LECTURE NO.

5 -surface of constant potential energy

(equipotential surface) that coincides
Leveling with mean sea level over the oceans.
- process or operation of directly or Reference Ellipsoid
indirectly measuring vertical distances -mathematical surface of reference.
-determine the elevation of points or
their differences in elevation.

Significance Bench Mark ( BM )

-Provides necessary data for -fixed point of reference whose elevation
engineering design, engineering is either known or assumed.
construction and production of Backsight ( BS ) ▪
topographic maps reading taken on a rod held on a point of
-Site Suitability Analysis known or assumed elevation.
-Proper design and laying out of vertical Backsight Distance ( BSD )
and horizontal structures measured from the center of the
instrument to the rod on which a
Level Surface backsight is taken.
-curved surface parallel to the mean Foresight ( FS )
spheroidal surface of the earth. reading taken on a rod held on a point
Horizontal surface whose elevation is to be determined.
-plane that is tangent to a level surface Foresight Distance ( FSD )
at a particular point horizontal distance from the center of
Level line the instrument to the rod on which a
-Line lying on level surface. foresight is taken
Horizontal line Turning Point ( TP )
-straight line in a horizontal plane which intervening point between two bench
is tangent to a level line at one point . marks upon which point foresight and
Vertical line backsight rod readings are taken to
-line parallel to the direction of gravity enable a leveling operation to continue
Elevation from a new instrument position
-vertical distance above or below mean Height of Instrument
sea level or any other selected datum -elevation of the line of sight of an
Difference in Elevation instrument above or below a selected
-vertical distance between the two level reference datum.
surfaces in which the points lie -determined by adding the rod reading
Datum on the backsight to the elevation of the
-Any convenient level surface coincident point on which the sight is taken.
or parallel with mean sea level to which
elevations of a particular area are Leveling Methods
referred Direct or Spirit Leveling – determining
Mean Sea Level the elevation of points some distance
-imaginary surface of the sea which is apart by a series of set ups of a leveling
midway between high and low tides . instrument along a selected route.
Geoid Forms of Direct Leveling
a. Differential Leveling
b. Double – Rodded Leveling
c. Three – Wire Leveling -requires a series of set ups of the
Reciprocal Leveling – commonly instrument along a general route and,
employed when leveling across a wide for each set up, a rod reading back to
river, a deep ravine, or across canyons the point of known elevation and forward
and gullies where it would be difficult or to a point of unknown elevation are
impossible to maintain a foresight and a taken.
backsight distance of nearly equal *Procedure of Differential Leveling*
lengths. -leveling instrument is set up at any
Profile Leveling – is used to determine convenient location along the level route
difference in elevation between points at and a backsight is taken on a leveling
designated short measured intervals rod held vertically on BMa .
along an established line to provide data -backsight reading added to the known
from which a vertical section of the or assumed elevation of the initial bench
ground surface can be plotted. mark gives the height of instrument
above datum or HI = Elev BMa + BS
Trigonometric Leveling – employed in -rodman moves forward along the
determining by trigonometric general direction of BMb and holds the
computations the difference in elevation rod at a convenient turning point ( TP1 )
between two points from measurements -instrumentman takes a foresight on the
of its horizontal and slope distance and rod.
the vertical angle between the points. -foresight reading subtracted from the
Stadia Leveling – combines features of height of instrument gives the elevation
direct leveling with those of above datum of the turning point or Elev
trigonometric leveling. It is in fact a form TP1 = HI – FS
of trigonometric leveling -the level is transferred again and a
Barometric Leveling – it involves the backsight is taken at TP1 and foresight
determination of differences in elevation at TP2 . Repeat procedures until
between points by measuring the foresight is taken on BMb .
variation in atmospheric pressure at
each point by means of altimeter or
barometer.
Cross-Section Leveling – In highways Three-Wire Leveling
or railroad constructions, it is often method of determining differences in
necessary to obtain a representation of elevation wherein three horizontal hairs
the ground surface on either side of the (or threads) are read and recorded
centerline. rather than from a single horizontal hair
Borrow-Pit Leveling – is a method of Types of Levels
determining the relative elevations of 1. Dumpy Level – most widely used
points in borrow-pit excavations for the direct leveling instrument. It has a long
purpose of calculating volumes of telescope which is rigidly attached to the
earthwork. level bar.
Differential Leveling - process of 2. Wye Level – identical to dumpy level.
determining the difference in elevation The only difference is the telescope are
between two or more points some attached to the supporting level bar.
distance apart. 3. Builder’s Level – often called a
construction level or an architect’s level.
The level vial is not as sensitive as in
other levels and its telescope has a -consists of three wooden or aluminum
much lesser magnifying power. legs which are securely fastened the
4. Automatic Level – Also termed as tripod head by means of a hinged joint.
self aligning level. Is equipped with a Length of Sight - always best to take
prismatic device called compensator. sights at moderate lengths to attain
5. Tilting Level – It consists of a speed and accuracy in leveling work.
telescope attached with a level tube -very short or extremely long sights
which can be tilted within few degrees in should be avoided.
vertical plane by a tilting screw. -not exceed 90 m where elevations to
6. Geodetic Level – are employed in the nearest 0.001 m are desired.
first-order leveling work where extreme Adjustment of the Dumpy Level
precision is an important requirement. Adjustment of the Cross Hairs ▪The
8. Laser Level – a new innovation reticule or the cross hair ring is adjusted
introduced to surveying operations is the to see to it that the horizontal cross hair
use of lasers. lies in a plane perpendicular to the
9. Hand Level – is a handheld vertical axis of the instrument.
instrument used on surveys involving Adjustment of the Level Vial ▪The
short sights and where a low order of purpose of this is to make the axis of the
accuracy is sufficient. level perpendicular to the vertical axis of
10. Digital Level – it uses electronic the instrument.
image processing to evaluate the Adjustment of the Line of Sight ▪The
special bar-coded staff reading. line of sight is adjusted to make it
Leveling Rods - graduated rod which is parallel to the axis of the level vial. ▪To
used for measuring the vertical distance check and adjust the line of sight, a
between the line of sight through a procedure known as the “TWO-PEG”
leveling instrument and the point whose test is employed.
elevation is either required or known.
Rod Level- device used for fast and
correct plumbing of a leveling rod LECTURE NO. 4
-L-shape in design and consists of a Pacing - counting the number of steps in a
small circular spirit level fastened to the required distance.
rod or to a small bracket held against -rapid means of approximately checking more
the side of the rod. precise measurement of distance
Telescope - metal tube containing a Pace ▪ length of a step in walking. It may be
system of lenses which are used to fix measured from heel to heel or from toe to toe.
the direction of the line of sight and in Stride ▪ It is equivalent to two paces or a double
magnifying the apparent size of the step.
objects in its field of view. Pace Factor ▪ It is the length of one’s pace.
Level Vial - sealed graduated glass Taping - involves direct measurement of
tube containing some amount of liquid distances with measuring tapes.
and a small air bubble. -consists of stretching a calibrated tape
-used to determine the direction of between two points and reading the distance
gravity. indicated on the tape.
Tripods - serves as a base to prevent -most common method of measuring or laying
movement of the instrument after it is out horizontal distances.
set up.
Breaking Tape - measurement of shorter Observation - single, unadjusted determination
distances which are accumulated to total a full of a linear or angular value
tape length. -quantity that is obtained by instrumental
Slope Taping - Taped measurements are made measurement of the quantity.
directly along the slopes when the ground is of direct observation is an observation of the
uniform inclination and fairly smooth, rather desired quantity
than break tape every few meters. indirect observation is a quantity computed
Temperature - measurements are taken at from direct observations.
temperatures above or below the standard Measurement - entire process of obtaining a
temperature of the tape. desired quantity.
-Proportional to the number of tape lengths. -entails performing a physical operation that
Tension - pull applied is different from standard usually consists of several more elementary
tension used in calibration. operations such as preparations
A function of: Errors - difference between the true value and
oDifference between applied and standard pulls the measured value of a quantity.
oMeasured length Mistakes - inaccuracies in measurements which
oCross-sectional area of the tape occur because some aspect of a surveying
oModulus of elasticity of the tape material operation is performed by the surveyor with
Sag - tape supports are only at its ends or at the carelessness, inattention, poor judgment, and
two points measured. improper execution.
Tacheometry - indirect method of measuring -not errors because they are usually so gross in
horizontal distances magnitude compared to the other types of
-based on the optical geometry of the errors.
instruments used. Systematic or Cumulative Errors
Stadia Method ▪ Uses a telescope with 2 -occur according to some deterministic system
horizontal cross hairs and a graduated rod -Caused by physical and natural conditions
called stadia rod. Types of Systematic Errors
Subtense Bar Method - set up at a distant 1. Constant Error ▪ If its magnitude and sign
station while a theodolite at the end of the line remains the same throughout the measuring
measures the horizontal angle subtended by the process/field conditions are unchanged. ▪
distance between the two targets Example: tape “too short” or “too long”
Photogrammetry – 2. Counteracting ▪ If its sign changes while its
Measuring of images on a photograph magnitude remains the same perhaps due to
▪Uses scale to obtain ground distance personal bias of the observer.
Global Navigation Satellite Systems
-Fixing of satellites to determine position of the Random and Accidental Errors
points. -irregular causes that are beyond the control of
Distance is determined from position of points. the observer and present in all surveying
Electronic Distance Measurements measurements.
-based on the invariant speed of light or Measure of Central Tendency
electromagnetic waves in a vacuum. -summary statistic that represents the center
TOTAL STATION - combination of electronic point or typical value of a dataset.
transit and electronic distance measuring device Random Variable ▪ It is defined as a variable
(EDM). that takes on any of several possible values,
with each of which is associated with a
LECTURE 3 probability.
Random Event ▪ It is one whose relative
frequency of occurrence approaches a stable
limit as the number of observations/repetitions
of an experiment is increased to infinity.
True Value - is the value which is absolutely free
from all the errors and this value is
indeterminate. ▪
Observed/Measured Value – is the value
obtained from the observation/measurement. ▪
Most Probable Value (MPV) - it refers to a
quantity which based on available data has
more chances of being correct than has any
other. It is the arithmetic mean or the average.
Residual- deviation and defined as the
difference between any measured value of a
quantity and its most probable value.
Probable Error - defines a range within which
there is a 50 percent chance that the true value
of the measured quantity lies inside ( or outside
) the limits thus set.
Relative Precision - magnitude of the error in
the numerator and the magnitude of a
measured quantity in the denominator.

LECTURE NO. 2