1. Measurements & Computations in Surveying
6/4/2018 6:00 PM
Measurements & Computations in Surveying
Dr. Dan Trent
Mississippi Valley State University
February 4, 2013
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The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

2. Objectives of tonight’s lecture
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Objectives of tonight’s lecture
1 Measurement of distances and angles is the essence of surveying – therefore we need to discuss appropriate units of measure for these and other quantities (area, volume, etc.)
2 Computation (or data reduction) is also essential to surveying. Surveyors must understand the concept of significant figures in measured and computed quantities
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

3. Units of Measure What are they?
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Units of Measure What are they?
SI – stands for Système International.
Most of the world uses this system
Metric system – based on units of 10
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

4. 6/4/2018 6:00 PM
Angles
An angle is simply a figure formed by the intersection of two lines.
An angle may be generated by the rotation of a line about a point – from an initial position to a terminal position.
The point of rotation is the vertex of the angle
Angular measurement is concerned with the amount of rotation
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

5. Degrees, Minutes, and Seconds
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Degrees, Minutes, and Seconds
Sexagesimal System.
Most Common
A complete rotation of a line (circle) is divided into 360 degrees of arc
1 degree = 60 minutes
1 minute = 60 seconds
Problem Example
89 59’ 60”
-54  17’ 14”
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

6. Angles Centesimal System
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Angles
Centesimal System
One complete rotation of a line (circle) is divided into 400 grades (or GRADS)
Written as 400g
Each grad is divided into 100 parts called centigrads (1g = 100c)
Each centigrad is divided into 100 parts called centi-centigrads (1c = 100cc)
For an angle represented as g the first 2 digits are centigrads and the second 2 are
centi-centigrads
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

7. Angles Important Conversion Formulae 1g = 0.9
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Angles
Important Conversion Formulae
1g = 0.9
Circumference of a circle
2R
There are about 2 radians in a circle
2 X 3.14 = 6.28
6.28 rad = 360
1 rad = 57.3 
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

8. Distance Basic unit is the FOOT In SI the basic unit is the METER
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Distance
Basic unit is the FOOT
Measured in decimals – NOT INCHES
75.25’ NOT 75’ 3”
In SI the basic unit is the METER
Also measures decimals
Decimeter = .1 meter
Centimeter = .01 meter
Millimeter = .001 meter
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

9. Beware AMERICAN SURVEY FOOT New standard (1959) Obsolete
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Beware
AMERICAN SURVEY FOOT
Obsolete
1 foot =
New standard (1959)
1 foot =
Difference of about 0.2 m in 100,000m
Or about 2” in 60 miles
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

10. 6/4/2018 6:00 PM
Older Units of Measure
In older deeds you may find these units referenced:
1 foot (ft) = 12 inches (in)
1 yard (yd) = 3 feet
1 mile (mi) = 5280 feet = 80 chains (ch)
1 chain = 66 feet
1 rod (rd) = 0.25 chain = 16.5 feet
1 link (lk) = 0.01 chain = 7.92 inches
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

11. Metric Distance Measure Review
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Metric Distance Measure Review
The meter:
1 m = 10 dm = 100 cm = 1000 mm
1 decimeter (dm) = 0.1 meter
1 centimeter (cm) = 0.01 meter
1 millimeter (mm) = meter
1 kilometer (km) = 1000 meters
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

12. 6/4/2018 6:00 PM
Area
Area is the amount of two dimensional space encompassed within the boundary of a closed figure or shape
Derived from basic unit of length
In the U.S. we use the square foot or sq ft or ft2
For land area we use the acre (ac)
1 acre = 43,560 ft2
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

13. More Equivalents 1 Square mile (mi2) = 640 acres (ac)
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More Equivalents
1 Square mile (mi2) = 640 acres (ac)
1 acre = 10 square chains (sq ch) = 43,560 ft2
1 square yard (yd2) = 3 ft X 3 ft = 9 square feet
1 hectacre (ha) = 100 acres = 10,000 sq meters
1 square kilometer (km2) = 100 hectacres = 1,000,000 square meters (m2)
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

14. Important Conversions
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Important Conversions
1 km2 = mi2
1 hectacre (ha) = 2.47 acres
1 square meter (m2) = 1.2 yd2 = ft2
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

15. Volume U.S. customary unit is cubic feet (ft3)
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Volume
U.S. customary unit is cubic feet (ft3)
In surveying we typically are concerned with greater volume so we use cubic yards (yd3)
Cubic meter (m3) is standard in SI
1 yd3 = 3 ft X 3 ft X 3 ft = 27 ft3
Use x3 for conversion - Not 9’
We will calculate volume next week
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

16. Conversion to SI metric
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Conversion to SI metric
1975 American Congress on Surveying and Mapping (ACSM)
Top 5
1976 U.S. Geological Survey (USGS) began using SI units on topographic maps
Problem Example
Convert an area of ac to an equivalent area expressed in hectacres
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

17. Computations Significant Figures
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Computations
Significant Figures
A measured distance or angle is never exact
There is no perfect measuring instrument
The “closeness” of the observed value to the true value depends on:
The quality of the measuring instrument
The care taken by the observer taking the measurement
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

18. Computations Significant Figures Rules
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Computations
Significant Figures
In a measured quantity, the number of significant figures is the number of sure or certain numbers plus one estimated digit
Rules
Zeros placed at the end of a decimal number are significant ( has 5 significant figures)
Zeros between other significant digits are significant (17.08 has 4 significant figures)
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

19. Computations Significant Figures
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Computations
Significant Figures
Zeros just to the right of the decimal in numbers smaller than unity (1) are not significant ( has 3 significant figures. So does – only 3 significant figures)
Trailing zeros to the right of the digits in a number written without a decimal are generally not significant (35,000 has only 2 significant figures)
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

20. Computations Significant Figures 25.35 4 significant figures
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Computations
Significant Figures
significant figures
significant figures
significant figures
significant figures
12, significant figures
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

21. Computations Rounding off numbers
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Computations
Rounding off numbers
Must take into account the number of significant figures in all calculations
Typically we “drop” all digits to the right of our significant figures if the next digit is less than 5
Typically we “add one” to the last significant figure if the next digit is 5 or more.
Round off to 2 significant figures
0.18
0.184
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

22. 6/4/2018 6:00 PM
Mistakes and Errors
The difference between a measured distance or angle and its true value may be the result of mistakes or errors
Blunder – A significant mistake caused by human error
Misreading a number on a scale
Measuring the wrong angle
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

23. Mistakes and Errors Systematic and Accidental Errors
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Mistakes and Errors
Systematic and Accidental Errors
Systematic Error – Repetitive errors that are caused by imperfections in the surveying equipment, by the specific method of observation, or by certain environmental factors
Mechanical errors
Cumulative errors
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

24. Mistakes and Errors Systematic and Accidental Errors
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Mistakes and Errors
Systematic and Accidental Errors
Accidental Error – The difference between a true quality and a measurement of that quality that is free from blunders or systematic errors
Accidental errors occur in every measurement
Relatively small and unavoidable errors in observation that are generally beyond the control of the surveyor
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

25. Mistakes and Errors Most Probable Value
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Mistakes and Errors
Most Probable Value
If 2 or more measurements of the same quantity made, random errors usually cause different values to be obtained. As long as each measurement is equally reliable, the average value the different measurements is taken to be the TRUE or most probable value.
Sum all measurements and divide by number of measurements
Problem Example
( ) ÷ 4 = 55.69
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

26. Mistakes and Errors The 90 Percent Error
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Mistakes and Errors
The 90 Percent Error
The most probable error is that which has an equal chance (50%) of either being exceeded or or not being exceeded in a particular measurement
Expressed as E90
A distance of ft is measured
90 Percent Error is assumed in one taping operation using a 100-ft tape  0.01 ft
Likelihood is 90% that the tape will fall within the range of – ft
Still 10% chance of greater than 0.01 ft error
Maximum anticipated error
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

27. Mistakes and Errors The 90 Percent Error    (  ) 2
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Mistakes and Errors
The 90 Percent Error

  (  ) 2
E90 = X  n(n – 1)
 = sigma, “the sum of”
 = delta, the difference between each individual measurement and the average of n measurements
N = The number of measurements
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

28. Mistakes and Errors The 90 Percent Error Problem Example
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Mistakes and Errors
The 90 Percent Error
Problem Example
A measurement was taken 5 times
( ) ÷ 5 = 75.7m
The value of  ( 2 ) may be computed by
(75.3 – 75.7)2 = 0.16
(75.3 – 76.2)2 = 0.25
(75.3 – 75.7)2 = 0.00
(75.3 – 75.5)2 = 0.04
(75.3 – 75.8)2 = 0.01
 ( 2 ) = 0.46
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

29. Mistakes and Errors The 90 Percent Error Problem Example
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Mistakes and Errors
The 90 Percent Error
Problem Example
 ( 2 ) = 0.46

E90 =1.645 X 0.46/ [ 5 ( 5 – 1 ) ] =  0.25 m
We are 90% sure that true distance is within the range of 75.7  0.25 m
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

30. Mistakes and Errors How accidental errors add up Problem Example
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Mistakes and Errors
How accidental errors add up
Problem Example
Lets say we measure a distance of 900 feet with a 100’ tape ( 9 – 100 ft measurements )
Maximum probable error for measuring 100’ was  ft
What is the maximum probable error for measuring the total distance of 900 ft with the same tape and the same procedure?
Could we reasonably say 9 X = ft?
NO! Some errors are likely positive, some negative
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

31. Mistakes and Errors How accidental errors add up Problem Example
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Mistakes and Errors
How accidental errors add up
Problem Example
Law of Compensation

E = E1 X  n
E = the total error of n measurements
E1 = the error for one measurement
n = the number of measurements 
E = 0.010  9 =  X 3 =  0.030ft
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

32. Mistakes and Errors Overview
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Mistakes and Errors
Overview
The surveyor must constantly be aware of the possibilities for mistakes and errors in survey work
4 Basic Principles
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

33. Accuracy and Precision
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Accuracy and Precision
NOT THE SAME!
Precision – the degree of perfection used in the survey
Accuracy – the degree of perfection obtained in the results
Surveyor A measures a distance and gets 750.1ft
Surveyor B measures the same distance and gets ft
Surveyor B used greater precision
If the true distance was , Surveyor A was more accurate See board example
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

34. Errors of Closure and Relative Accuracy
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Errors of Closure and Relative Accuracy
The difference between a measured quantity and its true, or actual, value is called the error of closure or just closure
Distance from Point A to Point B is determined to be m. The same line is measured a 2nd time using the same instruments and procedures and is found to be m.
Error of closure is – = 0.06m
Due to accidental errors
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

35. Errors of Closure and Relative Accuracy
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Errors of Closure and Relative Accuracy
Suppose the actual distance was know not be m. Closure determined as the difference between the average measured value and the known true value.
( ) ÷ 2 = m
Error of closure would be – = 0.08m
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

36. 6/4/2018 6:00 PM
Relative Accuracy
For horizontal distances, the ratio of the error of closure to the actual distance is called the relative accuracy
Degree of accuracy
Order of accuracy
Accuracy ratio
Relative precision
Precision
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

37. Relative Accuracy Relative Accuracy = 1 : D/C
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Relative Accuracy
Relative Accuracy = 1 : D/C
D = distance measured
C = error of closure
A distance of 500 ft is measured with a closure of 0.25 ft
Relative accuracy is 0.25 ft per 500 ft (0.25/500)
Relative accuracy is 1/2000
Relative accuracy is 1:2000
For every 2000 ft measured there is an error of 1 ft
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

38. Relative Accuracy Problem Example A distance of 577.80 ft is measured
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Relative Accuracy
Problem Example
A distance of ft is measured
A true distance of is found
What is relative accuracy of the measurement?
Error of closure is – = ft
Relative accuracy is 1: D/C
1: /0.18 = 1: 3200
IF survey was 4 times as long, estimated error of closure would be 
0.18 X  = ft
Relative accuracy is 1:(4 X ) / 0.36 = 1:6400
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

39. Standards of Accuracy First order accuracy Second order accuracy
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Standards of Accuracy
First order accuracy
1: 1,000,000
Second order accuracy
Class I accuracy 1: 50,000
Class II accuracy 1: 20,000
Third order accuracy
Class I accuracy 1: 10,000
Class II accuracy 1: 5,000
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

40. Choice of Survey Procedure
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Choice of Survey Procedure
Surveyor should choose equipment and methods that have a rating or maximum anticipated error closely equal to that for maximum allowable closure
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

41. Choice of Survey Procedure
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Choice of Survey Procedure
A horizontal control traverse survey is required to close with third order class II accuracy. Total distance of the traverse is about 10,000 ft. What is the required rating or maximum anticipated error per 1000 ft for the survey method to be used?
Relative accuracy for third order class II survey is 1: 5000
Therefore in 10,000 ft the maximum error of closure is 1/5000 X 10,000 = 2 ft
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

42. Choice of Survey Procedure
6/4/2018 6:00 PM
Choice of Survey Procedure
Relative accuracy for third order class II survey is 1: 5000
Therefore in 10,000 ft the maximum error of closure is 1/5000 X 10,000 = 2 ft
E90 for 1000 ft 2
  10,000

2 X 
E90 for 1000 ft =   ft
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

43. The Assessment
Quiz #1 will be available on the course website at 3:00 p.m. on February 5, 2013.
Bonus period for early submission will end February 7, 2013 at 5:00 p.m.
Drop Dead Deadline is 5:00 p.m. on Friday, February 8, 2013
Include ANSWERS to Problems – I will take up your work sheets on Monday, February 11, 2013

44. Submission Guidelines
At the TOP of your paper write:
AT – 403 Your Name Week 2 Quiz
Papers must be word processed using Microsoft WORD
Write out each question, then answer it using complete sentences, correct grammar and spelling below each question
Use 12 point Ariel or 12 point Times New Roman font, double spaced
completed paper to Dr. Trent with the subject line heading EXACTLY LIKE THIS:
AT 403 – Your Name – Week 2