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6.20 In Figure 6.14, he, hr, z, and the measured slope length L were 5.53 ft, 6.00 ft,
93°20'06" and 489.65 ft, respectively. Calculate the horizontal length between A and
B if a total station measures the distance.
6.21* Similar to Problem 6.20, except that the values were 1.45 m, 1.55 m, 96°05'33" and
1663.254 m, respectively.
6.22 What is the actual wavelength and velocity of a near-infrared beam (1 = 0.901 um)
of light modulated at a frequency of 330 MHz through an atmosphere with a dry
bulb temperature, T, of 26°C; a relative humidity, h, of 75%; and an atmospheric
pressure of 893 hPa?
6.23 What is the actual wavelength and velocity of a near-infrared beam (1 = 0.901 um)
of light modulated at a frequency of 330 MHz through an atmosphere with a dry
bulb temperature, T, of 26°C; a relative humidity, h, of 75%; and an atmospheric
pressure of 893 hPa?
6.24 If the temperature and pressure at measurement time are 18°C and 760 mm Hg,
respectively, what will be the error in electronic measurement of a line 3 km long
if the temperature at the time of observing is recorded 10°C too high? Will the ob-
served distance be too long or too short?
6.25* The standard deviation of taping a 30 m distance is 5 mm. What should it be for a
90 m distance?
6.26 Determine the most probable length of a line AB, the standard deviation, and the
95% error of the measurement for the following series of taped observations made
under the same conditions: 215.382, 215.381, 215.384, 215.374, 215.391, 215.382,
215.374, 215.382, 215.389, and 215.387 m.
6.27 If an EDM instrument has a purported accuracy capability of + (1.5 mm + 2ppm),
what error can be expected in a measured distance of: (a) 25 m, (b) 483.40 ft,
(c) 387.563 m? (Assume that the instrument and target miscentering errors are
equal to zero.)
6.28 The estimated error for both instrument and target miscentering errors is 1.5 mm;
For the EDM in Problem 6.27, what is the estimated error in the observed distances?
6.29 If a certain EDM instrument has an accuracy capability of + (2 mm + 2 ppm).
what is the precision of measurements, in terms of parts per million, for line lengths
of: (a) 20.000 m, (b) 200.000 m, (c) 2000.000 m? (Assume that the instrument and
target miscentering errors are equal to zero.)
6.30 The estimated error for both instrument and target miscentering
For the EDM and distances listed in Problem 6.29, what is the estimated error in each
distance? What is the precision of the measurements in terms of parts per million?
6.31 Create a computational program that solves Problem 6.22.
errors is +1.5 mm.
PROBLEMS
Asterisks (*) indicate problems that have partial answers given in Appendix G.
6.1 What distance in travel corresponds to 1 usec of time for electromagnetic energy?
6.2* A student counted 92, 90, 92, 91, 93, and 91 paces in six trials of walking along a
course of 200-ft known length on level ground. Then 85, 86, 86, and 84 paces were
counted in walking four repetitions of an unknown distance AB. What is (a) the
pace length and (b) the length of AB?
6.3 What difference in temperature from standard, if neglected in use of a steel tape,
will cause an error of 1 part in 10,000?
6.4 An add tape of 101 ft is incorrectly recorded as 100 ft for a 200 ft distance. What is
the correct distance?
6.5* List five types of common errors in taping.
6.6 List the proper procedures taping a horizontal distance of about 84 ft down a 4%
slope.
6.7 For the following data, compute the horizontal distance for a recorded slope dis-
tance AB.
(a) AB 104.93 ft, slope angle = 2°13'46"
(b) AB 86.793 m, difference in elevation A to B = -2.499 m
6.8* When measuring a distance AB, the first taping pin was placed 1.0 ft to the right of
line AB and the second pin was set 0.5 ft left of line AB. The recorded distance was
236.89 ft. Calculate the corrected distance. (Assume three taped segments, the first
two 100 ft each.)
6.9 List the possible errors that can occur when measuring a distance with an EDM.
6.10 Briefly describe how a distance can be measured by the method of phase comparison.
6.11 Describe why the sight line for electronic distance measurement should be at least
0.5 m off the surface of the pavement along its entire line of sight.
6.12* Assume the speed of electromagnetic energy through the atmosphere is
299,784,458 m/sec for measurements with an EDM instrument. What time lag in
the equipment will produce an error of 800 m in a measured distance?
6.13 What is the length of the partial wavelength for electromagnetic energy with a fre-
quency of the 14.9989 MHz and a phase shift of 156°?
6.14 What “actual” wavelength results from transmitting electromagnetic energy
through an atmosphere having an index of refraction of 1.0043, if the frequency is
*(a) 29.988 MHz
(b) 14.989 MHz
6.15 Using the speed of electromagnetic energy given in Problem 6.12, what distance
corresponds to each microsecond of time?
6.16 To calibrate an EDM instrument, distances AC, AB, and BC along a straight line
were observed as 90.158 m, 60.025 m, and 30.164 m, respectively. What is the system
measurement constant for this equipment? Compute the length of each segment
corrected for the constant.
d with an EDM instrument: (a) A dis-
Homework
Problems:
6.4
6.5
6.20
6.29
6.30