# Surveying Homework

Table of Contents

*Surveying Homework*

Surveying Homework. Assignment #3 Problems: 3.6 & 3.9 3.11 & 3.14 3.18 3.19 In the text book 3.18* A field party is capable of making taping observations with a standard deviation of +0.010 ft per 100-ft tape length. What standard deviation would be expected in a distance of 200 ft taped by this party? 3.19 Repeat Problem 3.18, except that the standard deviation per 30-m tape length is +0.005 m and a distance of 90 m is taped. What is the expected 95% error in 90 m? 3.20 A distance of 200 ft must be taped in a manner to ensure a standard deviation smaller than 0.05 ft. What must be the standard deviation per 100-ft tape length to achieve the desired precision? 3.21 Lines of levels were run requiring n instrument setups.

*Surveying Homework*

If the rod reading for each backsight and foresight has a standard deviation o, what is the standard deviation in each of the following level lines? (a) n = 15,0 = +0.015 ft (b) n = 28, o = +5 mm 3.22 A line AC was observed in two sections AB and BC, with lengths and standard de- viations listed below. What is the total length AC, and its standard deviation?

*Surveying Homework*

(a) AB = 60.00 + 0.015 ft; BC 60.00 + 0.015 ft; BC = 86.13 + 0.018 ft (b) AB = 30.000 + 0.005 m; 15.413 + 0.005 m 3.23 Line AD is observed in three sections AB, BC, and CD, with lengths and standard deviations as listed below. What is the total length AD and its standard deviation? (a) AB +236.57 + 0.01 ft; BC = 608.99 + 0.01 ft; CD = 426.87 + 0.01 ft (b) AB = 688.980 m + 0.003 m; BC = 1274.865 m + 0.003 m: CD = 2542.373 m + 0.005 m 3.24 A difference in elevation between A and B was observed four times as 29.85, 29.83, 29.88, and 29.79 ft.

*Surveying Homework*

The observations were given weights of 2,3,1, and 2, respectively, by the observer. *(a) Calculate the weighted mean for distance AB. (b) What differ- ence results if later judgment revises the weights to 2,3,1, and 1, respectively? 3.25 Determine the weighted mean for the following angles: *(a) 222°12’36”, wt 2; 222°12’42”, wt 1; 222°12’34”, wt 3 (b) 106°28’54” + 1″, 106°28’46” 3″; 106°28’56” +1″ 3.26 Specifications for observing angles of an n-sided polygon limit the total angular mis- hserved for was most probable values for the adjusted quantities.

*Surveying Homework*

In addition, (cate the computation of precisions of the adjusted values, (2) reveals istakes so steps can be taken to eliminate them, and (3) Posta school design of survey proce- dures in the office before Ukrvations. PROBLEMS Asterisks (*) indicate problems that have been give appendix G. 3.1 Discuss the differences between an error andsidaai. 3.2 Give two examples of (a) direct and (b) indirect measurements. 3.3 Define the term systematic error and give two surveying examples of a systematic error. 3.4 Define the term random error and give two surveying examples of a random error. 3.5 Discuss the difference between accuracy and precision.

*Surveying Homework*

A distance AB is observed repeatedly using the same equipment and procedures, and the results, in meters, are listed in Problems 3.6 through 3.10. Calculate (a) the line’s most probable length, (b) the standard deviation, and (c) the standard deviation of the mean for each set of results. 3.6* 65.401, 65.400, 65.402, 65.396, 65.406, 65.401, 65.396, 65.401, 65.405, and 65.404. 3.7

*Surveying Homework*

Same as Problem 3.6, but discard one observation, 65.406. 3.8 Same as Problem 3.6, but discard two observations, 65.405 and 65.406. 3.9 Same as Problem 3.6, but include two additional observations, 65.408 and 65.409. 3.10 Same as Problem 3.6, but include three additional observations, 65.408, 65.409, and 65.410. In Problems 3.11 through 3.14, determine the range within which observations should fall (a) 90% of the time and (b) 95% of the time.

*Surveying Homework*

List the percentage of values that actually fall within these ranges. 3.11* For the data of Problem 3.6. 3.12 For the data of Problem 3.7. 3.13 For the data of Problem 3.8. 3.14 For the data of Problem 3.9. In Problems 3.15 through 3.17, an angle is observed repeatedly using the same equipment and procedures. Calculate (a) the angle’s most probable value, (b) the stan- dard deviation, and (c) the standard deviation of the mean. 3.15* 23° 30’00”, 23° 29′ 40″, 23° 30’15”, and 23°29’50”. 3.16 Same as Problem 3.15, but with three additional observations, 23°29′ 40″, 23°29’45”, and 23°29’50”. 3.17 Same as Problem 3.15, but with two additional observations, 23°30’05″and 23°29’55”.

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