DYNATIRE "ROAD & TRACK"
A STATISTICAL TIRE MODEL
For ROAD & TRACK APPLICATION
DYNATIRE "ROAD & TRACK" is A Generic Tire Model Based on A UNIQUE MULTI-DIMENSIONAL Statistical Fit TO a POOL OF STATISTICALLY REPRESENTATIVE combinationS OF TIRE Properties & Operating points ("DATA SETS"), ALLOWING TO predict Key Fundamental Tire Characteristics FOR GIVEN Vertical Loads, Tire Dimensions and Inflation Pressures.
INPUT DATA
The DYNATIRE "RT" Statistical Tire Model is based on a Multi-Dimensional Data Fit on a statistically representative quantity of specific Operating Points ("DATA SETS") of STREET-LEGAL and SLICK / RACE Tires. For User Convenience, Input Data Sets can be entered for 2 Different Tires allowing an easy comparison.
|
Input "Data Set" for DYNATIRE "RT" are:
|
|
|
The picture to the left does show the Input Parameters and their Valid "Operating" Ranges - for which the Prediction Model in DYNATIRE "RT" has been calibrated - both for Road as for Track (Racing) Tires.
|
PRIMARY RESULTS
The DYNATIRE "RT" Model provides instantly - for a given Selection of Specific Input Data Sets - Numerical and Graphical Results for the following Key Tire Characteristics:
- Tire Lateral Grip Coefficient µ
- Tire Cornering Stiffness CS
- Tire Aligning Torque Stiffness ATS
- Tire Vertical Stiffness (Rolling Tire) Kz
- Tire Dynamic Rolling Radius DLR
- Tire Vertical Load Sensitivity for µ , CS, ATS, Kz & DLR as function of Vertical Load Fz
- Tire Lateral Grip Coefficient µ
- Tire Cornering Stiffness CS
- Tire Aligning Torque Stiffness ATS
- Tire Vertical Stiffness (Rolling Tire) Kz
- Tire Dynamic Rolling Radius DLR
- Tire Vertical Load Sensitivity for µ , CS, ATS, Kz & DLR as function of Vertical Load Fz
PRIMARY GRAPHICAL RESULTS
The above mentioned Tire Characteristics are presented graphically in 5 separate charts, all as a Function of Vertical Load Fz Variance, allowing an instant Panoramic Overview of all Key Performance Characteristics:
PRIMARY NUMERICAL RESULTS
Specific Numerical Results for selected Input Data Sets are presented in 2 Different Data Formats.
|
The first Data Format provides the above mentioned Tire Characteristics in the DYNATUNE-XL ENHANCED TIRE MODEL Data Format, allowing a direct implementation into the DYNATUNE-XL RIDE & HANDLING MODULE. 
|
|
|
The second available data format presents the tire characteristics using a Reduced-Order 4-Term PACEJKA TIRE MODEL, based on the widely recognized B, C, D₁, and D₂ Coefficients. These parameters define the fundamental PACEJKA MAGIC FORMULA used to model Lateral Force and Aligning Moment, as illustrated in the MAGIC FORMULA to the left.
|
The PACEJKA MAGIC FORMULA does represent the Key Tire Performance Characteristics with specifically fitted Coefficients. Due some inherent differences in this data representation numeric values for Cornering Stiffness and Aligning Torque Stiffness can differ slightly from the DYNATUNE-XL ENHANCED TIRE MODEL Values.
|
|
Special Feature: The Graphical Representation of the Statistical Results are available as Quadratic Curve Fits allowing a quick implementation in for instance Bicycle Models etc in other Software Tools.
SECONDARY RESULTS
The Primary Results presented above from the DYNATIRE "RT" STATISTICAL TIRE MODEL effectively reflect the core Statistical Outputs. Users familiar with the DYNATUNE-XL RIDE & HANDLING MODULE will recognize that these parameters closely resemble the Input Data Set used in the original DYNATUNE-XL BASE TIRE MODEL.
During the development of the DYNATUNE-XL ENHANCED TIRE MODEL - which provides look-up table–based tire characteristics - DYNATUNE-XL developed and implemented a unique algorithm. This proprietary method empirically blends Initial Cornering and Aligning Torque Stiffness values (derived from the BASE TIRE MODEL) with characteristic Slip-Angle Performance Curves to generate detailed Tire Behavior Maps. This approach and resulting Tire Maps have proved to be quite consistent with Experimentally Logged Vehicle Data and are as such well suited procedures for creating realistic Tire Maps.
By integrating this approach into DYNATIRE "RT", the model can now also produce predictions of look-up tables for Lateral Force and Aligning Moment as functions of Slip-Angle and Vertical Load. These Tire Maps are available in both the DYNATUNE-XL ENHANCED TIRE MODEL Format and the BCD₂ PACEJKA TIRE Model format. While both formats are highly consistent, minor differences may appear due to their distinct fitting methodologies.
During the development of the DYNATUNE-XL ENHANCED TIRE MODEL - which provides look-up table–based tire characteristics - DYNATUNE-XL developed and implemented a unique algorithm. This proprietary method empirically blends Initial Cornering and Aligning Torque Stiffness values (derived from the BASE TIRE MODEL) with characteristic Slip-Angle Performance Curves to generate detailed Tire Behavior Maps. This approach and resulting Tire Maps have proved to be quite consistent with Experimentally Logged Vehicle Data and are as such well suited procedures for creating realistic Tire Maps.
By integrating this approach into DYNATIRE "RT", the model can now also produce predictions of look-up tables for Lateral Force and Aligning Moment as functions of Slip-Angle and Vertical Load. These Tire Maps are available in both the DYNATUNE-XL ENHANCED TIRE MODEL Format and the BCD₂ PACEJKA TIRE Model format. While both formats are highly consistent, minor differences may appear due to their distinct fitting methodologies.
|
While the DYNATUNE-XL ENHANCE TIRE MODEL automatically generates tire maps, a Dedicated Fitting Procedure is required to derive the Curvature Coefficients for the BCD2 PACEJKA TIRE MODEL. For maximum User Convenience, this process can be executed Automatically by simply clicking one of the action buttons provided on the right.
|
|
SECONDARY GRAPHICAL RESULTS
The image below shows the Graphical Representation of the Tire Maps generated by each tire modeling approach. While the Lateral Force Fy and the corresponding Grip Coefficient μ are nearly identical across models, more noticeable differences appear in the shape of the Aligning Moment. These variations are primarily caused by the more refined approximation of Aligning Torque behavior achieved through the PACEJKA Curve Fitting Procedure, which is directly influenced by the Curvature "C" Factor Value.
SECONDARY NUMERICAL RESULTS
The Tire Maps are also available to the User in Numerical Format for the above shown Tire Characteristics. For convenient navigation on the Worksheet these tables can be hidden if not needed.
FEATURES
TIRE DATA SCALABILITY
|
Since all DYNATIRE "RT" results represent Average "Market" Values for Each Tire Dimension, Scaling Factors have been introduced to allow users to adjust key output parameters as needed. The underlying Multi-Dimensional Fit Model accounts for a wide range of tire dimensions, meaning that many inherent characteristics - such as Grip and Cornering Stiffness - are already embedded in the results. For example, a 355/25/21 Tire naturally provides more grip than a 155/65/13 Tire due to its size and construction. Additionally, Super Sporty Road Tires are often based on existing tire constructions and can be Custom-Scaled by experienced users to better reflect specific performance targets or design preferences.
|
|
EXPORT TIRE DATA
|
Users can export all data from the protected DYNATIRE "RT" workbook into an external Microsoft Excel ® Workbook. This would either facilitate further Custom Post-Processing of the Tire Data or allow a seamless Import of the Tire Characteristics into the DYNATUNE-XL RIDE & HANDLING MODULE.
|
|
PACEJKA MF 52 MAGIC FORMULA TIRE PERFORMANCE ANALYSIS TOOL
For user convenience, DYNATUNE-XL has integrated a dedicated PACEJKA MF 5.2 TIRE DATA PLOTTER and PERFORMANCE ANALYSIS TOOL directly into the DYNATIRE "RT" workbook. Users can import original MF 5.1 / MF 5.2 *.TIR files for detailed visualization and analysis.
In addition to advanced plotting features, the tool-set also enables Automatic Conversion of the imported PACEJKA DATA into a corresponding DYNATUNE-XL ENHANCED TIRE MODEL Input Dataset, streamlining the process of integrating legacy MF 52 Data into the DYNATUNE-XL RIDE & HANDLING MODULE environment.
In addition to advanced plotting features, the tool-set also enables Automatic Conversion of the imported PACEJKA DATA into a corresponding DYNATUNE-XL ENHANCED TIRE MODEL Input Dataset, streamlining the process of integrating legacy MF 52 Data into the DYNATUNE-XL RIDE & HANDLING MODULE environment.
|
The data shown above can be exported to a standalone Microsoft Excel ® Workbook. Additionally, Expert Users have the option to modify the standard PACEJKA MF Scaling Factors, allowing them to generate a Custom MF5.2 Tire Data Set tailored to specific requirements or performance targets.
|
Below one can see the User Interface which does allow to customize the Performance Evaluation of the presented Tire Data:
Below a selection of the available Data Graphs for Fx, Fy, Mx, Mz and Combined Slip Conditions:
LONGITUDINAL FORCE Fx
COMBINED SLIP Fx & Fy
OVERTURNING MOMENT Mx
|
LATERAL FORCE Fy
ALIGNING MOMENT Mz
|
MODELING
DYNATIRE “RT” is a Generic Tire Model developed through the fitting of a statistically sufficiently large volume of Specific Tire Operating Points, using a multi-dimensional, non-linear fitting method originally pioneered by Honda Motor Company. The core concept is illustrated in the images below, which demonstrates how "Data Sets" from various Tire Properties and their Operating Points are merged into a Single, Comprehensive Multi-Dimensional Model.
DYNATUNE-XL has further refined this methodology, developing its own proprietary algorithm to enhance fit accuracy and model generalization.
DYNATUNE-XL has further refined this methodology, developing its own proprietary algorithm to enhance fit accuracy and model generalization.
|
Classic Tire Data Fitting
Picture courtesy of Honda Motor Company
|
|
Multi-Dimensional Fitting with Statistical Operating Point Distribution
Picture courtesy of Honda Motor Company
|
As with any Tire model, the Quality of the Fit directly determines the accuracy of the results, always bearing in mind that the data of the measured Tire Operating Point is inherently influenced by the boundary conditions of the Testing Procedure & Test Equipment used to define the numerical values for that specific operating point.
In the histograms below, all characteristics have been normalized with respect to vertical load (Fz). The statistical distributions shown have been generated based on the DYNATIRE “RT” fit, and are compared - across all available Tire Properties - for specific combinations of Vertical Load, Tire Dimensions, and Inflation Pressure, against the Original Reference Tire Operating Points.
In the histograms below, all characteristics have been normalized with respect to vertical load (Fz). The statistical distributions shown have been generated based on the DYNATIRE “RT” fit, and are compared - across all available Tire Properties - for specific combinations of Vertical Load, Tire Dimensions, and Inflation Pressure, against the Original Reference Tire Operating Points.
The error distributions for Track Tires are shown below. While the correlation is, generally speaking, slightly lower - due to the increased complexity of slick tire behavior - the Results produced by the DYNATIRE “RT” Slick Tire Prediction Model remain adequate and fit for purpose.
