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CHAPTER 2 DISTANCE MEASUREMENT

CHAPTER 2 DISTANCE MEASUREMENT. 3/17/03. CHAPTER 2 DISTANCE MEASUREMENT. Read Chapter 2 Kavanagh 2.1-2.6 Read to supplement class lecture 2.7 , 2.18 Read to supplement field exercise

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CHAPTER 2 DISTANCE MEASUREMENT

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  1. CHAPTER 2 DISTANCE MEASUREMENT 3/17/03

  2. CHAPTER 2 DISTANCE MEASUREMENT • Read Chapter 2 Kavanagh 2.1-2.6 Read to supplement class lecture 2.7 , 2.18 Read to supplement field exercise 2.8-2.17 Understand taping corrections, sources of error, random and systematic errors, and systematic error correction

  3. 2.2 Taping (or “Chaining”) In 1800's, U.S. Government Land Office surveys which partitioned the land for homesteading used Gunter’s 66' chain. This century, the steel ribbon tape is most common. But “taping” and “chaining” terms still used. Two types of chains: 66-ft Gunter’s chain & 100-ft engineer’s chain. If not otherwise specified (particularly if looking at 19th century maps) 66-ft chain is implied.

  4. 2.2 Taping, cont. • Steel tapes: • Invar tapes (not common): • Cloth and fiberglass tapes:

  5. 2.2 Taping, cont. • Why taping is used for <100' distances: Nikon A-10 EDM accuracy: 5 mm constant error ± 3 ppm error for instrument = ± 0.02' Add setup error 0.01' or 0.02‘ Total EDM measurement error maybe 0.03' > 1/10,000 error in good taping = 0.01', or 1/5000 error standard = 0.02' for 100' dist.

  6. 2.3 Taping Methodology • Reading a steel tape Add tape (most common): Cut tape (more prone to error):

  7. 2.3 Taping Methodology, cont. • Good practice is to measure all distances both forward and backward. • A taping crew should have the following equipment 1) 1- 100' steel tape 2) 3- range poles 3) 1- set of 11 chaining pins (also called “taping pins”) 4) 1- 50' woven or cloth or fiberglass tape 5) 2- plumb bobs 6) 1- hand level 7) 1-tape clamp

  8. 2.3 Taping Methodology, cont. • Taping over Level Ground (Distance > 100 ft.) 1) If the distance to be measured is level, you may lay the tape on the ground. 2) The head tapeman takes the 0' end at the tape and walks in the direction to be taped. 3) When the rear tapeman gets to 100' on the tape he calls “tape” or “chain” to stop the head tapeman. 4) The rear tapeman then aligns the head tapeman using a range pole placed behind the end point. 5) Once located, the rear tapeman places the 100' mark over the starting point and the head tapeman pulls the tape tight to 10-15 lb tension (to the specified standard tension). 6) If on soil, a taping pin is inserted z to the tape at a vertical angle of 45E± If on pavement, mark zero point with chalk, crayon, or scribe it. Leave a taping pin next to the point for the rear chainman to pick up.

  9. 2.3 Taping Methodology, cont. • Taping over Level Ground (Distance > 100 ft.) 7) Once a measurement have been made, the rear tapeman picks up the taping pin. By counting taping pins, the rear tapeman knows how many 100' lengths have been measured. 8) When the end of the distance to be measured is reached, the head tapeman stops at the point. The rear tapeman pulls the tape to a whole-foot mark that will bring the subgraduations at the zero end of the tape over the point marking the end of the line. 9) The head tapeman then reads out the reading on the graduated portion of the tape to the nearest hundredth foot.

  10. 2.3 Taping Methodology, cont. • Taping over Sloping Ground Two taping methods: • Hold the tape horizontal. • Tape along the slope, compute the slope, correct for the slope.

  11. 2.3 Taping Methodology, cont. 1) Slope Taping: Horizontal Taping Method • Same procedure as level ground procedure with following added notations: • One or both tapemen may need to hold the tape off the ground. Use a plumb bob to position the tape over the mark. • Downhill tapeman may need to use a hand level to make sure both ends are at the same height. If relative accuracy better than 1/2500 - 1/3000 is desired, eyesight not good enough. • If S < 5'/100' (<5% grade) you can measure an entire 100' horizontal distance (i.e., if you can hold the tape at shoulder level or lower).

  12. 2.3 Taping Methodology, cont. • 2) Slope Taping: Taping Along the Slope • Lay tape on the slope • Suitable for smooth and constant slope; can be more precise than horizontal taping because it is difficult to hang a plumb bob from the tape accurately. • Use transit or theodolite to determine slope (ft/ft) or grade (%).

  13. 2.4 Applying Corrections to Tape Measurements • Types of Systematic Errors Tape Characteristics 1) Incorrect tape length (standardization error) 2) Temperature variation (from standard temperature) 3) Sag 4) Non-standard tension Operational error 5) Tape not horizontal (when assumed horizontal) or error in estimating slope 6) Incorrect alignment (tape is off-line) 7) Tape not straight (bent around trees or bushes) • Applying corrections: measured length + Correction = actual length

  14. 2.4 Applying Corrections, cont. 1) Incorrect Tape Length or Standardization Error During manufacture, the tape was graduated under standard temperature (say 68E), tension (say 10 lb), and method of support (fully supported). The difference between the actual tape length (under specified conditions of temperature, tension, and method of support) compared to a standard length and the nominal tape length = “absolute error” of the tape. Absolute correction Ca = true length - nominal length Example: A distance was measured and found to be 876.24 ft. The tape was later found to be 100.04 feet long. What is the correct distance? Absolute correction Ca occurs 8.76 times = 8.76 x 0.04 ft = 876.24 ft x 0.04 ft per 100' measured = 0.35 ft measured length + Correction = actual length 876.24 ft + 0.35 ft = 876.59 ft Summary: If the tape is too long we didn’t use it enough times so the actual distanceis longer.

  15. 2.4 Applying Corrections, cont. 2) Temperature Variation Coefficient of thermal expansion of steel, k = 6.45 x 10-6/ º F (Note: Invar coef. of thermal expansion is about 1/30th that of steel) Difference of 15 ºF ± 0.01 ft in a 100-ft tape The correction to be added to the measured distance to obtain the true distance: Ct = Lk(T-Ts) where Ct = correction to be applied (ft or m) L = length of tape used k = coefficient of thermal expansion T = temperature of tape during measurement Ts = temperature at which tape was standardized Temperature of tape fully supported on ground may >> air temp. Use tape thermometer attached to the tape.

  16. 3) Sag • Correction for sag needed when tape has been standardized with a fully supported length. Tape takes form of catenary, and horizontal length is shortened: Cs = - n w2 l3 (ft or m) 24P2 Where n = number of unsupported lengths w = weight/foot of tape l = unsupported length P = tension applied (lb or kg) • Due to sag, the observed (measured) distance is always greater than the true distance. • Correction length to be added to measured distance to obtain true value is always a negative value. • Measured Distance +Cs = True Distance • One way to minimize the sag correction is to minimize the length of tape in the sag. • OR increase the tape tension sufficiently to compensate for the effect of sag.

  17. 4) Non-standard tension If you pull a tape in tension it will stretch. The National Bureau of Standards standardizes the tapes under 2 conditions: 1) 12 lbf pull, fully supported (Note: FE2’s tape was standardized at 15 lbf pull) 2) 20 lbf pull, fully unsupported Correction for pull or tension is: Cp = (P-Ps) L AE where P = tension applied (lb or kg) Ps = standard tension L = length A = cross-sectional area of tape E = modulus of elasticity of steel = 2.8 x 107 to 3.0 x 107 psi

  18. Normal tension = the tension applied to a tape such that the lengthening due to tension equals the shortening due to sag. For a full tape supported at two ends: Cs + CP = 0 Cs = - W2 L - W2 L + (Pn -Ps) L = 0 24 Pn2 AE Pn = 0.204 W (AE)0.5 (Pn – Ps)0.5 • Solve the equation iteratively using trial and error. Or use a chart supplied by the manufacturer. • For most tapes Pn in the range of 20 lb. will do.

  19. 5) Tape not horizontal • When tape is assumed horizontal but is actually inclined: For 100’ tape, the threshold for 0.01’ roundoff error: H = L cos a 99.995’ = 100 cos a a = 0o 34’ 23” or 99.9952 = 1002 - d2 d = 1.00 ft • Use a hand level to minimize this error.

  20. Departures from normal producing 0.01-ft error per 100’ tape length

  21. Example: Combined Taping Corrections • A distance was measured as 365.20 ft on an 8% grade. No field corrections were made, and the slope was considered horizontal. The taping was done with the tape held off the ground along its whole length. The temperature at the time was 18E F. What is the correct horizontal distance if the tape is 100.03 ft long under standard conditions? • Solution: • Measured distance = 365.20' • Corrections per tape length: • Sag

  22. Temperature Incorrect length Slope

  23. Total correction: • Corrected horizontal distance =

  24. 2.1 Other Methods of Measuring Distances Pacing Odometer Car odometer precision = 0.1 mile Measuring wheel with counter attached Stadia Stadia tacheometry = procedure that utilizes two supplementary horizontal hairs (“stadia hairs”) placed at equal distances above and below the central horizontal hair in an instrument’s telescope

  25. 2.2 Methods, cont. Subtense bar (not common) EDMs (EDMIs) Electronic Distance Measurement instruments Either a unit mounted on top a theodolite, or a built-in unit If it cannot resolved H, V, S automatically, it is commonly termed “EDM theodolite” Uses infrared light of varying wave length and assessing the phase delay of the returning signal

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