Steer Angle given Understeer Gradient Solution

STEP 0: Pre-Calculation Summary
Formula Used
Steer Angle = (57.3*(Wheelbase of Vehicle/Radius of Turn))+(Understeer Gradient*Horizontal Lateral Acceleration)
δ = (57.3*(b/R))+(K*Aα)
This formula uses 5 Variables
Variables Used
Steer Angle - (Measured in Radian) - Steer Angle is the angle made by the wheel with respect to the vertical when steering is rotated.
Wheelbase of Vehicle - (Measured in Meter) - Wheelbase of Vehicle is the center distance between the front and the rear axle of the vehicle.
Radius of Turn - (Measured in Meter) - Radius of Turn is defined as the distance of the c.g of vehicle from the instantaneous center while taking a turn.
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.
Horizontal Lateral Acceleration - (Measured in Meter per Square Second) - Horizontal Lateral Acceleration is the lateral acceleration in the horizontal direction due to cornering forces.
STEP 1: Convert Input(s) to Base Unit
Wheelbase of Vehicle: 2700 Millimeter --> 2.7 Meter (Check conversion here)
Radius of Turn: 10500 Millimeter --> 10.5 Meter (Check conversion here)
Understeer Gradient: 0.104 Radian --> 0.104 Radian No Conversion Required
Horizontal Lateral Acceleration: 1.6 Meter per Square Second --> 1.6 Meter per Square Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
δ = (57.3*(b/R))+(K*Aα) --> (57.3*(2.7/10.5))+(0.104*1.6)
Evaluating ... ...
δ = 14.9006857142857
STEP 3: Convert Result to Output's Unit
14.9006857142857 Radian --> No Conversion Required
FINAL ANSWER
14.9006857142857 14.90069 Radian <-- Steer Angle
(Calculation completed in 00.019 seconds)

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Ramaiah University of Applied Sciences (RUAS), bangalore
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6 Angles Related to Steering System Calculators

Caster Angle
Go Caster Angle = sin(Camber 1)-sin(Camber 2)-(cos(Camber 2)*cos(Toe Angle 2)-cos(Camber 1)*cos(Toe Angle 1))*tan(Steering Axis Inclination)/(cos(Camber 2)*sin(Toe Angle 2)-cos(Camber 1)*sin(Toe Angle 1))
Steering Angle at High Cornering Speed
Go Ackermann Steering Angle at High Cornering Speed = 57.3*(Wheelbase of Vehicle/Radius of Turn)+(Slip Angle of Front Wheel-Slip Angle of Rear Wheel)
Steer Angle given Understeer Gradient
Go Steer Angle = (57.3*(Wheelbase of Vehicle/Radius of Turn))+(Understeer Gradient*Horizontal Lateral Acceleration)
Ackermann Steering Angle at Low Speed Cornering
Go Ackermann Steering Angle in Slow Speed cornering = Wheelbase of Vehicle/Radius of Turn
Slip Angle at High Cornering Speed
Go Slip Angle at High Cornering Speed = Cornering Force/Cornering Stiffness
Vehicle Body Slip Angle at High Cornering Speed
Go Vehicle Body Slip Angle = Lateral Velocity Component/Total Velocity

Steer Angle given Understeer Gradient Formula

Steer Angle = (57.3*(Wheelbase of Vehicle/Radius of Turn))+(Understeer Gradient*Horizontal Lateral Acceleration)
δ = (57.3*(b/R))+(K*Aα)

What is steer angle and what is its significance?

Steering angle means the angle between the projection of a longitudinal axis of the vehicle and the line of intersection of the wheel plane (being the central plane of the wheel, normal to the axis around which it rotates) and the road surface. At higher speeds, the lateral acceleration during cornering increases and it cannot be neglected. This gives rise to slip angles at the wheels and the tires produce lateral forces in order to counteract the lateral acceleration.

How to Calculate Steer Angle given Understeer Gradient?

Steer Angle given Understeer Gradient calculator uses Steer Angle = (57.3*(Wheelbase of Vehicle/Radius of Turn))+(Understeer Gradient*Horizontal Lateral Acceleration) to calculate the Steer Angle, The Steer angle given understeer gradient formula is defined as the angle between the front of the vehicle and the steered wheel direction when the understeer gradient is known. Steer Angle is denoted by δ symbol.

How to calculate Steer Angle given Understeer Gradient using this online calculator? To use this online calculator for Steer Angle given Understeer Gradient, enter Wheelbase of Vehicle (b), Radius of Turn (R), Understeer Gradient (K) & Horizontal Lateral Acceleration (Aα) and hit the calculate button. Here is how the Steer Angle given Understeer Gradient calculation can be explained with given input values -> 14.90069 = (57.3*(2.7/10.5))+(0.104*1.6).

FAQ

What is Steer Angle given Understeer Gradient?
The Steer angle given understeer gradient formula is defined as the angle between the front of the vehicle and the steered wheel direction when the understeer gradient is known and is represented as δ = (57.3*(b/R))+(K*Aα) or Steer Angle = (57.3*(Wheelbase of Vehicle/Radius of Turn))+(Understeer Gradient*Horizontal Lateral Acceleration). Wheelbase of Vehicle is the center distance between the front and the rear axle of the vehicle, Radius of Turn is defined as the distance of the c.g of vehicle from the instantaneous center while taking a turn, 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 & Horizontal Lateral Acceleration is the lateral acceleration in the horizontal direction due to cornering forces.
How to calculate Steer Angle given Understeer Gradient?
The Steer angle given understeer gradient formula is defined as the angle between the front of the vehicle and the steered wheel direction when the understeer gradient is known is calculated using Steer Angle = (57.3*(Wheelbase of Vehicle/Radius of Turn))+(Understeer Gradient*Horizontal Lateral Acceleration). To calculate Steer Angle given Understeer Gradient, you need Wheelbase of Vehicle (b), Radius of Turn (R), Understeer Gradient (K) & Horizontal Lateral Acceleration (Aα). With our tool, you need to enter the respective value for Wheelbase of Vehicle, Radius of Turn, Understeer Gradient & Horizontal Lateral Acceleration and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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