Vehicle motion using coastdown testing coefficients
Powertrain Blockset / Vehicle Dynamics
Vehicle Dynamics Blockset / Vehicle Body
The Vehicle Body Total Road Load block implements a one degreeoffreedom (1DOF) rigid vehicle model using coastdown testing coefficients. You can use this block in a vehicle model to represent the load that the driveline and chassis applies to a transmission or engine. It is suitable for systemlevel performance, component sizing, fuel economy, or drive cycle tracking studies. The block calculates the dynamic powertrain load with minimal parameterization or computational cost.
You can configure the block for kinematic, force, or total power input.
Kinematic — Block uses the vehicle longitudinal velocity and acceleration to calculate the tractive force and power.
Force — Block uses the tractive force to calculate the vehicle longitudinal displacement and velocity.
Power — Block uses the engine or transmission power to calculate the vehicle longitudinal displacement and velocity.
To calculate the total road load acting on the vehicle, the block implements this equation.
$${F}_{road}=a+b\dot{x}+c{\dot{x}}^{2}+mg\mathrm{sin}(\theta )$$
To determine the coefficients a, b, and c, you can use a test procedure similar to the one described in Road Load Measurement and Dynamometer Simulation Using Coastdown Techniques. You can also use Simulink^{®} Design Optimization™ to fit the coefficients to measured data.
To calculate the vehicle motion, the block uses Newton’s law for rigid bodies.
$${F}_{total}=m\ddot{x}+{F}_{road}$$
Total power input is a product of the total force and longitudinal velocity. Power due to road and gravitational forces is a product of the road force and longitudinal velocity.
$$\begin{array}{l}{P}_{total}={F}_{total}\dot{x}\\ {P}_{road}={F}_{road}\dot{x}\end{array}$$
For the power accounting, the block implements these equations.
Bus Signal  Description  Variable  Equations  



 Externally applied force power  P_{FxExt}  ${P}_{FxExt}={F}_{total}\dot{x}$ 
 PwrFxDrag  Drag force power  P_{D}  ${P}_{d}=(a+b\dot{x}+c{\dot{x}}^{2})\dot{x}$  
 wrStoredGrvty  Rate change in gravitational potential energy  P_{g}  ${P}_{g}=mg\dot{Z}$  
PwrStoredxdot  Rate in change of longitudinal kinetic energy  P_{xdot}  ${P}_{\dot{x}}=m\ddot{x}\dot{x}$ 
The equations use these variables.
a  Steadystate rolling resistance coefficient 
b  Viscous driveline and rolling resistance coefficient 
c  Aerodynamic drag coefficient 
g  Gravitational acceleration 
x  Vehicle longitudinal displacement with respect to ground, in the vehiclefixed frame 
$$\dot{x}$$  Vehicle longitudinal velocity with respect to ground, in the vehiclefixed frame 
$$\ddot{x}$$  Vehicle longitudinal acceleration with respect to ground, vehiclefixed frame 
m  Vehicle body mass 
Θ  Road grade angle 
F_{total}  Total force acting on vehicle 
F_{road}  Resistive road load due to losses and gravitational load 
P_{total}  Total tractive input power 
P_{road}  Total power due to losses and gravitational load 
$$\dot{Z}$$  Vehicle vertical velocity along the vehiclefixed

[1] Gillespie, Thomas. Fundamentals of Vehicle Dynamics. Warrendale, PA: Society of Automotive Engineers (SAE), 1992.
[2] Light Duty Vehicle Performance And Economy Measure Committee. Road Load Measurement and Dynamometer Simulation Using Coastdown Techniques. Standard J1263_201003. SAE International, March 2010.