Downgrade given Length based on Centrifugal Ratio Calculator

Downgrade Formula:

\[ g_2 = g_1 - \left(\frac{L_c \times 100 \times f}{V^2}\right) \]

Upgrade (g₁):

Length of Curve (Lc):

Allowable Centrifugal Acceleration (f):

m/s²

Vehicle Velocity (V):

km/h

Downgrade (g₂):

1. What is Downgrade given Length based on Centrifugal Ratio?

Definition: This calculator determines the required downgrade (g₂) based on the initial upgrade (g₁), curve length, allowable centrifugal acceleration, and vehicle velocity.

Purpose: It helps in designing vertical curves in road construction to ensure comfortable and safe vehicle movement.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ g_2 = g_1 - \left(\frac{L_c \times 100 \times f}{V^2}\right) \]

Where:

\( g_2 \) — Downgrade (%)
\( g_1 \) — Upgrade (%)
\( L_c \) — Length of Curve (m)
\( f \) — Allowable Centrifugal Acceleration (m/s²)
\( V \) — Vehicle Velocity (km/h)

Explanation: The formula calculates the required downgrade to maintain comfortable centrifugal acceleration for vehicles moving at a given speed through a curve of specified length.

3. Importance of Downgrade Calculation

Details: Proper downgrade calculation ensures smooth vehicle transition between grades, prevents discomfort from rapid acceleration changes, and maintains safety standards.

4. Using the Calculator

Tips: Enter the upgrade (%), curve length (m), allowable centrifugal acceleration (default 0.6 m/s²), and vehicle velocity (km/h). All values except upgrade must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical value for allowable centrifugal acceleration?
A: For comfort, typically 0.6 m/s² is used, but this may vary based on road type and design standards.

Q2: Can the upgrade (g₁) be negative?
A: Yes, if the initial slope is already a downgrade, enter a negative value for g₁.

Q3: How does vehicle speed affect the result?
A: Higher speeds require gentler downgrades to maintain the same comfort level, as centrifugal acceleration increases with the square of velocity.

Q4: What if my result is positive?
A: A positive result means the required slope is still an upgrade, just less steep than the initial upgrade.

Q5: How is curve length determined?
A: Curve length depends on design speed, algebraic difference between grades, and sight distance requirements.