The test may be performed using two alternative test methods: a A constant-radius test method, where the initial conditions are defined by driving on a fixed-radius circular path and lat
Variables to be determined
The following variables shall be determined:
⎯ instant of power-off initiation, t 0 ;
⎯ yaw angle, ψ, or yaw velocity, ψ ;
⎯ sideslip angle, β, or lateral velocity, v Y
In addition, the following variables may be determined:
Variables are defined according to ISO 8855, with the exception of the instant of accelerator pedal release (t₀), which marks the moment the accelerator pedal is released (see 8.3) These variables are not intended to provide a comprehensive list but serve specific measurement purposes within the standard.
Description
Variables designated for testing must be measured using suitable transducers, with their time histories recorded by a multi-channel recording system equipped with a precise time base According to ISO 15037-1 and Table 1, the standard specifies typical operating ranges and maximum permissible errors for both transducers and recording systems These values are provisional within the scope of this International Standard, pending further data and practical experience.
Transducer installations
The requirements of ISO 15037-1 shall apply.
Data processing
The requirements and specifications of ISO 15037-1 shall be followed
Limits and specifications for the ambient and the vehicle test conditions established in ISO 15037-1 shall be followed
Under standard test conditions, ensure that the engine and driveline components—such as differentials, clutches, locks, free-wheel shifts, and engine idle calibration—are adjusted and maintained according to the vehicle manufacturer's specifications for accurate and consistent testing results.
Table 1 — Typical operating ranges and recommended maximum errors for recorded variables — additions and exceptions to ISO 15037-1 Variable Typical operating range
Recommended maximum error of the combined transducer and recorder system
Instant of power-off initiation — 0,05 s
NOTE Increased measuring accuracy may be desirable for computation of some of the characteristic values given in Clause 9
Warm-up
The procedure specified in ISO 15037-1 shall be followed to warm up the tyres and other vehicle components prior to the test.
Initial driving condition
For both the constant-radius and the constant-speed test methods, the initial driving condition is a steady-state circular run as defined in ISO 15037-1
To ensure accurate test results, initial runs should begin from a steady-state circular condition with a lateral acceleration of approximately 4 m/s² Successive test runs should progressively increase the steady-state lateral acceleration of the initial turn in small increments, not exceeding 1 m/s² per step It is recommended to use smaller increments of 0.5 m/s² or less when there are significant changes in the power-off response between runs at larger steps, such as 1 m/s².
For vehicles with manual transmissions, testing should be conducted in the lowest gear possible, excluding first gear The engine speed must not exceed 80% of the engine speed at maximum power, as specified by the vehicle manufacturer If maintaining a constant-radius during the test necessitates a gear change due to increasing vehicle speed, the test must be performed in both gears at the same speed to ensure accurate results.
For vehicles equipped with automatic transmission, the standard drive mode must be used during testing The transmission lever position and the selected driving program should be documented in the test report, as specified in Annex A.
Vehicles equipped with adaptive gear selection or CVT continuously adjust gear ratios at a given speed, requiring precise recording of engine speed to accurately determine the gear ratio This engine speed data must be included in the test report to ensure compliance and proper assessment of the vehicle's transmission performance.
8.2.2 Initial driving condition — constant-radius method
During initial driving conditions, the vehicle should be steered to follow a circular path with a desired radius, typically set at 100 meters to enhance the accuracy and comparability of test results A smaller radius can be used, with a minimum permissible radius of 30 meters and a recommended minimum of 40 meters, to ensure consistent and reliable vehicle performance assessments Increasing test speeds heighten the importance of the chosen radius, as they improve the ability to distinguish between different vehicles.
From run to run, the initial driving speeds shall be those which establish the required steady-state lateral accelerations as described in 8.2.1
8.2.3 Initial driving condition — constant-speed method
The standard speed for the initial driving condition is 100 km/h If higher or lower test speeds are selected, they shall be in 20 km/h increments
From run to run, the steady-state lateral accelerations as required in 8.2.1 shall be established by either of the following two methods
Test runs are conducted using a series of discrete turn radii, which consist of marked circles or circular segments with varying radii These are selected to establish the necessary initial lateral accelerations at the designated test speed.
Test runs are conducted using a series of discrete, constant steer angles without constraining the initial vehicle path These angles are selected to generate the necessary initial lateral accelerations at the chosen test speed, ensuring accurate assessment of vehicle handling and stability.
The use of an adjustable steering stop is recommended for maintaining constant steer angles.
Power-off procedure
Maintaining a consistent position of the steering wheel and accelerator pedal is essential during the initial driving phase The initial condition is deemed stable when the parameters outlined in the relevant regulations are met, ensuring safe and controlled vehicle operation.
In the constant-radius method, the initial driving radius should not deviate by more than ± 2% of the target value or ± 2 meters—whichever is smaller—during the interval from 1.3 seconds to 0.3 seconds prior to power-off initiation.
The constant-speed method requires that the vehicle's longitudinal velocity in the initial driving condition remains within ±1 km/h of the desired value during the critical time interval of 1.3 to 0.3 seconds before power-off initiation Ensuring minimal speed deviation within this timeframe is essential for optimal vehicle performance and safety This control criterion helps maintain precise speed regulation and contributes to the overall reliability of the driving system.
When the initial steady-state driving condition has been established, the steering wheel shall be held fixed by a mechanical device or, alternatively, shall be firmly held by the driver
The accelerator pedal should be released as quickly as possible to ensure safety For vehicles with manual transmission, keep the clutch engaged during this process In vehicles with automatic transmission, maintain the shift lever in its initial position to prevent unintended movement.
The data signal indicating the instant of power-off initiation, t 0 , shall be generated when the foot force on the acceleration pedal is lower than 10 N (contact switch)
Transducer signals must be recorded from at least 1.3 seconds before to at least 2 seconds after the initiation of power-off The recording duration should include the settling time of all filters used, which ranges from 0.2 seconds to 1 second depending on the filter type.
During the recording process, the steering-wheel angle must stay within ± 3% of the steady-state value to ensure accuracy To enhance measurement reliability, it is recommended to perform at least three valid test runs at each lateral acceleration level.
Tests shall be carried out for both left and right turns
9 Data evaluation and presentation of results
General
General data must be included in the test report according to Annex A, ensuring comprehensive documentation Any modifications to the vehicle's equipment, such as load changes, require updating and re-recording the general data to maintain accuracy.
Currently, it remains unclear which variables most accurately capture the subjective feelings of the driver Additionally, the specific characteristics that best characterize the dynamic response of vehicles have yet to be identified Further research is needed to determine the key factors influencing driver perception and vehicle behavior.
The following specified variables therefore represent only examples for the evaluation of results.
Time histories
During each test run, time histories of the variables specified in Clause 5 should be recorded and presented These time histories are essential for evaluating test results, ensuring accurate test performance, and verifying the proper functioning of transducers, as illustrated in Figure B.1.
Initial point in time t 0
The initial point in time t 0 for the following characteristic values is the instant of the power-off initiation.
Characteristic values
Characteristic values should be determined as functions of the initial steady-state lateral acceleration, as outlined in Annex B During steady-state conditions, these values are defined as mean values measured over the interval from 1.3 seconds to 0.3 seconds before the power-off initiation time, t0 Additional characteristic values are obtained during a 2-second observation period starting at t0 At any given time tn, representative values are calculated by averaging data within a ±0.1 second window around tn For standard evaluation, the primary time point is tn = t0 + 1 second, although other tn values may be used depending on the analysis requirements.
For each set of initial conditions, calculate and visualize key characteristic values to better understand vehicle dynamics The reference yaw velocity and lateral acceleration values used in subsequent formulas are based on the hypothetical scenario where the initial turn radius is maintained, factoring in the vehicle's current longitudinal velocity (v_x,t) These reference values represent the conditions that would be observed if the vehicle sustained its initial turn radius throughout its motion, providing essential insights for accurate analysis and modeling of vehicle behavior.
Passenger cars are typically designed so that when the throttle is released, the vehicle slightly reduces its turn radius, affecting the driving path Consequently, the reference trajectory, which assumes the vehicle maintains the same curvature after throttle-off, may not represent the optimal or safest course Understanding this throttle-off behavior is crucial for accurate vehicle dynamics modeling and enhancing safety features in modern automotive systems.
This should be kept in mind for the assessment of the following evaluation metrics
9.4.2 The mean longitudinal acceleration during the time interval t 0 to t n (see Figure B.2):
9.4.3 The ratio of the value of the yaw velocity at time t n to the value of the reference yaw velocity at time t n
9.4.4 The ratio of the maximum value attained by the yaw velocity to the corresponding reference value of the yaw velocity (see Figure B.4): max max 3 , 0
( Y ) t f a ψ ψ = where t max is the instant when the maximum value of the yaw velocity is reached
9.4.5 The difference between the values of the instantaneous yaw velocity at time t n and the reference yaw velocity at time t n (see Figure B.5):
X t t t t t Y v f a ψ =ψ −ψ =ψ − R 9.4.6 The maximum value of the difference between the yaw velocity during power-off and the affiliated reference yaw velocity (see Figure B.6):
The instantaneous yaw acceleration at time tn, typically one second after throttle release (tn = t0 + 1 second), is calculated by differentiating yaw velocity, as illustrated in Figure B.7.
9.4.8 The ratio of the value of the lateral acceleration at time t n to the reference value of the lateral acceleration at time t n (see Figure B.8):
The maximum value of the sideslip angle during the observation period, denoted as Beta-Max, indicates the peak lateral deviation of the vehicle's trajectory The parameter t_bm (Beta-Max time) represents the elapsed time from the initial moment t_0 until the sideslip angle reaches its maximum, providing crucial insights into vehicle stability Understanding these parameters is essential for assessing vehicle behavior and safety performance during dynamic maneuvers, as detailed in Figure B.9.
9.4.10 The difference between the values of the sideslip angle at time t n and the initial steady-state value of the sideslip angle (see Figure B.10):
The article discusses key parameters in vehicle dynamics analysis, highlighting the difference between the maximum sideslip angle during the observation period and its initial steady-state value, which is essential for assessing vehicle stability It also emphasizes the importance of measuring the deviation between the instantaneous yaw velocity at a specific time and the calculated yaw velocity at that same moment, providing insights into vehicle handling performance These metrics are crucial for comprehensive evaluation of vehicle behavior during dynamic maneuvers, aiding in optimizing safety and control systems.
X t a f a β ′ =ψ −v where β ′ is the sideslip-angle velocity uncorrected for the effects of the sideslip angle itself and the deceleration
This metric provides information on the vehicle’s yaw stability
9.4.13 The path deviation at time t n (see note) defined as the radial distance of the reference point and its initial circular path (see Figure B.13):
Figure 1 — Definition of path deviation
The path deviation is calculated by the path of the reference point in the earth fixed axis system (see Figure 1)
The coordinates of the reference point can be determined for example by transforming the vehicle fixed velocity vectors vG X and vG Y into the earth fixed system and subsequent integration
The documentation of general data and test conditions shall be in compliance with Annex A and Annex B of
The characteristic values of the vehicle dynamic reaction shall be presented as functions of the initial steady-state lateral acceleration or initial radius, as shown in Figures B.2 to B.13
Y longitudinal velocity (m/s), lateral acceleration (m/s 2 ), steering wheel angle (°), sideslip angle (°), yaw velocity (°/s)
Figure B.1 — Time histories of variables during the time interval −1,5 s before and 2,0 s after power-off initiation (scaling depends on variables and test conditions)
Figure B.2 — Mean longitudinal acceleration−a X t , n during the time interval t 0 to t n as a function of the initial lateral acceleration a Y, 0
Figure B.3 — The ratio of the value of the yaw velocity at time t n to the value of the reference yaw velocity at time t n as a function of the initial lateral acceleration a Y, 0
Figure B.4 illustrates the ratio of the maximum yaw velocity (ψ max) to its reference value (ψ Re f,t max) depending on the initial lateral acceleration (a Y, 0) This analysis highlights how variations in initial lateral acceleration influence the peak yaw velocity relative to the reference, providing insights into vehicle dynamic behavior during lateral maneuvers Understanding this relationship is crucial for optimizing vehicle stability and ensuring safe handling under different initial conditions.
Figure B.5 — Difference between the value of the yaw velocity at time t n and the value of the reference yaw velocity at time t n as a function of the initial lateral acceleration a Y, 0
Figure B.6 — The maximum value of the difference between the yaw velocity during power-offψ t and the affiliated reference yaw velocityψ Ref, t as a function of the initial lateral acceleration a Y, 0
Figure B.7 — The instantaneous value of yaw acceleration at time t n as a function of the initial lateral acceleration a Y, 0
Figure B.8 — The ratio of the value of the lateral acceleration at time t n to the value of the reference lateral acceleration at time t n as a function of the initial lateral acceleration a Y, 0
Figure B.9 — Maximum value of the sideslip angleβ max during the observation period from 0 s to 2 s and the affiliated time t bm ,β max as a function of the initial lateral acceleration a Y, 0
Figure B.10 — Difference between the value of the sideslip angle at time t n and the initial value of the sideslip angleβ 0 as a function of the initial lateral acceleration a Y, 0
Figure B.11 illustrates the difference between the maximum sideslip angle observed from time t₀ to tₙ and the initial sideslip angle β₀, highlighting how this variation correlates with the initial lateral acceleration aᵧ,₀ This analysis demonstrates the influence of initial lateral acceleration on sideslip behavior during vehicle dynamics studies Understanding these relationships is essential for optimizing vehicle stability and enhancing safety in automotive engineering.
Figure B.12 — Difference between the values of the instantaneous yaw velocity at time t n and the calculated yaw velocity at time t n as a function of the initial lateral acceleration a Y,0
Figure B.13 — Path deviation of the reference point ,
∆s at time t n = t 0 + 2 s as a function of the initial lateral acceleration a Y,0
[1] ISO 1176, Road vehicles — Masses — Vocabulary and codes
[2] ISO 2416, Passenger cars — Mass distribution
[3] ISO 4138, Passenger cars — Steady-state circular driving behaviour — Open-loop test methods