Length of Curve when S is Less than L Calculator

Length of Curve Formula:

\[ L_c = \frac{SSD^2 \times (g_1 - g_2)}{200 \times (\sqrt{H} + \sqrt{h_2})^2} \]

Sight Distance (SSD):

meters

Upgrade (g₁):

Downgrade (g₂):

Height of Observer (H):

meters

Height of Object (h₂):

meters

Length of Curve (Lc): meters

1. What is Length of Curve when S is Less than L?

Definition: This calculation determines the minimum length of a vertical curve required when the sight distance (S) is less than the curve length (L).

Purpose: It ensures safe sight distances for drivers on vertical curves in road design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_c = \frac{SSD^2 \times (g_1 - g_2)}{200 \times (\sqrt{H} + \sqrt{h_2})^2} \]

Where:

\( L_c \) — Length of curve (meters)
\( SSD \) — Stopping sight distance (meters)
\( g_1 \) — Upgrade gradient (%)
\( g_2 \) — Downgrade gradient (%)
\( H \) — Height of observer's eye (meters)
\( h_2 \) — Height of object (meters)

Explanation: The formula calculates the curve length needed to provide adequate sight distance considering vertical grades and eye/object heights.

3. Importance of Curve Length Calculation

Details: Proper curve length ensures driver safety by providing sufficient visibility to stop or maneuver when encountering obstacles.

4. Using the Calculator

Tips: Enter all required values. Note that upgrade and downgrade can be positive or negative values (use negative for opposite directions).

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for observer and object heights?
A: Standard values are 1.2m for driver eye height and 0.15m for object height.

Q2: How do I input downgrade values?
A: Enter as negative percentage (e.g., -2.5% for a 2.5% downgrade).

Q3: When is this formula applicable?
A: When the sight distance (S) is less than the curve length (L).

Q4: What units should be used?
A: All distance measurements should be in meters, gradients in percentage.

Q5: How does grade affect the calculation?
A: Steeper grade differences require longer curves to maintain sight distance.