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

Are simpler to stake in the field than circular arcs

Answer

Always produce the longest available sight distance

Answer

Require less earthwork volume than equivalent circular arcs

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 PVI is positioned along the alignment

Answer

The horizontal distance equals exactly half the curve length

Answer

The elevation equals the elevation of the PVI

Question 3

The length of a vertical curve is formally measured as:

Accepted Answer

The horizontal distance from PVC to PVT

Answer

The arc distance along the parabolic curve

Answer

The vertical distance from the PVI to the midpoint of the curve

Answer

The slope distance along the steeper incoming grade

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

The distance x from the PVC

Answer

The algebraic grade difference A = g2 − g1 only

Answer

The distance from the PVI to the point

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

The first grade g1 is greater than the second grade g2 (concave downward)

Answer

Both approach and departure grades are ascending

Answer

The grades are equal, producing a flat section

Question 6

The minimum length of a crest vertical curve is most commonly governed by:

Accepted Answer

Stopping sight distance for a driver approaching an obstacle

Answer

Headlight sight distance for nighttime driving

Answer

Passing sight distance between two opposing vehicles

Answer

The minimum algebraic grade difference A required by design standards

Question 7

The elevation at a distance x from the PVC on a parabolic vertical curve is calculated using:

Accepted Answer

Elev = Elev_PVC + g1·x + (A / 2L)·x²

Answer

Elev = Elev_PVI + g2·x − (A / 2L)·x²

Answer

Elev = Elev_PVC + ((g1 + g2) / 2)·x

Answer

Elev = Elev_PVC + g1·x − g2·x²