 metres, places one leg of the dividers at 30 and the other at 7.

**Caution:**

Avoid the common error of laying down centimetres and dividing the left hand centimetre into 3 parts and numbering the others as 3, 6, 9, 12 etc. Such a scale is an inconvenient for taking direct distances and will involve unnecessary counting.

**B. Diagonal Scale:**

This is used when it is required to read in three different dimensions such as units, tenths and hundredths; metres, decimetres and centimetres etc. The deficiency of plain scale of reading only in two dimensions is overcome by this scale.

**The principle of construction of a diagonal scale is based upon the fact that similar triangles have their like sides proportional and is explained below: **

Refer to fig. 3.39, suppose a short line AB is required to be divided into 10 equal parts.

Draw a line BC of any convenient length perpendicular to AB and divide it into 10 equal parts. Join AC and draw lines 1-1′, 2-2′, 3-3′ etc. parallel to AB.

It is obvious that the triangles CBA, C-1-1’, C-2-2’ etc. are similar.

**Now consider the ∆s CBA and C-9-9’: **

**Example 2:**

Construct a diagonal scale, 1 cm = 4 km and show on it 47.6 km.

**Solution: **

Draw a line 15 cm long which represents 15 x 4 = 60 km length. Divide it into 6 parts, each part represents 10 km. Sub-divide the extreme left hand division into 10 equal parts each sub-division reading up to 1 km. At the extreme left, draw a line perpendicular to the scale line and divide it into 10 equal parts of suitable length. Through each of these points, draw lines parallel to the scale line.

Project the points of sub-divisions of the extreme left division on the top most parallel line and then join them together diagonally.

Complete the scale as shown in fig. 3.40 measure 47.6 km, place one leg of the dividers at the intersection of vertical 40 and horizontal 6 and the other leg at the intersection of diagonal 7 and horizontal 6.

**C. Comparative or Corresponding Scale:**

When the given scale of a plain reads in a certain measure and it is required to construct a new scale for the same plan to read in some other measure such that the R.F. of both the scales remains the same, then the new scale is called the comparative or corresponding scale. The comparative scale has an advantage of taking measurements directly from the plan in the desired units without any calculation work.

**Example 3: **

The scale of a plan is, 1 inch = 200 ft, and it reads to a foot. Draw a comparative scale to read to a metre.

**Solution: **

The R.f of the new scale should also be the same so that it may correspond to the previous one.

i.e. new scale is, 1cm = 24m

To construct the required scale, take a line 25 cm long to represent a length of 25 x 24 = 600m. Divide it into 6 equal parts, each part reading to 100 m. Sub-divide the extreme left, hand part into 10 sub parts each representing 10m.

Then at the extreme left erect a perpendicular to the scale line and divide it into 10 equal parts of convenient length. Through each of these points, draw lines parallel to the scale line and complete the scale as shown in fig. 3.42.

Comparative Diagonal Scale, 1 cm = 24 m, corresponding to 1 in. = 200ft.

**D. Vernier Scale:**

The vernier is a device used for determining the fractional parts of the smallest division of the main scale more accurately than it can be done by simply estimating by eye. It consists of a small scale called the vernier scale which moves with its graduated edge along the graduated edge of a long fixed scale called the main scale. The scale may be either straight or curved.

**E. The Scale of Chords:**

It is used to make angles and to measure angles of any magnitude with high degree accuracy. It is generally marked on a rectangular protractor or on an ordinary box wood scale, the method of construction being given below in fig. 3.43.

Draw a line MN of suitable length. At N, draw a perpendicular NT to MN. With N as centre and radius NM, draw an arc MP cutting NT at P. Then the arc MP or the chord MP subtends an angle of 90° at the centre N.

Divide the arc MP into 18 equal parts each part therefore subtends at N an angle of = 5°. Now with M as centre turn down the divisions to 18 the line MR and complete the scale as shown. Then MR is the required scale of chords to read up to 5°.

It may be noted that the distance from M to each division on the scale is the chord of the angle containing that number of degrees e.g. M-30 is equal to the chord of 30° and M-60 is equal to the chord of 60° and so on. The chord of 60° (i.e. the distance M- 60) is always equal to the radius MN.

**Example 4:**

Construct angles of 20° and 35° by using scale of chords.

**Solution: **

(i) Draw a line OX of any suitable length as shown in fig. 3.44 (i). With O as centre, and radius equal to MN from the scale of chords fig. 3.43, draw an arc AD cutting OX at A. With A as centre and radius equal to 0-20 draw an arc cutting the previous arc AD at B. Join O with B. Then angle AOB is the required angle of 20°.

(ii) Similarly obtain the point B by drawing an arc with A as centre and radius equal to 0.35 as shown in fig. 3.44. (ii) Angle AOB is then the required angle of 35°.

Note:

If the angle to be constructed is greater than 90°, then it can be constructed in two parts so -than the sum of the two angles is equal to the given angle e.g. an angle of 105° can be constructed in two parts viz. 60° and 45°.

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]]>The post 3 Main Types of Obstacles in Chaining of a Line | Land Survey | Surveying appeared first on Engineering Notes India.

]]>It sometimes happens that a survey line passes through some object such as a pond, a building, a river, a hedge etc. which prevents the direct measurement of that part of the line which the object intersects. The interfering object in such a case is called on obstacle.

It is necessary to overcome obstacles so that chaining may be continued in a straight line. Special methods are, therefore, employed in measuring distances across the obstacles.

In this type of obstacles, the ends of the lines are not intervisible e.g. rising ground, hill or jungle intervening.

**Here two cases may arise: **

(i) Both ends may be visible from any intermediate point lying on the line such as in the case of a hill. The obstacle of this kind may easily be crossed over by reciprocal ranging and length measured by stepping method of chaining.

(ii) Both ends may not be visible from any intermediate point such as in the case of a jungle. The obstacle of this kind may be crossed over by **“Random line method”.** In fig. 3.20, let AB be the line whose length is required. From A, run a line AB’ called a random line, in the approximate convenient direction of AB and continue it until point B is visible from B’ Chain the line to B’ where BB’ is perpendicular to AB’ and measure BB’.

**If any other length AC’ is measured along AB’, a point C can be located on the line AB by measuring the perpendicular distance = **

Similarly a number of points can be located on the true line. The line is then cleared and chained.

The typical obstacle of this type is a sheet of water, the width of which in the direction of measurement exceeds the length of the chain or tape. The problem consists in finding the distance between convenient points on the chain line on either side of obstacle.

**Two cases may arise: **

(a) When the obstacle can be chained around, e.g. a pond, a thorny hedge etc.

(b) When the obstacle cannot be chained around e.g. a river.

**Case:** **(i) The distance between two points A and B on either side of the pond may be determined by any of the following methods convenient at site: **

(a) Set out equal perpendiculars AC and BD [Fig. 3.21 (a)]. Measure CD which is equal to AB.

(b) Erect perpendicular AC [Fig .3.21(b)] of such a length that CB clears the obstacle and measure AC and CB.

(c) Find by optical square or a cross-staff a point C such that ∠ACB is right angle [Fig. 3.21(c)] Measure AC and BC.

(d) Mark a point C so that CA and CB clear the obstacle [Fig. 3.21. (d)]. Range E in line with AC so that CE = AC. Then range D in the line with BC so that CD = BC. The triangles CAB and CED are congruent. Therefore DE = AB.

**Case (ii):** **Any one of the following methods may be employed to find the width of the river along the direction of the chain line: **

(a) Select two points A and B on the chain line on opposite banks of the river. [Fig. 3.22 (a)]. From A and C, erect perpendicular or parallel lines AD and CE, such that E, D and B are in line. Measure AC, AD and CE. If a line DF is drawn parallel to AC, meeting CE in F, the triangles ABD and FDE are similar.

(b) Select two points A and B on the chain line on either side of the river [Fig. 3.22. (b)]. Set a perpendicular AC and mark its midpoint D. From C, erect CE perpendicular to AC such that E, D and B are in the same range and measure CE. Then triangles ABD and CED are congruent. Therefore AB = CE.

(c) Select two points A and B as before [Fig. 3.22 (c)]. Erect a perpendicular AC and using an optical square at C, find D on the chain line so that ∠BCD is a right angle. Measure AC and AD. Triangles ABC and ACD are similar.

(d) Fix two points A and B as before [Fig. 3.22 (d)].

Erect a perpendicular AC of such a length that triangle ABC is well conditioned. Measure AC and the angle ACB with prismatic compass or box-sextant or with any other angle measuring instrument.

**(e) If a survey line crosses the river obliquely, then the following method is used to find the width of the river: **

Select two points A and B as before [Fig. 3.22. (e)].

At A, set out a line AC in a convenient direction so that C is the foot of the perpendicular from B on AC. Produce CA to D and measure AD = AC. At D, erect a perpendicular DE, E being a point on the chain line. Then triangles ABC and AED are congruent. Therefore AB = AE (the oblique width of the river.

A building is a typical example of this class of obstacles. The problem in this case consists both in prolonging the line beyond the obstacle and finding the distance across it.

**Any one of the following methods may be employed: **

(a) Select two points A and B on the chain line [Fig. 3.23 (a)]. At A and B, erect equal perpendiculars AC and BD. Join CD and produce it past the obstacle. Select two points E and F on it. At E and F, set out perpendiculars EG and FH, each equal in length to AC. The points G and H then lie on the chain line and BG = DE.

The direction and length of perpendiculars must be set out with great accuracy. The check can be made by measuring diagonals of the rectangles. For the same rectangle, diagonals should be equal. Here AD should be equal to BC, and EH equal to FG.

(b) Choose two points A and B on the chain line [Fig. 3.23. (b)]. With AB as base, construct an equilateral triangle ABC by swinging equal arcs with a tape. Produce AC to D and take a point E of DA. Again contract an equilateral triangle DEF with DE as the base.

Produce the line DF to G such that DG = DA. ADG then forms an equilateral triangle and G is a point on the chain line. Determine the second point K on the chain line by forming an equilateral triangle GHK on GH as the base. The line joining KG determines the direction of the chain line past the obstacle, and the obstructed length BK = AG-AB-GK = DA – AB – GK.

**Example:**

There is an obstacle in the form of a pond on the main chain line AB. Two points C and D were taken on the opposite sides of the pond. On left of CD, a line CE was laid out 100 m in length and a second line CF, 80 m long was laid out on the right of CD such that E, D and F are in the same straight line. ED and DF were measured and found to be 60 m and 56 m respectively. Find out the obstructed length CD.

**Solution: **

In Fig. 3.24, CD is the obstructed length of the pond on the chain line AB. CE and CF are known to be 100 and 80 m respectively and EF = 60 + 56= 116 m.

The post 3 Main Types of Obstacles in Chaining of a Line | Land Survey | Surveying appeared first on Engineering Notes India.

]]>The post Filed-Book: 2 Main Types of Filed-Book (With Diagram) | Chain Surveying | Surveying appeared first on Engineering Notes India.

]]>

The field measurements, sketches and relevant notes are recorded for future reference in a note book, known as field-book. The field-book in general use is about 20cm * 12cm and opens length wise.

Every page of this kind of the field-book has a single red line ruled down the middle. This line represents the chain line and against it are entered the total length of the line and the changes at which the offsets are taken. The space on either side of the line is available for sketching the various features along the chain line and for writing the offset distances.

The offsets are noted opposite to the changes from which they are taken to the right or left of the middle line according as they are on the right or left of the chain line.

It is similar to the single line field-book but instead of a single red line in the centre, two blue or red lines about 1.5 cm apart are ruled down in the middle of each page. The space between these lines represents the chain line and is reserved for entering changes, which are thus kept entirely separate from the other dimensions.

Single line field-book is convenient for large scale and much detailed dimension-work while for ordinary work, the double line field-book is commonly used. The pages of the field-book are machine numbered.

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]]>The post How to Plot a Chain Survey? | Chain Surveying | Surveying appeared first on Engineering Notes India.

]]>**The plotting of a chain survey is done in the following steps:*** *

(i) A suitable scale is chosen before starting the plotting work. The scale depends upon the importance of the work and extent of survey.

(ii) Leave a suitable margin (2 cm to 4 cm) all round the paper.

(iii) Select a suitable position of the base line so that the map or plan is shown to the best advantages. The base line should be plotted as accurately as possible because the entire accuracy of the frame-work depends upon it.

(iv) Mark the intermediate stations on the base line and complete the frame-work of triangles.

(v) Check the accuracy of the plotted frame work by means of check and tie lines. If the error is within the permissible value, then adjust the lengths of the sides of the wrong triangles. But if the error exceeds the permissible limits, then resurvey the wrong lines.

(vi) For plotting the offsets, mark the changes of the points along the chain line from where offsets were measured and then draw the perpendicular lines with set squares and scale off lengths of the offsets.

The method of plotting the offset is much simplified if offset-scale (Fig. 3.19) is used for plotting them. In this method, the long scale is placed along the chain line with its zero exactly at start of the line. The offset scale is then placed at right angles to the long scale and is then moved along it to the required changes and the offset lengths are marked with a pricked.

(vii) While plotting keep the field-book side by side in the same direction as the work proceeded in the field parallel to the chain line to be plotted and then plot the various offsets. After plotting one line completely, transfer the offset scale along the second line and open the filed-book page for that line, keep it in the same direction and plot the off-sets. Similarly plot all the lines and details and complete the plan.

(viii) After completing the plan in pencil and checking it, ink the lines and objects and then colour them in according with the conventional signs. The inking and colouring should be commenced from the top left hand corner of the sheet working from left to right and downwards.

(ix) Print the title of the survey in right hand corner at the bottom or at the top of the drawing and then draw the scale of the plan below it.

(x) Mark the north direction in any convenient blank space near the top.

**Equipment required for Plotting: **

(i) A drawing-board.

(ii) A tee-square.

(iii) Set squares.

(iv) A protractor.

(v) A drawing instrument box.

(vi) A rolling parallel ruler for drawing parallel lines.

(vii) A set of French curves for drawing irregular and curved figures.

(viii) A set of metric scales.

(ix) A set of offset scales which are 5 cm long and are divided in exactly the same way as the long scales. They are much useful for plotting the offsets.

(x) Drawing-paper of good-quality of required size.

(xi) Pencils of grade 2H, 3H or 4H.

(xii) Ink and colours of the required shades.

(xiii) Sundries such as rubber, brushes, drawing-pins, weights, sandpaper, knife etc.

The post How to Plot a Chain Survey? | Chain Surveying | Surveying appeared first on Engineering Notes India.

]]>The post Right Angles and Foot of Perpendicular on the Lines | Chain Surveying | Surveying appeared first on Engineering Notes India.

]]>**It is generally found in two patterns:**

(i) Open cross- staff and

(ii) French cross-staff, the first one being in common use.

**(i) ****Open Cross-Staff:**

The simplest form of cross-staff is the open wooden cross-staff shown in fig. 3.7. It consists of a round or square piece of wood about 4 cm thick and varying form 15 cm to 30 cm in diameter or side mounted on an iron shod wooden staff about 2.5 cm diameter and 1.5 m long. The disc is provided with two saw cuts about 1 cm deep at right angles to each other, giving two lines of sight.

The modified form of the open cross-staff is the metal arm cross-staff (Fig. 3.8) in which the wooden head is replaced by four metal arms with vertical slits for sighting through at right angles to each other.

**(ii) ****French Cross-Staff (Fig. 3.9.): **

It consists of an octagonal brass tube with slits on all the eight sides. It has an alternate vertical sighting slit and an opposite vertical window with a vertical fine wire or horse hair on each of the four sides. These are used for setting out right angles. On the other sides are vertical slits, which are at 45° to those mentioned above for setting out angles of 45°. The sights are about 8 cm apart.

It carries a sockets at the base so that it may be mounted on the pointed staff when in use. The sights being too close, it is not as accurate as the open cross-staff.

**Using the Cross-Staff:**

For setting out a right angle at given point on a chain line, it is held vertically over the given point and turned until one of the saw cuts or (the pair of sights) is ranged along the chain line. Then the line of sights through the other saw cut or the pair of sights) is at right angles to the chain line and a ranging rod can be fixed in this direction at a convenient position.

To find the foot of the perpendicular from an object on a chain line, the cross staff is held vertically at an approximate position of the required object and turned until one of the saw cuts or (the pair of sights) is ranged along the chain line.

If on looking through the other saw cut or (the pair of sights) is seen the object from which the foot of the perpendicular is to be drawn, then the point where the cross-staff is held is the correct position of the foot of the perpendicular from the given object. If not, the cross- staff is moved forward or backward along the chain line until the line of sight through the saw cut or (the pair of sights) at right angles to the chain line bisects the given object.

**Testing a Cross-Staff (Refer fig. 3.10): **

Direct one of the saw cuts or (the pair of sights) say ab along the chain line XY and fix a ranging rod at R in the direction of the other saw cut or (the pair of sights) say ‘cd’. Now move the cross-staff horizontally through 90° so that the saw cut or (the pair of sights) ‘cd’ is along XY. If the instrument is correct, the other saw cut or (the pair of sights) ‘ba’ will point towards the ranging rod R, otherwise not, and then it should be rejected.

The cross-staff is a nonadjustable instrument and is not capable of high accuracy. However out of the above two types, the open one being light and strong is more commonly used.

It is more accurate than the cross-staff and is used for setting out accurately the long offsets. It is a small compact hand instrument based upon the principle of reflection.

**There are two forms of the optical square: **

(i) Round or cylindrical and

(ii) Wedge shaped commonly known as Indian optical square.

**(i) Round or Cylindrical Optical Square (fig 3.11):**

It is a round brass box about 5 cm in diameter and 1.25 cm deep fig. 3.11 (a). It is protected by a metal cover fig. 3.11. (b) which can slide round the box as so as to cover the openings and thus prevents the interior from dust, moisture, etc. when the instrument is not in use. Fig. 3.12 (a) shows the sectional plan of the important parts of the instrument.

H and I are two mirrors placed at an angle of 45° to each other. The mirror H, known as the horizon mirror, is half silvered and half unsilvered and is rigidly attached to the base plate of the box. The mirror I, called the index mirror, is wholly silvered and is attached to the box in such a way that it can be adjusted to any position. In some forms of the instrument, the index mirror is also permanently fixed to the base plate.

Three openings are made in the rims of the box: a is a small hole for the eye ; b is a small rectangular slot for the horizon sight placed diametrically opposite to the eye-hole ; and c is a large rectangular slot for index sight placed at right angles to the line joining a and b.

Three similar openings are also made in the rims of the cover such that each of them is brought over the corresponding opening in the rims of the box when the instruments is in use. A small circular hole is also provided on the top of the cover for inserting the key by means of which the index mirror is adjusted.

The lines ab and cl are called the horizon and the index sights respectively both being at right angles to each other. The horizon mirror makes an angle of 120° to the horizon sight while the index mirror makes an angle of 105° to the index sight, the angle between both the mirror being 45°.

A ray of light from the object or ranging rod O strikes the index mirror (I) and is reflected along IH. Thus reflected ray again strikes the silvered portion of the horizon mirror (H) and is then reflected along HE. Thus the observer, looking through the eye-hole, can see the ranging rod at the far end B of the chain line directly through the unsilvered portion of the horizon mirror and at the same time he can see the image of the ranging rod at O in the silvered portion of the horizon mirror.

If the ranging rod at O is at right angles to the horizon sight (chain line) exactly, then the ranging rod at B and the image of O are exactly coincident as in fig. 3.12 (b) otherwise they do not coincide as in fig. 3.12 (c).

**Principle of Optical Square:**

If there are two plane mirrors whose reflecting surfaces make a given angle with each other and if a ray of light is reflected successively from both of them, then the angle between the first incident ray and the last reflected ray is twice the angle between the two mirrors.

Since we want to set out right angles with the optical square, it follows that the two mirrors in it must make an angle with each other equal to half the right angle i.e 90°/2 = 45°

**The principle underlying the construction of the optimal square can be explained as follows (fig 3.13):**

EB is a chain line and O is an object on the line OI which is at right angles to EB.

A ray of light from O strikes the index mirror (I) and is reflected along (IH). The reflected ray again strikes the horizon mirror (H) and is then reflected towards Eye (E) of the observer.

i.e. the angle between the two mirrors (∠ILH)=45°=1/2 of 90°, which is the angle between the index sight and the horizon sight (chain line).

**Use:**

To find out the foot of the perpendicular from any object upon the chain line, place the eye opposite to the eye-hole so that the small slot (aperture) and the large slot (object-hole) are towards the far end of the chain line and the object respectively.

Then walking forward and backward along the chain line, the point where the reflection of the object as seer on the silvered portion of the horizon mirror appears to be coincident with the ranging rod at the farther extremity of the chain line as seen through the plane portion of the same mirror (fig. 3.12b) is the required point.

**Note: **

If the object lies on the left hand side of the chain line, the instrument is held in the right hand and vice-versa.

To set out a perpendicular from any point on the chain line, stand on the chain line holding the instruments exactly above the point. Now place the small slot (aperture) towards farther end of the chain line and the large slot (object-hole) towards the direction in which perpendicular is to be set out. Sight the end ranging rod through the aperture.

Then instruct the assistant to move to and fro until image of his ranging rod seen through the silvered portion of the horizon mirror appears to be coincident with the ranging rod at the farther end of the chain line as seen through the plane portion of the same mirror. The assistant is then directed to fix the ranging rod in that position. The line joining this position of the ranging rod and the point below the optical square is at right angles to the chain line.

**(ii) Indian Optical Square (Fig 3.14): **

It is a brass wedge shaped hollow box of about 5 cm sides and about 3 cm deep with a handle about 8 cm long fixed underneath, m_{1} and m_{2} are two mirrors fixed to the inclined sides of the box at an angle of 45°; ab and cd are two rectangular openings above these mirrors. PQRS is the open face which is to be turned towards the object to which the offset is to be taken.

**Use (Fig. 3.15):**

In taking an offset from an object say O, the observer holding the instrument in his hand stands on the chain line AB and turns the open face towards the object. He then sights the ranging rod B at the forward station by looking through the openings in the direction cb or ad, according as the object is to his left or right and moves along the chain line forward or backward until the image of the object appears exactly in line with the ranging rod B. The point vertically under the instrument is foot of the perpendicular from the object O and OC is perpendicular to the chain line AB.

In using the instrument, hold it quite erect and always apply the eye to the lower corner of the opening which is nearer the open face PQRS and look diagonally to the forward ranging rod. Thus if the object is to the left of the chain line, apply the eye at c and look in the direction of cb and if to the right, apply it at a and look in the direction of ad.

For setting out a right angle from any point ‘C’ on the chain line, stand on the chain line holding the instrument exactly above the point and turn the open face of the optical square towards the direction in which right angle is to be set out. Sight the end ranging rod ‘B’ through the openings.

Then instruct the assistant to move to and fro until image of his ranging rod ‘O’ seen through the mirror appears to be coincident with the ranging rod at the farther end of the chain line as seen through the openings as in fig. 3.16. (b). The line joining this position of the ranging rod and the point below the optical square is a right angles to the chain line.

It is based upon the same principle as that of the optical square. It is more reliable and bright than the optical square. It requires no adjustment since the angle of 45° between the reflecting surfaces of the prism is fixed.

It using the instrument hold it in your hand and see directly over the prism a ranging rod at B. Then walk along the chain line until the image of the object ‘O’ seen in the prism appears to coincide with the ranging rod at B.

When it is used for taking the offset, the perpendicular direction is first ascertained by judgement and then the offset rod is turned over end for end as many times consecutively as may be required to reach the object. This method of offsetting is not preferable as errors accumulate rapidly. This is used only for taking small offsets.

When measuring tape is to be used for taking the offset hold its zero end at the point to which an offset is to be taken and swing the other end on the chain line and note the point of minimum reading on it, which denotes the length of the offset.

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]]>The post Classification of Offsets (With Diagram) | Chain Surveying |Surveying appeared first on Engineering Notes India.

]]>(i) Perpendicular offsets, and

(ii) Oblique offsets.

**(i) Perpendicular Offsets:**

The distances measured at right angles to the chain line from the objects are known as perpendicular or rectangular or right offsets such as CD (Fig. 3.3.) Usually the offsets are perpendicular offsets. In the strict sense, an offset means a perpendicular offset.

**(ii) Oblique Offsets:**

All offsets which are not at right angles to the main survey lines are known as oblique or tie line offsets such as CD and CE (Fig. 3.4.) When the object to be plotted is at a long distance apart from the chain line or it is an important one such as a corner of a building, oblique offsets are taken. These are also taken to check the accuracy of right angled offsets and to locate the position of stations in various surveys. Sometimes they help in reducing the number of main survey lines.

(i) Short offsets and

(ii) Long offsets.

Generally the offsets are called short when they are less than 15 m in length and long when their length exceeds 15 m.

The Offsets should as far as possible be short ones as they are less liable to be erroneous due to incorrect length of tape or incorrect direction than if they are long. Also short offsets can be measured more quickly and accurately than long ones. Tie lines should be drawn to avoid long offsets.

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]]>The post How to Book Field-Notes | Chain Surveying | Surveying appeared first on Engineering Notes India.

]]>(i) Booking is commenced at the bottom of the page and worked upwards and carried continuously through the successive pages so that while writing, the centre line of the book and the chain on the ground correspond with the Surveyor’s own direction.

(ii) The number or name of the line and the name of the station from where the line starts are written at the commencement of each line.

(iii) All distances along the chain line (changes) are entered in the central column.

(iv) The objects offsetted are sketched with conventional signs towards right or left of the central column according as they are on the right or left of the chain line on the ground. The sketches need not be to the scale but must be drawn proportionately and the names of the objects are written along them. Figures denoting the dimensions of the details of the objects are included between the arrow-heads.

(v) Offset measurements are written close to the points offsetted and exactly opposite to and in line with the changes from which they are taken.

(vi) Sufficient space is allowed between rows of booking along or across the page to avoid congestion. About 1 ½ cm space is left between the two entries in the central column.

(vii) When any features such as a road, fence, hedge or a wall etc. crosses the chain line, changes of the point of intersection is entered in the central column and direction of the feature sketched. The line representing the feature is not carried across the central column, but it is drawn meeting the column.

To continue it on the other side of the column, a line parallel to its direction is drawn from a point directly opposite on the other side of the column as shown in Fig. 3.18 (a) at changes 74.0 and 79.0.

(viii) A symbol ∆ is used to denote a main station in the field-book. The zero changes at the commencement and the closing changes at the end of a line are written inside the symbol. The name of the station is written close to the symbol.

Tie or subsidiary stations are indicated by circles or ovals round their changes.

(ix) The directions of the survey lines starting off or ending at any of main or tie stations are clearly shown with their names or numbers.

(x) At the commencement of the tie or check line in the field-book, the position of the tie station is described e.g. tie station (T_{3}) on AC at 30 m from A. Similarly it is described at the finish of the line.

**The following points should be kept in view while booking the field-notes: **

(i) It is one of the most important survey records. It should be carefully and neatly written up with a good quality pencil.

(ii) Each chain line should be started on a fresh page.

(iii) The surveyor should always face the ‘direction of chaining while booking.

(iv) The notes should be complete. Nothing should be left to memory,

(v) The notes should be clear, neat and accurate. Over-writing and erasing should be avoided. When a correction is to be made, the figures should be neatly crossed over and fresh entry made above it and the correction initialled and dated. If however, the entire page is to be discarded, it should be marked ‘cancelled’ and a reference to the other page on which the correct notes are written should be made on this page.

(vi) Explanatory notes and reference sketches of important objects should be drawn on separate page.

**(vii) Each survey must indicate the following: **

(a) Name of Survey.

(b) Site of Survey.

(c) Dates of commencement and completion.

(d) The length of chain used and whether tested or not.

(e) The rough sketch of the area to be surveyed showing north direction, proposed station-points, main and tie lines etc.

(J) Line diagram showing the skeleton of survey and the page index.

(g) Magnetic bearing of at least one line together with the amount of declination at the time of survey.

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]]>The post Chain Surveying of Land: Definition, Principles and Equipment appeared first on Engineering Notes India.

]]>It is the method of surveying in which the area is divided into network of triangles and the sides of the various triangles are measured directly in the field with chain or tape and no angular measurements are taken.

It is the simplest kind of surveying and is most suitable when the area to be surveyed is small in extent and is fairly level and open with simple details. It is unsuitable for large areas and for areas crowded with many details and over difficult country as in such cases the formation of triangles becomes difficult.

The principle of chain surveying is to divide the area to be surveyed into a network of connected triangles as a triangle is the only simple figure that can be plotted from the lengths of its sides measured in the field. Since triangulation forms the principle of chain surveying, the chain survey is also sometimes called as chain triangulation.

If the area to be surveyed is triangular in shape and if the lengths and sequence of its three sides are recorded, the plan of the area can be easily drawn.

But if the area has more than three straight boundaries, for example as in fig 3.1 (a) it is no longer sufficient to measures lengths of the sides only. The field measurements must be so arranged that the area can be plotted by laying down triangles. Several arrangements should be made satisfying this condition but only two are given here as shown in fig. 3.1. (b) and (c).

**The equipment required in chain surveying includes the following: **

(i) A chain with a set of ten arrows.

(ii) A metallic tape 20 m or 30 m in length.

(iii) About one dozen ranging rods (the actual number depends upon the extent of survey).

(iv) An offset rod.

(v) An optical square or a cross-staff.

(vi) A plumb-bob.

(vii) About 2 dozen pegs (the actual number depends upon the extent of survey).

(viii) A mallet or a hammer.

(ix) A field-book and a good pencil.

(x) Sundries such as chalk, nails, field-glass, etc.

**Field-Party:**

**The field party consists of four persons as given, below: **

(i) Surveyor who is in-charge of the party and records chain ages and offsets etc. in the field-book.

(ii) Two chainmen or tape-men to measure all lines and offsets to different objects such as buildings, roads, hedges, wire fencing, drains etc.

(iii) Flagman to fix and carry the ranging rods and also to fix pegs for stations as directed by the surveyor.

**A chain survey may be executed in the following steps: **

**(i) Reconnaissance:**

The preliminary inspection of the area to be surveyed is called reconnaissance.

The surveyor should walk over the area to be surveyed carefully noting all its details such as buildings, roads, hedges, etc. and also the probable position of the station-points and the chain lines etc. The object is to get an intimate knowledge of the area so as to form an idea regarding the difficulties of work, the time required for the survey work etc.

A rough sketch bearing a general resemblance to the plan of the area and showing the north line should be drawn in the field-book.

A base line should be selected in the heart of the survey and whole of the area should then be divided into triangles. The station-points should be marked in the field-book as well as on the rough sketch.

**(ii) Marking Stations:**

Having completed the reconnaissance, the survey-stations should be marked on the ground so that they may be readily discovered when required. If the survey is small in extent and can be finished in a single day, a station may be marked by fixing vertically a ranging rod. The rod may be supported by a heap of stones if the ground is hard.

If the survey is extensive, wooden pegs of small size about 3 cm square and 15 cm long are driven into the ground for ordinary soil, while wooden pegs about 5 cm square and 40 cm long are used to denote the stations in soft ground.

In pasture land, a turf should be cut in the form of a triangle of about 50 cm side and a peg fixed in the centre. If the surface is very hard such as a road, street etc., it is necessary to fix nails or spikes driven flush with the surface.

**(iii) Locating Stations by Reference Sketches:**

After the stations are marked, they should be located by tie measurements essentially from two and preferably from three permanent and well-defined objects in the vicinity of the station. These measurements should be taken precisely and recorded in the field-book by means of a sketch called a reference sketch or location sketch as shown in fig. 3.17.

Reference sketches are necessary to recover the positions of stations in case they are displaced or lost or required at a future date. The referenced stations can be easily restored by swinging arcs with reference points as centres and the respective measurements as radii. The intersection of arcs is the required position of the station-mark.

**(iv) Running Survey Lines:**

Having finished the preliminary work such as selection, marking and location of stations, chaining may be commenced from the base line and carried throughout all the lines of the frame work as continuously as possible. The process of chaining, taking offsets and booking for each line is repeated separately.

**1. Frame Work: **

The system of lines or triangles covering the area to be surveyed is called Frame work or skeleton or survey such as ABCDE in fig. 3.2. The arrangement of triangles depends upon the nature and shape of the area to be surveyed.

Since an equilateral triangle can be more accurately plotted than an obtuse-angled triangle, therefore, as far as possible, the triangles formed in a chain survey should be nearly equilateral. The triangles in which the angles are neither very acute nor very obtuse i.e. all angles are greater than 30° and less than 120° are called well-conditioned or well-shaped triangles and are always preferred in a chain survey.

A triangle which is almost an equilateral one is the best suited for plotting work and is known as the best conditioned triangle. The triangles having angles less than 30° or greater than 120° are known as bad conditioned or ill conditioned triangles and should always be avoided. If however they cannot be avoided, great care must be taken during their chaining and plotting.

**2. Survey Stations:**

The ends of a chain line denote the survey stations.

**These are:**

(i) Main survey stations, and

(ii) Subsidiary or tie stations.

(i) Main Survey Stations are the ends of the lines which command the boundary of the survey, such as A, B, C, D and E in fig. 3.2 ; and the lines joining the main stations are known as Main Survey Lines such as AB, BC, CD, DE, EA, AC and AD in fig. 3.2.

(ii) Subsidiary or Tie-Stations are the fixed point selected on the main survey lines when it is necessary to draw the lines to sub-divide the area for locating the interior details such as T_{1}, T_{2}, T_{3}, T_{4} T_{5} and d in fig. 3.2.

**Selection of Survey Station:**

**The following points should be kept in view while selecting the stations for the frame work: **

(i) A station-point should be located on plain ground so that it is clearly visible from all station-points to which it is connected and gives clear straight lines for measurement.

(ii) The main triangles should be so large as is consistent with the features of the ground. These should be sub-divided by the lines if necessary to bring the objects within easy reach of chain lines so that the work is done according to the principle **“work from whole to the part.” **

(iii) The sides of the larger triangles should pass as close as possible and as parallel as possible to the important buildings, roads, etc., so as to avoid long offsets and to reduce the number of tie lines.

(iv) The triangles should as far as possible be best conditioned and ill conditioned triangles should be strictly avoided.

(v) Each triangle should be provided with at least one check line.

(vi) Station points should not be on thoroughfare.

**3. Base Line:**

A line which is generally longest of all the survey lines and upon which the entire frame work is built up is known as a base line such as AD in fig. 3.2. It generally runs in the centre of the area to be surveyed and should be laid off on the level ground.

It is very important line and since the entire accuracy of the survey work depends upon its accuracy and straightness, therefore, it should be measured accurately twice or thrice by independent methods and its straightness should also be ensured. In large surveys or where convenient, two base lines should be run in the form of a cross (x) through the centre of the area.

**4. Check Line:**

A line which is used to check or prove the accuracy of the frame work as well as that of the plotting work is known as a check line or a proof line such as BT_{3}, CT_{2}, and Dd in fig. 3.2. It is a line which runs from apex of a triangle to any other fixed points on any two sides of a triangle. If while plotting, the length of this line on the plan agrees to the length measured in the field, then the work is correct and thus the accuracy of the triangle is checked or proved.

**5. Tie Line:**

A line joining two tie stations is known as a tie line such as T_{1}, T_{2}, T_{2}, T_{3}, T_{4}, T_{5} in fig. 3.2. It is run to take the interior details which are far away from the main lines and also to avoid long offsets. It can also serve the purpose of a check line.

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