## 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

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]

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 (XE, YE, ZE) 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.

AxisDescription
XE

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

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

YE
ZE

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

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

### Vehicle Coordinate System

The vehicle coordinate system axes (XV, YV, ZV) are fixed in a reference frame attached to the vehicle. The origin is at the vehicle sprung mass.

Z-Down Orientation

AxisDescription
XVThe XV axis points forward and is parallel to the vehicle plane of symmetry.
YV

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

In the Z-down orientation:

• YV axis points to the right

• ZV axis points downward

ZV

### Tire and Wheel Coordinate Systems

The tire coordinate system axes (XT, YT, ZT) 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 (XW, YW, ZW) are fixed in a reference frame attached to the wheel. The origin is at the wheel center.

Z-Up Orientation1

Z-Down Orientation

AxisDescription
XTXT and YT are parallel to the road plane. The intersection of the wheel plane and the road plane define the orientation of the XT axis.
YT
ZT

ZT points:

• Upward in the Z-up orientation

• Downward in the Z-down orientation

XW

XW and YW are parallel to the wheel plane:

• XW is parallel to the local road plane.

• YW is parallel to the wheel-spin axis.

YW
ZW

ZW 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.

AxisDescription
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

## 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.

## External Websites

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