L3: Levelling Flashcards
List the general uses of levelling and its results
To design highways, railroads, canals, water supply systems
To lay out construction projects according to planned elevations
To calculate volumes of earthwork and other materials
To investigate drainage characteristics of an area
To develop maps showing general ground configurations
To study earth subsidence and crustal motion
Define levelling
The processing of finding elevations of points or their differences in elelvations
What is the reference datum universally employed in surveying for levelling?
Mean sea level (MSL): the average height for the surface of the seas for all stages of tide (over a 19-year period as defined by the National Geodetic Vertical Datum of 1929)
Define vertical line
A line that follows the local direction of gravity as indicated by a plumb line
Define local plumb line
A line that follows the direction in which gravity acts
Define level surface
A curved surface that at every point is perpendicular to the local plumb line
Define level line
A line in a level surface (it is therefore curved)
Define horizontal plane
A plane perpendicular to the LOCAL direction of gravity (it is NOT curved)
Define horizontal line
A line which is normal to the LOCAL direction of gravity at a particular point
They are tangential to level lines at those individual points
Define vertical datum
Any level surface to which elevations are referenced
This is the surface that is arbitrarily assigned an elevation of zero
Define elevation
The distance measured along a vertical line from a vertical datum to a point/object
Define vertical control
A series of benchmarks or other points of known elevation established throughout an area
Also termed: basic control, level control
What are five principle methods of levelling (briefly describing each)?
BAROMETRIC LEVELLING: using the fact that air pressure is inversely proportional to altitude
GRAVIMETRY: by measuring the gravitational force between different points
TRIGONOMETRIC LEVELLING: by using a theodolite to measure the vertical angle and horizontal distance to then use trig
SATELLITE POSITIONING: using satellites
DIFFERENTIAL LEVELLING: by stationing a level in between two points
What are the two types of vertical angles and where is each measured from?
Zenith angles: measured from the vertical
Altitude angles: measured from the horizontal
What is the formula for a difference in elevation between points A and B using trigonometric leveling with a theodolite?
ΔElev = HI + S*sinα - r
Where:
ΔElev - change in elevation
HI - height of instrument
S - slope distance
α - altitude angle
r - height of rod (from theodolite crosshair)
What are the formulas for calculating the departure of a horizontal line from the level line?
C (ft) = 0.667M² = 0.0239F²
C (m) = 0.0785K²
Where:
C - departure from level line
M - distance in miles
F - distance in thousands of feet
K - distance in kilometers
Define refraction and explain its relevance
Light rays passing through Earth’s atmosphere are bent towards the Earth’s surface
A theoretically horizontal line of sight is actually bent
What are the formulas for calculating the effects of refraction?
R (ft) = 0.093M² = 0.0033F²
R (m) = 0.011K²
Where:
R - error from refraction
M - distance in miles
F - distance in thousands of feet
K - distance in kilometers
NOTE: the effect of refraction is 1/7 of that of curvature but in the opposite direction
What is the formula for the combined effect of curvature and refraction?
h (ft) = 0.574M² = 0.0206F²
h (m) = 0.0675K²
Where:
h - combined error
M - distance in miles
F - distance in thousands of feet
K - distance in kilometers
List the four types of benchmarks in decreasing accuracy (briefly describing each)
GREAT TRIGONMETRICAL SURVEY (GTS) benchmarks:
very accurate from high precision surveys; take MSL as datum; established by higher survey authorities of a particular country; usually a very permanent object
PERMANENT benchmarks: established with reference to GTS benchmarks; established by local state government agencies
TEMPORARY benchmarks: created by surveyors in the field to mark the point in the field; easier to continue survey from that point after time gap
ARBITRARY benchmarks: when strictly the difference in elevation is necessary, can pick some arbitrary fixed point to be a benchmark and assign to it an arbitrary benchmark value
What are the four categories of levels in increasing level of accuracy (and some characteristics of each)?
DUMPY levels: use level vials to orient lines of site
TILTING levels: also called optical levels; slightly more complex and accurate than dumpy levels; need rounded head tripod
AUTOMATIC levels: telescope with compensator; self-leveling feature to ensure horizontal line of sight
DIGITAL levels: set up same way as optical level but have rod with barcode so that measurement is done electronically; data stored automatically
What are the three main knobs on an automatic level and what do they do?
TURNING KNOBS: fine turn with high precision
FOCUSING KNOB: focus the lens
CROSSHAIRS KNOB: fine tune crosshairs, remove parallax
What are the steps for using an automatic level?
1) Set tripod in position for initial readings
2) Firmly push tripod legs into the ground
3) Ensure top is levelled by eye
4) Attach level to the tripod with clamp and use three foot screws to centralize circular bubble (fine adjustments made by compensator)
To what precision can foot rods be read? What about metric rods?
Foot rods: 0.01 ft
Metric rods: 0.01m with mm being estimated
What are some precautions for handling a level?
The safest way to transport a levelling instrument is to leave it in the container
The case is closed only when the instrument is set correctly in the padded supports
A level should be removed from its container by lifting by its base not the telescope
The head must be screwed on the tripod
The container should be kept closed once the instrument is removed
The legs of a tripod should be tightened correctly
Define benchmark (BM)
A permanent point of known elevation; they are established by using precise levelling techniques and instrumentation
Define temporary benchmark (TBM)
A semi-permanent point of known elevation; ex: flange blots on hydrants, nails in roots of trees, etc.
Define turning point (TP)
A point temporarily used to transfer an elevation
Define backsight (BS)
A rod reading taken on a point of known elevation to establish the elevation of the instrument line of sight
Define height of instrument (HI)
The elevation of the line of sight through a level
Define foresight (FS)
A rod reading taken on a TP, BM, or TBM to determine its elevation
Define intermediate foresight (IS)
A rod treading taken at any other point where the elevation is to be known
What are the two formulas necessary for calculating elevations from differential levelling?
Existing elevation + BS = HI
HI - FS = new elevation
Why is it important to place the level in the middle of two rods (having roughly equal BS and FS distances)?
So that the errors due to instrument maladjustment, curvature, and refraction cancel each other out (the error will be the same for both the BS and the FS so when subtraction occurs, the error is cancelled)
When are TPs used?
When you can’t position a level in between two points such that a line of sight can be accurately established
What are the three distinct perspectives a route is considered from in engineering surveying?
PLAN: view of a route as looking from an airplane
PROFILE: side view longitudinally such that elevations along the route are visible
CROSS SECTION: end view of a section at a station
Describe the process of reciprocal levelling and why it is sometimes necessary
Normally the levelling instrument is placed in the middle of two points to eliminate errors from curvature and refraction; sometimes not possible due to obstacle
Repeat measurements and calculations twice - once closer to A and once closer to B; take the average of the results
Describe the process of three-wire levelling (TWL)
On a level take and record the upper stadia, middle crosshair, and lower stadia values for both BS and FS
Average the three readings for BS and FS
To get the new elevation, add the average of the BS readings and subtract the average of the FS readings
Note: you should also calculate the sight distances by taking the differences between the top and bottom stadia; check that the sight distance is roughly equal for BS and FS
Describe the two peg test
Chose two points relatively close to each other
First station the level in the middle of them and find the elevation difference through that set up
Then move the level closer to one of the points and repeat the process to find the elevation difference between the points
Compare the calculated elevations: they should be roughly equal if the instrument has no error
What are two different possible ways to assess whether a misclosure is permissible in levelling?
By number of intermittent steps
By distance (recommended and how the standards are set)
What is the formula for acceptable misclosure according to the number of set ups?
E = 0.02ft * sqrt(n)
E = 5mm * sqrt(n)
Where:
E - acceptable misclosure
n - number of set ups
What is the formula for acceptable misclosure according to distance?
E = m * sqrt(K)
Where:
E - acceptable misclosure (mm)
K - total length in km
m - determined based on code
m =
First Order, Class I: 4 mm
First Order, Class II: 5 mm
Second Order, Class I: 6 mm
Second Order, Class II: 8 mm
Third Order: 12 mm
How are adjustments applied to levelling calculations?
Divide the total misclosure by the number of instrument set ups and switch signs (since if there is a + misclosure adjustments must be -)
For each point, multiply the value from the previous calculation by the number of set ups preceding the measurement to get the adjustment for that point
Add the adjustments to the initially calculated values
What happens if the calculated misclosure is greater than the allowable misclosure?
The measurements must be redone
List some of the possible sources of errors in levelling
Equipment:
- collimation error
- compensator not working
- parallax
- staff defects
- tripod defects
Field:
- staff not vertical
- unstable ground
- mishandling instruments, tripod
- instrument not level
- reading and booking errors
- temperature variations
Describe the inverted staff methods and when it often used
Used to determine the reduced levels of points such as underside of bridge
The rod is placed inverted so that its base is on the bottom of whatever is being measured
The reading on the rod is recorded in the table with a negative sign with following calculations taking the sign into account
