# Coordinate Systems and Output Requests

Outputs for tires are reported in the various coordinate systems described below.

## Tydex-C Axis System

The “C” is for wheel center, and the C axis system has these properties:
• The origin of the C-Axis system is the wheel center.
• The X axis lies in the wheel plane and is parallel to the ground plane and points in the forward direction.
• The Y axis is perpendicular to the wheel plane and points towards the vehicle’s left side so that a positive rotation of the wheel and tire about the Y axis rolls the tire forward.
• The Z axis lies in the wheel plane, differs from vertical by inclination angle, and is perpendicular to the X and Y axes (Z = X x Y).

## Tydex-W Axis System

The “W” is for wheel. The Tydex-W axis system considers the local slope of the road where the tire contacts the road, rather than assuming the road is flat. The Tydex-W axis system has these properties:
• The origin of the W axis system lies at the ideal contact point between the wheel plane and local road plane, which is the intersection of the Tydex C System Z axis with local road plane.
• The X axis points forward along the line of intersection between the wheel plane and the local road plane.
• The Z axis is parallel to the local road normal and hence perpendicular to the local road plane.
• The Y axis is the projection of the wheel spin axis (Tydex C-Axis System Y) into the local road plane. The Y axis is perpendicular to both the X and Z axis (Y = Z x X).

## SAE System

• X is forward
• Y is to the right
• Z is down
Models built using MotionView will automatically include many output requests specific to the tires. The browser image below shows examples of these outputs:
In the tables below the x,y,z,r1,r2, and r3 reflect how the results will show in HyperGraph:
Tire rolling states
(Branch ID 1)
Component Name Units
Tire kinematic properties in TYDEX-W (ISO) axis system
(Branch ID 2)
Component Name Units
x longitudinal slip %
Tire contact patch forces in TYDEX-W (ISO) axis system
(Branch ID 3)
Component Name Units
x longitudinal force model units
y lateral force model units
z vertical force model units
r1 residual overturning moment model units
r2 rolling resistance moment model units
r3 aligning moment model units
Tire contact patch forces in SAE axis system
(Branch ID 4)
Component Name Units
x longitudinal force model units
y lateral force model units
z vertical force model units
r1 residual overturning moment model units
r2 rolling resistance moment model units
r3 aligning moment model units
Tire kinematic properties in SAE axis system
(Branch ID 5)
Component Name Units
x longitudinal slip %
Tire forces at hub in TYDEX-C axis system
(Branch ID 6)
Component Name Units
x longitudinal force model units
y lateral force model units
z vertical force model units
r1 residual overturning moment model units
r2 rolling resistance moment model units
r3 aligning moment model units
Contact patch locations along the plane of the tire in the GFORCE rm marker
(Branch ID 10)
Component Name Units
x road contact point x location model units
y road contact point y location model units
z road contact point z location model units
Hub velocities of the tire in the GFORCE rm marker
(Branch ID 11)
Component Name Units
x rim center velocity in longitudinal direction model units
y n/a n/a
z rim center velocity in vertical direction, along road normal model units
An example of an output request in the MotionSolve input deck is shown below:
  <Post_Request
id                  = "70000063"
comment             = "Tire - Front Rad, OmegaActual, OmegaFree (left)"
type                = "USERSUB"
usrsub_param_string = "USER(902,1,11001)"
usrsub_dll_name     = "mbdtire.dll"
usrsub_fnc_name     = "tireReq"
/>