Understeer Gradient Calculator

⤿

Front Axle and Steering

Driveline

Race Car Vehicle Dynamics

Suspension Geometry

Vehicle Collision

⤿

Steering System

Moments, Loads, Angles acting on Steering system and Axles

Movement Ratio

Pivot Centre, Wheel Base and Track

Turning Radius

⤿

Angles Related to Steering System

✖Load on Front Axle at High Speed Cornering is the partial load acting on the front axle when the vehicle takes a turn at high speed.ⓘ Load on Front Axle at High Speed Cornering [W_fl]			+10% -10%
✖Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖Cornering Stiffness of Front Wheels is defined as the slope of the cornering force of front wheel versus slip angle curve.ⓘ Cornering Stiffness of Front Wheels [C_af]			+10% -10%
✖Load on rear axle at high speed Cornering is the partial load acting on the rear axle when the vehicle is taking a turn at higher speeds.ⓘ Load on Rear Axle at High Speed Cornering [W_r]			+10% -10%
✖Cornering Stiffness of Rear Wheels is the slope of the cornering force of rear wheels versus slip angle curve.ⓘ Cornering Stiffness of Rear Wheels [C_αr]			+10% -10%

✖Understeer Gradient is defined as the derivative of the front tires average steer angle with respect to the lateral acceleration imposed to the vehicle at its center of gravity.ⓘ Understeer Gradient [K]

⎘ Copy

👎

Formula

✖

Understeer Gradient

Formula

`"K" = ("W"_{"fl"}/("g"*"C"_{"af"}))-("W"_{"r"}/("g"*"C"_{"αr"}))`

Example

`"0.218659rad"=("9000N"/("9.8m/s²"*"40N"))-("7800N"/("9.8m/s²"*"35N"))`

Calculator

LaTeX

Reset

👍

Download Steering System Formulas PDF PDF Image

Understeer Gradient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Understeer Gradient = (Load on Front Axle at High Speed Cornering/(Acceleration due to Gravity*Cornering Stiffness of Front Wheels))-(Load on Rear Axle at High Speed Cornering/(Acceleration due to Gravity*Cornering Stiffness of Rear Wheels))
K = (W_fl/(g*C_af))-(W_r/(g*C_αr))
This formula uses 6 Variables

Variables Used

Understeer Gradient - (Measured in Radian) - Understeer Gradient is defined as the derivative of the front tires average steer angle with respect to the lateral acceleration imposed to the vehicle at its center of gravity.
Load on Front Axle at High Speed Cornering - (Measured in Newton) - Load on Front Axle at High Speed Cornering is the partial load acting on the front axle when the vehicle takes a turn at high speed.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Cornering Stiffness of Front Wheels - (Measured in Newton) - Cornering Stiffness of Front Wheels is defined as the slope of the cornering force of front wheel versus slip angle curve.
Load on Rear Axle at High Speed Cornering - (Measured in Newton) - Load on rear axle at high speed Cornering is the partial load acting on the rear axle when the vehicle is taking a turn at higher speeds.
Cornering Stiffness of Rear Wheels - (Measured in Newton) - Cornering Stiffness of Rear Wheels is the slope of the cornering force of rear wheels versus slip angle curve.

STEP 1: Convert Input(s) to Base Unit

Load on Front Axle at High Speed Cornering: 9000 Newton --> 9000 Newton No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Cornering Stiffness of Front Wheels: 40 Newton --> 40 Newton No Conversion Required
Load on Rear Axle at High Speed Cornering: 7800 Newton --> 7800 Newton No Conversion Required
Cornering Stiffness of Rear Wheels: 35 Newton --> 35 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K = (W_fl/(g*C_af))-(W_r/(g*C_αr)) --> (9000/(9.8*40))-(7800/(9.8*35))

Evaluating ... ...

K = 0.218658892128278

STEP 3: Convert Result to Output's Unit

0.218658892128278 Radian --> No Conversion Required

FINAL ANSWER

0.218658892128278 ≈ 0.218659 Radian <-- Understeer Gradient

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Automobile » Front Axle and Steering » Steering System » Understeer Gradient

Credits

Created by Syed Adnan

Ramaiah University of Applied Sciences (RUAS), bangalore

Syed Adnan has created this Calculator and 200+ more calculators!

Verified by Kartikay Pandit

National Institute Of Technology (NIT), Hamirpur

Kartikay Pandit has verified this Calculator and 400+ more calculators!

< 6 Steering System Calculators

Understeer Gradient

Go Understeer Gradient = (Load on Front Axle at High Speed Cornering/(Acceleration due to Gravity*Cornering Stiffness of Front Wheels))-(Load on Rear Axle at High Speed Cornering/(Acceleration due to Gravity*Cornering Stiffness of Rear Wheels))

Understeer Increment due to Steering System Compliance

Go Under Steer Increment due to Steering Compliance = (Weight under Front Axle*(Turning Radius of Car*Caster Angle+Pneumatic Trail of Tire))/Effective Stiffness of Steering System

Pinion Pitch Circle Radius

Go Pinion Pitch Circle Radius = (Number of Pinion Teeth*Linear or Circular Pitch)/(2*pi)

Steering Ratio

Go Steering Ratio = Steering Wheel Radius/Pinion Pitch Circle Radius

Motion Ratio or Installation Ratio in Suspension

Go Motion Ratio in Suspension = Spring/Shock Travel/Wheel Travel

Torque Acting on Steering Arm

Go Torque = Frictional Force*Scrub Radius

Understeer Gradient Formula

What is understeer gradient?

Understeer and oversteer are defined by an understeer gradient (K) that is a measure of how the steering needed for a steady turn changes as a function of lateral acceleration. Steering at a steady speed is compared to the steering that would be needed to follow the same circular path at low speed.The vehicle has a positive understeer gradient if the difference between required steer and the Ackermann steer increases with respect to incremental increases in lateral acceleration. The vehicle has a negative gradient if the difference in steer decreases with respect to incremental increases in lateral acceleration.

How to Calculate Understeer Gradient?

Understeer Gradient calculator uses Understeer Gradient = (Load on Front Axle at High Speed Cornering/(Acceleration due to Gravity*Cornering Stiffness of Front Wheels))-(Load on Rear Axle at High Speed Cornering/(Acceleration due to Gravity*Cornering Stiffness of Rear Wheels)) to calculate the Understeer Gradient, The Understeer gradient formula is defined as the tendency for a vehicle to require more or less steering input relative to the Ackermann steer angle is a measure of under steer. The gain due to lateral acceleration is the understeer gradient. Understeer Gradient is denoted by K symbol.

How to calculate Understeer Gradient using this online calculator? To use this online calculator for Understeer Gradient, enter Load on Front Axle at High Speed Cornering (W_fl), Acceleration due to Gravity (g), Cornering Stiffness of Front Wheels (C_af), Load on Rear Axle at High Speed Cornering (W_r) & Cornering Stiffness of Rear Wheels (C_αr) and hit the calculate button. Here is how the Understeer Gradient calculation can be explained with given input values -> 717.8148 = (9000/(9.8*40))-(7800/(9.8*35)).

FAQ

What is Understeer Gradient?

The Understeer gradient formula is defined as the tendency for a vehicle to require more or less steering input relative to the Ackermann steer angle is a measure of under steer. The gain due to lateral acceleration is the understeer gradient and is represented as K = (W_fl/(g*C_af))-(W_r/(g*C_αr)) or Understeer Gradient = (Load on Front Axle at High Speed Cornering/(Acceleration due to Gravity*Cornering Stiffness of Front Wheels))-(Load on Rear Axle at High Speed Cornering/(Acceleration due to Gravity*Cornering Stiffness of Rear Wheels)). Load on Front Axle at High Speed Cornering is the partial load acting on the front axle when the vehicle takes a turn at high speed, Acceleration due to Gravity is acceleration gained by an object because of gravitational force, Cornering Stiffness of Front Wheels is defined as the slope of the cornering force of front wheel versus slip angle curve, Load on rear axle at high speed Cornering is the partial load acting on the rear axle when the vehicle is taking a turn at higher speeds & Cornering Stiffness of Rear Wheels is the slope of the cornering force of rear wheels versus slip angle curve.

How to calculate Understeer Gradient?

The Understeer gradient formula is defined as the tendency for a vehicle to require more or less steering input relative to the Ackermann steer angle is a measure of under steer. The gain due to lateral acceleration is the understeer gradient is calculated using Understeer Gradient = (Load on Front Axle at High Speed Cornering/(Acceleration due to Gravity*Cornering Stiffness of Front Wheels))-(Load on Rear Axle at High Speed Cornering/(Acceleration due to Gravity*Cornering Stiffness of Rear Wheels)). To calculate Understeer Gradient, you need Load on Front Axle at High Speed Cornering (W_fl), Acceleration due to Gravity (g), Cornering Stiffness of Front Wheels (C_af), Load on Rear Axle at High Speed Cornering (W_r) & Cornering Stiffness of Rear Wheels (C_αr). With our tool, you need to enter the respective value for Load on Front Axle at High Speed Cornering, Acceleration due to Gravity, Cornering Stiffness of Front Wheels, Load on Rear Axle at High Speed Cornering & Cornering Stiffness of Rear Wheels and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search