Tyre Rate given Roll Rate Calculator

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Race Car Vehicle Dynamics

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Rates for Axle Suspension in Race Car

Ride Rate and Ride Frequency for Race Cars

Tire Behavior in Racing Car

Vehicle Cornering in Race Cars

Weight Transfer during Braking

Wheel Centre Rates for Independent Suspension

✖Roll Rate or Roll stiffness is the resistance moment generated per unit of roll angle of the sprung mass.ⓘ Roll Rate [K_Φ]			+10% -10%
✖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.ⓘ Wheel Centre Rate [K_W]			+10% -10%
✖Spring Track Width is the distance between the springs on either side of the axle.ⓘ Spring Track Width [T_s]			+10% -10%
✖Rear Track Width is the distance between the centers of the rear wheels.ⓘ Rear Track Width [t_R]			+10% -10%

✖Tyre Vertical Rate is the spring rate controlled by the tyre compound, sidewall stiffness and operating pressure.ⓘ Tyre Rate given Roll Rate [K_t]

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Formula

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Tyre Rate given Roll Rate

Formula

`"K"_{"t"} = ("K"_{"Φ"}*("K"_{"W"}*("T"_{"s"}^2)/2))/(("K"_{"W"}*("T"_{"s"}^2)/2-"K"_{"Φ"})*("t"_{"R"}^2)/2)`

Example

`"33539.54N/m"=("11805Nm/rad"*("42419.8N/m"*(("0.9m")^2)/2))/(("42419.8N/m"*(("0.9m")^2)/2-"11805Nm/rad")*(("1.5m")^2)/2)`

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Download Rates for Axle Suspension in Race Car Formulas PDF

Tyre Rate given Roll Rate Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
K_t = (K_Φ*(K_W*(T_s^2)/2))/((K_W*(T_s^2)/2-K_Φ)*(t_R^2)/2)
This formula uses 5 Variables

Variables Used

Tyre Vertical Rate - (Measured in Newton per Meter) - Tyre Vertical Rate is the spring rate controlled by the tyre compound, sidewall stiffness and operating pressure.
Roll Rate - (Measured in Newton Meter per Radian) - Roll Rate or Roll stiffness is the resistance moment generated per unit of roll angle of the sprung mass.
Wheel Centre Rate - (Measured in Newton per Meter) - 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.
Spring Track Width - (Measured in Meter) - Spring Track Width is the distance between the springs on either side of the axle.
Rear Track Width - (Measured in Meter) - Rear Track Width is the distance between the centers of the rear wheels.

STEP 1: Convert Input(s) to Base Unit

Roll Rate: 11805 Newton Meter per Radian --> 11805 Newton Meter per Radian No Conversion Required
Wheel Centre Rate: 42419.8 Newton per Meter --> 42419.8 Newton per Meter No Conversion Required
Spring Track Width: 0.9 Meter --> 0.9 Meter No Conversion Required
Rear Track Width: 1.5 Meter --> 1.5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_t = (K_Φ*(K_W*(T_s^2)/2))/((K_W*(T_s^2)/2-K_Φ)*(t_R^2)/2) --> (11805*(42419.8*(0.9^2)/2))/((42419.8*(0.9^2)/2-11805)*(1.5^2)/2)

Evaluating ... ...

K_t = 33539.5402397647

STEP 3: Convert Result to Output's Unit

33539.5402397647 Newton per Meter --> No Conversion Required

FINAL ANSWER

33539.5402397647 ≈ 33539.54 Newton per Meter <-- Tyre Vertical Rate

(Calculation completed in 00.004 seconds)

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Created by Peri Krishna Karthik

National Institute of Technology Calicut (NIT Calicut), Calicut, Kerala

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< 10+ Rates for Axle Suspension in Race Car Calculators

Roll Rate with Anti-Roll Bar

Go Roll Rate = (Tyre Vertical Rate*(Rear Track Width^2)/2*(Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width^2)/2))/(Tyre Vertical Rate*(Rear Track Width^2)/2+Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width^2)/2)

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

Go 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))

Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar

Go 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)

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

Go 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))

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

Go 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)

Roll Rate

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

Rear Track Width given Roll Rate

Go 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))

Spring Track Width given Roll Rate

Go 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))

Tyre Rate given Roll Rate

Go 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)

Vertical Tyre Axle Rate given Roll Rate

Go 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)

Tyre Rate given Roll Rate Formula

How these calculations differ from those of Independent suspension?

Beam axle suspension has a slightly more complex approach to calculating the ride and roll rates due to springs not being located at the outboard track locations like an independent suspension system. Due to the springs being further inboard of the track, the spring rates are effectively softer in roll than the equivalent rates would be in an independent suspension system. Therefore the springs must be decoupled from ride and roll modes and we must look directly at the springs in their mounted position at the axle as opposed to using ideal ride and roll rates.

How to Calculate Tyre Rate given Roll Rate?

Tyre Rate given Roll Rate calculator 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 calculate 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 K_t symbol.

How to calculate Tyre Rate given Roll Rate using this online calculator? To use this online calculator for Tyre Rate given Roll Rate, enter Roll Rate (K_Φ), Wheel Centre Rate (K_W), Spring Track Width (T_s) & Rear Track Width (t_R) and hit the calculate button. Here is how the Tyre Rate given Roll Rate calculation can be explained with given input values -> 33539.54 = (11805*(42419.8*(0.9^2)/2))/((42419.8*(0.9^2)/2-11805)*(1.5^2)/2).

FAQ

What is Tyre Rate given Roll 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 and is represented as K_t = (K_Φ*(K_W*(T_s^2)/2))/((K_W*(T_s^2)/2-K_Φ)*(t_R^2)/2) or 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). Roll Rate or Roll stiffness is the resistance moment generated per unit of roll angle of the sprung mass, 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, Spring Track Width is the distance between the springs on either side of the axle & Rear Track Width is the distance between the centers of the rear wheels.

How to calculate Tyre Rate given Roll 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 is calculated using 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 calculate Tyre Rate given Roll Rate, you need Roll Rate (K_Φ), Wheel Centre Rate (K_W), Spring Track Width (T_s) & Rear Track Width (t_R). With our tool, you need to enter the respective value for Roll Rate, Wheel Centre Rate, Spring Track Width & Rear Track Width and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Tyre Vertical Rate?

In this formula, Tyre Vertical Rate uses Roll Rate, Wheel Centre Rate, Spring Track Width & Rear Track Width. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)

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