Roll Rate Calculator

✖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%
✖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%

✖Roll Rate or Roll stiffness is the resistance moment generated per unit of roll angle of the sprung mass.ⓘ Roll Rate [K_Φ]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Rates for Axle Suspension in Race Car Formulas PDF PDF Image

Roll Rate Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.

STEP 1: Convert Input(s) to Base Unit

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
Wheel Centre Rate: 30366.46 Newton per Meter --> 30366.46 Newton per 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_Φ = (K_t*(t_R^2)/2*K_w*(T_s^2)/2)/(K_t*t_R^2/2+K_w*T_s^2/2) --> (321300*(0.4^2)/2*30366.46*(0.9^2)/2)/(321300*0.4^2/2+30366.46*0.9^2/2)

Evaluating ... ...

K_Φ = 8318.37875991059

STEP 3: Convert Result to Output's Unit

8318.37875991059 Newton Meter per Radian --> No Conversion Required

FINAL ANSWER

8318.37875991059 ≈ 8318.379 Newton Meter per Radian <-- Roll Rate

(Calculation completed in 00.066 seconds)

You are here -

Home » Physics » Automobile » Race Car Vehicle Dynamics » Mechanical » Rates for Axle Suspension in Race Car » Roll Rate

Credits

Created by Peri Krishna Karthik

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

Peri Krishna Karthik has created this Calculator and 200+ more calculators!

Verified by sanjay shiva

national institute of technology hamirpur (NITH ), hamirpur , himachal pradesh

sanjay shiva has verified this Calculator and 100+ more calculators!

< 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)

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 Roll Rate?

Roll Rate calculator uses 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) to calculate the Roll Rate, The Roll rate formula is used to find the stiffness of the car with an axle suspension in the roll mode. Roll Rate is denoted by K_Φ symbol.

How to calculate Roll Rate using this online calculator? To use this online calculator for Roll Rate, enter Tyre Vertical Rate (K_t), Rear Track Width (t_R), Wheel Centre Rate (K_w) & Spring Track Width (T_s) and hit the calculate button. Here is how the Roll Rate calculation can be explained with given input values -> 8318.379 = (321300*(0.4^2)/2*30366.46*(0.9^2)/2)/(321300*0.4^2/2+30366.46*0.9^2/2).

FAQ

What is Roll Rate?

The Roll rate formula is used to find the stiffness of the car with an axle suspension in the roll mode and is represented as K_Φ = (K_t*(t_R^2)/2*K_w*(T_s^2)/2)/(K_t*t_R^2/2+K_w*T_s^2/2) or 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). 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, 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.

How to calculate Roll Rate?

The Roll rate formula is used to find the stiffness of the car with an axle suspension in the roll mode is calculated using 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). To calculate Roll Rate, you need Tyre Vertical Rate (K_t), Rear Track Width (t_R), Wheel Centre Rate (K_w) & Spring Track Width (T_s). With our tool, you need to enter the respective value for Tyre Vertical Rate, Rear Track Width, Wheel Centre Rate & 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 Roll Rate?

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

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)

Home

FREE PDFs

🔍 Search