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✖Track Width of Vehicle is the distance between the center line of each of the two wheels on the same axle (front/rear axle).ⓘ Track Width of Vehicle [a] | +10% -10% | ||
✖Wheel rate of vehicle is effectively the spring rate when measured at the wheel as opposed to at the spring.ⓘ Wheel rate of vehicle [Kt] | +10% -10% |
| ✖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.ⓘ Roll rate or Roll stiffness [KΦ] | ⎘ Copy |
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Formula
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Roll rate or Roll stiffness
Formula
`"K"_{"Φ"} = (("a"^2)*"K"_{"t"})/2`
Example
`"72Nm/rad"=((("1.2m")^2)*"100N/m")/2`
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Download Race Car Vehicle Dynamics Formula PDF
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 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. STEP 1: Convert Input(s) to Base Unit Track Width of Vehicle: 1.2 Meter --> 1.2 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 FINAL ANSWER 72 Newton Meter per Radian <-- Roll rate/ Roll stiffness (Calculation completed in 00.004 seconds)
KΦ = ((a^2)*Kt)/2
This formula uses 3 Variables
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.
Wheel rate of vehicle: 100 Newton per Meter --> 100 Newton per Meter No Conversion Required
12 Race Car Vehicle Dynamics Calculators
Height of Center of Gravity of Vehicle by method of jacking Vehicle from Rear
Go Height of Center of gravity (C.G.) of vehicle = (Loaded radius of front wheels*(Horizontal distance of C.G. From rear axle/Wheelbase of Vehicle))+(Loaded radius of rear wheels*(Horizontal distance of C.G. From rear axle/Wheelbase of Vehicle))+(((Weight of front wheels with rear elevated*Wheelbase of Vehicle)-(Mass of vehicle*Horizontal distance of C.G. From rear axle))/(Mass of vehicle*tan(Angle through which rear axle of vehicle raised)))
Spring rate required for coilover given desired droop and motion ratio
Go Stiffness of Spring = Corner sprung mass of vehicle*Acceleration due to Gravity/(Motion ratio in suspension*Wheel travel*cos(Angle of spring/shock absorber from vertical))
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)))
Installation Ratio given Wheel Rate
Go Installation ratio = sqrt(Wheel rate of vehicle/(Spring rate*cos(Damper angle from vertical)))
Damper angle from Vertical given wheel rate
Go Damper angle from vertical = acos(Wheel rate of vehicle/(Spring rate*(Installation ratio^2)))
Spring rate given wheel rate
Go Spring rate = Wheel rate of vehicle/((Installation ratio^2)*cos(Damper angle from vertical))
Wheel rate
Go Wheel rate of vehicle = Spring rate*(Installation ratio^2)*cos(Damper angle from vertical)
Wheel rate in vehicle
Go Wheel rate of vehicle = Stiffness of Spring*((Motion ratio in suspension)^2)*(Spring angle correction factor)
Track Width of Vehicle given Wheel rate and Roll rate
Go Track Width of Vehicle = sqrt((2*Roll rate/ Roll stiffness)/Wheel rate of vehicle)
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
Wheel rate given Roll rate
Go Wheel rate of vehicle = (2*Roll rate/ Roll stiffness)/Track Width 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.
