CVG 2171 Surveying & Measurements Lecture 5 - Distance Measurements - Winter 2025 PDF

CVG 2171 – Surveying & Measurements Lecture 5 Distance Measurements Professor: Agnes Bezerra Winter 2025  Distance Measurement In plane survey, distance is typically measured as a horizontal “straight line”...

CVG 2171 – Surveying & Measurements Lecture 5 Distance Measurements Professor: Agnes Bezerra Winter 2025  Distance Measurement In plane survey, distance is typically measured as a horizontal “straight line” between two points. If the points have different elevations, the distance is the horizontal length between vertical lines extended from the points. This is necessary because the horizontal distance between two points does not change even if the ground is disturbed. Distance is required in many instances, such as specifying scale to a network of control points, fixing the position of topographic detail by offsets or polar coordinates, setting out the position of a point in construction work, etc. 2  Units of Distance Meter (SI unit): is commonly used in geodetic and highway surveys. Foot (English unit): decimally divided, is typically used in the United States. Foot, divided into inches and fractions of an inch, is commonly used in some construction works. Other units used, but not so often are yard, chain, rod, vera, etc. 3  Methods of Measuring Distance 1. Pacing 2. Odometer 3. Tacheometry 4. Subtense bar 5. Taping 6. Electronic distance measurement (EDM) 7. Satellite systems 4  Distance Measurement Tape Pacing An odometer Subtense bar Principle of tacheometry 5  Taping 1. Taping is used in surveying to measure the distance between two points or lay out a point from an established reference. With the advent of precise methods of measurement (specifically EDM), taping is seldom used nowadays. 2. Instruments needed in taping are: a) tapes b) taping pins c) hand level d) range poles e) plum bobs f) pocket thermometer g) tension & clamp handles 6  Instruments for Taping (a) Surveyor’s and engineer’s tapes (b) Cloth (or metallic) tapes (c) Chaining pins or taping pins (d) hand level (e) Range poles (lining rods) 7  Steps for taking tape measurements and Taping on a Sloping Ground 1. Lining in 2. Applying tension 3. Plumbing 4. Marking tape lengths 5. Taking reading 6. Recording the distance 8  Sources of Error in Taping Incorrect Length Incorrect Tape Length – Purchased tapes are not guaranteed by the manufacturers to be exactly as indicated by their nominal length. Standardization is undertaken to determine the true length. Length correction is calculated as 𝒍 − 𝒍′ 𝑪𝑳 = ′ 𝑳 𝒍 Where 𝒍 is the actual tape length, 𝒍′ is the nominal tape length, and 𝑳 is the measured/recorded length. 9  Sources of Error in Taping Temperature Variation Temperature variation– Steel tapes are usually standardized for a certain temperature (68oF/20oC in the US). Any temperature higher or lower than that will cause a change in the length due to linear expansivity. Temperature correction is calculated as 𝑪𝑻 = 𝒌(𝑻𝟏 − 𝑻)𝑳 Where 𝒌 is the coefficient of thermal expansion, 𝑻 is the tape temperature during standardization, 𝑻𝟏 is the tape temperature at the time of measurement, 𝑳 is the observed length. 10  Sources of Error in Taping Inconsistent Pull Inconsistent pull – Also, tapes are standardized to measure the graduated length based on a standard tension or pull. When a different amount of tension is applied, the tape may either be over stretched or under stretched. A pull of 12 lb is usually applied during standardization. Correction due to pull is 𝑷𝟏 − 𝑷 𝑪𝑷 = 𝑳 𝑨𝑬 Where P is the applied pull during standardization, 𝑷𝟏 is the applied pull at the time of measurement, 𝑨 is the cross-sectional area of the tape, 𝑬 is the modulus of elasticity of the steel, 𝑳 is the observed length. 11  Sources of Error in Taping Sagging Sagging – The weight of the tape produces a sag if the tape is not supported in its entire length. When this happens, the actual horizontal distance measured would be less than the graduated distance read from the tape. Sag is calculated as: 𝒘𝟐 𝑳𝟑𝑺 𝑪𝑺 = − 𝟐𝟒𝑷𝟐𝟏 Where 𝑳𝑺 is the unsupported length of the tape, 𝒘 is the weight of the tape per unit length, and 𝑷𝟏 is the applied pull at the time of measurement. 12  Sources of Error in Taping Improper plumbing – The plumb could easily sway by a slight wind or, if it is not held calmly and steady. Errors caused by improper plumbing are usually random, and practice is required to avoid them. Tape off-line or not horizontal – This happens when the tape is inclined during measurements. Careful alignment and keeping elevations of tape ends equal can help reduce this error. Corrections can be applied using Pythagoras’ formula if the difference in elevation is known. Faulty marking – Taping pins are supposed to be set perpendicular to the taped line but inclined to the ground at 45o. If this is not achieved or if it is tempered by stones or grass on the ground, an error may occur. Incorrect reading or interpolation—Interpolating to read the smaller division while the tape graduation has lower accuracy may lead to errors. This error can be minimized by using magnifying glasses or small scales to determine the last figure. 13  Questions? 14 14