Length of Curve when Height of Observer and Object are Same Calculator

Length of Curve Formula:

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

Sight Distance (SSD):

meters

Height of Vertical Curves:

meters

Upgrade (g₁):

Downgrade (g₂):

Length of Curve (Lc): meters

1. What is Length of Curve when Height of Observer and Object are Same?

Definition: This calculator determines the minimum length of a vertical curve when the height of the observer and object are equal, based on sight distance, curve height, and grade changes.

Purpose: It helps transportation engineers design safe vertical curves that provide adequate stopping sight distance.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( L_c \) — Length of vertical curve (meters)
\( SSD \) — Stopping sight distance (meters)
\( h \) — Height of observer and object (meters)
\( g_1 \) — Upgrading slope (%)
\( g_2 \) — Downgrading slope (%)

Explanation: The formula ensures the curve length provides sufficient visibility when driver's eye height and object height are equal.

3. Importance of Length of Curve Calculation

Details: Proper vertical curve length is critical for road safety, preventing accidents by ensuring drivers can see obstacles in time to stop.

4. Using the Calculator

Tips: Enter the stopping sight distance (SSD), height of vertical curves, upgrade percentage (positive value), and downgrade percentage (negative value).

5. Frequently Asked Questions (FAQ)

Q1: What is standard height for observer and object?
A: Typically 1.08 meters for driver's eye height and 0.6 meters for object height, but this calculator assumes they're equal.

Q2: How does grade affect curve length?
A: Steeper grade differences require longer curves to maintain sight distance.

Q3: What if denominator (g₁-g₂) is zero?
A: The calculation is undefined when upgrade equals downgrade (flat grade).

Q4: When is this formula applicable?
A: For crest vertical curves where the height of observer and object are equal.

Q5: How to determine stopping sight distance?
A: SSD depends on design speed, driver reaction time, and deceleration rate.