Horizontal Distance of C.G from Rear Axle with Rear Wheel Brake Calculator

Formula Used:

\[ x = b - \mu \cdot h - \frac{R_R \cdot b}{W \cdot \cos(\theta)} \]

Vehicle Wheelbase (b):

Friction Coefficient (μ):

Height of C.G. (h):

Normal Reaction at Rear Wheel (R_R):

Vehicle Weight (W):

Inclination Angle of Road (θ):

rad

Horizontal Distance of C.G. from Rear Axle (x):

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1. What is Horizontal Distance of C.G from Rear Axle?

The horizontal distance of center of gravity from rear axle is a critical parameter in vehicle dynamics that determines the weight distribution between front and rear axles. It affects braking performance, stability, and handling characteristics of the vehicle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ x = b - \mu \cdot h - \frac{R_R \cdot b}{W \cdot \cos(\theta)} \]

Where:

\( x \) — Horizontal distance of C.G. from rear axle (m)
\( b \) — Vehicle wheelbase (m)
\( \mu \) — Friction coefficient between wheels and ground
\( h \) — Height of center of gravity of vehicle (m)
\( R_R \) — Normal reaction at rear wheel (N)
\( W \) — Vehicle weight (N)
\( \theta \) — Inclination angle of road (rad)

Explanation: This formula calculates the horizontal position of the center of gravity relative to the rear axle, considering braking forces, road inclination, and vehicle parameters.

3. Importance of C.G. Position Calculation

Details: Accurate determination of center of gravity position is crucial for vehicle design, braking system optimization, stability analysis, and safety assessment. It affects weight transfer during braking and acceleration.

4. Using the Calculator

Tips: Enter all parameters in consistent units. Wheelbase and height in meters, forces in Newtons, and angle in radians. Ensure all values are positive and physically realistic.

5. Frequently Asked Questions (FAQ)

Q1: Why is C.G. position important in vehicle dynamics?
A: The center of gravity position affects weight distribution, braking performance, rollover tendency, and overall vehicle stability during various maneuvers.

Q2: How does road inclination affect the calculation?
A: Road inclination changes the normal forces on wheels and affects weight distribution, which is accounted for through the cosine term in the formula.

Q3: What is the typical range for friction coefficient?
A: Friction coefficient between tires and road typically ranges from 0.3 (wet road) to 1.0 (dry asphalt), with racing tires achieving up to 1.7 on optimal surfaces.

Q4: How does C.G. height affect vehicle stability?
A: Higher center of gravity increases rollover risk and affects weight transfer during cornering and braking, making the vehicle less stable.

Q5: Can this formula be used for all vehicle types?
A: While the basic principles apply to all vehicles, specific applications may require modifications for motorcycles, trucks, or specialized vehicles with unique weight distributions.