36 Instructor’s Solution Manual
Elementary Surveying: An Introduction to Geomatics
6 DISTANCE MEASUREMENT
Asterisks
(*)
indicate problems that have partial answers given in Appendix G.
6.1 What distance in travel corresponds to 1 𝜇sec 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 5,000?
Instructor’s Solution Manual 37
6.9 List the possible errors that can occur when measuring a distance with an EDM.
from standard, tape not level, plumbing, marking, reading)
6.10 Briefly describe how a distance can be measured by the method of phase comparison.
See Section 6.18
6.11 Describe why the sight line for electronic distance measurement should be at least 0.5 m
away from a parked vehicle near the line of sight.
the vehicle due a microclimate that lies immediately around it.
6.12* Assume the speed of electromagnetic energy through the atmosphere is 299,836,182
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?
299,836,182 =0.00000267sec
6.13 What is the length of the partial wavelength for electromagnetic energy with a frequency
of 29.988 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:
⁄
6.15 What index of refraction in the atmosphere will produce the speed of light given in
Problem 6.12?
6.16 To calibrate an EDM instrument, distances AC, AB, and BC along a straight line were
observed as 91.694 m, 60.025 m, and 31.698 m, respectively. What is the system
measurement constant for this equipment? Compute the length of each segment
corrected for the constant.
6.17 Which causes a greater error in a line measured with an EDM instrument: (a) A
disregarded 5° C temperature variation from standard or (b) a neglected atmospheric
pressure difference from standard of 25 mm of mercury?
38 Instructor’s Solution Manual
6.18* In Figure 6.14, he, hr, elevA, elevB and the measured slope length L were 5.56, 6.00,
603.45, 589.06, and 408.65 ft, respectively. Calculate the horizontal length between A
and B.
6.19 Similar to Problem 6.18, except that the values were 1.389, 1.500, 236.489, 254.876, and
312.049 m, respectively.
and 698.75 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
( 0.901 m)
of
light modulated at a frequency of 320 MHz through an atmosphere with a dry bulb
temperature, T, of 20° C, a relative humidity, h, of 88%, and an atmospheric pressure of
1034.56 hPa?
6.23 What is the actual wavelength and velocity of a near-infrared beam (λ = 0.901 μm) of
light modulated at a frequency of 340 MHz through an atmosphere with a dry bulb
temperature, T, of 25° C, a relative humidity, h, of 75%, and an atmospheric pressure of
893 hPa?
6
100
293.738139 893
273.15 11.27
1 10 1.00023627
1013.25 25 273.15 25 273.15
a
e
n
6
3
299,792,458 299,721,642 m/s
1.000236273
299,721,642 0.881534 m
340 10
V
6.24 If the temperature and pressure at measurement time are 18°C and 760 mm Hg, 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 observed 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: 215.380, 215.381, 215.382, 215.378, 215.388, 215.382, 215.374,
215.382, 215.389, and 215.387 m.
6.27 If an EDM instrument has a purported accuracy capability of ±(3.0 mm + 0.5 ppm),
what error can be expected in a measured distance of (a) 10 m (b) 586.08 ft (c) 405.957
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) 30.000
m (b) 300.000 m (c) 3000.000 m? (Assume that the instrument and target miscentering
6.30 The estimated error for both instrument and target miscentering errors is ±1.5 mm. 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 part-per-million?
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