FUNDAMENTAL SURVEYING Horizontal and Vertical Curves 3

Question 1

Parabolic curves are preferred over circular arcs for vertical curves in highway design because they:

Accepted Answer

Provide a uniform rate of change of grade throughout the curve length

Answer

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.

Question 2

On a parabolic vertical curve, the high point (or low point) is located where:

Accepted Answer

The grade of the curve (instantaneous slope) equals zero

Answer

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.

Question 3

The length of a vertical curve is formally measured as:

Accepted Answer

The horizontal distance from PVC to PVT

Answer

Vertical curve length L is defined as the horizontal distance between the PVC (start) and PVT (end) of the curve, not the arc length.

Question 4

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:

Accepted Answer

The square of the distance x from the PVC

Answer

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.

Question 5

A sag vertical curve is described as one where:

Accepted Answer

The algebraic difference A = g2 − g1 is positive and the curve is concave upward

Answer

A sag curve is concave upward (bowl-shaped), where A = g2 − g1 > 0, meaning the vehicle descends then ascends — like driving through a valley.

FUNDAMENTAL SURVEYING Practice Test

FUNDAMENTAL SURVEYING Practice Test

FUNDAMENTAL SURVEYING Horizontal and Vertical Curves 3