Survey Exam 3

Vertical Curves

Needed to provide smooth transitions between straight segments (tangents) of grade lines for highways and railroads

Two Basic Types of Vertical Curves

Crest and Sag

Vertical Crest Curve

Negative change in grade; curve turns downwards

Vertical Sag Curve

Positive change in grade; curve turns upwards

Factors for designing vertical curves

1. Providing a good fit with the existing ground profile, minimizing cuts and fills.

2. Balancing the volume of cut material against fill.

3. Maintaining adequate drainage.

4. Not exceeding maximum specified grades.

5. Meeting fixed elevations such as intersections with other roads.

Curves must be designed to

(a) fit the grade lines they connect,
(b) have lengths sufficient to meet specifications covering a maximum rate of change of grade (which affects the comfort of vehicle occupants), and
(c) provide sufficient sight distance for safe vehicle operation.

Horizontal Curves

Curves that connect two straight tangent sections in a horizontal plane

Two Basic Types of Horizontal Curves

Circular Arcs and Spirals

A simple horizontal curve is

A circular arc connecting two tangents; used most oftenly

Easement curves are desirable for

Railroads and rapid transit systems

Maps

Visual expressions of portions of the Earth’s surface

Features of a map

Points, lines, and standard symbols

CADD

Computer Aided Drafting and Design

Maps are important for

Planning project locations, designing facilities, and estimating contract quantities

Maps are esstial in the development of

Land Information Systems (LIS) and Geographic Information Systems (GIS)

Mapping Surveys

Made to determine the locations of natural and cultural features on the Earth’s surface

Natural features on a map

Rivers, lakes, vegetation, oceans

Cultural features on a map

Roads, railroads, buildings, bridges, canals, boundary lines

Two types of mapping

Planimetric and Topographic

Planimetric Maps

Depicts natural and cultural features on an (X-Y) plane view

Topographic mapping

Include planimetric features but additionally show the configuration of the Earth’s surface

Planimetric and and Topographic maps are used to determine

Locations of highways, railroads, canals, pipelines, transmission lines, reservoirs

Sum of Interior Angles

( n - 2 )* 180 deg

n = number of angles

To find a missing angle

1. Use sum of interior angles to find what the angles should add up to

2. Sum angles given in problem

3. Subtract sum of given angles from the sum of interior angles

4. Get missing angle

To find angular misclosure

1. Use sum of interior angles to find the correct degree value

2. Sum angles given in the problem

3. Find different between the sum of interior angles and the angles given in the problem

4. Get angular misclosure

FGCS

Federal Geodetic Control Subcomitee

To find angular adjustment

1. Find the angular misclosure

2. Use (C_A / n ) to find adjustment per angle

3. Multiply the adjustment with the angles number in the traverse (1,2,3…)

4. Round Each Correction

5. Record successive dfferences (difference between each correction 1 to 2 = 1 or 2 to 4= 2)

6. Apply successive differences to the given angles

7. Check by adding the adjusted angles and comparing to the sum of interior angles

Acceptable Angle Misclosure (k): First Order

1.7”

Acceptable Angle Misclosure (k): Second Order, First Class

3”

Acceptable Angle Misclosure (k): Second Order,Second Class

4.5”

Acceptable Angle Misclosure (k): Third Order, First Class

10”

Acceptable Angle Misclosure (k): Third Order, Second Class

12”

Allowable Angular Misclosure Equation

c = k*sqrt(n)

n = number of angles

k = misclosure order constant

Preliminary Azimuth Equation

AZ_NEXT = AZ_PREVIOUS - (180deg - INTERIOR ANGLE_NEXT)

Departure

L sin( AZ )

L = length between points

AZ = azimuth to line between points

Latitude

L cos( AZ )

L = length between points

AZ = azimuth to line between points

In a closed circut the sum of Departures and Latitudes should be zero, if not they give you

Departure and Latitude Misclosure

Map Scales

Quantity of Length on the Map : Quantity of Length In Real Life

Ground Error on a Map

GROUND ERROR = (PLOTTING ERROR) * (SCALE DENOMINATOR)

Calculating Contour Intervals

1. Given elevation range and and interval scale

2. Round minimum and maximum elevations to the closest number that would fit on the scale

• Minimum elevation rounded upwards

• Maximum elevation rounded downwards

3. Count every number that would fit between the minimum and maximum along this interval scale (EX: 2-ft scale, 24, 26, 28, 30)

Drawing Contour Map

1. Calculate Contour Intervals

2. Label the contour intervals between the given elevations on the diagram

3. Connect equal elevations with curved lines on the diagram (usually spanning height to height or width to width

Distance Between Countor Points Equation

Y₀ = Y₁ + ( X₀ - X₁ ) ( Y₂ - Y₁ / X₂ - X₁ )

X = ELEVATIONS

Y = COORDINATE SQUARES

Topographic Map: Contour Intervals

Numerical difference between elevation contour line values

Topographic Map: Calculating Distances

1. Measure with ruler

2. Multiply value found with ruler by the scale denominator to get actual distance

Topographic Map: Calculating Elevation Change

1. Compute the difference between two lines to get the change

2. If between contour lines, take the average between the two to calculate instead

Topographic Map: Calculating Percent Slope

1. Measure distance between points and convert to actual distance

2. Find elevation change between points

3. Use % = (ELEVATION CHANGE / ACTUAL DISTANCE) * 100%

Topographic Map: Flow of Storm Water Run Off

Water will flow from the highest elevations to the lowest elevations; it will pool in valleys between elevation peaks

Horizontal Angles: Deflection Angles

DELTA = (S * D) / 200 + DELTA_PREVIOUS

S = DISTANCE BETWEEN STATIONS

D = DEGREE OF CURVATURE

Horizontal Angles: Increment Chords

C_STATION = 2R sin( DELTA_STATION )

C = CHORD LENGTH

R = RADIUS

Vertical Angles: High or Low Point

X = (G₁ * L) / (G₁ - G₂)

DISTANCE FROM THE BEGINNING OF VERTICAL CURVE (BVC)

G = GRADE

L = LENGTH OF CURVE

Vertical Curve: Elevation

Y = Y_BVC + (G₁ X) + (R / 2) * X²

Y = ELEVATION

BVC = BEGINNING OF CURVE

X = DISTANCE FROM BVC

Vertical Curve: Rate of Change

R = (G₂ - G₁) / L

G = GRADE

L = LENGTH OF CURVE

Four types of circular curves

simple curve, compound curve, broken-back curve, reverse curve