Horizontal and Vertical Curves Flashcards
7 cards from real FUNDAMENTAL SURVEYING practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Horizontal and Vertical Curves flashcards as text
Parabolic curves are preferred over circular arcs for vertical curves in highway design because they:
Answer: Provide a uniform rate of change of grade throughout the curve length
The parabola provides a constant rate of change of grade (constant second derivative), which corresponds to uniform acceleration and is ideal for vehicle dynamics and driver comfort.
On a parabolic vertical curve, the high point (or low point) is located where:
Answer: The grade of the curve (instantaneous slope) equals zero
The high or low point occurs at the location where the parabola's instantaneous grade equals zero, i.e., where the tangent to the curve is horizontal.
The length of a vertical curve is formally measured as:
Answer: The horizontal distance from PVC to PVT
Vertical curve length L is defined as the horizontal distance between the PVC (start) and PVT (end) of the curve, not the arc length.
On a parabolic vertical curve, the vertical offset from the tangent grade to the curve at a point distance x from the PVC is proportional to:
Answer: The square of the distance x from the PVC
For a parabola, vertical offsets from the initial tangent grade vary as the square of the horizontal distance from the PVC: offset = (A / 2L) × x².
A sag vertical curve is described as one where:
Answer: The algebraic difference A = g2 − g1 is positive and the curve is concave upward
A sag curve is concave upward (bowl-shaped), where A = g2 − g1 > 0, meaning the vehicle descends then ascends — like driving through a valley.
The minimum length of a crest vertical curve is most commonly governed by:
Answer: Stopping sight distance for a driver approaching an obstacle
Stopping sight distance (SSD) governs minimum crest vertical curve length, ensuring a driver can see and stop for a hazard within their available sight distance.
The elevation at a distance x from the PVC on a parabolic vertical curve is calculated using:
Answer: Elev = Elev_PVC + g1·x + (A / 2L)·x²
The standard parabolic vertical curve equation is Elev = Elev_PVC + g1·x + (A/2L)·x², where A = g2 − g1 and L is the horizontal curve length.