Rear Track Width given Roll Rate Calculator

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Race Car Vehicle Dynamics

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Front Axle and Steering

Suspension Geometry

Vehicle Collision

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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

Wheel Centre Rates for Independent Suspension

✖Roll Rate or Roll stiffness is the resistance moment generated per unit of roll angle of the sprung mass.ⓘ Roll Rate [K_Φ]			+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]			+10% -10%
✖Spring Track Width is the distance between the springs on either side of the axle.ⓘ Spring Track Width [T_s]			+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%

✖Rear Track Width is the distance between the centers of the rear wheels.ⓘ Rear Track Width given Roll Rate [t_R]

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Formula

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Rear Track Width given Roll Rate

Formula

`"t"_{"R"} = sqrt(("K"_{"Φ"}*"K"_{"W"}*"T"_{"s"}^2)/(("K"_{"W"}*("T"_{"s"}^2)/2-"K"_{"Φ"})*"K"_{"t"}))`

Example

`"0.484635m"=sqrt(("11805Nm/rad"*"42419.8N/m"*("0.9m")^2)/(("42419.8N/m"*(("0.9m")^2)/2-"11805Nm/rad")*"321300N/m"))`

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Download Rates for Axle Suspension in Race Car Formulas PDF PDF Image

Rear Track Width given Roll Rate Solution

STEP 0: Pre-Calculation Summary

Formula Used

Rear Track Width = sqrt((Roll Rate*Wheel Centre Rate*Spring Track Width^2)/((Wheel Centre Rate*(Spring Track Width^2)/2-Roll Rate)*Tyre Vertical Rate))
t_R = sqrt((K_Φ*K_W*T_s^2)/((K_W*(T_s^2)/2-K_Φ)*K_t))
This formula uses 1 Functions, 5 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Rear Track Width - (Measured in Meter) - Rear Track Width is the distance between the centers of the rear wheels.
Roll Rate - (Measured in Newton Meter per Radian) - Roll Rate or Roll stiffness is the resistance moment generated per unit of roll angle of the sprung mass.
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.
Spring Track Width - (Measured in Meter) - Spring Track Width is the distance between the springs on either side of the axle.
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

Roll Rate: 11805 Newton Meter per Radian --> 11805 Newton Meter per Radian No Conversion Required
Wheel Centre Rate: 42419.8 Newton per Meter --> 42419.8 Newton per Meter No Conversion Required
Spring Track Width: 0.9 Meter --> 0.9 Meter No Conversion Required
Tyre Vertical Rate: 321300 Newton per Meter --> 321300 Newton per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_R = sqrt((K_Φ*K_W*T_s^2)/((K_W*(T_s^2)/2-K_Φ)*K_t)) --> sqrt((11805*42419.8*0.9^2)/((42419.8*(0.9^2)/2-11805)*321300))

Evaluating ... ...

t_R = 0.484634635545522

STEP 3: Convert Result to Output's Unit

0.484634635545522 Meter --> No Conversion Required

FINAL ANSWER

0.484634635545522 ≈ 0.484635 Meter <-- Rear Track Width

(Calculation completed in 00.004 seconds)

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Created by Peri Krishna Karthik

National Institute of Technology Calicut (NIT Calicut), Calicut, Kerala

Peri Krishna Karthik has created this Calculator and 200+ more calculators!

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< 10+ Rates for Axle Suspension in Race Car Calculators

Roll Rate with Anti-Roll Bar

Go Roll Rate = (Tyre Vertical Rate*(Rear Track Width^2)/2*(Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width^2)/2))/(Tyre Vertical Rate*(Rear Track Width^2)/2+Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width^2)/2)

Rear Track Width given Roll Rate of Suspension with Anti-Roll Bar

Go Rear Track Width = sqrt(2*(Roll Rate*(Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width)^2/2))/((Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width^2)/2-Roll Rate)*Tyre Vertical Rate))

Tyre Rate given Roll Rate of Suspension with Anti-Roll Bar

Go Tyre Vertical Rate = (Roll Rate*(Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width^2)/2))/((Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width^2)/2-Roll Rate)*(Rear Track Width^2)/2)

Spring Track Width given Roll Rate of Suspension with Anti-Roll Bar

Go Spring Track Width = sqrt(2*(((Roll Rate*Tyre Vertical Rate*(Rear Track Width^2)/2)/((Tyre Vertical Rate*(Rear Track Width^2)/2-Roll Rate))-Roll Rate of Anti-Roll Bar)/Wheel Centre Rate))

Vertical Tyre Axle Rate given Roll Rate of Suspension with Anti-Roll Bar

Go Wheel Centre Rate = ((Roll Rate*Tyre Vertical Rate*(Rear Track Width^2)/2)/(Tyre Vertical Rate*(Rear Track Width^2)/2-Roll Rate)-Roll Rate of Anti-Roll Bar)/((Spring Track Width^2)/2)

Roll Rate

Go Roll Rate = (Tyre Vertical Rate*(Rear Track Width^2)/2*Wheel Centre Rate*(Spring Track Width^2)/2)/(Tyre Vertical Rate*Rear Track Width^2/2+Wheel Centre Rate*Spring Track Width^2/2)

Rear Track Width given Roll Rate

Go Rear Track Width = sqrt((Roll Rate*Wheel Centre Rate*Spring Track Width^2)/((Wheel Centre Rate*(Spring Track Width^2)/2-Roll Rate)*Tyre Vertical Rate))

Spring Track Width given Roll Rate

Go Spring Track Width = sqrt((Roll Rate*Tyre Vertical Rate*Rear Track Width^2)/((Tyre Vertical Rate*(Rear Track Width^2)/2-Roll Rate)*Wheel Centre Rate))

Tyre Rate given Roll Rate

Go Tyre Vertical Rate = (Roll Rate*(Wheel Centre Rate*(Spring Track Width^2)/2))/((Wheel Centre Rate*(Spring Track Width^2)/2-Roll Rate)*(Rear Track Width^2)/2)

Vertical Tyre Axle Rate given Roll Rate

Go Wheel Centre Rate = (Roll Rate*Tyre Vertical Rate*(Rear Track Width^2)/2)/(Tyre Vertical Rate*(Rear Track Width^2)/2-Roll Rate*(Spring Track Width^2)/2)

Rear Track Width given Roll Rate Formula

How these calculations differ from those of Independent suspension?

Beam axle suspension has a slightly more complex approach to calculating the ride and roll rates due to springs not being located at the outboard track locations like an independent suspension system. Due to the springs being further inboard of the track, the spring rates are effectively softer in roll than the equivalent rates would be in an independent suspension system. Therefore the springs must be decoupled from ride and roll modes and we must look directly at the springs in their mounted position at the axle as opposed to using ideal ride and roll rates.

How to Calculate Rear Track Width given Roll Rate?

Rear Track Width given Roll Rate calculator uses Rear Track Width = sqrt((Roll Rate*Wheel Centre Rate*Spring Track Width^2)/((Wheel Centre Rate*(Spring Track Width^2)/2-Roll Rate)*Tyre Vertical Rate)) to calculate the Rear Track Width, The Rear track width given roll rate formula is used to find the distance between the centres of the rear wheels. Rear Track Width is denoted by t_R symbol.

How to calculate Rear Track Width given Roll Rate using this online calculator? To use this online calculator for Rear Track Width given Roll Rate, enter Roll Rate (K_Φ), Wheel Centre Rate (K_W), Spring Track Width (T_s) & Tyre Vertical Rate (K_t) and hit the calculate button. Here is how the Rear Track Width given Roll Rate calculation can be explained with given input values -> 0.484635 = sqrt((11805*42419.8*0.9^2)/((42419.8*(0.9^2)/2-11805)*321300)).

FAQ

What is Rear Track Width given Roll Rate?

The Rear track width given roll rate formula is used to find the distance between the centres of the rear wheels and is represented as t_R = sqrt((K_Φ*K_W*T_s^2)/((K_W*(T_s^2)/2-K_Φ)*K_t)) or Rear Track Width = sqrt((Roll Rate*Wheel Centre Rate*Spring Track Width^2)/((Wheel Centre Rate*(Spring Track Width^2)/2-Roll Rate)*Tyre Vertical Rate)). Roll Rate or Roll stiffness is the resistance moment generated per unit of roll angle of the sprung mass, 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, Spring Track Width is the distance between the springs on either side of the axle & Tyre Vertical Rate is the spring rate controlled by the tyre compound, sidewall stiffness and operating pressure.

How to calculate Rear Track Width given Roll Rate?

The Rear track width given roll rate formula is used to find the distance between the centres of the rear wheels is calculated using Rear Track Width = sqrt((Roll Rate*Wheel Centre Rate*Spring Track Width^2)/((Wheel Centre Rate*(Spring Track Width^2)/2-Roll Rate)*Tyre Vertical Rate)). To calculate Rear Track Width given Roll Rate, you need Roll Rate (K_Φ), Wheel Centre Rate (K_W), Spring Track Width (T_s) & Tyre Vertical Rate (K_t). With our tool, you need to enter the respective value for Roll Rate, Wheel Centre Rate, Spring Track Width & 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 Rear Track Width?

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

Rear Track Width = sqrt(2*(Roll Rate*(Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width)^2/2))/((Roll Rate of Anti-Roll Bar+Wheel Centre Rate*(Spring Track Width^2)/2-Roll Rate)*Tyre Vertical Rate))

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