Wheel Centre 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

✖Ride Rate is defined as vertical force per unit vertical displacement of the tire ground contact with respect to chassis.ⓘ Ride Rate [K_r]			+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%

✖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]

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Formula

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Wheel Centre Rate

Formula

`"K"_{"W"} = ("K"_{"r"}*"K"_{"t"})/("K"_{"t"}-"K"_{"r"})`

Example

`"35239N/m"=("31756.4N/m"*"321330N/m")/("321330N/m"-"31756.4N/m")`

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Download Wheel Centre Rates for Independent Suspension Formulas PDF

Wheel Centre Rate Solution

STEP 0: Pre-Calculation Summary

Formula Used

Wheel Centre Rate = (Ride Rate*Tyre Vertical Rate)/(Tyre Vertical Rate-Ride Rate)
K_W = (K_r*K_t)/(K_t-K_r)
This formula uses 3 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.
Ride Rate - (Measured in Newton per Meter) - Ride Rate is defined as vertical force per unit vertical displacement of the tire ground contact with respect to chassis.
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.

STEP 1: Convert Input(s) to Base Unit

Ride Rate: 31756.4 Newton per Meter --> 31756.4 Newton per Meter No Conversion Required
Tyre Vertical Rate: 321330 Newton per Meter --> 321330 Newton per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_W = (K_r*K_t)/(K_t-K_r) --> (31756.4*321330)/(321330-31756.4)

Evaluating ... ...

K_W = 35238.9997292571

STEP 3: Convert Result to Output's Unit

35238.9997292571 Newton per Meter --> No Conversion Required

FINAL ANSWER

35238.9997292571 ≈ 35239 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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< 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 Formula

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

Why to use this formula?

With the tyre selected able to generate our required cornering forces, we can add in our tyre vertical spring rate to come to a wheel centre rate. In reality, there are two springs acting between the chassis and the ground. These two springs are the wheel centre rate, controlled by the spring and anti-roll bar, and the vertical tyre rate, controlled by the tyre compound, sidewall stiffness and operating pressure. In order to combine these two spring effects to create one, we must add them together. Although they are acting in series, the equation is slightly different than our linear springs in series equation due to the tyre rate being involved. Therefore, we use this formula.

How to Calculate Wheel Centre Rate?

Wheel Centre Rate calculator uses Wheel Centre Rate = (Ride Rate*Tyre Vertical Rate)/(Tyre Vertical Rate-Ride Rate) to calculate the Wheel Centre Rate, The Wheel centre rate formula is defined to find 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 is denoted by K_W symbol.

How to calculate Wheel Centre Rate using this online calculator? To use this online calculator for Wheel Centre Rate, enter Ride Rate (K_r) & Tyre Vertical Rate (K_t) and hit the calculate button. Here is how the Wheel Centre Rate calculation can be explained with given input values -> 35239 = (31756.4*321330)/(321330-31756.4).

FAQ

What is Wheel Centre Rate?

The Wheel centre rate formula is defined to find 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 and is represented as K_W = (K_r*K_t)/(K_t-K_r) or Wheel Centre Rate = (Ride Rate*Tyre Vertical Rate)/(Tyre Vertical Rate-Ride Rate). Ride Rate is defined as vertical force per unit vertical displacement of the tire ground contact with respect to chassis & Tyre Vertical Rate is the spring rate controlled by the tyre compound, sidewall stiffness and operating pressure.

How to calculate Wheel Centre Rate?

The Wheel centre rate formula is defined to find 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 is calculated using Wheel Centre Rate = (Ride Rate*Tyre Vertical Rate)/(Tyre Vertical Rate-Ride Rate). To calculate Wheel Centre Rate, you need Ride Rate (K_r) & Tyre Vertical Rate (K_t). With our tool, you need to enter the respective value for Ride Rate & Tyre Vertical 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 Ride Rate & Tyre Vertical Rate. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)

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