FUNDAMENTAL SURVEYING Horizontal and Vertical Curves 2 — Questions and Answers
Question 1: Using the chord definition, the degree of curve (Dc) is the central angle subtended by a chord of:
- 50 feet
- 100 feet (Correct answer)
- 200 feet
- 300 feet
Correct answer: 100 feet
Both the arc and chord definitions use a 100-foot standard length; the chord definition uses a 100-foot chord rather than a 100-foot arc.
Question 2: A reverse curve is characterized by:
- Two curves of different radii turning in the same direction
- Two simple curves joined at a point where they turn in opposite directions (Correct answer)
- A curve with a uniformly increasing radius
- Two curves of identical radii turning in the same direction
Correct answer: Two simple curves joined at a point where they turn in opposite directions
A reverse curve consists of two simple circular curves that curve in opposite directions, joined at the Point of Reverse Curvature (PRC), forming an S-shape.
Question 3: The long chord (C) of a simple horizontal curve connecting PC to PT is given by:
- C = R × sin(Δ)
- C = 2R × sin(Δ/2) (Correct answer)
- C = 2R × tan(Δ/2)
- C = R × (1 − cos(Δ/2))
Correct answer: C = 2R × sin(Δ/2)
The long chord C = 2R × sin(Δ/2), derived from the isosceles triangle formed by the two radii drawn to PC and PT and the chord itself.
Question 4: A spiral (transition) curve inserted between a straight tangent and a circular curve primarily serves to:
- Increase the degree of curve abruptly at the PC
- Provide a gradual change in centrifugal force and allow smooth superelevation runoff (Correct answer)
- Shorten the total alignment length between two control points
- Eliminate the need for superelevation on the circular curve
Correct answer: Provide a gradual change in centrifugal force and allow smooth superelevation runoff
Spiral curves allow the centrifugal force and superelevation to increase gradually from zero on the tangent to their full values on the circular curve, improving driver comfort and safety.
Question 5: Using the arc definition, what is the radius of a 2-degree curve?
- 1,000.0 feet
- 2,864.8 feet (Correct answer)
- 5,729.6 feet
- 573.0 feet
Correct answer: 2,864.8 feet
R = 5729.58 / Da = 5729.58 / 2 = 2864.79 ≈ 2,864.8 feet, using the standard arc-definition relationship.
Question 6: Superelevation on a horizontal curve is designed primarily to:
- Improve cross-slope drainage away from the roadway centerline
- Counteract the centrifugal force acting on vehicles navigating the curve (Correct answer)
- Allow higher posted speed limits on curved sections
- Reduce the required pavement structural thickness on curves
Correct answer: Counteract the centrifugal force acting on vehicles navigating the curve
Superelevation tilts the roadway inward on a curve so that the component of gravity helps counteract centrifugal force, improving vehicle stability and safety.
Question 7: When staking a horizontal curve using the deflection angle method, the deflection angle from the PC to any point on the curve equals:
- The full central angle subtended to that point
- Half the central angle subtended by the arc from PC to that point (Correct answer)
- The intersection angle divided by the total number of stations
- The bearing angle from the PC to the given point
Correct answer: Half the central angle subtended by the arc from PC to that point
By the inscribed angle theorem, the deflection angle from the PC equals half the central angle subtended by the arc from the PC to that point.
FUNDAMENTAL SURVEYING Horizontal and Vertical Curves 2
Using the chord definition, the degree of curve (Dc) is the central angle subtended by a chord of: