Rear Track Width Given Roll Rate Of Suspension With Anti-Roll Bar Calculator

Formula Used:

\[ \text{Rear Track Width} = \sqrt{\frac{2 \times \left(\text{Roll Rate} \times \left(\text{Roll Rate of Anti-Roll Bar} + \text{Wheel Centre Rate} \times \frac{\text{Spring Track Width}^2}{2}\right)\right)}{\left(\left(\text{Roll Rate of Anti-Roll Bar} + \text{Wheel Centre Rate} \times \frac{\text{Spring Track Width}^2}{2} - \text{Roll Rate}\right) \times \text{Tyre Vertical Rate}\right)}} \]

Roll Rate (KΦ):

N·m/rad

Roll Rate of Anti-Roll Bar (Rarb):

N·m/rad

Wheel Centre Rate (Kw):

N/m

Spring Track Width (Ts):

Tyre Vertical Rate (Kt):

N/m

Rear Track Width (tR):

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1. What is Rear Track Width?

Rear Track Width is the distance between the centers of the rear wheels. It is a critical parameter in vehicle dynamics that affects stability, handling, and overall performance.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ tR = \sqrt{\frac{2 \times \left(KΦ \times \left(Rarb + Kw \times \frac{Ts^2}{2}\right)\right)}{\left(\left(Rarb + Kw \times \frac{Ts^2}{2} - KΦ\right) \times Kt\right)}} \]

Where:

\( tR \) — Rear Track Width (m)
\( KΦ \) — Roll Rate (N·m/rad)
\( Rarb \) — Roll Rate of Anti-Roll Bar (N·m/rad)
\( Kw \) — Wheel Centre Rate (N/m)
\( Ts \) — Spring Track Width (m)
\( Kt \) — Tyre Vertical Rate (N/m)

Explanation: This formula calculates the optimal rear track width based on suspension parameters and roll characteristics to achieve desired vehicle dynamics.

3. Importance of Rear Track Width Calculation

Details: Proper rear track width calculation is essential for vehicle stability, cornering performance, weight distribution, and overall handling characteristics. It affects tire wear, roll center height, and suspension geometry.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure positive values for all parameters. The denominator must be positive for valid calculation results.

5. Frequently Asked Questions (FAQ)

Q1: Why is rear track width important in vehicle design?
A: Rear track width affects vehicle stability, cornering ability, and overall handling characteristics. It influences weight distribution and tire contact patch during maneuvers.

Q2: How does anti-roll bar affect track width calculation?
A: The anti-roll bar contributes to the overall roll stiffness, which directly influences the required track width to maintain desired roll characteristics.

Q3: What is the relationship between spring track width and rear track width?
A: Spring track width is the distance between springs, while rear track width is the distance between wheel centers. The relationship is mathematically defined by the suspension geometry and the given formula.

Q4: How does tire vertical rate affect the calculation?
A: Tire vertical rate represents the spring rate of the tire itself, which contributes to the overall vertical stiffness and affects the suspension's response to roll forces.

Q5: What are typical values for rear track width in different vehicles?
A: Rear track width varies significantly between vehicle types: approximately 1.4-1.6m for passenger cars, 1.6-1.8m for SUVs, and up to 2.0m or more for commercial vehicles and race cars.