Calculation Of Simple Vertical Curve

Simple Vertical Curve Equation:

\[ elevation = PVC_{elev} + g1 \times x + \frac{(g2 - g1) \times x^2}{2 \times L} \]

PVC Elevation (PVC_elev):

feet

Initial Grade (g1):

Distance from PVC (x):

feet

Final Grade (g2):

Curve Length (L):

feet

Elevation:

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1. What is the Simple Vertical Curve Equation?

The Simple Vertical Curve Equation calculates the elevation at any point along a vertical curve in roadway or railway design. It accounts for the transition between two different grades (slopes) to ensure smooth vertical alignment.

2. How Does the Calculator Work?

The calculator uses the vertical curve equation:

\[ elevation = PVC_{elev} + g1 \times x + \frac{(g2 - g1) \times x^2}{2 \times L} \]

Where:

\( PVC_{elev} \) — Elevation at Point of Vertical Curve (PVC) in feet
\( g1 \) — Initial grade (percentage)
\( x \) — Distance from PVC along the curve in feet
\( g2 \) — Final grade (percentage)
\( L \) — Length of the vertical curve in feet

Explanation: The equation combines the initial elevation with the linear effect of the initial grade and the parabolic adjustment for the grade change.

3. Importance of Vertical Curve Calculation

Details: Proper vertical curve design is essential for driver comfort, safety, drainage, and sight distance in transportation engineering projects.

4. Using the Calculator

Tips: Enter all values in consistent units (feet for distances, % for grades). Ensure curve length (L) is positive and distance (x) is non-negative and within the curve length.

5. Frequently Asked Questions (FAQ)

Q1: What is PVC in vertical curves?
A: PVC stands for Point of Vertical Curve - the point where the initial grade (g1) begins to transition to the final grade (g2).

Q2: What's the difference between sag and crest vertical curves?
A: Crest curves occur when the change is from positive to negative grade (hilltop), while sag curves occur when changing from negative to positive grade (valley).

Q3: How do I determine the appropriate curve length?
A: Curve length depends on design speed, algebraic difference in grades, and design standards (AASHTO provides guidelines).

Q4: What is the high/low point on a vertical curve?
A: The point where the derivative of the elevation equation equals zero, found at \( x = (g1 \times L)/(g1 - g2) \).

Q5: Can this be used for unsymmetrical vertical curves?
A: No, this equation is only for simple (symmetrical) vertical curves. Compound curves require different calculations.