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Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar Formula

GoRear Track Width given Roll Rate Formula

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

t R = \sqrt{2 \cdot \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 K t}}

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

Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar Example

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

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

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

0.4 = \sqrt{2 \cdot \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 321300}}

0.4m = \sqrt{2 \cdot \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 321300N/m}}

0.4 = \sqrt{2 \cdot \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 321300}}

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Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar Solution

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

FIRST Step Consider the formula

t R = \sqrt{2 \cdot \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 K t}}

Next Step Substitute values of Variables

∴

t R = \sqrt{2 \cdot \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 321300N/m}}

Next Step Prepare to Evaluate

∴

t R = \sqrt{2 \cdot \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 321300}}

Next Step Evaluate

∴

t R = 0.400000019210795m

LAST Step Rounding Answer

∴

t R = 0.4m

Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar Formula Elements

Variables

Functions

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

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

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Rear Track Width

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}}

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 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}}

How to Evaluate Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar?

Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar evaluator uses Rear Track Width = sqrt(2*(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)*Tyre Vertical Rate)) to evaluate the Rear Track Width, The Rear track width given roll rate of suspension with anti-roll bar formula is used to find the distance between the centers of the rear wheels. Rear Track Width is denoted by t_R symbol.

How to evaluate Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar using this online evaluator? To use this online evaluator for Rear Track Width 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) & Tyre Vertical Rate (K_t) and hit the calculate button.

FAQs on Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar

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

The formula of Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar is expressed as Rear Track Width = sqrt(2*(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)*Tyre Vertical Rate)). Here is an example- 0.316835 = sqrt(2*(10297.43*(4881.6+30366.46*(0.9)^2/2))/((4881.6+30366.46*(0.9^2)/2-10297.43)*321300)).

How to calculate Rear Track Width 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) & Tyre Vertical Rate (K_t) we can find Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar using the formula - Rear Track Width = sqrt(2*(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)*Tyre Vertical Rate)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Rear Track Width?

Here are the different ways to Calculate Rear Track Width-

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

Can the Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar be negative?

No, the Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar, measured in Length cannot be negative.

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

Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar can be measured.

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Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar Formula

​GoRear Track Width given Roll Rate Formula

Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar Example

Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar Solution

Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar Formula Elements

Other Formulas to find Rear Track Width

Other formulas in Rates for Axle Suspension in Race Car category

How to Evaluate Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar?

FAQs on Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar

Variable Name

GoRear Track Width given Roll Rate Formula