Leveling

ميزانيهال

Leveling lecture 1:

Readings: 4-1 through 4-4, 4-5.2, 4-6 through 4-12, 4-14

Lecture 2:

Readings: 5-1 through 5-5, 5-8

Lecture Outline • Remarks and introduction

• Definitions

• Vials

• Levels: optical, laser, digital

• Rods

• Differential Leveling

• A leveling Loop

Surveying Measurements • Surveyors, regardless of how complicated the

technology they use, measure two quantities: angles and distances.

• Angles are measured in horizontal or vertical planes only to produce horizontal angles and vertical angles.

• Distances are measured in horizontal, vertical, or sloped directions.

• Our calculations are usually in a horizontal or a vertical plane for simplicity, sloped values can be calculated if needed.

• For example: maps are horizontal projections of

data, distances are horizontal on a map and so

are the angles.

• If you are given the horizontal coordinates X

and Y of two points A and B: (20,20) and (30,

40). If you measure the horizontal angle α =

(CAB) and the horizontal distance AC, found

them to be: 10 20’ and 15m respectively, then

the coordinates of C can easily be computed.

A

B

C

α

• But, if you were given a slope distance or a

slope angle, you won’t be able to compute the

location of C

We will learn measurements of distances first:

vertical, horizontal, and sloped. Then we will

learn about angles: horizontal and vertical.

Next step is to learn about the use of the

measured values in producing surveying

products or in setting –out of objects.

• Distances measured in the vertical through a

process called “leveling ميزانيهال ” and the vertical

distances represent differences in “elevations

using a measuring device called a ”المناسيب

“level المنسوب“

• You need: an instrument that provides a

horizontal line “the level” a graded ruler قامة او

مسطرة

DATUM ELEVATION = 0.0 (MSL)

10

0 m

Elevation B = 100 + 4.12 - 6.24= 97.88 m

Elevation computation حساب المناسيب:

Compute the elevation of point B if the elevation of point A was

100.00 m.

4.12 m 6.24 m

Definitions

• Horizontal Line: a line that is perpendicular to the vertical at one point on it.

• Horizontal Plane: a plane that is perpendicular to vertical at one point on it

• Vertical Line: a line in the direction of gravity

Why leveling??

Definitions:

• Level Line: a line that that is perpendicular to the direction of gravity at any point on it.

• Level Surface: a surface that is perpendicular to the direction of gravity at any point on it.

• Vertical Datum: a level surface from which elevations are measured

• Elevation منسوب : vertical distance from a vertical datum

• Mean sea level (MSL): the average surface of the sea, a level surface measured over 19 years for all tide stages.

• Benchmarks (BM) روبير: a relatively permanent object of known elevation.

• Leveling الميزانيه : the process of finding elevations of points, or their difference in elevation.

Level vials موازيين التسوية Their function is to provide a horizontal line or

plane for adjustment of the instrument.

• Tube level اسطوانى

Other level vials

• Coincidence-Type level متطابق

• Bull’s-eye level

• مستدير

Levels الموازيين • They provide

a horizontal line of sight

• Major types: • Tilting

levels: the coincidence level must be adjusted before each reading, the telescope can be tilted by one screw. Very accurate.

•Automatic levels: use an

automatic compensator to level

the line of sight. The

compensator is a group of

prisms suspended by wires as a

pendulum. Accuracy varies. Can

include a parallel plate

micrometer to measure to 1/100

mm.

•Automatic Compensator in an

automatic Level:

An automatic Level

Automatic Precise level

Laser Levels

•Transmit laser beams,

received on a detector.

•Creates a horizontal or a

vertical plane.

•May stop if not

horizontal.

•More than one detector

can be used

simultaneously.

Digital Levels

• Employ digital image processing. A micro computer compares the rod image to a pre-stored image of the rod to compute the reading. Rod is bar coded.

Rods القامات • Graded in feet or meters.

Made of wood, metal or fiber

glass.

• Pay attention when the rod is

telescopic.

• Metric is graded to 1 cm, and

decimeters. Dots for meters.

• A sliding micrometer can be

used.

Rod Remarks • Before observing,

understand the rod.

Where the zero is and

how it is graded.

• Try a certain reading

without a level.

• Pay attention if the

telescope inverts the

vision.

• Keep the rod vertical

4.12 m 6.24 m

Elevation C = 100+ 4.12 – 5.42= 98.70 m

Elevation computation حساب المناسيبusing the HI method:

Compute the elevation of point B if the elevation of point A was

100.00 m.

5.42 m

C Elevation B = 100+4.12-6.24= 97.88

Backsight (BS) at BM Foresight (FS) at X

•Definition of Backsight (BS) مؤخرة , Foresight مقدمة(FS), and (IS)

متوسطة

•Elevation of line of sight (HI)= BM elevation + BS at BM

•Elevation of point X = HI - FS at X

In general:

Elevation of point B =

Elevation of point A + backsight at A - foresight at B

Elevation of (b) = Ea + B.Sa – F.Sb ….............(1)

Similarly,

Ed = Eb + B.S b – F.Sd ……………………...(2)

Ee = Ed + B.S d – F.S e, and so on. Also, if you

subatitute for Eb in eq. (2) by the value in eq. (1)

you get: Ed = Ea + BS - FS

a b d

Now, b is known, we

can use it as if it was a

benchmark instead of

a and repeat the work

Elevation of Final Point = BM elevation + (BS) - (FS)

• We call point (b) a turning point (TP), why?

• If more elevations are needed without moving

the level, the readings between the BS and FS

are called Intermediate Sights (IS).

• To compute the elevations,

• Compute the HI, or the elevation of line of sight

= EBM +BSBM

• Compute the elevation of any ISi point

= HI – ISi

• Finally, the last reading is a FS, say at point N

• EN = HI - FSN

a b

BS IS IS IS FS

BS FS

1 2

3

4 5

6

A LEVELING PROCESS THAT INCLUDED 6 POINTS

AND 7 READINGS.

Point BS IS FS HI =

E + BS

Elevation (E)

= HI – (IS or) FS

BM 761 2.11 22.13

1 1.14

2 0.95

3 1.76 0.84

4 2.01 1.55

5 1.88

Example: Compute the elevations of points 1 through 5 if the elevation

of the BM is 22.13 m