Roll Rate With Anti-Roll Bar Calculator

Roll Rate Formula:

\[ K\Phi = \frac{Kt \times \frac{tR^2}{2} \times (Rarb + Kw \times \frac{Ts^2}{2})}{Kt \times \frac{tR^2}{2} + Rarb + Kw \times \frac{Ts^2}{2}} \]

Tyre Vertical Rate (Kt):

N/m

Rear Track Width (tR):

Roll Rate of Anti-Roll Bar (Rarb):

Nm/rad

Wheel Centre Rate (Kw):

N/m

Spring Track Width (Ts):

Roll Rate (KΦ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Roll Rate With Anti-Roll Bar?

Roll Rate or Roll stiffness is the resistance moment generated per unit of roll angle of the sprung mass. The anti-roll bar contributes significantly to the overall roll stiffness of a vehicle's suspension system.

2. How Does the Calculator Work?

The calculator uses the Roll Rate formula:

\[ K\Phi = \frac{Kt \times \frac{tR^2}{2} \times (Rarb + Kw \times \frac{Ts^2}{2})}{Kt \times \frac{tR^2}{2} + Rarb + Kw \times \frac{Ts^2}{2}} \]

Where:

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

Explanation: The formula calculates the combined roll stiffness considering the contributions from both the anti-roll bar and the suspension springs.

3. Importance of Roll Rate Calculation

Details: Accurate roll rate calculation is crucial for vehicle dynamics, handling characteristics, and stability control. It helps in optimizing suspension design for better cornering performance and ride comfort.

4. Using the Calculator

Tips: Enter all values in appropriate units (N/m for rates, m for distances). All values must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the purpose of an anti-roll bar?
A: An anti-roll bar reduces body roll during cornering by transferring force from the heavily loaded outer wheel to the less loaded inner wheel, improving stability.

Q2: How does tyre vertical rate affect roll rate?
A: Tyre vertical rate contributes to the overall vertical stiffness, which influences how the vehicle responds to roll forces during cornering.

Q3: What is the relationship between track width and roll rate?
A: Wider track widths generally increase roll resistance as they provide greater leverage against rolling forces.

Q4: Can this calculator be used for front and rear suspensions?
A: Yes, the formula applies to both front and rear suspensions, though parameter values will differ between axles.

Q5: How does wheel centre rate differ from spring rate?
A: Wheel centre rate includes the effect of suspension geometry and leverage ratios, while spring rate is the pure stiffness of the spring itself.