Length of Summit Curve Less than Sight Distance Calculator

Length of Curve Formula:

\[ L_s = 2S - \frac{(\sqrt{2h_1} + \sqrt{2h_2})^2}{N} \]

Sight Distance (S):

Driver Sight Height (h₁):

Obstruction Height (h₂):

Deviation Angle (N):

rad

Tolerance:

Length of Curve (Ls): m

1. What is Length of Summit Curve Less than Sight Distance?

Definition: This calculator determines the minimum length of a summit (crest) vertical curve when the sight distance is less than the curve length.

Purpose: It ensures adequate sight distance for drivers approaching a crest curve, preventing accidents due to limited visibility.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_s = 2S - \frac{(\sqrt{2h_1} + \sqrt{2h_2})^2}{N} \]

Where:

\( L_s \) — Length of summit curve (meters)
\( S \) — Sight distance (meters)
\( h_1 \) — Driver's eye height (meters, typically 1.05m)
\( h_2 \) — Obstruction height (meters, typically 0.15m)
\( N \) — Deviation angle (radians)

Explanation: The formula calculates the curve length needed to maintain visibility between a driver and an obstruction on the road.

3. Importance of Summit Curve Calculation

Details: Proper summit curve design prevents blind spots, ensures safe stopping distances, and complies with transportation engineering standards.

4. Using the Calculator

Tips: Enter sight distance, driver height (default 1.05m), obstruction height (default 0.15m), deviation angle, and tolerance percentage (default ±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's the typical driver eye height?
A: Standard is 1.05m for passenger vehicles, but may vary for trucks (2.0m) or motorcycles (1.2m).

Q2: Why is obstruction height typically 0.15m?
A: This represents the height of taillights on most vehicles, ensuring you can see the vehicle ahead.

Q3: How do I determine deviation angle?
A: It's the algebraic difference between incoming and outgoing grades (e.g., +3% to -2% = 5% or 0.05 rad).

Q4: When would I adjust the tolerance?
A: For critical applications (high-speed roads), use lower tolerance (2-3%). For rough estimates, higher tolerance (5-10%) may suffice.

Q5: What if my sight distance exceeds curve length?
A: Use a different formula: \( L_s = \frac{NS^2}{(\sqrt{2h_1} + \sqrt{2h_2})^2} \) when \( S < L \).