FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Assumed Initial Roll Rate given Required Anti-Roll Bar Rate Formula

Fx Copy

LaTeX Copy

The Assumed Initial Roll Rate is the initial spring rate of the anti-roll bar assumed before calculating the required anti-roll bar rate. Check FAQs

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}}

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

Assumed Initial Roll Rate given Required Anti-Roll Bar Rate Example

With values

With units

Only example

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

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

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

76693.2625 = (89351 + 35239 \cdot \frac{{1.2}^{2}}{2}) \cdot \frac{321330 \cdot \frac{{1.2}^{2}}{2}}{321330 \cdot \frac{{1.2}^{2}}{2} + 89351 + 35239 \cdot \frac{{1.2}^{2}}{2}}

76693.2625Nm/rad = (89351Nm/rad + 35239N/m \cdot \frac{{1.2m}^{2}}{2}) \cdot \frac{321330N/m \cdot \frac{{1.2m}^{2}}{2}}{321330N/m \cdot \frac{{1.2m}^{2}}{2} + 89351Nm/rad + 35239N/m \cdot \frac{{1.2m}^{2}}{2}}

76693.2625 = (89351 + 35239 \cdot \frac{{1.2}^{2}}{2}) \cdot \frac{321330 \cdot \frac{{1.2}^{2}}{2}}{321330 \cdot \frac{{1.2}^{2}}{2} + 89351 + 35239 \cdot \frac{{1.2}^{2}}{2}}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Physics » Category

Mechanical » Category

Automobile » fx Assumed Initial Roll Rate given Required Anti-Roll Bar Rate

Assumed Initial Roll Rate given Required Anti-Roll Bar Rate Solution

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

FIRST Step Consider the formula

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}}

Next Step Substitute values of Variables

∴

K Φ = (89351Nm/rad + 35239N/m \cdot \frac{{1.2m}^{2}}{2}) \cdot \frac{321330N/m \cdot \frac{{1.2m}^{2}}{2}}{321330N/m \cdot \frac{{1.2m}^{2}}{2} + 89351Nm/rad + 35239N/m \cdot \frac{{1.2m}^{2}}{2}}

Next Step Prepare to Evaluate

∴

K Φ = (89351 + 35239 \cdot \frac{{1.2}^{2}}{2}) \cdot \frac{321330 \cdot \frac{{1.2}^{2}}{2}}{321330 \cdot \frac{{1.2}^{2}}{2} + 89351 + 35239 \cdot \frac{{1.2}^{2}}{2}}

Next Step Evaluate

∴

K Φ = 76693.2625462017Nm/rad

LAST Step Rounding Answer

∴

K Φ = 76693.2625Nm/rad

Assumed Initial Roll Rate given Required Anti-Roll Bar Rate Formula Elements

Variables

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

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

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

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 Tyre Rate given Required Anti-Roll Bar Rate

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}}

Go Wheel Centre Rate

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

How to Evaluate Assumed Initial Roll Rate given Required Anti-Roll Bar Rate?

Assumed Initial Roll Rate given Required Anti-Roll Bar Rate evaluator uses Assumed Initial Roll Rate = (Required Anti Roll Bar Rate+Wheel Centre Rate*(Track Width of Vehicle^2)/2)*(Tyre Vertical Rate*(Track Width of Vehicle^2)/2)/(Tyre Vertical Rate*(Track Width of Vehicle^2)/2+Required Anti Roll Bar Rate+Wheel Centre Rate*(Track Width of Vehicle^2)/2) to evaluate the Assumed Initial Roll Rate, The Assumed initial roll rate given required anti-roll bar rate formula is used to find the initially assumed spring rate of the anti-roll bar which would be used to find the required anti-roll bar rate of the system considered. Assumed Initial Roll Rate is denoted by K_Φ symbol.

How to evaluate Assumed Initial Roll Rate given Required Anti-Roll Bar Rate using this online evaluator? To use this online evaluator for Assumed Initial Roll 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) & Tyre Vertical Rate (K_t) and hit the calculate button.

FAQs on Assumed Initial Roll Rate given Required Anti-Roll Bar Rate

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

The formula of Assumed Initial Roll Rate given Required Anti-Roll Bar Rate is expressed as Assumed Initial Roll Rate = (Required Anti Roll Bar Rate+Wheel Centre Rate*(Track Width of Vehicle^2)/2)*(Tyre Vertical Rate*(Track Width of Vehicle^2)/2)/(Tyre Vertical Rate*(Track Width of Vehicle^2)/2+Required Anti Roll Bar Rate+Wheel Centre Rate*(Track Width of Vehicle^2)/2). Here is an example- 76693.26 = (89351+35239*(1.2^2)/2)*(321330*(1.2^2)/2)/(321330*(1.2^2)/2+89351+35239*(1.2^2)/2).

How to calculate Assumed Initial Roll 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) & Tyre Vertical Rate (K_t) we can find Assumed Initial Roll Rate given Required Anti-Roll Bar Rate using the formula - Assumed Initial Roll Rate = (Required Anti Roll Bar Rate+Wheel Centre Rate*(Track Width of Vehicle^2)/2)*(Tyre Vertical Rate*(Track Width of Vehicle^2)/2)/(Tyre Vertical Rate*(Track Width of Vehicle^2)/2+Required Anti Roll Bar Rate+Wheel Centre Rate*(Track Width of Vehicle^2)/2).

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

No, the Assumed Initial Roll Rate given Required Anti-Roll Bar Rate, measured in Torsion Constant cannot be negative.

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

Assumed Initial Roll Rate given Required Anti-Roll Bar Rate is usually measured using the Newton Meter per Radian[Nm/rad] for Torsion Constant. Newton Centimeter per Radian[Nm/rad] are the few other units in which Assumed Initial Roll Rate given Required Anti-Roll Bar Rate can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

Assumed Initial Roll Rate given Required Anti-Roll Bar Rate Formula

Assumed Initial Roll Rate given Required Anti-Roll Bar Rate Example

Assumed Initial Roll Rate given Required Anti-Roll Bar Rate Solution

Assumed Initial Roll Rate given Required Anti-Roll Bar Rate Formula Elements

Other formulas in Wheel Centre Rates for Independent Suspension category

How to Evaluate Assumed Initial Roll Rate given Required Anti-Roll Bar Rate?

FAQs on Assumed Initial Roll Rate given Required Anti-Roll Bar Rate

Variable Name