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Vertical Tyre Axle Rate given Roll Rate Formula

GoVertical Tyre Axle Rate given Roll Rate of Suspension with Anti-Roll Bar 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 K t \cdot \frac{{t R}^{2}}{2}}{K t \cdot \frac{{t R}^{2}}{2} - K Φ \cdot \frac{{T s}^{2}}{2}}

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

Vertical Tyre Axle Rate given Roll Rate Example

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Here is how the Vertical Tyre Axle Rate given Roll Rate equation looks like with Values.

Here is how the Vertical Tyre Axle Rate given Roll Rate equation looks like with Units.

Here is how the Vertical Tyre Axle Rate given Roll Rate equation looks like.

12291.7611 = \frac{10297.43 \cdot 321300 \cdot \frac{{0.4}^{2}}{2}}{321300 \cdot \frac{{0.4}^{2}}{2} - 10297.43 \cdot \frac{{0.9}^{2}}{2}}

12291.7611N/m = \frac{10297.43Nm/rad \cdot 321300N/m \cdot \frac{{0.4m}^{2}}{2}}{321300N/m \cdot \frac{{0.4m}^{2}}{2} - 10297.43Nm/rad \cdot \frac{{0.9m}^{2}}{2}}

12291.7611 = \frac{10297.43 \cdot 321300 \cdot \frac{{0.4}^{2}}{2}}{321300 \cdot \frac{{0.4}^{2}}{2} - 10297.43 \cdot \frac{{0.9}^{2}}{2}}

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Vertical Tyre Axle Rate given Roll Rate Solution

Follow our step by step solution on how to calculate Vertical Tyre Axle Rate given Roll Rate?

FIRST Step Consider the formula

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}}

Next Step Substitute values of Variables

∴

K w = \frac{10297.43Nm/rad \cdot 321300N/m \cdot \frac{{0.4m}^{2}}{2}}{321300N/m \cdot \frac{{0.4m}^{2}}{2} - 10297.43Nm/rad \cdot \frac{{0.9m}^{2}}{2}}

Next Step Prepare to Evaluate

∴

K w = \frac{10297.43 \cdot 321300 \cdot \frac{{0.4}^{2}}{2}}{321300 \cdot \frac{{0.4}^{2}}{2} - 10297.43 \cdot \frac{{0.9}^{2}}{2}}

Next Step Evaluate

∴

K w = 12291.7611443359N/m

LAST Step Rounding Answer

∴

K w = 12291.7611N/m

Vertical Tyre Axle Rate given Roll 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

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

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 Wheel Centre Rate

Go Vertical Tyre Axle Rate given Roll Rate of Suspension with Anti-Roll Bar

K w = \frac{\frac{K Φ \cdot K t \cdot \frac{{t R}^{2}}{2}}{K t \cdot \frac{{t R}^{2}}{2} - K Φ} - R arb}{\frac{{T s}^{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 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 Vertical Tyre Axle Rate given Roll Rate?

Vertical Tyre Axle Rate given Roll Rate evaluator uses Wheel Centre Rate = (Roll Rate*Tyre Vertical Rate*(Rear Track Width^2)/2)/(Tyre Vertical Rate*(Rear Track Width^2)/2-Roll Rate*(Spring Track Width^2)/2) to evaluate the Wheel Centre Rate, The Vertical tyre axle rate given roll rate formula is used to find the vertical force acting on the tire axle per unit vertical displacement at the location along the spindle corresponding to the wheel centerline, measured relative to the chassis. Wheel Centre Rate is denoted by K_w symbol.

How to evaluate Vertical Tyre Axle Rate given Roll Rate using this online evaluator? To use this online evaluator for Vertical Tyre Axle Rate given Roll Rate, enter Roll Rate (K_Φ), Tyre Vertical Rate (K_t), Rear Track Width (t_R) & Spring Track Width (T_s) and hit the calculate button.

FAQs on Vertical Tyre Axle Rate given Roll Rate

What is the formula to find Vertical Tyre Axle Rate given Roll Rate?

The formula of Vertical Tyre Axle Rate given Roll Rate is expressed as Wheel Centre Rate = (Roll Rate*Tyre Vertical Rate*(Rear Track Width^2)/2)/(Tyre Vertical Rate*(Rear Track Width^2)/2-Roll Rate*(Spring Track Width^2)/2). Here is an example- 9573.095 = (10297.43*321300*(0.4^2)/2)/(321300*(0.4^2)/2-10297.43*(0.9^2)/2).

How to calculate Vertical Tyre Axle Rate given Roll Rate?

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

Can the Vertical Tyre Axle Rate given Roll Rate be negative?

No, the Vertical Tyre Axle Rate given Roll Rate, measured in Surface Tension cannot be negative.

Which unit is used to measure Vertical Tyre Axle Rate given Roll Rate?

Vertical Tyre Axle Rate given Roll 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 Vertical Tyre Axle Rate given Roll Rate can be measured.

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Vertical Tyre Axle Rate given Roll Rate Formula

​GoVertical Tyre Axle Rate given Roll Rate of Suspension with Anti-Roll Bar Formula

Vertical Tyre Axle Rate given Roll Rate Example

Vertical Tyre Axle Rate given Roll Rate Solution

Vertical Tyre Axle Rate given Roll Rate Formula Elements

Other Formulas to find Wheel Centre Rate

Other formulas in Rates for Axle Suspension in Race Car category

How to Evaluate Vertical Tyre Axle Rate given Roll Rate?

FAQs on Vertical Tyre Axle Rate given Roll Rate

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