Wltp-2013-019 Consolidated Draft gtr 12. 04. 2013 Running history of the consolidated draft gtr

WEB/TELEPHONE CONFERENCE WEDNESDAY, NOVEMBER 21 STOPS AT §4.3.1.4.1.

4.3.1.4.2. These measurements shall be carried out in both directions until a minimum of three consecutive pairs of figures have been obtained which satisfy the statistical accuracy p, in per cent, defined below.

where:

p is the statistical accuracy;

n is the number of pairs of measurements;

T_j is the mean coastdown time at speed V_j, in seconds, given by the equation:

_

T_ji is the harmonised average coastdown time of the i^th pair of measurements at speed V_j, in seconds, given by the equation:

T_jai and T _jbi are the coastdown times of the i^th measurement at speed V_j in each direction, respectively, s;
σ is standard deviation, in seconds, defined by:


t is a coefficient given in Table 2 below.

t	n	t/	t	n	t/
4.3	3	2.48	2.2	10	0.73
3.2	4	1.60	2.2	11	0.66
2.8	5	1.25	2.2	12	0.64
2.6	6	1.06	2.2	13	0.61
2.5	7	0.94	2.2	14	0.59
2.4	8	0.85	2.2	15	0.57
2.3	9	0.77

Table 2
4.3.1.4.3. If, during a measurement in one direction, the driver causes any sudden change of direction of the vehicle, that measurement and the paired measurement in the opposite direction shall be rejected.

4.3.1.4.3. If, during a measurement in one direction, any (a) external factor or (b) driver action which influences the road load test occurs, that measurement and the paired measurement in the opposite direction shall be rejected.
4.3.1.4.4. The total resistances, F_ja and F_jb at speed V_j in directions a and b, in newtons, are determined by the equations:

where:

Fja is the total resistance at speed j in direction a, N;

Fjb is the total resistance at speed j in direction b, N;

m is the average of the test vehicle masses at the beginning and end of road load determination, kg;

m_r is the equivalent effective mass of all the wheels and vehicle components rotating with the wheels during coastdown on the road, in kilograms (kg); m_r shall be measured or calculated using an appropriate technique. Alternatively, m_r may be estimated to be 3 per cent of the unladen vehicle mass (UM) for the vehicle family;

t_ja and t_jb

are the mean coastdown times in directions a and b, respectively, corresponding to speed V_j, in seconds (s), given by the equations:

4.3.1.4.5. The total resistance curve shall be determined as follows.

The following regression curve shall be fit to the data sets (V_j, F_ja) and (V_j, F_jb) corresponding to all the speed points V_j (j = 1, 2, etc.) and direction (a, b) to determine f₀, f₁ and f₂:

F_a = f_0a + f_1av + f_2av²

F_b = f_0b + f_1bv+ f_2bv²

where:

F_a and F_b are the total resistances in each direction, N;

f_0a and f_0b are constant terms in each direction, N;

f_1a and f_1b are the first-order term coefficients of the vehicle speed in each direction, N·h/km;

f_2a and f_2b are the second-order term coefficients of the vehicle speed in each direction, N·(h/km)²;

V is vehicle speed, km/h.

The average total resistance F_avg shall be calculated by:

F_avg = f₀ + f₁v + f₂v²
where the coefficients f₀, f₁ and f₂ shall be calculated using the following equations:








where:

f₀, f₁ and f₂ are the average coefficients.



4.3.1.4.5.1. As an alternative to the above calculation, the following equation may be applied to compute the average total resistance, where the harmonised average of the alternate coastdown time shall be used instead of the average of alternate total resistance.







where:

t_j is the harmonised average of alternate coastdown time measurements at speed V_j, in seconds (s), given by the equation:


where:

t_ja and t_jb are the coastdown times at speed V_j in each direction, respectively, in seconds (s).

The coefficients f₀, f₁ and f₂ in the total resistance equation shall be calculated with regression analysis.

4.3.2. Average deceleration method

As an alternative to the determination procedure in 4.3.1, the total resistance may also be determined by the procedures described in 4.3.2.1 to 4.3.2.4. following mathematical approach.
4.3.2.1. Selection of speed points for road load curve determination

Speed points shall be selected as specified in 4.3.1.1.

4.3.2.2. Data collection

Data shall be measured and recorded as specified in 4.3.1.2.

4.3.2.3. Vehicle coastdown procedure

Vehicle coastdown shall be conducted as specified in 4.3.1.3.

4.3.2.4. Determination of total resistance by coastdown measurements
4.3.2.4.1. The speed versus time data during coastdown from vehicle speed (V_j + V) to (V_j + V) (V_j + V) to (V_j - V) shall be recorded, where V is more than 10 km/h.
4.3.2.4.2. The following function shall be fit to the group of data by polynomial regression to determine the coefficients A₀, A₁, A₂ and A₃:
v_a(t) = A_0a + A_1at + A_2at² + A_3at³

v_b(t) = A_0b + A_1bt + A_2bt² + A_3bt³

where:

v_a(t), v_b(t) is vehicle speed, in kilometres per hour (km/h), in directions a and b;

t is time, in seconds (s);

A_0a, A_1a, A_2a, A_3a, A_0b, A_1b, A_2b and A_3b are coefficients.

4.3.2.4.3. The deceleration, _j, in metres per second squared, at speed V_j , shall be determined as follows:




where:

t_j is the time at which the vehicle speed given by the function in 4.3.2.4.2 is equal to V_j.

4.3.2.4.4. The measurements shall be repeated in both directions, until a minimum of four consecutive pairs of the data have been obtained which satisfy the statistical accuracy p, in percent, below. The validity of the data shall be decided in accordance with 4.3.1.4.3.



where

n is the number of pairs of measurements;

_j is the mean average deceleration at the speed V_j, m/s², given by the equation:

where:

_
_jai and _jbi are the decelerations of the i^th measurement at the speed v_j defined in 4.3.2.4.3 for each direction, respectively, m/s²;

σ is the standard deviation, m/s², defined by the equation:

t is the coefficient given in Table 2.
4.3.2.4.5. The total resistance F_j at speed v_j shall be determined by the following equation, using m and m_r as defined in 4.3.1.4.4:

F_j = (m + m_r) * _j

where:

F_j is the total resistance at speed vj;

m is the average of the test vehicle masses at the beginning and end of road load deter mination, kg;

m_r is the equivalent effective mass of all the wheels and vehicle components rotating with the wheels during coastdown on the road, in kilograms (kg); m_r shall be measured or calculated using an appropriate technique. Alternatively, m_r may be estimated to be 3 per cent of the unladen vehicle mass (UM) for the vehicle family;

_j is #################
4.3.2.4.6. Total resistance curve determination

Determine the total resistance curve as specified in 4.3.1.4.5.

4.3.3. Direct regression method

As an alternative to the determination in 4.3.1.4.5, the total resistance may also be determined by the following mathematical approach.

4.3.3.1. Selection of speed range for road load curve determination

The test speed range (i.e. the maximum speed and the minimum speed) shall be so determined that it covers the range of the reference speeds, over which total resistance is measured. If the test is carried out using split runs, each split speed range shall be determined accordingly.

4.3.3.2. Data collection

Data shall be measured and recorded as specified in 4.3.1.2.

4.3.3.3. Vehicle coastdown procedure

Vehicle coastdown shall be conducted as specified in 4.3.1.3.

4.3.3.4. Determination of total resistance by coastdown measurement

The coefficients f₀, f₁ and f₂ shall be calculated by approximating the relation between V and t to tangent with Equation (4), of which the mathematical process is as follows.

4.3.3.4.1. Total resistance force F shall be calculated using the following equations: (1) and (2):

F = f₀ + f₁v+ f₂v² (1)

_ (2)

where:

F is the total resistance, N;

f₀ is a constant term, N;

f₁ is the coefficient of the first-order term, N·(h/km);

f₂ is the coefficient of the second-order term, N(h/km)²;

m is the test vehicle mass, kg;

m_r is the equivalent effective mass of all the wheels and vehicle components rotating with the wheels during coastdown on the road, kg; m_r should be measured or calculated by an appropriate technique; as an alternative, m_r may be estimated as 3 per cent of the unladen vehicle mass (UM) for the vehicle family;

v is the vehicle speed, km/h.
4.3.3.4.2. The equation below Equation (3) is derived from the equations in §4.3.3.4.1. (1) and (2).

_ (3)
4.3.3.4.3. The equation below Equation (4) is obtained by integrating the equation in §4.3.3.4.2. (3).

_ (4)

where:

v is #############

f₀, f₁, f₂ are #############

m is ###########

m_r is #############

t is the time, s;

C₀ is the integration constant.

4.3.3.4.4. The equation in §4.3.3.4.3. Equation (4) shall be replaced with the equation below: equation (5). _ (5)

where:

A,B,C,D are terms calculated by the least squares method.
4.3.3.4.5. The coefficients f₀, f₁ and f₂ shall be determined using the following equations:



<sub>

</sub>
If coastdowns are carried out using split runs, the total resistance, F, shall be calculated as follows:

(a) The road load force for each reference speed included in the actual coastdown speed range shall be calculated.

(b) Split data shall be placed into one set, one road load force equation shall be calculated for each direction a and b.

(b) Data from split runs shall be combined into one road load force equation, calculated separately for directions a and b.
4.3.3.4.6. Total resistance curve determination

The total resistance curve shall be determined as specified in 4.3.1.4.5.

#############################################
4.4. On-board anemometer-based coastdown method

As an alternative to the determination in 4.3.1, 4.3.2 or 4.3.3, total resistance may also be determined by the procedure described in 4.4.1 to 4.4.5. This method is applicable to a wind speed range up to 10 m/s on a test road as given in Table 1.
4.4.1. Selection of speed range for road load curve determination

The test speed range as specified in 4.3.3.1. shall be selected.
4.4.2. Data collection

The following data shall be measured and recorded at a maximum of 0.2 s intervals during the test.

a) elapsed time;

b) vehicle speed (measured by on-board anemometry);

c) wind speed and direction (measured by on-board anemometry).
4.4.3. Vehicle coastdown procedure

Vehicle coastdown shall be conducted as specified in 4.3.1.3.1. to 4.3.1.3.4. with an onboard anemometer installed on the vehicle. The anemometer shall be installed in a position such that the effect on the operating characteristics of the vehicle is minimised. It is recommended to install the anemometer at the vehicle’s forward aerodynamic stagnation point and approximately 2 m in front of it. Before the coastdown, the anemometer shall be installed on the vehicle and calibrated as specified by the manufacturer.

An example of an anemometer calibration procedure is given in Annex A.
4.4.4. Determination of coefficients a_mech, b_mech and c_mech

Each coefficient shall be calculated by the following equation with multi-regression analysis, using coastdown time and wind data.



where

m is the test vehicle mass, kg;

m_r is the equivalent effective mass of all the wheels and vehicle components rotating with the wheels during coastdown on the road,kg; m_r should be measured or calculated using an appropriate technique; as an alternative, m_r may be estimated to be 3per cent of the unladen vehicle mass;

dV/dt is acceleration, (km/h)/s;

a_mech is a first order coefficient of mechanical drag, N;

b_mech is a second order coefficient of mechanical drag, N/(km/h);

c_mech is a third order coefficient of mechanical drag, N/(km/h)²;

V is vehicle speed, km/h;

V_r is relative wind speed, km/h;

 is air density, in kilograms per cubic metre (kg/m³);

S is the projected frontal area of the vehicle, m²;

a_{i (i = 0 to 4)} is the aerodynamic drag coefficient as a function of yaw angle, in degrees^-n;

 is the yaw-angle apparent wind relative to the direction of vehicle travel, in degrees.

If the wind speed is close to 0 km/h, the equation theoretically cannot separate c_mech and (1/2) x a₀  S appropriately. Therefore, a constrained analysis, where a₀ is fixed if it is previously determined, for example in a wind tunnel, or c_mech is assumed to be zero, may be employed.

4.4.5. Determination of total resistance using coastdown measurements

The total resistance, F, shall be calculated where all the wind effects are eliminated, by the following equation with the coefficients obtained in 4.4.4.



#############################################
4.5. Measurement of running resistance by the torque meter method

As an alternative to the coastdown methods, the torque meter method may also be used, in which the running resistance is determined by measuring wheel torque as described in 4.5.1. to 4.5.3.

4.5.1. Installation of torque meter

One or more torque meter(s) shall be installed on the drivetrain of the test vehicle. Wheel torque meters shall be installed on each driven wheel.
4.5.2. Procedure and data sampling
4.5.2.1. Start of data collection

Data collection may be started following warm-up and stabilisation of the vehicle at the speed V_j, where the running resistance is to be measured.

4.5.2.2. Data collection

At least 10 data sets of speed, torque and time over a period of at least 5 s shall be recorded.

4.5.2.3. Speed deviation

The speed deviation from the mean speed shall be within the values in Table 3.

Table 3

Time period, seconds	Speed deviation, km/h
5	 0.2
10	 0.4
15	 0.6
20	 0.8
25	 1.0
30	 1.2

4.5.3. Calculation of mean speed and mean torque

4.5.3.1. Calculation process

Mean speed V_jm,(km/h) and mean torque C_jm, (N·m) over a time period, shall be calculated as follows:

_

and

_
where:

v_ji is vehicle speed of the i^th data set, km/h;

k is the number of data sets;

C_ji is torque of the i^th data set, Nm;

C_js is the compensation term for speed drift, Nm, given by the following equation:

C_js = (m + m_r) _* _j r_j

(C_js shall be no greater than 5 per cent of the mean torque before compensation, and may be neglected if _j is no greater than  0.005 m/s²)

where:

m and m_r are the test vehicle mass and the equivalent effective mass, respectively, kg, defined in 4.3.1.4.4;

r_j is the dynamic radius of the tyre, m, given by equation:

where

N is the rotational frequency of the driven tyre, in revolutions per second (s^-1);

α_j is the mean acceleration, in metres per second squared (m/s²), which shall be calculated by the equation:

t_i is the time at which the i^th data set was sampled, in seconds (s).

4.5.3.2. Accuracy of measurement

These measurements shall be carried out in both directions until a minimum of four consecutive figures have been obtained which satisfy accuracy p, in per cent, below. The validity of the data shall be decided in accordance with 4.3.1.4.2.

where

k is the number of data sets;

C_j is the running resistance at the speed Vj, in newton metres (N·m), given by the equation:

where

C_jmi is the average torque of the i^th pair of data sets at speed V_j, in newton metres (Nm), given by the equation:

C_jmai and C_jmbi are the mean torques of the i^th data sets at speed V_j determined in 4.5.3.1 for each direction, a and b respectively, in newton metres (Nm);

s is the standard deviation, in newton metres Nm), defined by the equation:

t is the coefficient given by replacing n in Table 2 with k.

4.5.3.3. Validity of the measured average speed

The average speed V_jmi, shall not deviate by more than  2 km/h from its mean, ^.

V_jmi and shall be calculated as follows:

where
V_jmai and V_jmbi are the mean speeds of the i^th pair of data sets at speed V_j determined in 4.5.3.1 for each direction, a and b respectively, in kilometres per hour (km/h).

4.5.4. Running resistance curve determination

The following regression curve shall be fitted to all the data pairs (V_jm, C_jma) and (V_jm, C_jmb) for both directions a and b at all speed points V_j (j = 1, 2, etc.) described in 4.3.1.1. to determine c_0a, c_0b, c_1a, c_1b, c_2a and c_2b:

C_a = c_0a + c_1aV + c_2aV²

C_b = c_0b + c_1bV + c_2bV²

where

C_a and C_b are the running resistances in each direction, in newton metres (N·m);

c_0a and c_0b are constant terms in each direction, in newton metres (N·m);

c_1a are c_1b are the coefficients of the first-order term in each direction, in newton metres per hour per kilometre (Nm(h/km)); c₁ may be assumed to be zero, if the value of c₁V is no greater than 3 per cent of C at the reference speed(s); in this case, the coefficients c₀ and c₂ shall be recalculated;

c_2a and c_2b are the coefficients of the second-order term in each direction, in newton metres per hour per kilometre squared (Nm(h/km)²);

V is vehicle speed, in kilometres per hour (km/h).

The average total torque equation is calculated by the following equation:

C_avg = c₀ + c₁V + c₂V²

where the average coefficients c₀, c₁ and c₂ shall be calculated using the following equations:

4.6. Correction to standard atmospheric reference conditions

4.6.1. Correction factors
4.6.1.1. Determination of correction factor for air resistance

The correction factor for air resistance K₂ shall be determined as follows:

where:

T is the mean atmospheric temperature, K;

 is the mean atmospheric pressure, kPa.

4.6.1.2. Determination of correction factor for rolling resistance

The correction factor, K₀, for rolling resistance, in reciprocal Kelvins, may be determined based on empirical data for the particular vehicle and tyre test, or may be assumed as follows:

K₀ = 8.6 x 10^-3 x K^-1
4.6.1.3. Wind correction

4.6.1.3.1. Wind correction, for absolute wind speed alongside the test road, shall be made by subtracting the difference that cannot be cancelled by alternate runs from the constant term f₀ given in 4.3.1.4.5, or from c₀ given in 4.5.4.

4.6.1.3.2. The wind correction shall not apply in the on-board-anemometer-based coastdown method (4.4) as the wind correction is made during the series of data sampling and subsequent analysis. The wind correction resistance w₁ for the coastdown method (4.3) or w₂ for the torque meter method shall be calculated by the equations:

w₁ = 3.6² x f₂v²_w or w₂ = 3.6² x c₂v²_w

where:

w₁ is the wind correction resistance, N;

f₂ is the coefficient of the aerodynamic term determined in § 4.3.1.4.5;

v_w is the average wind speed alongside the test road during the test, m/s;

w₂ is the wind correction resistance, N;

c is the coefficient of the aerodynamic term determined in §4.5.4.

4.6.2. Road load curve correction
4.6.2.1. The curve determined in 4.3.1.4.5. shall be corrected to reference conditions as follows:

where:

F* is the corrected total resistance, N;

f₀ is the constant term, N;

f₁ is the coefficient of the first-order term, N·(h/km);

f₂ is the coefficient of the second-order term, N(h/km)²;

K₀ is the correction factor for rolling resistance as defined in §4.6.1.2.;

K₂ is the correction factor for air resistance as defined in §4.6.1.1.;

V is vehicle speed, km/h;

w₁ is the wind correction resistance as defined in §4.6.1.3.

4.6.2.2. The curve determined in 4.4.5. shall be corrected to reference conditions as follows:

where:

F* is the corrected total resistance, N;

a_mech is the coefficient of mechanical drag, N;

b_mech is the coefficient of mechanical drag, N/(km/h);

c_mech is the coefficient of mechanical drag, N/(km/h)²;

 is air density, kg/m³;

S is the projected frontal area of the vehicle, m²;

a₀ is the coefficient for aerodynamic drag, as a function of yaw angle;

K₀ is the correction factor for rolling resistance as defined in §4.6.1.2.;

K₂ is the correction factor for air resistance as defined in §4.6.1.1.;

V is vehicle speed, km/h.
4.6.2.3. The curve determined in 4.5.4. shall be corrected to reference conditions as follows:

where:

C* is the corrected total running resistance, N·m;

c₀ is the constant term, N·m;

c₁ is the coefficient of the first-order term, N·m (h/km);

c₂ is the coefficient of the second-order term, Nm(h/km)²;

K₀ is the correction factor for rolling resistance as defined in §4.6.1.2.;

K₂ is the correction factor for air resistance as defined in §4.6.1.1.;

V is vehicle speed, km/h;

w₂ is the wind correction resistance as defined in §4.6.1.3..

5. Road load measurement using a combination of a wind tunnel and chassis dynamometer

The processes described in sections 5.1. and 5.2. below may be conducted simultaneously in a wind tunnel providing the test equipment meets the specifications prescribed in both sections.

5.1. Aerodynamic drag measurement in wind tunnel

5.1.1. Requirements for wind tunnel

The wind tunnel design, the test methods and the corrections shall be sufficient to provide a value of S * C_d representative of the on-road S * C_d value.
5.1.2. Testing procedure
5.1.2.1. The test vehicle shall be positioned according to the specifications of the wind tunnel laboratory, so as to ensure that the air stream is parallel to the longitudinal axis of the test vehicle. The test vehicle’s ground clearance shall be checked according to the vehicle manufacturer’s specification, and shall be adjusted if required. The engine bonnet, moveable panels and all windows shall be closed. The test vehicle shall be affixed in a way that minimises the effect on the airflow.

The vehicle shall be prepared as described in section 4.2. of this annex.

5.1.2.2. The measurement shall be conducted according to the specification of the wind tunnel laboratory.

It is recommended to use the test section wind speed of 140 km/h, but the lowest wind speed shall be 80 km/h.

Two measurements shall be conducted. If the difference in the resultant SC_d values is greater than 1 per cent, the test vehicle set-up and the wind tunnel set-up shall be checked and corrected if necessary. Two further tests shall then be performed. This procedure shall be repeated until a difference of no more than 1 per cent between two values is obtained.
5.1.3 Test result

Determine the test result (S * C_d), in square metres, by averaging a pair of the measure ment values.

5.2. Rolling resistance determination with a chassis dynamometer or a moving belt
5.2.1 Testing device

5.2.1.1. The chassis dynamometer shall have:

(a) a single roller (double single rollers for permanent four-wheel-drive vehicles);

(b) roller diameters of no less than 1.2 m;

(c) roller surface be of smooth steel, or other equivalent materials, or textured and shall be kept clean. In cases where a textured surface is used, this shall be noted in the test report, and the surface texture shall be 180 µm deep (80 grit).
5.2.1.2. The moving belt shall:

(a) be flat with no parasitic forces,

(b) have a polyurethane surface, or other equivalent materials, and shall be clean,

(c) have a width and length which exceeds the tyre footprints.

An external vehicle cooling fan shall have the characteristics described in §1.1. of Annex 5.
5.2.2. Testing procedure

The rolling resistance of the front and rear wheels shall be measured. When a double-single-axis type chassis dynamometer is used for a permanent four-wheel- drive vehicle, the resistance of both axles shall be measured simultaneously. During the test, the vehicle shall be cooled with an external cooling fan.

This procedure is based on force measurement at several steady speed points and not under deceleration.
5.2.2.1. The vehicle conditions as specified in 4.2.1.1. shall be adjusted.
5.2.2.2. The test room temperature shall be adjusted to 293 +6/-2 K. The chassis dynamometer shall be warmed up according to the chassis dynamometer specifications. Measure the chassis dynamometer running losses.
5.2.2.3. The non-driving wheels shall be placed in the normal front-driving direction on the chassis dynamometer and the following shall be performed;

a) restrain the vehicle, taking care not to apply an abnormal load on the measured axle;

b) warm up the axle until the chassis dynamometer force is stabilised, or up to a maximum of 30 minutes at the highest reference speed;

c) measure the axle rolling resistance for this speed;

d) decrease the speed to the immediate lower reference speed;

e) measure the axle rolling resistance for this new speed;

f) repeat c) to e) for each reference speed;

g) once the loads have been measured for each reference speed, repeat the entire measurement procedure from c) to f);

h) if the difference is greater than 4 per cent at any reference speed, the test vehicle set-up and the chassis dynamometer set-up shall be checked and corrected, if necessary. Two further tests shall then be performed. This procedure shall be repeated until a difference of no more than 4 per cent between two values, at any reference speed, is obtained;

i) once two satisfactory measurements have been obtained, the final result shall be the average of the two measurements for each reference speed.