Permissible Grade given Length Calculator

Permissible Rate Formula:

\[ PN = \frac{N}{L} \]

Permissible Rate (%/m):

1. What is Permissible Grade given Length?

Definition: This calculator determines the permissible rate of change in grade for vertical curves based on the change in grade and the length of the vertical curve.

Purpose: It helps engineers ensure that vertical curves in transportation design meet safety and comfort standards.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ PN = \frac{N}{L} \]

Where:

\( PN \) — Permissible Rate (%/m)
\( N \) — Change in Grade (%)
\( L \) — Length of Vertical Curve (m)

Explanation: The change in grade is divided by the length of the vertical curve to determine the permissible rate of change.

3. Importance of Permissible Rate Calculation

Details: Proper calculation ensures smooth transitions between grades, preventing discomfort or safety issues for vehicles and passengers.

4. Using the Calculator

Tips: Enter the change in grade (algebraic difference between two grades) in percentage and the length of the vertical curve in meters.

5. Frequently Asked Questions (FAQ)

Q1: What are typical permissible rates?
A: For railways, 0.1% per chain is permitted at summits and 0.05% per chain at sags.

Q2: Why is the permissible rate important?
A: It ensures gradual grade transitions for safety and comfort in transportation design.

Q3: How does curve length affect the permissible rate?
A: Longer curves allow for more gradual grade changes, resulting in lower permissible rates.

Q4: What's the difference between summit and sag curves?
A: Summit curves (crests) and sag curves (valleys) have different comfort and safety considerations.

Q5: How do I determine the change in grade?
A: It's the algebraic difference between the incoming and outgoing grades (G2 - G1).