A&D Technology, Inc.

4622 Runway Blvd., Ann Arbor, MI 48108

PH: 734-973-1111 FAX: 734-973-1103

www.aanddtech.com

Vehicle Road Load Module

1/2 R.Evans, R.Skinner 8/15/2011

1.1 VEH.ROAD.LOAD (VEH1)

The Veh1 is a utility module that contains the vehicle model for road load calculation. This module 

takes as an input the shaft speed and outputs the respective torque equivalent of road load that is 

used in the Dm1 module for the torque setpoint.

1.1.1 Road Load Model

The model used to calculate the road load force, FRL [N], is given by:

FRL  Ff  F  FJ(1)

where Ff[N] is the friction, F [N] the banking and FJ [N] inertial forces, respectively. These load 

components are defined as:

Ff  Cv  Bv  A

2

(2)

F  mg sin (3)

dt

dv FJ  m (4)

where A [N], B [[N·h/km] and C [N·h2/(km)2] are vehicle specific constants, v [km/h] is vehicle 

speed, m [kg] is the vehicle mass,g [m/s2] is the acceleration due to gravity, and  is the road 

grade. 

Equation (2) can also be expressed as: 

1 0

2

2

1

f f d air R mgCR F  A C  v  mgC v  (5)

Where Af[m2] is the frontal area of the vehicle, Cd [ ] is the coefficient of drag, ρair [kg/m3] is the 

density of air, CR2 [h2/(km)

2

] is the second order coefficient of rolling friction for the vehicle, CR1

[h/km] is the first order coefficient of rolling friction, and CR0 [ ] is the zeroth order coefficient of 

rolling friction.

The vehicle speed is related to the engine shaft speed, ne [min-1], transmission ratio, kt[ ], 

differential ratio, kd [ ], and loaded wheel radius, r [m], by:

    













1000

1

60 12 e

t d

n

k k

v  r

t d

e

k k

0.12 rn

 (6)

For a partial powertrain consisting only of an engine and transmission, the output shaft of the 

transmission is connected to a dynamometer. In this case, the dyno measures the speed and 

torque on the driveshaft. Since the driveshaft speed, nds [rpm], is equal to:
A&D Technology, Inc.

4622 Runway Blvd., Ann Arbor, MI 48108

PH: 734-973-1111 FAX: 734-973-1103

www.aanddtech.com

Vehicle Road Load Module

2/2 R.Evans, R.Skinner 8/15/2011

t

e

ds k

n

n 

Then equation (6) can be rewritten as:

d

ds

k

rn

v

0.12

 (7)

The road load torque at the driveshaft , TRL [N], is related to the road load force FRL by:

d

RLs

RL k

rF

T  (8)

1.1.2 Dyno Control

The Dyno control can be realized by controlling the torque (based on RL and 

vehicle mass) and allowing the speed to be a result.

The Dyno can also be controlled in speed (the integral of acceleration) according 

to a=F/m (F=ma) where F is the imbalanced force, m is the vehicle mass and a is 

the calculated acceleration.

The imbalanced torque is calculated according to:

Ti  Tdyno  TRL (9)

Where Tiis the imbalanced torque and Tdyno is the torque measured by the inline 

torque meter of the dyno.

The addition of requested brake torque (Tbrake) from the driver model yields the 

following:

Tib  Tdyno TRL  Tbrake (10)

This imbalanced force should lead to an acceleration of the dyno according to:

dyno ib vehilce   T / J (11)

The mass of the vehicle translated into a rotational inertia Jvehicle is calculated as:

/(2 )

2

vehilce vehilce t d

J  m  d k k (12)

The Jvehicle is a constant for a given vehicle arrangement