Road Loads
The present section describes the work performed in order to define a standard process for the calculation of a vehicle's Road Loads to be used for the Parametric CO2MPAS simulations.
A standard issue when trying to simulate a vehicle is the lack of available information concerning the definition of its road loads. The present work describes the various assumptions for the definition of a standardized process allowing the definition of both NEDC and WLPT road loads, starting from standard / easy to access characteristics of a vehicle.
In order to achieve the previous, various sources have been used:
- Addendum 82: Regulation No. 83, UNECE
- The BOSCH Guide
- The draft document "RL_transformation_formulas.doc"
- Various spreadsheets developed and used along the WLTP/NEDC Correlation Exercise (e.g. AF's spreadsheet for the Calculation of Road Load Coefficients for WLTP derived from NEDC Road Loads)
- ... .
--> To be cross-checked with the script for the preparation of the web database
A list of the required vehicle masses for the calculation of the Road Loads is provided bellow:
- Mass in Running Order (MRO) is defined as in Article 2(4)(a) of Commission Regulation (EU) No 1230/2012.
-
Reference Mass (RM) is defined as
RM = MRO - 75 + 100[kg] -
Max Permissible Mass (MM), when not available is defined as
MM = RM + 500[kg] -
Unladen Mass Min (UMMin) is defined as
UMMin = RM - 100[kg] -
Unladen Mass Max (UMMax) is defined as
UMMax = UMMin + DUM[kg], whereDUM = 0.00009 * UMMin^2 - 0.0364 * UMMin[kg] - @GEORGE????????? - -
Laden Mass Max (LM) is defined as equal to MM,
LM = MM[kg] -
Test Mass High (TMH) is calculated as
TMH = UMMax + 100 + 0.15 * (LM - UMMax - 100)[kg], source: AF's spreadsheet -
Test Mass Low (TML) is calculated as
TML = UMMim + 100 + 0.15 * (LM - UMMax - 100)[kg], source: AF's spreadsheet.
The Aerodynamic Drag (Drag) is defined as Drag = FA * Cw, where FA and Cw are defined as presented in the following paragraphs.
The Delta Drag (DCDA) which captures the effect in the drag of the difference between the "best case" and the "worst case" cars within the same "category", is defined as DCDA = 2 * 0.04, source: AF's spreadsheet.
The Frontal Area (FA) of the vehicle is defined as FA = W * H * 0.84, where W represents the width [m] and H the height [m] of the vehicle.
The factor 0.84 is an empirical factor used for the correction of the "dead" areas of the product of width and height, e.g. area between ground and vehicle's bottom side in-between the wheels, side areas between vehicle's sides and tips of mirrors, etc. This factor is provided here, while it is validated also by an in-house exercise as it can be demonstrated here (TO BE DEFINED, @Ankostis script on this definition, where is that?).
The Aerodynamic Coefficient (Cw) of the vehicle is provided by the following dictionary, based on the vehicles carbody type.
These values are taken from the BOSCH Guide XXX and ammended in order to capture the effect of advanced aerodynamic design of modern cars - when it was judged that the minimum value does not well define modern cars another value has been picked from the defined range.
def Cw(c):
cw = {'cabriolet' : 0.28,
'sedan' : 0.27,
'hatchback' : 0.3,
'stationwagon' : 0.28,
'suv/crossover' : 0.35,
'mpv' : 0.3,
'coupe' : 0.27,
'pick-up' : 0.4,
}
return cw[c]
B Regulation (EC) No 1222/2009 of the European Parliament and of the Council defines the energy classes of the various tyres based on their rolling resistances:
For the purposes of the present exercise C1 tyres of Energy Efficiency Class A are considered representative and thus the Wheel Rolling Resistance (WRR) is defined as equal to WRR = 0.0065 [-].
The Delta Wheel Rolling Resistance (DRR) which captures the effect of the different tyres / in the rolling resistance of the difference between the "best case" and the "worst case" cars within the same "category", is defined as DRR = 0.0105 - 0.008, source: AF's spreadsheet.
In preparing the chassis-dynamometer for the execution of a type-approval test, the vehicle is pre-conditioned in order to reach similar conditions to those used in the coast-down test. The pre-conditioning procedure used in the WLTP test differs from that used for the purpose of NEDC so that, with equal road loads, the vehicle is considered subject to higher forces under the WLTP. That difference, defined as Pre-conditioning Effect (PCE) shall be set at 6 Newtons, such as PCE = 6 [N].
According to the WLTP, the lowest tyre pressure for the vehicle test mass shall be used, while this is not specified in the NEDC. For the purpose of determining the tyre pressure to be taken into account for the purpose of calculating the NEDC road load, the tyre pressure shall, taking into account the different tyre pressure per vehicle axle, be the average between the two axles of the average between the minimum and the maximum tyre pressure permitted for the selected tyres on each axle for the NEDC reference mass of the vehicle. The calculation shall be carried out for both the "best case" vehicle / vehicle L and the "worst case" vehicle / vehicle H.
For the purpose of the present exercise we define:
-
Pmax = 3[bar], is the average of the maximum tyre pressures of the selected tyres for the two axles; considered constant for both vehicles L and H -
Pmin = 2[bar], is the average of the minimum tyre pressures of the selected tyres for the two axles; considered constant for both vehicles L and H, -
Pavg = (Pmax + Pmin) / 2[bar], the average between the previous two.
The corresponding effect in terms of resistance applied to the vehicle, defined as TP, shall be calculated using the following formulae: TP = (Pavg / Pmin)^-0.4, source: RL_transformation_formulas document.
A minimum tyre tread depth of 80% is to be considered for the WLTP test, while the minimum allowed tyre tread depth for the purpose of the NEDC test is to be considered as equal to 50% of the nominal value. This resutls in an average difference of 2mm in tread depth between the two procedures. The corresponding effect in terms of the resistance applied to the vehicle, defined as TTD, shall be determined for the purpose of the NEDC road load calculation in accordance with the following formulae: TTD = 2 * 0.1 * RM * 9.81 / 1000, source: RL_transformation_formulas document.
During the WLTP test four rotating wheels are to be considered, while for the purpose of the NEDC tests only two rotating wheels are to be considered. The effect this has on the forces applied to the vehicle, defined as RI, shall be taken into account in accordance with the formulae: RI = 1.015 / 1.03.
The three functions bellow define the "physical" road loads which are later used for the calculation of the regulated road load coefficients.
-
F0 = RM * WRR * 9.81[N] -
F2 = 0.5 * 1.2 * Drag / 3.6^2[N/(km/h)^2] -
F1 = -71.735 * F2 + 2.7609[N/(km/h)], this function is derived from the measured cars and the known road load coefficients.
Starting from the physical coefficients F0, F1, F2, and taking into account the respective procedural differences we calculate the road load coeffients for NEDC, along with the respective reference mass, as follows:
-
F0N = (F0 - TTD) * TP * RI[N] -
F2N = F2[N/(km/h)^2] -
F1N = F1 / 2[N/(km/h)], GEORGE??????????????? -
RMN = RM[kg].
Starting from the NEDC coefficients F0N, F1N, F2N, and performing all correction in order to take into account the respective procedural differences we calculate the road load coeffients for WLTP High, along with the respective reference mass, as follows:
-
F0H = (F0N + PCE + TTD) / RI / TP * (TMH / RM) + (DRR * TMH * 9.81)[N] -
F2H = F2N / RI + (1.189 / 2 * DCDA / 3.6^2)[N/(km/h)^2] -
F1H = F1N / RI[N/(km/h)] -
RMH = TMH[kg].
Starting from the NEDC coefficients F0N, F1N, F2N, and performing all correction in order to take into account the respective procedural differences we calculate the road load coeffients for WLTP Low, along with the respective reference mass, as follows:
-
F0L = (F0N + PCE + TTD) / RI / TP * (TML / RM)[N] -
F2L = F2N / RI[N/(km/h)^2] -
F1L = F1N / RI[N/(km/h)] -
RML = TML[kg].