General Surveying 1: Chapter 2 - Measurement of Horizontal Distances PDF

**General Surveying 1** **Chapter 2: Measurement of Horizontal Distances** Instructor: Engr. Frank Stephen Balbanera Distance Measurement by Pacing Pace -- defined as the length of a step in walking. It may be measured from heel to heel or from toe to toe. Pacing -- in surveying, pacing means m...

**General Surveying 1** **Chapter 2: Measurement of Horizontal Distances** Instructor: Engr. Frank Stephen Balbanera Distance Measurement by Pacing Pace -- defined as the length of a step in walking. It may be measured from heel to heel or from toe to toe. Pacing -- in surveying, pacing means moving with measured steps; and if steps are counted, distances can be determined if the length of a step is known. Stride -- equivalent to two paces or a double step. - To pace a distance, it is necessary to first determine the length of one's pace. This is referred to as the *pace factor.* Methods: determine the average length of an individual's normal step, adjust one's pace to some predetermined length such as 1 m. - Length of pace varies with different persons. Pace factor = m/pace (see illustrative problems for exercise) 1. Electronic Total Stations 2. Taping and Theodolite Advantages of EDM (Electronic Distance Measurement) 1. Speed and accuracy in measurement 2. Lightweight and portable 3. Low power requirement 4. Easy to operate 5. Ease in measurement over inaccessible terrain 6. Applicable to the measurement of short and long lengths 7. Automatically measures displays and records slope ranges, azimuth, vertical angle, horizontal distance, departure, and latitude 8. Slope measurements are internally reduced to horizontal and vertical components by built-in computers thereby eliminating the need to calculate these values 9. Automatically accumulates and averages reading for slope range, horizontal and vertical angles. Measuring Tapes 1. Steel Tape- surveyor's or engineer's tape, made of ribbon of steel 0.5 to 1.0 cm in width, and weighs 0.8 to 1.5 kg per 30 meters. Lengths of 10, 20, 30, 50, 100 m are available. The 30-m tape is most common. It is designed for most conventional measurements in surveying and construction work. 2. Metallic Tape 3. Non-Metallic 4. Invar Tape- a special tape made of an alloy of nickel (35%) and steel (65%) with a very low coefficient of thermal expansion which makes it less affected by temperature changes. 5. Lovar Tape 6. Fiberglass Tape 7. Wires 8. Builder's Tape 9. Phosphor-Bronze Tape 10. Nylon-coated Steel Tape Procedures of Taping 1. Aligning the Tape 2. Stretching the Tape 3. Plumbing 4. Marking Full Tape Lengths 5. Tallying Taped Measurements 6. Measuring Fractional Lengths Breaking the tape -- a standard practice of measuring shorter distances which are accumulated to total a full tape length. This procedure is always done especially when the course is sloping or has an uneven terrain surface. **Corrections in Taping** **Too Long** **Too Short** ------------- -------------- --------------- **Measure** Add (+) Subtract (-) **Layout** Subtract (-) Add (+) **Slope Taping** **d = s cos α** where d = horizontal distance between the two points, s = measured slope length between the points, and α is the angle of inclination from the horizontal. If the difference in elevation, h, is known, the horizontal distance is computed using the following expression derived from the Pythagorean theorem **d =** [\$\\sqrt{\\mathbf{(}\\mathbf{s}\^{\\mathbf{2}}\\mathbf{\\ --\\ }\\mathbf{h}\^{\\mathbf{2}}\\mathbf{)}}\$]{.math.inline} **Corrections due to incorrect tape length** Coor = TL (true/actual length) -- NL (nominal length) **If difference is (+), tape is too long, if difference is (-) tape is too short** C~1~ = Corr (ML / NL) CL = ML [±]{.math.inline} C~1~ Where: C~1~ = total correction to be applied to the measured length or length to be laid out CL = corrected length of the line to be measured or laid-out ML = measured length or length to be laid out NL = nominal length of rope - An incorrect length of tape introduces an error each time the tape is used and is classified as a systematic error. 1. **Correction due to Slope** a. Gentle Slope (less than 20%) \ [\$\$C\_{h} = \\ \\frac{h\^{2}}{2s}\$\$]{.math.display}\ b. Steep Slopes (between 20% and 30%) \ [\$\$C\_{h} = \\ \\frac{h\^{2}}{2s} + \\ \\ \\frac{h\^{4}}{8s\^{3}}\$\$]{.math.display}\ c. Very steep slopes (greater than 30%) \ [*C*~*h*~= *s* (1 − cos ⌀)]{.math.display}\ Equivalent horizontal distance (d) [*d* = *s* − *C*~*h*~ ]{.math.inline} 2. **Correction due to Temperature** \ [*C*~*t*~= *c* (*T* − *T*~*S*~)]{.math.display}\ Where **c** is the coefficient of linear expansion or the amount of change in length per unit length per degree in temperature, L is the length of the tape or length of line measured, T is the observed temperature of the tape at the time of measurement, and [*T*~*S*~]{.math.inline} is the temperature at which the tape is standardized. - The value of Ts is usually taken as 20°C. If the tape used is made of steel, the value of c is 0.0000116 / ᵒC. - The resulting sign of C~t~ will be either positive or negative and is added algebraically to the length measured to obtain the correct length. - As a general rule, to obtain more accurate measured values, taping should be undertaken when the temperature does not vary significantly from the temperature used during standardization. 3. **Correction due to Tension** \ [\$\$C\_{p} = \\ \\frac{\\left( P\_{m} - P\_{s} \\right)\\text{L\\ }}{\\text{AE}}\$\$]{.math.display}\ And \ [*L*^′^= *L* ±  *C*~*P*~]{.math.display}\ Where C~p~ = total elongation in tapel length due to pull or the correction due to incorrect pull applied on the tape (m) P~M~ = pull applied to the tape during measurement (kg) P~s~ = standard pull for the tape or pull for which the tape is calibrated (kg) L = measured length of line (m) A = cross-sectional area of the tape (sq.cm) E = modulus of elasticity of the tape material (kg/cm^2^) L' = corrected length of the measured line (m) \ [\$\$A = \\ \\frac{\\text{W\\ }}{L\\ (Unit\\ Weight)}\$\$]{.math.display}\ Unit weight = 7.866 x 10^-3^ kg/cm^3^ Modulus of elasticity = 2.00 x 10^6^ to 2.10 x 10^6^ kg/cm^2^ Illustrative Problems **Correction Due to Slope** 1. Slope distances AB and BC measures 330.49m and 660.97 m, respectively. The differences in elevation are 12.22 m for points A and B, and 10.85 m for points B and C. Using the approximate slope correction formula for gentle slopes, determine the horizontal length of line ABC. Assume that line AB has a rising slope and BC a falling slope. **Correction Due to Temperature** 1. A steel tape with a coefficient of linear expansion of 0.0000116 / ᵒC is known to be 50m long at 20ᵒC. The tape was used to measure a line which was found to be 532.28 meters long when the temperature was 35ᵒC. Determine the following: a. Temperature correction per tape length b. Temperature correction for the measured line c. Correct length of the line 2. A steel tape, known to be of standard length at 20ᵒC, is used in laying out a runway 2500 m long. If its coefficient of linear expansion is 0.0000116/ᵒC, determine the temperature correction and the correct length to be laid out when the temperature is 42ᵒC. **Correction Due to Tension** 1. A heavy 50-m tape having a cross-sectional area of 0.05 cm^2^ has been standardized at a tension of 5.5 kg. If E = 2.10 x 10^6^ kg/cm^2^, determine the elongation of the tape if a pull of 12 kg is applied. 2. A 30-m steel tape weighing 1.45 kg is of standard length under a pull of 5 kg, supported for full length. The tape was used in measuring a line 938.55 m long on smooth level ground under a steady pull of 10 kg. Assuming E = 2.0 x 10^6^ kg/cm^2^ and the unit weight of steel to be 7.9 x 10^-3^ kg/cm^3^, determine the following: a. Cross-sectional area of the tape b. Correction for increase in tension c. Correct length of the line measured **Correction Due to Sag** 1. A 30-m tape is supported only at its ends and under a steady pull of 8 kg. If the tape weighs 0.91 kg, determine the sag correction and the correct distance between the ends of the tape. 2. A 50-m steel tape weighs 0.04 kg/m and is supported at its end points and at the 8-m and 25-m marks. If a pull of 6 kg is applied, determine the following: a. Correction due to sag between the 0-m and 8-m marks, 8-m and 25-m marks, and the 25-m and 50-m marks. b. Correction due to sag for one tape length c. Correct distance between the ends of the tape **Normal Tension** 1. A steel tape weighing 0.85 kg has a cross-sectional area of 0.05 cm^2^. The tape measures exactly 30.00 m when supported throughout its length under a standard pull of 5.5 kg. If the modulus of elasticity is 2.10 x 10^6^ kg/cm^2^~,~ determine the tension required to make the tape equal to its nominal length when supported only at the end points.