Tyre Vertical Rate given Wheel Centre Rate Calculator

✖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]			+10% -10%
✖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 given Wheel Centre Rate [K_t]

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Formula

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Tyre Vertical Rate given Wheel Centre Rate

Formula

K t = \frac{K w \cdot K r}{K w - K r}

Example

321330 N/m = \frac{35239 N/m \cdot 31756.4 N/m}{35239 N/m - 31756.4 N/m}

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Tyre Vertical Rate given Wheel Centre Rate Solution

STEP 0: Pre-Calculation Summary

Formula Used

Tyre Vertical Rate = (Wheel Centre Rate*Ride Rate)/(Wheel Centre Rate-Ride Rate)
K_t = (K_w*K_r)/(K_w-K_r)
This formula uses 3 Variables

Variables Used

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.
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.

STEP 1: Convert Input(s) to Base Unit

Wheel Centre Rate: 35239 Newton per Meter --> 35239 Newton per Meter No Conversion Required
Ride Rate: 31756.4 Newton per Meter --> 31756.4 Newton per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_t = (K_w*K_r)/(K_w-K_r) --> (35239*31756.4)/(35239-31756.4)

Evaluating ... ...

K_t = 321329.977488084

STEP 3: Convert Result to Output's Unit

321329.977488084 Newton per Meter --> No Conversion Required

FINAL ANSWER

321329.977488084 ≈ 321330 Newton per Meter <-- Tyre Vertical Rate

(Calculation completed in 00.004 seconds)

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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

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

Tyre Vertical Rate given Wheel Centre Rate Formula

Tyre Vertical Rate = (Wheel Centre Rate*Ride Rate)/(Wheel Centre Rate-Ride Rate)
K_t = (K_w*K_r)/(K_w-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 Tyre Vertical Rate given Wheel Centre Rate?

Tyre Vertical Rate given Wheel Centre Rate calculator uses Tyre Vertical Rate = (Wheel Centre Rate*Ride Rate)/(Wheel Centre Rate-Ride Rate) to calculate the Tyre Vertical Rate, The Tyre vertical rate given wheel centre rate formula is used to find the spring rate controlled by the tyre compound, sidewall stiffness and operating pressure of the tyre. Tyre Vertical Rate is denoted by K_t symbol.

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

FAQ

What is Tyre Vertical Rate given Wheel Centre Rate?

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

How to calculate Tyre Vertical Rate given Wheel Centre Rate?

The Tyre vertical rate given wheel centre rate formula is used to find the spring rate controlled by the tyre compound, sidewall stiffness and operating pressure of the tyre is calculated using Tyre Vertical Rate = (Wheel Centre Rate*Ride Rate)/(Wheel Centre Rate-Ride Rate). To calculate Tyre Vertical Rate given Wheel Centre Rate, you need Wheel Centre Rate (K_w) & Ride Rate (K_r). With our tool, you need to enter the respective value for Wheel Centre Rate & Ride 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 Tyre Vertical Rate?

In this formula, Tyre Vertical Rate uses Wheel Centre Rate & Ride Rate. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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