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Tyre Vertical Rate is the spring rate controlled by the tyre compound, sidewall stiffness and operating pressure. Check FAQs
Kt=KΦ(KwTs22)(KwTs22-KΦ)tR22
Kt - Tyre Vertical Rate?KΦ - Roll Rate?Kw - Wheel Centre Rate?Ts - Spring Track Width?tR - Rear Track Width?

Tyre Rate given Roll Rate Example

With values
With units
Only example

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

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

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

791122.8638Edit=10297.43Edit(30366.46Edit0.9Edit22)(30366.46Edit0.9Edit22-10297.43Edit)0.4Edit22
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Tyre Rate given Roll Rate Solution

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

FIRST Step Consider the formula
Kt=KΦ(KwTs22)(KwTs22-KΦ)tR22
Next Step Substitute values of Variables
Kt=10297.43Nm/rad(30366.46N/m0.9m22)(30366.46N/m0.9m22-10297.43Nm/rad)0.4m22
Next Step Prepare to Evaluate
Kt=10297.43(30366.460.922)(30366.460.922-10297.43)0.422
Next Step Evaluate
Kt=791122.863760417N/m
LAST Step Rounding Answer
Kt=791122.8638N/m

Tyre Rate given Roll Rate Formula Elements

Variables
Tyre Vertical Rate
Tyre Vertical Rate is the spring rate controlled by the tyre compound, sidewall stiffness and operating pressure.
Symbol: Kt
Measurement: Surface TensionUnit: N/m
Note: Value should be greater than 0.
Roll Rate
Roll Rate or Roll stiffness is the resistance moment generated per unit of roll angle of the sprung mass.
Symbol: KΦ
Measurement: Torsion ConstantUnit: Nm/rad
Note: Value should be greater than 0.
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: Kw
Measurement: Surface TensionUnit: N/m
Note: Value should be greater than 0.
Spring Track Width
Spring Track Width is the distance between the springs on either side of the axle.
Symbol: Ts
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Rear Track Width
Rear Track Width is the distance between the centers of the rear wheels.
Symbol: tR
Measurement: LengthUnit: m
Note: Value should be greater than 0.

Other Formulas to find Tyre Vertical Rate

​Go Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar
Kt=KΦ(Rarb+KwTs22)(Rarb+KwTs22-KΦ)tR22

Other formulas in Rates for Axle Suspension in Race Car category

​Go Roll Rate
KΦ=KttR22KwTs22KttR22+KwTs22
​Go Vertical Tyre Axle Rate given Roll Rate
Kw=KΦKttR22KttR22-KΦTs22
​Go Spring Track Width given Roll Rate
Ts=KΦKttR2(KttR22-KΦ)Kw
​Go Rear Track Width given Roll Rate
tR=KΦKwTs2(KwTs22-KΦ)Kt

How to Evaluate Tyre Rate given Roll Rate?

Tyre Rate given Roll Rate evaluator uses 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) to evaluate the Tyre Vertical Rate, The Tyre rate given roll rate 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 Kt symbol.

How to evaluate Tyre Rate given Roll Rate using this online evaluator? To use this online evaluator for Tyre Rate given Roll Rate, enter Roll Rate (KΦ), Wheel Centre Rate (Kw), Spring Track Width (Ts) & Rear Track Width (tR) and hit the calculate button.

FAQs on Tyre Rate given Roll Rate

What is the formula to find Tyre Rate given Roll Rate?
The formula of Tyre Rate given Roll Rate is expressed as 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). Here is an example- 321300 = (10297.43*(30366.46*(0.9^2)/2))/((30366.46*(0.9^2)/2-10297.43)*(0.4^2)/2).
How to calculate Tyre Rate given Roll Rate?
With Roll Rate (KΦ), Wheel Centre Rate (Kw), Spring Track Width (Ts) & Rear Track Width (tR) we can find Tyre Rate given Roll Rate using the formula - 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).
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*(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)OpenImg
Can the Tyre Rate given Roll Rate be negative?
No, the Tyre Rate given Roll Rate, measured in Surface Tension cannot be negative.
Which unit is used to measure Tyre Rate given Roll Rate?
Tyre 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 Tyre Rate given Roll Rate can be measured.
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