Ramp Radius Calculator

Formula

To calculate the Ramp Radius (R):

\[ R = \frac{V^2}{g \times \tan(\theta)} \]

Where:

\(R\) is the radius of the ramp (feet)
\(V\) is the speed of the vehicle (feet per second)
\(g\) is the acceleration due to gravity (32.2 feet per second squared)
\(\theta\) is the central angle of the ramp curve (radians)

What is Ramp Radius?

Ramp radius is the minimum curve radius required for a vehicle to safely navigate a ramp at a certain speed without skidding or overturning. It is a critical parameter in the design of roads, especially for ramps and curved sections, to ensure the safety and comfort of the drivers. The radius depends on the speed of the vehicle, the slope of the ramp, and the friction between the tires and the road surface.

Example Calculation 1

Let's assume the following values:

Speed of Vehicle (V) = 60 feet per second
Central Angle of Ramp Curve (\(\theta\)) = 0.5 radians

Using the formula:

\[ R = \frac{60^2}{32.2 \times \tan(0.5)} \approx \frac{3600}{32.2 \times 0.5463} \approx \frac{3600}{17.57} \approx 204.88 \text{ feet} \]

The Ramp Radius is approximately 204.88 feet.

Example Calculation 2

Let's assume the following values:

Speed of Vehicle (V) = 80 feet per second
Central Angle of Ramp Curve (\(\theta\)) = 0.3 radians

Using the formula:

\[ R = \frac{80^2}{32.2 \times \tan(0.3)} \approx \frac{6400}{32.2 \times 0.3093} \approx \frac{6400}{9.95} \approx 642.52 \text{ feet} \]

The Ramp Radius is approximately 642.52 feet.