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Roll Rate with Anti-Roll Bar Formula

GoRoll Rate Formula

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Roll Rate or Roll stiffness is the resistance moment generated per unit of roll angle of the sprung mass. Check FAQs

K Φ = \frac{K t \cdot \frac{{t R}^{2}}{2} \cdot (R arb + K w \cdot \frac{{T s}^{2}}{2})}{K t \cdot \frac{{t R}^{2}}{2} + R arb + K w \cdot \frac{{T s}^{2}}{2}}

K_Φ - Roll Rate?K_t - Tyre Vertical Rate?t_R - Rear Track Width?R_arb - Roll Rate of Anti-Roll Bar?K_w - Wheel Centre Rate?T_s - Spring Track Width?

Roll Rate with Anti-Roll Bar Example

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Here is how the Roll Rate with Anti-Roll Bar equation looks like with Values.

Here is how the Roll Rate with Anti-Roll Bar equation looks like with Units.

Here is how the Roll Rate with Anti-Roll Bar equation looks like.

10297.4296 = \frac{321300 \cdot \frac{{0.4}^{2}}{2} \cdot (4881.6 + 30366.46 \cdot \frac{{0.9}^{2}}{2})}{321300 \cdot \frac{{0.4}^{2}}{2} + 4881.6 + 30366.46 \cdot \frac{{0.9}^{2}}{2}}

10297.4296Nm/rad = \frac{321300N/m \cdot \frac{{0.4m}^{2}}{2} \cdot (4881.6Nm/rad + 30366.46N/m \cdot \frac{{0.9m}^{2}}{2})}{321300N/m \cdot \frac{{0.4m}^{2}}{2} + 4881.6Nm/rad + 30366.46N/m \cdot \frac{{0.9m}^{2}}{2}}

10297.4296 = \frac{321300 \cdot \frac{{0.4}^{2}}{2} \cdot (4881.6 + 30366.46 \cdot \frac{{0.9}^{2}}{2})}{321300 \cdot \frac{{0.4}^{2}}{2} + 4881.6 + 30366.46 \cdot \frac{{0.9}^{2}}{2}}

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Roll Rate with Anti-Roll Bar Solution

Follow our step by step solution on how to calculate Roll Rate with Anti-Roll Bar?

FIRST Step Consider the formula

K Φ = \frac{K t \cdot \frac{{t R}^{2}}{2} \cdot (R arb + K w \cdot \frac{{T s}^{2}}{2})}{K t \cdot \frac{{t R}^{2}}{2} + R arb + K w \cdot \frac{{T s}^{2}}{2}}

Next Step Substitute values of Variables

∴

K Φ = \frac{321300N/m \cdot \frac{{0.4m}^{2}}{2} \cdot (4881.6Nm/rad + 30366.46N/m \cdot \frac{{0.9m}^{2}}{2})}{321300N/m \cdot \frac{{0.4m}^{2}}{2} + 4881.6Nm/rad + 30366.46N/m \cdot \frac{{0.9m}^{2}}{2}}

Next Step Prepare to Evaluate

∴

K Φ = \frac{321300 \cdot \frac{{0.4}^{2}}{2} \cdot (4881.6 + 30366.46 \cdot \frac{{0.9}^{2}}{2})}{321300 \cdot \frac{{0.4}^{2}}{2} + 4881.6 + 30366.46 \cdot \frac{{0.9}^{2}}{2}}

Next Step Evaluate

∴

K Φ = 10297.4296037473Nm/rad

LAST Step Rounding Answer

∴

K Φ = 10297.4296Nm/rad

Roll Rate with Anti-Roll Bar Formula Elements

Variables

Roll Rate

Roll Rate or Roll stiffness is the resistance moment generated per unit of roll angle of the sprung mass.

Symbol: K_Φ

Measurement: Torsion ConstantUnit: Nm/rad

Note: Value should be greater than 0.

Formulas to find Roll Rate

Tyre Vertical Rate

Tyre Vertical Rate is the spring rate controlled by the tyre compound, sidewall stiffness and operating pressure.

Symbol: K_t

Measurement: Surface TensionUnit: N/m

Note: Value should be greater than 0.

Formulas to find Tyre Vertical Rate

Rear Track Width

Rear Track Width is the distance between the centers of the rear wheels.

Symbol: t_R

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Rear Track Width

Roll Rate of Anti-Roll Bar

The Roll Rate of Anti-Roll Bar is the stiffness of the anti-roll bar in the roll mode.

Symbol: R_arb

Measurement: Torsion ConstantUnit: Nm/rad

Note: Value should be greater than 0.

Formulas to find Roll Rate of Anti-Roll Bar

Wheel Centre Rate

Wheel Centre Rate is the vertical force acting on the tire per unit vertical displacement at the location along the spindle corresponding to the wheel centerline, measured relative to the chassis.

Symbol: K_w

Measurement: Surface TensionUnit: N/m

Note: Value should be greater than 0.

Formulas to find Wheel Centre Rate

Spring Track Width

Spring Track Width is the distance between the springs on either side of the axle.

Symbol: T_s

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Spring Track Width

Other Formulas to find Roll Rate

Go Roll Rate

K Φ = \frac{K t \cdot \frac{{t R}^{2}}{2} \cdot K w \cdot \frac{{T s}^{2}}{2}}{K t \cdot \frac{{t R}^{2}}{2} + K w \cdot \frac{{T s}^{2}}{2}}

Other formulas in Rates for Axle Suspension in Race Car category

Go Vertical Tyre Axle Rate given Roll Rate

K w = \frac{K Φ \cdot K t \cdot \frac{{t R}^{2}}{2}}{K t \cdot \frac{{t R}^{2}}{2} - K Φ \cdot \frac{{T s}^{2}}{2}}

Go Spring Track Width given Roll Rate

T s = \sqrt{\frac{K Φ \cdot K t \cdot {t R}^{2}}{(K t \cdot \frac{{t R}^{2}}{2} - K Φ) \cdot K w}}

Go Tyre Rate given Roll Rate

K t = \frac{K Φ \cdot (K w \cdot \frac{{T s}^{2}}{2})}{(K w \cdot \frac{{T s}^{2}}{2} - K Φ) \cdot \frac{{t R}^{2}}{2}}

Go Rear Track Width given Roll Rate

t R = \sqrt{\frac{K Φ \cdot K w \cdot {T s}^{2}}{(K w \cdot \frac{{T s}^{2}}{2} - K Φ) \cdot K t}}

How to Evaluate Roll Rate with Anti-Roll Bar?

Roll Rate with Anti-Roll Bar evaluator uses Roll Rate = (Tyre Vertical Rate*(Rear Track Width^2)/2*(Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width^2)/2))/(Tyre Vertical Rate*(Rear Track Width^2)/2+Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width^2)/2) to evaluate the Roll Rate, The Roll rate with Anti-roll bar formula used to find the stiffness of the car with an axle suspension and anti-roll bar in the roll mode. Roll Rate is denoted by K_Φ symbol.

How to evaluate Roll Rate with Anti-Roll Bar using this online evaluator? To use this online evaluator for Roll Rate with Anti-Roll Bar, enter Tyre Vertical Rate (K_t), Rear Track Width (t_R), Roll Rate of Anti-Roll Bar (R_arb), Wheel Centre Rate (K_w) & Spring Track Width (T_s) and hit the calculate button.

FAQs on Roll Rate with Anti-Roll Bar

What is the formula to find Roll Rate with Anti-Roll Bar?

The formula of Roll Rate with Anti-Roll Bar is expressed as Roll Rate = (Tyre Vertical Rate*(Rear Track Width^2)/2*(Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width^2)/2))/(Tyre Vertical Rate*(Rear Track Width^2)/2+Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width^2)/2). Here is an example- 10297.43 = (321300*(0.4^2)/2*(4881.6+30366.46*(0.9^2)/2))/(321300*(0.4^2)/2+4881.6+30366.46*(0.9^2)/2).

How to calculate Roll Rate with Anti-Roll Bar?

With Tyre Vertical Rate (K_t), Rear Track Width (t_R), Roll Rate of Anti-Roll Bar (R_arb), Wheel Centre Rate (K_w) & Spring Track Width (T_s) we can find Roll Rate with Anti-Roll Bar using the formula - Roll Rate = (Tyre Vertical Rate*(Rear Track Width^2)/2*(Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width^2)/2))/(Tyre Vertical Rate*(Rear Track Width^2)/2+Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width^2)/2).

What are the other ways to Calculate Roll Rate?

Here are the different ways to Calculate Roll Rate-

Roll Rate=(Tyre Vertical Rate*(Rear Track Width^2)/2*Wheel Centre Rate*(Spring Track Width^2)/2)/(Tyre Vertical Rate*Rear Track Width^2/2+Wheel Centre Rate*Spring Track Width^2/2)

Can the Roll Rate with Anti-Roll Bar be negative?

No, the Roll Rate with Anti-Roll Bar, measured in Torsion Constant cannot be negative.

Which unit is used to measure Roll Rate with Anti-Roll Bar?

Roll Rate with Anti-Roll Bar is usually measured using the Newton Meter per Radian[Nm/rad] for Torsion Constant. Newton Centimeter per Radian[Nm/rad] are the few other units in which Roll Rate with Anti-Roll Bar can be measured.

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Roll Rate with Anti-Roll Bar Formula

​GoRoll Rate Formula

Roll Rate with Anti-Roll Bar Example

Roll Rate with Anti-Roll Bar Solution

Roll Rate with Anti-Roll Bar Formula Elements

Other Formulas to find Roll Rate

Other formulas in Rates for Axle Suspension in Race Car category

How to Evaluate Roll Rate with Anti-Roll Bar?

FAQs on Roll Rate with Anti-Roll Bar

Variable Name

GoRoll Rate Formula