3. leveling by tarun sharma

LEVELINGLeveling is the process by means of which the difference in elevation ( relative height) of various points on the earth’s surface is calculated.

Prepared By:-

Er. TARUN SHARMAASSISTANT PROFESSOR

Department of Civil EngineeringChandigarh Univertsity

Definitions1. Datum line ( M.S.L. ) :-is an imaginary level line from which the

vertical distances of different points are measured. In india, datum is the mean sea level at Mumbai.

2. Reduced level ( R.L) :- Is the vertical distance of a point from datum line.

3. Benchmark (B .M ) :-These are fixed points or marks of known RL determined with reference to the datum line. They serve as reference to the points for finding the RL of new points.

4. Back sight ( B.S.) :- Is the first staff reading taken in any setup of the instrument after the levelling has been perfectly done.

5. Fore sight (F.S) :- Is the last staff reading taken in any setup of the instrument.

6. Intermediate sight ( I.S.) :- Is reading taken between the back sight and fore sight reading .

7. Elevation of line of sight ( H.I) :- is the RL of the line of collimation. This is obtained by adding the BS reading to the RL of the BM or CP on which the staff reading was taken.

• A Level is an instrument with a telescope that can be leveled with a spirit bubble.

• The optical line of sight forms a horizontal plane, which is at the same elevation as the telescope crosshair.

• By reading a graduated rod held vertically on a point of known elevation (Bench Mark) a difference in elevation can be measured and a height of instrument (H.I.) calculated by adding the rod reading to the elevation of the bench mark.

• Once the height of instrument is established, rod readings can be taken on subsequent points and their elevations calculated by simply subtracting the readings from the height of instrument.

Benchmarks

Types of Level

1. Dumpy Level

2. Wye ( or Y ) Level

3. Reversible Level

4. Tilting Level

5. Automatic Level

1. Dumpy Level

Telescope is rigidly fixed.

Can neither be removed from its supports nor rotated about its longitudinal axis.

It is commonly used.

2. Wye Level

Telescope is held in two ‘Y’ supports.

Can be removed from its supports.

It can be rotated about its longitudinal axis.

3. Reversible Level Combination of dumpy

level and the ‘Y’ level.

Supported by two rigid sockets.

Can be rotated about its longitudinal axis.

Can be withdrawn from the socket.

4. Tilting Level

Can be tilted slightly about its horizontal axis with the help of a tilting screw.

5. Automatic Level

Also known as self aligning level.

Levelling Staff

Graduated wooden rod used for measuring the vertical distances between the points on the ground and the line of collimation.

Usually of length 4m.

Least count = 0.005 m

Point of interest

Bottom plane of staff

Bottom plane of staff

Point of interest

Error

(a) (b)

Base of Staff at Slope

Correct Incorrect

Leveling of the instrument is done to make the vertical axis of the instrument truly vertical. 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. 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.

TEMPORARY ADJUSTMENT OF LEVEL

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.

Types of Leveling Operation

1. Differential Leveling

2. Fly Leveling

3. Longitudinal or Profile Leveling

4. Cross sectional Leveling

5. Check Leveling

Differential Leveling

Fly Leveling

Longitudinal or Profile Leveling

Cross Sectional Leveling

Check Leveling

Methods of Calculating R.L.

Rise and Fall Method

Height of Instrument / Line of Collimation Method

Compute all rises & falls Start at a BM with known RL To get RL of next station:

add rise to previous RL, or subtract fall from previous RL

Repeat for all subsequent stations

Rise & fall method

Rise & Fall MethodStation Bearing Distance Staff Reading Difference R.L. Remarks

Back Inter Fore Rise Fall

Sum

Check : Sum of Back Reading - Sum of Fore Reading = Total Rise - Total Fall = Last R.L. - First R.L.

Rise & Fall MethodStation Bearing Distance Staff Reading Difference R.L. Remark

sBack Inter Fore Rise Fall

A 46°15' 00 5.42 100 B.M.

50 7.24100 6.46150 5.38200 6.55

B 75°45' 250 8.78 6.92 Change Pt

300 8.52350 6.24400 5.96450 6.35500 7.54

Rise & Fall MethodStation Bearing Distance Staff Reading Difference R.L. Remarks

Back Inter Fore Rise Fall

A 46°15' 00 5.42 100 B.M.

Rise & Fall MethodStation Bearing Distance Staff Reading Difference R.L. Remark

sBack Inter Fore Rise Fall

A 46°15' 00 5.42 100 B.M.

50 7.24100 6.46150 5.38200 6.55

Rise & Fall MethodStation Bearing Distance Staff Reading Difference R.L. Remark

sBack Inter Fore Rise Fall

A 46°15' 00 5.42 100 B.M.

50 7.24 1.82 98.18100 6.46 0.78 98.96150 5.38 1.08 100.04200 6.55 1.17 98.87

Rise & Fall MethodStation Bearing Distance Staff Reading Difference R.L. Remarks

Back Inter Fore Rise Fall

A 46°15' 00 5.42 100 B.M.

50 7.24 1.82 98.18100 6.46 0.78 98.96150 5.38 1.08 100.04200 6.55 1.17 98.87

B 75°45' 250 8.78 6.92 0.37 98.50 Change Pt

Rise & Fall MethodStation Bearing Distanc

eStaff Reading Difference R.L. Remark

sBack Inter Fore Rise Fall

A 46°15' 00 5.42 100 B.M.

50 7.24 1.82 98.18100 6.46 0.78 98.96150 5.38 1.08 100.04200 6.55 1.17 98.87

B 75°45' 250 8.78 6.92 0.37 98.50 Change Pt

300 8.52 0.26 98.76350 6.24 0.28 101.04400 5.96 0.28 101.32450 6.35 0.39 100.93500 7.54 1.19 99.74

Rise & Fall MethodStation Bearing Distance Staff Reading Difference R.L. Remarks

Back Inter Fore Rise Fall

A 46°15' 00 5.42 100 B.M.

50 7.24 1.82 98.18100 6.46 0.78 98.96150 5.38 1.08 100.04200 6.55 1.17 98.87

B 75°45' 250 8.78 6.92 0.37 98.50 Change Pt

300 8.52 0.26 98.76350 6.24 0.28 101.04400 5.96 0.28 101.32450 6.35 0.39 100.93500 7.54 1.19 99.74

Sum 14.20 14.46 4.68 4.96

Rise & Fall MethodStation Bearing Distance Staff Reading Difference R.L. Remarks

Back Inter Fore Rise Fall

A 46°15' 00 5.42 100 B.M.

50 7.24 1.82 98.18100 6.46 0.78 98.96150 5.38 1.08 100.04200 6.55 1.17 98.87

B 75°45' 250 8.78 6.92 0.37 98.50 Change Pt

300 8.52 0.26 98.76350 6.24 2.28 101.04400 5.96 0.28 101.32450 6.35 0.39 100.93500 7.54 1.19 99.74

Sum 14.20 14.46 4.68 4.96

Check : Sum of Back Reading ~Sum of Fore Reading= Total Rise ~ Total Fall 14.20 ~ 14.46=0.26 4.68

~4.96=0.26 Last R.L. ~ First R.L. =99.74 ~100=0.26

Any Question about Rise & Fall Method ?

????????

Formula:- 1. R.L. + B.S. = H.I.2. H.I. – ( I.S. / F.S. ) = R.L.

• Height of Instrument / Line of Collimation Method

Height of Instrument MethodStation Bearing Distance Staff Reading Ht of Instrument R.L. Remarks

Back Inter Fore

Check : Sum of Back Reading - Sum of Fore Reading = Last R.L. - First R.L.

Height of Instrument MethodStation Bearin

gDistanc

eStaff Reading Ht of

InstrumentR.L. Remarks

Back Inter Fore

A 46°15' 00 5.42 100 B.M.

50 7.24

100 6.46

150 5.38

200 6.55

B 75°45' 250 8.78 6.92 Change Pt.

300 8.52

350 6.24

400 5.96

450 6.35

500 7.54

Height of Instrument MethodStation Bearing Distance Staff Reading Height of

InstrumentR.L. Remarks

Back Inter Fore

A 46°15' 00 5.42 100 B.M.

Height of Instrument MethodStation Bearing Distance Staff Reading Height of

InstrumentR.L. Remarks

Back Inter Fore

A 46°15' 00 5.42 105.42 100 B.M.

Height of Instrument MethodStation Bearing Distance Staff Reading Height of

InstrumentR.L. Remarks

Back Inter Fore

A 46°15' 00 5.42 105.42 100 B.M.

50 7.24100 6.46150 5.38200 6.55

Height of Instrument MethodStation Bearing Distance Staff Reading Height of

InstrumentR.L. Remarks

Back Inter Fore

A 46°15' 00 5.42 105.42 100 B.M.

50 7.24 98.18100 6.46 98.96150 5.38 100.04200 6.55 98.87

Height of Instrument MethodStation Bearing Distance Staff Reading Height of

InstrumentR.L. Remarks

Back Inter Fore

A 46°15' 00 5.42 105.42 100 B.M.

50 7.24 98.18100 6.46 98.96150 5.38 100.04200 6.55 98.87

B 75°45' 250 8.78 6.92 107.28 98.50 Change Pt

300 8.52 98.76350 6.24 101.04400 5.96 101.32450 6.35 100.93500 7.54 99.74

Sum

Check : Sum of Back Reading ~Sum of Fore Reading = Last R.L. ~ First R.L.

Height of Instrument MethodStation Bearing Distance Staff Reading Height of

InstrumentR.L. Remarks

Back Inter Fore

A 46°15' 00 5.42 105.42 100 B.M.

50 7.24 98.18100 6.46 98.96150 5.38 100.04200 6.55 98.87

B 75°45' 250 8.78 6.92 107.28 98.50 Change Pt

300 8.52 98.76350 6.24 101.04400 5.96 101.32450 6.35 100.93500 7.54 99.74

Sum 14.20 14.46

Check : Sum of Back Reading ~Sum of Fore Reading= Last R.L. ~ First R.L.

14.20 ~ 14.46=0.26 99.74 ~100=0.26

Any Question about Height of Instrument Method ?

????????

Drawing of Profile on a Graph Paper Approx profile of Leveling

0 50 100 150 200 250

100 ft

100 98.18 98.96 100.04 98.87 98.50

R

O

AC

B

LEVEL

STAFF

OAC :

(OC)2 = (AC)2 (OA)2

Or, (R+h)2 = l2 + R2

Or, R2+ 2Rh+h2 = l2 +R2

So, h = l2/(2R+h)Since R >>> hSo, h = l2/(2R)R= 6370 km

R

h

The Earth

l

EFFECT OF CURVATURE & REFRACTION ON LEVELING

Problem on Effect of Curvature A student of MIST standing on a deck of a ship just sees a light

house ( 42 meter above MSL). Height of student eye is 6 meter from sea level. Find the distance of MIST student from the light house.

Two Peg Test

x x

AyA

ByB

x x

y2y

Problem on Two Peg Test Point A and B have known RL of 100 and 101 meter

respectively. During leveling the H.I. was 102 meter and Staff Reading was 4.0 meter at B. What will be Staff Reading of point A ?

100 meter

100 meter

A B 101

C 100

Errors in Leveling

Instrumental Imperfect Adjustment Sluggish Bubble Incorrect Marking on Staff Defective joint of Staff Wear at Staff bottom Misalignment of TelescopeAccumulation of Dirt at base of Staff

Errors in Leveling

Natural Curvature of the Earth Refraction Temperature Wind vibration on Level & Staff Soft Ground

Errors in Leveling

Personal Handling of Instrument Verticality of Staff Mistakes in taking Staff Reading Mistakes in Recording

Any Doubt on Leveling as a whole