Higher Technological Institute Course Title: Surveying (iii)
Civil Engineering Department Topic: Coordinates
10th of RamadanSheet No: 1
1- In order to determine the length and bearing of a line AB (on which direct observations are not possible). The following observations were taken from two other points P and Q.
Line
/ Length / BearingPA
PQQB / 418
1050
400 / S 65° 30` E
N 25 12 E
N 75 54 W
Calculate the length and bearing of line AB. Also find out the angle QBA.
2- A line bearing N 62° 19` 43`` W passes through point K, whose coordinates are [E = 2819.43 m and N = 1666.97 m]. Compute the perpendicular distance and direction to this line from point L, whose co-ordinates are [E = 1122.63 m and N=2315.70 m].
3- A straight tunnel is to be run between two points A and B, the co-ordinates of which are listed below. It is desired to sink a shaft at D, the middle point of AB, but it is impossible to measure along AB directly. D is thus to be fixed from C, the third known point.
Station / Easting / NorthingA
B
C / 0.0
3014.0
1764.0 / 0.0
256.0
1398.0
Calculate the following:-
a- The co-ordinates of D.
b- The length and bearing of CD.
c- The angle DCA to enable D to be set out.
Higher Technological Institute Course Title: Surveying (i)
Civil Engineering Department Topic: Intersection
10th of RamadanSheet No: 2
1- The co-ordinates of two points are as follows:
point / Easting / NorthingA
B / 1577.58
1235.71 / 7428.09
7236.85
From A a peg Z is placed in the ground such that AZ lies to the left of AB and makes an angle of 81° 33` 04`` with it. The distance AZ is 127.83 m. Compute the bearing and distance BZ. [Ans. BZ = 393.80; Bearing of BZ = 79° 30` 23``]
2- A new control point C is to be located from two triangulation stations A and B, the horizontal clockwise angles recorded being
BAC = 49° 27` 18`` and
ABC = 322° 45` 24``.
Determine the co-ordinates of C given that those of A and B is:
A 950.00 m E 1200.00m N
B 982.50 m E 1340.00m N
3- A new control station F, is to be established from existing Co-ordinated points T and D. The horizontal clockwise angles at T and D have been observed as DTF = 44° 52` 36`` and TDF = 284° 26` 38`` respectively. Calculate the co-ordinates of station F given that the co-ordinates of T are 3931.82m E, 7491.98 m N and of D are 2959.39m E, 7487.09m N. [Ans. E = 3145.00 m; N = 8258.7 m]
4- Observation was made at a station A and B to station C and the following data were obtained:
Point / Easting / Northing / Line / BearingA
B / 263479.263
264827.381 / 487288.142
488199.426 / AC
BC / 132° 7` 30``
165° 22` 40``
Calculate the co- ordinates of point C .
Higher Technological Institute Course Title: Surveying (i)
Civil Engineering Department Topic: Resection
10th of RamadanSheet No: 3
1- What is meant by resection and what is it used for?
2- Draw a neat sketch of the three cases may be arises in resection method.
3- State the sequence of computations used in resection method.
4- The co-ordinates of three stations A , B and C and the clockwise angles are given as :
Station / Easting(m) / Northing(m) /Angle
/ Adjusted value / Side / Length / BearingA
B
C / 24078.31
26266.48
28377.67 / 29236.48
31493.20
29661.04 / AOB
BOC
COA / 142° 48` 32``
92° 12` 22``
124° 59` 06`` / AB
BC
AC / 3143.386
2795.341
4320.272 / N 44° 7` E
S 49° 3` E
N 84° 22` E
A point O is set up inside the triangle, and the observations in the table are taken. Calculate the co-ordinates of station O.
5- Point P was established within the triangle formed by control stations A(1020m E, 2560m N ) , B( 1360m E, 2520m N ), C(1150m E, 2070m N ), such that angles APB=128° 20` 20`` and BPC=135° 47` 40``. What is the distance of point X (1200mE, 2450m N) from point P and what is the WCB of XP?
6- The co-ordinates in meters of three control points are as follows:
Point / Northing / EastingA
B
C / 98202.66
110002.65
89102.32 / 38762.50
61252.84
78565.12
a- From an unknown point P1 lying southerly from A , the clockwise angle from A to B is measured as 22° 30` 14.6`` and that from B to C as 29° 48` 50.6`` . Compute the co-ordinates of P1.
b- From a point P2 lying easterly from A inside the triangle formed by the control points , the clockwise angle from A to B is measured as 102° 28` 29.7`` and that from B to C as 86° 20` 4.4``. Compute the co-ordinates of P2
c- From a point P3 lying northerly from C to B is measured as 12° 52` 22.6`` and that from B to A as 53° 28` 33.4``. Compute the co-ordinates of P3.
Higher Technological Institute Course Title: Surveying (iii)
Civil Engineering Department Topic: Transformation
10th of RamadanSheet No: 4
------
1- What is meant by Transformation of co-ordinates?
2- What are the apparent changes that have affected a line, and mention the relationships?
3- The co-ordinates of two points A and B in a local national system (both meters) are as follows:
Point
/ E / N / E’ / N’A
B / 10966.92
15000.00 / 3911.23
2000.00 / 409577.36
413613.47 / 643649.19
641750.63
The local system co-ordinates of three other points, to be transformed into the national system, are:
Point / E / NC
DE / 12846.45
13986.04
15321.66 / 3632.62
1920.61
3869.70
4- The co-ordinates of six points in a local triangulation system are as follows:
Point / E / NA
BC
D
E / 0.00
392.593
653.413
948.538
904.426 / 0.00
-29.873
15.921
174.046
277.534
Points A and B is fixed in the national survey grid co-ordinates system, with co-ordinates:
Point /E’
/ N’A
B / 556821.63
556941.16 / 447219.42
447208.74
Compute the national survey grid co-ordinates of the remaining three points.
5- The local triangulation system of four points A; B; C; and D and the National system of points A and B are as follow :-
Point
/ Local /National
E
/N
/E’
/N’
AB
C
D / 8568.24
12423.80
2000.00
1000.00 / 10360.73
12606.60
1000.00
1000.00 / 800.309
2002.942 / 1755.932
2070.091
Compute the National triangulation system of points C and D.
Higher Technological Institute Course Title: Surveying (iii)
Civil Engineering Department Topic: EDM
10th of RamadanSheet No: 5
Question (1)
In EDM instrument has a basic wavelength of 3 m with frequency 99.902667 x 106 Hz and velocity 299708.00 km/s . The data for measured distance were as follows:
Wavelength ( λ ) / Phase difference ( Δλ )λ1 = 3 m
λ2 = 30 m
λ3 = 300 m
λ4 = 3000 m / 0.904
0.690
0.569
0.557
Calculate the distance measured.
Question (2) :-
A distance between two points had been measured by EDM instrument which has four wave lengths. The results of the measurements were as shown in the attached table. If the basic frequency λ1 has a velocity of 3 x 10 8 m/sec and a frequency of 108 Hertz, Calculate:-
a- Slope distance AB.
b- The horizontal distance if the atmospheric correction factor K = 5.08 x 10-4 and the vertical angle is equal to 20° 30`, (take the distance computed from (a) as the mean distance.
Wavelength ( λ ) / Phase difference ( Δλ )λ1 = 3 m
λ2 = 30 m
λ3 = 300 m
λ4 = 3000 m / 0.908
0.690
0.965
0.566
Higher Technological Institute Course Title: Surveying (iii)
Civil Engineering Department Topic: Intervisibility
10th of RamadanSheet No: 6
Higher Technological Institute Course Title: Surveying (iii)
Civil Engineering Department Topic: Strength of figure
10th of RamadanSheet No: 7
1- Compute the strength of the accompanying figure between the two lines AB and DE.
Solution
D=15
C = (6-5+1) + (11-2x6 +3) = 4
R=
Triangle / Angles used /ABE
EBO
EOD / 115°, 50
30 , 130
60 , 60° / 2
10
4
Sum / 16
1/13
Strength of figure =
Where
1/13
Higher Technological Institute Course Title: Surveying (iii)
Civil Engineering Department Topic: Triangulation
10th of RamadanSheet No: 8
(1)What are the modern and classical methods for establishing framework?
(2) State the equations of conditions that must be satisfied in the adjustment of the following figures:
Higher Technological Institute Course Title: Surveying (i)
Civil Engineering Department Topic: Spherical trigonometry
10th of RamadanSheet No: 9
1-The latitudes and longitudes of two places A and B are given below:
A = 22° 35` N and 80° 25` E
B = 23° 42` N and 90° 25` E
a- What will be the direction of flight from A to B?
b- What is the shortest distance between them? Assume R= 6400 Km.
c- What is the convergence?
2-What is the geodetic area enclosed by the spherical triangle ABC on the earth’s surface when the co-ordinates of the stations are as follows:
Co-ordinates of A = 88° 20` E; 22° 32` N
Co-ordinates of B = 72° 50` E; 18° 58` N
Co-ordinates of C = 77° 13` E; 28° 38` N
Assume that the radius of the earth = 6370 Km.
3- A traverse is run from a station X , latitude 52° 10` 16`` N , longitude 8°56`26``W, to a station Y , latitude 52° 32` 48`` N and longitude 9° 15` 18``W . Calculate:-
a- The direction and distance of line XY at X and also at Y.
b- The convergence of meridian.
c- The geodetic area enclosed by the spherical triangle PXY.
Assume the radius of the earth = 6400 Km.
4- Calculate the spherical excess of the triangle ABC where the coordinates of its vertices are: A (60 N, 30 E) & B (55 N, 35 E) & C (90 N).
Higher Technological Institute Course Title: Surveying (i)
Civil Engineering Department Topic: Theory of errors
10th of RamadanSheet No: 8
------
1-How are errors classified, and what are accidental errors?
2-Distinguish between accuracy and precision?
3- Two EDM were used to measure line XY and the following readings recorded:
Instrument A / Instrument B156.276
156.279
156.280
156.277
156.280
156.279
156.281
156.279 / 156.285
156.275
156.280
156.278
156.279
What is the relative precision of the two instruments?
4-A distance has been measured repeatedly on three different occasions. The mean values recorded and their standard error is listed below.
Measurement 1 112.125m ±0.007 m
Measurement 2 112.130m ±0.002 m
Measurement 3 112.128m ±0.005 m
Determine the weighted mean of the three sets of measurements. [Answer: 112.129m]
5-Two observations A and B measure the same quantity d five times each with the following recorded data:
A 149.75 149.78 149.83 149.80149.74
B 149.80 149.82 149.78 149.70149.75
Compute the most probable value of the quantity and its standard error.
6-The following observations were made on a test line. Compute the most probable value and the standard deviation of:
a- A single observation of unit weight.
b- A single observation of weight two.
c- The weighted mean . [Answer 363.266 m±2.9mm; 2.1 mm;±0.8mm]
Length
/ Weight363.263
363.264
363.265
363.267
363.265
363.267
363.262
363.268
363.270
363.270 / 1
1
2
2
2
2
1
2
1
1
Higher Technological Institute Course Title: Surveying (i)
Civil Engineering Department Topic: Theory of errors
10th of RamadanSheet No: 9
------
1- What is meant by weight of an observation?
2- What is the rule for the distribution of corrections to quantities?
3- Line AE is assumed in four segments with lengths and standard deviations as follows:
AB = 478.62 ft ± 0.029 ft
BC= 637.34 ft ± 0.034 ft
CD = 314.08 ft ± 0.016 ft
DE = 763.91 ft ±0.041 ft
What is the length and standard deviation of line AE? [ Ans. AE=2202.95 ±0.063ft]
4- If the standard deviation of a back sight reading from a setup of a level is ±0.02 ft , and the standard deviation of the foresight reading from the same setup is also ±0.02 ft , what is the standard deviations of the difference in the elevation between the two turning points on which the readings are taken ?
5- In the triangle ABC, the base ( a) and the two angles B and C are measured . If the standard deviations σb in b and σc in c.
a = 2000.00 ± 0.05 m
B = 34° 30` 25`` ± 15``
C = 61° 23` 42`` ± 10``
6- Calculate the standard deviation of the volume of the cuboids whose sides along with their standard deviation are:
a= 35 ± 0.03 m
b= 20 ± 0.02 m
a= 15 ± 0.01 m
Higher Technological Institute Course Title: Surveying (i)
Civil Engineering Department Topic: Geodesy
10th of RamadanSheet No: 12
------
1- Write short notes on:-
a- Geoid
b- Ellipsoid
2-Determine the value of radius of curvature along meridian at a point A situated in geodetic latitude = 40° N.
Take a= 6,378,200 meters
b= 6,356,700 meters
3-Calculate the four radii of curvature at station has 30° latitude and α = 40°. The used ellipsoid has: a = 6378135 m & e = 0.08.
4-Determine the geodetic co-ordinates of point B ( Ф ,λ and α ) , if the co-ordinates of point A (30° ,31° , 42° ) and the distance AB= 2500 Km ,and a = 6378135 m & e = 0.08
5-Determine the reduced co-ordinates X and Y of a point M on the ellipsoid situated in geodetic latitude = 40° N, given that:
a= 6,378,200 meters
b= 6,356,700 meters
6- Given: φ= 42° 11` 42``, λ= 27° 11` 16``
φ= 43° 23` 12`` , λ= 30° 17` 23``
a = 6378135 m, e = 0.08
Required: S12,α12 and α21.
Higher Technological Institute
Civil Engineering Dept.
Surveying Section
Surveying(III) CT 277
Topic: Spherical Triangle
1-What is the geodetic area enclosed by the spherical triangle ABC on the earth’s surface when the co-ordinates of the stations are as follows:
Co-ordinates of A = 88° 20` E ; 22° 32` N
Co-ordinates of B = 72° 50` E ; 18° 58` N
Co-ordinates of C = 77° 13` E ; 28° 38` N
Assume that the radius of the earth = 6370 Km.
2-The latitudes and longitudes of two places A and B are given below:
A= 22° 35` N and 80° 25` E
B= 23° 42` N and 90° 25` E
a- What will be the direction of flight from A to B?
b- What is the shortest distance between them? Assume R= 6400 Km.
c- What is the convergence?
3-A traverse is run from a station X , latitude 52° 10` 16`` N , longitude 8°56`26``W, to a station Y , latitude 52° 32` 48`` N and longitude 9° 15` 18``W . Calculate:-
a- The direction and distance of line XY at X and also at Y.
b- The convergence of meridian.
c- The geodetic area enclosed by the spherical triangle PXY.
Assume the radius of the earth =6400 Km.
4-Calculate the spherical excess of the triangle ABC where the coordinates of its vertices are : A (60 N , 30 E ) & B ( 55 N , 35 E ) & C (90 N ) .
1/13