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
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