Week 13. Prof. Dr. Ergin TARI Assoc. Prof. Dr. Himmet KARAMAN JDF211E COURSE - ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING

Size: px

Start display at page:

Download "Week 13. Prof. Dr. Ergin TARI Assoc. Prof. Dr. Himmet KARAMAN JDF211E COURSE - ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING"

Asher Fisher
6 years ago
Views:

1 Week 13 Prof. Dr. Ergin TAI Assoc. Prof. Dr. immet KAAMAN JDF11E COUE - ITANBUL TECNICAL UNIVEITY - DEPATMENT OF GEOMATIC ENGINEEING

2 Information for Users The following slides are compiled from; The references given for the course, The course notes of the lecturers from all around the world, Notes and slides published in the world wide web without restrictions. Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

3 Information for tudents These presentations are compiled from the previous versions of the urveying II course slides which were created by Prof. Dr. Muhammed ahin and Prof. Dr. Ergin Tarı between the years of 1998 and 008. The update process of these presentations will continue, and will never end. The responsibilities of the students for the exams will be from the presentations, applications and practices covered during the course. 3 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

4 Trigonometric Leveling The difference in elevation between two points can be determined by measuring distance (slope or horizontal) and vertical angle. By this way, the elevation difference between two points A and B can be calculated by using the following equation; D AB = i + cosz r where i is the height of instrument, r is the rod reading (center hair reading), Z is the vertical angle and is the slope distance between A and B. 4 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

5 Trigonometric Leveling for hort Distances 5 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

6 Plumb Line ITANBUL TECNICAL UNIVEITY - DEPATMENT OF GEOMATIC ENGINEEING Trigonometric Leveling for hort Distances V = sin α or V = cot z elevation + r = hi + V elevation = hi + V r Elevation of B = Elevation of A + hi + V - r Z = zenith angle α = vertical angle Z od (r) V α orizontal Line B hi elevation orizontal Distance () A Elevation known 6 Vertical Datum Elevation 0.000m Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

7 Curvature 7 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

8 efraction Line of sight is not really horizontal and bent downwards towards the Earth Value not constant, affected by pressure, temperature, latitude, humidity etc. Usually taken as 1/7 and opposite of the correction of curvature 8 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

9 Curvature and efraction 9 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

$Curvature and efraction (cont d) 10 Class$

10 Curvature and efraction (cont d) 10 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

11 Curvature and efraction (cont d) 11 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

12 Curvature (cont d) From the definition of a level surface and a horizontal line, it is evident that the horizontal departs from a level surface because of curvature of the earth. The deviation is expressed by the formula where is the distance in km. C = * 1 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

13 Curvature (cont d) L + = ( + c) L = ( + c) - L = c + c L c c L / (km) = L (m) where radius of the Earth, 6370 km and L in km 13 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

14 efraction (cont d) Displacement resulting from refraction is variable. It depends on atmospheric conditions, the length of line, and the angle a sight line makes with the vertical. ence the refraction correction is expressed as the formula where is the distance in km. = * This is about one-seventh(1/7) the effect of curvature of the earth, but in the opposite direction. 14 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

15 Curvature and efraction (cont d) Combined correction = L * (6/7) = L (m) where L in km Ex: If L = 10m, c = m 0.001m 1mm The combined effect of curvature and refraction is approximately C + = * Although the combined effects of curvature and refraction produce rod readings that are slightly too large, proper field procedures can practically eliminate the error due to these causes. (km) C+ (m) C+ (mm) Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

16 Trigonometric Leveling for Long Distances For long lines, earth curvature and refraction become factors that must be considered. The elevation difference is where D AB = i + cosz + (C + ) r C is the correction due to the earth curvature and is the correction due to the refraction. 16 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

17 Trigonometric Leveling for Long Distances () 17 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

18 Trigonometric Leveling for Long Distances (cont d) elevation + r + = hi + C + V and V = tan α elevation = hi + V + (C ) - r ecorded taff eading efraction () Observed ay efracted ay r B α Curvature (C) hi A (known elevation) 18 Note: The effects of earth curvature and refraction can be eliminated by reciprocal observations. Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

19 Example The slope distance and vertical angle between A and B were measured as 43.47m and 18 o respectively. The height of the instrument and rod reading were equal. If the elevation of A is 31.46m above mean sea level, compute the elevation of B. C + = * C+ = 4 mm D AB = 43.47sin18 o = m 19 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

20 Applications of Trigonometric Leveling (1) eight of a Tower T a N Tower A 0 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

21 Applications of Trigonometric Leveling () Measurement from Mid-Point C t A A A,C B t B C, B 1 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

22 Accuracy of Trigonometric eights (1) Over hort Distances; 1 1 Differentiating the first equation gives: and standard deviation is: cot z i t where cos z i t where s cot z s sin s sin z i t z cot z s z z horizontal distance slope distance i t Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

23 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN Accuracy of Trigonometric eights () ITANBUL TECNICAL UNIVEITY - DEPATMENT OF GEOMATIC ENGINEEING 3 Over Long Distances(slope distance and zenith angle); By differentiating; tandard deviation equation is; z where t i k z sin ) (1 cos 1 t i k z z cos cos t i k z z

24 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN Accuracy of Trigonometric eights (3) ITANBUL TECNICAL UNIVEITY - DEPATMENT OF GEOMATIC ENGINEEING 4 Over Long Distances(slope distance and slope angle); By differentiating; tandard deviation equation is; t i k ) (1 sin 1 t i k k ) (1 ) ( cos sin ) (1 ) ( cos sin t i k k

25 eciprocal Leveling 5 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

26 eciprocal Leveling eciprocal leveling is utilized at such locations. As in the figure, two levels are set up on both side of a river at X and at Y, then rod readings are taken on points A and B reciprocally. 6 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

27 eciprocal Leveling 7 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

28 eciprocal Leveling ince XB and YA are very long, several readings are taken for averaging. This is done by reading, turning the leveling screws to throw the instrument out of level, re-leveling, and reading again. 8 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

29 eciprocal Leveling Two differences in elevation between A and B, determined with an instrument at X and Y, normally will not agree because of curvature, refraction, and personal and instrumental errors. efraction changes can occur if there is a long delay between two observations. If the precision appears satisfactory an average of the two elevation differences is accepted as the correct value. 9 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

$INTUMENT AT X On the staff held at A = a 1 On the staff held at B = b 1 - e where e = curvature correction refraction correction ± correction due$

30 INTUMENT AT X On the staff held at A = a 1 On the staff held at B = b 1 - e where e = curvature correction refraction correction ± correction due to inclined line of collimation True h AB = (b 1 e) - a 1 = (b 1 a 1 ) - e 30 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

$INTUMENT AT Y On the staff held at A = a - e On the staff held at B = b where e = curvature correction refraction correction ± correction$

31 INTUMENT AT Y On the staff held at A = a - e On the staff held at B = b where e = curvature correction refraction correction ± correction due to inclined line of collimation True h AB = b - (a e) = (b a ) + e 31 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

32 eciprocal Leveling Adding two corresponding equations, True h AB = (b 1 a 1 ) e + True h AB = (b a ) + e * True h AB = (b 1 a 1 ) + (b a ) o that, the true difference in elevation is obtained by averaging the differences in elevations obtained from the instruments settings. All the errors, those due to curvature and refraction and that due to inclined line of sight, are eliminated. For very accurate work, two precise instruments are used and the readings are taken simultaneously. 3 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

33 imultaneous eciprocal Leveling By means of simultaneous reciprocal leveling, the need for applying curvature and refraction corrections may be avoided similar instruments in correct adjustment are required = ((a1 b1) + (a b)) / 33 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

34 imultaneous eciprocal Leveling For very accurate work, two precise instruments are used and the readings are taken simultaneously. 34 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

35 imultaneous-eciprocal Trigonometric Leveling Measurement model of imultaneous- eciprocal Trigonometric Leveling 35 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

36 imultaneous-eciprocal Trigonometric Leveling Z' i and Z' j are the model zenith angles, Z i and Z j are the observed zenith angles, dz ri and dz rj are the model errors due to the refraction effect, ε i and ε j are the model errors due to the deviation of the plumb line ij is the rectilinear slope distance between P i and P j, h i and h j are the ellipsoidal heights of P i and P j, m is the radius of the earth spheroid ( 6371 km), Δh ij is the orthometric height difference from P i to P j from P i to P j ; and from P j to P i, respectively 36 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

$height difference, the second term is the spherical effect of the earth, the third term is the total effect due to the deviation of the plumb line and the vertical refraction.$

37 imultaneous-eciprocal Trigonometric Leveling The height differences from P i to P j ; and from P j to P i are formulated separately, so the arithmetic mean is : (1) the first term is the nominal height difference, the second term is the spherical effect of the earth, the third term is the total effect due to the deviation of the plumb line and the vertical refraction. 37 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

$imultaneous-eciprocal Trigonometric Leveling The coefficient of refraction i k, is defined as the ratio of the refraction angle dz r to half the centre angle γ ij () (3) The centre angle γ ij, can$

38 imultaneous-eciprocal Trigonometric Leveling The coefficient of refraction i k, is defined as the ratio of the refraction angle dz r to half the centre angle γ ij () (3) The centre angle γ ij, can be computed as, (4) If (4) is introduced (3), the model error due to the refraction effect dz ri, is obtained as follows, (5) 38 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

39 imultaneous-eciprocal Trigonometric Leveling In (1), sin Zi can be assumed equal to sin Z j with sufficient accuracy. The height difference between the station points P i and P j for simultaneous-reciprocal zenith angle observations is formulated using (1) and (5) (1) (5) 39 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

40 imultaneous-eciprocal Trigonometric Leveling If the distance greater than 500 m. If the distance less than 500 m, the effect of deviation of plumb line [ 1 sinz i Ɛ i Ɛ j ] can be ignored because it is very small. 40 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

41 41 Class Presentations for urveying II (JDF11E) Course by E. TAI,.KAAMAN

Leveling. 3.1 Definitions

Leveling. 3.1 Definitions Leveling 3.1 Definitions Leveling is the procedure used to determine differences in elevation between points that are remote from each other. Elevation is a vertical distance above or below a reference