Tire model for wet road simulation

Abstract

Provides a tire model for simulating wet road conditions. [Solution] 1. A computer-implemented method for predicting the behavior of a vehicle tire on a wet road surface, the method comprising the steps of providing a computer-implemented tire model, and configuring the tire model to incorporate a tire normal load (F z ) and tire longitudinal velocity (v); and using said computer implemented tire model, calculating a lateral load dependent friction coefficient (μ y ) is the tire vertical load (F z ) and dependent on said tire longitudinal velocity (v); and outputting said tire grip prediction from said computer implemented tire model.

Description

[Technical Field]

[0001] The present invention relates to a computer-implemented method for predicting the behavior of vehicle tires on wet road surfaces. [Background technology]

[0002] It is well known that Professor Hans B. Pacejka presented his now-famous "Magic Formula" for modeling the interaction of vehicle tires with the road surface in his book "Tyre and Vehicle Dynamics" published in 1987. This empirical model predicts braking / traction and cornering forces that depend on longitudinal and lateral slip, normal load, and camber angle. Summary of the Invention [Problem to be solved by the invention]

[0003] Various commercially available software products are available for performing vehicle simulations to evaluate ride and handling performance, and these are semi-empirical tire performance models based on the Paseica Magic Formula. These vehicle simulations are limited to performance on dry roads only. The Magic Formula approach has been found to provide poor correlation with experimental tire results on wet roads.

[0004] Several complex models have been proposed in the literature to predict tire forces on low-coefficient road surfaces, for example, taking into account complex phenomena such as hydrodynamic lubrication. A practical approach to tire modeling is needed to reasonably simulate tire behavior on wet roads in real time.

[0005] The present invention seeks to provide a model for predicting tire behavior on wet road surfaces. [Means for solving the problem]

[0006] In a first aspect of the present invention, there is provided a computer-implemented method for predicting the behavior of a vehicle tire on a wet road surface, the method comprising the steps of providing a computer-implemented tire model, and inputting a tire normal load (F z ) and tire longitudinal velocity (v), and using the computer-implemented tire model, calculate a lateral load dependent friction coefficient (μ y ) is the tire vertical load (F z ) and depending on tire longitudinal velocity (v); and outputting the tire grip prediction from the computer-implemented tire model.

[0007] Thus, the lateral load dependent friction coefficient (μ y ) is determined by the tire longitudinal velocity (v) and tire vertical load (F z It has been found that such computer-implemented tire models improve the accuracy of tire grip predictions when the tire grip is calculated as a function of the tire velocity (v). In this method, tire longitudinal velocity (v) is taken as a direct input to the tire model, and tire grip is modified depending on the velocity. It is therefore recognized that tire longitudinal velocity (v), which represents vehicle speed, is a direct factor in changing the lateral force applied to the tire at its contact patch with the wet road, and therefore tire grip on the wet, which is not taken into account in the current magic formula approach.

[0008] By using tire grip predictions output from computer-implemented tire models in vehicle simulations, it is possible to predict tire behavior on wet roads, which was previously not possible, thereby reducing the need for physical tire testing.

[0009] In at least some embodiments, the lateral load dependent coefficient of friction (μ y ) and the tire vertical load (F z) and another term that is linearly dependent on tire longitudinal velocity (v). For example, the other term can be a second term that is linearly dependent on tire longitudinal velocity (v). For example, the other term can additionally or alternatively be a third term that has a quadratic dependency on tire longitudinal velocity (v). For example, the other term can additionally or alternatively have a higher-order (i.e., n>2) non-linear dependency on tire longitudinal velocity (v). It is therefore recognized that tire grip on wet surfaces can be modified as a linear and / or non-linear function of tire longitudinal velocity. In some preferred embodiments, the third term is always included in the calculation, as a strong quadratic dependency of tire grip on wet surfaces on vehicle speed has been observed.

[0010] In at least some embodiments, a lateral load dependent coefficient of friction (μ y ) to the tire vertical load (F z The calculation is based on a blending term that depends on the product of the tire longitudinal velocity (v) and the tire longitudinal velocity (v). It is thus recognized that tire grip on wet roads can be modified as a function of this blending term. This is based on the observation from actual data that tire grip on wet roads increases or decreases as a function of tire normal load depending on vehicle speed.

[0011] In any of the above embodiments, the lateral load dependent friction coefficient (μ y ) can be calculated as the sum of one or more of the first, second, third and mixed terms.

[0012] It was also found that such computer-implemented tire models improve the accuracy of cornering stiffness predictions when the tire longitudinal velocity (v) is taken into account as an input to the model.

[0013] In at least some embodiments, the method additionally or alternatively includes using a computer-implemented tire model to calculate the tire normal load (F zand calculating a cornering stiffness prediction that is dependent on the tire longitudinal velocity (v) and the vehicle speed (v), and outputting the cornering stiffness prediction from a computer-implemented tire model. Thus, it is recognized that tire longitudinal velocity (v), which represents vehicle speed, is a direct cause of wet cornering stiffness changes. This is also a significant departure from current magic formula approaches.

[0014] In at least some embodiments, the cornering stiffness is determined by the tire normal load (F z ), a second term that is linearly dependent on tire longitudinal velocity (v), and, optionally, a third term that has a quadratic dependence on tire longitudinal velocity (v). In this manner, it is recognized that wet cornering stiffness can be modified as a linear and / or non-linear function of tire longitudinal velocity. In some embodiments, the third term is omitted from the calculation because no strong non-linear dependence on vehicle speed has been observed for wet cornering stiffness.

[0015] In any of the above embodiments, cornering stiffness is calculated as the sum of one or more of the first, second and third terms.

[0016] By combining the various embodiments described above, the computer-implemented tire model can calculate the lateral load dependent coefficient of friction (μ y It can be seen that the method can predict both the lateral load dependent coefficient of friction (μ ) and the cornering stiffness. As a result, the method is particularly suited to predicting the overall cornering force. Therefore, in some preferred embodiments, the method uses a computer implemented tire model to calculate the lateral load dependent coefficient of friction (μ y ) and cornering stiffness (K y ) and the tire vertical load (F z) and dependent on tire longitudinal velocity (v); and outputting the tire cornering force prediction from a computer-implemented tire model.

[0017] In at least some embodiments, the method uses a computerized tire model to calculate tire grip predictions (and optionally cornering stiffness predictions) without inputting tire temperature into the computerized tire model, recognizing that this direct dependence on vehicle speed without considering tire temperature improves prediction of tire grip (and optionally cornering stiffness) since tire temperature is known to be less dominant on wet road surfaces.

[0018] In at least some embodiments, the method includes providing a computer-implemented tire model that includes one or more dimensionless coefficients pre-calculated based on experimental data collected for a given tire on a wet road surface, and further, the dimensionless coefficients may be pre-calculated based on experimental data collected for the given tire on a wet road surface at a plurality of different tire longitudinal speeds.

[0019] In some cases, the lateral load dependent friction coefficient (μ y ) is calculated based on a second term having a linear dependence on tire longitudinal velocity (v) as a product of a first dimensionless coefficient ("first grip microparameter") calculated based on experimental data collected for the tire on wet roads, and a third term having a quadratic dependence on tire longitudinal velocity (v) as a product of a second dimensionless coefficient ("second grip microparameter") calculated based on experimental data collected for the tire on wet roads. For example, the lateral load dependent coefficient of friction (μ y ) is the tire vertical load (F z), tire longitudinal velocity (v), and a third dimensionless coefficient (“third grip microparameter”) calculated based on experimental data collected for the tire on wet roads. Thus, in some examples, the computer-implemented tire model may include at least three dimensionless coefficients for grip calculated based on experimental data collected for the tire on wet roads, and thus different from the dimensionless coefficients included in existing magic formulas.

[0020] In some examples, cornering stiffness is calculated based on a second term having a linear dependence on tire longitudinal velocity (v) as a product of a first dimensionless coefficient (the “first stiffness microparameter”) calculated based on experimental data collected for the tire on wet roads, and a third term having a quadratic dependence on tire longitudinal velocity (v) as a product of a second dimensionless coefficient (the “third stiffness microparameter”) calculated based on experimental data collected for the tire on wet roads. In this manner, the computer-implemented tire model can include one or two dimensionless coefficients for cornering stiffness calculated based on experimental data collected for the tire on wet roads, and thus differ from the dimensionless coefficients included in existing magic formulas.

[0021] In at least some embodiments, the one or more non-dimensional coefficients depend on the tire type, which may include at least one of the tire size, tire manufacturer, tire age, tire tread pattern (and its design), tire finish, etc. The one or more non-dimensional coefficients may be calculated based on empirical data collected for a particular tire type on a wet road surface.

[0022] The methods disclosed herein can be used for a variety of purposes, including vehicle simulations and driving simulators that allow a human driver to virtually drive a vehicle on wet roads. Because the methods use vehicle speed as an input to a tire model, the outputs provided by the methods can adapt to changes in vehicle speed in real time. Thus, in at least some embodiments, the methods include inputting tire longitudinal velocity (v) into the tire model in real time and outputting tire grip predictions from the computerized tire model in real time. Optionally, cornering stiffness predictions are also output from the computerized tire model in real time.

[0023] The computer-implemented tire model disclosed herein has been found to provide accurate outputs over a range of typical vehicle speeds when compared to experimental data obtained for tires on wet roads. In at least some embodiments, inputting the tire longitudinal velocity (v) into the tire model includes selecting the tire longitudinal velocity (v) in the range of 30-70 km / h.

[0024] In this disclosure, a wet road surface means a road surface covered with a uniform and consistent layer of water of 2.0 mm.

[0025] In a second aspect of the present invention, there is provided a computer system for carrying out the method described herein for predicting vehicle tyre behaviour on wet road surfaces, which may comprise a processor and tangible memory storing computer executable instructions that, when executed by the processor, cause the system to carry out any of the methods described herein.

[0026] Yet another aspect of the present invention provides a vehicle driving simulator including such a computer system. As described above, in at least some embodiments, vehicle speed can be input to the tire model in real time. In at least some embodiments, the vehicle driving simulator may include a driver interface configured to allow a human driver to input vehicle speed to the computer system in real time. This vehicle speed is obtained by the computer system (i.e., its processor) and used to input tire longitudinal velocity (v) to the tire model in real time.

[0027] In yet another aspect of the present invention, there is provided a computer software product configured to perform any of the methods disclosed herein. [Brief explanation of the drawings]

[0028] [Figure 1] FIG. 1 shows a vehicle tire and the main parameters of a computer-implemented tire model. [Figure 2] FIG. 1 shows experimental data collected for a first tire type on wet roads compared with the original tire model formulation by Paseica (1987). [Figure 3] FIG. 2 shows experimental data collected for a first tire type on a wet road surface compared with a computer-implemented tire model according to a first embodiment of the present invention. [Figure 4] FIG. 4 shows experimental data collected on a first tire type on a wet road surface compared with a computer-implemented tire model according to a second embodiment of the present invention. [Figure 5] FIG. 10 shows experimental data collected on a first tire type on a wet road surface compared with a computer-implemented tire model according to a third embodiment of the present invention. [Figure 6] FIG. 10 shows experimental data collected on a first tire type on a wet road surface compared with a computer-implemented tire model according to a fourth embodiment of the present invention. [Figure 7] FIG. 2 illustrates experimental data collected on a first tire type on a wet road surface in terms of cornering stiffness compared to a computer-implemented tire model according to another embodiment of the present invention. [Figure 8] FIG. 10 illustrates experimental data collected on a first tire type on a wet road surface in relation to cornering stiffness compared with a computer-implemented tire model according to yet another embodiment of the present invention. [Figure 9] Figure 1 shows experimental data collected for the second type on wet roads compared with the original formulation of the tire model by Paseica (1987). [Figure 10] FIG. 4 shows experimental data collected for a second type on a wet road surface compared with a computer-implemented tire model according to a first embodiment of the invention. [Figure 11] FIG. 10 shows experimental data collected for a second type of wet road surface compared with a computer-implemented tire model according to a second embodiment of the present invention. [Figure 12] FIG. 10 shows experimental data collected for a second type on a wet road surface compared with a computer-implemented tire model according to a third embodiment of the present invention. [Figure 13] FIG. 10 shows experimental data collected for a second type on a wet road surface compared with a computer-implemented tire model according to a fourth embodiment of the present invention. [Figure 14] FIG. 10 shows experimental data collected for a second type on a wet road surface compared with a computer-implemented tire model according to another embodiment of the present invention in terms of cornering stiffness. [Figure 15] FIG. 10 shows experimental data collected for a second type on a wet road surface in comparison with a computer-implemented tire model according to yet another embodiment of the present invention in terms of cornering stiffness. DETAILED DESCRIPTION OF THE INVENTION

[0029] FIG. 1 shows the tire vertical load F z The figure shows that the tire has a longitudinal velocity v that is determined by the vehicle speed and is affected by the lateral force F y is the lateral load dependent friction coefficient μ y Through the tire vertical load F z This works in conjunction with the force F to determine the tire's grip on the road surface. y is also known as cornering force. The method described herein uses a computer-implemented tire model to calculate the tire normal load (F z ) and the tire longitudinal speed (v), y ) to calculate the predicted tire grip value. It can be seen that the tire longitudinal velocity v is different from the tire angular velocity ω.

[0030] 2 to 8 show experimental data collected on a wet road surface for a first tire type (Bridgestone Tire Type 1) in comparison with various tire models.

[0031] FIG. 2 shows the experimental data compared with the original formulation of the tire model by Paseica (1987), the so-called "magic formula" (see equation (1)).

[0032]

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[0033] This tire model uses a lateral load dependent friction coefficient (μ y ) is the tire vertical load (f z ) and camber angle (γ), but not vehicle speed. μy As can be seen in Figure 2, this tire model does not fit well with the experimental data collected on wet roads.

[0034] Figure 3 shows the above experimental data compared with a computer-implemented tire model according to a first embodiment of the present invention, in which the tire model has a lateral load dependent coefficient of friction μ y is the vertical tire load f z The tire grip is predicted under the condition that it is a linear function of and a linear function of the tire longitudinal velocity v.

[0035]

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[0036] In this first embodiment, the tire model is based on the tire normal load f z and a second term that is linearly dependent on the tire longitudinal velocity v. Compared to Figure 2, this tire model provides a slightly better fit to the experimental data collected on wet roads.

[0037] 4 compares the above experimental data with a computer-implemented tire model according to a second embodiment of the present invention, in which the tire model has a lateral load dependent coefficient of friction μ y is the vertical tire load f z The tire grip is predicted under the condition that it is a linear function of , and is a function of the tire longitudinal velocity v that includes linear and non-linear components.

[0038]

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[0039] In this second embodiment, the tire model is based on the tire normal load f z The tire model includes a first term that is linearly dependent on , a second term that is linearly dependent on the tire longitudinal velocity v, and a third term that has a quadratic dependence on the tire longitudinal velocity v. Compared to Figure 2, this tire model provides an improved fit to the experimental data collected on wet roads.

[0040] 5 shows the above experimental data compared with a computer-implemented tire model according to a third embodiment of the present invention, in which the tire model has a lateral load dependent coefficient of friction μ y is the vertical tire load f z and is a linear function of the tire longitudinal velocity v, and includes a mixed term.

[0041]

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[0042] In this third embodiment, the tire model is based on the tire normal load f z The first term is linearly dependent on the tire longitudinal velocity v, the second term is linearly dependent on the tire vertical load f z and a mixing term that depends on the product of v and the tire longitudinal velocity v. Compared to Figure 2, this tire model provides an improved fit to the experimental data collected on wet roads.

[0043] 6 shows the above experimental data compared with a computer-implemented tire model according to a fourth embodiment of the present invention. In this third embodiment, the tire model has a lateral load dependent coefficient of friction μ y is the vertical tire load f z , which is a linear function of the tire longitudinal velocity v, and which is a linear and non-linear function of the tire vertical load f z The tire grip is predicted under the condition that it includes a mixed term that depends on the product of σ and the tire longitudinal velocity v.

[0044]

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[0045] In this fourth example, the tire model includes the first, second, third, and mixed terms described above. Comparing with Figure 2, it can be seen that this tire model fits the experimental data collected on a wet road very well.

[0046] In each of the above equations 1 to 5, the tire vertical load f z A dimensionless coefficient p that depends on Dy1 , p Dy2 , p Dy3 is included in the first term. It is already known that such dimensionless coefficients are included in tire models based on the "magic formula," but conventionally, these coefficients have been calculated in advance based on experimental data collected on dry roads. In this example, the dimensionless coefficient p Dy1 , p Dy2 , p Dy3 These non-dimensional coefficients are pre-calculated based on experimental data collected for a given tire type on wet surfaces, and differ from known "magic formula" based tire models. This comes from the recognition that the absolute values ​​of these coefficients will change when a tire is tested on dry and wet surfaces because the tire's grip level (i.e., lateral coefficient of friction) is different on dry and wet surfaces. The experimental data used to pre-calculate these non-dimensional coefficients may be for a single vehicle speed or for multiple vehicle speeds, e.g., at least three different vehicle speeds.

[0047] In each of the above equations 2 to 5, the additional velocity-dependent terms further include several dimensionless coefficients p vdy1 , p vdy2 , p vdy3 Contains p vdy1 is the second (first order) term, and p vdy2 is the third (non-linear) term, and p vdy3 are included in the blending term. These additional dimensionless coefficients are pre-calculated based on experimental data collected for a particular tire type on wet roads. Furthermore, due to the speed dependence of these additional terms, the experimental data used to pre-calculate these dimensionless coefficients may be for multiple vehicle speeds, for example, at least three different vehicle speeds.

[0048] Methods for pre-calculating such dimensionless coefficients from experimental data are generally known in the art: for example, least-squares fitting or other iterative fitting techniques can be employed.

[0049] Figure 7 shows the experimental data for the cornering stiffness K y , compared to a computer-implemented tire model according to another embodiment of the present invention. As is well known in the art, cornering stiffness is defined as the slope of the cornering force at the origin. In this embodiment, the tire model is z The cornering stiffness K is calculated based on the first term (similar to the magic formula) which is linearly dependent on the tire longitudinal velocity v, and the second term which is linearly dependent on the tire longitudinal velocity v. y is predicted.

[0050]

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[0051] From Figure 7, it can be seen that adding the second term to the first term provides a good fit to the experimental data collected on wet road surfaces.

[0052] Figure 8 shows the experimental data for the cornering stiffness K y , compared with a computer-implemented tire model according to yet another embodiment of the present invention. In this embodiment, the tire model is z The cornering stiffness K is calculated based on the first term (similar to the magic formula) which is linearly dependent on the tire longitudinal velocity v, the second term which is linearly dependent on the tire longitudinal velocity v, and the third term which has quadratic dependence on the tire longitudinal velocity v. y is predicted.

[0053]

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[0054] From Figure 8, it can be seen that adding the second and third terms to the first term provides a good fit to the experimental data collected on wet road surfaces.

[0055] In the above formulas 6 and 7, the tire vertical load F z The first term depends on the dimensionless coefficient p Ky1 , p Ky2 , p Ky3 It is already known that such dimensionless coefficients are included in tire models based on the "magic formula," but conventionally, these coefficients have been calculated in advance based on experimental data collected on dry roads. In this example, the dimensionless coefficient p Ky1 , p Ky2 , p Ky3 These dimensionless coefficients are pre-calculated based on experimental data collected for a given tire type on wet surfaces, and differ from known "magic formula" based tire models. This comes from the recognition that the absolute values ​​of these coefficients will change when a tire is tested on dry and wet surfaces because the tire's grip level (i.e., lateral coefficient of friction) is different on dry and wet surfaces. The experimental data used to pre-calculate these dimensionless coefficients may be for a single vehicle speed or for multiple vehicle speeds, e.g., at least three different vehicle speeds.

[0056] In Equation 6, the velocity-dependent second (first-order) term is supplemented with a dimensionless coefficient p vKdy1 In Equation 7, the third (quadratic) term, which is a velocity-dependent term, is further enriched with a dimensionless coefficient p vKdy2 These further dimensionless coefficients are pre-calculated based on experimental data collected for a particular tire type on wet roads. Furthermore, due to the speed dependence of the second and third terms, the experimental data used to pre-calculate these dimensionless coefficients may relate to multiple vehicle speeds, for example at least three different vehicle speeds.

[0057] As mentioned above, methods for pre-calculating such dimensionless coefficients from experimental data are generally known in the art: for example, least-squares fitting or other iterative fitting techniques can be employed.

[0058] Figures 9-15 compare experimental data collected on wet roads for a second tire type (Bridgestone Tire Type 2) with a different pattern design and size, with the same tire model described above with respect to Figures 2-8. These figures show that the tire model using Equations 2-7 provides a good fit to the experimental data collected on wet roads for this different tire type.

Claims

1. 1. A computer-implemented method for predicting vehicle tire behavior on a wet road surface, the method comprising: providing a computer-implemented tire model; The tire model is subjected to a tire vertical load (F ｚ ) and tire longitudinal velocity (v); The computer-implemented tire model is used to determine the lateral load dependent coefficient of friction (μ ｙ ) is the tire vertical load (F ｚ Calculating a tire grip prediction value under the condition that it depends on the tire longitudinal speed (v) and the tire longitudinal speed (v); outputting the tire grip prediction from the computer-implemented tire model; Including, A computer-implemented method for calculating the lateral load dependent friction coefficient (μ y ) based on a first term that is linearly dependent on the tire normal load (F z ) and another term that is linearly and / or non-linearly dependent on the tire longitudinal velocity (v).

2. A computer-implemented method for predicting vehicle tire behavior on a wet road surface, the method comprising: providing a computer-implemented tire model; inputting a tire vertical load (F z ) and a tire longitudinal velocity (v) into the tire model; using the computer implemented tire model to calculate a tire grip prediction where a lateral load dependent coefficient of friction (μ y ) depends on the tire normal load (F z ) and on the tire longitudinal velocity (v); outputting the tire grip prediction from the computer-implemented tire model; Including, The lateral load dependent friction coefficient (μ ｙ ) to the tire vertical load (F ｚ ) and another term having a quadratic dependence on the tire longitudinal velocity (v).

3. A computer-implemented method for predicting vehicle tire behavior on a wet road surface, the method comprising: providing a computer-implemented tire model; inputting a tire vertical load (F z ) and a tire longitudinal velocity (v) into the tire model; using the computer implemented tire model to calculate a tire grip prediction where a lateral load dependent coefficient of friction (μ y ) depends on the tire normal load (F z ) and on the tire longitudinal velocity (v); outputting the tire grip prediction from the computer-implemented tire model; Including, The lateral load dependent friction coefficient (μ ｙ ) to the tire vertical load (F ｚ ) and the tire longitudinal velocity (v).

4. The computer-implemented tire model is used to calculate the tire normal load (F ｚ ) and said tire longitudinal velocity (v); outputting the cornering stiffness prediction from the computer-implemented tire model; The computer-implemented method of any one of claims 1 to 3, comprising:

5. The cornering stiffness is calculated by the tire vertical load (F ｚ 5. The computer-implemented method of claim 4, wherein the calculation is based on a first term that is linearly dependent on the tire longitudinal velocity (v) and a second term that is linearly dependent on the tire longitudinal velocity (v).

6. The cornering stiffness is calculated by the tire vertical load (F ｚ 5. The computer-implemented method of claim 4, wherein the calculation is based on a first term that is linearly dependent on the tire longitudinal velocity (v) and a third term that is quadratically dependent on the tire longitudinal velocity (v).

7. Using a computer-implemented tire model, the lateral load dependent friction coefficient (μ ｙ ) and cornering stiffness (K ｙ ) and the tire vertical load (F ｚ ) and the tire longitudinal speed (v), ｙ ) and The tire cornering force prediction (F ｙ ) outputting the The computer-implemented method of any one of claims 1 to 3, comprising:

8. 4. The computer-implemented method of claim 1, comprising providing a computer-implemented tire model including one or more dimensionless coefficients pre-calculated based on experimental data collected for a given tire on a wet road surface.

9. 9. The computer-implemented method of claim 8, wherein the one or more dimensionless coefficients are pre-calculated based on experimental data collected for a given tire on a wet road surface at a number of different tire longitudinal speeds.

10. inputting tire longitudinal velocity (v) into the tire model in real time; outputting the tire grip prediction in real time from the computer-implemented tire model; The computer-implemented method of any one of claims 1 to 3, comprising:

11. A computer system comprising means for executing the method for predicting the behavior of a vehicle tire on a wet road surface according to any one of claims 1 to 3.

12. 12. The computer system of claim 11, wherein said means comprises a processor and tangible memory storing computer-executable instructions that, when executed by the processor, cause the computer system to perform the method.

13. A vehicle driving simulator comprising the computer system of claim 11.

14. A computer program product comprising instructions which, when executed by a computer, cause the computer to carry out the method according to any one of claims 1 to 3.

15. A computer-implemented method for predicting vehicle tire behavior on a wet road surface, the method comprising: providing a computer-implemented tire model; inputting a tire vertical load (F z ) and a tire longitudinal velocity (v) into the tire model; using the computer implemented tire model to calculate a tire grip prediction where a lateral load dependent coefficient of friction (μ y ) depends on the tire normal load (F z ) and on the tire longitudinal velocity (v); outputting the tire grip prediction from the computer-implemented tire model; using the computer implemented tire model to calculate a cornering stiffness prediction dependent on the tire normal load (F z ) and the tire longitudinal velocity (v); outputting the cornering stiffness prediction from the computer-implemented tire model; Including, A computer-implemented method for calculating the cornering stiffness based on a first term that is linearly dependent on the tire normal load (F z ) and a third term that has a quadratic dependence on the tire longitudinal velocity (v).

16. A computer-implemented method for predicting vehicle tire behavior on a wet road surface, the method comprising: providing a computer-implemented tire model; inputting a tire vertical load (F z ) and a tire longitudinal velocity (v) into the tire model; using the computer implemented tire model to calculate a tire grip prediction where a lateral load dependent coefficient of friction (μ y ) depends on the tire normal load (F z ) and on the tire longitudinal velocity (v); outputting the tire grip prediction from the computer-implemented tire model; A computer-implemented method comprising providing a computer-implemented tire model including one or more dimensionless coefficients pre-calculated based on experimental data collected for a given tire on a wet road surface.

17. A computer-implemented method for predicting vehicle tire behavior on a wet road surface, the method comprising: providing a computer-implemented tire model; inputting a tire vertical load (F z ) and a tire longitudinal velocity (v) into the tire model; using the computer implemented tire model to calculate a tire grip prediction where a lateral load dependent coefficient of friction (μ y ) depends on the tire normal load (F z ) and on the tire longitudinal velocity (v); outputting the tire grip prediction from the computer-implemented tire model; inputting tire longitudinal velocity (v) into the tire model in real time; outputting the tire grip prediction in real time from the computer-implemented tire model; 11. A computer-implemented method comprising:

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