Surveying Theory and Practice PDF

Surveying Theory and Practice I. Concepts on Surveying II. Basic Survey Measurements I. Concepts on Surveying  Surveying  Uses of Surveying  Types of Surveying  Survey Measurements and Adjustments II. Basic Survey Measurements...

Surveying Theory and Practice I. Concepts on Surveying II. Basic Survey Measurements I. Concepts on Surveying  Surveying  Uses of Surveying  Types of Surveying  Survey Measurements and Adjustments II. Basic Survey Measurements  Distance Measurement  Vertical Distance Measurement  Angle and Direction Measurement  CONCEPTS ON SURVEYING SURVEYING Definition - is the art of measuring horizontal and vertical distances between objects, of measuring angles between lines, of determining the direction of lines, and of establishing points by predetermined angular and linear measurements. – Davis, Foote, etc. - is the art of making such measurements of relative positions of points on the surface of the earth that, on drawing them to scale, natural and artificial features may be exhibited in their correct horizontal or vertical relationships. – Clarke - is the art and science of determining angular and linear measurements to establish the form, extent, and relative position of points, lines and areas on or near the surface of the earth or on other extraterrestrial bodies through applied mathematics and the use of specialized equipment and techniques. – La Putt General Classifications of Surveying 1. Plane Surveying - is that type of surveying in which the earth is considered to be a flat surface, and where distances and areas involved are of limited extent that the exact shape of the earth is disregarded. 2. Geodetic Surveying – are surveys of wide extent that takes into account the spheroidal shape of the earth. SURVEY MEASUREMENTS Measurement - is the process determining the extent, size, or dimensions of a particular quantity in comparison to a given standard. ex. angles, lengths, elevations, etc. Methods of Obtaining Measurements 1. Direct Measurements – is a comparison of the measured quantity with a standard measuring unit. 2. Indirect Measurements – the observed value is obtained by its relationship with other known values. Units of Measurement 1. Linear, Area, Volume – ex. meter, hectare, liter or cubic meters 2. Angular – 2rad = 360 degs = 400 grads = 6400 mils SEXAGESIMAL SYSTEM A circle of 360 degrees 1 degree = 60 minutes 1 minute = 60 seconds CENTESIMAL SYSTEM A circle of 400 grads 100C centesimal minutes per grad 100CC centesimal seconds per centesimal minute MIL SYSTEM Divides the circle into 6400 increments or mils One mil subtends an arc of approximately 0.98 unit on a circle of 1000 unit radius. RADIAN SYSTEM Is the angle subtended at the center of a circle by an arc equal in length to the circles radius. Degrees Grads Mils Radians 1 deg 1 1.11111 17.77778 0.017453 1 grad 0.9 1 16.0 0.015708 1 mil 0.05625 0.0625 1 0.000875 1 radian 57.29578 63.66198 1018.59164 1 ERRORS IN MEASUREMENTS Errors – are defined as the difference between the true value and the measured value of a quantity  beyond the control of the surveyor, therefore is inherent in all measurements Mistakes - are inaccuracies in measurements which occur because of carelessness, inattention, poor judgment and improper execution of the surveyor Blunder - is a large mistake Types of Errors 1. Systematic Errors – always have the same sign, thus accumulating. It occurs because of instrumental factors, natural causes and human limitations. 2. Accidental Errors – occurrences are matter of chance, varying in signs, hence compensating. Also called random, compensating, irregular and erratic errors. Sources of Errors 1. Instrumental Errors – imperfections in to the instrument like measuring with a steel tape of incorrect length 2. Natural Errors – caused by variations in of nature such as changes in magnetic declination, wind, temperature, etc. 3. Personal or Human Errors – caused by limitations of the sense of sight, touch, hearing; hence errors committed by humans. Accuracy – indicates how close a given measurement is to the absolute or true value of the quantity measured. Precision – refers to the degree of refinement and consistency with which the physical measurement is made. Theory of Probability  – is defined as the number of times something will probably occur over the range of possible occurrences - is useful only if accidental errors are present, systematic errors are corrected - is based on the following assumptions: 1. Small errors are numerous than large errors. 2. Very large errors do not occur. 3. Errors are as likely to be positive as negative. 4. The true or ideal value of quantity is taken as the mean of an infinite number of like observations. - results obtained after adjustments are not the true values, but most probable values or MPV True Value - an ideal value that can never be obtained. Most Probable Value or MPV - refers to a quantity which, based on the available data, has more chances of being correct than any other. Based on the arithmetic mean. _ MPV or X = X / n = (X1 + X2 + X3 + ……. + Xn) / n Residual or Deviation – is the difference of the measured value of a quantity and it’s most probable value. _ v=X-X where v = the residual X = measurement of a particular quantity X = MPV of the quantity measured Probable Error or PE– is a quantity which, when added to or subtracted from the MPV, defines a range within there is a 50% chance that the true value of the measured quantity lies inside or outside the limits thus set. PES = + 0.6745 wv2 / (n-1) PEm = + 0.6745 wv2 / n(n-1)  where PES = PE of any single measurement PEm = PE of the mean v2 = summation of the squares of the residual n = number of observations If the MPV of a value is say 425.4 and the PEm is +.20 then the expression of the probable limits of precision is 425.4 +.20 Relative or Precision - is expressed by a fraction having the magnitude of the error in the numerator and the magnitude of a measured quantity in the denominator. The RE of the above example is.20 / 425.4 or 1: 2127 Weighted Observation – is defined by the reliability of the observations in terms of conditions in the field, repetitive observations, etc. Adjustments of Weighted Observation 1. The weights are inversely proportional to the square of the corresponding probable errors. 2. The weights are also proportional to the number of observations. 3. Errors are directly proportional to the square roots of distances. Interrelationship of Errors 1. Summation of Errors PESum = + w PE12 + PE22 + PE32 + …… PEn2 where PESum = probable error of the sum PE1,PE2, etc = PE of each measurement Ex. Find the probable error of the sum and the most probable value of the perimeter of a triangle whose sides are A = 125.41 + 0.04, B= 362.01 + 0.10 and C = 35.24 + 0.07. 2. Product of Errors PEpro = + w (Q2 x PE1)2 + (Q1 x PE2)2 where PEpro = probable error of the product PE1 and PE2 = PE of corresponding quantities Q1 and Q2 = measured quantities Ex. Determine the area of the lot and the probable error if the sides of a rectangular lot is as follows: L = 45.23 + 0.05 and W = 10.56 + 0.02. BASIC SURVEY MEASUREMENTS DISTANCE MEASUREMENT Methods of Distance Measurements I. Pacing – consists of counting the number of steps or paces in required distance. Pace – length of a step in walking (from toe to toe, heel to heel) Stride – two paces or a double step Pace factor – is determined by dividing the known distance by the average paces required to traverse it. Ex. A 50 m course, AB, on level ground was paced by a GE student for the purpose of determining his pace factor. The number of paces for each trial taken is shown in the accompanying table. Trial Line Taped No. of paces Distace 1 AB 58 2 BA 57 3 AB 50.0 m 59 4 BA 57 5 AB 58 6 BA 60 Determine the following. a) The pace factor b) If the student then took 551, 553, 555, 552 and 556 paces in walking an unknown distance CD, what is the length of the line? c) Assuming that the taped length of the line CD is 478 m, what is the relative precision? II. Taping – consists of stretching a calibrated tape between two points and reading the distance indicated on the tape. Gunter’s Chain – 66 feet long consisting of 100 links with each link measuring 7.92 inches.  INCORRECT LENGTH OF TAPE Applying corrections caused by incorrect length of tape is a simple matter but should be carefully considered. Assume that the actual length of a 100 m tape is 99.98 m, and a distance between fixed points measured with this tape was recorded as 1322.78 m. Since each full tape length was short by 0.02 m, the correct length is: 1322.78 - 0.02 * (1322.78) = 1322.78 – 0.26 = 1322.52 m 100.00 However, if a certain distance is to be established, such as in staking out, with a tape known to be too short, the reverse is true. So add the 0.26 m – i.e. lay out a length of 1323.04 m. Corrections for incorrect tape lengths WHEN TAPE IS TO LAY OUT A TO MEASURE A DISTANCE LINE BETWEEN FIXED POINTS Too long Subtract Add Too short Add Subtract Correction in Taping 1. due to SLOPE or ALIGNMENT fig. B s h A d s = slope distance between A and B h = difference in elevation between A and B d = horizontal distance AC Ch = slope correction = s – d For gentle slopes (less than 20%): Ch = h2 / 2s For steep slopes (20% to 30%): Ch = h2 / 2s + h4 / 8s3 For very steep slopes ( > 30% ): Ch = s ( 1-cosθ ) 2. due to TEMPERATURE  when temperature increases, tape expands causing the tape to be too long.  When temperature decreases, tape contracts causing the tape to be too short. Ct = α L (T – To) Ct= correction α = coefficient of thermal expansion L = measured length T = temperature at which measurement is taken To= standard temperature α = 0.0000116 units / oC α = 0.00000645 units / oF 3. due to TENSION  when tension or pull is great, tape elongates causing the tape to be too long.  CP = ( P – PO ) L AE CP = correction P = applied tension PO = tension on which tape is standardized L = length A = cross sectional area E = modulus of elasticity 4. due to SAG or WIND  sag causes the tape measurement longer and layout shorter. CS = w2L3 = W2L 24p2 24p2 CS = correction w = weight of tape, lb/ft or kg/m W = total weight of tape between supports, lb or kg L = distance between supports P = applied pull 5. STANDARDIZATION OF TAPE LENGTH CD = ( SL  correction ) ( D/L ) SL = standard length of tape L = length of tape used D = measured distance III. Graphical and Mathematical Computations– distances on the ground are calculated by photogrammetry, trilateration and triangulation. IV. Mechanical and Electronic Devices - like the odometer, optical rangefinder, measuring wheel, edm apparatus (geodimeter, tellurometer) and total station. V. Tachymetry and Tacheomatry – is based on the optical geometry of the instruments employed and is an indirect method of measurement. A transit or a theodolite is used to determine subtended intervals and angles on a graduated rod or scale from which distances are computed by trigonometry. It is performed by either subtense bar method or stadia method. 1. Subtense Bar Method – is done by measuring a horizontal angle between two vertical planes formed by the azimuth axis of the theodolite and the respective ends of the subtense bar. Any inclination has no effect. Subtense Bar – 2 meters long, consists of a rounded steel tube through which runs an invar rod. Principle: X A B Y Horizontal Distance (HD) note: subtense bar XY is set up perpendicular to line AB, Tan (θ/2) = (XY/2) -------- AB = (XY/2)  AB Tan (θ/2) and since XY is equal to 2.00 m and HD = AB, we have HD = 1 / Tan (θ/2) where: HD = horizontal distance θ = subtended horizontal angle 2. Stadia Method – is done by observing through the telescope the apparent locations of the two stadia hairs in a vertically held rod. A. Horizontal Sight Stadia rod B a a’ F horizontal b b’ c f C d A D by ratio and proportion: f/i = d/s d = (s) f/i D = c+f+d = s (f/i) + (f + c) If K = f/i = stadia interval factor C = f + c = stadia constant then D = Ks + C usually K = 100 B. Inclined Sights V = 1/2Kssin2 + Csin  H = Kscos2 + Ccos by ratio and proportion: f/i = d / s cos θ  d = f/i s cos θ H = ( f + d + c ) cos θ H = (f / i)s cos2 θ + (f + c)cos θ V = ( f + d + c ) sin θ V = (f / i)s cos θ sin θ + (f + c)sin θ V = (f / i)s sin 2θ + (f + c)sin θ 2 Or better yet: Id = Ks(cos θ) + C Hd = (Ks(cos θ) + C) cos θ Vd = (Ks(cos θ) + C)sin θ De = HI + Vd - RR where: De = Difference in Elevation HI = Height of Instrument RR = Rod reading MEASUREMENT OF VERTICAL DISTANCES Leveling Leveling - is the procedure used to determine differences in elevation between points. Elevation - is the vertical distance above or below a reference datum. Vertical line - is a line from the surface of the earth to the earth’s center. It is also referred to as a plumb line or a line of gravity. Level line - is a line in a level surface. Level surface - is a curved surface parallel to the mean surface of the earth. It is best visualized as the surface of a large body of water at rest. Horizontal line - is a straight line perpendicular to a vertical line. Bench Mark (BM) - is a permanent point of known elevation. Temporary Bench Mark (TBM) - is a semi permanent point of known elevation. Turning Point (TP) - is a point temporarily used to transfer elevations. Backsight (BS) - is a rod reading on a rod of known elevation in order to establish the instrument line of sight. Height of Instrument (HI) - is the elevation of the line of sight through the level. Foresight (FS) - is a rod reading taken on a turning point, benchmark, or temporary benchmark in order to determine its elevation.  These two equations completely describe the differential leveling process: Existing elevation + BS = HI  HI – FS = new elevation Example Given that the elevation of point A is 410.26 m above sea level, determine the elevation of B. Rod Rod FS = 2.80 HI = 414.97 BS = 4.71 B Ground surface A Solution: Elevation of point A = 410.26 Backsight rod reading at A = +04.71 BS Height (Elev) of Instrument = 414.97 Foresight rod reading at B = -02.80 FS _________ Elevation of point B = 412.17 m Methods of Leveling 1. Direct or Spirit Leveling – commonly used method of determining the elevation of points some distance apart by a series of set-up of a leveling instrument some distance apart. It is the most precise method of leveling, and is used when a high degree of accuracy is required. Some forms of direct leveling are: a) Differential leveling Ex. 1 Complete the differential level notes shown below and perform the customary arithmetic check. STA BS HI FS ELEV BM1 1.211 129.032 TP1 1.115 1.688 TP2 1.235 1.752 BM2 1.174 2.264 BM3 1.065 2.710 TP3 1.832 2.666 BM4 2.567 Check: BS - FS = Elevinitial - Elevfinal Ex. 2 Prepare and complete the differential notes for the information shown in the accompanying illustration. Also do the necessary checks. b) Double Rodded Leveling - determines elevation between points by employing two level routes simultaneously. Ex. 1 Complete the following differential level notes for a double-rodded line from BM1 to BM2. Show the customary arithmetic check.  STA BS HI FS ELEV BM1 1.946 250.549 1.946 TP1H 2.781 1.104 TP1L 2.926 1.549 TP2H 1.393 1.794 TP2L 1.785 2.201 TP3H 0.215 2.989 TP3L 0.679 3.412 BM2 2.632 2.632 Ex. 2 Complete the following differential level notes for a double-rodded line from BM1 to BM2. Show the customary arithmetic check. STA BS HI FS ELEV BM1 2.768 146.890 2.768 TP1H 3.079 0.488 TP1L 3.732 1.137 TP2H 3.024 0.329 TP2L 3.366 0.674 TP3H 0.267 2.628 TP3L 0.834 3.000 BM2 3.434 3.436 c) Three-wire Leveling – three horizontal hairs are read rather tham a single horizontal hair. The most precise. Ex. 1 Complete the differential level notes shown below and perform the customary arithmetic check.  STA BACKSIGHT HI FORESIGHT ELEV HAIR MEA S HAIR MEA S RDG N RDG N S RDG S RDG BM1 1.152 502.321 0.935 0.718 TP1 2.784 1.117 2.420 0.899 2.057 0.682 TP2 1.713 1.900 1.440 1.537 1.166 1.172 TP3 2.591 1.450 2.094 1.177 1.599 0.904 TP4 0.913 2.210 0.730 1.714 0.547 1.218 BM2 1.593 1.410 1.227 2. Reciprocal Leveling – used when the two intervisible points are located at a considerable distance apart and which leveling methods cannot be performed in the usual manner. Leveling across a wide river, across a ravine or canyon are instances to use this method. 3. Profile Leveling – is used to determine differences in elevation between points at designated short measured intervals along a established line to provide data from which a vertical section of the ground surface can be plotted. 4. Trigonometric Leveling – is employed in determining the difference in elevation between two points from measurements of it’s horizontal or slope distance and the vertical angle between the points by trigonometric computations. Fig. Set-up for trigonometric leveling Formulas: V = dtan θ or s(sin θ) DE = dtan θ + HI – RR or s(sin θ) + HI - RR However if the horizontal distance is greater than 300 meters, there will be an additional hcr correction. Hence, DE = dtan θ + HI – RR + 0.067(d/1000)2 = s(sin θ) + HI – RR + 0.067(d/1000)2  + if the sight is inclined upward - if the sight is incline downward 5. Rise and Fall Leveling – is based on the principle that two consecutive readings from the same instrument position gives the difference in elevation of the two points sighted. Ex. Complete the profile level notes. ROD READINGS DIFFERENCE IN ELEV REDUC STA BS IFS FS RISE FALL ED LEVEL 1.24 525.28 BM100 2.35 0+00 1.76 +30 2.50 +50 2.73 +90 3.00 1+00 2.72 +10 1.93 +60 1.05 +95 0.86 2+00 2.06 2.78 TP-1 0.68 2+50 0.98 +70 1.29 3+00 2.45 +30 2.67 +65 2.36 BM101 6. Inverse Leveling – used when the line of sight is higher than the leveling rod, or when obstructions exist. The rod is placed upside down and its base is placed up at the desired point. 7. Stadia Leveling – combines the features of direct leveling with those of the trigonometric leveling.  Ex. Complete the table given the following set of stadia level notes. The instrument used has a stadia interval factor of 100 and equipped with an internal focusing telescope. Sta Backsight Foresight Ele Elev v inter Vert RR inter Vert RR cept angle (V cept angle (Vd) (s) (θ) d) (s) (θ) Bma 1.55 -5O25’ 1.50 550.50 TP1 1.74 +8O15’ 1.68 1.76 +10 O30’ 1.48 TP2 0.95 -4O48’ 1.77 1.98 +12 O08’ 1.66 BMb 2.49 -12O50’ 2.53 1.06 +7 O 22’ 2.05 TP3 2.14 +14O05’ 1.79 2.67 -15 O32’ 1.92 TP4 1.92 -9O41’ 1.33 2.16 -7 O 59’ 1.25 BMc 2.65 +7 O 32’ 1.88 8. Altimeter Surveys Ex. Given the following data gathered from an altimeter survey: Elevation of the high base, 518 m; elevation of the low base, 122 m; altimeter reading at the high base, 5954; and altimeter reading at the low base, 2708. If the altimeter reading is 4150, determine the elevation of the station. 9. Barometric Leveling Ex. 1 The barometric reading at the base of the hill was 74.5 cm of mercury and the observed temperature was 29O C. The other barometer on top of the hill reads 70.8 cm of mercury and the temperature was 21OC. If the barometers were read simultaneously, determine the difference in elevation between 2 points of observation. Ex. 2 The reading on the altitude scale at one station is 146.41 m and the temperature was 27.8O C. At another station, the barometer reading is 830.52 m and the temperature is 21.0O C. Find the difference in elevation between the two points. Errors in Leveling Works 1. Instrumental Errors - Instrument out of adjustment - Rod not standard length - Defective tripod 2. Personal Errors - Bubble not centered - Parallax - Faulty rod readings - Rod not held plumb - Incorrect setting of target - Unequal backsight and foresight distances 3. Natural Errors - Curvature of the earth - Atmospheric Refraction - Temperature Variations - Wind - Settlement of the Instrument - Faulty turning points Mistakes in Leveling Works 1. In correct rod reading 2. Incorrect recording 3. Erroneous computations 4. Rod not fully extended 5. Moving turning points Errors in Leveling Works Problems 1. A line of levels 8 km long is run between elevation of 64.305 m. It was found out however that the line of sight of the instrument is inclined upward by 0.003 m for every 10 meter distance. If BS and FS distances are consistently 100 m and 150 m respectively, determine the correct elevation of BM2. 2. Differential leveling is run from BM1 to BM2 at a distance of 6 km. Average length per set-up is 250 m. The average backsight reading is 2.3 m and every time it is taken, the rod is inclined to the side from the vertical by 2O. What would be the correct elevation of BM2 if the recorded elevation is 189.54 m a.s.l.? GE BOARD A line of levels was run from BM1 to BM2 covering a distance of 5 km. BS and FS distances every set-up averages 100 m each. If at every turning point, the rod settles by 0.04 m, compute the correct elevation of BM2 if its computed elevation is 126.42 m. GE BOARD Two points, A and B, are 600 meters apart. A level is set-up on the line between A and B and at a distance of 200 meters from A. If the RR of A is 2.150 and B is 4.321, determine the difference of elevation between the two points, taking into account the effects of curvature and refraction. Level Tube The level tube is a sealed glass tube mostly filled with alcohol or a similar substance. The degree of precision of a surveyor’s level is partly a function of the sensitivity of the level tube; the sensitivity of the level tube is directly related to the radius of curvature of the upper surface of the level tube. The larger the radius of curvature, the more sensitive the level tube is. Sensitivity is usually expressed as the central angle subtending one division (usually 2mm). The sensitivity of many engineer’s levels is 30’’; that is for a 2-mm arc, the central angle is 30’’ (R=13.75 m or 45 ft). Establishing an angle/arc ratio: 30’’ = 0.002 360O 2 R R = (360/0.00833) x (0.002/2 ) R = 13.75 m (or 45 ft) GE BOARD To check the sensitiveness of the bubble of a transit, a rod 100m away is sighted and the rod reading was 1.389 m. The bubble in the tube is allowed to move over 5 divisions and the new reading was 1.421 m. If 1 division is 2mm, determine the radius of curvature of the level tube and find the angular value of one division of the level tube. Earth’s Curvature and Atmospheric Refraction Point of Tangency Horizontal line Line of sight c&r Level line Atmospheric Refraction – causes the ray of light slightly to bend downwards. Approximately (-) 0.0110 per kilometer. Earth’s curvature - Approximately 0.0785 per kilometer. hcr = combined effect of earth’s curvature and atmospheric refraction K = distance from the point of tangency to the point observed (point of observation) hcr = 0.0675 k2 hcr in meters K in kilometers hcr = 0.574 k2 hcr in feet K in miles hcr = 0.0206 M2 hcr in feet M in thousands of feet Peg Method of Adjustments CASE I: Instrument set at A and B The difference in elevation is equal to the mean of the difference in rod reading of the two set-ups. GE BOARD In the two-peg test of the dumpy level, the following observations were taken: instrument is set-up at A, rod reading at A was 1.723 m and the foresight at B is 2.775 m. The instrument is transferred at B. The rod reading at B was 1.527 m and the foresight reading at A was 0.471 m. Find the correct rod reading at A with the instrument still at pt B to give a level line of sight. CASE II: Instrument set between A and B 1st set up - inst. set between A & B, nearer to A than to B. 2nd set up - inst. set between A & B, nearer to B than to A. In the two-peg test of a dumpy level the following observations were taken: ROD READING INSTRUMENT SET UP INSTRUMENT SET NEAR A UP NEAR B On Point A 1.505 m 0.938 m On Point B 2.054 m 1.449 m a) Determine if the line of sight is in adjustment b) If the line of sight is not in adjustment, determine the correct rod reading on A with the instrument still set up near B. c) Determine the error in the line of sight for the net distance AB. In the two-peg test of a dumpy level the following observations were taken: ROD READING INSTRUMENT SET UP INSTRUMENT SET UP NEAR A NEAR B On Point A 0.296 m 1.563 m On Point B 0.910 2.140 a) determine the true difference in elevation between points A and  b) check if the line of sight needs further adjustment. c) determine the following: “false” difference in elevation, inclination of the line of sight, and the error in the reading on the far rod. PROBLEM To make a peg adjustment, the following data were taken; wye level @ 1 wye level @ 2 Rod reading @ A 1.926 m 3.778 m Rod reading @ B 0.914 m 2.748 m Point 1 is along line AB and midway the points A and B. Point 2 is along line AB as well but not between the two points, but is 24 m from A and 260 m from B. With the instrument at point 2, what is the correct rod reading at A for a level sight? MEASUREMENTS OF ANGLE AND DIRECTIONS Locating Points Meridians – fixed reference line Types of Meridian 1. True Meridian – line passing through the poles 2. Magnetic Meridian - lies parallel with the magnetic lines of force of the earth 3. Grid Meridian – parallel to the central meridian of the system of plane rectangular coordinates 4. Assumed Meridian – line taken in convenience Designation of North Points 1. True North 2. Magnetic North 3. Grid North 4. Assumed North Direction of Lines 1. Interior Angles and Exterior Angles – angles between adjacent lines in a close polygon. Total inner angle = (n-2) 180 2. Deflection Angles( L or R) – angle between the a line and a prolongation of the preceding line. - in any closed polygon, the sum of all the deflection angles is 360 deg. 3. Angles to the Right – angles measured to the right from the proceeding to the succeeding line 4. Bearings (forward and back) - is the acute horizontal angle between the reference meridian and the line N NW NE 90 W 90 E SW SE S 5. Azimuths (forward and back) – the angle between the meridian and the line measured in a clockwise direction from either the north or south branch of the meridian. Note: in the Philippines, azimuths are reckoned from the south. Compass – is a hand-held device for determining the horizontal direction of a line with reference to the magnetic meridian. Magnetic Declination – is the horizontal angle and direction by which the needle of a compass deflects from the true meridian at any particular locality. Ex. 1 The magnetic declination of a locality is 1 O 20’ W. Find the true bearing and true azimuth reckoned from the south of the following magnetic bearings. a) OA, S 25 O 40’ E b) OB, N 12 O 20’ W c) OC, N 85 O 45’ E d) OD, S 34 O 20’ W Ex. 2 In a compass survey made 20 years ago the observed magnetic bearing of a reference line OP was N 45 O 20 E with a magnetic declination of 6 O 25 W. Lately you were hired to survey again the area and found that the area’s magnetic declination changed to 5 O 40 E. Determine the: a) true bearing b) True azimuth from the south c) New Magnetic bearing d) Latest Magnetic Azimuth from south Variation in Magnetic Declination 1. Daily Variation – also called “solar-diurnal variation. It is a periodic swing of the magnetic needle occurring each day. 2. Annual Variation – a small annual swing distinct from the secular variation. 3. Secular Variation – is a slow, gradual, but unexplainable shift in the position of the Earth’s magnetic meridian over a regular cycle. 4. Irregular Variations – uncertain and cannot be predicted, most likely to occur in sun spot’, and auroral display Isogonic – lines connecting points of same magnetic declination Agonic – lines connecting points of zero magnetic declination Local Attraction – is any deviation of the magnetic needle of a compass from it’s normal pointing towards magnetic north. Caused by iron deposits, current fluctuations. or any objects made of steel and iron. Magnetic Dip – is the characteristic phenomenon of the compass needle to be attracted downward from the horizontal plane due to the earth’s magnetic line of force. Isoclinic – a line connecting points of same magnetic dip Ex. 1 The Magnetic Bearing of line OP was N 48 O 15’ W with a declination of 3 O 20’ E. Also there exist a local attraction of 2 O 10’E. Determine the true bearing of the same line and the true azimuth. Ex. 2 In 1980, the magnetic bearing of the line was S 40 O 24’ W. At that time the declination was 0 O 30’ E. The secular variation per year was 0O30’E. What is the new magnetic bearing of the same line in the year 2000? Compass Surveying – one of the most basic and widely used method of obtaining relative location of points where a high degree of precision is not required. Types of Compass Surveys 1. Open Compass Traverse 2. Close Compass Traverse Sources of Errors in Compass Work 1. Bent Needle 2. Bent Pivot 3. Sluggish Needle 4. Plane of Sight not Vertical 5. Electrically charged Compass Box 6. Local Attraction 7. Magnetic Variations 8. Errors in Reading the Needle Ex. 1 Adjustment of an Open Compass Traverse Line Length Observed Bearings Forward Back AB 400.63 N 25 O 45’ E S25 O 40’ W BC 450.22 S 20 O 30’ E N 20 O 25 W CD 500.89 S 35 O 30’ W N 35 O 30’ E DE 640.46 S 75 O 30’ E N 75 O 25’ W EF 545.41 N 58 50’ E O S 58 O 15’ W FG 700.05 N 22 O 05’ E S 21 O 55’’ W Ex. 2 Adjustment of Closed Compass Traverse Line Length Observed Bearing Forward Back AB 46.50 S 30 O 40’ W N 30 O 40’ E BC 75.15 S 83 O 50’ E N 84 O 30’ W CD 117.35 N 02 O 00’W S 02 O 15’ E DE 74.92 S 89 O 30’ W Due East EA 60.25 S 28 O 50’ E N 28 O 00’ W Index Error and Correction The correct value of the vertical angle is just the mean of the readings taken in both normal and reverse position since both measurements are made independent each other. θt = (θn + θr)/ 2 Index Error – due to inclination of the vertical axis, LOS not parallel to the level tube, and the vertical circle does not read zero when the telescope bubble is centered. Ie = (θn - θr)/ 2 Index Correction – same magnitude but opposite sign from index error Ex. 1 A vertical angle θ was measured above the horizontal as 45 O 09’ with the telescope in direct position and as 45 O 11’ in reversed position. Determine the index error, index correction and the corrected vertical angle. What if it is measured below the horizontal? Measurement of Angles by Repetitions – used to reduce if not totally eliminate mistakes, to gain better accuracy beyond the least count of the instrument. Number of Repetitions – 3 for most engineering surveys, 6-8 for precise geodetic surveys Telescope Position – half taken direct, half reverse Procedure… Ex. 1 A horizontal angle was measured by repetitions eight times with an engineer’s transit. Prior to measurement, the horizontal scale was set at 00-00-00 and the reading on the scale was 65-35-20 after the angle was measured once. If the final reading was 162-36-12, determine the average value of the angle measured. Ex 2. Assume that a horizontal angle was measured with a transit three times direct and three times reversed, starting with an initial backsight reading of 0-34-20. After the first and sixth measurements the readings on the horizontal scale were 130-20-20 and 61-46-00. Determine the average value of the angle measured. Ex. 3 An angle is repeated three times direct and three times reversed with an engineer’s transit. The circle reading for the initial backsight is 321-45-00 and after the first repetition is 150-25-00. If the circle reading after the sixth repetition is 140-25-00, determine the average angle measured.