L4: Distance Measurement Flashcards
What are the two main objectives of distance measurements?
1) Measuring an unknown distance between fixed points
2) Laying out a known/required distance with only knowing of the starting point
What technology did the Ancient Egyptians use to measure distance?
Ropes with knots tied at convenient points
What is a cubit?
An ancient (Egyptian) measure of length approximately equal to the length of a forearm (18 in, 44 cm)
Who is Edmund Gunter?
The inventor of the Gunter chain in the 1500s
What is the Gunter’s chain?
A chain (66 ft long) that is subdivided into 100 links (25 links in 1 rod, 4 rods in one chain)
Most of North America’s early legal plans and records are measured in chains and links
It is catered towards English units (1 mile = 80 chains)
What technology was developed to measure distance in the 1900s?
Various types of reel-mounted tapes (made out of cloth, copper wire-reinforced cloth, fiberglass, and steel)
What instrument came to use in the latter half of the 20th century to measure distances?
EDM, especially integrated into total stations
Describe the process of measuring distances with pacing and where/when it is most often used
Determine the length of your pace by walking natural steps back and forth over a level course of a known distance and divide the known distance by the number of steps taken
To take a measurement, count the number of steps between two points and multiply by the pace length
This is most often used ad a rough check of key points in construction layouts or to look for survey markers in a field
Describe the process of measuring distances with an odometer and when/where it is most often used
An odometer is a wheel of known circumference that is rolled over the distance being measured
The odometer counts the number of revolutions and converts that into the distance traversed
This technique is employed where low-order precision is acceptable such as for police sketches of an accident or car odometers
Describe the process of measuring distances with a subtense bar and when/where it is most often used
A subtense bar is a tripod-mounted bar with targets set specifically 2 m apart
The subtense bar is positioned over the desired point and perpendicular to survey line whose distance is being measured
A theodolite (1” capability) is set up at the start of the survey line to measure the horizontal angle between the subtense bar targets so that trig can be used
The accuracy of this method diminishes as length increases since the angle becomes smaller, approaching the error of a theodolite
This was used to obtain distances over difficult terrain (ex: across free-ways, water, or steep slopes) though nowadays EDMs have largely replaced them
Describe the process of measuring distances with stadia tacheometery and when/where it is most often used
Set up a level or theodolite and sight a rod at the end of the line being measured
Record the readings of the upper and lower stadia and calculate the difference between them
Use the formula to calculate the distance:
D = KIcos²θ
Where:
D - horizontal distance
K - instrument coefficient (often 100)
I - difference between stadia readings
θ - altitude angle (0 if using level)
Describe the process of measuring distances with electronic distance measurement (EDM) and when/where it is most often used
A light wave is sent along the path being measured from the instrument station towards a reflecting prism at the other end
The instrument measures the phase differences between the transmitted light wave and the one reflected back to calculate the distance
EDM is often used where direct measurement is difficult when terrain is rough or site is congested
Electromagnetic waves require no medium to travel so this method can be used in space as well
What are three different types of EDM
Telescope mounted EDM
Total station: combination EDM and theodolite
Distomat: a small compact EDM device often used in engineering and construction works that is pointed at a reflector and then reads the result
What are the three ranges of EDM and the corresponding wave used as a signal?
Short range: <5 km; infrared wave
Medium range: <100 km;
microwave
Long range: >100 km; radio wave
How can you derive the distance from analysis of position coordinates?
After coordinates are found using other techniques, use trig to find the distance and directions if desired
What is a plumb bob and how is it used in taping?
It is a weight (bob) on a string (normally 200 to 500 g made from brass)
In general, checks if objects are vertical
Used to transfer measurements from the tape to the ground when the tape is being held above ground to keep a horizontal alignment
How is a hand level used in taping?
To keep the tape horizontal when measuring
The person at higher elevation holds the hand level while the person at lower elevation takes the measurement using a plumb bob
What are range rods and how are they used in taping?
6 ft / 2 m aluminum poles with steel points, usually painted in alternating red and white (every 1 ft / 0.5 m)
Used in taping and theodolite work to provide alignment sights
How is a clamp handle used in taping?
Helps grip the tape at an intermediate point without bending/distorting the tape
When are pegs used and what are some of their characteristics?
Used when certain points on the field require more permanent marking
Generally made from wood about 40 to 60 cm tall
Should be driven into the soil vertically and kept visible
Describe tapes and some of their characteristics
Come in various lengths (most popular 100 ft and 30 m)
Woven tapes can be made out of various materials such as linen or Dacron; often interwoven with copper strands for strength, resistance to deformation from long use and moisture
Woven tapes need to be checked for accuracy periodically
Don’t use metal tapes when near electric stations
What are invar tapes and what is their advantage?
Composed 35% nickel, 65% steel
Thermal coefficient of expansion is only about 1/30 to 1/60 of that of steel tape so much more accurate measurement
What are some precautions when measuring with tape?
Make sure to eliminate any loops and kinks before pulling to take any measurements
If a tape gets wet, first wipe with a dry cloth and then with an oily one
What is the measuring process with tape?
The head surveyor carries the zero end of the tape forward to the final point
The head surveyor continues walking until the tape is unwound and the rear surveyor calls “Tape” and then a measurement is taken
The rear surveyor is responsible for keeping the head surveyor in a straight line through sighting a range pole or theodolite
What are some typical taping errors?
Systematic:
- slope
- erroneous length
- temperature
- tension and sag
Random:
- slope
- temperature
- tension and sag
- allignment
- marking and plumbing
What are the standard conditions for the use of steel tapes?
1) Temperature = 20 C (68 F)
2) Tape under a tension of 50 N (10 lb)
3) Tape fully supported throughout
Discuss slope measurements
In general, survey measurements in the end must be shown on horizontal
Sometimes, it is difficult or impossible to measure the horizontal distance so a slope distance can be measured
However, either the slope angle, the zenith angle, or the vertical distance must be also measured to convert the slope distance to horizontal distance before plotting
How do you correct a measurement of a tape with defective length?
The correction per tape length is how much one tape actually is compared to the assumed length
Divide a measurement by the assumed length and multiply that by the correction per tape length to get the total correction
Add the total correction to the original measurement to get the corrected distance
OR
Multiply the original measurement by the ratio of the actual length over the the assumed length
What are the formulas for temperature corrections of steel tape?
C:
C t = 0.0000116(T-20)L
F:
C t = 0.00000645(T-68)L
Where:
C t - correction due to temperature
T - actual temperature
L - distance measurement
What is the formula for correction of a tape measurement due to inconsistent pull?
C p = (P - Ps)L / AE
Where:
C p - correction due to inconsistent pull (the elongation of the tape due to the pull)
P - actual pull applied
Ps - standard pull
L - distance measurement
A - cross sectional area of tape
E - modulus of elasticity of tape material
What is the formula for correction of a tape measurement due to sag?
C s = -w²L³ / 24P²
OR
C s = - W²L / 24P²
Where:
C s - correction due to sag
w - weight of tape per unit length
W - weight of tape between supports
L - length of tape between supports
P - pull applied
How can errors due to sag be eliminated?
Supporting the tape at short intervals or throughout
Computing a sag correction for each unsupported segment and applying the total to the recorded length
List some common mistakes that may occur in taping
Measuring to / from the wrong marker
Reading the tape incorrectly or transposing figures
Losing proper count of full tape lengths
Recording values incorrectly in notes
Ambiguous figure calling
Not identifying zero point of tape
Arithmetic mistakes in sums of dimensions and error corrections
In what conditions are microwave systems advantageous over infrared and laser systems?
In poorer weather conditions
What are the disadvantages to using EDM?
Slower to set up
Minimum error of 3-8 mm for all distances
(great for long distances but too much for short ones)
Also extremely expensive
What is the formula for wavelength of light?
λ = c / f
Where:
λ - wavelength
c - speed of light
f - frequency
What is the formula that is used to calculate distance in an EDM?
2L = nλ + φ
Where:
L - distance measurement
n - number of whole wavelengths
λ - whole wavelength
φ - partial wavelength
