Introduction to Surveying - Distance Measurement Methods PDF

FUNDAMENTALS OF SURVEYING CE-PC 210 Introduction  Methods of Measuring Distance ► Direct 1. Pacing Method of Measuring Distance: 1. Pacing: Where approximate result is required, distance may be determined by pacing. This method is used for r...

FUNDAMENTALS OF SURVEYING CE-PC 210 Introduction  Methods of Measuring Distance ► Direct 1. Pacing Method of Measuring Distance: 1. Pacing: Where approximate result is required, distance may be determined by pacing. This method is used for reconnaissance survey, for preparation of military plans. Also used for approximate checking distance. The method consists of walking over a line and counting the number of paces (80cm) the required distance may be obtained by multiplying the number of paces by the average length of pace.  Methods of Measuring Distance ❖ The length of pace varies with the: ► Individual, age, height and physical condition ► The nature of the ground (uphill and down hill) ► The slope of the country and ► The speed of pacing  Methods of Measuring Distance 2. Passometer: It is a pocket instrument. It automatically records the number of paces. It should be carried vertically, in waistcoat pocket or suspended from a button. The mechanism being operated by motion and strain of the body.  Methods of Measuring Distance ►3. Pedometer: ► It is similar to passometer. But it registers the distance walked by the persons carrying it. The distance is read by means of an indicator. It is fitted with a stud or knob, which when pressed release indicator to zero, it may be carried in the same way as the passometer.  Methods of Measuring Distance 4. Odometer: It measures the distance approximately. It can be attached to the wheel of any vehicle, such as carriage, cart bicycle, etc. It registers the number of revolution of the wheel. Knowing the circumference of the wheel, the distance traversed may be obtained by multiplying the number of revolutions. By the circumference of the wheel  Methods of Measuring Distance 5. Speedometer: The Speedometer of an automobile may be used to measure distances approximately. It gives better results than pacing, provided the route is smooth.  Methods of Measuring Distance 6. Perambulator: It can measure distance rapidly. It consist a single wheel provided with forks and a handle. It is wheeled along the line, the length of which is desired. The distance traversed is automatically registered on the dial. The reading approximates on rough ground. Methods of Measuring Distance  Methods of Measuring Distance 7. Judging distance: This is very rough method of determining distance. It is used reconnaissance survey. 8. Time Measurement: Distance is roughly determined by time intervals of travel. Knowing the average time per km for a person at walk or a horse, the distance traversed may be easily obtained.  Methods of Measuring Distance 9. Chaining: Measuring distance with chain or rope is the most accurate and common method, called as chaining. For work of ordinary precision a chain is used. Where great accuracy is required, a steel tape is used.  Measurement of Distance 2 Problems exist in Taping: 1. Measuring the distance between two existing points 2. Laying out a known distance with only the starting point in place  Measurement of Distance 6 Steps of Taping 1. Lining in – shortest distance between two points is a straight line. 2. Applying tension – rear chain is anchor and head chain applies required tension. 3. Plumbing – horizontal distance requires tape to be horizontal. 4. Marking tape lengths – each application of the tape requires marking using chaining pins to obtain total length. 5. Reading the tape – the graduated tape must be read correctly. 6. Recording the distance – the total length must be reported and recorded correctly.  Slope Measurements: ► Generally, measurements are made horizontally, but on even, often man-made slopes the distance can be measured directly on the slope, but the vertical or zenith angle must be obtained. ▪ Horizontal Distance = sin Zenith Angle X Slope Distance ▪ Horizontal Distance = cos Vertical Angle X Slope Distance  Taping Error: 1. Instrumental Error – a tape may have different length due to defect in manufacture or repair or as the result of kinks 2. Natural Error – length of tape varies from normal due to temperature, wind and weight of tape (sag) 3. Personal Error – tape person may be careless in setting pins, reading the tape, or manipulating the equipment  Tape Error Correction: 1) Measuring between two existing points: 1) If a tape is long, the distance will be short, thus any correction must be added 2) If tape is short, the distance will be long, thus any correction must be subtracted 3) If you are setting or establishing a point, the above rule is reversed.  MOST PROBABLE VALUE ► From the theory of probability a basic assumption is that the most probable value (mpv) of a group of repeated measurements made under similar conditions is the arithmetic mean or the average. Most probable value refers to a quantity which, based on available data, has more chances of being correct than any other.  Illustrative Example ►A surveying instructor sent out six groups of students to measure a distance between two points marked on the ground. The students came up with the following six different values: 250.25, 250.15, 249.90, 251.04, 250.50 and 251.22 meters. Assuming these values are equally reliable and that variations result from accidental errors, determine the most probable value of the distance measured. ►  Another Example ►  CE-PC 210 z MEASUREMENT OF HORIZONTAL DISTANCES z MEASUREMENT OF DISTANCE ▪ THE ACCURATE DETERMINATION OF THE DISTANCE BETWEEN POINTS ON ANY SURFACE IS ONE OF THE BASIC OPERATIONS OF PLANE SURVEYING ▪ IF THE POINTS ARE AT DIFFERENT ELEVATIONS, THE DISTANCE IS THE HORIZONTAL LENGTH BETWEEN PLUMB LINES AT THE POINTS. IN MANY INSTANCES MEASUREMENTS ARE TAKEN ALONG AN INCLINED LINE. THESE DISTANCES ARE SUBSEQUENTLY REDUCED TO THEIR EQUIVALENT HORIZONTAL PROJECTION z THREE TYPES OF DISTANCES ▪ VERTICAL ▪ HORIZONTAL ▪ SLOPE z TECHNIQUES OF DISTANCE MEASUREMENT ▪ PACING ▪ TAPING ▪ TACHYMETRY ▪ GRAPHICAL AND MATHEMATICAL METHODS ▪ MECHANICAL DEVICES ▪ PHOTOGRAMMETRY z DISTANCE BY PACING ▪ PACING CONSISTS OF COUNTING THE NUMBER OF STEPS OR PACES IN A REQUIRED DISTANCE. A PACE IS DEFINED AS THE LENGTH OF A STEP IN WALKING. IT MAY BE MEASURED FROM HEEL TO HEEL OR FROM TOE TO TOE.  z DISTANCE BY PACING ▪ TO PACE A DISTANCE IT IS NECESSARY TO FIRST DETERMINE THE LENGTH OF ONE’S PACE FACTOR. THIS IS REFERRED TO AS THE PACE FACTOR ▪ THE LENGTH OF A PACE VARIES WITH DIFFERENT PERSONS. THIS CAN BE DETERMINED BY WALKING ALONG A LINE OF KNOWN LENGTH ON A LEVEL GROUND AT A UNIFORM GAIT/PACE, AND COUNTING THE PACE IS ESTIMATED TO THE NEAREST QUARTER PACE. ▪ IT IS IMPORTANT TO WALK NATURALLY WHEN CALIBRATING ONE’S PACE AND IN PACING DISTANCES. CARE SHOULD BE TAKEN TO WALK ALONG A STRAIGHT LINE. A SLIGHT DEVIATION TO THE LEFT OR RIGHT OF THE LINE WILL DEFINITELY AFFECT THE ACCURACY OF PACING z DISTANCE BY TAPING THE USE OF A GRADUATED TAPE IS PROBABLY THE MOST COMMON METHOD OF MEASURING OR LAYING OUT HORIZONTAL DISTANCES. TAPING CONSISTS OF STRETCHING A CALIBRATED TAPE BETWEEN TWO POINTS AND READING THE DISTANCE INDICATED ON THE TAPE. THE TECHNIQUE USED IN MEASUREMENT AND THE PRECAUTIONS TAKEN WILL DEFINE THE DEGREE OF REFINEMENT WITH WHICH TAPER MEASUREMENTS CAN BE MADE z TAPING STEPS ▪ CARRIES THE TAPE FORWARD, ENSURING THE TAPE IS FREE OF LOOPS ▪ PREPARE THE GROUND SURFACE FOR THE MARK ▪ APPLIES PROPER TENSION AFTER ENSURING THAT THE TAPE IS STRAIGHT ▪ PLACE MARKS (WOODEN STAKES, IRON BARS) ▪ TAKE AND RECORD THE MEASUREMENTS OF DISTANCES  z TAPING ACCESSORIES ▪ PLUMB BOB ▪ Used to maintain the horizontal alignment ▪ HAND LEVEL ▪ Used to keep the steel tape horizontal when measuring z z z z DISTANCE BY TACHYMETRY ▪ TACHYMETRY OR TACHEOMETRY IS ANOTHER PROCEDURE OF OBTAINING HORIZONTAL DISTANCES ▪ IT 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.  z STADIA METHOD ▪ THIS METHOD PROVIDES A RAPID MEANS OF DETERMINING HORIZONTAL DISTANCES. IT WAS INTRODUCED IN 1771 BY JAMES WATT OF SCOTLAND AND WAS AT THAT TIME REFERRED TO AS A MICROMETER FOR MEASURING DISTANCES. ▪ THE PRECISION OF THE STADIA METHOD DEPENDS UPON THE FOLLOWING FACTORS ▪ REFINEMENT WITH WHICH THE INSTRUMENT WAS MANUFACTURED ▪ SKILL OF THE OBSERVER ▪ LENGTH OF MEASUREMENT ▪ EFFECTS OF REFRACTION AND PARALLAX z STADIA METHOD ▪ THE EQUIPMENT FOR STADIA MEASUREMENTS CONSISTS OF A TELESCOPE WITH TWO HORIZONTAL HAIRS CALLED STADIA HAIRS AND A GRADUATED ROD CALLED A STADIA ROD. ▪ IT IS IMPORTANT THAT THE LINE OF SIGHT IS HORIZONTAL AND IT INTERSECTS THE ROAD AT RIGHT ANGLES.  z STADIA METHOD ▪ THE EQUATION D = Ks + C is employed in computing horizontal distances from stadia intervals when sights are horizontal. ▪ The stadia constant C is the distance from the center of the instrument to the principal focus. Its value is usually equal to zero for internal focusing telescopes. ▪ K is the stadia interval factor of the instrument. Most instruments are so designed that this value is made equal to 100. ▪ The stadia interval “s” is determined in the field by observing the difference between the upper stadia hair reading and the lower stadia hair reading  z SUBTENSE BAR METHOD ▪ A CONVENIENT AND PRACTICAL DEVICE USED FOR QUICK AND ACCURATE MEASUREMENT OF HORIZONTAL DISTANCES. ▪ THE BAR WHICH IS PRECISELY 2 METERS LONGS, CONSISTS OF A ROUNDED STEEL TUBE THROUGH WHICH RUNS A THIN INVAR ROD. ▪ AT EACH END OF THE FRAME THE TARGET MARKS ARE HOUSED z z PRINCIPLE OF SUBTENSE MEASUREMENT  z DISTANCE BY GRAPHICAL AND MATHEMATICAL METHODS ▪ DISTANCE FORMULA ▪ PYTHAGOREAN PRINCIPLE ▪ TRIGONOMETRIC FUNCTIONS ▪ PLOTTING OF POINTS ▪ PLANE TABLE SURVEYS ▪ TRIANGULATION  z DISTANCE BY MECHANICAL DEVICES ▪ PASSOMETER ▪ PEDOMETER ▪ ODOMETER ▪ SPEEDOMETER ▪ PERAMBULATOR  z DISTANCE BY PHOTOGRAMMETRY ▪ THE TERM PHOTOGRAMMETRY REFERS TO THE MEASUREMENT OF IMAGES ON PHOTOGRAPH ▪ THE TYPES OF PHOTOGRAPHS USED ARE THOSE TAKEN FROM AN AIRCRAFT WITH THE AXIS OF THE CAMERA POINTED VERTICALLY TOWARDS THE TERRAIN PHOTOGRAPHED z z ILLUSTRATIVE EXAMPLES z DISTANCE BY PACING ▪ A 45 – m course, AB, on level ground was paced by a surveyor for the purpose of determining his pace factor. The number of paces for each trial taken are shown in the accompanying tabulation. TRIAL LINE TAPED DIST NO. OF PACES MEAN 1 AB 50 2 BA 53 45.0 52 3 AB 51 4 BA 53 5 AB 52 6 BA 53  z REQUIREMENTS ▪ DETERMINE HIS PACE FACTOR ▪ IF THE SURVEYOR THEN TOOK 771, 770, 768, 770, 772, AND 769 PACES IN WALKING AN UNKNOWN DISTANCE CD, WHAT IS THE LENGTH OF THE LINE? ▪ ASSUMING THAT THE TAPED LENGTH OF LINE CD IS 667.0 M, DETERMINE THE RELATIVE PRECISION OF THE MEASUREMENT PERFORMED. ▪ DETERMINE THE PERCENTAGE OF ERROR  z a) Determining Pace Factor L = 45 m (length of line AB) n1 = 6 (number of trials taken on line AB) Sum1 = (50 + 53 + 51 + 53 + 52 + 53) = 312 paces M1 = Sum1 / n1 = 312/6 = 52 paces (mean number of paces to walk line AB) PF = L/M1 = 45 m / 52 paces = 0.865 m/pace (pace factor of surveyor)  z b) Determining Unknown Distance n2 = 6 (number of trials taken on line CD) Sum2 = (771 + 770 + 768 + 770 + 772 + 769) = 4620 paces M2 = Sum2 / n2 = 4620/6 = 770 paces (mean number of paces to walk line CD) PL = M2(PF) = 770 paces (0.865 m/pace) = 666.1 m (paced length of line CD)  z c) Determining Relative Precision TD = 667.0 m (taped distance) PD = 666.1 m (paced distance) RP = (TD – PD)/TD RP = (667.0 – 666.1) / 667.0 = 0.9 / 667.0 = 1 / 741 say 1/700 (relative precision of the measurement)  z d) Determining Percentage of Error TD = 667.0 m (taped distance) PD = 666.1 m (paced distance) PE = [(TD – PD)/TD] [100%] PE = [(667.0 – 666.1)/667.0][100%] PE = 0.135 % (percentage of error) z DISTANCE BY STADIA ▪ A STADIA ROD HELD AT A DISTANT POINT B IS SIGHTED BY AN INSTRUMENT SET UP AT A. THE UPPER AND LOWER STADIA HAIR READINGS WERE OBSERVED AS 1.300 M AND 0.900 M, RESPECTIVELY. IF THE STADIA INTERVAL FACTOR (K) IS 100, AND THE INSTRUMENT CONSTANT (C) IS ZERO, DETERMINE THE LENGTH OF LINE AB ▪ SOLUTION D = Ks + C = 100(1.300 – 0.900) + 0 = 40.0 m (length of line AB) z DISTANCE BY SUBTENSE BAR ▪ z z FIELD ACTIVITY #1 – DISTANCE BY PACING ▪ OBJECTIVES ▪ TO DETERMINE THE PACE FACTOR ▪ TO DETERMINE THE PACED DISTANCE ▪ SOLVE FOR THE RELATIVE PRECISION AND % OF ERROR z PROCEDURE ▪ IN DETERMINING PACE FACTOR ▪ USING MEASURING TAPE, MEASURE 50 M DISTANCE ON A LEVELED GROUND ▪ MAKE 6 TRIALS FOR THE NUMBER OF PACES z PROCEDURE ▪ DETERMINING UNKNOWN DISTANCE ▪ THE STUDENT WILL ESTABLISH POINTS IN THE FIELD (2 UNKNOWN DISTANCES) ▪ THE STUDENT WILL MEASURE THAT DISTANCE USING MEASURING TAPE AS TAPED DISTANCE ▪ THE STUDENT WILL PERFORM 6 TRIALS FOR EACH UNKNOWN DISTANCE FOR PACED DISTANCE ▪ COMPUTE FOR THE UNKNOWN DISTANCE USING PACE FACTOR, AND CALCULATE RELATIVE PRECISION AND PERCENTAGE OF ERROR