Vehicle Body 3DOF

3DOF rigid vehicle body to calculate longitudinal, lateral, and yaw motion

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Libraries:
Vehicle Dynamics Blockset / Vehicle Body

Description

The Vehicle Body 3DOF block implements a rigid two-axle vehicle body model to calculate longitudinal, lateral, and yaw motion. The block accounts for body mass and aerodynamic drag between the axles due to acceleration and steering.

Use this block in vehicle dynamics and automated driving studies to model nonholonomic vehicle motion when vehicle pitch, roll, and vertical motion are not significant.

In the Vehicle Dynamics Blockset™ library, there are two types of Vehicle Body 3DOF blocks that model longitudinal, lateral, and yaw motion.

Block	Vehicle Track Setting	Implementation
Vehicle Body 3DOF Single Track	Single (bicycle)	Forces act along the center line at the front and rear axles. No lateral load transfer.
Vehicle Body 3DOF Dual Track	Dual	Forces act at the four vehicle corners or hard points.

Use the Axle forces parameter to specify the type of force.

Axle Forces Setting	Implementation
External longitudinal velocity	The block assumes that the external longitudinal velocity is in a quasi-steady state, so the longitudinal acceleration is approximately zero. Because the motion is quasi-steady, the block calculates lateral forces using the tire slip angles and linear cornering stiffness. Consider this setting when you want to: Generate virtual sensor signal data. Conduct high-level software studies that are not impacted by driveline or nonlinear tire responses.
External longitudinal forces	The block uses the external longitudinal force to accelerate or brake the vehicle. The block calculates lateral forces using the tire slip angles and linear cornering stiffness. Consider this setting when you want to: Account for changes in the longitudinal velocity on the lateral and yaw motion. Specify the external longitudinal motion through a force instead of an external longitudinal velocity. Connect the block to tractive actuators, wheels, brakes, and hitches.
External forces	The block uses the external lateral and longitudinal forces to steer, accelerate, or brake the vehicle. The block does not use the steering input to calculate vehicle motion. Consider this setting when you need tire models with more accurate nonlinear combined lateral and longitudinal slip.

You can use these block parameters to create additional input ports. This table summarizes the settings.

Input Signals Pane Parameter	Input Port	Description
Front wheel steering	WhlAngF	Front wheel angle, δF
External wind	WindXYZ	Wind speed, WX, WY, WZ, in the inertial reference frame
External forces	FExt	External force on vehicle center of gravity (CG), Fx, Fy, Fz, in the vehicle-fixed frame
Rear wheel steering	WhlAngR	Rear wheel angle, δR
External friction	Mu	Friction coefficient
External moments	MExt	External moment about vehicle CG, Mx, My, Mz, in vehicle-fixed frame
Hitch forces	Fh	Hitch force applied to the body at the hitch location, Fhx, Fhy, and Fhz, in the vehicle-fixed frame
Hitch moments	Mh	Hitch moment at the hitch location, Mhx, Mhy, and Mhz, about the vehicle-fixed frame
Initial longitudinal position	X_o	Initial vehicle CG displacement along the earth-fixed X-axis, in m
Initial lateral position	Y_o	Initial vehicle CG displacement along the earth-fixed Y-axis, in m
Initial longitudinal velocity	xdot_o	Initial vehicle CG velocity along the vehicle-fixed x-axis, in m/s
Initial lateral velocity	ydot_o	Initial vehicle CG velocity along the vehicle-fixed y-axis, in m/s
Initial yaw angle	psi_o	Initial rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw), in rad
Initial yaw rate	r_o	Initial vehicle angular velocity about the vehicle-fixed z-axis (yaw rate), in rad/s
Air temperature	AirTemp	Ambient air temperature. Considering this option if you want to vary the temperature during run-time.

Theory

The Vehicle Body 3DOF block implements a rigid two-axle vehicle body model to calculate longitudinal, lateral, and yaw motion. The block accounts for body mass, aerodynamic drag, and weight distribution between the axles due to acceleration and steering. To determine the vehicle motion, the block implements these equations for the single track, dual track, and drag calculations.

Single Track

Calculation	Description
Dynamics	The block uses these equations to calculate the rigid body planar dynamics. $\begin{array}{l}\ddot{y}=-\dot{x}r+\frac{F_{yf}+F_{yr}+F_{yext}}{m}\\ \dot{r}=\frac{a{F}_{yf}-b{F}_{yr}+M_{zext}}{I_{zz}}\\ r=\dot{\psi }\end{array}$ If you set Axle forces to either External longitudinal forces or External forces, the block uses this equation for the longitudinal acceleration. $\ddot{x}=\dot{y}r+\frac{F_{xf}+F_{xr}+F_{xext}}{m}$ If you set Axle forces to External longitudinal velocity, the block assumes a quasi-steady state for the longitudinal acceleration. $\ddot{x}=0$
External forces	External forces include both drag and external force inputs. The forces act on the vehicle CG. $\begin{array}{l}{F}_{x,y,z ext}=F_{d x,y,z}+F_{x,y,z input}\\ M_{x,y,z ext}=M_{d x,y,z}+M_{x,y,z input}\end{array}$ If you set Axle forces to External longitudinal forces, the block uses these equations. $\begin{array}{l}{F}_{xft}=F_{xfinput}\\ F_{yft}=-C_{yf}{\alpha }_f{\mu }_f\frac{F_{zf}}{F_{znom}}\\ F_{xrt}=F_{xrinput}\\ F_{yrt}=-C_{yr}{\alpha }_r{\mu }_r\frac{F_{zr}}{F_{znom}} \end{array}$ If you set Axle forces to External longitudinal velocity, the block uses these equations. $\begin{array}{l}{F}_{xft}=0\\ F_{yft}=-C_{yf}{\alpha }_f{\mu }_f\frac{F_{zf}}{F_{znom}}\\ F_{xrt}=0\\ F_{yrt}=-C_{yr}{\alpha }_r{\mu }_r\frac{F_{zr}}{F_{znom}}\end{array}$ The block divides the normal forces by the nominal normal load to vary the effective friction parameters during weight and load transfer. The block uses these equations to maintain pitch and roll equilibrium. $\begin{array}{l}{F}_{zf}=\frac{bmg-\left(\ddot{x}-\dot{y}r\right)mh+h{F}_{xext}+b{F}_{zext}-M_{yext}}{a+b}\\ F_{zr}=\frac{amg+\left(\ddot{x}-\dot{y}r\right)mh-h{F}_{xext}+a{F}_{zext}+M_{yext}}{a+b}\end{array}$
Tire forces	The block uses the ratio of the local and longitudinal and lateral velocities to determine the slip angles. $\begin{array}{l}{\alpha }_f=atan\left(\frac{\dot{y}+ar}{\dot{x}}\right)-{\delta }_f\\ {\alpha }_r=atan\left(\frac{\dot{y}-br}{\dot{x}}\right)-{\delta }_r\end{array}$ To determine the tire forces, the block uses the slip angles. $\begin{array}{l}{F}_{xf}=F_{xft}\cos \left({\delta }_f\right)-F_{yft}\sin \left({\delta }_f\right)\\ F_{yf}=-F_{xft}\sin \left({\delta }_f\right)+F_{yft}\cos \left({\delta }_f\right)\\ F_{xr}=F_{xrt}\cos \left({\delta }_r\right)-F_{yrt}\sin \left({\delta }_r\right)\\ F_{yr}=-F_{xrt}\sin \left({\delta }_r\right)+F_{yrt}\cos \left({\delta }_r\right)\end{array}$ If you set Axle forces to External forces, the block sets the tire forces equal to the external input force. $\begin{array}{l}{F}_{xf}=F_{xft}=F_{xfinput}\\ F_{yf}=F_{yft}=F_{yfinput}\\ F_{xr}=F_{xrt}=F_{xrinput}\\ F_{yr}=F_{yrt}=F_{yrinput}\end{array}$

Dual Track

Calculation	Description
Dynamics	The block uses these equations to calculate the rigid body planar dynamics. $\begin{array}{l}\ddot{x}=\dot{y}r+\frac{F_{xfl}+F_{xfr}+F_{xrl}+F_{xrr}+F_{xext}}{m}\\ \ddot{y}=-\dot{x}r+\frac{F_{yfl}+F_{yfr}+F_{yrl}+F_{yrr+}{F}_{yext}}{m}\\ \dot{r}=\frac{a(F_{yfl}+F_{yfr})-b\left(F_{yrl}+F_{yrr}\right)+\frac{w_f(F_{xfl}-F_{xfr})}{2}+\frac{w_r(F_{xrl}-F_{xrr})}{2}+M_{zext}}{I_{zz}}\\ r=\dot{\psi }\end{array}$ If you set Axle forces to External longitudinal velocity, the block assumes a quasi-steady state for the longitudinal acceleration. $\ddot{x}=0$
External forces	External forces include both drag and external force inputs. The forces act on the vehicle CG. $\begin{array}{l}{F}_{x,y,z ext}=F_{d x,y,z}+F_{x,y,z input}\\ M_{x,y,z ext}=M_{d x,y,z}+M_{x,y,z input}\end{array}$ If you set Axle forces to External longitudinal forces, the block uses these equations. $\begin{array}{l}{F}_{xflt}=F_{xflinput}\\ F_{yflt}=-C_{yfl}{\alpha }_{fl}{\mu }_{fl}\frac{F_{zfl}}{2F_{znom}}\\ F_{xfrt}=F_{xlrinput}\\ F_{yfrt}=-C_{yfr}{\alpha }_{fr}{\mu }_{fr}\frac{F_{zfr}}{2F_{znom}}\\ F_{xrlt}=F_{xrlinput}\\ F_{yrlt}=-C_{yrl}{\alpha }_{rl}{\mu }_{rl}\frac{F_{zrl}}{2F_{znom}}\\ F_{xrrt}=F_{xrrinput}\\ F_{yrrt}=-C_{yrr}{\alpha }_{rr}{\mu }_{rr}\frac{F_{zrr}}{2F_{znom}}\end{array}$ If you set Axle forces to External longitudinal velocity, the block uses these equations. $\begin{array}{l}{F}_{xflt}=0\\ F_{yflt}=-C_{yfl}{\alpha }_{fl}{\mu }_{fl}\frac{F_{zfl}}{2F_{znom}}\\ F_{xfrt}=0\\ F_{yfrt}=-C_{yfr}{\alpha }_{fr}{\mu }_{fr}\frac{F_{zfr}}{2F_{znom}}\\ F_{xrlt}=0\\ F_{yrlt}=-C_{yrl}{\alpha }_{rl}{\mu }_{rl}\frac{F_{zrl}}{2F_{znom}}\\ F_{xrrt}=0\\ F_{yrrt}=-C_{yrr}{\alpha }_{rr}{\mu }_{rr}\frac{F_{zrr}}{2F_{znom}}\end{array}$ The block divides the normal forces by the nominal normal load to vary the effective friction parameters during weight and load transfer. The block uses these equations to maintain pitch and roll equilibrium. $\begin{array}{l}{F}_{zf}=\frac{bmg-\left(\ddot{x}-\dot{y}r\right)mh+h{F}_{xext}+b{F}_{zext}-M_{yext}}{a+b}\\ F_{zr}=\frac{amg+\left(\ddot{x}-\dot{y}r\right)mh-h{F}_{xext}+a{F}_{zext}+M_{yext}}{(a+b)}\\ F_{zfl}=F_{zf}+\left(mh(\ddot{y}+\dot{x}r\right)-h{F}_{yext}-M_{xext})\frac{2}{w_f}\\ F_{zfr}=F_{zf}+\left(-mh(\ddot{y}+\dot{x}r\right)+h{F}_{yext}+M_{xext})\frac{2}{w_f}\\ F_{zrl}=F_{zr}+\left(mh(\ddot{y}+\dot{x}r\right)-h{F}_{yext}-M_{xext})\frac{2}{w_r}\\ F_{zrr}=F_{zr}+\left(-mh(\ddot{y}+\dot{x}r\right)+h{F}_{yext}+M_{xext})\frac{2}{w_r}\end{array}$
Tire forces	The block uses the ratio of the local and longitudinal and lateral velocities to determine the slip angles. $\begin{array}{l}{\alpha }_{fl}=atan\left(\frac{\dot{y}+ar}{\dot{x}+r\frac{w_f}{2}}\right)-{\delta }_{fl}\\ {\alpha }_{fr}=atan\left(\frac{\dot{y}+ar}{\dot{x}-r\frac{w_f}{2}}\right)-{\delta }_{fr}\\ {\alpha }_{rl}=atan\left(\frac{\dot{y}-ar}{\dot{x}+r\frac{w_r}{2}}\right)-{\delta }_{rl}\\ {\alpha }_{rr}=atan\left(\frac{\dot{y}-ar}{\dot{x}-r\frac{w_r}{2}}\right)-{\delta }_{rr}\end{array}$ The block uses the steering angles to transform the tire forces to the vehicle-fixed frame. $\begin{array}{l}{F}_{xf}=F_{xft}\cos \left({\delta }_f\right)-F_{yft}\sin \left({\delta }_f\right)\\ F_{yf}=-F_{xft}\sin \left({\delta }_f\right)+F_{yft}\cos \left({\delta }_f\right)\\ F_{xr}=F_{xrt}\cos \left({\delta }_r\right)-F_{yrt}\sin \left({\delta }_r\right)\\ F_{yr}=-F_{xrt}\sin \left({\delta }_r\right)+F_{yrt}\cos \left({\delta }_r\right)\end{array}$ If you set Axle forces to External forces, the block uses these equations. The blocks assumes that the externally provided forces are in the vehicle-fixed frame at the axle-wheel location. $\begin{array}{l}{F}_{xf}=F_{xft}=F_{xfinput}\\ F_{yf}=F_{yft}=F_{yfinput}\\ F_{xr}=F_{xrt}=F_{xrinput}\\ F_{yr}=F_{yrt}=F_{yrinput}\end{array}$

Drag

Calculation	Description
Coordinate transformation	The block transforms the wind speeds from the inertial frame to the vehicle-fixed frame. $\begin{array}{l}{w}_x=W_x\cos \left(\psi \right)+W_y\sin \left(\psi \right)\\ w_y=W_y\cos \left(\psi \right)-W_x\sin \left(\psi \right)\\ w_z=W_z\end{array}$
Drag forces	To determine a relative airspeed, the block subtracts the wind speed from the CG vehicle velocity. Using the relative airspeed, the block determines the drag forces. $$\begin{array}{l}\overline{w}=\sqrt{{(\dot{x}-w_x)}^2+{(\dot{y}-w_y)}^2+{(w_z)}^2}\\ \\ F_{dx}=-\frac{1}{2TR}{C}_d{A}_f{P}_{abs}{(}^{\overline{w}}\\ F_{dy}=-\frac{1}{2TR}{C}_s{A}_f{P}_{abs}{(}^{\overline{w}}\\ F_{dz}=-\frac{1}{2TR}{C}_l{A}_f{P}_{abs}{(}^{\overline{w}}\end{array}$$
Drag moments	Using the relative airspeed, the block determines the drag moments. $$\begin{array}{l}{M}_{dr}=-\frac{1}{2TR}{C}_{rm}{A}_f{P}_{abs}{(}^{\overline{w}}(a+b)\\ M_{dp}=-\frac{1}{2TR}{C}_{pm}{A}_f{P}_{abs}{(}^{\overline{w}}(a+b)\\ M_{dy}=-\frac{1}{2TR}{C}_{ym}{A}_f{P}_{abs}{(}^{\overline{w}}(a+b)\end{array}$$

Lateral Corner Stiffness and Relaxation Dynamics

Description	Implementation
Constant values.	The block uses constant stiffness values for Cyf and Cyr.
Lookup tables as a function of corner stiffness data and slip angles.	The block uses lookup tables that are functions of the corner stiffness data and slip angles. $$\begin{array}{l}C{y}_f=f({\alpha }_f,C{y}_{fdata})\\ C{y}_r=f({\alpha }_r,C{y}_{rdata})\end{array}$$
Lookup tables as a function of corner stiffness data and slip angles. Slip angles include the relaxation length dynamic settings.	The block uses lookup tables that are functions of the corner stiffness data and slip angles. The slip angles include the relaxation length dynamic settings. The relaxation length approximates an effective corner stiffness force that is a function of wheel travel. $$\begin{array}{l}C{y}_f=f({\alpha }_{f\sigma },C{y}_{fdata})\\ C{y}_r=f({\alpha }_{r\sigma },C{y}_{rdata})\\ \\ {\alpha }_{f\sigma }=\frac{1}{s}\left[\frac{\left({\alpha }_f-{\alpha }_{f\sigma }\right)v_{wf}}{{\alpha }_f}\right]\\ \\ {\alpha }_{r\sigma }=\frac{1}{s}\left[\frac{\left({\alpha }_r-{\alpha }_{r\sigma }\right)v_{wr}}{{\alpha }_r}\right]\end{array}$$

The equations use these variables.

$$x,\dot{x},\ddot{x}$$	Vehicle CG displacement, velocity, and acceleration, along the vehicle-fixed x-axis
$$y,\dot{y},\ddot{y}$$	Vehicle CG displacement, velocity, and acceleration, along the vehicle-fixed y-axis
ψ	Rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw)
r,$$\dot{\Psi }$$	Vehicle angular velocity, about the vehicle-fixed z-axis (yaw rate)
Fxf, Fxr	Longitudinal forces applied to front and rear wheels, along the vehicle-fixed x-axis
Fyf, Fyr	Lateral forces applied to front and rear wheels, along vehicle-fixed y-axis
Fxext, Fyext, Fzext	External forces applied to vehicle CG, along the vehicle-fixed x-, y-, and z-axes
Fdx, Fdy, Fdz	Drag forces applied to vehicle CG, along the vehicle-fixed x-, y-, and z-axes
Fxinput, Fyinput, Fzinput	Input forces applied to vehicle CG, along the vehicle-fixed x-, y-, and z-axes
Mxext, Myext, Mzext	External moment about vehicle CG, about the vehicle-fixed x-, y-, and z-axes
Mdx, Mdy, Mdz	Drag moment about vehicle CG, about the vehicle-fixed x-, y-, and z-axes
Mxinput, Myinput, Mzinput	Input moment about vehicle CG, about the vehicle-fixed x-, y-, and z-axes
Izz	Vehicle body moment of inertia about the vehicle-fixed z-axis
Fxft, Fxrt	Longitudinal tire force applied to front and rear wheels, along the vehicle-fixed x-axis
Fyft, Fyft	Lateral tire force applied to front and rear wheels, along vehicle-fixed y-axis
Fxfl, Fxfr	Longitudinal force applied to front left and front right wheels, along the vehicle-fixed x-axis
Fyfl, Fyfr	Lateral force applied to front left and front right wheels, along the vehicle-fixed y-axis
Fxrl, Fxrr	Longitudinal force applied to rear left and rear right wheels, along the vehicle-fixed x-axis
Fyrl, Fyrr	Lateral force applied to rear left and rear right wheels, along the vehicle-fixed y-axis
Fxflt, Fxfrt	Longitudinal tire force applied to front left and front right wheels, along the vehicle-fixed x-axis
Fyflt, Fyfrt	Lateral force tire applied to front left and front right wheels, along the vehicle-fixed y-axis
Fxrlt, Fxrrt	Longitudinal tire force applied to rear left and rear right wheels, along the vehicle-fixed x-axis
Fyrlt, Fyrrt	Lateral force applied to rear left and rear right wheels, along the vehicle-fixed y-axis
Fzf,Fzr	Normal force applied to front and rear wheels, along vehicle-fixed z-axis
Fznom	Nominal normal force applied to axles, along the vehicle-fixed z-axis
Fzfl,Fzfr	Normal force applied to front left and right wheels, along vehicle-fixed z-axis
Fzrl,Fzrr	Normal force applied to rear left and right wheels, along vehicle-fixed z-axis
m	Vehicle body mass
a, b	Distance of front and rear wheels, respectively, from the normal projection point of vehicle CG onto the common axle plane
h	Height of vehicle CG above the axle plane
d	Lateral distance from the geometric centerline to the center of mass along the vehicle-fixed y-axis
hh	Height of the hitch above the axle plane along the vehicle-fixed z-axis
dh	Longitudinal distance of the hitch from the normal projection point of tractor CG onto the common axle plane
hl	Lateral distance from center of mass to hitch along the vehicle-fixed y-axis.
αf, αr	Front and rear wheel slip angles
αfl, αfr	Front left and right wheel slip angles
αrl, αrr	Rear left and right wheel slip angles
δf, δr	Front and rear wheel steering angles
δrl, δrr	Rear left and right wheel steering angles
δfl, δfr	Front left and right wheel steering angles
wf, wr	Front and rear track widths
Cyf, Cyr	Front and rear wheel cornering stiffness
Cyfdata, Cyrdata	Front and rear wheel cornering stiffness data
σf, σr	Front and rear wheel relaxation length
αfσ, αrσ	Front and rear wheel slip angles that include relaxation length
vwf, vwr	Magnitude of front and rear wheel hardpoint velocity
μf, μr	Front and rear wheel friction coefficient
μfl, μfr	Front left and right wheel friction coefficient
μrl, μrr	Rear left and right wheel friction coefficient
Cd	Air drag coefficient acting along vehicle-fixed x-axis
Cs	Air drag coefficient acting along vehicle-fixed y-axis
Cl	Air drag coefficient acting along vehicle-fixed z-axis
Crm	Air drag roll moment acting about the vehicle-fixed x-axis
Cpm	Air drag pitch moment acting about the vehicle-fixed y-axis
Cym	Air drag yaw moment acting about the vehicle-fixed z-axis
Af	Frontal area
R	Atmospheric specific gas constant
T	Environmental air temperature
Pabs	Environmental absolute pressure
wx, wy, wz	Wind speed, along the vehicle-fixed x-, y-, and z-axes
Wx, Wy, Wz	Wind speed, along inertial X-, Y-, and Z-axes

Examples

Three-Axle Tractor Towing a Three-Axle Trailer

Simulates three-axle tractor towing a three-axle trailer for commercial trucking applications. Implements hitch subsystem, sinusoidal wave steering or braking test, and axle torque applied to tractor rear wheels.

• Open Model

Two-Axle Tractor Towing a Two-Axle Trailer

Simulate a two-axle tractor towing a two-axle trailer for a commercial trucking application. Model implements a hitch subsystem, sinusoidal wave steering input, and an axle torque applied to the rear wheels of the tractor.

• Open Model

Ports

Input

WhlAngF — Front wheel steering angles

scalar | array

Front wheel steering angles, δ_F, in rad.

Vehicle Track Setting	Variable	Signal Dimension
Single (bicycle)	δF	Scalar – 1
Dual	$${\delta }_F=[\begin{array}{cc}{\delta }_{fl}& {\delta }_{fr}\end{array}]\text{ or }\left[\begin{array}{c}{\delta }_{fl}\\ {\delta }_{fr}\end{array}\right]$$	Array – [1x2] or [2x1]

Dependencies

To enable this port, on the Input signals pane, select Front wheel steering.

WhlAngR — Rear wheel steering angles

scalar | array

Rear wheel steering angles, δ_R, in rad.

Vehicle Track Setting	Variable	Signal Dimension
Single (bicycle)	δR	Scalar – 1
Dual	$${\delta }_R=[\begin{array}{cc}{\delta }_{rl}& {\delta }_{rr}\end{array}]\text{ or }\left[\begin{array}{c}{\delta }_{rl}\\ {\delta }_{rr}\end{array}\right]$$	Array – [1x2] or [2x1]

Dependencies

To enable this port, on the Input signals pane, select Rear wheel steering.

xdotin — Longitudinal velocity

scalar

Vehicle CG velocity along the vehicle-fixed x-axis, in m/s.

Dependencies

To enable this port, set Axle forces to External longitudinal velocity.

FwF — Total force on the front wheels

scalar | array

Force on the front wheels, Fw_F, along the vehicle-fixed axis, in N.

Vehicle Track Setting	Axle Forces Setting	Description	Variable	Signal Dimension
Single (bicycle)	External longitudinal forces	Longitudinal force on the front wheel	$$FwF=F{x}_f$$	Scalar – 1
	External forces	Longitudinal and lateral forces on the front wheel	$$FwF=\left[\begin{array}{cc}F{x}_f& F{y}_f\end{array}\right]\text{ or }\left[\begin{array}{c}F{x}_f\\ F{y}_f\end{array}\right]$$	Array – [1x2] or [2x1]
Dual	External longitudinal forces	Longitudinal force on the front wheels	$$FwF=\left[\begin{array}{cc}{F}_{xfl}& F_{xfr}\end{array}\right]\text{ or }\left[\begin{array}{c}{F}_{xfl}\\ F_{xfr}\end{array}\right]$$	Array – [1x2] or [2x1]
	External forces	Longitudinal and lateral forces on the front wheels	$$FwF=\left[\begin{array}{cc}{F}_{xfl}& F_{xfr}\\ F_{yfl}& F_{yfr}\end{array}\right]$$	Array – [2x2]

Dependencies

To enable this port, set Axle forces to one of these options:

• External longitudinal forces

• External forces

FwR — Total force on the rear wheels

scalar | array

Force on the rear wheels, Fw_R, along the vehicle-fixed axis, in N.

Vehicle Track Setting	Axle Forces Setting	Description	Variable	Signal Dimension
Single (bicycle)	External longitudinal forces	Longitudinal force on the rear wheel	$$FwR=F{x}_r$$	Scalar – 1
	External forces	Longitudinal and lateral forces on the rear wheel	$$FwR=\left[\begin{array}{cc}F{x}_r& F{y}_r\end{array}\right]\text{ or }\left[\begin{array}{c}F{x}_r\\ F{y}_r\end{array}\right]$$	Array – [1x2] or [2x1]
Dual	External longitudinal forces	Longitudinal force on the rear wheels	$$FwR=\left[\begin{array}{cc}{F}_{xrl}& F_{xrr}\end{array}\right]\text{ or }\left[\begin{array}{c}{F}_{xrl}\\ F_{xrr}\end{array}\right]$$	Array – [1x2] or [2x1]
	External forces	Longitudinal and lateral forces on the rear wheels	$$FwR=\left[\begin{array}{cc}{F}_{xrl}& F_{xrr}\\ F_{yrl}& F_{yrr}\end{array}\right]$$	Array – [2x2]

Dependencies

To enable this port, set Axle forces to one of these options:

• External longitudinal forces

• External forces

FExt — External force on vehicle CG

array

External forces applied to vehicle CG, F_xext, F_yext, F_zext, in vehicle-fixed frame, in N. Signal vector dimensions are [1x3] or [3x1].

Dependencies

To enable this port, on the Input signals pane, select External forces.

MExt — External moment about vehicle CG

array

External moment about vehicle CG, M_x, M_y, M_z, in the vehicle-fixed frame, in N·m. Signal vector dimensions are [1x3] or [3x1].

Dependencies

To enable this port, on the Input signals pane, select External moments.

Fh — Hitch force on the body

array

Hitch force applied to the body at the hitch location, Fh_x, Fh_y, Fh_z, in the vehicle-fixed frame, in N, specified as a 1-by-3 or 3-by-1 array.

Dependencies

To enable this port, under Input signals, select Hitch forces.

Mh — Hitch moment about body

array

Hitch moment at the hitch location, Mh_x, Mh_y, Mh_z, about the vehicle-fixed frame, in N·m, specified as a 1-by-3 or 3-by-1 array.

Dependencies

To enable this port, under Input signals, select Hitch moments.

WindXYZ — Wind speed

array

Wind speed, W_x, W_y, W_z along inertial X-, Y-, and Z-axes, in m/s. Signal vector dimensions are [1x3] or [3x1].

Dependencies

To enable this port, on the Input signals pane, select External wind.

Mu — Tire friction coefficient

scalar

Tire friction coefficient, μ. The value is dimensionless.

Vehicle Track Setting	Description	Variable	Signal Dimension
Single (bicycle)	Longitudinal force on the front wheel	$$Mu=\left[\begin{array}{cc}{\mu }_f& {\mu }_r\end{array}\right]\text{ or }\left[\begin{array}{c}{\mu }_f\\ {\mu }_r\end{array}\right]$$	Array – [1x2] or [2x1]
Dual	Longitudinal force on the front wheels	$$Mu=\left[\begin{array}{cc}{\mu }_{fl}& {\mu }_{fr}\\ {\mu }_{rl}& {\mu }_{rr}\end{array}\right]$$	Array – [2x2]

Dependencies

To enable this port, on the Input signals pane, select External friction.

AirTemp — Ambient air temperature

scalar

Ambient air temperature, in K.

Dependencies

To enable this port, on the Input signals pane, select Air temperature.

X_o — Initial longitudinal position

scalar

Initial vehicle CG displacement along the earth-fixed X-axis, in m.

Dependencies

To enable this port, on the Input signals pane, select Initial longitudinal position.

Y_o — Initial lateral position

scalar

Initial vehicle CG displacement along the earth-fixed Y-axis, in m.

Dependencies

To enable this port, on the Input signals pane, select Initial lateral position.

xdot_o — Initial longitudinal position

scalar

Initial vehicle CG velocity along the vehicle-fixed x-axis, in m/s.

Dependencies

To enable this port:

1. Set Axle forces to one of these options:

   • External longitudinal forces

   • External forces

2. On the Input signals pane, select Initial longitudinal velocity

ydot_o — Initial lateral position

scalar

Initial vehicle CG velocity along the vehicle-fixed y-axis, in m/s.

Dependencies

To enable this port, on the Input signals pane, select Initial lateral velocity.

psi_o — Initial yaw angle

scalar

Rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw), in rad.

Dependencies

To enable this port, on the Input signals pane, select Initial yaw angle.

r_o — Initial yaw rate

scalar

Initial vehicle angular velocity about the vehicle-fixed z-axis (yaw rate), in rad/s.

Dependencies

To enable this port, on the Input signals pane, select Initial yaw rate.

Output

Info — Bus signal

bus

Bus signal containing these block values.

Signal						Description	Value	Units
InertFrm	Cg	Disp	X			Vehicle CG displacement along the earth-fixed X-axis	Computed	m
			Y			Vehicle CG displacement along the earth-fixed Y-axis	Computed	m
			Z			Vehicle CG displacement along the earth-fixed Z-axis	0	m
		Vel	Xdot			Vehicle CG velocity along the earth-fixed X-axis	Computed	m/s
			Ydot			Vehicle CG velocity along the earth-fixed Y-axis	Computed	m/s
			Zdot			Vehicle CG velocity along the earth-fixed Z-axis	0	m/s
		Ang	phi			Rotation of the vehicle-fixed frame about the earth-fixed X-axis (roll)	0	rad
			theta			Rotation of the vehicle-fixed frame about the earth-fixed Y-axis (pitch)	0	rad
			psi			Rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw)	Computed	rad
	FrntAxl	Lft	Disp	X		Front left wheel displacement along the earth-fixed X-axis	Computed	m
				Y		Front left wheel displacement along the earth-fixed Y-axis	Computed	m
				Z		Front left wheel displacement along the earth-fixed Z-axis	0	m
			Vel	Xdot		Front left wheel velocity along the earth-fixed X-axis	Computed	m/s
				Ydot		Front left wheel velocity along the earth-fixed Y-axis	Computed	m/s
				Zdot		Front left wheel velocity along the earth-fixed Z-axis	0	m/s
		Rght	Disp	X		Front right wheel displacement along the earth-fixed X-axis	Computed	m
				Y		Front right wheel displacement along the earth-fixed Y-axis	Computed	m
				Z		Front right wheel displacement along the earth-fixed Z-axis	0	m
			Vel	Xdot		Front right wheel velocity along the earth-fixed X-axis	Computed	m/s
				Ydot		Front right wheel velocity along the earth-fixed Y-axis	Computed	m/s
				Zdot		Front right wheel velocity along the earth-fixed Z-axis	0	m/s
	RearAxl	Lft	Disp	X		Rear left wheel displacement along the earth-fixed X-axis	Computed	m
				Y		Rear left wheel displacement along the earth-fixed Y-axis	Computed	m
				Z		Rear left wheel displacement along the earth-fixed Z-axis	0	m
			Vel	Xdot		Rear left wheel velocity along the earth-fixed X-axis	Computed	m/s
				Ydot		Rear left wheel velocity along the earth-fixed Y-axis	Computed	m/s
				Zdot		Rear left wheel velocity along the earth-fixed Z-axis	0	m/s
		Rght	Disp	X		Rear right wheel displacement along the earth-fixed X-axis	Computed	m
				Y		Rear right wheel displacement along the earth-fixed Y-axis	Computed	m
				Z		Rear right wheel displacement along the earth-fixed Z-axis	0	m
			Vel	Xdot		Rear right wheel velocity along the earth-fixed X-axis	Computed	m/s
				Ydot		Rear right wheel velocity along the earth-fixed Y-axis	Computed	m/s
				Zdot		Rear right wheel velocity along the earth-fixed Z-axis	0	m/s
	Hitch	Disp	X			Hitch offset from axle plane along the earth-fixed X-axis	Computed	m
			Y			Hitch offset from center plane along the earth-fixed Y-axis	Computed	m
			Z			Hitch offset from axle plane along the earth-fixed Z-axis	Computed	m
		Vel	Xdot			Hitch offset velocity from axle plane along the earth-fixed X-axis	Computed	m/s
			Ydot			Hitch offset velocity from center plane along the earth-fixed Y-axis	Computed	m/s
			Zdot			Hitch offset velocity from axle plane along the earth-fixed Z-axis	Computed	m/s
	Geom	Disp	X			Vehicle chassis offset from axle plane along the earth-fixed X-axis	Computed	m
			Y			Vehicle chassis offset from center plane along the earth-fixed Y-axis	Computed	m
			Z			Vehicle chassis offset from axle plane along the earth-fixed Z-axis	Computed	m
		Vel	Xdot			Vehicle chassis offset velocity along the earth-fixed X-axis	Computed	m/s
			Ydot			Vehicle chassis offset velocity along the earth-fixed Y-axis	Computed	m/s
			Zdot			Vehicle chassis offset velocity along the earth-fixed Z-axis	Computed	m/s
BdyFrm	Cg	Vel	xdot			Vehicle CG velocity along the vehicle-fixed x-axis	Computed	m/s
			ydot			Vehicle CG velocity along the vehicle-fixed y-axis	Computed	m/s
			zdot			Vehicle CG velocity along the vehicle-fixed z-axis	0	m/s
		Ang	Beta			Body slip angle, β $$\beta =\frac{V_y}{V_x}$$	Computed	rad
		AngVel	p			Vehicle angular velocity about the vehicle-fixed x-axis (roll rate)	0	rad/s
			q			Vehicle angular velocity about the vehicle-fixed y-axis (pitch rate)	0	rad/s
			r			Vehicle angular velocity about the vehicle-fixed z-axis (yaw rate)	Computed	rad/s
		Acc	ax			Vehicle CG acceleration along the vehicle-fixed x-axis	Computed	gn
			ay			Vehicle CG acceleration along the vehicle-fixed y-axis	Computed	gn
			az			Vehicle CG acceleration along the vehicle-fixed z-axis	0	gn
			xddot			Vehicle CG acceleration along the vehicle-fixed x-axis	Computed	m/s^2
			yddot			Vehicle CG acceleration along the vehicle-fixed y-axis	Computed	m/s^2
			zddot			Vehicle CG acceleration along the vehicle-fixed z-axis	0	m/s^2
		AngAcc	pdot			Vehicle angular acceleration about the vehicle-fixed x-axis	0	rad/s
			qdot			Vehicle angular acceleration about the vehicle-fixed y-axis	0	rad/s
			rdot			Vehicle angular acceleration about the vehicle-fixed z-axis	Computed	rad/s
		DCM	Direction cosine matrix				Computed	rad
	Forces	Body	Fx			Net force on vehicle CG along the vehicle-fixed x-axis	Computed	N
			Fy			Net force on vehicle CG along the vehicle-fixed y-axis	Computed	N
			Fz			Net force on vehicle CG along the vehicle-fixed z-axis	0	N
		Ext	Fx			External force on vehicle CG along the vehicle-fixed x-axis	Computed	N
			Fy			External force on vehicle CG along the vehicle-fixed y-axis	Computed	N
			Fz			External force on vehicle CG along the vehicle-fixed z-axis	0	N
		Hitch	Fx			Hitch force applied to body at the hitch location along the vehicle-fixed x-axis	Input	N
			Fy			Hitch force applied to body at the hitch location along the vehicle-fixed y-axis	Input	N
			Fz			Hitch force applied to body at the hitch location along the vehicle-fixed z-axis	Input	N
		FrntAxl	Lft	Fx		Longitudinal force on left front wheel, along the vehicle-fixed x-axis	Computed	N
				Fy		Lateral force on left front wheel along the vehicle-fixed y-axis	Computed	N
				Fz		Normal force on left front wheel, along the vehicle-fixed z-axis	Computed	N
			Rght	Fx		Longitudinal force on right front wheel, along the vehicle-fixed x-axis	Computed	N
				Fy		Lateral force on right front wheel along the vehicle-fixed y-axis	Computed	N
				Fz		Normal force on right front wheel, along the vehicle-fixed z-axis	Computed	N
		RearAxl	Lft	Fx		Longitudinal force on left rear wheel, along the vehicle-fixed x-axis	Computed	N
				Fy		Lateral force on left rear wheel along the vehicle-fixed y-axis	Computed	N
				Fz		Normal force on left rear wheel, along the vehicle-fixed z-axis	Computed	N
			Rght	Fx		Longitudinal force on right rear wheel, along the vehicle-fixed x-axis	Computed	N
				Fy		Lateral force on right rear wheel along the vehicle-fixed y-axis	Computed	N
				Fz		Normal force on right rear wheel, along the vehicle-fixed z-axis	Computed	N
		Tires	FrntTires	Lft	Fx	Front left tire force, along the vehicle-fixed x-axis	Computed	N
					Fy	Front left tire force, along the vehicle-fixed y-axis	Computed	N
					Fz	Front left tire force, along the vehicle-fixed z-axis	Computed	N
				Rght	Fx	Front right tire force, along the vehicle-fixed x-axis	Computed	N
					Fy	Front right tire force, along the vehicle-fixed y-axis	Computed	N
					Fz	Front right tire force, along the vehicle-fixed z-axis	Computed	N
			RearTires	Lft	Fx	Rear left tire force, along the vehicle-fixed x-axis	Computed	N
					Fy	Rear left tire force, along the vehicle-fixed y-axis	Computed	N
					Fz	Rear left tire force, along the vehicle-fixed z-axis	Computed	N
				Rght	Fx	Rear right tire force, along the vehicle-fixed x-axis	Computed	N
					Fy	Rear right tire force, along the vehicle-fixed y-axis	Computed	N
					Fz	Rear right tire force, along the vehicle-fixed z-axis	Computed
		Drag	Fx			Drag force on vehicle CG along the vehicle-fixed x-axis	Computed	N
			Fy			Drag force on vehicle CG along the vehicle-fixed y-axis	Computed	N
			Fz			Drag force on vehicle CG along the vehicle-fixed z-axis	Computed	N
		Grvty	Fx			Gravity force on vehicle CG along the vehicle-fixed x-axis	Computed	N
			Fy			Gravity force on vehicle CG along the vehicle-fixed y-axis	Computed	N
			Fz			Gravity force on vehicle CG along the vehicle-fixed z-axis	Computed	N
	Moments	Body	Mx			Body moment on vehicle CG about the vehicle-fixed x-axis	0	N·m
			My			Body moment on vehicle CG about the vehicle-fixed y-axis	Computed	N·m
			Mz			Body moment on vehicle CG about the vehicle-fixed z-axis	0	N·m
		Drag	Mx			Drag moment on vehicle CG about the vehicle-fixed x-axis	0	N·m
			My			Drag moment on vehicle CG about the vehicle-fixed y-axis	Computed	N·m
			Mz			Drag moment on vehicle CG about the vehicle-fixed z-axis	0	N·m
		Ext	Mx			External moment on vehicle CG about the vehicle-fixed x-axis	0	N·m
			My			External moment on vehicle CG about the vehicle-fixed y-axis	Computed	N·m
Mz			External moment on vehicle CG about the vehicle-fixed z-axis	0	N·m
Hitch	Mx			Hitch moment at the hitch location about vehicle-fixed x-axis	0	N·m
	My			Hitch moment at the hitch location about vehicle-fixed y-axis	Computed	N·m
	Mz			Hitch moment at the hitch location about vehicle-fixed z-axis	0	N·m
FrntAxl	Lft	Disp	x		Front left wheel displacement along the vehicle-fixed x-axis	Computed	m
			y		Front left wheel displacement along the vehicle-fixed y-axis	Computed	m
			z		Front left wheel displacement along the vehicle-fixed z-axis	Computed	m
		Vel	xdot		Front left wheel velocity along the vehicle-fixed x-axis	Computed	m/s
			ydot		Front left wheel velocity along the vehicle-fixed y-axis	Computed	m/s
			zdot		Front left wheel velocity along the vehicle-fixed z-axis	0	m/s
	Rght	Disp	x		Front right wheel displacement along the vehicle-fixed x-axis	Computed	m
			y		Front right wheel displacement along the vehicle-fixed y-axis	Computed	m
			z		Front right wheel displacement along the vehicle-fixed z-axis	Computed	m
		Vel	xdot		Front right wheel velocity along the vehicle-fixed x-axis	Computed	m/s
			ydot		Front right wheel velocity along the vehicle-fixed y-axis	Computed	m/s
			zdot		Front right wheel velocity along the vehicle-fixed z-axis	0	m/s
	Steer	WhlAngFL			Front left wheel steering angle	Computed	rad
		WhlAngFR			Front right wheel steering angle	Computed	rad
RearAxl	Lft	Disp	x		Rear left wheel displacement along the vehicle-fixed x-axis	Computed	m
			y		Rear left wheel displacement along the vehicle-fixed y-axis	Computed	m
			z		Rear left wheel displacement along the vehicle-fixed z-axis	Computed	m
		Vel	xdot		Rear left wheel velocity along the vehicle-fixed x-axis	Computed	m/s
			ydot		Rear left wheel velocity along the vehicle-fixed y-axis	Computed	m/s
			zdot		Rear left wheel velocity along the vehicle-fixed z-axis	0	m/s
	Rght	Disp	x		Rear right wheel displacement along the vehicle-fixed x-axis	Computed	m
			y		Rear right wheel displacement along the vehicle-fixed y-axis	Computed	m
			z		Rear right wheel displacement along the vehicle-fixed z-axis	Computed	m
		Vel	xdot		Rear right wheel velocity along the vehicle-fixed x-axis	Computed	m/s
			ydot		Rear right wheel velocity along the vehicle-fixed y-axis	Computed	m/s
			zdot		Rear right wheel velocity along the vehicle-fixed z-axis	0	m/s
	Steer	WhlAngRL			Rear left wheel steering angle	Computed	rad
		WhlAngRR			Rear right wheel steering angle	Computed	rad
Hitch	Disp		x		Hitch offset from axle plane along the vehicle-fixed x-axis	Input	m
			y		Hitch offset from center plane along the vehicle-fixed y-axis	Input	m
			z		Hitch offset from axle plane along the vehicle-fixed z-axis	Input	m
	Vel		xdot		Hitch offset velocity along the vehicle-fixed x-axis	Computed	m/s
			ydot		Hitch offset velocity along the vehicle-fixed y-axis	Computed	m/s
			zdot		Hitch offset velocity along the vehicle-fixed z-axis	Computed	m/s
Pwr	Ext				Applied external power	Computed	W
	Hitch				Power loss due to hitch	Computed	W
	Drag				Power loss due to drag	Computed	W
Geom	Disp		x		Vehicle chassis offset from axle plane along the vehicle-fixed x-axis	Input	m
			y		Vehicle chassis offset from center plane along the vehicle-fixed y-axis	Input	m
			z		Vehicle chassis offset from axle plane along the earth-fixed z-axis	Input	m
	Vel		xdot		Vehicle chassis offset velocity along the vehicle-fixed x-axis	Computed	m/s
			ydot		Vehicle chassis offset velocity along the vehicle-fixed y-axis	Computed	m/s
			zdot		Vehicle chassis offset velocity along the vehicle-fixed z-axis	0	m/s
	Beta		Beta		Body slip angle, β $$\beta =\frac{V_y}{V_x}$$	Computed	rad

Signal			Description		Value	Units
PwrInfo	PwrTrnsfrd	PwrFxExt	Externally applied longitudinal force power		Computed	W
		PwrFyExt	Externally applied lateral force power		Computed	W
		PwrMzExt	Externally applied roll moment power		Computed	W
		PwrFwFLx	Longitudinal force applied at the front left axle power		Computed	W
		PwrFwFLy	Lateral force applied at the front left axle power		Computed	W
		PwrFwFRx	Longitudinal force applied at the front right axle power		Computed	W
		PwrFwFRy	Lateral force applied at the front right axle power		Computed	W
		PwrFwRLx	Longitudinal force applied at the rear left axle power		Computed	W
		PwrFwRLy	Lateral force applied at the rear left axle power		Computed	W
		PwrFwRRx	Longitudinal force applied at the rear right axle power		Computed	W
		PwrFwRRy	Lateral force applied at the rear right axle power		Computed	W
	PwrNotTrnsfrd	PwrFxDrag	Longitudinal drag force power		Computed	W
		PwrFyDrag	Lateral drag force power		Computed	W
		PwrMzDrag	Drag pitch moment power		Computed	W
	PwrStored	PwrStoredGrvty	Rate change in gravitational potential energy		Computed	W
		PwrStoredxdot	Rate of change of longitudinal kinetic energy		Computed	W
		PwrStoredydot	Rate of change of lateral kinetic energy		Computed	W
		PwrStoredr	Rate of change of rotational yaw kinetic energy		Computed	W

xdot — Vehicle longitudinal velocity

scalar

Vehicle CG velocity along the vehicle-fixed x-axis, in m/s.

ydot — Vehicle lateral velocity

scalar

Vehicle CG velocity along the vehicle-fixed y-axis, in m/s.

psi — Yaw

scalar

Rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw), in rad.

r — Yaw rate

scalar

Vehicle angular velocity, r, about the vehicle-fixed z-axis (yaw rate), in rad/s.

FzF — Normal force on front wheels

scalar | array

Normal force on front wheels, Fz_F, along the vehicle-fixed z-axis, in N.

Vehicle Track Setting	Description	Variable	Signal Dimension
Single (bicycle)	Normal force on front axle	$$FzF=F{z}_f$$	Scalar – 1
Dual	Normal force on the front wheels	$$FzF=\left[\begin{array}{cc}F{z}_{fl}& F{z}_{fr}\end{array}\right]$$	Array – [1x2]

FzR — Normal force on rear wheels

scalar | array

Normal force on rear wheels, Fz_R, along the vehicle-fixed z-axis, in N.

Vehicle Track Setting	Description	Variable	Signal Dimension
Single (bicycle)	Normal force on rear wheel	$$FzR=F{z}_r$$	Scalar – 1
Dual	Normal force on the rear wheels	$$FzR=\left[\begin{array}{cc}F{z}_{rl}& F{z}_{rr}\end{array}\right]$$	Array – [1x2]

Parameters

Options

Vehicle track — Number of wheels

Single (bicycle) | Dual

In the Vehicle Dynamics Blockset library, there are two types of Vehicle Body 3DOF blocks that model longitudinal, lateral, and yaw motion.

Block	Vehicle Track Setting	Implementation
Vehicle Body 3DOF Single Track	Single (bicycle)	Forces act along the center line at the front and rear axles. No lateral load transfer.
Vehicle Body 3DOF Dual Track	Dual	Forces act at the four vehicle corners or hard points.

Axle forces — Type of axle force

External longitudinal velocity | External longitudinal forces | External forces

Use the Axle forces parameter to specify the type of force.

Axle Forces Setting	Implementation
External longitudinal velocity	The block assumes that the external longitudinal velocity is in a quasi-steady state, so the longitudinal acceleration is approximately zero. Because the motion is quasi-steady, the block calculates lateral forces using the tire slip angles and linear cornering stiffness. Consider this setting when you want to: Generate virtual sensor signal data. Conduct high-level software studies that are not impacted by driveline or nonlinear tire responses.
External longitudinal forces	The block uses the external longitudinal force to accelerate or brake the vehicle. The block calculates lateral forces using the tire slip angles and linear cornering stiffness. Consider this setting when you want to: Account for changes in the longitudinal velocity on the lateral and yaw motion. Specify the external longitudinal motion through a force instead of an external longitudinal velocity. Connect the block to tractive actuators, wheels, brakes, and hitches.
External forces	The block uses the external lateral and longitudinal forces to steer, accelerate, or brake the vehicle. The block does not use the steering input to calculate vehicle motion. Consider this setting when you need tire models with more accurate nonlinear combined lateral and longitudinal slip.

Input Signals

Front wheel steering — WhlAngF input port

on (default) | off

Specify to create input port WhlAngF.

External wind — WindXYZ input port

off (default) | on

Specify to create input port WindXYZ.

External forces — FExt input port

off (default) | on

Specify to create input port FExt.

External moments — MExt input port

off (default) | on

Specify to create input port MExt.

Rear wheel steering — WhlAngR input port

off (default) | on

Specify to create input port WhlAngR.

External friction — Mu input port

off (default) | on

Specify to create input port Mu.

Hitch forces — Fh input port

on (default) | off

Select to create input port Fh.

Hitch moments — Mh input port

on (default) | off

Specify to create input port Mh.

Initial longitudinal position — X_o input port

off (default) | on

Specify to create input port X_o.

Initial lateral position — Y_o input port

off (default) | on

Specify to create input port Y_o.

Initial longitudinal velocity — xdot_o input port

off (default) | on

Specify to create input port xdot_o.

Initial lateral velocity — ydot_o input port

off (default) | on

Specify to create input port ydot_o.

Initial yaw angle — psi_o input port

off (default) | on

Specify to create input port psi_o.

Initial yaw rate — r_o input port

off (default) | on

Specify to create input port r_o.

Air temperature — AirTemp input port

off (default) | on

Specify to create input port AirTemp.

Longitudinal

Number of wheels on front axle, NF — Front wheel count

2 (default) | scalar

Number of wheels on front axle, N_F. The value is dimensionless.

Number of wheels on rear axle, NR — Rear wheel count

2 (default) | scalar

Number of wheels on rear axle, N_R. The value is dimensionless.

Vehicle mass, m — Vehicle mass

2000 (default) | scalar

Vehicle mass, m, in kg.

Longitudinal distance from center of mass to front axle, a — Front axle distance

1.4 (default) | scalar

Horizontal distance a from the vehicle CG to the front wheel axle, in m.

Longitudinal distance from center of mass to rear axle, b — Rear axle distance

1.6 (default) | scalar

Horizontal distance b from the vehicle CG to the rear wheel axle, in m.

Vertical distance from center of mass to axle plane, h — Height

0.35 (default) | scalar

Height of vehicle CG above the axles, h, in m.

Longitudinal distance from center of mass to hitch, dh — Distance from CM to hitch

1 (default) | scalar

Longitudinal distance from center of mass to hitch, dh, in m.

Dependencies

To enable this parameter, on the Input signals pane, select Hitch forces or Hitch moments.

Vertical distance from hitch to axle plane, hh — Distance from hitch to axle plane

0.2 (default) | scalar

Vertical distance from hitch to axle plane, hh, in m.

Dependencies

To enable this parameter, on the Input signals pane, select Hitch forces or Hitch moments.

Initial inertial frame longitudinal position, X_o — Position

0 (default) | scalar

Initial vehicle CG displacement along earth-fixed X-axis, in m.

Initial longitudinal velocity, xdot_o — Velocity

0 (default) | scalar

Initial vehicle CG velocity along vehicle-fixed x-axis, in m/s.

Dependencies

For the Vehicle Body 3DOF Single Track or Vehicle Body 3DOF Dual Track blocks, to enable this parameter, set Axle forces to one of these options:

• External longitudinal forces

• External forces

Lateral

Front tire corner stiffness, Cy_f — Stiffness

12e3 (default) | scalar

Front tire corner stiffness, Cy_f, in N/rad.

Dependencies

For the Vehicle Body 3DOF Single Track or Vehicle Body 3DOF Dual Track blocks, to enable this parameter:

1. Set Axle forces to one of these options:

   • External longitudinal velocity

   • External longitudinal forces

2. Clear Mapped corner stiffness.

Rear tire corner stiffness, Cy_r — Stiffness

11e3 (default) | scalar

Rear tire corner stiffness, Cy_r, in N/rad.

Dependencies

For the Vehicle Body 3DOF Single Track or Vehicle Body 3DOF Dual Track blocks, to enable this parameter:

1. Set Axle forces to one of these options:

   • External longitudinal velocity

   • External longitudinal forces

2. Clear Mapped corner stiffness.

Initial inertial frame lateral displacement, Y_o — Position

0 (default) | scalar

Initial vehicle CG displacement along earth-fixed Y-axis, in m.

Initial lateral velocity, ydot_o — Velocity

0 (default) | scalar

Initial vehicle CG velocity along vehicle-fixed y-axis, in m/s.

Mapped corner stiffness — Selection

off (default) | on

Enables mapped corner stiffness calculation.

Dependencies

To enable this parameter, set Axle forces to one of these options:

• External longitudinal velocity

• External longitudinal forces

Include relaxation length dynamics — Enable relaxation length dynamics

on (default) | off

Enables relaxation length dynamics.

Dependencies

To enable this parameter:

1. Set Axle forces to one of these options:

   • External longitudinal velocity

   • External longitudinal forces

2. Clear Mapped corner stiffness.

Lateral distance from geometric centerline to center of mass, d — Distance

0 (default) | scalar

Lateral distance from geometric centerline to center of mass, d, in m, along the vehicle-fixed y. Positive values indicate that the vehicle CM is to the right of the geometric centerline. Negative values indicate that the vehicle CM is to the left of the geometric centerline.

Lateral distance from geometric centerline to hitch, hl — Distance

0 (default) | scalar

Lateral distance from geometric centerline to the hitch, hl, in m, along the vehicle-fixed y. Positive values indicate that the hitch is to the right of the geometric centerline. Negative values indicate that the hitch is to the left of the geometric centerline.

Dependencies

To enable this parameter, on the Input signals pane, select Hitch forces or Hitch moments.

Track width — Width

[1.4,1.4] (default) | 1-by-2 vector

Track width, w, in m.

Dependencies

To enable this parameter, set Vehicle track to Dual.

Front tire(s) relaxation length, sigma_f — Relaxation length

.1 (default) | scalar

Front tire relaxation length, σ_f, in m.

Dependencies

To enable this parameter:

1. Set Vehicle track to one of these options:

   • Single 2-axle

   • Dual 2-axle

   • Single 3-axle

   • Dual 3-axle

2. Set Axle forces to one of these options:

   • External longitudinal velocity

   • External longitudinal forces

3. Do either of these:

   • Select Mapped corner stiffness.

   • Clear Mapped corner stiffness and select Include relaxation length dynamics.

Rear tire(s) relaxation length, sigma_r — Relaxation length

.1 (default) | scalar

Rear tire relaxation length, σ_r, in m.

Dependencies

To enable this parameter:

1. Set Vehicle track to one of these options:

   • Single 2-axle

   • Dual 2-axle

   • Single 3-axle

   • Dual 3-axle

2. Set Axle forces to one of these options:

   • External longitudinal velocity

   • External longitudinal forces

3. Do either of these:

   • Select Mapped corner stiffness.

   • Clear Mapped corner stiffness and select Include relaxation length dynamics.

Front axle slip angle breakpoints, alpha_f_brk — Breakpoints

[-.1 .1] (default) | vector

Front axle slip angle breakpoints, α_fbrk, in rad.

Dependencies

To enable this parameter:

1. Set Axle forces to one of these options:

   • External longitudinal velocity

   • External longitudinal forces

2. Select Mapped corner stiffness.

Front axle corner data, Cy_f_data — Breakpoints

[-9e3 9e3] (default) | vector

Front axle corner data, Cy_fdata, in N/rad.

Dependencies

To enable this parameter:

1. Set Axle forces to one of these options:

   • External longitudinal velocity

   • External longitudinal forces

2. Select Mapped corner stiffness.

Rear axle slip angle breakpoints, alpha_r_brk — Breakpoints

[-.1 .1] (default) | vector

Rear axle slip angle breakpoints, α_rbrk, in rad.

Dependencies

To enable this parameter:

1. Set Axle forces to one of these options:

   • External longitudinal velocity

   • External longitudinal forces

2. Select Mapped corner stiffness.

Rear axle corner data, Cy_r_data — Data

[-9e3 9e3] (default) | vector

Rear axle corner data, Cy_rdata, in N/rad.

Dependencies

To enable this parameter:

1. Set Axle forces to one of these options:

   • External longitudinal velocity

   • External longitudinal forces

2. Select Mapped corner stiffness.

Yaw

Yaw polar inertia, Izz — Inertia

4000 (default) | scalar

Yaw polar inertia, in kg*m^2.

Initial yaw angle, psi_o — Psi rotation

0 (default) | scalar

Rotation of the vehicle-fixed frame about earth-fixed Z-axis (yaw), in rad.

Initial yaw rate, r_o — Yaw rate

0 (default) | scalar

Vehicle angular velocity about the vehicle-fixed z-axis (yaw rate), in rad/s.

Aerodynamic

Longitudinal drag area, Af — Effective vehicle cross-sectional area

2 (default) | scalar

Effective vehicle cross-sectional area, A_f, to calculate the aerodynamic drag force on the vehicle, in m².

Longitudinal drag coefficient, Cd — Air drag coefficient

.3 (default) | scalar

Air drag coefficient, C_d. The value is dimensionless.

Longitudinal lift coefficient, Cl — Air lift coefficient

.1 (default) | scalar

Air lift coefficient, C_l. The value is dimensionless.

Longitudinal drag pitch moment, Cpm — Pitch drag

.1 (default) | scalar

Longitudinal drag pitch moment coefficient, C_pm. The value is dimensionless.

Relative wind angle vector, beta_w — Wind angle

[0:0.01:0.3] (default) | vector

Relative wind angle vector, β_w, in rad.

Side force coefficient vector, Cs — Side force coefficient

[0:0.03:0.9] (default) | vector

Side force coefficient vector coefficient, C_s. The value is dimensionless.

Yaw moment coefficient vector, Cym — Yaw moment drag

[0:0.01:0.3] (default) | vector

Yaw moment coefficient vector, C_ym. The value is dimensionless.

Environment

Absolute pressure, Pabs — Pressure

101325 (default) | scalar | scalar

Environmental absolute pressure, P_abs, in Pa.

Air temperature, Tair — Temperature

273 (default) | scalar

Environmental absolute temperature, T, in K.

Dependencies

To enable this parameter, clear Air temperature.

Gravitational acceleration, g — Gravity

9.81 (default) | scalar

Gravitational acceleration, g, in m/s^2.

Nominal friction scaling factor, mu — Friction scale factor

1 (default) | scalar

Nominal friction scale factor, μ. The value is dimensionless.

Dependencies

For the Vehicle Body 3DOF Single Track or Vehicle Body 3DOF Dual Track blocks, to enable this parameter:

1. Set Axle forces to one of these options:

   • External longitudinal velocity

   • External longitudinal forces

2. Clear External Friction.

Simulation

Longitudinal velocity tolerance, xdot_tol — Tolerance

.01 (default) | scalar

Longitudinal velocity tolerance, in m/s.

Nominal normal force, Fznom — Normal force

5000 (default) | scalar

Nominal normal force, in N.

Dependencies

For the Vehicle Body 3DOF Single Track or Vehicle Body 3DOF Dual Track blocks, to enable this parameter, set Axle forces to one of these options:

• External longitudinal velocity

• External longitudinal forces

Geometric longitudinal offset from axle plane, longOff — Longitudinal offset

0 (default) | scalar

Vehicle chassis offset from axle plane along body-fixed x-axis, in m. When you use the 3D visualization engine, consider using the offset to locate the chassis independent of the vehicle CG.

Geometric lateral offset from center plane, latOff — Lateral offset

0 (default) | scalar

Vehicle chassis offset from center plane along body-fixed y-axis, in m. When you use the 3D visualization engine, consider using the offset to locate the chassis independent of the vehicle CG.

Geometric vertical offset from axle plane, vertOff — Vertical offset

0 (default) | scalar

Vehicle chassis offset from axle plane along body-fixed z-axis, in m. When you use the 3D visualization engine, consider using the offset to locate the chassis independent of the vehicle CG.

Wrap Euler angles, wrapAng — Selection

off (default) | on

Wrap the Euler angles to the interval [-pi, pi]. For vehicle maneuvers that might undergo vehicle yaw rotations that are outside of the interval, consider deselecting the parameter if you want to:

• Track the total vehicle yaw rotation.

• Avoid discontinuities in the vehicle state estimators.

References

[1] Gillespie, Thomas. Fundamentals of Vehicle Dynamics. Warrendale, PA: Society of Automotive Engineers (SAE), 1992.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2018a