Tuesday, August 30, 2016
Lesson Note On Coordinate Calculations
Coordinate Calculations
1. Co-ordinate calculations
Calculations involving rectangular co-ordinates are:
a) Calculation of Whole Circle Bearing (WCB) and distance between two co-ordinated points.
i) Calculate the difference in easting( E) and difference in northings ( N) between the two points.
ii) Determine the Reduced Bearing from:
E
Reduced bearing= tan ------
N
Iii) Convert the reduced bearing to a Whole Circle Bearing.
1st quadrant same
2nd quadrant 180 – rb
3rd quadrant 180 + rb
4th quadrant 360 – rb
The correct quadrant can be found by inspection of the relative positions of the co-ordinated points.
iii)Calculate the horizontal distance from:
E N
Distance = -------------- and --------------
Sin WCB Cos WCB
Using both these formulae separately gives a check on the calculation of the WCB
A further formulae could be used to determine distance but this does no check WCB calculation.
Distance = E + N
Example calculation
Given: Stn A 179.724 mE 414.132 mN
Stn B 142.171 mE 372.916 mN
A 179.724 414.132
B 142.171 372.916
------------ -----------
E 37.553 N 41.216
Reduced bearing = tan –1 37.553
41.216
= 42.2015
WCB= 180 + 42 20 15
= 222 20 15
Distance = 37.553 = -55.758 m
Sin 222 20 15
= 41,216 = -55.758 m
cos 222 20 15
The two distances should be the same and of course, the negative sign is ignored.
a) Calculation of rectangular co-ordinates of a point (B) knowing the co-ordinates of another point (A), the WCB from that point to B (A to B) and the horizontal distance between them.
The procedure is as follows:
i) Calculate the difference in eastings and northings using the following formulae:
E = distance x sin WCB
N = distance x cos WCB
ii) Add E and N to the eastings and northings respectively of the known point.
Example- calculation
Given: Co-ords A 137.629 mE 473.126 mN
WCB A to B 136 27 19
Distance A to B 53.249
E = 53.249 x sin 136 27 19
= 36.684 m
N = 53.249 x cos 136 27 19
= 38.597 m
Co-ords A 137.629 473.126
Difference 36.684 -38.597
------------ --------------
Co-ords B 174.313E 434.529N
-------------- --------------
2. Traverse calculation
The commonest form of traverse is the ring traverse, which starts and finishes at the same point, and is calculated as follows:
a) The following data is required to compute the traverse.
i) All internal horizontal angles
ii) All horizontal distances
iii) The WCB of one leg.
iv) The rectangular co-ordinates of one point.
i)and (ii) measured in the field
(iii) Usually an assumed bearing but could be magnetic, grid or true.
(vi) Usually an assumed value unless the traverse is to be tied to the Ordnance survey horizontal control or similar.
b) Distribute angular misclose equally to each measured angle.
c) Calculate the forward bearing of each line, working anticlockwise around the traverse, using:
Forward bearing = back bearing of previous line + included angle
Ensure you finish back on the original bearing as a check against error.
d) Calculate E and N for each leg using the forward bearing and measured distance.
e) Add up all E’s and N’s to check for large errors in observation or calculation. The sums should be close to zero.
f)Starting at the origin station, compute the co-ordinates of each station around the traverse (working anticlockwise) finishing back at the origin. Any variation in the co-ordinates of this station is the eastings and northings misclose.
g)Distribute the misclosures using either the Bowditch or Transit methods.
Bowditch correction = Distance from origin x E (or N) misclose
Traverse length
Transit correction (for eastings) = E from origin x easting misclose
E
Note that all E are treated as positive when calculating corrections.
h) Calculate corrected co-ordinates.
An example traverse calculation is tabulated in Figure 4.10.
3 Co-ordinate setting out
Co-ordinated points can be set out from a horizontal control by either:
a) Using bearing and distance.
b) By intersecting theodolite rays
The following notes detail the general approach.
a) Bearing and distance method
i) Two control stations are required. Calculate the WCB and distance from each station to the point to be set out and the WCB between the two stations.
ii) Set a theodolite over one control station and sight the other station (RO) with the computed WCB between the two stations.
iii) Release the theodolite upper plate and rotate the instrument until the computed WCB to the point is obtained.
iv) Mark the direction with a nail in a peg at approximately he correct distance away.
v) Change face and repeat to check for instrument error.
vi) Measure the distance to the peg at the trial position applying whatever corrections are deemed necessary (see paragraph-4). Using a pocket tape, position a new peg at the correct position from the trial position.
vii) Check by using a WCB or distance from another station.
a) Intersection by theodolite
i) Calculate WCB and distance as in (a) (i)
ii) Two theodolites are required one set up over each control station.
iii) Each theodolite is sighted on to the opposite station with the computed bearing on the lower plate.
iv) Each theodolite is then turned until the required WCB to the point is found. Establish a peg on line and change face to check.
v) The required point is at the intersection of the two theoidolite lines
vi) The set out position must be checked by either a distance measured from a station or a WCB from a third station.
vii) This method should only be used if the resultant triangle formed by the two control stations and the set out point is well onditioned.
(b) Other checks
Once all the points are set out from the control, it is essential that they are checked relative to each other. Some slight adjustment to peg position may be required.
Calculations involving rectangular co-ordinates are:
a) Calculation of Whole Circle Bearing (WCB) and distance between two co-ordinated points.
i) Calculate the difference in easting( E) and difference in northings ( N) between the two points.
ii) Determine the Reduced Bearing from:
E
Reduced bearing= tan ------
N
Iii) Convert the reduced bearing to a Whole Circle Bearing.
1st quadrant same
2nd quadrant 180 – rb
3rd quadrant 180 + rb
4th quadrant 360 – rb
The correct quadrant can be found by inspection of the relative positions of the co-ordinated points.
iii)Calculate the horizontal distance from:
E N
Distance = -------------- and --------------
Sin WCB Cos WCB
Using both these formulae separately gives a check on the calculation of the WCB
A further formulae could be used to determine distance but this does no check WCB calculation.
Distance = E + N
Example calculation
Given: Stn A 179.724 mE 414.132 mN
Stn B 142.171 mE 372.916 mN
A 179.724 414.132
B 142.171 372.916
------------ -----------
E 37.553 N 41.216
Reduced bearing = tan –1 37.553
41.216
= 42.2015
WCB= 180 + 42 20 15
= 222 20 15
Distance = 37.553 = -55.758 m
Sin 222 20 15
= 41,216 = -55.758 m
cos 222 20 15
The two distances should be the same and of course, the negative sign is ignored.
a) Calculation of rectangular co-ordinates of a point (B) knowing the co-ordinates of another point (A), the WCB from that point to B (A to B) and the horizontal distance between them.
The procedure is as follows:
i) Calculate the difference in eastings and northings using the following formulae:
E = distance x sin WCB
N = distance x cos WCB
ii) Add E and N to the eastings and northings respectively of the known point.
Example- calculation
Given: Co-ords A 137.629 mE 473.126 mN
WCB A to B 136 27 19
Distance A to B 53.249
E = 53.249 x sin 136 27 19
= 36.684 m
N = 53.249 x cos 136 27 19
= 38.597 m
Co-ords A 137.629 473.126
Difference 36.684 -38.597
------------ --------------
Co-ords B 174.313E 434.529N
-------------- --------------
2. Traverse calculation
The commonest form of traverse is the ring traverse, which starts and finishes at the same point, and is calculated as follows:
a) The following data is required to compute the traverse.
i) All internal horizontal angles
ii) All horizontal distances
iii) The WCB of one leg.
iv) The rectangular co-ordinates of one point.
i)and (ii) measured in the field
(iii) Usually an assumed bearing but could be magnetic, grid or true.
(vi) Usually an assumed value unless the traverse is to be tied to the Ordnance survey horizontal control or similar.
b) Distribute angular misclose equally to each measured angle.
c) Calculate the forward bearing of each line, working anticlockwise around the traverse, using:
Forward bearing = back bearing of previous line + included angle
Ensure you finish back on the original bearing as a check against error.
d) Calculate E and N for each leg using the forward bearing and measured distance.
e) Add up all E’s and N’s to check for large errors in observation or calculation. The sums should be close to zero.
f)Starting at the origin station, compute the co-ordinates of each station around the traverse (working anticlockwise) finishing back at the origin. Any variation in the co-ordinates of this station is the eastings and northings misclose.
g)Distribute the misclosures using either the Bowditch or Transit methods.
Bowditch correction = Distance from origin x E (or N) misclose
Traverse length
Transit correction (for eastings) = E from origin x easting misclose
E
Note that all E are treated as positive when calculating corrections.
h) Calculate corrected co-ordinates.
An example traverse calculation is tabulated in Figure 4.10.
3 Co-ordinate setting out
Co-ordinated points can be set out from a horizontal control by either:
a) Using bearing and distance.
b) By intersecting theodolite rays
The following notes detail the general approach.
a) Bearing and distance method
i) Two control stations are required. Calculate the WCB and distance from each station to the point to be set out and the WCB between the two stations.
ii) Set a theodolite over one control station and sight the other station (RO) with the computed WCB between the two stations.
iii) Release the theodolite upper plate and rotate the instrument until the computed WCB to the point is obtained.
iv) Mark the direction with a nail in a peg at approximately he correct distance away.
v) Change face and repeat to check for instrument error.
vi) Measure the distance to the peg at the trial position applying whatever corrections are deemed necessary (see paragraph-4). Using a pocket tape, position a new peg at the correct position from the trial position.
vii) Check by using a WCB or distance from another station.
a) Intersection by theodolite
i) Calculate WCB and distance as in (a) (i)
ii) Two theodolites are required one set up over each control station.
iii) Each theodolite is sighted on to the opposite station with the computed bearing on the lower plate.
iv) Each theodolite is then turned until the required WCB to the point is found. Establish a peg on line and change face to check.
v) The required point is at the intersection of the two theoidolite lines
vi) The set out position must be checked by either a distance measured from a station or a WCB from a third station.
vii) This method should only be used if the resultant triangle formed by the two control stations and the set out point is well onditioned.
(b) Other checks
Once all the points are set out from the control, it is essential that they are checked relative to each other. Some slight adjustment to peg position may be required.
Lesson Note On Theodolite: Part B
Theodolite:
Axes of theodolite:
The most important relationships are as follows:
1.The axis of plate bubble should be in a plane perpendicular to the vertical axis.(main axis order).
2.The line of sight should be perpendicular to the horizontal axis.
3.The horizontal axis should be perpendicular to the vertical axis.
Instrument setup:
At each station point, before taking any observation, it is required to carryout some operations in sequence. The set of operations those are required to be done on an instrument in order to make it ready for taking observation.
Axes of theodolite:
The most important relationships are as follows:
1.The axis of plate bubble should be in a plane perpendicular to the vertical axis.(main axis order).
2.The line of sight should be perpendicular to the horizontal axis.
3.The horizontal axis should be perpendicular to the vertical axis.
Instrument setup:
At each station point, before taking any observation, it is required to carryout some operations in sequence. The set of operations those are required to be done on an instrument in order to make it ready for taking observation.
- Setting
- Centering
- Leveling
- Focusing
Instrument setup:
1.Tripod height –upper about chest height to make observation
easily.Place the instrument over the point with the tripod plate as
level aspossible. Then place the theodolite on the top of tripod.
Theodolite must be hold by hand until the theodolite is attached to
tripod head.
2.Check that the station point can be seen
through the optical plummet. (Rotate the
focus reticle –pull in or out to focus
on the ground-monument)
Then push in the tripod legs firmly by pressing down on the tripod shoe spurs. If the point is now not visible in the optical plumb sight, leave one leg in the ground, lift the other two legs, and rotate the instrument, all the while looking through the optical plumb sight. When the point is sighted,carefully lower the two legs to the ground and reseat them keeping the station point view.
While looking through the optical plumb, manipulate the leveling screws until the crosshair of the optical plummet is directly on the station mark.
3.Level the theodolite circular (pond) bubble by adjusting the tripod legs up or down (approximate leveling). This is accomplished by noting which leg, when slid up or down, moves the circular bubble to ward the bull’s eye. Upon adjusting the leg, either the bubble will move into the circle, or it will slide around until it is exactly opposite another tripod leg. That leg should then be adjusted up or down until the bubble moves into the circle. If the bubble does not move into the circle, repeat the process. If this manipulation has been done correctly, the bubble will be centered after the second leg has been adjusted;
Performa check through the optical plummet to confirm that it is still close to being over the station mark/turn one or more leveling screws to been sure that circular bubble is now exactly centered (if necessary).
The instrument can be now be leveled precisely by centering the plate (tubular) bubble.
a) Set the plate bubble so that it is aligned in the same direction as two of the foots crews. Turns these two screws in opposite direction until the bubble is centered.
b)Turn the instrument 100g, at which plate bubble will be aligned with the third leveling (foot) screw. Finally turn that third screw to center bubble.
Finally,check the axis of plate bubble should be in a plane perpendicular to the vertical axis. main axis order). It is always checked by turning the instrument through 200g. If the plate bubble is centered, the instrument is leveled.
Lesson Note On Theodolite Part A
Theodolite:
A theodolite is an instrument which is used primarily to measure angles, both horizontal and vertical. It is also used for many other subsidiary work during surveying such as setting up of intermediate points between intervisible points, establishment of intervisible points,prolonging a line, laying out traverse etc.
Types of theodolites:
Classification with respect to a construction:
Classification with respect to accuracy:
A theodolite is an instrument which is used primarily to measure angles, both horizontal and vertical. It is also used for many other subsidiary work during surveying such as setting up of intermediate points between intervisible points, establishment of intervisible points,prolonging a line, laying out traverse etc.
Types of theodolites:
Classification with respect to a construction:
- Open-faced,vernier-equipped engineer’s transit
- Optical theodolites with direct digital read-out sormicrometer-equipped read-outs(formoreprecisereadings)
- Electronic theodolites
Classification with respect to accuracy:
- One-minute theodolites:the least division of the scale is 1 or 2 minutes
- One-second theodolites: the least division of the scale is 1 or 2 seconds
Components of theodolite:
The vertical axis of these instruments goes up through the center of the spindles and is oriented over a specific point on the earth surface. The circle assembly and alidade rotate about this axis.
Horizontal axis of the telescope is perpendicular to the vertical axis, and telescope and vertical circle tiltonit.
The line of sight (line of collimation) is a line joining the intersection of the reticle crosshairs and the center of the objective lens.The line of sight is perpendicular to the horizontal axis and should be exactly horizontal when the telescope level bubble is centered and when the vertical circle is set at 100g–300g or 0g for vernier transits.
Plate bubble axis is assumed to be tangent to the plate bubble.
Axes of theodolite:
SS:Vertical(standing)axis
TT: Horizontal (Trunnion)axis
PP: Plate bubble axis
CC:Collimation axis (line of sight)
Saturday, August 27, 2016
LESSON NOTE ON SETTING OUT WORKS - FOUNDATION MARKING
SETTING OUT WORKS - FOUNDATION MARKING |
AIM |
To set out the foundation marking for the proposed construction of building. |
APPARATUS USED |
1.Theodolite, 2. Chain (or) Tape 3.Ranging rods, 3. Pegs or Arrows, 4. String. |
GENERAL |
The operation of the marking on the site the centr e lines of the foundation of a building is called |
setting out. Setting out of a foundation is the first step in the construction of any structure. |
PROCEDURE |
1. |
A centre line sketch of the building is prepared. (The centres of cross walls are also to be indicated.) |
2. |
The base line is set out with reference to given reference points. |
3. |
The ends of the centre line of the walls, points A and B from the base line are marked. |
4. |
As the end marks A,B,C,etc. are disturbed during excavation, stakes are fixed at L,M,N etc., a little |
away (about 2 to 3 m) for end mark and tied accur ately using a string. |
5. |
The centre line for all other walls AD,BC,etc are marked by dropping perpendicular. For small |
buildings the perpendiculars may be set out by using a chain or a tape by ‘3-4-5’ method. For an |
important and big building when sides are long a Theodolite may be employed to accurately set out the |
perpendiculars and to range the lines. |
6. |
For every wall, the pegs are driven a little away for marking the end and tied accurately using a string. |
7. |
Diagonals ar e measured and checked with their corresponding calculated lengths. |
8. |
Width of foundation from the centerline are marked and the corners 1,2,3,4,5 etc., are fix up. Pegs are |
driven at these corners. The cord is stretched and lime is spread along the chords. |
RESULT: |
Thus the trench plan being marked on the ground, and excavation may be started.
|
What Is Visual Survey?
What Is Visual Survey?
This is also called reconnaissance survey.
⇒It is the preliminary inspection of an area to be surveyed.
⇒ It is a see-for-yourself walk-over of the ground to be used for a fish pond or a
fish farm. It is first done with a view to visualise the work to be done.
⇒ It is the venture taken to note and identify all the parameters to be measured or surveyed.
⇒ It is a rough sketch of the field or fields in which all positions and stations are made in the field book.
⇒It is preliminary work done whereby the routes of the main chain lines are noted.
What do you do during visual survey?
(i) The purposes of the survey should be noted.
This includes (a) is it for pond construction?
(b) Is it for damming? (c) Is it for irrigation purposes; (d) Is it for Hydro-electric
power (HEP)?
The purpose will determine the extent of the reconnaissance survey.
(ii) The water parameters to be measured should be noted as from the
beginning. Such parameters include : (a) Water level; (b) Geological attributes;
(c) Soil conditions (texture, structure and permeability); (d) Water pH, hardness,
alkalinity, chloride, phosphate, ammonia, sulphide, sulphite, dissolved oxygen
etc
This is also called reconnaissance survey.
⇒It is the preliminary inspection of an area to be surveyed.
⇒ It is a see-for-yourself walk-over of the ground to be used for a fish pond or a
fish farm. It is first done with a view to visualise the work to be done.
⇒ It is the venture taken to note and identify all the parameters to be measured or surveyed.
⇒ It is a rough sketch of the field or fields in which all positions and stations are made in the field book.
⇒It is preliminary work done whereby the routes of the main chain lines are noted.
What do you do during visual survey?
(i) The purposes of the survey should be noted.
This includes (a) is it for pond construction?
(b) Is it for damming? (c) Is it for irrigation purposes; (d) Is it for Hydro-electric
power (HEP)?
The purpose will determine the extent of the reconnaissance survey.
(ii) The water parameters to be measured should be noted as from the
beginning. Such parameters include : (a) Water level; (b) Geological attributes;
(c) Soil conditions (texture, structure and permeability); (d) Water pH, hardness,
alkalinity, chloride, phosphate, ammonia, sulphide, sulphite, dissolved oxygen
etc
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