Problem 6

An equal tangent vertical crest curve is 1500 ft long and has the following grades:

g1 = 3% and g2 = -4%. What is the elevation of its vertex V if the elevation of the

BVC is 5180 ft?

Problem 7

At what distance from the BVC is the high point of the curve in problem 6?

Problem 8

Using 100' stationing, what is the minimum sight distance required with a curve

20 stations long and the following information: grades g1 = +3.7%, g2 = -2.9%,

h1 = 3.5 ft, h2= 3.0 ft. Assume S

s²(g₁-9₂)

Hint: Rearrange L =-

2√₁/n 48+00

YBVC

48+50.45

I

Tangent

49+00

L/2

Vertical Curve Hints

g1= -6.6%

50+00

d

Xpvi

University of Colorado - Denver

L12

-Ypvi

51+00

1/2

g2= +5.4%

L/2

52+00

Tangent

YEVC

Stations

X

1. Stations are counted from way back, from some starting point along the highway. Note how they count

100-foot segments. So, the counting started some 50 stations back, and here we are at about 5000 ft

from that start. This "stations" axis is at ground level.

53+00

2. Each curve has its own X axis, that starts where the curve starts. For all practical purposes, the curve

NEVER starts at a full station, but somewhere in-between (like 48+50.45 in this case). At that point,

X=0 (or Xpvc = 0 ft). This X axis is at ground level, and only goes from beginning to end of one curve.

3. All Y values are actual elevations (related to datum or sea level). They are expressed in the same units

as the X values (feet in this case). In Colorado, these values are 5,280' or more. Elevations are not

restricted to just this one curve. These elevations come from the overall vertical design of a highway,

following the positions of the vertical tangents.

Engineering Surveying CVEN 2212 4. Units of curve parameters follow one basic rule that applied to all mathematical equations: Units have

to match. An equation that mixes units does not work, as in the case of Y[ft] =g1 [%] + 500 [oranges].

It is necessary to perform a "dimensional analysis". If every parameter has the same units, then things

work. See the example below, while keeping in mind that:

●

●

L can be a distance in [feet] or in [number of stations]

g1 and g2 can be in [%] or in decimals (a simple number like -0.03)

A grade expressed in % (or "per-cent") demands a distance expressed as a number (like “number of

stations"). Example:_r=(g2-g1)/L, where r results in [%] (it is the rate of change of grade, which

is a percentage of grade per station).

The equation Y = YBvc + 9₁ X +

X² only works when:

Y is a distance (elevation)

YBVC is a distance (elevation)

... gl X is a distance and g1 must be in decimals, like -0.03

() x² must be a distance, and therefore r must be a distance-¹ (or g1 and g2 are decimals and L

is in feet)

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Engineering Surveying CVEN 2212