## Roll rate or Roll stiffness Solution

STEP 0: Pre-Calculation Summary
Formula Used
Roll rate/ Roll stiffness = ((Track Width of Vehicle^2)*Wheel rate of vehicle)/2
KΦ = ((a^2)*Kt)/2
This formula uses 3 Variables
Variables Used
Roll rate/ Roll stiffness - (Measured in Newton Meter per Radian) - Roll rate/ Roll stiffness is the resistance moment generated per unit of roll angle of the sprung mass, and it has SI units of Nm/rad.
Track Width of Vehicle - (Measured in Meter) - Track Width of Vehicle is the distance between the center line of each of the two wheels on the same axle (front/rear axle).
Wheel rate of vehicle - (Measured in Newton per Meter) - Wheel rate of vehicle is effectively the spring rate when measured at the wheel as opposed to at the spring.
STEP 1: Convert Input(s) to Base Unit
Track Width of Vehicle: 1.2 Meter --> 1.2 Meter No Conversion Required
Wheel rate of vehicle: 100 Newton per Meter --> 100 Newton per Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
KΦ = ((a^2)*Kt)/2 --> ((1.2^2)*100)/2
Evaluating ... ...
KΦ = 72
STEP 3: Convert Result to Output's Unit
72 Newton Meter per Radian --> No Conversion Required
72 Newton Meter per Radian <-- Roll rate/ Roll stiffness
(Calculation completed in 00.004 seconds)
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## <Race Car Vehicle Dynamics Calculators

Spring rate provided Wheel rate
​ Go Stiffness of Spring = Wheel rate of vehicle/(((Motion ratio in suspension)^2)*(cos(Angle of spring/shock absorber from vertical)))
Wheel rate in vehicle
​ Go Wheel rate of vehicle = Stiffness of Spring*((Motion ratio in suspension)^2)*(Spring angle correction factor)
Spring angle correction factor
​ Go Spring angle correction factor = cos(Angle of spring/shock absorber from vertical)
Roll rate or Roll stiffness
​ Go Roll rate/ Roll stiffness = ((Track Width of Vehicle^2)*Wheel rate of vehicle)/2

## Roll rate or Roll stiffness Formula

Roll rate/ Roll stiffness = ((Track Width of Vehicle^2)*Wheel rate of vehicle)/2
KΦ = ((a^2)*Kt)/2

## What is roll rate or Stiffness?

When cornering, the sprung mass of the car will roll by an amount Φ, the roll angle. This is reacted by the roll stiffness (or roll rate), KΦ of the car. Roll stiffness is defined as the resistance moment generated per unit of the roll angle of the sprung mass, and it has SI units of Nm/rad.

## How to Calculate Roll rate or Roll stiffness?

Roll rate or Roll stiffness calculator uses Roll rate/ Roll stiffness = ((Track Width of Vehicle^2)*Wheel rate of vehicle)/2 to calculate the Roll rate/ Roll stiffness, Roll rate or Roll stiffness is defined as the resistance moment generated per unit of the roll angle of the sprung mass. Roll rate/ Roll stiffness is denoted by KΦ symbol.

How to calculate Roll rate or Roll stiffness using this online calculator? To use this online calculator for Roll rate or Roll stiffness, enter Track Width of Vehicle (a) & Wheel rate of vehicle (Kt) and hit the calculate button. Here is how the Roll rate or Roll stiffness calculation can be explained with given input values -> 72 = ((1.2^2)*100)/2.

### FAQ

What is Roll rate or Roll stiffness?
Roll rate or Roll stiffness is defined as the resistance moment generated per unit of the roll angle of the sprung mass and is represented as KΦ = ((a^2)*Kt)/2 or Roll rate/ Roll stiffness = ((Track Width of Vehicle^2)*Wheel rate of vehicle)/2. Track Width of Vehicle is the distance between the center line of each of the two wheels on the same axle (front/rear axle) & Wheel rate of vehicle is effectively the spring rate when measured at the wheel as opposed to at the spring.
How to calculate Roll rate or Roll stiffness?
Roll rate or Roll stiffness is defined as the resistance moment generated per unit of the roll angle of the sprung mass is calculated using Roll rate/ Roll stiffness = ((Track Width of Vehicle^2)*Wheel rate of vehicle)/2. To calculate Roll rate or Roll stiffness, you need Track Width of Vehicle (a) & Wheel rate of vehicle (Kt). With our tool, you need to enter the respective value for Track Width of Vehicle & Wheel rate of vehicle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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