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Tyre Rate given Required Anti-Roll Bar Rate Formula

GoTyre Vertical Rate given Wheel Centre Rate Formula

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

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}}

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

Tyre Rate given Required Anti-Roll Bar Rate Example

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

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

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

321326.6816 = (\frac{(89351 + 35239 \cdot \frac{{1.2}^{2}}{2}) \cdot 76693}{(89351 + 35239 \cdot \frac{{1.2}^{2}}{2}) - 76693}) \cdot \frac{2}{{1.2}^{2}}

321326.6816N/m = (\frac{(89351Nm/rad + 35239N/m \cdot \frac{{1.2m}^{2}}{2}) \cdot 76693Nm/rad}{(89351Nm/rad + 35239N/m \cdot \frac{{1.2m}^{2}}{2}) - 76693Nm/rad}) \cdot \frac{2}{{1.2m}^{2}}

321326.6816 = (\frac{(89351 + 35239 \cdot \frac{{1.2}^{2}}{2}) \cdot 76693}{(89351 + 35239 \cdot \frac{{1.2}^{2}}{2}) - 76693}) \cdot \frac{2}{{1.2}^{2}}

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Tyre Rate given Required Anti-Roll Bar Rate Solution

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

FIRST Step Consider the formula

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}}

Next Step Substitute values of Variables

∴

K t = (\frac{(89351Nm/rad + 35239N/m \cdot \frac{{1.2m}^{2}}{2}) \cdot 76693Nm/rad}{(89351Nm/rad + 35239N/m \cdot \frac{{1.2m}^{2}}{2}) - 76693Nm/rad}) \cdot \frac{2}{{1.2m}^{2}}

Next Step Prepare to Evaluate

∴

K t = (\frac{(89351 + 35239 \cdot \frac{{1.2}^{2}}{2}) \cdot 76693}{(89351 + 35239 \cdot \frac{{1.2}^{2}}{2}) - 76693}) \cdot \frac{2}{{1.2}^{2}}

Next Step Evaluate

∴

K t = 321326.681641071N/m

LAST Step Rounding Answer

∴

K t = 321326.6816N/m

Tyre Rate given Required Anti-Roll Bar Rate Formula Elements

Variables

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

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

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

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

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

Other Formulas to find Tyre Vertical Rate

Go Tyre Vertical Rate given Wheel Centre Rate

K t = \frac{K w \cdot K r}{K w - 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 Wheel Centre Rate given Required Anti-Roll Bar Rate

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}}

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 Wheel Centre Rate

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

How to Evaluate Tyre Rate given Required Anti-Roll Bar Rate?

Tyre Rate given Required Anti-Roll Bar Rate evaluator uses Tyre Vertical Rate = (((Required Anti Roll Bar Rate+Wheel Centre Rate*(Track Width of Vehicle^2)/2)*Assumed Initial Roll Rate)/((Required Anti Roll Bar Rate+Wheel Centre Rate*(Track Width of Vehicle^2)/2)-Assumed Initial Roll Rate))*2/Track Width of Vehicle^2 to evaluate the Tyre Vertical Rate, The Tyre rate given required anti-roll bar rate formula is used to find the spring rate of tyre controlled by the tyre compound, sidewall stiffness and operating pressure. Tyre Vertical Rate is denoted by K_t symbol.

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

FAQs on Tyre Rate given Required Anti-Roll Bar Rate

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

The formula of Tyre Rate given Required Anti-Roll Bar Rate is expressed as Tyre Vertical Rate = (((Required Anti Roll Bar Rate+Wheel Centre Rate*(Track Width of Vehicle^2)/2)*Assumed Initial Roll Rate)/((Required Anti Roll Bar Rate+Wheel Centre Rate*(Track Width of Vehicle^2)/2)-Assumed Initial Roll Rate))*2/Track Width of Vehicle^2. Here is an example- 321326.7 = (((89351+35239*(1.2^2)/2)*76693)/((89351+35239*(1.2^2)/2)-76693))*2/1.2^2.

How to calculate Tyre Rate given Required Anti-Roll Bar Rate?

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

What are the other ways to Calculate Tyre Vertical Rate?

Here are the different ways to Calculate Tyre Vertical Rate-

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

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

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

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

Tyre 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 Tyre Rate given Required Anti-Roll Bar Rate can be measured.

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Tyre Rate given Required Anti-Roll Bar Rate Formula

​GoTyre Vertical Rate given Wheel Centre Rate Formula

Tyre Rate given Required Anti-Roll Bar Rate Example

Tyre Rate given Required Anti-Roll Bar Rate Solution

Tyre Rate given Required Anti-Roll Bar Rate Formula Elements

Other Formulas to find Tyre Vertical Rate

Other formulas in Wheel Centre Rates for Independent Suspension category

How to Evaluate Tyre Rate given Required Anti-Roll Bar Rate?

FAQs on Tyre Rate given Required Anti-Roll Bar Rate

Variable Name

GoTyre Vertical Rate given Wheel Centre Rate Formula