1. Surveying With Construction Applications, 7th Edition
Chapter 3 Distance Measurement

2. Timeline: Methods of Linear Measurement
Historically, distances have been measured directly by applying an instrument of known length against the distance between two or more ground points
Egyptians used ropes for distance measurements having knots tied at convenient points
Gunter’s chain was 66 feet with 100 links that was the instrument used by North American Surveyors to lay out the townships during the 1700 and 1800s
In the early 1900s, various types of reel-mounted tapes came into use (made out of cloth, copper wire-reinforced cloth, fiberglass, and steel
All precise measurements were made with steel tapes
In the latter part of the 1900s, EDMs and total stations were widely used
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

3. Three Types of Distances
Vertical
Horizontal
Slope
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

4. Two principles of measuring distance
1) It takes two points to form a line.
2) The shortest distance between two points is a straight line.

5. Selecting The “Best” Method
The best distance measuring method/device to use is influenced by many factors.
Personal preference
Topography
Client specifications
Regulations
Standard practice
Use of the data
Equipment available
Expertise of individuals
Environment
The most important factor is the intended use of the data.

6. Techniques of Distance Measurement
Pacing
Odometer
Stadia
Electronic distance measurement (EDM)
Subtense bar
Fiberglass tapes
Steel tapes
Distance Derived from the analysis of position coordinates
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

7. Distance Measuring Methods--Pacing
Distance is calculated by multiplying the number of paces by the individuals pace factor.
Measuring distance by counting steps (paces).
Advantages
Simple
Low tech
No specialized equipment
Disadvantages
Topography affects accuracy
Requires practice to take a consistent pace.
Must be able to traverse the distance.
Only measures slope distance.

8. Distance Measuring Methods--Odometer Wheel
An odometer is a mechanical revolution counter.
An odometer wheel is a wheel which uses an odometer to count the rotations of the wheel.
The gear ratio of the odometer is usually designed to provide a measurement of the distance in standard units--feet, decimal feet, feet and inches and/or meters.
Advantages
Easy to use
Low tech
Disadvantages
Accuracy is influenced by surface conditions.
Must be able to traverse distance.
Only measures slope distance.
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

9. Subtense bar
Distances are determined using a theodolite to determine a horizontal angle subtended by two targets precisely spaced at a fixed distance of 2 meters apart on a subtence bar Distance AB= Cot α/2 m
Subtence Bar A α B
Distance 2m
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

10. Steel Tape Graduations
Graduated throughout
In feet and hundredths (0.01) of afoot, the distance (38.23ft) is read directly from the tape.
Cut tape
Is marked throughout in feet, with the first &last foot graduated in tenths & hundredths
Add tape
Is marked throughout in feet, with the last foot graduated in hundredths of foot . Additional foot , graduated in hundredths is included prior to zero mark
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

11. Steel Tape Graduations
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

12. Steel Tape and Plumb bob
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

13. Taping Accessories Plumb bob Hand level Clinometer Range pole
Made of brass and weigh Oz, used in taping to transfer from tape to ground
Hand level
used to keep the steel tape horizontal when measuring
Clinometer
Clinometer (Abney hand level): used to record vertical angles for slope distance reduction to horizontal or to determine the heights of objects
Range pole
wooden or aluminum 6-ft poles; usually painted red and white in alternate 1-ft sections and are used to provide alignment sights in taping and theodolite work
Tension handle
help to hold the tape correctly and with the right tension
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

14. Hand Level Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

15. Abney Clinometer Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

16. Horizontal Taping Using a Plumb Bob at One End
If the distance to be measured is across uneven or sloping land, one end of the tape must be raised up off the ground to keep the tape horizontal; the raised end is referenced back to the ground mark using a plumb bob
is usually done with the tape held horizontally
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

17. Horizontal Taping Using Plumb Bobs at Both Ends of the Tape
Normally the only time that both ends of the tape are plumbed is when the ground rises between the marks being measured
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

18. Measuring Procedures
The head surveyor carries the zero end of the tape forward to the final point
When the tape has been completely unwound, the rear surveyor calls out so that the head surveyor can stop and prepare for taking measurements
The rear surveyor keeps the head surveyor on line by sighting a range pole or other target at the final mark and holds the appropriate graduation of the tape against the starting mark
The head surveyor ensures the tape is straight, at the proper tension and then marks the ground with a chaining pin
This is repeated to check the measurement; if necessary, corrections are made and the check is repeated
If the ground is not horizontal, one or both surveyors must use a plumb bob
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

19. Standard Conditions for the Use of a Steel Tape
ft tape
Temperature = 68°F
Tape is fully supported
Tension = 10 lbs
m tape
Temperature = 20ºC
Tension = 50 Newtons (11.24 lbs)
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

20. Systematic Taping Errors
Slope
Erroneous length
Temperature
Tension and Sag
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

21. Random Taping errors Slope (Estimating Horizontal) Temperature
Tension and sag
Alignment
Marking and Plumbing
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

22. Steel Chain Temperature Correction
Steel expands and contracts at fixed rate dependent upon the temperature.
The temperature correction for a steel tape is:

23. Example
A distance is recorded as being ft at a temp. of 38 o F. What is the corrected distance?
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

24. Example ( Erroneous Correction)
A measurement is recorded as m with 30-m tape that is found to be only m under standard conditions . What is the corrected measurements? Solution: Correction per tape length= Number of tape lengths = / 30 Total Correction= ( / 30) = Corrected distance = = m
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

25. Slope Corrections:
Survey distances can be measured either horizontally or on a slope
Since measurements are usually shown on a plan, distances taken on a slope must be converted into horizontal distances (plan distances) before they can be plotted
To convert slope distances to their horizontal distances, the surveyor must know the slope angle (), the zenith angle (90 - ), or the vertical distance (V):
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

26. This can also be written as: H = sin (90 - ) or H = S sin (90 - ) S
H (horizontal) = cos 
S (slope)
This can also be written as:
H = sin (90 - ) or H = S sin (90 - ) S
where  is the angle of inclination (slope) and (90 - ) is the zenith angle.
H = S2 – V2
where V is the difference in elevation.
Slope can also be defined as gradient, or rate of grade. This is expressed as a ratio of the vertical distance over the horizontal distance; when multiplied by 100, this ratio gives a percentage gradient.
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

27. Sag &Tension Corrections
Tension correction Cp= (P-Ps )L ∕ AE Sag Correction Cs = - W2 L ∕ 24P2 Cp = Correction due to tension per tape Length Cs = Correction due to sag per tape Length L: length of tape under consideration Ps :Standard Tension P : Applied tension A : Cross – Sectional area E : average modulus of elasticity W: weight of tape
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

28. Distance Measuring Methods—Stadia~.
The distance between the TSR and BSR is called the stadia interval.
This results in the equation:
Disadvantages of stadia
Must have instrument with stadia crosshairs.
May require multiple instrument setups.
Advantages of stadia
Works by line of sight. Not necessary to walk distance.
Distances can be measured with the same setup used to record elevations.
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

29. Distance Measuring Methods--Stadia~Cont.
Because SI = TSR - BSR, the more common equation is:
For modern instruments the stadia factor (SF) is 100.
What is the stadia distance for the illustration?
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

30. Horizontal Distance--1/2 Stadia
When the top or bottom stadia hair rod reading is obscured, a process called 1/2 stadia can be used.
Because this stadia interval is 1/2 of the standard interval, it is multiplied by two.
When I/2 stadia is used the elevation crosshair, and which ever stadia crosshair that can be read, is used.
Example: Determine the horizontal distance when the TRS = 7.34 and the elevation = 6.21.

31. Specifications for Achieving 1:5,000 Accuracy
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

32. Taping field notes for a closed traverse
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

33. Taping field notes for building dimensions
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

34. Electronic Survey Measurements
Electronic distance measurement (EDM)
Electronic angle measurement
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

35. EDM Instruments was first introduced in the 1950s
they are made to be used with theodolites and as components of total station instruments
they employ infrared light, laser light, or microwaves
microwave systems use a receiver/transmitter at both ends and infrared and laser systems use a transmitter at one end and a reflecting prism at the other end
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

36. Electronic angle measurement
electronic digital theodolites were first introduced in the late 1960s
it is one of the components of a total station, the other components being an EDM device, a microprocessor and a data collector
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

37. Distance Measuring Methods--EDM
EDM = Electronic Distance Measuring
The term EDM is used to describe a category of instruments that measure distance using an electronic signal.
The instrument broadcasts a focused signal that is returned by a prism or reflection from the object.
How the process works can be shown using the velocity equation.
Rearranging the equation for distance results in:

38. Distance Measuring Methods--EDM~cont.
Therefore, if the speed of the signal is known (speed of light), and the time for the signal to travel to the target and back is known, the distance can be calculated.
Advantages of EDM’s
Precise measurement of distance.
Line of sight instrument
Capable of measuring long distances
Reflectorless are single person operation
Disadvantages of EDM’s
Electronic = batterers
Accuracy affected by atmospheric conditions.
Can be expensive
Error ± (2 mm + 2 ppm x D)

39. Electro-magnetic Energy
A wave of wavelength  travels along the x-axis at a velocity of 299 , km/s (in vacuum). The frequency of the wave is the time taken for one complete wavelength:
 = c/f
 = wavelength, in meters
C = velocity, in km/s
F = frequency, in hertz (one cycle per second)
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

40. Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

41. Atmospheric Errors Associated with EDM
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

42. EDM Instrument Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

43. Geometry of an EDM Calculation
Surveying With Construction Applications, 7th Edition
Barry F. Kavanagh

44. Distance Measuring Methods--GPS
GPS (global Positioning System) is a system of satellites in orbit around the earth.
Each satellite knows its position and uses a unique signal to continuously broadcasts this information.
Along with the position information is a time signal.
When a GPS receiver receives a signal from at least four (4) satellites it can compute its position by trilateration.
The receiver position can be expressed in degrees of latitude and longitude, or distance (meters) using Universal Transverse Mercator (UTM) coordinates.

45. Distance Measuring Methods--GPS~cont.
Because UTM distances are based on a x-y coordinate system distances between points can be determined by simple math.
Example: Determine the distance between Stillwater and Oklahoma City when the UTM coordinates for Stillwater are E & N and the UTM coordinates for Oklahoma City are E & N

46. Distance Measuring Methods--GPS~Example
Subtracting the coordinates gives the two sides of a right triangle.
The hypotenuse of the triangle is the distance between the two towns (44.6 mi).
Note: this is the plane distance between these points not the surface distance.

47. Slope vs. Horizontal Distance
Distances can be measured in two ways:
Horizontal distance
Slope (surface) distance
The horizontal distance between two points is the distance between those points measured on a horizontal plane.
The slope distance between two points is a distanced measured along the surface of the earth.
When should horizontal distance be used?
When should slope distance be used?

48. Horizontal Distance
When horizontal distance is required, the individual has two choices.
Use equipment and techniques that record horizontal distance.
Record slope distance and collect the additional information required to calculate horizontal distance.

49. Measuring Horizontal Distance
Chain
Stadia
EDM

50. Horizontal Distance-cont. Chaining
To measure horizontal distance with a chain, a level and plumb bob must be used.
The chain is held level, horizontal, and the measurement at the elevated end is transferred using a plumb bob.
This method is limited to slopes of 5% or less.
When horizontal distances are measured by chaining on slopes > 5%, the technique called “breaking chain” must be used.

51. Horizontal Distance-cont. Breaking Chain
“Breaking Chain” is used when ever the slope is > 5% because when a 100 foot chain is used on a 5% slope, the elevated end will be 5 feet above the ground.
“Breaking the Chain” into shorter segments reduces the height of the elevated end of the chain.
Using a standard distance reduces the change of errors.
A standard distance was not used in the illustration.