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

GoSpring Track Width given Roll Rate Formula

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Spring Track Width is the distance between the springs on either side of the axle. Check FAQs

T s = \sqrt{2 \cdot (\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}{K w})}

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

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

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

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

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

0.9 = \sqrt{2 \cdot (\frac{\frac{10297.43 \cdot 321300 \cdot \frac{{0.4}^{2}}{2}}{(321300 \cdot \frac{{0.4}^{2}}{2} - 10297.43)} - 4881.6}{30366.46})}

0.9m = \sqrt{2 \cdot (\frac{\frac{10297.43Nm/rad \cdot 321300N/m \cdot \frac{{0.4m}^{2}}{2}}{(321300N/m \cdot \frac{{0.4m}^{2}}{2} - 10297.43Nm/rad)} - 4881.6Nm/rad}{30366.46N/m})}

0.9 = \sqrt{2 \cdot (\frac{\frac{10297.43 \cdot 321300 \cdot \frac{{0.4}^{2}}{2}}{(321300 \cdot \frac{{0.4}^{2}}{2} - 10297.43)} - 4881.6}{30366.46})}

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

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

FIRST Step Consider the formula

T s = \sqrt{2 \cdot (\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}{K w})}

Next Step Substitute values of Variables

∴

T s = \sqrt{2 \cdot (\frac{\frac{10297.43Nm/rad \cdot 321300N/m \cdot \frac{{0.4m}^{2}}{2}}{(321300N/m \cdot \frac{{0.4m}^{2}}{2} - 10297.43Nm/rad)} - 4881.6Nm/rad}{30366.46N/m})}

Next Step Prepare to Evaluate

∴

T s = \sqrt{2 \cdot (\frac{\frac{10297.43 \cdot 321300 \cdot \frac{{0.4}^{2}}{2}}{(321300 \cdot \frac{{0.4}^{2}}{2} - 10297.43)} - 4881.6}{30366.46})}

Next Step Evaluate

∴

T s = 0.900000040357577m

LAST Step Rounding Answer

∴

T s = 0.9m

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

Variables

Functions

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

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

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

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 Spring Track Width

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}}

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 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 Spring Track Width given Roll Rate of Suspension with Anti-Roll Bar?

Spring Track Width given Roll Rate of Suspension with Anti-Roll Bar evaluator uses Spring Track Width = sqrt(2*(((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)/Wheel Centre Rate)) to evaluate the Spring Track Width, The Spring track width given roll rate of suspension with anti-roll bar formula is used to find the distance between the springs on either side of the axle of the system having anti-roll bar. Spring Track Width is denoted by T_s symbol.

How to evaluate Spring Track Width given Roll Rate of Suspension with Anti-Roll Bar using this online evaluator? To use this online evaluator for Spring Track Width given Roll Rate of Suspension with Anti-Roll Bar, enter Roll Rate (K_Φ), Tyre Vertical Rate (K_t), Rear Track Width (t_R), Roll Rate of Anti-Roll Bar (R_arb) & Wheel Centre Rate (K_w) and hit the calculate button.

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

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

The formula of Spring Track Width given Roll Rate of Suspension with Anti-Roll Bar is expressed as Spring Track Width = sqrt(2*(((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)/Wheel Centre Rate)). Here is an example- 0.698919 = sqrt(2*(((10297.43*321300*(0.4^2)/2)/((321300*(0.4^2)/2-10297.43))-4881.6)/30366.46)).

How to calculate Spring Track Width given Roll Rate of Suspension with Anti-Roll Bar?

With Roll Rate (K_Φ), Tyre Vertical Rate (K_t), Rear Track Width (t_R), Roll Rate of Anti-Roll Bar (R_arb) & Wheel Centre Rate (K_w) we can find Spring Track Width given Roll Rate of Suspension with Anti-Roll Bar using the formula - Spring Track Width = sqrt(2*(((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)/Wheel Centre Rate)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Spring Track Width?

Here are the different ways to Calculate Spring Track Width-

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

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

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

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

Spring 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 Spring Track Width given Roll Rate of Suspension with Anti-Roll Bar can be measured.

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

​GoSpring Track Width given Roll Rate Formula

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

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

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

Other Formulas to find Spring Track Width

Other formulas in Rates for Axle Suspension in Race Car category

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

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

Variable Name

GoSpring Track Width given Roll Rate Formula