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

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

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

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.

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.

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

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.

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

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

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

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

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

Taping Accessories Plumb bob Hand level Clinometer Range pole Made of brass and weigh 10-12 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

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

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

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

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

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

Standard Conditions for the Use of a Steel Tape 100.00 ft tape Temperature = 68°F Tape is fully supported Tension = 10 lbs 30.000 m tape Temperature = 20ºC Tension = 50 Newtons (11.24 lbs) Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

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

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

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

Example A distance is recorded as being 471.37 ft at a temp. of 38 o F. What is the corrected distance? Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

Example ( Erroneous Correction) A measurement is recorded as 171.278 m with 30-m tape that is found to be only 29.996 m under standard conditions . What is the corrected measurements? Solution: Correction per tape length= - 0.004 Number of tape lengths = 171.278 / 30 Total Correction= -0.004( 171.278 / 30) =-0.023 Corrected distance = 171.278- 0.023 =171.255 m Surveying With Construction Applications, 7th Edition Barry F. Kavanagh

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

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

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

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

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

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.

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

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

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

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

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

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

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:

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)

Electro-magnetic Energy A wave of wavelength  travels along the x-axis at a velocity of 299 ,792. 458 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

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

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

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

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

Distance Measuring Methods--GPS GPS (global Positioning System) is a system of 21-24 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.

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 675087E & 3998345N and the UTM coordinates for Oklahoma City are 639982E & 3925518N

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.

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?

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.

Measuring Horizontal Distance Chain Stadia EDM

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.

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.