Coordinate Systems in Vehicle Dynamics Blockset

Vehicle Dynamics Blockset™ uses these coordinate systems to calculate the vehicle dynamics and position objects in the 3D visualization environment.

Environment	Description	Coordinate Systems
Vehicle dynamics in Simulink^®	The right-hand rule establishes the X-Y-Z sequence and rotation of the coordinate axes used to calculate the vehicle dynamics. The Vehicle Dynamics Blockset 3D simulation environment uses these right-handed (RH) Cartesian coordinate systems defined in the SAE J670^[2] and ISO 8855^[3] standards: Earth-fixed (inertial) Vehicle Tire Wheel The coordinate systems can have either orientation: Z-down — Defined in SAE J670^[2] Z-up — Defined in SAE J670^[2] and ISO 8855^[3]	Earth-Fixed (Inertial) Coordinate System Vehicle Coordinate System Tire and Wheel Coordinate Systems
3D visualization engine	To position objects and query the 3D visualization environment, the Vehicle Dynamics Blockset uses a world coordinate system.	World Coordinate System

Environment

Description

Coordinate Systems

Vehicle dynamics in Simulink^®

The right-hand rule establishes the X-Y-Z sequence and rotation of the coordinate axes used to calculate the vehicle dynamics. The Vehicle Dynamics Blockset 3D simulation environment uses these right-handed (RH) Cartesian coordinate systems defined in the SAE J670^[2] and ISO 8855^[3] standards:

Earth-fixed (inertial)
Vehicle
Tire
Wheel

The coordinate systems can have either orientation:

Z-down — Defined in SAE J670^[2]
Z-up — Defined in SAE J670^[2] and ISO 8855^[3]

Earth-Fixed (Inertial) Coordinate System

Vehicle Coordinate System

Tire and Wheel Coordinate Systems

3D visualization engine

To position objects and query the 3D visualization environment, the Vehicle Dynamics Blockset uses a world coordinate system.

World Coordinate System

Earth-Fixed (Inertial) Coordinate System

The earth-fixed coordinate system (X_E, Y_E, Z_E) axes are fixed in an inertial reference frame. The inertial reference frame has zero linear and angular acceleration and zero angular velocity. In Newtonian physics, the earth is an inertial reference.

Diagrams of vehicle and earth-fixed coordinate systems with the z-axis pointing down

Axis	Description
X_E	The X_E axis is in the forward direction of the vehicle. The X_E and Y_E axes are parallel to the ground plane. The ground plane is a horizontal plane normal to the gravitational vector.
Y_E
Z_E	In the Z-up orientation, the positive Z_E axis points upward. In the Z-down orientation, the positive Z_E axis points downward.

Axis

Description

X_E

The X_E axis is in the forward direction of the vehicle.

The X_E and Y_E axes are parallel to the ground plane. The ground plane is a horizontal plane normal to the gravitational vector.

Y_E

Z_E

In the Z-up orientation, the positive Z_E axis points upward.

In the Z-down orientation, the positive Z_E axis points downward.

Vehicle Coordinate System

The vehicle coordinate system axes (X_V, Y_V, Z_V) are fixed in a reference frame attached to the vehicle. The origin is at the vehicle sprung mass.

Z-Down Orientation

Diagram of vehicle coordinate systems with the z-axis pointing down

Axis	Description
X_V	The X_V axis points forward and is parallel to the vehicle plane of symmetry.
Y_V	The Y_V axis is perpendicular to the vehicle plane of symmetry. In the Z-down orientation: Y_V axis points to the right Z_Vaxis points downward
Z_V

Axis

Description

X_V

The X_V axis points forward and is parallel to the vehicle plane of symmetry.

Y_V

The Y_V axis is perpendicular to the vehicle plane of symmetry.

In the Z-down orientation:

Y_V axis points to the right
Z_Vaxis points downward

Z_V

Tire and Wheel Coordinate Systems

The tire coordinate system axes (X_T, Y_T, Z_T) are fixed in a reference frame attached to the tire. The origin is at the tire contact with the ground.

The wheel coordinate system axes (X_W, Y_W, Z_W) are fixed in a reference frame attached to the wheel. The origin is at the wheel center.

Z-Up Orientation^a	Z-Up Orientation with Radii and Deflection Defined	Z-Down Orientation

^a Reprinted with permission Copyright © 2008 SAE International. Further distribution of this material is not permitted without prior permission from SAE.

Axis	Description
X_T	X_T and Y_T are parallel to the road plane. The intersection of the wheel plane and the road plane define the orientation of the X_T axis.
Y_T
Z_T	Z_T points: Upward in the Z-up orientation Downward in the Z-down orientation
X_W	X_W and Y_W are parallel to the wheel plane: X_W is parallel to the local road plane. Y_W is parallel to the wheel-spin axis.
Y_W
Z_W	Z_W points: Upward in the Z-up orientation Downward in the Z-down orientation

World Coordinate System

The 3D visualization environment uses a world coordinate system with axes that are fixed in the inertial reference frame.

Inertial reference frame with X, Y, Z, Yaw, Pitch, and Roll labeled

Axis	Description
X	Forward direction of the vehicle Roll — Right-handed rotation about X-axis
Y	Extends to the right of the vehicle, parallel to the ground plane Pitch — Right-handed rotation about Y-axis
Z	Extends upwards Yaw — Left-handed rotation about Z-axis

Axis

Description

Forward direction of the vehicle

Roll — Right-handed rotation about X-axis

Extends to the right of the vehicle, parallel to the ground plane

Pitch — Right-handed rotation about Y-axis

Extends upwards

Yaw — Left-handed rotation about Z-axis

References

[1] Gillespie, Thomas. Fundamentals of Vehicle Dynamics. Warrendale, PA: Society of Automotive Engineers, 1992.

[2] Vehicle Dynamics Standards Committee. Vehicle Dynamics Terminology. SAE J670. Warrendale, PA: Society of Automotive Engineers, 2008.

[3] Technical Committee. Road vehicles — Vehicle dynamics and road-holding ability — Vocabulary. ISO 8855:2011. Geneva, Switzerland: International Organization for Standardization, 2011.