reinforcement sheet on errors measurement

KING ABDUL AZIZ UNIVERSITY FACULTY OF ENGINEERING DEPARTMENT OF CIVIL ENGINEERING CE‐371 SURVEYING REINFORCEMENT SHEETS FOR STUDENTS Student Name:____________________________ Student ID_____________ Section ________ Date_______________ 1. A line has been observed 10 times using the same equipment and procedures. The results are shown in column (1) of the following table. It is assumed that no mistakes exist, and that the observations have already been corrected for all systematic errors. Compute the most probable value for the line length, its standard deviation, and errors having 50%, 90%, and 95% probability. Table 1- Measured length 538.57 538.39 538.37 538.39 538.48 538.49 538.33 538.46 538.47 538.55 Solution Steps: A. Calculate mean B. Calculate residual using equation 3.3 C. Calculate standard deviation using equation 3.4 D. Apply equation 3.6-3.8 to find errors having 50%, 90%, and 95% probability.

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ERROR ON DISTANCE MEASUREMENT

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KINGABDULAZIZUNIVERSITY FACULTYOFENGINEERING

DEPARTMENTOFCIVILENGINEERINGCE371SURVEYING

REINFORCEMENTSHEETSFORSTUDENTSStudentName:____________________________StudentID_____________Section________Date_______________

1. A line has been observed 10 times using the same equipment and procedures. The results are

shown in column (1) of the following table. It is assumed that no mistakes exist, and that the observations have already been corrected for all systematic errors. Compute the most probable value for the line length, its standard deviation, and errors having 50%, 90%, and 95% probability.

Table 1- Measured length 538.57 538.39 538.37 538.39 538.48 538.49 538.33 538.46 538.47 538.55

Solution Steps:

A. Calculate mean B. Calculate residual using equation 3.3 C. Calculate standard deviation using equation 3.4 D. Apply equation 3.6-3.8 to find errors having 50%, 90%, and 95% probability.
KINGABDULAZIZUNIVERSITY FACULTYOFENGINEERING

DEPARTMENTOFCIVILENGINEERINGCE371SURVEYING

REINFORCEMENTSHEETSFORSTUDENTSStudentName:____________________________StudentID_____________Section________Date_______________

2. Assume that a line is observed in three sections, with the individual parts equal (753.810.012),

(1238.400.028) and (1062.950.020) respectively. Determine the lines total length and its anticipated standard deviation.

Solution Steps:

A. Calculate total length B. Calculate anticipated standard deviation using equation 3.11

3. Assume that any distance of 100 ft can be taped with an error of if certain techniques are employed. Determine the error in taping 5000 ft using these skills.

Solution A. Use Equation (3.12)

4. A distance of 1000 ft is to be taped with an error of not more than 0.10 ft. Determine how accurately each 100 ft length must be observed to ensure that the error will not exceed the permissible limit.

Solution A. Use Equation (3.12)
KINGABDULAZIZUNIVERSITY FACULTYOFENGINEERING

DEPARTMENTOFCIVILENGINEERINGCE371SURVEYING

REINFORCEMENTSHEETSFORSTUDENTSStudentName:____________________________StudentID_____________Section________Date_______________