Distance Measurement PDF - CE 010 Fundamentals of Surveying

9/15/2023 Technological Institute of the Philippines Civil Engineering department Distance Measurement Engr. Harvey Ian P. Aquino, M.Sc. Instructor 1 - PACING Civil Engine...

9/15/2023 Technological Institute of the Philippines Civil Engineering department Distance Measurement Engr. Harvey Ian P. Aquino, M.Sc. Instructor 1 - PACING Civil Engineering CE 010 FUNDAMENTAL OF SURVEYING PRELIM 2 1  9/15/2023 PACING Pacing is the act of counting the number of steps or strides required to cover a given distance. A 'pace' is defined as the length of a single step taken while walking, which can be measured from heel to heel or toe to toe. Pacing in surveying involves walking with methodically measured steps, and by counting these steps, one can determine distances, assuming the length of an individual's step is known. Mastering the skill of pacing is extremely valuable in the field of surveying due to its numerous practical applications. 3 PACING Pacing is a quick method for cross-checking measurements obtained using other techniques. It is especially useful for estimating approximate distances when a lower degree of precision is required. To accurately pace a distance, one must first determine the length of one's personal stride, also known as the 'pace factor.’ There are two methods for calibrating one's pace: the first involves calculating the average length of an individual's typical step, while the second involves adjusting one's stride to a predetermined length, such as 1 meter. 4 2  9/15/2023 EXAMPLE (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 TAPED NO. OF below. TRIAL LINE DISTANCE PACES 1 AB 50 2 BA 5. 3 AB 51 45.0 m 4 BA 5. Determine the following Surveyor’s pace factor 5 AB 52 If the surveyor then took 771, 770, 768, 770, 772 6 BA 53 amd 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. 5 ODOMETERS AND MEASURING WHEELS Civil Engineering CE 010 FUNDAMENTAL OF SURVEYING PRELIM 6 3  9/15/2023 ODOMETERS AND MEASURING WHEELS Distances can be roughly measured by rolling a wheel along the line in question and counting the number of revolutions. An odometer is a device attached to the wheel (similar to the distance recorder used in a car), which does the counting and from the circumference of the wheel converts the number of revolutions to a distance. The odometer may be useful for preliminary surveys, perhaps when pacing would take too long. It is occasionally used for initial route-location surveys and for quick checks on other measurements. 7 ODOMETERS AND MEASURING WHEELS A similar device is the measuring wheel, which is a wheel mounted on a rod. Its user can push the wheel along the line to be measured. It is frequently used for curved lines. Some odometers are available that can be attached to the rear end of a motor vehicle and used while the vehicle is moving at a speed of several miles per hour. 8 4  9/15/2023 - TACHYMETRY Civil Engineering CE 010 FUNDAMENTAL OF SURVEYING PRELIM 9 TACHYMETRY The term tachymetry or tacheometry, which means “swift measurements,” is derived from the Greek words takus, meaning “swift,” and metron, meaning “measurement.” Actually, any measurement made swiftly could be said to be tacheometric, but the generally accepted practice is to list under this category only measurements made with subtense bars or by stadia. Thus, the extraordinarily fast electronic distance-measuring devices are not listed in this section. 10 5  9/15/2023 SUBTENSE BAR (OBSOLETE) A tachymetric method that was occasionally used until a few decades ago for rural property surveys made use of the subtense bar. This obsolete device has been replaced by electronic distance-measuring devices. In Europe, where the method was most commonly used, a horizontal bar with sighting marks on it, usually located 2 m apart, was mounted on a tripod. The tripod was centered over one end of the line to be measured and the bar was leveled and turned so that it was made roughly perpendicular to the line. 11 SUBTENSE BAR (OBSOLETE) Theodolite was set up at the other end of the line and sighted on the subtense bar. It was used to align the bar precisely in a position perpendicular to the line of sight by observing the sighting mark on the subtense bar. This mark could be seen clearly only when the bar was perpendicular to the line of sight. The angle subtended between the marks on the bar was carefully measured (preferably with a theodolite measuring to the nearest second of arc) and the distance between the ends of the line was computed. The distance D from the theodolite to the subtense bar was computed from the following expression: 12 6  9/15/2023 STADIA Although the subtense bar was occasionally used in the United States, the stadia method was far. Its development is generally credited to the Scotsman James Watt in 1771. The word stadia is the plural of the Greek word stadium, which was the name given to a foot race track approximately 600 ft in length. more common. Many transit, theodolite, and leveling telescopes are equipped with three horizontal cross hairs that are mounted on the cross-hair ring. The top and bottom hairs are called stadia hairs. The surveyor sights through the telescope and takes readings where the stadia hairs intersect a scaled rod. The difference between the two readings is called the rod intercept. 13 STADIA The equipment for stadia measurement consists of a telescope with two horizontal haors called stadia hairs and a graduated rod called a stadia rod. The telescopes of most surveying instruments are equipped with stadia hairs which are placed an equal distance on the either side of the horizontal cross hair. The spacing of the stadia hairs is so designed that at a distance of 100 meters their intercept on a vertical rod will be about 1 meter. At 200 3.86 m 2.00 m 1.00 m meter, the, the intercept will shoud be about 2 meters. D = 100 m D = 200 m D = 386 m 14 7  9/15/2023 STADIA The same principle can be used to estimate the heights of buildings, trees, or other objects, as illustrated in the Figure. A ruler is held upright at a given distance such as arm’s length (about 2 ft for many people) in front of the observer’s eye so that its top falls in line with the top of the tree. Then the thumb is moved down so that it coincides with the point where the line of sight strikes the ruler when the observer looks at the base of the tree. Finally, the distance to the base of the tree is measured by pacing or taping. By assuming the dimensions shown in the Figure , the height of the tree shown can be estimated as follows: 15 STADIA The process of taking stadia measurement consists in observing through the telescope the apparent locations of the two stadia hairs on vertically held rod. From the observed interval read on the rod, the distance from the telescope to the rod is found by proportional relationships in similar triangles. The equation D = Ks+C is employed 𝐷 = 𝐾𝑠 + 𝐶 Where C – is the Stadia constant is the distance from the center of the instrument to the principal focus. It values is usually equal to zero for internal focusing telescopes. K – is the Stadia interval factor of the instrument. 16 8  9/15/2023 EXAMPLE (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. Of the stadia interval factor (K) is 100, and the instrument constant (C) is zero, determine the length of the line AB 17 EXAMPLE (STADIA) A stadia rod held at a distant point C is sighted by an instrument set up at D. The upper and lower stadia hair readings were observed as 1.567 m and 1.136 m, respectively. Of the stadia interval factor (K) is 100, and the instrument constant (C) is zero, determine the length of the line AB 18 9  9/15/2023 - TAPING Civil Engineering CE 010 FUNDAMENTAL OF SURVEYING PRELIM 19 TAPING OR CHAINING For many centuries, surveyors measured distances with ropes, lines, or cords that were treated with wax and calibrated in cubits or other ancient units. These devices are obsolete today, although precisely calibrated wires are sometimes used. For the first two-thirds of the twentieth century the 100-ft steel ribbon tape was the common device used for measuring distances. Such measuring is often called chaining, a carryover name from the time when Gunter’s chain was introduced. The English mathematician Edmund Gunter (1581–1626) invented the surveyor’s chain (Figure 3-6) early in the seventeenth century. His chain, which was a great improvement over the ropes and rods used up until that time, was available in several lengths, including 33 ft, 66 ft, and 100 ft. The 66-ft length was the most common. 20 10  9/15/2023 - SUMMARY Civil Engineering CE 010 FUNDAMENTAL OF SURVEYING PRELIM 21 SUMMARY Table 3-1 presents a brief summary of the various methods for measuring distances. There is a great variation in the precision obtainable with these different methods and the surveyor will select one that is appropriate for the purposes of the particular survey. 22 11  9/15/2023 MEASURING TAPES & ACCESSORIES Civil Engineering CE 010 FUNDAMENTAL OF SURVEYING PRELIM 23 MEASURING TAPE Measuring tape are made in a variety of length, materials, and weights. They are also graduated in several ways. Graduation marks and number are either etched, stamped or printed in the tape. The following are some of the commonly used types of measuring tapes: 1. Steel Tape - Until recently, most surveying distance measurements requiring high precision were done with steel tapes. Although electronic distance measurement is now preferred because of its accuracy and convenience, steel tapes are still used for short distance measurements (e.g., a few hundred feet or less). The most common are lightweight steel tapes that are nylon coated. ese tapes are quite strong as long as they are kept straight, but if they are tightened when they have loops or kinks in them, they will break very easily. If a tape gets wet, it should be wiped with a dry cloth and then again with an oily cloth. Heavy steel tapes are usually very close to the correct length when they are continuously supported and subjected to a tension of usually 10 to 12 lb and a temperature of 68F. 24 12  9/15/2023 MEASURING TAPE 2. Fiberglass tapes - In recent years, fiberglass tapes made of thousands of glass fibers and coated with polyvinyl chloride have been introduced on the market. These less-expensive and more durable tapes are available in 50-ft, 100-ft, and other lengths. They are strong and flexible and will not change lengths appreciably with changes in temperature and moisture. They may also be used with little hazard in the vicinity of electrical equipment. When tension forces of 5 lb or less are applied, tension corrections are probably not necessary, but for values greater than 5 lb, length corrections are necessary. 25 ACCESSORIES The following are the different accessories used in taping work. Range pole - which is also known as flags or lining rods, are used as temporary signals to indicate the location of points or the direction of lines, and to mark alignment. They are either circular, hexagonal, or octagonal in cross section and with one end pointed. Taping pins - taping pins are used for marking the ends of tapes or intermediate points while taping. They are easy to lose and are generally painted with alternating red and white bands. If the paint wears off, they can be repainted any bright color or they can have strips of cloth tied to them which can readily be seen. The pins are carried on a wire loop which can conveniently be carried by a tapeman, perhaps by placing the loop around his or her belt. Plumb Bobs - Plumb bobs for surveying were formerly made of brass to limit possible interference with the compasses that were used on old surveying equipment. (Iron or steel plumb bobs could cause errors in compass readings.) Plumb bobs usually weigh from 6 to 18 oz and have sharp replaceable points and a device at the top to which plumb-bob strings may be tied. Very commonly, plumb bobs are fastened to a gammon reel 26 13  9/15/2023 ACCESSORIES The following are the different accessories used in taping work. 4. Hand levels - The hand level is a device that is very useful to the surveyor for helping hold tapes horizontally while making measurements. It also may be used for the rough determination of elevation. It consists of a metal sighting tube on which is mounted a bubble tube. 5. Spring Balances - When a steel tape is tightened, it will stretch. The resulting increase in length may be determined with the formula presented in Section 4.6. For average taping the tension applied can be estimated sufficiently to obtain desired precisions, but for very precise taping a spring balance or tension handle is necessary. 6. Clamping Handles - Leather thongs are usually placed through the loops provided at the ends of the tapes. With these thongs or with spring balances attached to the same loops, the tapes may be tensioned to esired values. When only partial lengths of tapes are used, it is somewhat difficult to pull the tape tightly. For such cases clamping handles are available. These have a scissors- type grip that enables one to hold the tape tightly without damaging it. 27 TAPING OVER GROUND Civil Engineering CE 010 FUNDAMENTAL OF SURVEYING PRELIM 28 14  9/15/2023 TAPING OVER LEVEL GROUND Ideally, a steel tape should be supported for its full length on level ground or pavement. Unfortunately, such convenient conditions are usually not available because the terrain being surveyed may be sloping and/or covered with underbrush. If taping is done on fairly smooth and level ground where there is little underbrush, the tape can rest on the ground. The taping party consists of the head tapeman and the rear tapeman. The head tapeman leaves one taping pin with the rear tapeman for counting purposes and perhaps to mark the starting point. The head tapeman takes the zero end of the tape and walks down the line toward the other end. 29 TAPING OVER LEVEL GROUND When the 50-m end of the tape reaches the rear tapeman, the rear tapeman calls “tape” or “chain” to stop the head tapeman. The rear tapeman holds the 50-m mark at the starting point and aligns the head tapeman (using hand and perhaps voice signals) on the range pole that has been set behind the ending point. Ordinarily, this “eyeball” alignment of the tape is satisfactory, but use of a telescope is better and will result in improved precision. Sometimes there are places along a line where the tapeman cannot see the end point and there may be positions where they cannot see the signals of the instrumentman. It is necessary to pull the tape firmly. This can be done by wrapping the leather thong at the end of the tape around the hand, by holding a taping pin that has been slipped through the eye at the end of the tape, or by using a clamp. When the rear tapeman has the 50-m mark at the starting point and has satisfactorily aligned the head tapeman, he or she calls “all right” or some other such signal. The head tapeman pulls the tape tightly and sticks a taping pin in the ground at right angles to the tape and sloping at 20 to 30 from the vertical. If the measurement is done on pavement, a scratch can be made at the proper point, a taping pin can be taped down to the pavement, or the point may be marked with a colored lumber crayon, called keel. 30 15  9/15/2023 TAPING ALONG SLOPING GROUND Civil Engineering CE 010 FUNDAMENTAL OF SURVEYING PRELIM 31 TAPING OVER LEVEL GROUND Should the ground be sloping there are three taping methods that can be used. 1. The tape may be held horizontally with one or both of the tapemen using plumb bobs as shown in Figures 3-13 and 3-14; 2. it may be held along the slope, the slope determined, and a correction made to obtain the horizontal distance; or 3. the sloping distance may be taped, a vertical angle measured for each slope, and the horizontal distance later computed. This latter method is sometimes referred to as dynamic taping. 32 16  9/15/2023 TAPING OVER LEVEL GROUND 1. Taping is being done downhill, the rear tapeman may be able to hold his or her end on the ground while the head tapeman uses a plumb bob [Figure 3-14(a)]. 2. If they are moving uphill the rear tapeman will have to hold his or her plumb bob over the last point, while the head tapeman may be able to hold his or her end on the ground [Figure 3-14(b)]. The head tapeman will always hold the socalled “smart” end or divided end of the tape. Normally, this is the zero end. Taping downhill is easier than taping uphill because the rear tapeman can hold the tape end on the ground at the last point instead of having to hold a plumb bob over the point while the head tapeman is pulling against him or her, as would be the case in taping uphill. 3. If the measurement is over uneven ground or ground where there is considerable underbrush, both tapemen may have to use plumb bobs as they hold their respective ends of the tape above the ground [Figure 3-14(c)]. 33 TAPING OVER LEVEL GROUND In Figure 3-15 we see various methods of using a hand level. In parts (a) and (b) of the figure the tapeman on the left with the hand level bubble centered moves his head up or down until the line of sight through the hand level telescope hits the ground at the other tapeman’s feet. This is the height at which he needs to hold his tape end (the other end being held on the ground) for the tape to be horizontal. In part (c) the tapeman with the hand level stands with normal posture and sights (bubble centered) on the other tapeman. From the position where the line of sight strikes the other tapeman he can tell the height to which he needs to hold his tape end. For instance, if the line of sight hits the other tapeman’s knee and they are both approximately the same height, the tapeman on the left is lower by the distance from his eye to his knee: that is, the difference in elevation shown in part (c) of the figure. 34 17  9/15/2023 TAPING OVER LEVEL GROUND This process of measuring with sections of the tape is referred to as breaking tape or breaking chain. If the head tapeman follows the customary procedure of leaving a taping pin at each of the positions that he occupies when breaking tape, counting the number of hundreds of feet taped (as represented by the number of pins in the possession of the rear tapeman) would be confusing. These measurements should give him or her a feeling for the magnitude of slope errors. 35 18