06/09/2019 Measurement of Horizontal Distances MODULE 09 Trial 1 2 3 4 5 6 Line AB BA AB BA AB BA Taped Distance 45.0m Measurement of Horizontal Distances MODULE 09 A 45m 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 table below. A 45m 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 table below. Trial 1 2 3 4 5 6 Number of Paces 50 53 51 53 52 53 Line AB BA AB BA AB BA Taped Distance 45.0m Number of Paces 50 53 51 53 52 53 If the surveyor then took 771, 770, 768, 770, 772, and 769 paces in walking an unknown distance CD, what is the length of line CD? Determine his pace factor. 0.865m/pace SURVEYING SURVEYING 666.346m CIVIL ENGINEERING CORRELATION COURSES 1 CIVIL ENGINEERING CORRELATION COURSES 2 MODULE Measurement of Horizontal Distances 09 A line AB cannot be measured directly because of an obstruction on the line. Accordingly, the two lines AC and CB were measured as 2,400.850m and 1,320.420m, respectively. Point C was set at a perpendicular distance of 155m from point D on line AB. Using approximate slope correction formula for steep slopes, determine the length of AB. A rectangular lot was measured using a 50m steel tape which was found to be 0.025m too short. The recorded length and width are 180.455m and 127.062m, respectively. Determine the actual dimension of the lot. L = 180.365m, W = 126.998m 3,707.13m SURVEYING SURVEYING CIVIL ENGINEERING CORRELATION COURSES 3 Measurement of Horizontal Distances MODULE 09 CIVIL ENGINEERING CORRELATION COURSES 4 1 06/09/2019 Measurement of Horizontal Distances MODULE Measurement of Horizontal Distances MODULE 09 09 A steel tape with a coefficient of linear expansion of 11.6 x 10-6/°C is known to be 50m long at 20°C. The tape was used to measure a line which was found to be 532.28m long when the temperature was 35°C. What is the correct length of the line? A heavy 50m tape having a cross-sectional area of 0.05cm2, has been standardized at a tension of 5.5kg. If E = 2.10 x 106kg/cm2, determine the change in the length of the tape if a pull of 12kg is applied. +0.0031m 532.37m SURVEYING SURVEYING CIVIL ENGINEERING CORRELATION COURSES 5 CIVIL ENGINEERING CORRELATION COURSES 6 Measurement of Horizontal Distances MODULE 09 Measurement of Horizontal Distances MODULE 09 A line was determined to be 2395.25m when measured with a 30m steel tape supported throughout its length under a pull of 4kg and at a mean temperature of 35°C. Determine the correct length of the line if the tape used is of standard length at 20°C under a pull of 5kg. The cross-sectional area of the tape is 0.03cm2, its coefficient of linear expansion is 11.6 x 10-6/°C, and the modulus of elasticity of steel is 2.0 x 106kg/cm2. The angle between two intersecting fences is to be determined with a tape. A point on each fence is established 30.0m from the point of intersection. If the distance between the established points is 12.20m, what is the intersection angle? 23°27’50” 2395.627m SURVEYING SURVEYING CIVIL ENGINEERING CORRELATION COURSES 7 CIVIL ENGINEERING CORRELATION COURSES 8 2 06/09/2019 Measurement of Horizontal Distances MODULE Errors, Accuracy, and Precision MODULE 09 09 In the figure shown, lines NQ and PR are established perpendicular to the line MNP, and points Q and R are lined up with the distant point M. If NQ = 318.55m, and PR = 475.62m, and NP = 210.38m, determine the length of MN which represents the width of the river? A surveying instructor sent out five groups of students to measure a distance between two points marked on the ground. The students came up with the following five different values: 250.25m, 250.15m, 251.04m, 250.50m, and 251.22m. Assuming these values are equally reliable and that variations result from accidental errors, determine the most probable value of the distance measured. 250.632m 426.67m SURVEYING SURVEYING CIVIL ENGINEERING CORRELATION COURSES 9 CIVIL ENGINEERING CORRELATION COURSES 10 Errors, Accuracy, and Precision MODULE Errors, Accuracy, and Precision MODULE 09 09 The following values were determined in a series of tape measurements of a line: 1000.58m, 1000.40m, 1000.38m, 1000.48m, 1000.40m, and 1000.46m. What is the most probable value of the measure length? The angles about a point Q have the following observed values: 130°15’20”, 142°37’30”, and 87°07’40”. Determine the most probable value of the second angle. 142°37’20” 1000.45m SURVEYING SURVEYING CIVIL ENGINEERING CORRELATION COURSES 11 CIVIL ENGINEERING CORRELATION COURSES 12 3 06/09/2019 Errors, Accuracy, and Precision MODULE Errors, Accuracy, and Precision MODULE 09 09 The following values were determined in a series of tape measurements of a line: 1000.58m, 1000.40m, 1000.38m, 1000.48m, 1000.40m, and 1000.46m. What is the probable error of the mean? The following values were determined in a series of tape measurements of a line: 1000.58m, 1000.40m, 1000.38m, 1000.48m, 1000.40m, and 1000.46m. What is the probable error of a single measurement? ±0.05m ±0.02m SURVEYING SURVEYING CIVIL ENGINEERING CORRELATION COURSES 13 CIVIL ENGINEERING CORRELATION COURSES 14 Errors, Accuracy, and Precision MODULE 09 The following values were determined in a series of tape measurements of a line: 1000.58m, 1000.40m, 1000.38m, 1000.48m, 1000.40m, and 1000.46m. What is the relative precision of a single measurement? The three sides of a triangular tract of land is given by the following measurements and corresponding probable errors: a = 162.54 ± 0.03m b = 234.26 ± 0.05m c = 195.70 ± 0.04m Determine most probable value of the perimeter. 1:20000 592.50m SURVEYING SURVEYING CIVIL ENGINEERING CORRELATION COURSES 15 Errors, Accuracy, and Precision MODULE 09 CIVIL ENGINEERING CORRELATION COURSES 16 4 06/09/2019 Errors, Accuracy, and Precision MODULE Errors, Accuracy, and Precision MODULE 09 09 The three sides of a triangular tract of land is given by the following measurements and corresponding probable errors: a = 162.54 ± 0.03m b = 234.26 ± 0.05m c = 195.70 ± 0.04m Determine the probable error of the perimeter. The two sides of a rectangular lot were measured with certain estimated probable errors as follows: W = 253.36 ± 0.06m L = 624.15 ± 0.08m Determine the most probable value of the area. 158,134.64m2 ±0.071m SURVEYING SURVEYING CIVIL ENGINEERING CORRELATION COURSES 17 CIVIL ENGINEERING CORRELATION COURSES 18 Errors, Accuracy, and Precision MODULE 09 The two sides of a rectangular lot were measured with certain estimated probable errors as follows: W = 253.36 ± 0.06m L = 624.15 ± 0.08m Determine the probable error of the area. ±42.58m2 SURVEYING CIVIL ENGINEERING CORRELATION COURSES 19 5