WLTP-12-07e (final, 09/09/2015)
ROAD LOAD MATRIX FAMILY gtr proposal
Overview of approach
Open
issue
#17
Description
Proposed approach
Review Default Road Load Parameters
(paragraph 5 of Annex 4)
Development of Road Load Matrix Family method
IWG#11 agreed with concept
Annex 4 TF advices IWG#12 to adopt this document
Based on WLTP-SG-Drafting-04-01e-GTR Version 28 07 2015
Changes to gtr presented in red.
Text of the global technical regulation
5.
General Requirements
(New)
5.8
Road load matrix family
The road load matrix family can be applied for vehicles designed for a technically permissible
maximum laden mass ≥ 3000 kg.
Only vehicles which are identical with respect to the following characteristics are permitted to be
part of the same road load matrix family:
(a) Transmission type (e.g. manual, automatic, CVT);
(b) Number of powered axles;
Annex 4
Road load and dynamometer setting
4.2.1
Test vehicle
(New)
4.2.1.4:
Application of the road load matrix family
(renumber 4.2.1.5 to 4.2.1.7 into 4.2.1.6 to 4.2.1.8)
A vehicle fulfilling the criterion of paragraph 5.8 of this GTR and that is representative of the
intended series of complete vehicles to be covered by the road load matrix family in terms of
estimated worst Cd value and body shape, , and that is representative of the intended series of
vehicles to be covered by the road load matrix family in terms of estimated average mass of
optional equipment shall be selected to determine the road load. In case no representative body
shape for a complete vehicle can be determined the test vehicle shall be equipped with a square
box with rounded corners with a radius of maximum of 25 mm and with width equal to the
maximum width of the vehicles covered by the road load matrix family and total height of test
vehicle 3.0 m ± 0.1 m.
The manufacturer and the responsible authority shall agree which vehicle test model is
representative.
The vehicle parameters test mass, tyre rolling resistance and frontal area of both a vehicle H M and
LM shall be determined in such a way that vehicle H M produces the highest cycle energy and
vehicle LM the lowest cycle energy from the road load matrix family. The manufacturer and the
responsible authority shall agree on the vehicle parameters for vehicle H M and LM.
The road load of all individual vehicles of the road load family (including HM and LM) shall be
calculated according to paragraph 5.1of this Annex.
(Current gtr)
4.2.1.7.
Test vehicle condition
4.2.1.7.1.
Run-in
The test vehicle shall be suitably run-in for the purpose of the subsequent test for at
least 10,000 but no more than 80,000 km.
4.2.1.7.1.1.
4.3.
At the request of the manufacturer, a vehicle with a minimum of
3,000 km may be used.
Measurement and calculation of total resistance by the coastdown method
The total resistance shall be determined by using stationary (paragraph 4.3.1. of this Annex) or
on-board anemometer (paragraph 4.3.2. of this Annex) method.
4.3.1.
Coastdown method with stationary anemometry
4.3.1.4.5
The following equation shall be used to compute the average total resistance where
the harmonised average of the alternate coastdown times shall be used.
Fj =
1
3.6
× (mav + mr ) ×
2 × ∆v
∆tj
(14)
where:
∆t j
is the harmonised average of alternate coastdown time
measurements at velocity vj , seconds (s), given by:
∆t j =
2
1
1
+
∆tja ∆tjb
(15)
where ∆t ja and ∆t jb are the coastdown times at velocity vj ,
seconds (s),in each direction, respectively;
mav
is the average of the test vehicle masses at the beginning and
end of road load determination, kg;
mr
is the equivalent effective mass of all the wheels and vehicle
components rotating with the wheels during coastdowns on the
road, in kilograms (kg); mr shall be measured or calculated
using an appropriate technique. Alternatively, mr may be
estimated to be 3 per cent of the sum of the mass in running
order and 25 kg.
The coefficients f0 , f1 and f2 in the total resistance equation shall be
calculated with a least squares regression analysis.
In the case that the tested vehicle is the representative vehicle of a
road load matrix family, the coefficient f1 shall be set to zero and the
coefficients f0 and f2 shall be recalculated with a least squares
regression analyses.
4.3.2.
Coastdown method with on-board anemometry
4.3.2.5.2.
Mechanical drag modelling
Mechanical drag consisting of separate components representing tyre, Dtyre , and
front and rear axle frictional losses, Df and Dr , including transmission losses) can
be modelled as a three-term polynomial as a function of speed, v, as in the equation
below:
Dmech = Am + Bm v + Cm v 2
(19)
where:
Am , Bm , and Cm are determined in the data analysis using the least squares method.
These constants reflect the combined driveline and tyre drag.
In the case that the tested vehicle is the representative vehicle of a road load matrix
family, the coefficient Bm shall be set to zero and the coefficients Am and Cm shall
be recalculated with a least squares regression analyses.
4.4.
Measurement of running resistance using the torque meter method
4.4.4.
Running resistance curve determination
The following least squares regression curves for each direction a and b shall be
fitted to all the data pairs (vjm , Cjma ) and (vjm , Cjmb ) at all reference speeds vj ,(j =
1, j = 2, etc.) described in paragraph 4.3.1.1. above to determine the coefficients
c0a , c0b , c1a , c1b , c2a and c2b :
Ca = c0a + c1a v + c2b v 2
(35)
2
(36)
Cb = c0b + c1b v + c2b v
where:
Ca and Cb
are the running resistances in directions a and b, Nm;
c0a and c0b are constant terms in directions a and b, Nm;
c1a and c1b are the coefficients of the first order term in directions a and
b, Nm∙(h/km);
c2a and c2b are the coefficients of the second order term in directions a and
b, Nm∙(h/km)2;
v is vehicle velocity, km/h.
The average total torque is calculated by the following equation:
Cavg = c0 + c1 v + c2 v 2
(37)
where the average coefficients c0 , c1 and c2 shall be calculated using the following
equations:
c
+c0b
c
+c1b
c
+c2b
c0 = 0a
2
(38)
c1 = 1a
2
(39)
c2 = 2a
2
(40)
The coefficient c1 may be assumed to be zero if the value of (c1 × v) 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 according to the least squares method.
The coefficients c0 , c1 and c2 as well as the coastdown times measured at the
chassis dynamometer (see paragraph 8.2.3.3. of this Annex) shall be recorded.
In the case that the tested vehicle is the representative vehicle of a road load matrix
family, the coefficient c1 shall be set to zero and the coefficients c0 and c2 shall be
recalculated with a least squares regression analyses.
4.5.
Correction to reference conditions
4.5.4.
Test mass correction factor
4.5.4.1
Test vehicle H
The correction factor, K1 , for the test mass of the test vehicle H shall be determined
as follows:
K1 = f0 × (1 −
K1 = f0 × (1 −
TM
m av
TMH
)
TMH,actual
)
(43)
where:
f0
is a constant term, N;
TMH
is the test mass of the test vehicle H, kg;
TMH,actual
is the actual test mass of test vehicle H (the average mass mav ); (see
paragraph 4.3.1.4.4. of this Annex), kg.
m av
is the actual test mass of the test vehicle (determined according to
paragraph 4.3.1.4.4. of this Annex), kg.
4.5.4.2
Test vehicle L
The correction factor, K1 , for the test mass of test vehicle L shall be
determined as follows:
K1 = f0 × (1 −
TML
TML,actual
)
(44)
where:
f0
is a constant term, N;
TML
is the test mass of test vehicle L, kg;
TML,actual
is the actual test mass of the test vehicle L (the average
mass mav ; see paragraph 4.3.1.4.4. of this Annex), kg.
4.5.5.
Road load curve correction
(Current gtr)
5.
Method for the calculation of default road load based on vehicle parameters
5.1.
Method for cCalculation of road load for vehicles based on a representative vehicle of a road load
matrix family
5.1.1
For the calculation of the road load of vehicles of a road load matrix family the vehicle parameters
determined in paragraph 4.2.1.4 of this Annex and the road load coefficients of the representative
test vehicle determined in paragraph 4.3 or 4.4 of this Annex shall be used.
5.1.2
The road load force for an individual vehicle shall be calculated using the following equation:
Fc = f0 + f1 × v + f2 × v 2
(47)
where:
Fc is the calculated road load force as a function of vehicle velocity, N;
f0 is the constant road load coefficient, N, defined by the equation:
f0 = Max((0.05 x f0r + 0.95 x (f0r x TM/TMr + (RR – RRr) x 9.81 x TM)); (0.2 x f0r +
0.8 x (f0r x TM/TMr + (RR – RRr) x 9.81 x TM)))
f0r is the constant road load coefficient of the representative vehicle of the road load matrix
family , N, determined in paragraph 4.2.1.4.
f1 is the first order road load coefficient and shall be equal to zero;
f2 is the second order road load coefficient, N·(h/km)², defined by the equation:
f2 = Max((0.05 x f2r + 0.95 x f2r x Af / Afr); (0.2 x f2r + 0.8 x f2r x Af / Afr))
f2r is the second order road load coefficient of the representative vehicle of the road load matrix
family, N·(h/km)², determined in paragraph 4.2.1.4.
v is the vehicle speed, km/h;
TM
is the actual test mass of the individual vehicle of the road load matrix family,
TMr
is the test mass of the representative vehicle of the road load matrix family,
determined in paragraph 4.2.1.4,
Af
is the frontal area of the individual vehicle of the road load family, m²,
Afr
is the frontal area of the representative vehicle of the road load matrix family, m2,
determined in paragraph 4.2.1.4
RR
is the tyre rolling resistance of the individual vehicle of the road load family,
kg/tonne,
RRr
is the tyre rolling resistance of the representative vehicle of the road load matrix
family, kg/tonne, determined in paragraph 4.2.1.4.
5.2.
Method for the cCalculation of default road load based on vehicle parameters
5.2.1
As an alternative for determining road load with the coastdown or torque meter method, a
calculation method for default road load may be used.
For the calculation of default road load based on vehicle parameters, several parameters such as
test mass, width and height of the vehicle shall be used. The default road load, F_c, shall be
calculated for the reference speed points..
5.2.2
The default road load force shall be calculated using the following equation:
Fc = f0 + f1 × v + f2 × v 2
(47)
where:
Fc
is the calculated default road load force as a function of vehicle velocity, N;
f0
is the constant road load coefficient, N, defined by the equation:
f0 = 0.140 × TM;
(48)
f1
is the first order road load coefficient and shall be equal to zero;
f2
is the second order road load coefficient, N·(h/km)², defined by the
equation:
f2 = (2.8 × 10−6 × TM) + (0.0170 × width × height);(49)
v
is vehicle velocity, km/h;
TM
test mass, kg;
width vehicle width, metres, as defined in 6.2. of Standard ISO 612:1978;
height vehicle height, metres, as defined in 6.3. of Standard ISO 612:1978.
(Current gtr)
8.
Chassis dynamometer load setting
8.1.
Chassis dynamometer setting by the coastdown method
This method is applicable when the road load is determined using the coastdown
method as specified in paragraph 4.3. of this Annex.
In the case of a road load matrix family this method is applicable when the road
load of the representative vehicle is determined using the coastdown method as
specified in paragraph 4.3. of this Annex. The target road load values are the values
calculated using the method as specified in paragraph 5.1. of this Annex.
8.2.
Chassis dynamometer load setting using the torque meter method
This method is applicable when the road load is determined using the torque meter
method, as specified in paragraph 4.4. of this Annex.
In the case of a road load matrix family this method is applicable when the road
load of the representative vehicle is determined using the torque meter method as
specified in paragraph 4.4. of this Annex. The target road load values are the values
calculated using the method as specified in paragraph 5.1. of this Annex.
Annex 6
(Current gtr)
1.2.3.
Test vehicle
1.2.3.1.
General
The test vehicle shall conform in all its components with the production series, or, if
the vehicle is different from the production series, a full description shall be
recorded. In selecting the test vehicle, the manufacturer and responsible authority
shall agree which vehicle model is representative for the interpolation family. In the
case of a road load matrix family, the test vehicle shall be the representative vehicle
selected under paragraph 4.2.1.4. of Annex 4.
For the measurement of emissions the road load as determined with test vehicle H
shall be applied. In the case of a road load matrix family, for the measurement of
emissions the road load as calculated for vehicle HM according to paragraph 5.1 of
Annex 4 shall be applied.
If at the request of the manufacturer the interpolation method is used (see
paragraph 3.2.3.2 of Annex 7), an additional measurement of emissions shall be
performed with the road load as determined with test vehicle L. Tests on vehicles
H and L should be performed with the same test vehicle and shall be tested with the
shortest final transmission ratio within the interpolation family. In the case of a road
load matrix family, an additional measurement of emissions shall be performed with
the road load as calculated for vehicle LM according to paragraph 5.1 of Annex 4
shall be applied.
1.2.3.2.
CO2 interpolation range
The interpolation method shall only be used if the difference in CO2 between test
vehicles L and H is between a minimum of 5 and a maximum of 30 g/km or 20 per
cent of the CO2 for vehicle H, whichever value is the lower.
At the request of the manufacturer and with approval of the responsible authority,
the interpolation line may be extrapolated to a maximum of 3 g/km above the CO2
emission of vehicle H and/or below the CO2 emission of vehicle L. This extension
is valid only within the absolute boundaries of the interpolation range specified
above.
This paragraph is not applicable for the difference in CO2 between vehicles HM and
LM of a road load matrix family.
Annex 7
(Current gtr)
3.2.3.
Fuel consumption and CO2 calculations for individual vehicles in an
interpolation family
3.2.3.1.
Fuel consumption and CO2 emissions without using the interpolation method
The CO2 value, as calculated in paragraph 3.2.1. above and FC, as calculated
according to paragraph 6 of this Annex, shall be attributed to all individual
vehicles in the interpolation family and the interpolation method shall not be
applicable.
3.2.3.2.
Fuel consumption and CO2 emissions using the interpolation method
The CO2 emissions and the fuel consumption for each individual vehicle in the
interpolation family may be calculated according to the interpolation method
outlined in paragraphs 3.2.3.2.1. to 3.2.3.2.5. inclusive.
…
3.2.3.2.2.4
Calculation of road load for individual vehicles in the interpolation family
The road load coefficients f0 , f1 and f2 (as defined in Annex 4) for test vehicles
H and L are referred to as f0,H , f1,H and f2,H ,and f0,L , f1,L and f2,L respectively. An
adjusted road load curve for the test vehicle L is defined as follows:
∗
∗
FL (v) = f0,L
+ f1,H × v + f2,L
× v2
(27)
Applying the least squares regression method in the range of the reference speed
∗
∗
points, adjusted road load coefficients f0,L
and f2,L
shall be determined for FL (v)
∗
with the linear coefficient f1,L set to f1,H . The road load coefficients f0,ind , f1,ind
and f2,ind for an individual vehicle in the interpolation family are calculated as
follows:
f0,ind = f0,H − ∆f0 ×
(TMH ×RRH −TMind ×RRind )
(TMH ×RRH −TML ×RRL )
(28)
or, if (TMH × RR H − TML × RR L ) = 0, equation 29 below shall apply:
f0,ind = f0,H − ∆f0
(29)
f1,ind = f1,H
f2,ind = f2,H − ∆f2
(30)
(∆[Cd ×Af ]LH −∆[Cd ×Af ]ind )
(∆[Cd ×Af ]LH )
(31)
or, if ∆(Cd × Af )LH = 0, equation 32 below shall apply:
f2,ind = f2,H − ∆f2
(32)
where:
∗
∆f0 = f0,H − f0,L
(33)
∗
∆f2 = f2,H − f2,L
(34)
In the case of a road load matrix family, the road load coefficients f0, f1 and f2
for an individual vehicle shall be calculated according to the formulas described
in 5.1.2 in Annex 4
3.2.3.2.3.
Calculation of cycle energy per phase
The cycle energy demand, Ek,p , and distance, dc,p , per cycle phase, p, applicable
for individual vehicles in the interpolation family shall be calculated according
to the procedure in paragraph 5. of this Annex, for the following sets k of road
load coefficients and masses:
k=1:
∗
∗
f0 = f0,L
, f1 = f1,H , f2 = f2,L
, m = TML
(35)
(test vehicle L)
k=2:
f0 = f0,H , f1 = f1,H , f2 = f2,H , m = TMH
(36)
(test vehicle H)
k=3:
f0 = f0,ind , f1 = f1,H , f2 = f2,ind , m = TMind
(37)
(an individual vehicle in the interpolation family)
3.2.3.2.4.3.
Calculation of the CO2 value for an individual vehicle using the interpolation
method
For each cycle phase, p, of the WLTC applicable for individual vehicles in the
interpolation family, the contribution to the total mass of CO2 for an individual
vehicle shall be calculated as follows:
E3,p −E1,p
MCO2−ind,p = MCO2 −L,p + (
E2,p −E1,p
) × (MCO2 −H,p − MCO2−L,p )
The terms E1,p, E2,p and E3,p are defined in paragraph 3.2.3.2.3. above.
(38)
The CO2 mass emissions attributed to an individual vehicle of the interpolation
family, MCO2−ind , shall be calculated by the following equation for all of the
applicable cycle phases, p:
MCO2−ind =
3.2.3.2.5.
∑p MCO2 −ind,p ×dc,p
∑p dc,p
Calculation of the fuel consumption, FC, value for an individual vehicle using
the interpolation method
For each cycle phase p of the WLTC applicable for individual vehicles in the
interpolation family, the contribution to the FC for an individual vehicle shall be
calculated as follows:
FCind,p = FCL,p + (
E3,p −E1,p
E2,p −E1,p
) × (FCH,p − FCL,p )
The terms E1,p, E2,p and E3,p are defined in paragraph 3.2.3.2.3. above.
The fuel consumption, FCind, attributed to an individual vehicle of the
interpolation family, shall be calculated for all applicable cycle phases using the
following equation:
FCind =
∑p FCind,p ×dc,p
∑p dc,p
.
…
3.2.4.
Fuel consumption and CO2 calculations for individual vehicles in a road load
matrix family
The CO2 emissions and the fuel consumption for each individual vehicle in the
road load matrix family may be calculated according to the interpolation method
outlined in paragraphs 3.2.3.2.3. to 3.2.3.2.5. inclusive.
Where applicable, references to vehicle L and/or H shall be replaced by
references to vehicle LM and/or HM respectively.
3.2.4.1.
Determination of fuel consumption and CO2 emissions of vehicles LM and HM
The mass of CO2 emissions, MCO2 , of vehicles LM and HM shall be determined
according to the calculations in paragraph 3.2.1. above for the individual cycle
phases p of the applicable WLTC and are referred to as MCO2 −LM,p and
MCO2−HM,p respectively. Fuel consumption for individual cycle phases of the
applicable WLTC shall be determined according to paragraph 6 of this Annex
and are referred to as FCLM,p and FCHM,p respectively.
3.2.4.1.1.
Road load calculation for an individual vehicle
The road load force shall be calculated according to the procedure described in
paragraph 5.1 of Annex 4.
3.2.4.1.1.1.
Mass of an individual vehicle
The test masses of vehicles HM and LM selected under paragraph 4.2.1.4. of
Annex 4 shall be used as input.
TMind, in kg, shall be the individual test mass of the vehicle according to
[definition 3.2.d. of II. text of the global technical regulation].
If the same test mass is used for vehicles LM and HM, the value of TMind shall be
set to the mass of vehicle HM for the road load matrix family method.
3.2.4.1.1.2.
Rolling resistance of an individual vehicle
The rolling resistance values for vehicle LM , RRLM, and vehicle HM, RRHM,
selected under paragraph 4.2.1.4. of Annex 4 shall be used as input.
(39)
If the tyres on the front and rear axles of vehicle LM or HM have different rolling
resistance values, the weighted average of the rolling resistances shall be
calculated using the following equation:
RR x = RR 𝑥,FA ∗ mp𝑥,FA + RR 𝑥,RA ∗ (1 − mp𝑥,FA )
where:
RR x,FA
is the rolling resistance of the front axle tyres, kg/tonne;
RR x,RA
is the rolling resistance of the rear axle tyres, kg/tonne;
mpx,FA is the percentage of the vehicle mass on the front axle;
𝑥
represents vehicle L, H or an individual vehicle.
For the tyres fitted to an individual vehicle, the value of the rolling resistance
RR ind shall be set to the class value of the applicable tyre rolling resistance
class, according to Table A4/1of Annex 4.
If the tyres have different rolling resistance class values on the front and the rear
axle, the weighted average shall be used, calculated with the equation above.
If the same rolling resistance is used for vehicles LM and HM, the value of RR ind
shall be set to RR HM for the road load matrix family method.
3.2.4.1.1.3.
Frontal area of an individual vehicle
The frontal area for vehicle LM , AfLM, and vehicle HM, AfHM, selected under
paragraph 4.2.1.4. of Annex 4 shall be used as input.
Af,ind, in m2, shall be the frontal area of the individual vehicle.
If the same frontal area is used for vehicles LM and HM, the value of Af,ind shall
be set to the frontal area of vehicle HM for the road load matrix family method.
(25)