Wheel Centre Rate given Required Anti-Roll Bar Rate Calculator

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Race Car Vehicle Dynamics

Driveline

Front Axle and Steering

Suspension Geometry

Vehicle Collision

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Wheel Centre Rates for Independent Suspension

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

✖The Assumed Initial Roll Rate is the initial spring rate of the anti-roll bar assumed before calculating the required anti-roll bar rate.ⓘ Assumed Initial 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%
✖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%
✖Required Anti Roll Bar Rate is the required amount of spring rate of the roll bar for the system.ⓘ Required Anti Roll Bar Rate [K_ΦA]			+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 given Required Anti-Roll Bar Rate [K_W]

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Formula

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Wheel Centre Rate given Required Anti-Roll Bar Rate

Formula

`"K"_{"W"} = ("K"_{"Φ"}*("K"_{"t"}*("a"^2)/2)/("K"_{"t"}*("a"^2)/2-"K"_{"Φ"})-"K"_{"ΦA"})/(("a"^2)/2)`

Example

`"35238.18N/m"=("76693Nm/rad"*("321330N/m"*(("1.2m")^2)/2)/("321330N/m"*(("1.2m")^2)/2-"76693Nm/rad")-"89351Nm/rad")/((("1.2m")^2)/2)`

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Download Wheel Centre Rates for Independent Suspension Formulas PDF

Wheel Centre Rate given Required Anti-Roll Bar Rate Solution

STEP 0: Pre-Calculation Summary

Formula Used

Wheel Centre Rate = (Assumed Initial Roll Rate*(Tyre Vertical Rate*(Track Width of Vehicle^2)/2)/(Tyre Vertical Rate*(Track Width of Vehicle^2)/2-Assumed Initial Roll Rate)-Required Anti Roll Bar Rate)/((Track Width of Vehicle^2)/2)
K_W = (K_Φ*(K_t*(a^2)/2)/(K_t*(a^2)/2-K_Φ)-K_ΦA)/((a^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.
Assumed Initial Roll Rate - (Measured in Newton Meter per Radian) - The Assumed Initial Roll Rate is the initial spring rate of the anti-roll bar assumed before calculating the required anti-roll bar rate.
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.
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).
Required Anti Roll Bar Rate - (Measured in Newton Meter per Radian) - Required Anti Roll Bar Rate is the required amount of spring rate of the roll bar for the system.

STEP 1: Convert Input(s) to Base Unit

Assumed Initial Roll Rate: 76693 Newton Meter per Radian --> 76693 Newton Meter per Radian No Conversion Required
Tyre Vertical Rate: 321330 Newton per Meter --> 321330 Newton per Meter No Conversion Required
Track Width of Vehicle: 1.2 Meter --> 1.2 Meter No Conversion Required
Required Anti Roll Bar Rate: 89351 Newton Meter per Radian --> 89351 Newton Meter per Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_W = (K_Φ*(K_t*(a^2)/2)/(K_t*(a^2)/2-K_Φ)-K_ΦA)/((a^2)/2) --> (76693*(321330*(1.2^2)/2)/(321330*(1.2^2)/2-76693)-89351)/((1.2^2)/2)

Evaluating ... ...

K_W = 35238.1840572726

STEP 3: Convert Result to Output's Unit

35238.1840572726 Newton per Meter --> No Conversion Required

FINAL ANSWER

35238.1840572726 ≈ 35238.18 Newton per Meter <-- Wheel Centre Rate

(Calculation completed in 00.004 seconds)

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< 12 Wheel Centre Rates for Independent Suspension Calculators

Assumed Initial Roll Rate given Required Anti-Roll Bar Rate

Go Assumed Initial Roll Rate = (Required Anti Roll Bar Rate+Wheel Centre Rate*(Track Width of Vehicle^2)/2)*(Tyre Vertical Rate*(Track Width of Vehicle^2)/2)/(Tyre Vertical Rate*(Track Width of Vehicle^2)/2+Required Anti Roll Bar Rate+Wheel Centre Rate*(Track Width of Vehicle^2)/2)

Tyre Rate given Required Anti-Roll Bar Rate

Go Tyre Vertical Rate = (((Required Anti Roll Bar Rate+Wheel Centre Rate*(Track Width of Vehicle^2)/2)*Assumed Initial Roll Rate)/((Required Anti Roll Bar Rate+Wheel Centre Rate*(Track Width of Vehicle^2)/2)-Assumed Initial Roll Rate))*2/Track Width of Vehicle^2

Wheel Centre Rate given Required Anti-Roll Bar Rate

Go Wheel Centre Rate = (Assumed Initial Roll Rate*(Tyre Vertical Rate*(Track Width of Vehicle^2)/2)/(Tyre Vertical Rate*(Track Width of Vehicle^2)/2-Assumed Initial Roll Rate)-Required Anti Roll Bar Rate)/((Track Width of Vehicle^2)/2)

Required Anti-Roll Bar Rate

Go Required Anti Roll Bar Rate = Assumed Initial Roll Rate*(Tyre Vertical Rate*(Track Width of Vehicle^2)/2)/(Tyre Vertical Rate*(Track Width of Vehicle^2)/2-Assumed Initial Roll Rate)-Wheel Centre Rate*(Track Width of Vehicle^2)/2

Power Absorbed by Disc Brake

Go Power Absorbed by Disc Brake = 2*Line Pressure*Area of One Piston per Caliper*Coefficient of Friction of Pad Material*Mean Radius of Caliper unit to Disc Axis*Number of Caliper Units*2*Number of Caliper Units*Revolution of Discs per Minute/60

Area of Brake Lining

Go Area of Brake Lining = (Brake Lining Width*Brake Drum Radius*Angle between Linings of Brake Shoes*pi)/180

Ride Rate given Wheel Centre Rate

Go Ride Rate = (Tyre Vertical Rate*Wheel Centre Rate)/(Tyre Vertical Rate+Wheel Centre Rate)

Wheel Centre Rate

Go Wheel Centre Rate = (Ride Rate*Tyre Vertical Rate)/(Tyre Vertical Rate-Ride Rate)

Tyre Vertical Rate given Wheel Centre Rate

Go Tyre Vertical Rate = (Wheel Centre Rate*Ride Rate)/(Wheel Centre Rate-Ride Rate)

Work Done in Braking

Go Work done in Braking = Braking Force on Brake Drum*Stopping Distance during Braking in Meters

Brake Fluid Pressure

Go Brake Fluid Pressure = Force Produced by Master Cylinder/Area of Master Cylinder Piston

Braking Efficiency

Go Braking Efficiency = (Braking Force on Brake Drum/Weight of Vehicle)*100

Wheel Centre Rate given Required Anti-Roll Bar Rate Formula

What are the main functions of anti-roll bar?

The first function is the reduction of body lean which is dependent on the total roll stiffness of the vehicle. Increasing which does not change the steady-state total load (weight) transfer from the inside wheels to the outside wheels, it only reduces body lean. The total lateral load transfer is determined by the CG height and track width. The other function is to tune the handling balance of a car. Understeer or oversteer behaviour can be tuned out by changing the proportion of the total roll stiffness that comes from the front and rear axles. Increasing the proportion of roll stiffness at the front increases the proportion of total load transfer that front axle reacts to—and decreases proportion that rear axle reacts to. In general, this makes outer front wheel run at a comparatively higher slip angle, and outer rear wheel run at a comparatively lower slip angle, which is an understeer effect. Increasing the proportion of roll stiffness at the rear axle has the opposite effect and decreases understeer.

What are the drawbacks of anti-roll bar?

Because an anti-roll bar connects wheels on opposite sides of the vehicle, the bar transmits the force of a bump on one wheel to the opposite wheel. On rough or broken pavement, anti-roll bars can produce jarring, side-to-side body motions (a "waddling" sensation), which increase in severity with the diameter and stiffness of the sway bars. Other suspension techniques can delay or dampen this effect of the connecting bar. Excessive roll stiffness, typically achieved by configuring an anti-roll bar too aggressively, can make the inside wheels lift off the ground during hard cornering. This can be used to advantage: many front-wheel-drive production cars lift a rear wheel when cornering hard in order to overload the opposite wheel, limiting understeer.

How to Calculate Wheel Centre Rate given Required Anti-Roll Bar Rate?

Wheel Centre Rate given Required Anti-Roll Bar Rate calculator uses Wheel Centre Rate = (Assumed Initial Roll Rate*(Tyre Vertical Rate*(Track Width of Vehicle^2)/2)/(Tyre Vertical Rate*(Track Width of Vehicle^2)/2-Assumed Initial Roll Rate)-Required Anti Roll Bar Rate)/((Track Width of Vehicle^2)/2) to calculate the Wheel Centre Rate, The Wheel centre rate given required anti-roll bar rate formula is defined to find the vertical force acting on the tire per unit vertical displacement at the location along with the spindle corresponding to the wheel centerline, measured relative to the chassis. Wheel Centre Rate is denoted by K_W symbol.

How to calculate Wheel Centre Rate given Required Anti-Roll Bar Rate using this online calculator? To use this online calculator for Wheel Centre Rate given Required Anti-Roll Bar Rate, enter Assumed Initial Roll Rate (K_Φ), Tyre Vertical Rate (K_t), Track Width of Vehicle (a) & Required Anti Roll Bar Rate (K_ΦA) and hit the calculate button. Here is how the Wheel Centre Rate given Required Anti-Roll Bar Rate calculation can be explained with given input values -> 35238.18 = (76693*(321330*(1.2^2)/2)/(321330*(1.2^2)/2-76693)-89351)/((1.2^2)/2).

FAQ

What is Wheel Centre Rate given Required Anti-Roll Bar Rate?

The Wheel centre rate given required anti-roll bar rate formula is defined to find the vertical force acting on the tire per unit vertical displacement at the location along with the spindle corresponding to the wheel centerline, measured relative to the chassis and is represented as K_W = (K_Φ*(K_t*(a^2)/2)/(K_t*(a^2)/2-K_Φ)-K_ΦA)/((a^2)/2) or Wheel Centre Rate = (Assumed Initial Roll Rate*(Tyre Vertical Rate*(Track Width of Vehicle^2)/2)/(Tyre Vertical Rate*(Track Width of Vehicle^2)/2-Assumed Initial Roll Rate)-Required Anti Roll Bar Rate)/((Track Width of Vehicle^2)/2). The Assumed Initial Roll Rate is the initial spring rate of the anti-roll bar assumed before calculating the required anti-roll bar rate, Tyre Vertical Rate is the spring rate controlled by the tyre compound, sidewall stiffness and operating pressure, Track Width of Vehicle is the distance between the center line of each of the two wheels on the same axle (front/rear axle) & Required Anti Roll Bar Rate is the required amount of spring rate of the roll bar for the system.

How to calculate Wheel Centre Rate given Required Anti-Roll Bar Rate?

The Wheel centre rate given required anti-roll bar rate formula is defined to find the vertical force acting on the tire per unit vertical displacement at the location along with the spindle corresponding to the wheel centerline, measured relative to the chassis is calculated using Wheel Centre Rate = (Assumed Initial Roll Rate*(Tyre Vertical Rate*(Track Width of Vehicle^2)/2)/(Tyre Vertical Rate*(Track Width of Vehicle^2)/2-Assumed Initial Roll Rate)-Required Anti Roll Bar Rate)/((Track Width of Vehicle^2)/2). To calculate Wheel Centre Rate given Required Anti-Roll Bar Rate, you need Assumed Initial Roll Rate (K_Φ), Tyre Vertical Rate (K_t), Track Width of Vehicle (a) & Required Anti Roll Bar Rate (K_ΦA). With our tool, you need to enter the respective value for Assumed Initial Roll Rate, Tyre Vertical Rate, Track Width of Vehicle & Required Anti Roll Bar Rate 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 Assumed Initial Roll Rate, Tyre Vertical Rate, Track Width of Vehicle & Required Anti Roll Bar Rate. We can use 1 other way(s) to calculate the same, which is/are as follows -

Wheel Centre Rate = (Ride Rate*Tyre Vertical Rate)/(Tyre Vertical Rate-Ride Rate)

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