Leveling
Objectives of
Leveling:
1)
To find the elevations of given points with respect to
any given or assumed datum. (used in planning
/design)
2)
To establish points at elevations given, with respect to
given or assumed datum. (used in setting out
all kinds of eng. Works.)
> Leveling deals with
measurements in vertical plane (linear or angular).
Important Terms:
Level surface:
> Level surface is the curved
surface which at each point is perpendicular to direction of gravity.
> Surface of still water (sea water) is truly level
surface.
> Any surface parallel to
mean spheroidal surface of earth is a level surface.
Level line:
> A line lying in a level
surface is a level line
> It is always normal to plumb lines at all points.
Horizontal plane:
It is the plane tangential to
level surface at a point. It is therefore, perpendicular to plumb line at that
point.
Horizontal line:
A straight line tangential to the
level line at a point.
Vertical line:
> Line normal to the level line at a point.
> Generally, it is a line
defined by a plumb line.
Datum:
Datum is any surface with
respect to which elevations are determined.
Elevation:
Elevation of a point is its
vertical distance above or below an arbitorrily assumed level surface or
datum.
Mean sea level:
Average hight of sea for all
tide levels Average over a period 19 years.
Bench mark:
>
Bench mark is a relatively
permanent point of reference whose elevation with respect to some assumed datum
is known.
>
Used as a either starting
point for levelling or as a point upon which to cloose as a check. Methods
of Leveling:
To determine difference in
elevation, three methods are used.
1)
Barometric leveling:
>
Based on the phenomena that
difference in elevations between two points is proportional to difference in
atmospheric pressures at those points.
2)
Trigonometric leveling (Indirect leveling)
>
It is the process of leveling
in which the elevations of pts are competed from observed vertical angles and
known distances.
3)
Spirit leveling (Direct leveling)
> A spirit level and a sighting
device (telescope) are combined and vertical distances are measured
by observing on graduated rods
placed at a point.
> Most precise and most commonly
used method.
Leveling Instruments:
Commonly used instruments in
direct leveling are
1)
Level
2)
Leveling staff.
1) Level
> A
level is to provide horizontal line of sight. > It
consists of four important parts.
1)
A. telescope – to provide line of sight
2)
A level tube – to make line of sight horizontal.
3)
A leveling head – to bring the bubble in centre of run.
4)
A tripod – to support the instrument. Types of levels:
1) Dumpy 2) Wye or y, 3) Reversible, and 4)
Tilting
1) Dumpy level
> Given by Gravatt.
> The name is so because formerly
this level was equipped with an inverting eye piece and hence
was shorter than wye level of
same magnifying power.
Advantages of dumpy level over
wye level.
1)
Simpler construction and fewer movable parts.
2)
Lesser adjustment to be made.
3)
Longer life of adjustments.
2)
Wye level or Y-level > In dumpy level telescope is
fixed to spindle while in wye level the telescope is carried in two vertical
‘Y’ supports. > In case of wye level adjustments can be tested with greater
rapidity and ease.
3)
Reversible level:
> It combines the features of both dumpy and wye
level.
4)
Tilting level:
> In case of dummy and wye
level, line of sight is perpendicular to vertical axis.
> While in tilting level line
of sight can be slightly tilted without tilting vertical axis.
Leveling staff:
The purpose ofleveling staffis
to determine the amount by which the station (i.e. foot ofthe staff)
is above or below the line of
sight.
There are three types of self
reading staff:
1)
Solid staff:
- Smallest division is 0.01 ft or 5 mm. However. Some
staff have fine graduations upto 2mm. - Made up wood having general length 10
ft or 4m.
2)
Folding staff:
3)
Telescopic staff (sop with pattern)
- 14 ft or 5 m in length.
- Since, telescope is used,
readings appear to be inverted. So, readings are taken from above
downwards.
The surveying
telescope:
> Surveyors telescope is
adaptation of keplers telescope which has two convex lenses, one nearer
to object called as objective and
other near the eye called as eyepiece.
Line of sight or line
of collimation:
- Line
passing through optical centre of objective and the intersection of cross hairs
is called line of sight.
Parallax:
>
If the image formed by objective lens is not in the same plane with cross
hairs, any movement of eye is likely to cause an apparent movement of the image
with respect to the cross hairs. This is called as “parallax”.
> Parallax can be eliminated by,
1)
Focusing the eye piece: to bring the cross hairs in the
plane of distinct vision.
2)
Focusing the objective: to bring the image of object in
the plane of cross hairs which are clearly visible. Parts of telescope:
1) Objective 2)
Eyepiece 3) diaphragm
4) Body and focusing device
1) Objective:
> It is a compound lens consisting ofthe front convex lens
made up of crown glass and back concave convex lens made ujp of flint glass
cemented together such compound lens is called achromatic lens.
> By using compound lens spherical
and chromatic are aberrations eliminated.
2) Eye piece:
Ramsden eye-piece: most commonly used. Composed of
plano-convex uses of equal focal length, with spacing of 2/3 F.
Huygevs eye piece: Not commonly
used.
3) Diaphragm: consists of cross hairs. Optical defects
in single lens: are
1)
Spherical aberrations:
> The
rays from a given points are not collected at one point > A plantation – absence of spherical aberrations.
2)
Chromatic aberrations:
> A
chromatin – absence of chromatic aberrations.
> A beam of light is made up of
seven colors and focal length of single lens is different for different
colors of light. So, all the
colour lights will not converge at a point.
> Violet ray is refracted most and
red least
3)
Coma
4)
Astigmation
5)
Curvature offield
6)
Distortion.
Temporary adjustments: 1) setting up the
level, 2) leveling up, 3) Elimination of parallax. Important terms in leveling:
1) Station: station is the point
at which the level rod is held and not where level is set up.
2)
Height
of instrument: (HT) it is
the elevation of line of sight (plane of sight) with respect to assumed datum.
3)
Back
sight (BS)
Back sight is the sight taken on
a rod at a point ofknown elevation, to find the height ofline of sight above
that point. (thus to botain height of instrument)
Also known as plus sight.
4)
Fore sight (FS)
Fore sight is the sight taken on a rod held at a
point ofunknown elevation, to ascertain the amount by which the point is below
line of sigtht and thus to obtain the eleven of point.
Also called as minus sight.
5)
Turning point: (TP) change point:
A point on which both BS and FS are taken on a line
of direct levels. To establish other instrument station with new H.I.
6)
Intermediate station: (IS) /intermediate sight:
A point
intermediate to two turning points on which only FS or minus sight is taken to determine
the elevation of station.
Booking and Reducing
of levels:
1) Height ofinstrument method, and 2)
Rise and fall method
1)
Height of instrument method: (collimation method)
In this method, HI is
calculated for each set up of the instrument.
The elevations of RL’s of the
turning points (other staff station) are then calculated by subtracting
FS from HI.
For next set up of the
instrument HI is calculated by adding BS taken on T.P.1 to its R.L. The
process continues till the R.L.
of last point.
If there are some intermediate
points, then the R.L. ofthese points is calculated by subtracting IS
(minus sight) from H.I. for that
set up.
Generally used for fly
leveling or to establish BM’s.
Check: BS FS Last RL First R.L
2)
Rise and fall method:
HI is not at all calculated.
The difference of level
between two consecutive points is found by comparing the staffreadings on
the two points for the same
setting of the instrument.
Higher staffreading of
consecutive point indicates fall while lesser indicate rise.
Ø Generally used in
contour survey, in small areas
Ø Used when large no. of intermediate station
readings are required. Check: : EBS —EFS = Last RL —
First R.L =Erise—Efall Curvature and Refraction:
Correction for curvature (-ve)
Therefore the correction for
curvature is negative.
C= 2Ralways
d 2 (—ve)
= 0.07849d2m,dinkm
Correction for refraction: (+ ve)
(C2)
Ø Due to refraction
line of sight curves downward, thus reading decreases.
Ø Therefore correction
for refraction is positive
2
Cr = ________ d and R in same units
Cr = 0 .01121d2m d in km
Combine correction for curvature
and refraction
6 d2
C = 7 2R always(—ve)
C = 0.06728d2m,d
in km Distance to the visible horizon:
Ø
Combine
correction is nothing but the difference in actual line of sight and level
surface (curved surface).
|
C
|
6
|
d
|
2
|
|
|
7 2
|
R
|
|||
d= _______________ c
in m,din km
0.06728
Special methods of
spirit leveling or direct leveling:
1)
Differential leveling:
The operation of leveling to determine the elevation
ofpoint at some distance apart is called differential leveling.
Or To determine difference in
elevations of two points regardless ofhorizontal position of the
points with respect to each
other.
- Need to set up instrument several times.
- Also called as fly leveling.
2)
Profile leveling:
>
To
determine elevations of pts at measured intervals along a given line in order
to detain profile of the surface along that line.
3) Cross – sectioning:
>
Process
of taking levels on each side of a main line at right angle to that line
Example: road survey
4) Precise leveling:
> Leveling in which
degree ofprecision required is too great.
5) Reciprocal leveling:
>
Leveling
in which difference in elevation between two pts is actually determined by
taking two sets of reciprocal observations.
> By reciprocal
leveling following errors can be eliminated.
1)
Error in instrument adjustment or error in line of
eliminated,
2)
Combine effect of earths curvature and refraction
3)
Variations in the average refraction.
True difference in elevation H
( 'h A— h B)+ (hA—hB')
2
Total error, e =(hA — hB)—(hA' —hB' )
2
Total error includes line of
collimation errors, curvature and refraction error.
e = ecol
+ ecur + eref
ecol = e— ecur
+ eref
Line of collimation error is
same as that of curvature error ifline ofcollimation is inclined upwards.
Sensitivity of bubble
tube:
> Sensitiveness of
bubble tube is angular value of one division ofthe bubble tube.
> Generally, the linear
value of one division is 2 mm
> For a same angular
change if bubble moves by more divisions it is called as more sensitive.
> Sensitiveness can be increased
by,
1)
Increasing the internal radius of tube.
2)
Increasing the diameter oftube
3)
Increasing the length ofthe bubble.
4)
Decreasing the roughness of wall
5)
Decreasing the viscocity of liquid.
oc s l
sensitivity = =_______ = radius
n n D R .
nl s
v
R d
α = angular change in radius when
bubble moves by n divisions.
l = length of one
division
s = staff intercept when bubble
moves by n divisions.
R = radius of curvature of
bubble tube.
D = dist. Between staff and
instrument.
Hypsometers:
The working of hypsometer for determination
of attitudes of stations depends on the fact that the
temp at which water boils varies
with the atmospheric pressure.
Altimeter is used to find heights based on barometric
pressure difference.
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