Deviation Angle given Length of Summit Curve Calculator

Deviation Angle Formula:

\[ N = \frac{2 \times L_s \times (\sqrt{h1} + \sqrt{h2})^2}{S^2} \]

Length of Curve (L_s):

Driver Sight Height (h1):

Height of Obstruction (h2):

Sight Distance (S):

Tolerance:

Deviation Angle (N):

1. What is Deviation Angle in Summit Curves?

Definition: The deviation angle (N) represents the angle change needed in a summit curve to ensure proper visibility for drivers.

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

2. How Does the Calculator Work?

The calculator uses the formula:

\[ N = \frac{2 \times L_s \times (\sqrt{h1} + \sqrt{h2})^2}{S^2} \]

Where:

\( N \) — Deviation angle
\( L_s \) — Length of summit curve (meters)
\( h1 \) — Driver's eye height (meters, typically 0.75m)
\( h2 \) — Obstruction height (meters, typically 0.36m)
\( S \) — Required sight distance (meters)

3. Importance of Deviation Angle Calculation

Details: Proper calculation ensures safe vertical curves that provide sufficient visibility for drivers to stop for obstacles.

4. Using the Calculator

Tips: Enter the curve length, driver eye height (default 0.75m), obstruction height (default 0.36m), sight distance, and tolerance percentage (default ±5%).

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for h1 and h2?
A: h1 (driver eye height) is typically 0.75m for cars. h2 (obstruction height) is typically 0.36m (tail light height).

Q2: How does tolerance affect the results?
A: The tolerance percentage (default ±5%) provides an acceptable range for the deviation angle calculation.

Q3: When would I need to adjust the default heights?
A: For trucks (higher eye level) or different obstruction types, adjust h1 and h2 accordingly.

Q4: What's the relationship between curve length and deviation angle?
A: Longer curves typically result in smaller deviation angles for the same sight distance.

Q5: How is this used in road design?
A: Engineers use this to ensure vertical curves provide adequate stopping sight distance for the design speed.