L4: Distance Measurement

Question 1

What are the two main objectives of distance measurements?

Answer 1

1) Measuring an unknown distance between fixed points

2) Laying out a known/required distance with only knowing of the starting point

Question 2

What technology did the Ancient Egyptians use to measure distance?

Answer 2

Ropes with knots tied at convenient points

Question 3

What is a cubit?

Answer 3

An ancient (Egyptian) measure of length approximately equal to the length of a forearm (18 in, 44 cm)

Question 4

Who is Edmund Gunter?

Answer 4

The inventor of the Gunter chain in the 1500s

Question 5

What is the Gunter’s chain?

Answer 5

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)

Question 6

What technology was developed to measure distance in the 1900s?

Answer 6

Various types of reel-mounted tapes (made out of cloth, copper wire-reinforced cloth, fiberglass, and steel)

Question 7

What instrument came to use in the latter half of the 20th century to measure distances?

Answer 7

EDM, especially integrated into total stations

Question 8

Describe the process of measuring distances with pacing and where/when it is most often used

Answer 8

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

Question 9

Describe the process of measuring distances with an odometer and when/where it is most often used

Answer 9

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

Question 10

Describe the process of measuring distances with a subtense bar and when/where it is most often used

Answer 10

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

Question 11

Describe the process of measuring distances with stadia tacheometery and when/where it is most often used

Answer 11

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)

Question 12

Describe the process of measuring distances with electronic distance measurement (EDM) and when/where it is most often used

Answer 12

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

Question 13

What are three different types of EDM

Answer 13

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

Question 14

What are the three ranges of EDM and the corresponding wave used as a signal?

Answer 14

Short range: <5 km; infrared wave

Medium range: <100 km;
microwave

Long range: >100 km; radio wave

Question 15

How can you derive the distance from analysis of position coordinates?

Answer 15

After coordinates are found using other techniques, use trig to find the distance and directions if desired

Question 16

What is a plumb bob and how is it used in taping?

Answer 16

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

Question 17

How is a hand level used in taping?

Answer 17

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

Question 18

What are range rods and how are they used in taping?

Answer 18

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

Question 19

How is a clamp handle used in taping?

Answer 19

Helps grip the tape at an intermediate point without bending/distorting the tape

Question 20

When are pegs used and what are some of their characteristics?

Answer 20

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

Question 21

Describe tapes and some of their characteristics

Answer 21

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

Question 22

What are invar tapes and what is their advantage?

Answer 22

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

Question 23

What are some precautions when measuring with tape?

Answer 23

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

Question 24

What is the measuring process with tape?

Answer 24

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

Question 25

What are some typical taping errors?

Answer 25

Systematic:
- slope
- erroneous length
- temperature
- tension and sag

Random:
- slope
- temperature
- tension and sag
- allignment
- marking and plumbing

Question 26

What are the standard conditions for the use of steel tapes?

Answer 26

1) Temperature = 20 C (68 F)

2) Tape under a tension of 50 N (10 lb)

3) Tape fully supported throughout

Question 27

Discuss slope measurements

Answer 27

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

Question 28

How do you correct a measurement of a tape with defective length?

Answer 28

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

Question 29

What are the formulas for temperature corrections of steel tape?

Answer 29

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

Question 30

What is the formula for correction of a tape measurement due to inconsistent pull?

Answer 30

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

Question 31

What is the formula for correction of a tape measurement due to sag?

Answer 31

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

Question 32

How can errors due to sag be eliminated?

Answer 32

Supporting the tape at short intervals or throughout

Computing a sag correction for each unsupported segment and applying the total to the recorded length

Question 33

List some common mistakes that may occur in taping

Answer 33

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

Question 34

In what conditions are microwave systems advantageous over infrared and laser systems?

Answer 34

In poorer weather conditions

Question 35

What are the disadvantages to using EDM?

Answer 35

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

Question 36

What is the formula for wavelength of light?

Answer 36

λ = c / f

Where:
λ - wavelength
c - speed of light
f - frequency

Question 37

What is the formula that is used to calculate distance in an EDM?

Answer 37

2L = nλ + φ

Where:
L - distance measurement
n - number of whole wavelengths
λ - whole wavelength
φ - partial wavelength