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Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar Formula

GoTyre Rate given Roll 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 Φ \cdot (R arb + K w \cdot \frac{{T s}^{2}}{2})}{(R arb + K w \cdot \frac{{T s}^{2}}{2} - K Φ) \cdot \frac{{t R}^{2}}{2}}

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

Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar Example

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

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

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

321300.0309 = \frac{10297.43 \cdot (4881.6 + 30366.46 \cdot \frac{{0.9}^{2}}{2})}{(4881.6 + 30366.46 \cdot \frac{{0.9}^{2}}{2} - 10297.43) \cdot \frac{{0.4}^{2}}{2}}

321300.0309N/m = \frac{10297.43Nm/rad \cdot (4881.6Nm/rad + 30366.46N/m \cdot \frac{{0.9m}^{2}}{2})}{(4881.6Nm/rad + 30366.46N/m \cdot \frac{{0.9m}^{2}}{2} - 10297.43Nm/rad) \cdot \frac{{0.4m}^{2}}{2}}

321300.0309 = \frac{10297.43 \cdot (4881.6 + 30366.46 \cdot \frac{{0.9}^{2}}{2})}{(4881.6 + 30366.46 \cdot \frac{{0.9}^{2}}{2} - 10297.43) \cdot \frac{{0.4}^{2}}{2}}

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Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

K t = \frac{10297.43Nm/rad \cdot (4881.6Nm/rad + 30366.46N/m \cdot \frac{{0.9m}^{2}}{2})}{(4881.6Nm/rad + 30366.46N/m \cdot \frac{{0.9m}^{2}}{2} - 10297.43Nm/rad) \cdot \frac{{0.4m}^{2}}{2}}

Next Step Prepare to Evaluate

∴

K t = \frac{10297.43 \cdot (4881.6 + 30366.46 \cdot \frac{{0.9}^{2}}{2})}{(4881.6 + 30366.46 \cdot \frac{{0.9}^{2}}{2} - 10297.43) \cdot \frac{{0.4}^{2}}{2}}

Next Step Evaluate

∴

K t = 321300.030862143N/m

LAST Step Rounding Answer

∴

K t = 321300.0309N/m

Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar 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

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

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

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

Other Formulas to find Tyre Vertical Rate

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}}

Other formulas in Rates for Axle Suspension in Race Car category

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}}

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 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 Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar?

Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar evaluator uses Tyre Vertical Rate = (Roll Rate*(Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width^2)/2))/((Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width^2)/2-Roll Rate)*(Rear Track Width^2)/2) to evaluate the Tyre Vertical Rate, The Tyre rate given roll rate of suspension with anti-roll bar formula is used to find the spring rate of the 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 Roll Rate of Suspension with Anti-Roll Bar using this online evaluator? To use this online evaluator for Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar, enter Roll Rate (K_Φ), Roll Rate of Anti-Roll Bar (R_arb), Wheel Centre Rate (K_w), Spring Track Width (T_s) & Rear Track Width (t_R) and hit the calculate button.

FAQs on Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar

What is the formula to find Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar?

The formula of Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar is expressed as Tyre Vertical Rate = (Roll Rate*(Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width^2)/2))/((Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width^2)/2-Roll Rate)*(Rear Track Width^2)/2). Here is an example- 201585 = (10297.43*(4881.6+30366.46*(0.9^2)/2))/((4881.6+30366.46*(0.9^2)/2-10297.43)*(0.4^2)/2).

How to calculate Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar?

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

What are the other ways to Calculate Tyre Vertical Rate?

Here are the different ways to Calculate Tyre Vertical Rate-

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

Can the Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar be negative?

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

Which unit is used to measure Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar?

Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar 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 Roll Rate of Suspension with Anti-Roll Bar can be measured.

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Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar Formula

​GoTyre Rate given Roll Rate Formula

Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar Example

Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar Solution

Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar Formula Elements

Other Formulas to find Tyre Vertical Rate

Other formulas in Rates for Axle Suspension in Race Car category

How to Evaluate Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar?

FAQs on Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar

Variable Name

GoTyre Rate given Roll Rate Formula