Vertical Tyre Axle Rate given Roll Rate Calculator

✖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%
✖Tyre Vertical Rate is the spring rate controlled by the tyre compound, sidewall stiffness and operating pressure.ⓘ Tyre Vertical Rate [K_t]			+10% -10%
✖Rear Track Width is the distance between the centers of the rear wheels.ⓘ Rear Track Width [t_R]			+10% -10%
✖Spring Track Width is the distance between the springs on either side of the axle.ⓘ Spring Track Width [T_s]			+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.ⓘ Vertical Tyre Axle Rate given Roll Rate [K_w]

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Vertical Tyre Axle Rate given Roll Rate Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
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.
Rear Track Width - (Measured in Meter) - Rear Track Width is the distance between the centers of the rear wheels.
Spring Track Width - (Measured in Meter) - Spring Track Width is the distance between the springs on either side of the axle.

STEP 1: Convert Input(s) to Base Unit

Roll Rate: 10297.43 Newton Meter per Radian --> 10297.43 Newton Meter per Radian No Conversion Required
Tyre Vertical Rate: 321300 Newton per Meter --> 321300 Newton per Meter No Conversion Required
Rear Track Width: 0.4 Meter --> 0.4 Meter No Conversion Required
Spring Track Width: 0.9 Meter --> 0.9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_w = (K_Φ*K_t*(t_R^2)/2)/(K_t*(t_R^2)/2-K_Φ*(T_s^2)/2) --> (10297.43*321300*(0.4^2)/2)/(321300*(0.4^2)/2-10297.43*(0.9^2)/2)

Evaluating ... ...

K_w = 12291.7611443359

STEP 3: Convert Result to Output's Unit

12291.7611443359 Newton per Meter --> No Conversion Required

FINAL ANSWER

12291.7611443359 ≈ 12291.76 Newton per Meter <-- Wheel Centre 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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< Rates for Axle Suspension in Race Car Calculators

Roll Rate

LaTeX 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)

Spring Track Width given Roll Rate

LaTeX 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

LaTeX 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

LaTeX 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)

Vertical Tyre Axle Rate given Roll Rate Formula

LaTeX Go

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 Vertical Tyre Axle Rate given Roll Rate?

Vertical Tyre Axle Rate given Roll Rate calculator uses 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) to calculate the Wheel Centre Rate, The Vertical tyre axle rate given roll rate formula is used to find the vertical force acting on the tire axle per unit vertical displacement at the location along the spindle corresponding to the wheel centerline, measured relative to the chassis. Wheel Centre Rate is denoted by K_w symbol.

How to calculate Vertical Tyre Axle Rate given Roll Rate using this online calculator? To use this online calculator for Vertical Tyre Axle Rate given Roll Rate, enter Roll Rate (K_Φ), Tyre Vertical Rate (K_t), Rear Track Width (t_R) & Spring Track Width (T_s) and hit the calculate button. Here is how the Vertical Tyre Axle Rate given Roll Rate calculation can be explained with given input values -> 9573.095 = (10297.43*321300*(0.4^2)/2)/(321300*(0.4^2)/2-10297.43*(0.9^2)/2).

FAQ

What is Vertical Tyre Axle Rate given Roll Rate?

The Vertical tyre axle rate given roll rate formula is used to find the vertical force acting on the tire axle per unit vertical displacement at the location along the spindle corresponding to the wheel centerline, measured relative to the chassis and is represented as K_w = (K_Φ*K_t*(t_R^2)/2)/(K_t*(t_R^2)/2-K_Φ*(T_s^2)/2) or 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). Roll Rate or Roll stiffness is the resistance moment generated per unit of roll angle of the sprung mass, Tyre Vertical Rate is the spring rate controlled by the tyre compound, sidewall stiffness and operating pressure, Rear Track Width is the distance between the centers of the rear wheels & Spring Track Width is the distance between the springs on either side of the axle.

How to calculate Vertical Tyre Axle Rate given Roll Rate?

The Vertical tyre axle rate given roll rate formula is used to find the vertical force acting on the tire axle per unit vertical displacement at the location along the spindle corresponding to the wheel centerline, measured relative to the chassis is calculated using 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). To calculate Vertical Tyre Axle Rate given Roll Rate, you need Roll Rate (K_Φ), Tyre Vertical Rate (K_t), Rear Track Width (t_R) & Spring Track Width (T_s). With our tool, you need to enter the respective value for Roll Rate, Tyre Vertical Rate, Rear Track Width & Spring 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 Wheel Centre Rate?

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

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)

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