Mdot Vertical Curve Calculator

MDOT Vertical Curve Formula:

\[ L = \frac{A \times S^2}{2 \times h + 2 \times H \times \tan(\theta)} \]

A (percentage):

S (feet):

h (feet):

H (feet):

θ (degrees):

Calculated Length (L):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the MDOT Vertical Curve Formula?

The MDOT Vertical Curve formula calculates the required length (L) of a vertical curve based on sight distance requirements. It considers the algebraic difference in grades (A), sight distance (S), eye height (h), object height (H), and the angle of inclination (θ).

2. How Does the Calculator Work?

The calculator uses the MDOT Vertical Curve formula:

\[ L = \frac{A \times S^2}{2 \times h + 2 \times H \times \tan(\theta)} \]

Where:

\( L \) — Length of vertical curve (feet)
\( A \) — Algebraic difference in grades (percentage)
\( S \) — Sight distance (feet)
\( h \) — Height of driver's eye above roadway (feet)
\( H \) — Height of object above roadway (feet)
\( \theta \) — Angle of inclination (degrees)

Explanation: The formula ensures adequate sight distance is maintained on vertical curves for safe highway design.

3. Importance of Vertical Curve Calculation

Details: Proper vertical curve design is essential for highway safety, providing smooth transitions between different grades and ensuring adequate stopping sight distance.

4. Using the Calculator

Tips: Enter all values in the specified units. A is the absolute value of the difference between entering and exiting grades. Typical values: h = 3.5 ft, H = 2.0 ft for passenger vehicles.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for eye height (h) and object height (H)?
A: For passenger vehicles: h = 3.5 ft, H = 2.0 ft. For trucks: h = 7.6 ft, H = 2.0 ft.

Q2: How is A (algebraic difference) calculated?
A: A is the absolute value of (grade2 - grade1), where grades are expressed as percentages (e.g., 5% grade = 5).

Q3: What's the minimum recommended sight distance?
A: Depends on design speed. For example: 30 mph = 200 ft, 60 mph = 570 ft (stopping sight distance).

Q4: When is this formula most applicable?
A: For crest vertical curves where sight distance is limited by the curve itself rather than roadway features.

Q5: How does θ affect the calculation?
A: Higher θ values (steeper inclinations) generally result in longer required curve lengths for the same sight distance.