Length of Curve when S is Less than L and h1 and h2 are same Calculator

Length of Curve Formula:

\[ L_c = \frac{(g_1 - g_2) \times SSD^2}{800 \times h} \]

Upgrade (g₁):

Downgrade (g₂):

Sight Distance (SSD):

meters

Height of Vertical Curves (h):

meters

Length of Curve (Lc): meters

1. What is Length of Curve when S is Less than L and h1 and h2 are same?

Definition: This calculator determines the required length of a vertical curve when the sight distance is less than the curve length and the heights of driver's eye and object are equal.

Purpose: It helps highway engineers design safe vertical curves that provide adequate sight distance for drivers.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_c = \frac{(g_1 - g_2) \times SSD^2}{800 \times h} \]

Where:

\( L_c \) — Length of vertical curve (meters)
\( g_1 \) — Upgrade gradient (%)
\( g_2 \) — Downgrade gradient (%)
\( SSD \) — Sight stopping distance (meters)
\( h \) — Height of driver's eye/object (meters)

Explanation: The formula calculates the minimum curve length needed to provide the required sight distance based on the algebraic difference between grades and eye/object height.

3. Importance of Curve Length Calculation

Details: Proper vertical curve design ensures driver safety by providing adequate visibility to stop or make decisions, especially at crest vertical curves.

4. Using the Calculator

Tips:

Enter upgrade and downgrade as percentages (e.g., 2.5% upgrade, -1.5% downgrade)
Sight distance should be the stopping sight distance for the design speed
Typical eye height (h) is 1.07 meters (3.5 ft) for passenger vehicles

5. Frequently Asked Questions (FAQ)

Q1: When is this formula applicable?
A: This formula is used when the sight distance (S) is less than the curve length (L) and when the heights of driver's eye and object are equal.

Q2: How do I determine the sight distance?
A: Sight distance depends on design speed, driver reaction time, and braking efficiency. Use standard tables or SSD formulas.

Q3: What's the typical height value (h)?
A: For passenger vehicles, h is typically 1.07m (3.5 ft). For trucks, use 2.13m (7 ft).

Q4: How do grades affect the curve length?
A: The greater the algebraic difference between grades (g₁ - g₂), the longer the required curve length for the same sight distance.

Q5: What if S is greater than L?
A: A different formula is used when sight distance exceeds curve length: \( L = 2S - \frac{800h}{(g_1 - g_2)} \)