Positive Grade Angle Given Sight Distance Calculator by Tons of Concrete

Positive Grade Angle Given Sight Distance Calculator

Positive Grade Angle Formula:

\[ n_1 = \frac{h_1}{S - \frac{L_s}{2} - \frac{h_2}{n_2}} \]

Driver Sight Height (h₁):

Sight Distance (S):

Length of Curve (Lₛ):

Height of Obstruction (h₂):

Negative Grade Angle (n₂):

Positive Grade Angle (n₁):

1. What is Positive Grade Angle Given Sight Distance?

Definition: This calculator determines the required positive grade angle (n₁) based on driver sight height, sight distance, curve length, obstruction height, and negative grade angle.

Purpose: It helps transportation engineers design safe vertical curves by ensuring adequate sight distance for drivers.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ n_1 = \frac{h_1}{S - \frac{L_s}{2} - \frac{h_2}{n_2}} \]

Where:

\( n_1 \) — Positive grade angle (%)
\( h_1 \) — Driver's eye height (m)
\( S \) — Sight distance (m)
\( L_s \) — Length of vertical curve (m)
\( h_2 \) — Height of obstruction (m)
\( n_2 \) — Negative grade angle (%)

Explanation: The formula calculates the required upward slope to ensure visibility over an obstruction when transitioning from a downward slope.

3. Importance of Positive Grade Angle Calculation

Details: Proper calculation ensures safe stopping sight distance, prevents blind spots, and meets transportation safety standards.

4. Using the Calculator

Tips: Enter all required measurements in meters except grade angles which are in percentage. Negative grade angle should be entered as a negative value.

5. Frequently Asked Questions (FAQ)

Q1: What's a typical driver eye height?
A: Standard is 1.08m (3.5ft) for passenger cars, 2.33m (7.6ft) for trucks.

Q2: How is sight distance determined?
A: Based on design speed, reaction time, and braking distance per AASHTO standards.

Q3: What if my result is negative?
A: A negative n₁ indicates the sight distance requirement isn't met with current parameters.

Q4: Typical obstruction heights?
A: Often 0.6m (2ft) for opposing vehicles, or actual obstacle height.

Q5: How does curve length affect the result?
A: Longer curves generally require gentler grade changes to maintain sight distance.