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Wheel Centre Rate given Required Anti-Roll Bar Rate Formula

GoWheel Centre Rate Formula

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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. Check FAQs

K w = \frac{K Φ \cdot \frac{K t \cdot \frac{a^{2}}{2}}{K t \cdot \frac{a^{2}}{2} - K Φ} - K a}{\frac{a^{2}}{2}}

K_w - Wheel Centre Rate?K_Φ - Assumed Initial Roll Rate?K_t - Tyre Vertical Rate?a - Track Width of Vehicle?K_a - Required Anti Roll Bar Rate?

Wheel Centre Rate given Required Anti-Roll Bar Rate Example

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Here is how the Wheel Centre Rate given Required Anti-Roll Bar Rate equation looks like with Values.

Here is how the Wheel Centre Rate given Required Anti-Roll Bar Rate equation looks like with Units.

Here is how the Wheel Centre Rate given Required Anti-Roll Bar Rate equation looks like.

35238.1841 = \frac{76693 \cdot \frac{321330 \cdot \frac{{1.2}^{2}}{2}}{321330 \cdot \frac{{1.2}^{2}}{2} - 76693} - 89351}{\frac{{1.2}^{2}}{2}}

35238.1841N/m = \frac{76693Nm/rad \cdot \frac{321330N/m \cdot \frac{{1.2m}^{2}}{2}}{321330N/m \cdot \frac{{1.2m}^{2}}{2} - 76693Nm/rad} - 89351Nm/rad}{\frac{{1.2m}^{2}}{2}}

35238.1841 = \frac{76693 \cdot \frac{321330 \cdot \frac{{1.2}^{2}}{2}}{321330 \cdot \frac{{1.2}^{2}}{2} - 76693} - 89351}{\frac{{1.2}^{2}}{2}}

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Wheel Centre Rate given Required Anti-Roll Bar Rate Solution

Follow our step by step solution on how to calculate Wheel Centre Rate given Required Anti-Roll Bar Rate?

FIRST Step Consider the formula

K w = \frac{K Φ \cdot \frac{K t \cdot \frac{a^{2}}{2}}{K t \cdot \frac{a^{2}}{2} - K Φ} - K a}{\frac{a^{2}}{2}}

Next Step Substitute values of Variables

∴

K w = \frac{76693Nm/rad \cdot \frac{321330N/m \cdot \frac{{1.2m}^{2}}{2}}{321330N/m \cdot \frac{{1.2m}^{2}}{2} - 76693Nm/rad} - 89351Nm/rad}{\frac{{1.2m}^{2}}{2}}

Next Step Prepare to Evaluate

∴

K w = \frac{76693 \cdot \frac{321330 \cdot \frac{{1.2}^{2}}{2}}{321330 \cdot \frac{{1.2}^{2}}{2} - 76693} - 89351}{\frac{{1.2}^{2}}{2}}

Next Step Evaluate

∴

K w = 35238.1840572726N/m

LAST Step Rounding Answer

∴

K w = 35238.1841N/m

Wheel Centre Rate given Required Anti-Roll Bar Rate Formula Elements

Variables

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

Assumed Initial Roll Rate

The Assumed Initial Roll Rate is the initial spring rate of the anti-roll bar assumed before calculating the required anti-roll bar rate.

Symbol: K_Φ

Measurement: Torsion ConstantUnit: Nm/rad

Note: Value should be greater than 0.

Formulas to find Assumed Initial 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

Track Width of Vehicle

Track Width of Vehicle is the distance between the center line of each of the two wheels on the same axle (front/rear axle).

Symbol: a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Track Width of Vehicle

Required Anti Roll Bar Rate

Required Anti Roll Bar Rate is the required amount of spring rate of the roll bar for the system.

Symbol: K_a

Measurement: Torsion ConstantUnit: Nm/rad

Note: Value should be greater than 0.

Formulas to find Required Anti Roll Bar Rate

Other Formulas to find Wheel Centre Rate

Go Wheel Centre Rate

K w = \frac{K r \cdot K t}{K t - K r}

Other formulas in Wheel Centre Rates for Independent Suspension category

Go Required Anti-Roll Bar Rate

K a = K Φ \cdot \frac{K t \cdot \frac{a^{2}}{2}}{K t \cdot \frac{a^{2}}{2} - K Φ} - K w \cdot \frac{a^{2}}{2}

Go Assumed Initial Roll Rate given Required Anti-Roll Bar Rate

K Φ = (K a + K w \cdot \frac{a^{2}}{2}) \cdot \frac{K t \cdot \frac{a^{2}}{2}}{K t \cdot \frac{a^{2}}{2} + K a + K w \cdot \frac{a^{2}}{2}}

Go Tyre Rate given Required Anti-Roll Bar Rate

K t = (\frac{(K a + K w \cdot \frac{a^{2}}{2}) \cdot K Φ}{(K a + K w \cdot \frac{a^{2}}{2}) - K Φ}) \cdot \frac{2}{a^{2}}

Go Ride Rate given Wheel Centre Rate

K r = \frac{K t \cdot K w}{K t + K w}

How to Evaluate Wheel Centre Rate given Required Anti-Roll Bar Rate?

Wheel Centre Rate given Required Anti-Roll Bar Rate evaluator uses Wheel Centre Rate = (Assumed Initial Roll Rate*(Tyre Vertical Rate*(Track Width of Vehicle^2)/2)/(Tyre Vertical Rate*(Track Width of Vehicle^2)/2-Assumed Initial Roll Rate)-Required Anti Roll Bar Rate)/((Track Width of Vehicle^2)/2) to evaluate the Wheel Centre Rate, The Wheel centre rate given required anti-roll bar rate formula is defined to find the vertical force acting on the tire per unit vertical displacement at the location along with the spindle corresponding to the wheel centerline, measured relative to the chassis. Wheel Centre Rate is denoted by K_w symbol.

How to evaluate Wheel Centre Rate given Required Anti-Roll Bar Rate using this online evaluator? To use this online evaluator for Wheel Centre Rate given Required Anti-Roll Bar Rate, enter Assumed Initial Roll Rate (K_Φ), Tyre Vertical Rate (K_t), Track Width of Vehicle (a) & Required Anti Roll Bar Rate (K_a) and hit the calculate button.

FAQs on Wheel Centre Rate given Required Anti-Roll Bar Rate

What is the formula to find Wheel Centre Rate given Required Anti-Roll Bar Rate?

The formula of Wheel Centre Rate given Required Anti-Roll Bar Rate is expressed as Wheel Centre Rate = (Assumed Initial Roll Rate*(Tyre Vertical Rate*(Track Width of Vehicle^2)/2)/(Tyre Vertical Rate*(Track Width of Vehicle^2)/2-Assumed Initial Roll Rate)-Required Anti Roll Bar Rate)/((Track Width of Vehicle^2)/2). Here is an example- 35238.18 = (76693*(321330*(1.2^2)/2)/(321330*(1.2^2)/2-76693)-89351)/((1.2^2)/2).

How to calculate Wheel Centre Rate given Required Anti-Roll Bar Rate?

With Assumed Initial Roll Rate (K_Φ), Tyre Vertical Rate (K_t), Track Width of Vehicle (a) & Required Anti Roll Bar Rate (K_a) we can find Wheel Centre Rate given Required Anti-Roll Bar Rate using the formula - Wheel Centre Rate = (Assumed Initial Roll Rate*(Tyre Vertical Rate*(Track Width of Vehicle^2)/2)/(Tyre Vertical Rate*(Track Width of Vehicle^2)/2-Assumed Initial Roll Rate)-Required Anti Roll Bar Rate)/((Track Width of Vehicle^2)/2).

What are the other ways to Calculate Wheel Centre Rate?

Here are the different ways to Calculate Wheel Centre Rate-

Wheel Centre Rate=(Ride Rate*Tyre Vertical Rate)/(Tyre Vertical Rate-Ride Rate)

Can the Wheel Centre Rate given Required Anti-Roll Bar Rate be negative?

No, the Wheel Centre Rate given Required Anti-Roll Bar Rate, measured in Surface Tension cannot be negative.

Which unit is used to measure Wheel Centre Rate given Required Anti-Roll Bar Rate?

Wheel Centre Rate given Required Anti-Roll Bar Rate is usually measured using the Newton per Meter[N/m] for Surface Tension. Millinewton per Meter[N/m], Gram-Force per Centimeter[N/m], Dyne per Centimeter[N/m] are the few other units in which Wheel Centre Rate given Required Anti-Roll Bar Rate can be measured.

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Wheel Centre Rate given Required Anti-Roll Bar Rate Formula

​GoWheel Centre Rate Formula

Wheel Centre Rate given Required Anti-Roll Bar Rate Example

Wheel Centre Rate given Required Anti-Roll Bar Rate Solution

Wheel Centre Rate given Required Anti-Roll Bar Rate Formula Elements

Other Formulas to find Wheel Centre Rate

Other formulas in Wheel Centre Rates for Independent Suspension category

How to Evaluate Wheel Centre Rate given Required Anti-Roll Bar Rate?

FAQs on Wheel Centre Rate given Required Anti-Roll Bar Rate

Variable Name

GoWheel Centre Rate Formula