FUNDAMENTAL SURVEYING Horizontal and Vertical Curves 1 — Questions and Answers
Question 1: According to the arc definition, the degree of curve (Da) is the central angle subtended by an arc of what length?
- 25 feet
- 50 feet
- 100 feet (Correct answer)
- 200 feet
Correct answer: 100 feet
The arc definition states that the degree of curve is the central angle subtended by a 100-foot arc, which is the standard used in US highway surveying.
Question 2: Which formula correctly expresses the tangent length (T) of a simple circular horizontal curve?
- T = R × sin(Δ/2)
- T = R × tan(Δ/2) (Correct answer)
- T = R × cos(Δ/2)
- T = R / sin(Δ/2)
Correct answer: T = R × tan(Δ/2)
The tangent length T = R × tan(Δ/2) is derived from the right triangle formed by the radius, the PI, and the PC.
Question 3: The external distance (E) of a horizontal curve is the distance from:
- The PC to the PT measured along the arc
- The PI to the midpoint of the arc (Correct answer)
- The PC to the midpoint of the long chord
- The center of the circle to the PI minus R
Correct answer: The PI to the midpoint of the arc
The external distance E is the distance from the PI (Point of Intersection) to the midpoint of the curve, calculated as E = R × (1/cos(Δ/2) − 1).
Question 4: For a horizontal curve with R = 500 ft and intersection angle Δ = 60°, what is the arc length?
- 261.8 feet
- 523.6 feet (Correct answer)
- 600.0 feet
- 314.2 feet
Correct answer: 523.6 feet
Arc length L = πRΔ/180 = π × 500 × 60/180 = 523.6 feet.
Question 5: The Point of Curvature (PC) in a horizontal curve alignment is defined as:
- The point where two tangents intersect
- The point where the straight tangent ends and the circular curve begins (Correct answer)
- The point where the circular curve returns to the tangent
- The center point of the circular curve
Correct answer: The point where the straight tangent ends and the circular curve begins
The PC (Point of Curvature) marks where the back tangent ends and the circular curve begins; the alignment sequence is PI → PC → curve → PT.
Question 6: A compound curve is best described as:
- Two curves of equal radius turning in opposite directions
- Two or more curves of different radii all curving in the same direction (Correct answer)
- A curve with a continuously changing radius throughout
- A circular curve combined with a straight tangent section
Correct answer: Two or more curves of different radii all curving in the same direction
A compound curve consists of two or more simple circular arcs of different radii that all turn in the same direction, joined at Points of Compound Curvature (PCC).
Question 7: The middle ordinate (M) of a horizontal curve is the distance measured from:
- The PI to the PC along the tangent
- The midpoint of the long chord to the midpoint of the arc (Correct answer)
- The PC to the PT along the tangent
- The center of the circle to the midpoint of the chord
Correct answer: The midpoint of the long chord to the midpoint of the arc
The middle ordinate M is the perpendicular distance from the midpoint of the long chord to the midpoint of the arc, calculated as M = R × (1 − cos(Δ/2)).
FUNDAMENTAL SURVEYING Horizontal and Vertical Curves 1
According to the arc definition, the degree of curve (Da) is the central angle subtended by an arc of what length?