Utilities to Calculate Tire Kinematics, Forces, and Moments
The following utilities to calculate tire kinematics, forces, and moments are available:
ACTCLC
 C Calling Sequence:
SUBROUTINE ACTCLC(TRAMAT, VEL, OMEGA, OMEGAR, RADIUS, RNORM,VLON, VCPLON, VCPLAT, VCPVRT,ALPHA, GAMMA, KAPPA,URAD, CPMTX)
 Arguments

Argument Type Description Symbol TRAMAT 3,3 array Input Transformation Matrix from ISO to Road Axis system VEL 3 array Input Velocity of Wheel Carrier in ISO OMEGA 3 array Input Angular Velocity of Wheel Carrier in ISO OMEGAR Double Precision Input Angular velocity of the Wheel RADIUS Double Precision Input Loaded Radius of the Wheel RNORM 3 array Input Road Normal Unit Vector in road axis system VLON Double Precision Output Longitudinal velocity of the tire in ISO VCPLON Double Precision Output Contactpatch longitudinal velocity in SAE VCPLAT Double Precision Output Contactpatch lateral velocity in SAE VCPRVT Double Precision Output Contactpatch vertical velocity in SAE ALPHA Double Precision Output Slip angle is SAE GAMMA Double Precision Output Inclination angle KAPPA Double Precision Output Slip Ratio in SAE URAD 3 array Output Unit vector from wheel centre to CP in road CPMTX 3,3 array Output Transformation Matrix from SAE to Road Axis system  Calculations
 Velocity of the Wheel Center in the Road reference frame is:
The Spin Axis (S) in the road reference frame is:
The coordinate system at the contact patch is defined by the transformation Matrix:
Here D represents unit vectors the directions corresponding to the Contact Patch:
The Longitudinal velocity of the Wheel center is given by:
Direction of the Unit Vector in the Direction of the CP from the wheel center:
The radius of the tire along the plane of the tire is:
Rigid body laws are applied to the tire to find the velocities at a different point on a rigid body in the road Frame of reference:
The Velocities in the Contact Patch Frame of reference is:
The SAE axis system is defined such that the Y and Z axis of the ISO axis system are flipped. This results in the following transformation matrix for moving any Vector from the ISO system to the SAE system:
The different components of the Contact patch velocities in the SAE axis system can be calculated from the following equation:
Since the Longitudinal velocity component is same in the SAE and the ISO system, they can be used interchangeably, which leads to the following SAE definition of Slip Angle and Slip Ratio:
The inclination angle is the angle between the road normal and the Wheel center to Contact Patch Vector:
XCP2HB
 C Calling Sequence:
SUBROUTINE XCP2HB(FCP, TCP, RAD, TRNMTX, FORCES, TORQUE)
 Arguments

Argument Type Description Symbol FCP 3 array Input Contact Patch Forces in SAE TCP 3 array Input Contact Patch Torques in SAE RAD 3 array Input Radius Vector from Wheel Centre to Contact Patch CPMTX 3,3 array Input Transformation Matrix from SAE to Road Axis system FORCE 3 array Output Hub Forces in road reference frame TORQUE 3 array Output Hub Torques in road reference frame  Calculations
 Force Translation to wheel center and move to road frame of reference:
Move to road reference frame followed by Torque translation to wheel center:
XCP2HB_ISO
 C Calling Sequence:
SUBROUTINE XCP2HB (FCP, TCP, RAD, TRAMAT, FORCE, TORQUE)
 Arguments

Argument Type Description Symbol FCP 3 array Input Contact Patch Forces in ISO TCP 3 array Input Contact Patch Torques in ISO RAD 3 array Input Radius Vector from Wheel Centre to Contact Patch TRAMAT 3,3 array Input Transformation Matrix from ISO to Road Axis system FORCE 3 array Output Hub Forces in road ISO TORQUE 3 array Output Hub Torques in road ISO  Calculations
 Force Translation to wheel center and move to road frame of reference:
Move to road reference frame followed by Torque translation to wheel center:
ACTFZ
 C Calling Sequence:
SUBROUTINE ACTFZ(VCPVRT, RADIUS, TIREK, TIREC, UNLRAD,FRCRAD, ERRMSG, IERR)
 Arguments

Argument Type Description Symbol VCPVRT Double Precision Input Vertical contact patch velocity (SAE coordinates) RADIUS Double Precision Input Loaded radius of the tire TIREK Double Precision Input Tire vertical stiffness TIREC Double Precision Input Tire vertical dampling UNLRAD Double Precision Input Unloaded Radius FRCRAD Double Precision Output Tire Vertical Force – Radial Direction ERRMSG Character Array Output Error Message IERR Integer Output Error Code  Calculations