Podcast
Questions and Answers
What does the intersection angle (I) represent in a simple circular curve?
What does the intersection angle (I) represent in a simple circular curve?
- The angle subtended at the center of the circle.
- The angle formed by the radius and the tangent.
- The angle by which the forward tangent deflects from the back tangent. (correct)
- The angle between two tangent lines.
Which of the following correctly describes the term 'middle ordinate' in the context of a circular curve?
Which of the following correctly describes the term 'middle ordinate' in the context of a circular curve?
- The distance from the mid-point of the long chord to the mid-point of the circular curve. (correct)
- The distance from the point of intersection to the tangent distance.
- The length of the arc between the point of curvature and the point of tangency.
- The distance from the vertex to the mid-point of the circular curve.
In circular curves, what is the relationship between the radius (R) and the degree of curve (D0)?
In circular curves, what is the relationship between the radius (R) and the degree of curve (D0)?
- Degree of curve is independent of radius.
- Sharpness can be described by either radius or degree of curve. (correct)
- A smaller radius indicates a smaller degree of curve.
- A larger radius means a sharper curve.
What does 'long chord (C)' refer to in a circular curve?
What does 'long chord (C)' refer to in a circular curve?
Which statement accurately defines the term 'tangent distance (T)' in the context of simple circular curves?
Which statement accurately defines the term 'tangent distance (T)' in the context of simple circular curves?
What is the formula for calculating offset Y in the context of the given procedures?
What is the formula for calculating offset Y in the context of the given procedures?
How is the offset at 10m calculated based on the provided information?
How is the offset at 10m calculated based on the provided information?
What is the significance of the deviation angle Δ in the calculations?
What is the significance of the deviation angle Δ in the calculations?
In the context of offsets from the long chord, what characteristic is primarily utilized?
In the context of offsets from the long chord, what characteristic is primarily utilized?
What does the length T represent in the calculation procedures?
What does the length T represent in the calculation procedures?
What is the angle $ heta_i$ between the tangent to the transition curve at point i and the entry straight calculated from?
What is the angle $ heta_i$ between the tangent to the transition curve at point i and the entry straight calculated from?
In vertical curves, what does a positive algebraic difference between gradients indicate?
In vertical curves, what does a positive algebraic difference between gradients indicate?
What is the main purpose of vertical curves in road design?
What is the main purpose of vertical curves in road design?
Which type of vertical curve is characterized by equal lengths from PVC to PVI and from PVI to PVT?
Which type of vertical curve is characterized by equal lengths from PVC to PVI and from PVI to PVT?
What gradient is represented by '1 in 25'?
What gradient is represented by '1 in 25'?
Which of the following is true regarding unsymmetrical parabolic curves?
Which of the following is true regarding unsymmetrical parabolic curves?
What results from the radial force acting on a vehicle in a vertical curve?
What results from the radial force acting on a vehicle in a vertical curve?
What determines the radius of curvature at the junction of the transition curve and the simple curve?
What determines the radius of curvature at the junction of the transition curve and the simple curve?
What is the significance of the Vertex (V) in a parabolic vertical curve?
What is the significance of the Vertex (V) in a parabolic vertical curve?
Which equation represents the elevation of points on the curve based on the rate of change of grade?
Which equation represents the elevation of points on the curve based on the rate of change of grade?
Which point is defined as the point of tangency where the parabolic vertical curve meets the forward grade?
Which point is defined as the point of tangency where the parabolic vertical curve meets the forward grade?
What does the symbol 'e' represent in the context of a vertical curve?
What does the symbol 'e' represent in the context of a vertical curve?
In the equation for determining offsets, which variable represents the length of the curve?
In the equation for determining offsets, which variable represents the length of the curve?
What gradient does the back tangent have in the example provided?
What gradient does the back tangent have in the example provided?
What is the correct expression for the elevation on the tangent?
What is the correct expression for the elevation on the tangent?
How is the length of the vertical curve (L) defined?
How is the length of the vertical curve (L) defined?
What is the elevation at the PVC station (4+920)?
What is the elevation at the PVC station (4+920)?
At a distance of 20m from the EPVC, what is the calculated EPC?
At a distance of 20m from the EPVC, what is the calculated EPC?
What is the value of y when calculating the elevation on a curve?
What is the value of y when calculating the elevation on a curve?
What is the elevation at station 5+000?
What is the elevation at station 5+000?
For an upward gradient of 3% meeting a downward gradient of 2%, what is the difference in elevation at station 1000.00?
For an upward gradient of 3% meeting a downward gradient of 2%, what is the difference in elevation at station 1000.00?
What factor is used to modify the elevation on a curve based on the length of the curve?
What factor is used to modify the elevation on a curve based on the length of the curve?
At an offset of +1.20 at station 5+000, how does the elevation change compared to the previous station?
At an offset of +1.20 at station 5+000, how does the elevation change compared to the previous station?
What does g1 represent in this context?
What does g1 represent in this context?
How is the elevation on a tangent (EPT) calculated from EPVC?
How is the elevation on a tangent (EPT) calculated from EPVC?
What happens to the elevation as one moves further along the tangent from EPVC?
What happens to the elevation as one moves further along the tangent from EPVC?
What is the calculation used to determine EPC at the full station of 4+940?
What is the calculation used to determine EPC at the full station of 4+940?
What is the slope of the tangent calculated at the point of intersection of gradients?
What is the slope of the tangent calculated at the point of intersection of gradients?
Which elevation represents the peak height at 5+020?
Which elevation represents the peak height at 5+020?
What is the formula used to calculate the offset Yn when given a radius R and a distance Xn?
What is the formula used to calculate the offset Yn when given a radius R and a distance Xn?
If the deviation angle is 60 degrees, what is the value of C when R = 50m?
If the deviation angle is 60 degrees, what is the value of C when R = 50m?
In the example provided, what is the offset at 20m based on the calculated values?
In the example provided, what is the offset at 20m based on the calculated values?
Calculate the ordinates for points at intervals of 20m on a circular curve with a long chord of 120m. What is the versed sine when the offset is given as 5m?
Calculate the ordinates for points at intervals of 20m on a circular curve with a long chord of 120m. What is the versed sine when the offset is given as 5m?
What is the correct radius R when the offset Yn at 10m is calculated using Yn = (R^2 - Xn^2) - a?
What is the correct radius R when the offset Yn at 10m is calculated using Yn = (R^2 - Xn^2) - a?
For the given offset Yn = (R^2 - Xn^2) - [R^2 - (C^2)], what does C represent in this scenario?
For the given offset Yn = (R^2 - Xn^2) - [R^2 - (C^2)], what does C represent in this scenario?
When calculating the offsets at various intervals from the tangents, what is the maximum value of Yn calculated in the example given?
When calculating the offsets at various intervals from the tangents, what is the maximum value of Yn calculated in the example given?
Which of the following is NOT involved in the calculation of offsets in the given examples?
Which of the following is NOT involved in the calculation of offsets in the given examples?
When determining the ordinates for a circular curve having a long chord of 120m and a versed sine of 5m, what is the method of measurement?
When determining the ordinates for a circular curve having a long chord of 120m and a versed sine of 5m, what is the method of measurement?
For a deviation angle of Δ = 45 degrees, what would be the value of C if R = 60m?
For a deviation angle of Δ = 45 degrees, what would be the value of C if R = 60m?
Flashcards
Vertex (V)
Vertex (V)
The point where two tangent lines intersect, marking the start and end of a curve.
Point of Curvature (PC)
Point of Curvature (PC)
The point where the straight tangent line transitions into the curve. It's the beginning of the circular curve.
Point of Tangency (PT)
Point of Tangency (PT)
The point where the circular curve transitions back to a straight tangent line.
Tangent Distance (T)
Tangent Distance (T)
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Intersection Angle (I) or Δ
Intersection Angle (I) or Δ
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Angle of a transition curve (θi)
Angle of a transition curve (θi)
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Length of a transition curve (LT)
Length of a transition curve (LT)
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Radius of curvature at the junction (R)
Radius of curvature at the junction (R)
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Distance along the transition curve (li)
Distance along the transition curve (li)
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Vertical Curve
Vertical Curve
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Crest Curve
Crest Curve
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Sag Curve
Sag Curve
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Parabolic Vertical Curve
Parabolic Vertical Curve
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Length of Vertical Curve (L)
Length of Vertical Curve (L)
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Symmetrical Parabolic Curve
Symmetrical Parabolic Curve
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Rate of Change of Grade (R)
Rate of Change of Grade (R)
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Method I: Based on Rate of Change of Grade
Method I: Based on Rate of Change of Grade
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Method II: Based on the Rule of Offsets
Method II: Based on the Rule of Offsets
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Offset from the tangent
Offset from the tangent
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Offset Formula
Offset Formula
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Offset from the long chord
Offset from the long chord
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Major Offset
Major Offset
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Constant 'a'
Constant 'a'
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Point of Vertical Intersection (PVI)
Point of Vertical Intersection (PVI)
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Length (L)
Length (L)
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Point of Vertical Curvature (PVC)
Point of Vertical Curvature (PVC)
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Elevation of PVC (EPVC)
Elevation of PVC (EPVC)
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Point of Vertical Tangency (PVT)
Point of Vertical Tangency (PVT)
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Elevation of PVT (EPVT)
Elevation of PVT (EPVT)
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Elevation Difference (ED)
Elevation Difference (ED)
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Elevation on Curve (EPC)
Elevation on Curve (EPC)
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Calculating EPC
Calculating EPC
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Elevation on Tangent (EPT)
Elevation on Tangent (EPT)
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Vertical Offset (y)
Vertical Offset (y)
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Radius (R)
Radius (R)
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Versine (C)
Versine (C)
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X
X
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Offset (Y)
Offset (Y)
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Deviation Angle (Δ)
Deviation Angle (Δ)
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Study Notes
Unit Three Curve
- Route Surveying encompasses surveying and mapping activities for planning, designing, and constructing transportation facilities like roads, railways, pipelines, and power transmission lines.
- Alignment refers to the shape or geometry of a transportation route, including horizontal and vertical components (plan and profile views).
- Horizontal alignment comprises a series of straight lines (tangents) connected by curves.
- Vertical alignment consists of straight segments (gradients) connected by vertical curves.
- Plan view elements include: bearing of tangents, angle of intersection, stationing, geometric data for horizontal curves, topography near the centerline, and details of existing structures affected by the project.
- Profile view elements include: existing ground surface, proposed route grade line, grades of tangents, and vertical curve data.
Types of Curves and Their Uses
- Curves are essential to gradually change direction in communication routes (roads, railways, canals).
- Two main curve types exist: horizontal and vertical curves.
- Horizontal curves connect tangents, usually circular but spirals may be used for transitions.
- Sharpness of a circular curve is defined by its radius (R) or degree of curve (D°).
- Simple circular curve is the most common type, joining two intersecting tangents.
Elements of Simple Circular Curve
- Vertex (V): point of intersection of the two tangents.
- Point of Curvature(PC): tangent point where curve begins.
- Point of Tangency (PT): tangent point where curve ends.
- Tangent Distance (T): distance from vertex to PC/PT.
- Intersection Angle (I): the angle between the tangents.
- Radius (R): radius of the circle.
- External Distance (E): distance from vertex to the midpoint of the curve.
- Long Chord (C): distance from PC to PT.
- Middle Ordinate (M): distance from the midpoint of long chord to the curve midpoint.
- Degree of Curve (D°): a way of describing the curve's sharpness, defined by the central angle subtended by a 20m arc or chord length.
Compound Circular Curve
- Consists of two or more simple curves with varying radii. Used to provide smoother transitions when changing curvature.
Reverse Circular Curve
- Two consecutive circular curves with the same or different radii. They might share a common tangent.
Spiral Curve or Transition Curve
- Used to transition from tangent to circular curve and from circular curve back to tangent.
- Gradually changes radius of curvature from infinity to a fixed value, to smoothly introduce radial force on vehicles.
- Properties: radial force change is gradual and constant.
- Another important function: smoothly introducing superelevation.
Vertical Curve
- Used to connect gradients (slope changes) in the vertical plane.
- Crest or summit curves have negatively calculated algebraic difference of gradients.
- Sag or valley curves have positively calculated algebraic difference of gradients.
- Generally parabolic, providing consistent rate of change of grade.
Equations of Vertical Curves
- Symmetrical parabola equations are used.
- Equations determine elevation(vertical offset) at any point along the curve given horizontal distances and other parameters.
Methods of Setting Out
- Detail center line survey is often used before construction.
- Deflection angle method uses theodolite measures along the curve using the chord lengths.
- Linear methods uses offsets from tangents to define points on a curve.
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