# Microscopic Models

We now review two microscopic emissions models to estimate hot-stabilized vehicle emissions. The models are used to calculate emissions at a given point t in time and require, as input, instantaneous vehicle kinematic parameters, such as speed and acceleration, or in more aggregated settings, parameters such as time spent in each trafﬁc mode, cruise, acceleration and deceleration.

## An Instantaneous Fuel Consumption Model

Bowyer et al. (1985) described an energy-related emissions estimation model which uses vehicle characteristics such as mass, energy, efﬁciency parameters, drag force and fuel consumption components associated with aerodynamic drag and rolling resistance, and approximates the fuel consumption per second. According to this model, the fuel consumption of a vehicle can be calculated as

where f(t) is the fuel consumption per unit time (mL/s), R(t) is the total tractive force (kN) required to move the vehicle and calculated as the sum of drag force, inertia force and grade force as RðtÞ¼ b1 þ b2υ2 þ Ma=1000 þ gMω=100000. Furthermore, α is the constant idle fuel rate (in mL/s), β1 is the fuel consumption per unit of energy (in mL/kJ), β2 is the fuel consumption per unit of energy-

acceleration (in mL/(kJ• m/s2)), b1 is the rolling drag force (in kN), and b2 is

the rolling aerodynamic force (in kN/(m/s2)). The total amount of fuel consumption

F(T) (mL) for a journey of duration T can be calculated as

The model works best at a micro-scale level and is better suited for short trip emission estimations.

## A Comprehensive Modal Emission Model

A comprehensive modal emission model (CMEM) for heavy-goods vehicles was developed and presented by Scora and Barth (2006), Barth et al. (2005) and Barth and Boriboonsomsin (2008). It is based on second-by-second tailpipe emissions. The CMEM needs detailed vehicle speciﬁc parameters for the estimations such as the engine friction coefﬁcient, and the vehicle engine speed. The CMEM follows, to some extent, the model of Ross (1994) and is composed of three modules, namely engine power, engine speed and fuel rate, which are detailed below.

• The engine power module: The power demand function for a vehicle is obtained from the total tractive power requirements Ptract (kW) placed on the vehicle at the wheels:

To translate the tractive requirement into engine power requirement, the following relationship is used:

where P is the second-by-second engine power output (kW), and ηtf is the vehicle drive train efﬁciency.

• The engine speed module: Engine speed is approximated in terms of vehicle speed as

where N(υ) is the engine speed (in rpm), S is the engine-speed/vehicle-speed ratio in top gear Lg, R(L) is the gear ratio in gear L = 1, .. ., Lg, and η is the efﬁciency parameter for diesel engines.

• The fuel rate module: The fuel rate (g/s) is given by the expression

The total fuel consumption (g) can be calculated as

The CMEM can be seen as a state-of-the-art microscopic emission model because of its ease of applicability.