Trailer Body 3DOF

Trailer body with longitudinal, lateral, and yaw motion

• 

Libraries:
Vehicle Dynamics Blockset / Vehicle Body

Description

The Trailer Body 3DOF block implements a rigid one-axle, two-axle or three-axle trailer body model to calculate longitudinal, lateral, and yaw motion. Configure the block for a single or dual track. The block accounts for axle and hitch reaction forces due to the trailer acceleration, aerodynamic drag, 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.

Use the Vehicle track parameter to specify the number of wheels.

Vehicle Track Setting	Implementation
Single 1-axle	Trailer with a single track and one axle. Forces act along the center line of the axle. No lateral load transfer.
Dual 1-axle	Trailer with a dual track and one axle. Forces act at the axle hard-point locations.
Single 2-axle	Trailer with a single track and two axles. Forces act along the center line of the axles. No lateral load transfer.
Dual 2-axle(default)	Trailer with a dual track and two axles. Forces act at the axle hard-point locations.
Single 3-axle	Trailer with a single track and three axles. Forces act along the center line of the axles. No lateral load transfer.
Dual 3-axle	Trailer with a dual track and three axles. Forces act at the axle hard-point locations.

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, and 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.

To create additional input ports, under Input signals, select these block parameters.

Input Signals Pane Parameter	Input Port	Description
Front wheel steering	WhlAngF	Front wheel angle, δF
Middle wheel steering	WhlAngM	Middle wheel angle, δM
Rear wheel steering	WhlAngR	Rear wheel angle, δR
External wind	WindXYZ	Wind speed, WX, WY, and WZ, in an inertial reference frame
External friction	Mu	Friction coefficient
External forces	FExt	External force on the vehicle center of gravity (CG), Fx, Fy, and Fz, in the vehicle-fixed frame
External moments	MExt	External moment about the vehicle CG, Mx, My, and Mz, in the vehicle-fixed frame
Front hitch forces	FhF	Hitch force applied to the body at the front hitch location, FhFx, FhFy, and FhFz, in the vehicle-fixed frame
Front hitch moments	MhF	Hitch moment at the front hitch location, MhFx, MhFy, and MhFz, about the vehicle-fixed frame
Rear hitch forces	FhR	Hitch force applied to the body at the rear hitch location, FhRx, FhRy, and FhRz, in the vehicle-fixed frame
Rear hitch moments	MhR	Hitch moment at the rear hitch location, MhRx, MhRy, and MhRz, about the vehicle-fixed frame
Initial longitudinal position	X_o	Initial vehicle CG displacement along the earth-fixed X-axis
Initial yaw angle	psi_o	Initial rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw)
Initial longitudinal velocity	xdot_o	Initial vehicle CG velocity along the vehicle-fixed x-axis
Initial yaw rate	r_o	Initial vehicle angular velocity about the vehicle-fixed z-axis (yaw rate)
Initial lateral position	Y_o	Initial vehicle CG displacement along the earth-fixed Y-axis
Air temperature	AirTemp	Ambient air temperature. Consider this option if you want to vary the temperature during run time.
Initial lateral velocity	ydot_o	Initial vehicle CG velocity along the vehicle-fixed y-axis

Theory

To determine the vehicle motion, the block solves the rigid body planar dynamics equations of motion.

Signal Track

Calculation	Description
Dynamics	The block uses these equations to calculate the rigid body planar dynamics. $\begin{array}{l}\ddot{y}=-\dot{x}r+\frac{F_{yf}+F_{ym}+F_{yr}+F_{yext}+F{h}_{yf}+F{h}_{yr}}{m}\\ \dot{r}=\frac{-a{F}_{yf}-b{F}_{ym}-c{F}_{yr}+d{h}_{f}F{h}_{yf}-d{h}_{r}F{h}_{yr}+M_{zext}+M{h}_{zf}+M{h}_{zr}}{I_{zz}}\\ r=\dot{\psi }\end{array}$ If you set Axle forces to either External longitudinal forces or External forces, the block uses this equation for the longitudinal acceleration. $\ddot{x}=\dot{y}r+\frac{F_{xf}+F_{xm}+F_{xr}-g\sin (\gamma )+F_{xext}+F{h}_{xf}+F{h}_{xr}}{m}$ 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. $$\begin{array}{l}{F}_{xft}=F_{xfinput}\\ F_{yft}=-C_{yf}{\alpha }_f{\mu }_f\frac{F_{zf}}{F_{znom}}\\ F_{xmt}=F_{xminput}\\ F_{ymt}=-C_{ym}{\alpha }_m{\mu }_m\frac{F_{zm}}{F_{znom}}\\ F_{xrt}=F_{xrinput}\\ F_{yrt}=-C_{yr}{\alpha }_r{\mu }_r\frac{F_{zr}}{F_{znom}} \end{array}$$ If you set Axle forces to External longitudinal velocity, the block uses these equations. $\begin{array}{l}{F}_{xft}=0\\ F_{yft}=-C_{yf}{\alpha }_f{\mu }_f\frac{F_{zf}}{F_{znom}}\\ F_{xmt}=0\\ F_{ymt}=-C_{ym}{\alpha }_m{\mu }_m\frac{F_{zm}}{F_{znom}}\\ F_{xrt}=0\\ F_{yrt}=-C_{yr}{\alpha }_r{\mu }_r\frac{F_{zr}}{F_{znom}}\end{array}$ The block divides the normal forces by the nominal normal load to vary the effective friction parameters during weight and load transfer. The block maintains pitch and roll equilibrium. $\begin{array}{l}{F}_{zf}=\frac{bmg\cos (\gamma )-\left(\ddot{x}-\dot{y}r\right)mh+h{F}_{xext}+b{F}_{zext}-M_{yext}}{a+b}\\ F_{zr}=\frac{amg\cos (\gamma )+\left(\ddot{x}-\dot{y}r\right)mh-h{F}_{xext}+a{F}_{zext}+M_{yext}}{a+b}\end{array}$
Tire forces	The block uses the ratio of the local, longitudinal, and lateral velocities to determine the slip angles. $\begin{array}{l}{\alpha }_f=\text{atan}\left(\frac{\dot{y}-ar}{\dot{x}}\right)-{\delta }_f\\ {\alpha }_m=\text{atan}\left(\frac{\dot{y}-br}{\dot{x}}\right)-{\delta }_m\\ {\alpha }_r=\text{atan}\left(\frac{\dot{y}-cr}{\dot{x}}\right)-{\delta }_r\end{array}$ The block uses the steering angles to transform the tire forces to the vehicle-fixed frame. $\begin{array}{l}{F}_{xf}=F_{xft}\cos \left({\delta }_f\right)-F_{yft}\sin \left({\delta }_f\right)\\ F_{yf}=-F_{xft}\sin \left({\delta }_f\right)+F_{yft}\cos \left({\delta }_f\right)\\ F_{xm}=F_{xmt}\cos \left({\delta }_m\right)-F_{ymt}\sin \left({\delta }_m\right)\\ F_{ym}=-F_{xmt}\sin \left({\delta }_m\right)+F_{ymt}\cos \left({\delta }_m\right)\\ F_{xr}=F_{xrt}\cos \left({\delta }_r\right)-F_{yrt}\sin \left({\delta }_r\right)\\ F_{yr}=-F_{xrt}\sin \left({\delta }_r\right)+F_{yrt}\cos \left({\delta }_r\right)\end{array}$ If you set Axle forces to External forces, the block assumes that the externally provided forces are in the vehicle-fixed frame at the axle-wheel location. $\begin{array}{l}{F}_{xf}=F_{xft}=F_{xfinput}\\ F_{yf}=F_{yft}=F_{yfinput}\\ F_{xm}=F_{xmt}=F_{xminput}\\ F_{ym}=F_{ymt}=F_{yminput}\\ F_{xr}=F_{xrt}=F_{xrinput}\\ F_{yr}=F_{yrt}=F_{yrinput}\end{array}$

Single Track — Three Axles

Single Track — Two Axles

Single Track — One Axle

Dual Track

Calculation	Description
Dynamics	The block uses these equations to calculate the rigid body planar dynamics. $\begin{array}{l}\ddot{x}=\dot{y}r+\frac{F_{xfl}+F_{xfr}+F_{xml}+F_{xmr}+F_{xrl}+F_{xrr}-g\sin (\gamma )+F_{xext}+F{h}_{xf}+F{h}_{xr}}{m}\\ \ddot{y}=-\dot{x}r+\frac{F_{yfl}+F_{yfr}+F_{yml}+F_{ymr}+F_{yrl}+F_{yrr+}{F}_{yext}+F{h}_{yf}+F{h}_{yr}}{m}\\ \dot{r}=\frac{-a\left(F_{yfl}+F_{yfr}\right)-b\left(F_{yml}+F_{ymr}\right)-c\left(F_{yrl}+F_{yrr}\right)+d{h}_{f}F{h}_{yf}-d{h}_{r}F{h}_{yr}+F_{xfl}\left(\frac{w_f}{2}+d\right)-F_{xfr}\left(\frac{wf}{2}-d\right)+F_{xml}\left(\frac{w_m}{2}+d\right)-F_{xmr}\left(\frac{w_m}{2}-d\right)+F_{xrl}\left(\frac{w_r}{2}+d\right)-F_{xrr}\left(\frac{wr}{2}-d\right)+M_{zext}+M{h}_{fz}+M{h}_{rz}-F{h}_{xf}h{l}_f-F{h}_{xr}h{l}_r}{I_{zz}}\\ r=\dot{\psi }\end{array}$ 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. $\begin{array}{l}{F}_{xflt}=F_{xflinput}\\ F_{yflt}=-C_{yfl}{\alpha }_{fl}{\mu }_{fl}\frac{F_{zfl}}{2F_{znom}}\\ F_{xfrt}=F_{xfrinput}\\ F_{yfrt}=-C_{yfr}{\alpha }_{fr}{\mu }_{fr}\frac{F_{zfr}}{2F_{znom}}\\ F_{xmlt}=F_{xmlinput}\\ F_{ymlt}=-C_{yml}{\alpha }_{ml}{\mu }_{ml}\frac{F_{zml}}{2F_{znom}}\\ F_{xmrt}=F_{xmrinput}\\ F_{ymrt}=-C_{ymr}{\alpha }_{mr}{\mu }_{mr}\frac{F_{zmr}}{2F_{znom}}\\ F_{xrlt}=F_{xrlinput}\\ F_{yrlt}=-C_{yrl}{\alpha }_{rl}{\mu }_{rl}\frac{F_{zrl}}{2F_{znom}}\\ F_{xrrt}=F_{xrrinput}\\ F_{yrrt}=-C_{yrr}{\alpha }_{rr}{\mu }_{rr}\frac{F_{zrr}}{2F_{znom}}\end{array}$ If you set Axle forces to External longitudinal velocity, the block uses these equations. $\begin{array}{l}{F}_{xflt}=0\\ F_{yflt}=-C_{yfl}{\alpha }_{fl}{\mu }_{fl}\frac{F_{zfl}}{2F_{znom}}\\ F_{xfrt}=0\\ F_{yfrt}=-C_{yfr}{\alpha }_{fr}{\mu }_{fr}\frac{F_{zfr}}{2F_{znom}}\\ F_{xmlt}=0\\ F_{ymlt}=-C_{yml}{\alpha }_{ml}{\mu }_{ml}\frac{F_{zml}}{2F_{znom}}\\ F_{xmrt}=0\\ F_{ymrt}=-C_{ymr}{\alpha }_{mr}{\mu }_{mr}\frac{F_{zmr}}{2F_{znom}}\\ F_{xrlt}=0\\ F_{yrlt}=-C_{yrl}{\alpha }_{rl}{\mu }_{rl}\frac{F_{zrl}}{2F_{znom}}\\ F_{xrrt}=0\\ F_{yrrt}=-C_{yrr}{\alpha }_{rr}{\mu }_{rr}\frac{F_{zrr}}{2F_{znom}}\end{array}$ The block divides the normal forces by the nominal normal load to vary the effective friction parameters during weight and load transfer. The block maintains pitch and roll equilibrium. $\begin{array}{l}{F}_{zf}=\frac{bmg\cos (\gamma )-\left(\ddot{x}-\dot{y}r\right)mh+h{F}_{xext}+b{F}_{zext}-M_{yext}}{a+b}\\ F_{zr}=\frac{amg\cos (\gamma )+\left(\ddot{x}-\dot{y}r\right)mh-h{F}_{xext}+a{F}_{zext}+M_{yext}}{(a+b)}\\ F_{zfl}=F_{zf}+\left(mh(\ddot{y}+\dot{x}r\right)-h{F}_{yext}-M_{xext})\frac{2}{w_f}\\ F_{zfr}=F_{zf}+\left(-mh(\ddot{y}+\dot{x}r\right)+h{F}_{yext}+M_{xext})\frac{2}{w_f}\\ F_{zrl}=F_{zr}+\left(mh(\ddot{y}+\dot{x}r\right)-h{F}_{yext}-M_{xext})\frac{2}{w_r}\\ F_{zrr}=F_{zr}+\left(-mh(\ddot{y}+\dot{x}r\right)+h{F}_{yext}+M_{xext})\frac{2}{w_r}\end{array}$
Tire forces	The block uses the ratio of the local, longitudinal, and lateral velocities to determine the slip angles. $\begin{array}{l}{\alpha }_{fl}=\text{atan}\left(\frac{\dot{y}-ar}{\dot{x}+r\frac{w_f}{2}}\right)-{\delta }_{fl}\\ {\alpha }_{fr}=\text{atan}\left(\frac{\dot{y}-ar}{\dot{x}-r\frac{w_f}{2}}\right)-{\delta }_{fr}\\ {\alpha }_{ml}=\text{atan}\left(\frac{\dot{y}-br}{\dot{x}+r\frac{w_m}{2}}\right)-{\delta }_{ml}\\ {\alpha }_{mr}=\text{atan}\left(\frac{\dot{y}-br}{\dot{x}-r\frac{w_m}{2}}\right)-{\delta }_{mr}\\ {\alpha }_{rl}=\text{atan}\left(\frac{\dot{y}-cr}{\dot{x}+r\frac{w_r}{2}}\right)-{\delta }_{rl}\\ {\alpha }_{rr}=\text{atan}\left(\frac{\dot{y}-cr}{\dot{x}-r\frac{w_r}{2}}\right)-{\delta }_{rr}\end{array}$ The block uses the steering angles to transform the tire forces to the vehicle-fixed frame. $$\begin{array}{l}{F}_{xfl}=F_{xflt}\cos \left({\delta }_{fl}\right)-F_{yflt}\sin \left({\delta }_{fl}\right)\\ F_{xfr}=F_{xfrt}\cos \left({\delta }_{fr}\right)-F_{yfrt}\sin \left({\delta }_{fr}\right)\\ F_{xml}=F_{xmlt}\cos \left({\delta }_{ml}\right)-F_{ymlt}\sin \left({\delta }_{ml}\right)\\ F_{xmr}=F_{xmrt}\cos \left({\delta }_{mr}\right)-F_{ymrt}\sin \left({\delta }_{mr}\right)\\ F_{yfl}=-F_{xflt}\sin \left({\delta }_{fl}\right)+F_{yflt}\cos \left({\delta }_{fl}\right)\\ F_{yfr}=-F_{xfrt}\sin \left({\delta }_{fr}\right)+F_{yfrt}\cos \left({\delta }_{fr}\right)\\ F_{yml}=-F_{xmlt}\sin \left({\delta }_{ml}\right)+F_{ymlt}\cos \left({\delta }_{ml}\right)\\ F_{ymr}=-F_{xmrt}\sin \left({\delta }_{mr}\right)+F_{ymrt}\cos \left({\delta }_{mr}\right)\\ F_{xrl}=F_{xrlt}\cos \left({\delta }_{rl}\right)-F_{yrlt}\sin \left({\delta }_{rl}\right)\\ F_{xrr}=F_{xrrt}\cos \left({\delta }_{rr}\right)-F_{yrrt}\sin \left({\delta }_{rr}\right)\\ F_{yrl}=-F_{xrlt}\sin \left({\delta }_{rl}\right)+F_{yrlt}\cos \left({\delta }_{rl}\right)\\ F_{yrr}=-F_{xrrt}\sin \left({\delta }_{rr}\right)+F_{yrrt}\cos \left({\delta }_{rr}\right)\end{array}$$ If you set Axle forces to External forces, the block assumes that the externally provided forces are in the vehicle-fixed frame at the axle-wheel location. $$\begin{array}{l}{F}_{xfl}=F_{xflt}=F_{xflinput}\\ F_{xfr}=F_{xfrt}=F_{xfrinput}\\ F_{xml}=F_{xmlt}{=}_{Fxmlinput}\\ F_{xmr}=F_{xmrt}=F_{xmrinput}\\ F_{yfl}=F_{yflt}=F_{yflinput}\\ F_{yfr}=F_{yfrt}=F_{yfrinput}\\ F_{yml}=F_{ymlt}=F_{ymlinput}\\ F_{ymr}=F_{ymrt}=F_{ymrinput}\\ F_{xrl}=F_{xrlt}=F_{xrlinput}\\ F_{xrr}=F_{xrrt}=F_{xrrinput}\\ F_{yrl}=F_{yrlt}=F_{yrlinput}\\ F_{yrr}=F_{yrrt}=F_{yrrinput}\end{array}$$

Dual Track — Three Axles

Dual Track — Two Axles

Dual Track — One Axle

The illustrations use these variables.

a, b, c	Longitudinal distance of the front, middle, and rear axles, respectively, from the normal projection point of the vehicle CG onto the common axle plane
h	Height of the tractor CG above the axle plane along the vehicle-fixed z-axis
d	Lateral distance from the geometric centerline to the center of mass along the vehicle-fixed y-axis
hh_f, hh_r	Height of the front and rear hitch, respectively, above the axle plane along the vehicle-fixed z-axis
dh_f, dh_r	Longitudinal distance of the front and rear hitch, respectively, from the normal projection point of tractor CG onto the common axle plane
wf, wm, wr	Front, middle, and rear track width, respectively

Drag

This table summarizes the block implementation for the drag calculation.

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. $$\begin{array}{l}{M}_{dr}=-\frac{1}{2TR}{C}_{rm}{A}_f{P}_{abs}{(}^{\overline{w}}(dh+c)\\ M_{dp}=-\frac{1}{2TR}{C}_{pm}{A}_f{P}_{abs}{(}^{\overline{w}}(dh+c)\\ M_{dy}=-\frac{1}{2TR}{C}_{ym}{A}_f{P}_{abs}{(}^{\overline{w}}(dh+c)\end{array}$$

Lateral Corner Stiffness and Relaxation Dynamics

To enable the mapped corner stiffness and relaxation length dynamic parameters, set Axle forces to External longitudinal forces or External longitudinal velocity.

Parameter Settings		Description
Mapped Corner Stiffness	Include Relaxation Length Dynamics
Off (default)	On (default)	The block uses constant corner stiffness values for Cyf, Cym, and Cyr. 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.
On	On (default)	The block uses lookup tables that are functions of the corner stiffness data and slip angles. $$\begin{array}{l}C{y}_f=f({\alpha }_{f\sigma },C{y}_{fdata})\\ C{y}_m=f({\alpha }_{m\sigma },C{y}_{mdata})\\ C{y}_r=f({\alpha }_{r\sigma },C{y}_{rdata})\\ \\ {\alpha }_{f\sigma }=\frac{1}{s}\left[\frac{\left({\alpha }_f-{\alpha }_{f\sigma }\right)v_{wf}}{{\alpha }_f}\right]\\ \\ {\alpha }_{m\sigma }=\frac{1}{s}\left[\frac{\left({\alpha }_m-{\alpha }_{m\sigma }\right)v_{mf}}{{\alpha }_m}\right]\\ \\ {\alpha }_{r\sigma }=\frac{1}{s}\left[\frac{\left({\alpha }_r-{\alpha }_{r\sigma }\right)v_{wr}}{{\alpha }_r}\right]\end{array}$$ 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.
Off (default)	Off	The block uses constant corner stiffness values Cyf, Cym and Cyr.

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, Fxm, Fxr	Longitudinal forces applied to front, middle, and rear wheels, along the vehicle-fixed x-axis
Fyf, Fym, Fyr	Lateral forces applied to front, middle, 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, Fxmt, Fxrt	Longitudinal tire force applied to front, middle, and rear wheels, along the vehicle-fixed x-axis
Fyft, Fymt, Fyrt	Lateral tire force applied to front, middle, 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
Fxmlt, Fxmrt	Longitudinal tire force applied to middle left and middle right wheels, along the vehicle-fixed x-axis
Fxrlt, Fxrrt	Longitudinal tire force applied to rear left and rear 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
Fymlt, Fymrt	Lateral force tire applied to middle left and middle right wheels, along the vehicle-fixed y-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 1-axle Single 2-axle Single 3-axle	δF	Scalar – 1
Dual 1-axle Dual 2-axle Dual 3-axle	$${\delta }_F=[\begin{array}{cc}{\delta }_{fl}& {\delta }_{fr}\end{array}]\text{ or }\left[\begin{array}{c}{\delta }_{fl}\\ {\delta }_{fr}\end{array}\right]$$	Array – [1x2] or [2x1]

Dependencies

To enable this port, under Input signals, select Front wheel steering.

WhlAngM — Middle wheel steering angles

scalar | array

Middle wheel steering angles, δ_M, in rad.

Vehicle Track Setting	Variable	Signal Dimension
Single 3-axle	δM	Scalar – 1
Dual 3-axle	$${\delta }_M=[\begin{array}{cc}{\delta }_{ml}& {\delta }_{mr}\end{array}]\text{ or }\left[\begin{array}{c}{\delta }_{ml}\\ {\delta }_{mr}\end{array}\right]$$	Array – [1x2] or [2x1]

Dependencies

To enable this port:

• Set Vehicle track to Single 3-axle or Dual 3-axle.

• To enable this port, under Input signals, select Middle wheel steering.

WhlAngR — Rear wheel steering angles

scalar | array

Rear wheel steering angles, δ_R, in rad.

Vehicle Track Setting	Variable	Signal Dimension
Single 1-axle Single 2-axle Single 3-axle	δR	Scalar – 1
Dual 1-axle Dual 2-axle Dual 3-axle	$${\delta }_R=[\begin{array}{cc}{\delta }_{rl}& {\delta }_{rr}\end{array}]\text{ or }\left[\begin{array}{c}{\delta }_{rl}\\ {\delta }_{rr}\end{array}\right]$$	Array – [1x2] or [2x1]

Dependencies

To enable this port, under Input signals, 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 1-axle Single 2-axle Single 3-axle	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 1-axle Dual 2-axle Dual 3-axle	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	$$FwF=\left[\begin{array}{cc}{F}_{xfl}& F_{yfl}\\ F_{xfr}& F_{yfr}\end{array}\right]$$	Array – [2x2]

Dependencies

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

• External longitudinal forces

• External forces

FwM — Total force on the middle wheels

scalar | array

Force on the middle wheels, Fw_M, along the vehicle-fixed axis, in N.

Vehicle Track Setting	Axle Forces Setting	Description	Variable	Signal Dimension
Single 3-axle	External longitudinal forces	Longitudinal force on the middle wheel	$$FwM=F{x}_r$$	Scalar – 1
	External forces	Longitudinal and lateral forces on the middle wheel	$$FwM=\left[\begin{array}{cc}F{x}_m& F{y}_m\end{array}\right]\text{ or }\left[\begin{array}{c}F{x}_m\\ F{y}_m\end{array}\right]$$	Array – [1x2] or [2x1]
Dual 3-axle	External longitudinal forces	Longitudinal force on the middle wheels	$$FwM=\left[\begin{array}{cc}{F}_{xml}& F_{xmr}\end{array}\right]\text{ or }\left[\begin{array}{c}{F}_{xml}\\ F_{xmr}\end{array}\right]$$	Array – [1x2] or [2x1]
	External forces	Longitudinal and lateral forces on the middle wheels	$$FwM=\left[\begin{array}{cc}{F}_{xml}& F_{xmr}\\ F_{yml}& F_{ymr}\end{array}\right]$$	Array – [2x2]

Dependencies

To enable this port, set:

• Vehicle track to Single 3-axle or Dual 3-axle.

• Axle forces to External longitudinal forces or 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 2-axle Single 3-axle	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 2-axle Dual 3-axle	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	$$FwR=\left[\begin{array}{cc}{F}_{xrl}& F_{yrl}\\ F_{xrr}& F_{yrr}\end{array}\right]$$	Array – [2x2]

Dependencies

To enable this port, set:

• Vehicle track to Single 3-axle, Single 2-axle, Dual 3-axle or Dual 2-axle.

• Axle forces to External longitudinal forces or External forces.

FExt — External force on the vehicle CG

array

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

Dependencies

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

MExt — External moment about vehicle CG

array

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

Dependencies

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

FhF — Front hitch force on the body

array

Hitch force applied to the body at the front hitch location, FhF_x, FhF_y, FhF_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 Front hitch forces.

MhF — Front hitch moment about body

array

Hitch moment at the front hitch location, MhF_x, MhF_y, MhF_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 Front hitch moments.

FhR — Rear hitch force on the body

array

Hitch force applied to the body at the rear hitch location, FhR_x, FhR_y, FhR_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 Rear hitch forces.

MhR — Rear hitch moment about body

array

Hitch moment at the rear hitch location, MhR_x, MhR_y, MhR_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 Rear hitch moments.

WindXYZ — Wind speed

array

Wind speed, W_x, W_y, W_z, along the inertial X-, Y-, and Z-axes, in m/s. The signal vector dimensions are 1-by-3 or 3-by-1.

Dependencies

To enable this port, under Input signals, select External wind.

Mu — Tire friction coefficient

array

Tire friction coefficient, μ. The value is dimensionless.

Vehicle Track Setting	Description	Variable	Signal Dimension
Single 1-axle	Friction coefficient on the wheels	$$Mu={\mu }_f$$	Array – [1x1]
Dual 1-axle	Friction coefficient on the wheels	$$Mu=\left[\begin{array}{cc}{\mu }_{fl}& {\mu }_{fr}\end{array}\right]\text{ or }\left[\begin{array}{c}{\mu }_{fl}\\ {\mu }_{fr}\end{array}\right]$$	Array – [1x2] or [2x1]
Single 2-axle	Friction coefficient on the wheels	$$Mu=\left[\begin{array}{cc}{\mu }_f& {\mu }_r\end{array}\right]\text{ or }\left[\begin{array}{c}{\mu }_f\\ {\mu }_r\end{array}\right]$$	Array – [1x2] or [2x1]
Dual 2-axle	Friction coefficient on the wheels	$$Mu=\left[\begin{array}{cc}{\mu }_{fl}& {\mu }_{fr}\\ {\mu }_{rl}& {\mu }_{rr}\end{array}\right]$$	Array – [2x2]
Single 3-axle	Friction coefficient on the wheels	$$Mu=\left[\begin{array}{ccc}{\mu }_f& {\mu }_m& {\mu }_r\end{array}\right]\text{ or }\left[\begin{array}{c}{\mu }_f\\ {\mu }_m\\ {\mu }_r\end{array}\right]$$	Array – [1x3] or [3x1]
Dual 3-axle	Friction coefficient on the wheels	$$Mu=\left[\begin{array}{cc}{\mu }_{fl}& {\mu }_{fr}\\ {\mu }_{ml}& {\mu }_{mr}\\ {\mu }_{rl}& {\mu }_{rr}\end{array}\right]$$	Array – [3x2]

Dependencies

To enable this port, under Input signals, select External friction.

AirTemp — Ambient air temperature

scalar

Ambient air temperature, in K.

Dependencies

To enable this port, under Input signals, 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, under Input signals, 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, under Input signals, 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. Under Input signals, 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, under Input signals, 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, under Input signals, select Initial yaw angle.

r_o — Initial yaw rate

scalar

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

Dependencies

To enable this port, under Input signals, select Initial yaw rate.

Output

Info — Trailer data

bus

Trailer data, returned as a 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
	MidlAxl	Lft	Disp	X		Middle left wheel displacement along the earth-fixed X-axis	Computed	m
				Y		Middle left wheel displacement along the earth-fixed Y-axis	Computed	m
				Z		Middle left wheel displacement along the earth-fixed Z-axis	0	m
			Vel	Xdot		Middle left wheel velocity along the earth-fixed X-axis	Computed	m/s
				Ydot		Middle left wheel velocity along the earth-fixed Y-axis	Computed	m/s
				Zdot		Middle left wheel velocity along the earth-fixed Z-axis	0	m/s
		Rght	Disp	X		Middle right wheel displacement along the earth-fixed X-axis	Computed	m
				Y		Middle right wheel displacement along the earth-fixed Y-axis	Computed	m
				Z		Middle right wheel displacement along the earth-fixed Z-axis	0	m
			Vel	Xdot		Middle right wheel velocity along the earth-fixed X-axis	Computed	m/s
				Ydot		Middle right wheel velocity along the earth-fixed Y-axis	Computed	m/s
				Zdot		Middle 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
	Geom	Disp	X			Trailer body offset from the axle plane along the earth-fixed X-axis	Computed	m
			Y			Trailer body offset from the center plane along the earth-fixed Y-axis	Computed	m
			Z			Trailer body offset from the axle plane along the earth-fixed Z-axis	Computed	m
		Vel	Xdot			Trailer body offset velocity along the earth-fixed X-axis	Computed	m/s
			Ydot			Trailer body offset velocity along the earth-fixed Y-axis	Computed	m/s
			Zdot			Trailer body offset velocity along the earth-fixed Z-axis	Computed	m/s
	HitchF	Disp	X			Trailer front hitch offset from the axle plane along the earth-fixed X-axis	Computed	m
			Y			Trailer front hitch offset from the center plane along the earth-fixed Y-axis	Computed	m
			Z			Trailer front hitch offset from the axle plane along the earth-fixed Z-axis	Computed	m
		Vel	Xdot			Trailer front hitch offset velocity along the earth-fixed X-axis	Computed	m/s
			Ydot			Trailer front hitch offset velocity along the earth-fixed Y-axis	Computed	m/s
			Zdot			Trailer front hitch offset velocity along the earth-fixed Z-axis	Computed	m/s
	HitchR	Disp	X			Trailer rear hitch offset from the axle plane along the earth-fixed X-axis	Computed	m
			Y			Trailer rear hitch offset from the center plane along the earth-fixed Y-axis	Computed	m
			Z			Trailer rear hitch offset from the axle plane along the earth-fixed Z-axis	Computed	m
		Vel	Xdot			Trailer rear hitch offset velocity along the earth-fixed X-axis	Computed	m/s
			Ydot			Trailer rear hitch offset velocity along the earth-fixed Y-axis	Computed	m/s
			Zdot			Trailer rear hitch 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
	Forces	Body	Fx			Net force on the vehicle CG along the vehicle-fixed x-axis	Computed	N
			Fy			Net force on the vehicle CG along the vehicle-fixed y-axis	Computed	N
			Fz			Net force on the vehicle CG along the vehicle-fixed z-axis	0	N
		Ext	Fx			External force on the vehicle CG along the vehicle-fixed x-axis	Computed	N
			Fy			External force on the vehicle CG along the vehicle-fixed y-axis	Computed	N
			Fz			External force on the vehicle CG along the vehicle-fixed z-axis	0	N
		HitchF	Fx			Hitch front force applied to the body at the hitch location along the vehicle-fixed x-axis	Computed	N
			Fy			Hitch front force applied to the body at the hitch location along the vehicle-fixed y-axis	Computed	N
			Fz			Hitch front force applied to the body at the hitch location along the vehicle-fixed z-axis	Computed	N
		HitchR	Fx			Hitch rear force applied to the body at the hitch location along the vehicle-fixed x-axis	Computed	N
			Fy			Hitch rear force applied to the body at the hitch location along the vehicle-fixed y-axis	Computed	N
			Fz			Hitch rear force applied to the body at the hitch location along the vehicle-fixed z-axis	Computed	N
		FrntAxl	Lft	Fx		Longitudinal force on the left front wheel along the vehicle-fixed x-axis	Computed	N
				Fy		Lateral force on the left front wheel along the vehicle-fixed y-axis	Computed	N
				Fz		Normal force on the left front wheel along the vehicle-fixed z-axis	Computed	N
			Rght	Fx		Longitudinal force on the right front wheel along the vehicle-fixed x-axis	Computed	N
				Fy		Lateral force on the right front wheel along the vehicle-fixed y-axis	Computed	N
				Fz		Normal force on the right front wheel along the vehicle-fixed z-axis	Computed	N
		MidlAxl	Lft	Fx		Longitudinal force on the left middle wheel along the vehicle-fixed x-axis	Computed	N
				Fy		Lateral force on the left middle wheel along the vehicle-fixed y-axis	Computed	N
				Fz		Normal force on the left middle wheel along the vehicle-fixed z-axis	Computed	N
			Rght	Fx		Longitudinal force on the right middle wheel along the vehicle-fixed x-axis	Computed	N
				Fy		Lateral force on the right middle wheel along the vehicle-fixed y-axis	Computed	N
				Fz		Normal force on the right middle wheel along the vehicle-fixed z-axis	Computed	N
		RearAxl	Lft	Fx		Longitudinal force on the left rear wheel along the vehicle-fixed x-axis	Computed	N
				Fy		Lateral force on the left rear wheel along the vehicle-fixed y-axis	Computed	N
				Fz		Normal force on the left rear wheel along the vehicle-fixed z-axis	Computed	N
			Rght	Fx		Longitudinal force on the right rear wheel along the vehicle-fixed x-axis	Computed	N
				Fy		Lateral force on the right rear wheel along the vehicle-fixed y-axis	Computed	N
				Fz		Normal force on the 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 the vehicle CG along the vehicle-fixed x-axis	Computed	N
			Fy			Drag force on the vehicle CG along the vehicle-fixed y-axis	Computed	N
			Fz			Drag force on the vehicle CG along the vehicle-fixed z-axis	Computed	N
		Grvty	Fx			Gravity force on the vehicle CG along the vehicle-fixed x-axis	Computed	N
			Fy			Gravity force on the vehicle CG along the vehicle-fixed y-axis	Computed	N
			Fz			Gravity force on the vehicle CG along the vehicle-fixed z-axis	Computed	N
Moments	Body	Mx			Body moment on the vehicle CG about the vehicle-fixed x-axis	0	N·m
		My			Body moment on the vehicle CG about the vehicle-fixed y-axis	Computed	N·m
		Mz			Body moment on the vehicle CG about the vehicle-fixed z-axis	0	N·m
	Drag	Mx			Drag moment on the vehicle CG about the vehicle-fixed x-axis	0	N·m
		My			Drag moment on the vehicle CG about the vehicle-fixed y-axis	Computed	N·m
		Mz			Drag moment on the vehicle CG about the vehicle-fixed z-axis	0	N·m
	Ext	Mx			External moment on the vehicle CG about the vehicle-fixed x-axis	0	N·m
		My			External moment on the vehicle CG about the vehicle-fixed y-axis	Computed	N·m
		Mz			External moment on the vehicle CG about the vehicle-fixed z-axis	0	N·m
	HitchF	Mx			Hitch moment at the front hitch location about vehicle-fixed x-axis	0	N·m
		My			Hitch moment at the front hitch location about vehicle-fixed y-axis	Computed	N·m
		Mz			Hitch moment at the front hitch location about vehicle-fixed z-axis	0	N·m
	HitchR	Mx			Hitch moment at the rear hitch location about vehicle-fixed x-axis	0	N·m
		My			Hitch moment at the rear hitch location about vehicle-fixed y-axis	Computed	N·m
		Mz			Hitch moment at the rear 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
MidlAxl	Lft	Disp	x		Middle left wheel displacement along the vehicle-fixed x-axis	Computed	m
			y		Middle left wheel displacement along the vehicle-fixed y-axis	Computed	m
			z		Middle left wheel displacement along the vehicle-fixed z-axis	Computed	m
		Vel	xdot		Middle left wheel velocity along the vehicle-fixed x-axis	Computed	m/s
			ydot		Middle left wheel velocity along the vehicle-fixed y-axis	Computed	m/s
			zdot		Middle left wheel velocity along the vehicle-fixed z-axis	0	m/s
	Rght	Disp	x		Middle right wheel displacement along the vehicle-fixed x-axis	Computed	m
			y		Middle right wheel displacement along the vehicle-fixed y-axis	Computed	m
			z		Middle right wheel displacement along the vehicle-fixed z-axis	Computed	m
		Vel	xdot		Middle right wheel velocity along the vehicle-fixed x-axis	Computed	m/s
			ydot		Middle right wheel velocity along the vehicle-fixed y-axis	Computed	m/s
			zdot		Middle right wheel velocity along the vehicle-fixed z-axis	0	m/s
	Steer	WhlAngRL			Middle left wheel steering angle	Computed	rad
		WhlAngRR			Middle 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
HitchF	Disp		x		Front hitch offset from axle plane along the vehicle-fixed x-axis	Input	m
			y		Front hitch offset from center plane along the vehicle-fixed y-axis	Input	m
			z		Front hitch offset from axle plane along the earth-fixed z-axis	Input	m
	Vel		xdot		Front hitch offset velocity along the vehicle-fixed x-axis	Computed	m/s
			ydot		Front hitch offset velocity along the vehicle-fixed y-axis	Computed	m/s
			zdot		Front hitch offset velocity along the vehicle-fixed z-axis	0	m/s
HitchR	Disp		x		Rear hitch offset from axle plane along the vehicle-fixed x-axis	Input	m
			y		Rear hitch offset from center plane along the vehicle-fixed y-axis	Input	m
			z		Rear hitch offset from axle plane along the earth-fixed z-axis	Input	m
	Vel		xdot		Rear hitch offset velocity along the vehicle-fixed x-axis	Computed	m/s
			ydot		Rear hitch offset velocity along the vehicle-fixed y-axis	Computed	m/s
			zdot		Rear hitch offset velocity along the vehicle-fixed z-axis	0	m/s
Pwr	Ext				Applied external power	Computed	W
	HitchF				Front hitch power	Computed	W
	HitchR				Rear hitch power	Computed	W
	Drag				Power loss due to drag	Computed	W
Geom	Disp		x		Trailer offset from axle plane along the vehicle-fixed x-axis	Input	m
			y		Trailer offset from center plane along the vehicle-fixed y-axis	Input	m
			z		Trailer offset from axle plane along the vehicle-fixed z-axis	Input	m
	Vel		xdot		Trailer offset velocity along the vehicle-fixed x-axis	Computed	m/s
			ydot		Trailer offset velocity along the vehicle-fixed y-axis	Computed	m/s
			zdot		Trailer offset velocity along the vehicle-fixed z-axis	0	m/s
	Ang		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 yaw 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
		PwrFwMLx	Longitudinal force applied at the middle left axle power		Computed	W
		PwrFwMLy	Lateral force applied at the middle left axle power		Computed	W
		PwrFwMRx	Longitudinal force applied at the middle right axle power		Computed	W
		PwrFwMRy	Lateral force applied at the middle 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 — Trailer longitudinal velocity

scalar

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

ydot — Trailer lateral velocity

scalar

Trailer 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 the front wheels

scalar | array

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

Vehicle Track Setting	Description	Variable	Signal Dimension
Single 2-axle Single 3-axle	Normal force on the front axle	$$FzF=F{z}_f$$	Scalar – 1
Dual 2-axle Dual 3-axle	Normal force on the front wheels	$$FzF=\left[\begin{array}{cc}F{z}_{fl}& F{z}_{fr}\end{array}\right]$$	Array – [1x2]

FzM — Normal force on the middle wheels

scalar | array

Normal force on the middle wheels, Fz_M, along the vehicle-fixed z-axis, in N.

Vehicle Track Setting	Description	Variable	Signal Dimension
Single 3-axle	Normal force on the middle axle	$$FzM=F{z}_m$$	Scalar – 1
Dual 3-axle	Normal force on the right and left middle wheels	$$FzM=\left[\begin{array}{cc}F{z}_{ml}& F{z}_{rl}\end{array}\right]$$	Array – [1x2]

Dependencies

To enable this port, set Vehicle track to Single 3-axle or Dual 3-axle.

FzR — Normal force on the rear wheels

scalar | array

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

Vehicle Track Setting	Description	Variable	Signal Dimension
Single 2-axle Single 3-axle	Normal force on the rear wheel	$$FzR=F{z}_r$$	Scalar – 1
Dual 2-axle Dual 3-axle	Normal force on the rear wheels	$$FzR=\left[\begin{array}{cc}F{z}_{rl}& F{z}_{rr}\end{array}\right]$$	Array – [1x2]

Fhz — Normal component of hitch force on the body

scalar

Normal hitch force applied to the body at the hitch location, Fh_z, in the vehicle-fixed frame z-axis, in N.

If you enable the Hitch forces parameter, the block offsets the normal hitch force, Fh_z, with the value of the Fh input port component along the vehicle-fixed z-axis.

Parameters

Options

Vehicle track — Type of vehicle track

Dual 2-axle (default) | Single 1-axle | Dual 1-axle | Single 2-axle | Dual 3-axle

Use the Vehicle track parameter to specify the number of wheels.

Vehicle Track Setting	Implementation
Single 1-axle	Trailer with a single track and one axle. Forces act along the center line of the axle. No lateral load transfer.
Dual 1-axle	Trailer with a dual track and one axle. Forces act at the axle hard-point locations.
Single 2-axle	Trailer with a single track and two axles. Forces act along the center line of the axles. No lateral load transfer.
Dual 2-axle(default)	Trailer with a dual track and two axles. Forces act at the axle hard-point locations.
Single 3-axle	Trailer with a single track and three axles. Forces act along the center line of the axles. No lateral load transfer.
Dual 3-axle	Trailer with a dual track and three axles. Forces act at the axle hard-point locations.

Axle forces — Type of axle force

External forces (default) | External longitudinal velocity | External longitudinal 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, and 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

off (default) | on

Select to create input port WhlAngF.

Middle wheel steering — WhlAngM input port

off (default) | on

Select to create input port WhlAngM.

Dependencies

To enable this parameter, set Vehicle track to Single 3-axle or Dual 3-axle.

Rear wheel steering — WhlAngR input port

off (default) | on

Select to create input port WhlAngR.

Dependencies

To enable this parameter, set Vehicle track to Single 2-axle, Dual 2-axle, Single 3-axle, or Dual 3-axle.

External wind — WindXYZ input port

off (default) | on

Select to create input port WindXYZ.

External friction — Mu input port

off (default) | on

Select to create input port Mu.

Dependencies

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

• External longitudinal forces

• External forces

External forces — FExt input port

off (default) | on

Select to create input port FExt.

External moments — MExt input port

off (default) | on

Select to create input port MExt.

Front hitch forces — FhF input port

on (default) | off

Select to create input port Fh.

Front hitch moments — MhF input port

on (default) | off

Select to create input port Mh.

Rear hitch forces — FhR input port

off (default) | on

Select to create input port Fh.

Rear hitch moments — MhR input port

off (default) | on

Select to create input port Mh.

Initial longitudinal position — X_o input port

off (default) | on

Select to create input port X_o.

Initial yaw angle — psi_o input port

off (default) | on

Select to create input port psi_o.

Initial longitudinal velocity — xdot_o input port

off (default) | on

Select to create input port xdot_o.

Dependencies

To enable this parameter, set Axle forces to External longitudinal forces or External forces.

Initial yaw rate — r_o input port

off (default) | on

Select to create input port r_o.

Initial lateral position — Y_o input port

off (default) | on

Select to create input port Y_o.

Air temperature — AirTemp input port

off (default) | on

Select to create input port AirTemp.

Initial lateral velocity — ydot_o input port

off (default) | on

Select to create input port ydot_o.

Longitudinal

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

2 (default) | scalar

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

Number of wheels on middle axle, NM — Middle wheel count

2 (default) | scalar

Number of wheels on the middle axle, N_M. The value is dimensionless.

Dependencies

To enable this parameter, set Vehicle track to Single 3-axle or Dual 3-axle.

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

2 (default) | scalar

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

To enable this parameter, set Vehicle track to Single 2-axle, Single 3-axle, Dual 2-axle, or Dual 3-axle.

Vehicle mass, m — Vehicle mass

26000 (default) | scalar

Vehicle mass, m, in kg.

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

4 (default) | scalar

Distance from the vehicle CM to the front axle, a, in m.

Longitudinal distance from center of mass to middle axle, b — Distance from CM to middle axle

4.5 (default) | scalar

Distance from vehicle CM to middle axle, b, in m.

Dependencies

To enable this parameter, set Vehicle track to Single 3-axle or Dual 3-axle.

Longitudinal distance from center of mass to rear axle, c — Distance from CM to rear axle

5 (default) | scalar

Distance from vehicle CM to the front axle, c, in m.

Dependencies

To enable this parameter, set Vehicle track to Single 2-axle, Single 3-axle, Single 3-axle, or Dual 3-axle.

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

2 (default) | scalar

Vertical distance from vehicle CM to the axle plane, h, in m.

Longitudinal distance from center of mass to front hitch, dh_f — Distance to front hitch

7.5 (default) | scalar

Longitudinal distance from the center of mass to the front hitch, dh_f, in m.

Dependencies

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

Vertical distance from front hitch to axle plane, hh_f — Distance from front hitch to axle plane

0.6 (default) | scalar

Vertical distance from the front hitch to the axle plane, hh_f, in m.

Dependencies

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

Longitudinal distance from center of mass to rear hitch, dh_r — Distance to front hitch

7.5 (default) | scalar

Longitudinal distance from the center of mass to the rear hitch, dh_r, in m.

Dependencies

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

Vertical distance from front hitch to axle plane, hh_r — Distance from rear hitch to axle plane

0.6 (default) | scalar

Vertical distance from the rear hitch to the axle plane, hh_r, in m.

Dependencies

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

Initial inertial frame longitudinal position, X_o — Initial inertial X location

0 (default) | scalar

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

Initial longitudinal velocity, xdot_o — Initial velocity

0 (default) | scalar

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

Dependencies

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

• External longitudinal forces

• External forces

Lateral

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 from centerline to CM

0 (default) | scalar

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

Lateral distance from geometric centerline to front hitch, hl_f — Distance from centerline to front hitch

0 (default) | scalar

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

Dependencies

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

Lateral distance from geometric centerline to rear hitch, hl_r — Distance from centerline to rear hitch

0 (default) | scalar

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

Dependencies

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

Front track width, w_f — Front track width

1.82 (default) | scalar

Front track width, wf, in m.

Dependencies

To enable this parameter, set Vehicle track to Dual 2-axle, Dual 2-axle, or Dual 3-axle.

Middle track width, w_m — Middle track width

1.82 (default) | scalar

Middle track width, wm, in m.

Dependencies

To enable this parameter, set Vehicle track to Dual 3-axle.

Rear track width, w_r — Rear track width

1.82 (default) | scalar

Rear track width, wr, in m.

Dependencies

To enable this parameter, set Vehicle track to Dual 2-axle or Dual 3-axle.

Front axle tire corner stiffness, Cy_f — Front axle tire stiffness

12.3 (default) | scalar

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

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.

Middle axle tire corner stiffness, Cy_m — Middle axle tire stiffness

11.3 (default) | scalar

Middle tire corner stiffness, Cy_m, in N/rad.

Dependencies

To enable this parameter:

1. Set Vehicle track to one of these options:

   • Single 3-axle

   • Dual 3-axle

2. Set Axle forces to one of these options:

   • External longitudinal velocity

   • External longitudinal forces

3. Clear Mapped corner stiffness.

Rear axle tire corner stiffness, Cy_r — Rear axle tire stiffness

11.3 (default) | scalar

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

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. Clear Mapped corner stiffness.

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.

Middle tire(s) relaxation length, sigma_m — Relaxation length

.1 (default) | scalar

Middle tire relaxation length, σ_m, in m.

Dependencies

To enable this parameter:

1. Set Vehicle track to one of these options:

   • 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.

Middle axle slip angle breakpoints, alpha_m_brk — Breakpoints

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

Middle axle slip angle breakpoints, α_mbrk, 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.

Middle axle corner data, Cy_m_data — Breakpoints

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

Middle axle corner data, Cy_mdata, 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.

Initial inertial frame lateral displacement, Y_o — Position

0 (default) | scalar

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

Initial lateral velocity, ydot_o — Velocity

0 (default) | scalar

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

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 air pressure, Pabs — Pressure

101325 (default) | 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

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

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

Geometric lateral offset from center plane, latOff — Lateral offset

0 (default) | scalar

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

Geometric vertical offset from axle plane, vertOff — Vertical offset

0 (default) | scalar

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

Wrap Euler angles, wrapAng — Wrap the Euler angles to the interval [-pi, pi]

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 this interval, consider clearing 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 R2020a