Wheel Centre Rate Calculator

✖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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Download Wheel Centre Rates for Independent Suspension Formulas PDF PDF Image

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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< Wheel Centre Rates for Independent Suspension Calculators

Assumed Initial Roll Rate given Required Anti-Roll Bar Rate

LaTeX 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

LaTeX 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

LaTeX 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

LaTeX 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

Wheel Centre Rate Formula

LaTeX Go

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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