Slip Ratio Defined According to SAE J670 Calculator

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Race Car Vehicle Dynamics

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Slip Ratio

Angular Velocity

Rolling

✖Wheel Angular Velocity is defined as the number of rotations the wheel makes in a given unit of time.ⓘ Wheel Angular Velocity [Ω_w]			+10% -10%
✖Effective Rolling Radius for Free Rolling is the rolling radius measured for free rolling and the tyre has to be at zero slip angle.ⓘ Effective Rolling Radius for Free Rolling [R_e]			+10% -10%
✖Axle Speed over Roadway is the translational speed of the axle with reference to the roadway.ⓘ Axle Speed over Roadway [V_Roadway]			+10% -10%
✖Slip Angle or sideslip angle is the angle between the direction in which a wheel is pointing and the direction in which it is actually traveling.ⓘ Slip Angle [α_slip]			+10% -10%

✖Slip Ratio is defined as the ratio of longitudinal slip to the angular velocity of the free rolling wheel.ⓘ Slip Ratio Defined According to SAE J670 [SR]

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Formula

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Slip Ratio Defined According to SAE J670

Formula

`"SR" = "Ω"_{"w"}*"R"_{"e"}/("V"_{"Roadway"}*cos("α"_{"slip"}))-1`

Example

`"0.207233"="44rad/s"*"0.82m"/("30m/s"*cos("0.0870rad"))-1`

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Download Tire Behavior in Racing Car Formulas PDF

Slip Ratio Defined According to SAE J670 Solution

STEP 0: Pre-Calculation Summary

Formula Used

Slip Ratio = Wheel Angular Velocity*Effective Rolling Radius for Free Rolling/(Axle Speed over Roadway*cos(Slip Angle))-1
SR = Ω_w*R_e/(V_Roadway*cos(α_slip))-1
This formula uses 1 Functions, 5 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Slip Ratio - Slip Ratio is defined as the ratio of longitudinal slip to the angular velocity of the free rolling wheel.
Wheel Angular Velocity - (Measured in Radian per Second) - Wheel Angular Velocity is defined as the number of rotations the wheel makes in a given unit of time.
Effective Rolling Radius for Free Rolling - (Measured in Meter) - Effective Rolling Radius for Free Rolling is the rolling radius measured for free rolling and the tyre has to be at zero slip angle.
Axle Speed over Roadway - (Measured in Meter per Second) - Axle Speed over Roadway is the translational speed of the axle with reference to the roadway.
Slip Angle - (Measured in Radian) - Slip Angle or sideslip angle is the angle between the direction in which a wheel is pointing and the direction in which it is actually traveling.

STEP 1: Convert Input(s) to Base Unit

Wheel Angular Velocity: 44 Radian per Second --> 44 Radian per Second No Conversion Required
Effective Rolling Radius for Free Rolling: 0.82 Meter --> 0.82 Meter No Conversion Required
Axle Speed over Roadway: 30 Meter per Second --> 30 Meter per Second No Conversion Required
Slip Angle: 0.087 Radian --> 0.087 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

SR = Ω_w*R_e/(V_Roadway*cos(α_slip))-1 --> 44*0.82/(30*cos(0.087))-1

Evaluating ... ...

SR = 0.207232557253867

STEP 3: Convert Result to Output's Unit

0.207232557253867 --> No Conversion Required

FINAL ANSWER

0.207232557253867 ≈ 0.207233 <-- Slip Ratio

(Calculation completed in 00.004 seconds)

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< 5 Slip Ratio Calculators

Slip Ratio Defined According to Calspan TIRF

Go Slip Ratio = Wheel Angular Velocity*Height of Axle above Road Surface (Loaded Radius)/(Axle Speed over Roadway*cos(Slip Angle))-1

Slip Ratio Defined According to Goodyear

Go Slip Ratio = 1-(Axle Speed over Roadway*cos(Slip Angle))/(Wheel Angular Velocity*Effective Rolling Radius for Free Rolling)

Slip Ratio Defined According to SAE J670

Go Slip Ratio = Wheel Angular Velocity*Effective Rolling Radius for Free Rolling/(Axle Speed over Roadway*cos(Slip Angle))-1

Slip Ratio given Velocity of Driven Wheel and Free Rolling Wheel

Go Slip Ratio = Angular Velocity of Driven (or braked) Wheel/Angular Velocity of Free Rolling Wheel-1

Slip Ratio given Longitudinal Slip Velocity and Velocity of Free Rolling Wheel

Go Slip Ratio = Longitudinal (Angular) Slip Velocity/Angular Velocity of Free Rolling Wheel

Slip Ratio Defined According to SAE J670 Formula

Slip Ratio = Wheel Angular Velocity*Effective Rolling Radius for Free Rolling/(Axle Speed over Roadway*cos(Slip Angle))-1
SR = Ω_w*R_e/(V_Roadway*cos(α_slip))-1

What is slip angle?

Slip angle also known as sideslip angle is the angle between the direction in which a wheel is pointing and the direction in which it is actually traveling. This slip angle results in a force, the cornering force, which is in the plane of the contact patch and perpendicular to the intersection of the contact patch and the midplane of the wheel. This cornering force increases approximately linearly for the first few degrees of slip angle, then increases non-linearly to a maximum before beginning to decrease.

What are the effects of slip angle?

The ratios between the slip angles of the front and rear axles (a function of the slip angles of the front and rear tires respectively) will determine the vehicle's behavior in a given turn. If the ratio of front to rear slip angles is greater than 1:1, the vehicle will tend to understeer, while a ratio of less than 1:1 will produce oversteer. Actual instantaneous slip angles depend on many factors, including the condition of the road surface, but a vehicle's suspension can be designed to promote specific dynamic characteristics. A principal means of adjusting developed slip angles is to alter the relative roll couple (the rate at which weight transfers from the inside to the outside wheel in a turn) front to rear by varying the relative amount of front and rear lateral load transfer. This can be achieved by modifying the height of the roll centers, or by adjusting roll stiffness, either through suspension changes or the addition of an anti-roll bar.

How to Calculate Slip Ratio Defined According to SAE J670?

Slip Ratio Defined According to SAE J670 calculator uses Slip Ratio = Wheel Angular Velocity*Effective Rolling Radius for Free Rolling/(Axle Speed over Roadway*cos(Slip Angle))-1 to calculate the Slip Ratio, The Slip ratio defined according to SAE J670 formula uses the effective rolling radius for free rolling at zero slip angle to evaluate the slip ratio. Slip Ratio is denoted by SR symbol.

How to calculate Slip Ratio Defined According to SAE J670 using this online calculator? To use this online calculator for Slip Ratio Defined According to SAE J670, enter Wheel Angular Velocity (Ω_w), Effective Rolling Radius for Free Rolling (R_e), Axle Speed over Roadway (V_Roadway) & Slip Angle (α_slip) and hit the calculate button. Here is how the Slip Ratio Defined According to SAE J670 calculation can be explained with given input values -> 0.221955 = 44*0.82/(30*cos(0.087))-1.

FAQ

What is Slip Ratio Defined According to SAE J670?

The Slip ratio defined according to SAE J670 formula uses the effective rolling radius for free rolling at zero slip angle to evaluate the slip ratio and is represented as SR = Ω_w*R_e/(V_Roadway*cos(α_slip))-1 or Slip Ratio = Wheel Angular Velocity*Effective Rolling Radius for Free Rolling/(Axle Speed over Roadway*cos(Slip Angle))-1. Wheel Angular Velocity is defined as the number of rotations the wheel makes in a given unit of time, Effective Rolling Radius for Free Rolling is the rolling radius measured for free rolling and the tyre has to be at zero slip angle, Axle Speed over Roadway is the translational speed of the axle with reference to the roadway & Slip Angle or sideslip angle is the angle between the direction in which a wheel is pointing and the direction in which it is actually traveling.

How to calculate Slip Ratio Defined According to SAE J670?

The Slip ratio defined according to SAE J670 formula uses the effective rolling radius for free rolling at zero slip angle to evaluate the slip ratio is calculated using Slip Ratio = Wheel Angular Velocity*Effective Rolling Radius for Free Rolling/(Axle Speed over Roadway*cos(Slip Angle))-1. To calculate Slip Ratio Defined According to SAE J670, you need Wheel Angular Velocity (Ω_w), Effective Rolling Radius for Free Rolling (R_e), Axle Speed over Roadway (V_Roadway) & Slip Angle (α_slip). With our tool, you need to enter the respective value for Wheel Angular Velocity, Effective Rolling Radius for Free Rolling, Axle Speed over Roadway & Slip Angle 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 Slip Ratio?

In this formula, Slip Ratio uses Wheel Angular Velocity, Effective Rolling Radius for Free Rolling, Axle Speed over Roadway & Slip Angle. We can use 4 other way(s) to calculate the same, which is/are as follows -

Slip Ratio = Longitudinal (Angular) Slip Velocity/Angular Velocity of Free Rolling Wheel
Slip Ratio = Angular Velocity of Driven (or braked) Wheel/Angular Velocity of Free Rolling Wheel-1
Slip Ratio = Wheel Angular Velocity*Height of Axle above Road Surface (Loaded Radius)/(Axle Speed over Roadway*cos(Slip Angle))-1
Slip Ratio = 1-(Axle Speed over Roadway*cos(Slip Angle))/(Wheel Angular Velocity*Effective Rolling Radius for Free Rolling)

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