CarSim Data

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CarSim Data Manual

Introduction This on-line manual is intended to help you understand the vehicle properties that must be defined to obtain accurate predictions of vehicle behavior using CarSim. Many of the model parameters and tables shown on the CarSim screens are described. The information included for model parameters includes:

� An explanation of the parameter and how it relates to measurable properties of the vehicle or related component.

� A discussion of the physical significance of the parameter and how it might affect vehicle behavior.

� The range of values that applies for many typical vehicles.

� Specific values associated with current or recently-sold vehicles.

Aerodynamics: Main Screen

Frontal Area (m2) Frontal area represents the cross-sectional area of the vehicle as viewed along its longitudinal axis.

Typical values are:

Small cars 1.6 – 1.8 m2

Intermediate cars 1.8 – 2.0 m2 Large cars 1.8 – 2.1 m2 SUVs 1.8 – 2.4 m2 Vans 2.3 – 2.8 m2

Values are given for a number of example vehicles in the table below.

© 2001 – 2004, Thomas D. Gillespie, Ph.D. and Mechanical Simulation Corporation. All rights reserved.

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Cars Pickup Trucks Vans & SUVs Year/Make Area

(m2) Year/Make Area

(m2) Year/Make

Area (m2)

1985 Oldsmobile Ciera 1985 Pontiac Fiero 1985 Pontiac Grand Am 1986 BMW 325i 1986 Buick Electra 1986 Buick Skylark 1986 Mazda 323 1986 Toyota MR2 1987 Chrysler Lebaron 1987 Ford Thunderbird 1987 Mercedes 190 1987 Nissan Sentra 1987 Plymouth Sundance 1987 Pontiac Lemans 1987 Subaru XT Coupe 1987 Toyota Camry 1987 Toyota Corolla FX 1988 Ford Mustang GT 1988 Ford Taurus 1988 Nissan Maxima

1.84 1.57 1.73 1.73 1.90 1.69 1.77 1.60 1.74 1.85 1.79 1.78 1.76 1.75 1.63 1.79 1.73 1.81 2.02 1.83

1979 Toyota Landcruiser 1982 Chevy C-20 P/U 1985 Ford F250 4x4 1985 Ford Ranger 1985 GMC C-15 Pickup 1985 Nissan Pickup 1987 Chevy C-15 P/U 1987 Dodge Dakota 1987 Dodge Raider 1987 Ford F150 1987 GMC 4x4 Sierra 1987 GMC Sierra 1987 Nissan Pathfinder 1987 Nissan Pickup XE 1987 Toyota LE

2.39 2.92 2.86 2.00 2.58 1.82 2.51 2.23 2.28 2.70 2.60 2.88 2.14 1.98 2.32

1983 Jeep CJ-7 1978 I.H. Scout 1983 Chevy Blazer 1983 Ford Bronco 1986 Jeep Cherokee 1987 Chevy Astro 1987 Chevy S10 Tahoe 1987 Ford Bronco II 1987 Jeep Cherokee 1987 Jeep Wrangler 1987 Nissan Van 1988 Dodge Caravan 1988 Ford Aerostar

2.30 2.36 1.82 2.90 2.11 2.78 2.10 2.25 2.09 2.42 2.37 2.31 2.57

Source: Garrott, Monk & Chrstos, SAE 881767

Reference Length for Aerodynamic Moments (mm) The equations for aerodynamic moments include characteristic dimensions of the vehicle used in defining moments (see SAE J1594, Vehicle Aerodynamics Terminology). Standard practice is to use the wheelbase of the vehicle as the reference length.

It is suggested that the wheelbase be entered as the value for this parameter, unless you have reason to use other choices.

X Distance (mm) This parameter defines the longitudinal position of the origin for computing aerodynamic reactions relative to the front axle. The common convention (see SAE J1594, Vehicle Aerodynamics Terminology) is to use the mid-wheelbase position. Thus, it should be set to a negative value equal to one-half of the wheelbase, unless you have reason to choose another value.


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Y Distance (mm) This parameter defines the lateral position of the origin for computing aerodynamic reactions relative to the vehicle centerline. A value of zero yields a symmetrical vehicle, which is the most common case. With a non-zero value, the aerodynamic reactions on the vehicle are offset from the centerline, creating an unsymmetrical vehicle.

Z Distance (mm) This parameter allows the aerodynamic reactions on the vehicle to be elevated above the ground plane. Most aerodynamic measurements on a vehicle are referenced to an origin in the ground plane, so this value should be set to zero unless you has reason to choose otherwise.

Table: Drag Coefficient vs. Slip Angle (-, deg) Aerodynamic drag is a longitudinal force acting on the vehicle at the aerodynamic origin, and is calculated from an equation of the following form (T. D. Gillespie, Fundamentals of Vehicle Dynamics, SAE, 1992):

DragForce =12

AirDensity • AirVelocity2 • DragCoefficient • FrontalArea

25201510500.3

0.4

0.5

0.6

Sideslip Angle

Dra

g C

oeffi

cien

t

Pickups

SUVs

Vans

Sedans

SportsCars

The drag coefficient is a dimensionless number that quantifies the efficiency with which the air flows over the vehicle. The coefficient is dependent on relative wind (sideslip)


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angle and the type of vehicle (see figure below). It is a minimum at zero angle and increases with sideslip angle up to 20 degrees. Above 20 degrees it gradually decreases to zero at 90 degrees.

Enter a table of drag coefficients versus slip angle. Typical values (T. D. Gillespie, unpublished data) for different kinds of vehicles are as follows:

Sedans 0.33 ± 0.03 increasing to 0.38 ± 0.04 at 20 degrees Sports cars 0.35 ± 0.03 increasing to 0.42 ± 0.02 at 20 degrees Pickup trucks 0.45 ± 0.03 increasing to 0.56 ± 0.04 at 15 degrees SUVs 0.42 ± 0.03 increasing to 0.52 ± 0.08 at 20 degrees Vans 0.36 ± 0.03 increasing to 0.44 ± 0.03 at 20 degrees

Examples are provided in CarSim.

Table: Side Force Coefficient vs. Slip Angle (-, deg) The aerodynamic side force is calculated from an equation of the following form (T. D. Gillespie, Fundamentals of Vehicle Dynamics, SAE, 1992):

SideForce =12

AirDensity • AirVelocity2 • SideForceCoefficient • FrontalArea

The side force coefficient is a dimensionless number that quantifies the magnitude of the lateral force imposed on the vehicle at the aerodynamic origin as a function of relative (slip) angle of the wind encountered by the vehicle. The coefficient is normally zero at zero wind angle, increasing linearly with angle up to 20 degrees (see figure below). At higher angles the coefficient may continue to increase.

25201510500.0

0.2

0.4

0.6

0.8

1.0

1.2

Sideslip Angle (deg)

Side

For

ce C

oeffi

cien

t

Sports CarsSedansPickups

Vans

SUVs


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Enter a table of side force coefficients versus slip angle. Typical values (T. D. Gillespie, unpublished data) for different kinds of vehicles are as follows:

Sedans 0 at zero angle increasing linearly to 0.67 ± 0.1 at 20 degrees Sports cars 0 at zero angle increasing linearly to 0.59 ± 0.03 at 20 degrees Pickup trucks 0 at zero angle increasing linearly to 0.6 ± 0.02 at 15 degrees SUVs 0 at zero angle increasing linearly to 1.0 ± 0.1 at 20 degrees Vans 0 at zero angle increasing linearly to 1.0 ± 0.15 at 20 degrees


Table: Lift Force Coefficient vs. Slip Angle (-, deg) Aerodynamic lift is a vertical force acting on the vehicle at the aerodynamic origin, and is calculated from an equation of the following form (T. D. Gillespie, Fundamentals of Vehicle Dynamics, SAE, 1992):

LiftForce =12

AirDensity • AirVelocity2 • LiftCoefficient • FrontalArea

The lift force coefficient is a dimensionless number that quantifies the magnitude of the vertical force imposed on the vehicle. It is sensitive to the relative (slip) angle of the wind encountered by the vehicle. The coefficient is normally small at zero wind angle, increasing in a parabolic form with angle up to 20 degrees (see figure below). Above this angle the coefficient can vary depending on the specific design of the vehicle.

25201510500.0

0.1

0.2

0.3

0.4

0.5

0.6


Lift

Coe

ffici

ent

Pickups

Sports Cars

Sedans

SUVsVans


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Enter a table of lift coefficients versus slip angle. Typical values (T. D. Gillespie, unpublished data) for different kinds of vehicles are as follows:

Sedans 0.15 ± 0.05 increasing parabolically to 0.57 ± 0.1 at 20 degrees Sports cars 0.05 ± 0.15 increasing parabolically to 0.5 ± 0.1 at 20 degrees Pickup trucks 0.19 ± 0.01 increasing parabolically to 0.43 ± 0.01 at 15 degrees SUVs 0.02 ± 0.02 increasing parabolically to 0.46 ± 0.13 at 20 degrees Vans 0.01 ± 0.02 increasing parabolically to 0.43 ± 0.04 at 20 degrees


Table: Rolling Moment Coefficient vs. Slip Angle (-, deg) The aerodynamic rolling moment acts about the longitudinal axis of the vehicle, and is calculated from an equation of the following form (T. D. Gillespie, Fundamentals of Vehicle Dynamics, SAE, 1992):

RollMoment =12

AirDensity • AirVelocity2 • RollMomentCoefficient • FrontalArea • Wheelbase

The roll moment coefficient is a dimensionless number that quantifies the magnitude of the moment imposed on the vehicle. It is sensitive to the relative (slip) angle of the wind encountered by the vehicle. The coefficient is normally zero at zero wind angle, increasing in a linear fashion with angle up to 20 degrees (see figure below). Above this angle the coefficient should continue to increase linearly.

25201510500.0

0.1

0.2

0.3


Rol

l Mom

ent C

oeffi

cien

t

Pickups

Sports Cars

Vans

SUVs

Sedans


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Enter a table of roll moment coefficients versus slip angle. Typical values (T. D. Gillespie, unpublished data) for different kinds of vehicles are as follows:

Sedans 0.0 increasing linearly to 0.15 ± 0.03 at 20 degrees Sports cars 0.0 increasing linearly to 0.13 ± 0.03 at 20 degrees Pickup trucks 0.0 increasing linearly to 0.14 ± 0.02 at 15 degrees SUVs 0.0 increasing linearly to 0.29 ± 0.04 at 20 degrees Vans 0.0 increasing linearly to 0.26 ± 0.08 at 20 degrees


Table: Pitching Moment Coefficient vs. Slip Angle (-, deg) The aerodynamic pitch moment acts about the lateral axis of the vehicle, and is calculated from an equation of the following form (T. D. Gillespie, Fundamentals of Vehicle Dynamics, SAE, 1992):

PitchMoment =12

AirDensity• AirVelocity2 • PitchMomentCoefficient • FrontalArea • Wheelbase

The pitch moment coefficient is a dimensionless number that quantifies the magnitude of the moment imposed on the vehicle. It is very sensitive to the pitch attitude of the vehicle and the relative (slip) angle of the wind encountered by the vehicle. The coefficient increases more or less in a linear fashion with wind (sideslip) angle up to 20 degrees (see figure below).

2520151050-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12


Pitc

h M

omen

t Coe

ffici

ent

Pickups

Sedans Vans

Sports Cars

SUVs


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Enter a table of pitch moment coefficients versus slip angle. Typical values (T. D. Gillespie, unpublished data) for different kinds of vehicles are as follows:

Sedans 0.01 ± 0.06 increasing linearly to 0.028 ± 04. at 15 degrees Sports cars 0.03 ± 0.1 increasing linearly to 0.05 ± 0.06 at 20 degrees Pickup trucks 0.03 ± 0.08 increasing linearly to 0.06 ± 0.07 at 15 degrees SUVs 0.08 ± 0.05 increasing linearly to 0.1 ± 0.05 at 20 degrees Vans 0.0 ± 0.03 increasing linearly to 0.03 ± 0.05 at 20 degrees


Table: Yawing Moment Coefficient vs. Slip Angle (-, deg) The aerodynamic yaw moment acts about the vertical axis of the vehicle, and is calculated from an equation of the following form (T. D. Gillespie, Fundamentals of Vehicle Dynamics, SAE, 1992):

YawMoment =12

AirDensity • AirVelocity2 • YawMomentCoefficient • FrontalArea • Wheelbase

The yaw moment coefficient is a dimensionless number that quantifies the magnitude of the moment imposed on the vehicle. It is very sensitive to the relative (sideslip) angle of the wind encountered by the vehicle. The coefficient increases in a diminishing fashion with wind (sideslip) angle up to 20 degrees (see figure below).

25201510500.0

0.1

0.2


Yaw

Mom

ent C

oeffi

cien

t

Pickups

Sports Cars

Vans

Sedans

SUVs

Enter a table of roll moment coefficients versus slip angle. Typical values (T. D. Gillespie, unpublished data) for different kinds of vehicles are as follows:


— 9 —

Sedans 0.0 increasing to 0.19 ± 0.01 at 20 degrees Sports cars 0.0 increasing to 0.15 ± 0.03 at 20 degrees Pickup trucks 0.0 increasing to 0.12 ± 0.02 at 15 degrees SUVs 0.0 increasing to 0.09 ± 0.02 at 20 degrees Vans 0.0 increasing to 0.17 ± 0.03 at 20 degrees


Brake System

ABS Control Settings The ABS Control Settings allow specification of a rudimentary Anti-Lock Brake System Control.

Slip OFF defines the wheel slip condition at which brakes are turned off (0 corresponds to free a rolling wheel speed, and 1 corresponds to lock up). This value is set at the slip condition above the point where the tire goes through its peak braking coefficient. The figure below shows a typical tire braking coefficient (Fx/Fz) on a dry, paved surface.

0 20 40 60 80 100

0.2

0.4

0.6

0.8

Wheel Slip (%)

Bra

king

Coe

ffici

ent

0

µs

µp

The purpose of the ABS is to turn the brakes off when tire slip exceeds that of the peak coefficient (µp), therefore the Slip OFF value would be set to a number greater than 0.2 for a tire like that illustrated in the figure above. Check the slip curves for the tires actually used on the simulated vehicle on the Tires: Longitudinal Force screen if necessary to set this parameter. For the brakes on the same axle, the left and right wheels are controlled independently.

Slip ON is the wheel slip condition at which the brakes are again turned on. A typical value would be less than 0.2 for a tire like that illustrated in the figure above. Check the slip curves for the tires actually used on the simulated vehicle on the Tires: Longitudinal


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Force screen if necessary to set this parameter. For the brakes on the same axle, the left and right wheels are controlled independently.

Note Mu-slip curves like that shown in the figure are typical of most tires on paved surfaces. On surfaces with loose materials, such as gravel or snow, the curve continues to rise throughout the slip range reaching a peak at 100% slip (locked-wheel sliding).

The ABS Cut-off Speed is the minimum vehicle speed for the ABS to function. When the absolute vehicle speed drops below this level, the ABS control is turned off and wheel lock is allowed. Normally it would be set at 10 km/hr or less. Average values are around 5 to 10 km/h.

Note To disable the ABS, set this speed to a high value (e.g., 1000).

Fluid Dynamics Time Constant These are the time constants associated with the fluid dynamics in each brake chamber. The time constant is one third of the time needed for the pressure to respond within 5% of the final value when subjected to a pure step input. For hydraulic brake systems (common to cars and light trucks) this value will be on the order of hundredths of a second (e.g., values like 0.0X, where X is a numerical value)\.

Fluid Transport Delay These are the times required for the fluid pressure variations from the brake input to reach the brake actuators on each axle. For hydraulic brake systems (common to cars) this value will be on the order of hundredths of a second (e.g., values like 0.0X, where X is a numerical value).

Brakes: Torque

Table: Torque vs. Pressure (N-m/Mpa) Tabular data for the magnitude of the brake torque developed as a function of application pressure in the wheel cylinder. Multiple curves are allowed for different initial speeds as brake torque performance is often speed sensitive due to thermal effects during operation.

The first value, in column 1 and row 1, is a placeholder. It must be present, but the value is not used. The remainder of the row lists the initial speeds that apply for each column. The first column under the placeholder lists the wheel cylinder pressure that applies to


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each row. All remaining numbers are values of brake torque magnitude as a function of pressure and speed.

Placeholder Speed 1 Speed 3 Speed 3 Speed …n Pressure 1 Brake Torque Brake Torque Brake Torque Etc. Pressure 2 Brake Torque Brake Torque Brake Torque Etc Pressure …n Brake Torque Brake Torque Brake Torque Etc

Typical brakes have a torque gain sufficient to allow lockup of the wheels on a dry road surface at maximum brake application pressure. Maximum pressure is on the order of 10 to 20 MPa depending on the vehicle. At 10 MPa the brake torque should be on the order of wheel load times the tire radius.

Negative values should not be entered into the table.

For values of pressure or speed that are higher than the range covered by the table, the simulation programs extrapolate the data in the table to calculate brake torque.

Brakes: Proportioning / Limiting Valve

Table: Delivery Pressure vs. Line Pressure The proportioning/limiting valve allows you to modify the pressure fed to either the front or rear brakes (or left and right) as pressure builds. For example, it can be used to simulate a pressure proportioning valve commonly used on cars and trucks. It also allows you to vary the proportioning as a function of load on the axle, simulating a load-sensing proportioning valve.

The table allows you to define the relationship between the line or supply pressure and the pressure delivered to the brake through the ABS controller. In the absence of an ABS it directly modifies the pressure fed downstream to the brakes through the fluid dynamics algorithm.

The first value, in column 1 and row 1, is a placeholder. It must be present, but the value is not used. The remainder of the first row lists the vertical loads that apply for each column. The first column below the placeholder lists line (supply) pressures that apply for each row. All remaining numbers are values of delivery pressure to the ABS control module.

Only positive (or zero) values should be entered into the table. Negative are not physically meaningful.

For values of line pressure or load that are higher than the range covered by the table, the simulation programs extrapolate the data in the table to calculate delivery pressure.


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Powertrain: Engine Defines the essential properties of the engine.

Rotational Inertial of Crankshaft (kg*m2) The rotational inertia of the engine represents the inertia of all the components that rotate with the engine crankshaft. This includes all components directly driven by the engine such as the torque converter impeller, alternator, power steering pump, air conditioner compressor, etc. During acceleration this adds to the effective mass of the vehicle that must be overcome by engine torque.

The inertia is related to engine size as measured by its displacement. Values should be in the following ranges:

2.5 liters displacement 0.14 – 0.21 kg-m2

4.0 liters 0.23 – 0.33 kg-m2 5.0 liters 0.31 – 0.45 kg-m2

Values can also be estimated (T. D. Gillespie, Vehicle Parameter Data, unpublished) using:

Automatic transmission: Inertia(kg − m2 ) = 0.0821 • Displacement(liters) 2 Manual transmission: Inertia(kg − m ) = 0.0573 • Displacement(liters)

Idle Speed (rpm) Engine idle speed is very important to a simulation run. It provides an initial speed for the engine at the beginning of the simulation. Typical idle speeds are 600 – 1000 rpm. Because of this feature the vehicle sitting stationary without the brakes applied will tend to “creep” forward just like an actual vehicle will.

Table: Engine Torque-Speed Map (N-m vs. rpm) This table specifies engine torque values as a function of speed and throttle position. Generic examples for a 2.5, 4.0 and 5.0 liter engine are provided in CarSim. As a general rule the power of the engine is in proportion to the vehicle mass. For cars the ratio is 1 kw/100 kg. “High-powered” sports cars may be twice that value, and while small, “under-powered” cars would be half that value.

Engine throttle position is specified as a fraction of wide-open throttle (WOP). The software interpolates between curves to actual engine operating condition using linear interpolation. The table format is as follows:

Row 1—0.0, values of engine throttle as a fraction of full throttle separated by commas Row 2—rpm, values of engine torque (N-m) at each throttle setting separated by commas Row 3—rpm, “ “ “ “ “ “ “ “ “ “ , etc.


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Powertrain: Torque Converter Defines the essential properties of the torque converter.

Table: Capacity Factor

The torque converter Capacity Factor defines the size or torque capacity of the converter that controls the amount of slip occurring. This parameter determines the speed to which the engine “revs” when the throttle is suddenly applied while the vehicle is stopped. It is defined as:

K =EngineSpeed(rpm)

EngineTorque(N − m)

The Capacity Factor goes to infinity as the ratio of output to input speed goes to unity. To make the graph easier to read, the table is a plot of the Inverse of the Capacity Factor. Thus, at unity speed ratio the plot goes to zero rather to a large number that distorts the scale of the plot.

The table format is as follows: Column 1— Speed ratios (-)

Column 2— 1/Capacity Factor ([N-m]2/rpm)

Examples are provided in CarSim for each of the engines in the library. Selection of an undersized torque converter will cause the engine to “rev” excessively on throttle application, so you should be sure to choose the torque converter identified for each engine.

Table: Torque Ratio The torque ratio defines the amount of torque amplification produced during slip. It is the ratio of converter output torque (into the transmission) to the input (engine) torque as a function of output-to-input speed ratio. At full slip (zero speed ratio) the amplification ranges from about 2.0 to 2.5. It decreases linearly to a value of 1.0 as the speed ratio approaches unity.

The table format is as follows:

Column 1— Output/input speed ratios (-) Column 2— Output/input torque ratios (-)

Examples are provided in CarSim for each of the engines in the library.

Inertial Properties – Input Shaft The moment of inertia measured at the input shaft of the torque converter.


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The inertia of this component (the torque converter impeller) is included with the engine moment of inertia. However, separate entries can be made at this point if desired.

Inertial Properties – Output Shaft The moment of inertia measured at the output shaft of the torque converter.

The inertia of this component (the torque converter turbine) is included with the transmission moment of inertia. However, separate entries can be made at this point if desired.

Powertrain: Transmission Defines the essential properties of the transmission.

Gear Ratios The gear ratios specify the numerical ratio between transmission input shaft speed and output (tail shaft) speed in each gear.

Gear ratios values generally follow these rules:

� First gear — Typically in the range of 2.4 to 4.25 for passenger cars

� Intermediate gears — Ratios of gears between first and direct drive have ratios close to geometric progression. I.e.,

FirstGearSecondGear

=SecondGearThirdGear

=ThirdGearFourthGear

...etc

� Direct drive — (1:1 ratio) For non-overdrive transmissions, this is the highest gear. For overdrive transmissions this is next to the highest gear.

� Overdrive — Highest gear is about 0.7 to 0.9 ratio.

� Reverse — Reverse gear ratio is equal (or sometimes slightly higher) than first gear. A negative ratio value is required.

Data on transmission gear ratios is available in the Bosch Automotive Handbook. Examples for some typical vehicles are shown in the table below.


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Make 1st gear 2nd gear 3rd gear 4th gear 5th gear Final drive Buick Park Avenue 2.92 1.57 1.00 0.70 2.84 Cadillac Seville Sedan 2.92 1.57 1.00 0.70 2.97 Chevrolet Caprice Sedan 3.06 1.63 1.00 0.70 2.56 Chrysler Voyager SE 2.84 1.57 1.00 0.69 3.47 Dodge Monaco 2.58 1.41 1.00 0.74 3.58 Ford Mustang GT 3.97 2.34 1.46 1.00 0.79 3.45 Ford Crown Victoria 2.40 1.47 1.00 0.67 3.08 Mercury Cougar LS 2.40 1.47 1.00 0.67 3.27 Oldsmobile Eighty-Eight 2.92 1.57 1.00 0.70 2.84 Pontiac Bonneville SSE 2.92 1.57 1.00 0.70 2.97 Toyota Camry 2.0 Gli 3.285 2.041 1.322 1.028 0.820 3.944 Toyota MR2 3.285 1.960 1.322 1.028 0.820 3.944 Toyota Supra Turbo 3.251 1.955 1.310 1.000 0.753 3.727 Saab 9000 CD 3.38 1.76 1.18 0.89 0.70 4.05 Volvo 960 2.80 1.53 1.00 0.75 3.73 Nissan Maxima 3.29 1.85 1.27 0.95 0.80 3.65 Mitsubishi Colt 1500 GLXi 3.363 1.947 1.285 0.939 0.777 4.021 Mazda RX-7 3.48 2.02 1.39 1.00 0.72 4.10 Mazda 323 1.6i GLX 3.42 1.84 1.29 0.92 0.73 4.11 Honda Civic 1.5i 3.250 1.894 1.259 0.937 0.771 4.250 Honda Accord 2.2i 3.307 1.809 1.230 0.933 0.757 4.266 Acura Legend 2.937 1.692 1.515 0.868 0.682 4.505 Jaguar XJ-S V12 Coupe 2.50 1.50 1.00 2.88 Volkswagen Golf GTI 3.46 2.12 1.44 1.13 0.91 3.67 Porsche 911 turbo 3.154 1.789 1.269 0.967 0.756 3.444 Mercedes-Benz 600 SEL 3.87 2.25 1.44 1.00 2.65 Ford Probe GT 3.250 1.772 1.194 0.926 0.711 4.100 BMW 535i 3.83 2.20 1.40 1.00 0.81 3.64 BMW 850i 4.25 2.53 1.68 1.24 1.00(0.83) 2.93

From Bosch Automotive Handbook.

Inertias (kg-m2) Moment of inertia of the rotating components in the transmission as measured at the input shaft. in each gear. The inertia value includes the torque converter turbine, unless the inertia is included in the torque converter input data. Values are less than 1.0 kg-m2. Very little good data is available on this parameter.


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Efficiencies-Natural The efficiency of the torque drive through the transmission in the driving direction (engine driving the wheels). The efficiencies are greater than 90%, or even 95% in the direct drive gear.

Efficiencies-Inverse The efficiency of the torque drive through the transmission in the coasting direction (wheels driving the engine). The efficiency in this direction is comparable to that in the driving direction.

Powertrain: Upshift Schedule Defines the conditions at which the transmission shifts to a higher gear (number).

Table: Speed (rpm) vs. Throttle (-) Defines the boundaries of transmission output shaft speed (rpm) and throttle position (-) at which the transmission shifts to a higher (lower numerical ratio) gear.

Each table is formatted as follows:

Column 1 — Throttle position (fraction of full throttle)

Column 2 — Transmission output shaft speed (rpm) at which shift is indicated.

Example shift tables are provided in CarSim. It is difficult for the casual user to synthesize these tables. But if necessary, use the rule of thumb that the full-throttle shift point should occur when the engine is at 80 – 90% of maximum rpm. The equivalent transmission output shaft speed is:

TransOutputSpeed (rpm) =0.9 • MaxEngineSpeed (rpm)

CurrentGearRatio

If in doubt, perform a full-throttle acceleration and check (on a plot of engine speed versus time) that the engine does not run to maximum rpm and they stay there without shifting promptly. If so the shift points need to be adjusted to lower speeds.

At low throttle (0 – 20%) the shift point should occur when the transmission output speed is approximately the engine idle speed divided by the current gear ratio. I.e.,

TransOutputSpeed (rpm) =EngineIdleSpeed (rpm)

CurrentGearRatio

The figure below shows a plot of the values for a typical up-shift table of a 5-speed transmission.


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1008060402000

1000

2000

3000

4000

5000

6000

Throttle (%)

Tran

smis

sion

Out

put S

peed

(RPM

)

1 - 2

2 - 3

3 - 4

4 - 5Example Upshift Table

Powertrain: Downshift Schedule Defines the conditions at which the transmission shifts to a lower gear (number).

Table: Speed (rpm) vs. Throttle (-) Defines the boundaries of transmission output shaft speed (rpm) and throttle position (-) at which the transmission shifts to a lower (higher numerical ratio) gear.

Each table is formatted as follows:

Column 1 — Throttle position (fraction of full throttle)

Column 2 — Transmission output shaft speed (rpm) at which shift is indicated.

Example shift tables are provided in CarSim. It is difficult for the casual user to synthesize these tables. But if necessary, use the rule of thumb that the off-throttle shift point should occur when the transmission output speed drops to the point that the input shaft speed is below engine idle rpm. The equivalent transmission output shaft speed is:

TransOutputSpeed (rpm) =EngineIdleSpeed (rpm)

CurrentGearRatio

The table below shows a plot of the up-shift and down-shift data for a typical 5-speed transmission.


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1008060402000

1000

2000

3000

4000

5000

6000

Throttle (%)

Tran

smis

sion

Out

put S

peed

(RPM

)

1 - 2

2 - 3

3 - 4

4 - 5

2 - 1

3 - 2

4 - 3

5 - 4

Powertrain: Differential Defines the essential properties of the differential.

Table: Torque Bias (N-m vs. rpm) The function of the differential is to allow each wheel on an axle to travel at a different speed when rounding a curve. In the absence of friction in the gears, the governing rules for differential operation are:

Torqueleft = Torqueright

Speedleft + Speedright

2

and

= FinalDriveRatio • DriveshaftSpeed

Free Differential — Ideally, a free differential would have no friction and would obey the above rules exactly. The example provided in CarSim exhibits no friction and acts like the ideal. In practice, the differential will exhibit some friction, nominally equal to 10 – 15% of the transmitted torque. A user can approximate this by putting a few hundred Newton-meters of torque in as a constant value. In that case, use negative torque with positive speed difference, and vice versa. Across zero it is helpful to give the line a small slope to minimize instability when the wheel are at the same speed.

Viscous Differential — A viscous differential incorporates a set of clutches between the left and right shafts immersed in a high-viscosity fluid. When the wheels attempt to operate at different speeds the viscous action transfers a torque (the bias torque) to the


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slow moving wheel. A typical viscous differential will develop a bias torque (N-m) that is about 10 times the speed difference (rpm).

Hydraulic Actuated Differentials — Some differentials incorporate a hydraulic pump between the axle shafts such that the speed difference creates a hydraulic pressure to actuate the clutches. These act much like the viscous differentials, although they may be designed to allow some speed difference to occur before actuating. Represent these by including a deadband of 10 – 20 rpm in which there is no bias torque.

Left - Right Wheel Speed (RPM)

Left

- RIg

ht T

orqu

e (N

-m) Viscous

Hydraulic

Lock

ed

Free with friction

Locking Differential — The differentials described above are sometimes called locking differentials. However, you can force the differential to lock by checking the Locked Differential box at the lower left of the screen. In this case, both wheels are forced to rotate at the same speed regardless of conditions.

Differential performance is characterized by the torque bias as a function of speed difference of the output shafts. The table format is as follows:

Column 1 — Speed difference between the two output shafts of the differential

(rpm)

Column 2 — Difference in the torque applied to each of the output shafts (N-m)

Examples of a free and a viscous differential are provided in CarSim.

Gear Ratios (-) The gear ratio of the differential is also known as the final drive ratio in most drivelines. The parameter defines the numerical ratio between the speed of the input shaft to the


— 20 —

differential and the average rotational speeds of the two driven wheels. Average ratios range between 2.5 and 4.5 (see Bosch Automotive Handbook). Example values for some actual vehicles are given in the table for Powertain: Transmission: Gear Ratios.

Efficiency Ratio: Natural (-) This parameter represents the efficiency of the differential when the engine is propelling (driving) the vehicle. It represents the loss of torque through the final drive, and is in the range of 90 – 95%.

Efficiency Ratio: Inverse (Coasting) This parameter represents the efficiency of the differential when the vehicle is coasting (wheels driving the engine). It represents the loss of torque through the final drive, and is in the range of 90 – 95%.

Spin Inertia: Drive Shaft (kg-m2) The spin inertia of the drive shaft is dependent on its mass and diameter. It is on the order of 0.0X, where X is any digit. In the case of a front wheel drive vehicle there is no driveshaft, so a zero value should be entered.

Spin Inertia: Half-Shaft to L Wheel (kg-m2) The spin inertia of the left half-shaft varies with the size of the vehicle and whether it is front or rear wheel drive. It is on the order of 0.00X, where X is any digit.

Spin Inertia: Half-shaft to R Wheel (kg-m2) The spin inertia of the right half-shaft varies with the size of the vehicle and whether it is front or rear wheel drive. In rear-wheel drive cars it is normally the same as the left. Due to asymmetry in the drive of a front-wheel drive system it may differ from that of the left. It is on the order of 0.00X, where X is any digit.

Steering System

Kinematics Kinematics defines the nominal ratio of angles between the steering wheel and the road wheels. This feature is provided to make it convenient to vary the steering ratio without having to make up separate tables for the individual wheels. That is, the nominal road wheel steer angle is simply the steering wheel angle divided by the kinematic ratio.


— 21 —

Typical front wheel steering ratios are:

Sports cars 16 to 18

Family sedans 18 to 21

Light trucks 20 to 24

For rear steer vehicles, higher ratios are commonly used so that the rear wheel angles are only a fraction of front wheel angles. Further, they will be limited to small angles (e.g., 3 degrees), and will depend on speed. This is particularly true on systems where the rear wheels steer out-of-phase at low speeds for enhanced maneuverability, and in-phase at high speeds for quicker handling.

To define the difference between steer angles of the inside and outside wheels, see the table on the screen Steering Systems: Kinematics for One Wheel. To set the speed sensitivity of a rear steer system, see the table on the screen Steering Systems: Rear-Wheel Gain.

Compliance Speed Limit to Prevent Instabilities As speeds drop to zero, calculation of the tire forces can become erratic due to difficulties in calculating slip. This in turn can cause steer angle fluctuations as the vehicle comes to a stop under some conditions. To avoid this, compliance effects are gradually reduced as the vehicle approaches a stop. This parameter sets the speed at which front and rear steering compliance is reduced in order to maintain stability of the steer angle calculations. The parameter can be set to 1 or 2 kph without significant error in the simulation.

Kingpin Geometry: Lateral Offset (mm) The lateral offset is the lateral distance between the steer axis and the wheel plane (center of the wheel) at the location of the spin axis. In order to fit in the brake hardware wheels must be offset outboard of the kingpin axis. This dimension is normally chosen so that the center of tire contact is close to the point where the kingpin axis intersects the ground. Because the brake forces acting on the moment arm of the offset at the ground produce a steering torque it is desirable to minimize this distance.

On front-wheel drive cars the center of tire contact will be zero to 10 mm inboard of the ground intercept. On rear-wheel drive cars it will be zero to 20 mm outboard of the ground intercept.

Kingpin Geometry: Inclination (deg) Inclination angle of the kingpin represents the lateral inclination of the steer rotation axis. Positive inclination corresponds to the axis being inclined inwards on the vehicle. Inclination angle falls in the range of 5 to 15 degrees. Vertical load on the tire acts on


— 22 —

inclination angle to produce a torque that always tries to steer the wheel to zero steer angle. Thus, vehicles with large inclination angles will take more effort to steer.

Kingpin Geometry: Xcoord of KP@center This parameter allows the wheel to be offset longitudinally to produce a mechanical caster trail. The wheel center (defined by its spin axis) passes through the kingpin axis, in which case the Xcoord is zero. In rare cases it may be up to about 10 mm. A positive value places the wheel spin axis behind the kingpin axis.

Kingpin Geometry: Caster Angle (deg) Caster angle of the kingpin represents the longitudinal inclination of the steer rotation axis. Positive caster corresponds to the axis being inclined backwards on the vehicle. Caster angle falls in the range of 0 to 8 degrees.

Positive caster moves the point at which the kingpin axis intersects the ground ahead of the center of tire contact. Lateral forces at the tire act on this longitudinal moment arm attempting to steer the wheels in their direction of travel, thereby reducing slip angle. On front wheels, positive caster is an understeer influence. On rear wheels it is oversteer.

Steering System: Rear-Wheel Gain

Table: Ratio of Rear Steer (-) vs. Vehicle Speed (kph) Rear-wheel steering systems are speed sensitive because the steer that improves maneuverability at low speeds would be unstable at high speeds. Conversely, the steer that improves high speed cornering response would reduce maneuverability at low speed. Therefore, the rear wheel steering gain is varied with speed.

In a typical system the rear wheels will be steered opposite to the front wheels at low speeds, albeit at a reduced ratio. Further, the rear steer angle will be limited to about 3 to 5 degrees. As speed increases the rear steer gain is reduced, reaching zero at about 25 kph, and transitions to in-phase steer as speed exceeds this value. At higher speeds the rear steer gain should only be a fraction of the front wheel angle, and again would be limited to small angles. (Note: If rear steer angles were made equal to front wheel angles, it would not be possible to change direction of the vehicle as needed to go around curves in the road.)


— 23 —

Steering System: Kinematics for One Wheel

Table: Steer at Ground (deg) vs. Gearbox Output (deg) These tables are used to convert the nominal road wheel steer angle (Steering Wheel Angle/Kinematic Ratio) to the left-right differences sometimes referred to as Ackerman Steer. Full or 100% Ackerman would be produced if the steer angles matched the relationships for the inside and outside wheels shown in the figure below. Since these are dependent on wheelbase, L, and track width, t, a table can be set up to match a given vehicle, and then the Kinematic ratio used to change the steering gain

L

t

δo i

Tur nCente r

R

δδA

δi = LR-t/2

tan-1

δo = LR+t/2 tan-1

δA = LR tan-1

The Ackerman steer angles for inside and outside wheels can be calculated from the nominal road wheel steer angle, δA as follows:

δleft = tan −1(L

L tanδA − t / 2) δright = tan −1(

LL tanδ A + t / 2

)

Note: The nominal steer angle, δA should be in degrees with positive angles being steer to the left. Also make sure the arc tangent is in degrees, not radians. A table of values using the equations above can be readily made up in a simple spreadsheet and pasted into the table.

Most steering systems on cars and light trucks only have 50% to 75% of Ackerman steer. If the table is a one-to-one ratio between gearbox output and steer at the ground, parallel steer is obtained. Fifty percent Ackerman means that the steer deviations in the table are 50% of the way between parallel steer and Ackerman.


— 24 —

Further deviations in the steer angle will be produced in the simulation as the force and moment reactions at the tires act on the compliances in the steering system.

Steering System: Compliance

Table: Steer Angle at Ground Due to Compliance (deg) vs. Kingpin Moment (N-m) The linkage connecting the steering wheel to the road wheels is compliant as illustrated in the figure below. Consequently, the actual road wheel steer angles do not exactly match that commanded from the steering wheel, but deviates slightly due to the kingpin moment caused by the forces and moments in the tire contact patch. This table allows definition of a non-linear compliance as a function of the torque imposed at the kingpin of each wheel. The same table is used for both the left and right wheels.

Kss Kss

To steering wheel

The compliance should have a magnitude no greater than 10/Fzs, where Fzs is the static load on the front wheel. E.g., for a typical car the value should be no greater than 0.001.

Steering Wheel Torque

Table: Torque ratio (-) vs. Steering Wheel Angle (deg) This table defines the ratio of steering wheel torque to total kingpin torque as a function of steering wheel angle. It is nominally equal to one over the steering ratio. However, it can be varied with angle to match the behavior of non-linear steering systems. In order to represent the inefficiency of a manual steering system it can be increased to the value one


— 25 —

over the efficiency. Or in the case of a power steering system, it can be decreased to replicate the influence of the power assist.

Suspension: Independent System

Track width (mm) Track width is the lateral distance between the centerlines of the left and right wheels on an axle.

Typical values fall in the range as follows:

Small cars 1360 – 1450 mm Intermediate cars 1450 – 1500 mm Large 1500 – 1575 mm Small SUVs 1300 – 1700 mm Large SUVs 1400 – 2000 mm

Roll Center Height (mm) Roll center height describes the height above the ground at which lateral forces from the wheels are reacted on the sprung mass (see illustration below). On independent suspensions an elevated roll center causes the tires to scrub sideways with suspension stroke. Thus, the roll center is designed to be close to the ground. For all vehicles with independent suspensions the roll center at normal ride position is in the range of 0 – 75 mm. When the height is elevated above the ground the lateral forces on the tires cause lift forces (jacking forces) to act on the sprung mass.

A

C

Fy Fy

Roll CenterHeight


— 26 —

Wheel Center Height (mm) The wheel center height is specified relative to the Sprung Mass Coordinate System. In effect this locates it relative to the sprung mass, such that any changes in tire radius move the wheel center up and down appropriately. When the vertical origin of the Sprung Mass Coordinate System is at ground level, this height is equal to the loaded tire radius.

Lateral Coordinate of Suspension Center (mm) Suspensions are not always perfectly symmetric on a vehicle. This coordinate allows the suspension center to be offset if desired.

Anti-dive Angle (-) Anti-dive angle describes the suspension reaction creating a vertical force within the suspension when it experiences a longitudinal force. The vertical reaction resists the tendency for the suspension to lift under forward load transfer in braking.

The angle is expressed in radians. A positive angle on the rear suspension creates anti-dive in braking. It also creates anti-squat in acceleration of a rear-wheel drive car. No anti-squat reaction is produced in the rear suspension of a front-wheel drive car.

A positive angle on the front suspension creates anti-dive in braking. It also creates anti-lift in acceleration of a front-wheel drive car. No anti-lift reaction is produced in the front suspension of a rear-wheel drive car.

Typical values range from 0.0 to 0.2.

Total Unsprung Mass (kg) The unsprung mass of a suspension is the total mass that moves with the wheel center. It consists of the wheel, spindle, brake, and approximately one-half of the mass of the moving suspension links. As a rule of thumb, the unsprung mass is approximately 10% of the total wheel load at the ground. For typical vehicles the values range from 35 to 50 kg for each wheel.

Spin Inertia of Wheel (-) The spin inertia of the wheel represents the inertia of the spinning components of the wheel — the tire, wheel, and the brake drum/rotor. Drive components attached to the wheel have separate entries for their inertia values. However, you can lump them all together at this point with no loss in simulation accuracy.

Values have been published (Metz, et al., SAE Paper 900760) for the inertia of tire/wheel assemblies, which are the major source of the inertia. The data is summarized in the table below.


— 27 —

Tire Size Mass (kg) Radius (mm Moment of Inertia (kg-m2) P165/80R13 (3 tires) 13.9 – 14.7 293.6 0.633 - 0.667 P185/80R13 14.5 293.6 0.652 P195/75R14 17.1 – 17.4 316.1 - 320.2 0.919 – 0.925 P205/55VR16 (3 tires) 17.5 – 18.2 316.3 – 320.9 0.921 – 1.067 P205/60HR14 19.3 308.3 0.988 P205/75R15 19.7 – 22.3 336.0 – 341.1 1.164 – 1.248

Ratios of Compression to Wheel Travel (-) The springs and shock absorbers within a suspension act through linkages that produce mechanical ratios between compression travel of the spring or shock and travel of the wheel. This parameter represents that ratio for each component.

For simplicity you can set this parameter to unity, in which case the spring force-deflection characteristics and the shock absorber force-velocity characteristics are applied directly at the wheel. Alternately, if you have specific information on the spring and shock absorber characteristics and wishes to enter them directly in their respective tables, it is necessary to specify these ratios. The spring and shock absorber ratios can be separate values as they may be mounted at different positions within the linkages.

These ratios normally fall within the range of 0.5 to 1.0. Note that the functional effect of a ratio is to change the characteristics of the spring or shock by the square of the ratio. That is, the spring rate at the wheel is the rate in the spring table multiplied by the square of the ratio.

This feature provides a convenient way to increase or decrease the rates of the springs and shocks. Remember that when the ratio is increased by 10% the effect of the spring or shock is increased by 21% (e.g. 1.12 = 1.21)

Toe vs. Fx (deg/N) The Toe vs Fx coefficient represents the compliance (deg/N) of the wheels in the steer direction to the imposition of a longitudinal (or tractive) force. A positive value corresponds to inward toe when force is applied to the tire in the forward direction.

Automotive designers necessarily keep this effect small, although it is not possible to keep it zero. The value can be of either sign (direction) but is generally not greater than 0.000X in magnitude, where X is a numerical value. Thus, the value entered should have at least three zeros after the decimal point to be reasonable in size.

Steer vs. Fy (deg/N) Steer vs. Fy represents lateral force compliance steer (deg/N). A positive value on the rear wheels causes understeer (i.e., a lateral force to the left causes the wheels to steer toward the left thereby reducing drift-out of the rear of the vehicle in a turn). A positive


— 28 —

value on the front wheels is an oversteer influence causing the wheels to steer more sharply into the turn.

For wheels that can be steered, the steer axis is inclined to intersect the ground in front of the center of tire contact. Thus, a positive lateral force (to the left), acting behind the steer axis usually causes some steer to the right (negative). Therefore, this coefficient is likely to have a small negative value for a steered wheel. For rear wheels, it should have a value close to zero.

The value can be of either sign (direction) but is generally not greater than 0.000X in magnitude, where X is a numerical value. Thus, the value entered should have at least three zeros after the decimal point to be reasonable in size.

Steer vs. Mz (deg/(N-m)) Steer vs. Mz is aligning torque compliance steer (deg/N-m) due both to compliance in the suspension and compliance in the steering system. The effect of this coefficient leads to a steering angle that is added to the steering due to other factors.

The suspension elements usually deflect when a steering torque is applied to the wheel. Because the steer and moment have the same sign convention, the compliance coefficient is positive. The value is generally not greater than 0.00X in magnitude, where X is a numerical value. Thus, the value entered should have at least two zeros after the decimal point to be reasonable in size.

Camber vs. Fx (deg/N) Camber is lateral inclination of the tire relative to the vertical plane of the vehicle. It is considered positive when the wheel leans outward at the top relative to the vehicle X-Z plane and negative when it leans inward. Camber may arise when longitudinal tire forces react through the suspension, as for example due to longitudinal forces reacting around the steer axis on a front axle. Camber vs. Fx can be of either sign (direction) but is generally not greater than 0.000X in magnitude, where X is a numerical value. Thus, the value entered should have at least three zeros after the decimal point to be reasonable in size.

Inclination vs. Fy (deg/N) Inclination is the lateral angle of the tire plane relative to the vertical, considered positive when the top of the tire leans to the right. This parameter arises from compliance in the suspension system when lateral forces at the ground cause the wheels to tip laterally. A positive lateral force (to the left) tends to bend the suspension and let the wheel incline to the right (positive inclination). Therefore, this parameter is expected to have a small positive value, usually not greater than 0.000X in magnitude, where X is a numerical value. Thus, the value entered should have at least three zeros after the decimal point to be reasonable in size.


— 29 —

Inclination vs. Mz (deg/(N-m)) Inclination is the lateral angle of the tire plane relative to the vertical, considered positive when the top of the tire leans to the right. This parameter arises from compliance in the suspension system when aligning moments cause the wheels to tip laterally. The value can be of either sign (direction) but is generally not greater than 0.00X in magnitude, where X is a numerical value. Thus, the value entered should have at least two zeros after the decimal point to be reasonable in size.

Roll Steer (w/o Jounce) (-) This parameter is the traditional roll steer coefficient. It quantifies steer when the chassis rolls about its longitudinal axis causing one suspension to move into compression (jounce) while that on the opposite side of the car moves into extensions (rebound). It is the average steer of the left and right wheels. (Differences between the left and right wheels are accounted for in the Toe vs. Jounce table that quantifies steer when both wheels of the suspension move the same amount vertically.)

Roll steer is dimensionless because it represents degrees steer per degree roll. Positive values on the front axle are oversteer. I.e., in a left hand turn the chassis rolls to the right (positive) causing the front wheels to steer into the turn (left is positive). Positive values on the rear axle are understeer because the rear wheels steer into the turn. The value can be of either sign (direction) but is generally not greater than 0.0X in magnitude, where X is a numerical value. Thus, the value entered should have at least one zero after the decimal point to be reasonable in size.

Suspension: Spring

Table: Spring Force (N) vs. Compression (mm) This table is used to represent the force characteristics of the spring as a function of its deflection. Zero compression corresponds to the normal position within the stroke when the suspension is at its design curb load. Going in either direction the force increases or decreases until the suspension reaches the limits of its stroke. At these extremes it encounters “bump stops” that limit the suspension travel. The bump stops are elastic elements that prevent direct metal to metal contact of the linkages with the limiting hardware. When into the bump stops the suspension spring rate increases by a factor of 10 or more.

The spring stiffness in the vicinity of zero compression should be such that the rate at the wheel produces a natural frequency of 1 - 1.5 Hz. To ensure an appropriate rate, determine the mass (kg) carried on the suspension (the wheel load minus the unsprung mass). Then check that the stiffness at the wheel (wheel rate) is approximately in the range shown in the equation below.


— 30 —

0.04 • Mass(kg) ≤ WheelRate(N / mm) ≤ 0.09 • Mass(kg)

If the Ratio of Compression to Wheel Travel for the suspension is not unity, the wheel rate must be corrected to a spring rate. The correction is as follows:

SpringRate(N / mm) =WheelRate(N / mm)

(RatioOfCompression)2

The spring table allows for different force-deflection curves in the compression (jounce) and extension (rebound) directions. The force difference between the two curves creates hysteresis or “stiction” in the suspension. This is a very practical consequence of the movement of the linkages that can affect vehicle performance. The magnitude of the force difference between the curves at zero compression should be no more than 5 to 10% of the nominal spring force at this point.

Compression Envelope This represents the force vs. deflection that would be measured while the spring is moving in compression (jounce). The Compression Envelope forces are higher than the Extension Envelope forces at any displacement position due to friction in the suspension resisting its motion.

Extension Envelope This represents the force vs. deflection that would be measured while the spring is moving in extension (rebound). The Extension Envelope forces are lower than the Compression Envelope forces at any displacement position due to friction in the suspension resisting its motion.

Characteristic Deflection (mm) As the suspension reverses direction operating between the two spring curves the force tends to transition between the curves with a first order lag on displacement. The sharpness of the transition can be adjusted by specification of the characteristic deflection. Values of a few millimeters are appropriate to most suspensions.

Suspension: Shock Absorber

Table: Shock force (N) vs. Compression rate (mm/s) The shock table of force versus compression rate characterizes the shock absorber damper. It is a two-column table of shock absorber compression rate (speed) and damping force. Each line should have a value of compression rate followed by a corresponding value of force, with a separating comma. Values are positive for increasing


— 31 —

compression and negative for extension (rebound). Positive force is applied upward on the body and downward on the wheel.

In general, the rate is nonlinear with the largest slope across zero, then diminishing at higher velocities. In addition, it is common to have the shock damping force in the compression direction (positive rate) only about half its value in the extension (negative rate) direction. The lower forces in the compression direction prevent sharp bumps from being transmitted to the sprung mass, while allowing for the necessary dissipation of energy when the suspension is extending.

The shock absorber should produce damping that is in the range of 30 - 40% of critical. Critical damping is given by the equation:

CriticalDamping = 4 • WheelRate • SprungMass

The slope of the line on the graph represents the damping coefficient. To ensure an appropriate coefficient, determine the mass (kg) carried on the suspension (the wheel load minus the unsprung mass). Then determine the vertical stiffness of the suspension at the wheel (the wheel rate). Check that the damping coefficient at the wheel is approximately in the range shown in the equation below.

0.0019 WheelRate(N / mm) • Mass(kg) ≤ DampingCoefficientatWheel(N / mm / s)

≤ 0.0025 WheelRate(N / mm)• Mass(kg)If the Ratio of Compression to Wheel Travel for the suspension is not unity, the damping coefficient at the wheel must be corrected to the coefficient (slope) in the shock table. The correction is as follows:

ShockTableSlope(N / mm / s) =DampingCoefficientatWheel(N / mm / s)

(RatioOfCompression)2

Since shock tables are normally nonlinear and asymmetric, the rules above are only guidelines. The slope across zero should be at the high end of the damping range, and lower at the extremes (above 500 mm/s). If the vehicle body is observed to oscillate continually during maneuvers or over bumps, the damping is probably too low.

Examples of typical shock tables are provided in CarSim.

Suspension: Auxiliary Roll Moment

Table: Auxiliary Roll Moment (N-m) vs. Suspension Roll (deg) This is tabular data representing the suspension auxiliary roll moment. The first value, in column 1 and row 1, is a placeholder. It must be present, but the value is not used. The remainder of the first row lists the vertical loads that apply to each column. The column below the placeholder lists the roll angles that apply for each row. All remaining numbers


— 32 —

are values of auxiliary roll moment as a function of roll and load. I.e., the table is of the form:

Placeholder Load 1 Load 3 Load 3 Load …n Roll Angle 1 Moment Value Moment Value Moment Value Etc. Roll Angle 2 Moment Value Moment Value Moment Value Etc Roll Angle …n Moment Value Moment Value Moment Value Etc

The auxiliary roll stiffness reflects the influence produced by a stabilizer bar. The suspension provides the baseline roll stiffness of the vehicle. For an independent suspension the stiffness is:

RollStiffness(N − m / deg) =WheelRate(N / mm) • TrackWidth2 (mm2 )

114,600

Auxiliary roll stiffness can be specified in this table as a nonlinear function, although it is relatively linear on actual vehicles. The general magnitude of the auxiliary roll stiffness should not be much more than the baseline provided by the suspension.

As a rule of thumb, typical cars have a roll rate of about 5 degrees per “g” of lateral acceleration. Adding auxiliary roll stiffness to the front suspension tends to induce more understeer. Adding it to the rear suspension tends to reduce understeer.

For values of load or roll angle that are higher than the range covered by the table, the simulation programs extrapolate the data in the table to calculate the roll moment value.

Suspension: Toe Angle

Table: Toe Angle (deg) vs. Suspension Compression (mm) Two-column table of values of wheel toe angle as a function of suspension compression. Each line should have a value of jounce followed by a corresponding value of toe angle, with a separating comma. Negative jounce corresponds to suspension extension from the zero point. The zero point is determined by you.

The sign convention for suspension travel (labeled Suspension compression on the screen) is that a positive value corresponds to suspension jounce. Negative values correspond to suspension extension from the zero point. The sign convention for toe-in in CarSim is positive and toe-out is negative. The zero point is determined by you on the Suspension: Independent Suspension screen. Two choices are offered. Specify jounce at design load causes the suspension travel to be measured with zero at the design load suspension position. Define jounce from spring data causes suspension travel to measured with zero at zero spring deflection (zero load).


— 33 —

Suspension: Camber Angle

Table: Camber Angle (deg) vs. Suspension Compression (mm) This table allows non-linear description of wheel camber versus suspensions stroke. Positive camber corresponds to inclination of the wheel plane outward from the vehicle. Positive suspension travel corresponds to compression or jounce. You are free to choose the zero point, which is taken to be the normal ride position (at curb weight) or suspensions mid-stroke. Specify jounce at design load causes the suspension travel to be measured with zero at the design load suspension position. Define jounce from spring data causes suspension travel to measured with zero at zero spring deflection (zero load).

Each line should have a value of jounce followed by a corresponding value of camber angle, with a separating comma.

Tires

Rolling Radius The tire rolling radius establishes the relationship between tire rotational speed and vehicle speed (in the absence of slip). The rolling radius can be estimated from the tire size imprinted on the sidewall. The meaning of the terms in the tire size designation are shown in the figure below.


— 34 —

P225/60R16 93Z

Section Width (mm)

Aspect Ratio

Rim Diameter

(in)

Speed RatingApplication

P - Passenger T - Temporary LT - Light truck

ST - Trailer service AT - All terrain vehicles

Speed Rating S - 180 km/h (112 mph) T - 190 km/h (118 mph) U - 200 km/h (124 mph) H - 210 km/h (130 mph) V - 240 km/h (149 mph) W - 270 km/h (168 mph) Y - 300 km/h (186 mph) Z - above 300 km/h

Tire Size Designation

Construction R - Radial B - Bias

Load Index

WidthHeight

Aspect Ratio = HeightWidth

The radii of some example tires are given in the table below. If no data are available for the tire of interest, the radius can be estimated from the size designation using the formula:

Radius(mm) =12.7 • RimDiameter(in) + SectionWidth•AspectRatio

100


— 35 —

Passenger Car Tires – Size, Maximum load at 240 kPa, and Radius Tire Size Load

(kg) Radius (mm)

Tire Size Load (kg)

Radius (mm)

Tire Size Load (kg)

Radius (mm)

P165/70R13 425 281 P245/60R15 795 337 P205/50R17 560 319 P185/70R13 515 295 P265/60R15 915 349 P215/50R17 600 324 P205/70R13 615 309 P295/60R15 1090 367 P235/50R17 690 334 P185/70R14 545 308 P205/60R16 615 326 P255/50R17 800 344 P205/70R14 650 322 P215/60R16 670 332 P255/50R18 825 356 P225/70R14 760 336 P225/60R16 730 338 P205/40R16 437 285 P245/70R14 880 350 P235/60R16 775 344 P215/40R17 437 302 P185/70R15 570 320 P285/60R16 1090 374 P245/40R17 530 314 P205/70R15 680 334 P175/50R13 355 253 P275/40R17 750 326 P225/70R15 795 348 P215/50R13 495 273 P285/40R17 800 330 P245/70R15 920 362 P235/50R13 575 283 P215/40R18 450 314 P265/70R15 1060 376 P245/50R13 620 288 P235/40R18 515 322 P215/70R16 775 354 P205/50R14 487 281 P255/40R18 600 330 P235/70R16 900 368 P225/50R14 560 291 P275/40R18 670 338 P255/70R16 1030 382 P245/50R14 650 301 P315/40R18 820 354 P275/70R16 1180 396 P195/50R15 462 288 P255/40R19 615 343 P185/60R13 450 276 P215/50R15 545 298 P245/40R20 600 352 P205/60R13 535 288 P245/50R15 680 313 P295/40R20 825 372 P235/60R13 675 306 P275/50R15 830 328 P285/35R17 560 316 P185/60R14 475 289 P305/50R15 995 343 P335/35R17 730 333 P205/60R14 560 301 P325/50R15 1110 353 P215/35R18 365 303 P225/60R14 660 313 P195/50R16 487 301 P255/35R18 475 317 P245/60R14 760 325 P215/50R16 580 311 P275/35R18 545 324 P265/60R14 875 337 P235/50R16 670 321 P295/35R18 615 331 P185/60R15 500 301 P255/50R16 765 331 P215/35R19 387 311 P205/60R15 590 313 P275/50R16 875 341 P275/35R20 580 350 P225/60R15 690 325 P295/50R16 975 351 P335/30R18 690 329

Data from 2001 Yearbook, The Tire and Rim Association, Inc., Copley, Ohio


— 36 —

Light Truck Tires – Size, Maximum load at 240 kPa, and Radius Tire Size Load

(kg) Radius (mm)

Tire Size Load (kg)

Radius (mm)

Tire Size Load (kg)

Radius (mm)

LT215/85R16 1215 386 LT255/75R15 381 LT245/70R17 1360 388 LT255/85R16 1360 420 LT205/70R14 925 322 LT265/70R17 1450 402 LT175/75R14 560 309 LT215/70R14 730 329 LT285/70R17 1450 416 LT185/75R14 615 317 LT245/70R15 925 362 LT315/70R17 1450 437 LT195/75R14 775 324 LT265/70R15 1030 376 LT245/65R15 850 349 LT215/75R14 750 339 LT315/70R15 1320 411 LT245/65R17 925 375 LT195/75R15 690 336 LT215/70R16 800 354 LT325/60R15 950 385 LT205/75R15 875 344 LT235/70R16 900 368 LT285/60R16 1030 374 LT215/75R15 950 351 LT255/70R16 1120 382 LT285/60R17 1060 387 LT225/75R15 1000 359 LT275/70R16 1360 396 LT345/55R16 1250 393 LT235/75R15 1150 366 LT315/70R16 1400 424 LT345/55R17 1285 406

Data from 2001 Yearbook, The Tire and Rim Association, Inc., Copley, Ohio

Spring Rate The tire is assumed to act like a simple vertical spring connecting the unsprung mass to the ground. If the stiffness is not known, it can be estimated based on the fact that a tire at its rated load will experience a deflection of approximately 25 mm. That is, the estimated stiffness is:

TireStiffness(N / mm) =Load(N)25(mm)

Maximum Allowed Force The maximum allowed force sets a limit to the tire force in order to avoid instability in the calculations. A value on the order of 20 times the tire load is reasonable.

L for Fx When a tire experiences longitudinal slip it must roll forward a distance while the longitudinal force builds. The lag potentially affects the dynamics of ABS operation. This distance is on the order of a fraction of the tire contact length.

L for Fy and Mz When the tire experiences a slip angle it must roll forward a distance known as the “relaxation length” while the lateral force builds up. The associated dynamic lag affects


— 37 —

responsiveness in cornering. The phenomenon is caused by lateral compliance of the tire carcass. The typical distance is on the order of 1/3 to 1/2 of a revolution.

Spin Inertia If separate data are available on the spin moment of inertia of the tire it can be entered here. However, it is often included in the spin inertia for the wheel on the Suspension screen, in which case a value of zero should be entered here.

Including the inertia here allows you to switch tires in the simulation and have the inertia of the rotating tire/wheel assembly change automatically. The spin inertias for some typical tires are given in the table below. The radius of gyration of most common tires is in the range of 87 – 90% of the tire radius. Thus, lacking other information you can estimate the inertia as follows:

SpinInertia(kg − m2 ) = Mass(kg)[0.9 • TireRadius(mm)]2

Spin Inertia Values for a Sample of Tires Tire Size Mass (kg) Radius

(mm) Inertia (kg-m2)

Tire Size Mass (kg)

Radius (mm)

Inertia (kg-m2)

2.25-14 1.02 236.0 0.056 P195/75R14 4 319.4 0.723 4.10-18 3.68 317.1 0.291 P205/60HR15 4 300.7 0.744 5.10-18 5.92 338.6 0.533 205/55VR16 .03 305.7 0.849

130/90-17 6.83 325.6 0.584 L78-15 6 353.7 1.170 130/90-16 6.98 312.3 0.525 DR78-14 6 310.3 0.625 25x12-9 7.94 268.0 0.239 26x15.0-13 1.6 322.1 0.963

150/90-15 8.22 317.8 0.665 225/50VR16 10.86 304.5 0.828 P165/80R13 5.70 287.5 0.371 P215/75R15 5 344.6 0.970 185/70SR13 7.40 289.8 0.492 P215/75R15 11.06 344.1 0.994 185/70GR13 7.48 290.0 0.508 P225/75R15 11.79 353.0 1.108 P195/75R14 7.14 311.8 0.534 P225/75R15 12.19 353.2 1.157 P145/75R14 9.64 318.3 0.734 P235/75R15 13.66 358.8 1.316 P185/75R14 9.13 309.7 0.686 P235/75R15 13.55 358.2 1.326 P185/75R14 9.50 310.8 0.726 12-16.5LT 25.43 381.3 2.880

Source: Metz, et al., SAE Paper 900760

Animator Settings The animator settings control the appearance of the wheel in animator playback. The tire width should be approximately equal to the Section Width of the tire to create a proper appearance. The Color setting allows you to select a color by name among the choices of: white, red, magenta, yellow, green, blue, light gray, dark gray or black. The number of points per polygon determines the number of circumferential segments used to generate the wheel image. A choice of 12 creates a reasonable tire appearance. Use of a larger number will improve the appearance, but may slow down the animation playback speed.


— 38 —

Rolling Resistance Tire rolling resistance is a small force resisting the deformation as it rolls along the ground. Rolling resistance is equal to about 1% of the vertical load on the tire.

Rolling resistance is represented on this screen by two parameters. Rr_c is the low-speed value of rolling resistance that can range up to about 0.01. The second parameter, Rr_v (units are 1/km/h), allows you to increase rolling resistance with forward velocity. Its value should be such that the overall coefficient does not go over about 0.05 at the maximum operating speed of the vehicle. (On actual vehicles, a rolling resistance coefficient greater that this value would indicate a tire that will overheat with prolonged running and be destroyed.)

The effect of surface condition on rolling resistance may be adjusted by the road surface coefficient, Rc_surf, which is entered on the Road: 3D Surface screen. The road surface coefficient is usually taken to be 1.0 for paved surfaces in good condition. It may be increased to 1.2 for rough or highly textured roads, and to 1.5 for hot (soft) asphalt.

Low-Speed Threshold At high speed the tire model determines the forces in the ground plane based on the slip conditions in the longitudinal and lateral directions. As the speed approaches zero, slip becomes less well defined such that the tire model will fail as the vehicle comes to a stop. Thus, modified equations for simulating the tire have been created to deal with near-zero speed. The cut-off speed allows you to specify the speed condition at which the simulation transitions to the modified equations. A speed choice of about 15 km/h is appropriate here.

Tire: Longitudinal Force

Tire/ground Friction Coefficient for this Data Tire longitudinal force performance varies with the frictional properties of the surface on which it is tested. CarSim scales the force generating properties of a tire in accordance with the friction level of the surface. Therefore, the friction level of the test surface needs to be specified with the data. If known, enter it here as a decimal value. Lacking other information, for data acquired on a dry surface it can be assumed that the friction coefficient is 0.8. When longitudinal traction data is measured on a wet surface, the friction coefficient of the surface is normally reported with the data, because it can vary significantly on different surfaces.


— 39 —

Table: Longitudinal Force (N) vs. Slip Ratio (-) The table of longitudinal force versus slip ratio defines how fast the longitudinal force builds up as the tire slips along the roadway. Slip is defined as:

Slip(−) =ForwardVelocity − TireSurfaceVelocity

ForwardVelocity

where the tire surface velocity is its rotational speed times its radius. Zero slip corresponds to the tire rolling freely at its forward speed. When it is locked up the slip value is 1.0.

Over the first few percent slip, the longitudinal force buildup is linear. As slip ratio increases the longitudinal force eventually peaks out at around 15 to 2o% slip. Thereafter, it drops off eventually approaching the sliding coefficient of friction at lockup (1.0 slip ratio).

The format of the table for entering data should be as follows:

Row 1 — 0.0, Load1, Load2, Load 3, etc. Row 2 — 0.0, 0.0, 0.0, 0.0,…….. Row 3 — Slip ratio 1, Longitudinal force, Longitudinal force, Longitudinal force, … Row 4 — Slip ratio 2, Longitudinal force, Longitudinal force, Longitudinal force, …

etc.

Example data for some tires are provided in CarSim.

Tire: Lateral Force

Tire/ground Friction Coefficient for this Data Tire lateral force performance varies with the frictional properties of the surface on which it is tested. CarSim scales the force generating properties of a tire in accordance with the friction level of the surface. Therefore, the friction level of the test surface needs to be specified with the data. If known, enter it here as a decimal value. Lacking other information, for data acquired on a dry surface it can be assumed that the friction coefficient is 0.8. Data are not normally measured on a wet surface, which would have a lower coefficient of friction.

Table: Lateral Force (N) vs. Slip Angle (deg) The table of lateral force versus slip angle defines how fast the lateral force builds up as the tire slips sideways. Over the first few degrees, the buildup is linear with angle. This slope is called the cornering stiffness and is dependent on the tire load. The initial slope (cornering stiffness) should be in the following ranges:


— 40 —

Bias-ply tires 0.11•Load (N/deg) High-aspect ratio (≥70) radial tires 0.15•Load (N/deg) Low-aspect ratio (≤ 60) radial tires 0.30•Load (N/deg)

As slip angle increases the lateral force eventually peaks out at around 15 to 20 degrees of slip angle. Thereafter, it drops off eventually approaching the sliding coefficient of friction at 90 degrees slip angle.

The format of the table for entering data should be as follows.

Row 1 — 0.0, Load1, Load2, Load 3, etc. Row 2 — 0.0, 0.0, 0.0, 0.0,…….. Row 3 — Slip angle 1, Lateral force, Lateral force, Lateral force, …… Row 4 — Slip angle 2, Lateral force, Lateral force, Lateral force, …… etc.


Tire: Aligning Moment

Table: Aligning Moment (N-m) vs. Slip Angle (deg) The table of aligning moment versus slip angle defines how the aligning moment varies with slip angle and load. At zero degrees slip angle the aligning moment is zero. Over the first few degrees of slip angle, the buildup is linear with angle. As slip angle increases the aligning moment peaks in the 2 to 4 degree range of slip angle. Thereafter, it drops off eventually approaching zero at 90 degrees slip angle.

The format of the table for entering data should be as follows:

Row 1 — 0.0, Load1, Load2, Load 3, etc. Row 2 — 0.0, 0.0, 0.0, 0.0,…….. Row 3 — Slip angle 1, Moment, Moment, Moment, …… Row 4 — Slip angle 2, Moment, Moment, Moment, …… etc.


Tire: Camber Thrust Coefficient

Table: Camber Thrust Coefficient (N/deg) vs. Vertical Load (N) A tire that operates inclined sideways on a road produces a lateral force known as camber thrust as illustrated in the figure below. For the small camber angles at which tires operate the lateral force is proportional to camber angle and load. The rate at which camber thrust increase with camber angle is known as the camber coefficient, Cγ.


— 41 —

0 1 2 3 4 5 6 7 8 9

Camber Angle (deg)

0

50

100

150

200LateralForce(lb)

F = 1000 lb

Zero Slip Anglez

γ

The sign of the camber coefficient is negative because an inclination to the right (positive) produces a force to the right (negative). The coefficient is nominally equal to 1% of the vertical load for radial-ply tires, and about 2% of the vertical load for bias-ply tires.

Cγ

Enter values in the table representing load and camber coefficient. The value should be zero at zero load.

Vehicle: Assembly Clicking on the blue link under the word Vehicle on the Run Control screen takes you to the Vehicle Assembly screen. This is the screen where you assemble a vehicle by selection of various parameter sets (Sprung Mass, Aerodynamics, etc.) along with the subsystems representing the powertrain, brakes, steering, suspensions and tires.

Systems: Powertrain Four different powertrain options are available:

1. Speed control (min. powertrain) — This option defines the powertrain in terms of minimum parameters. The vehicle is propelled at the desired speed by applying torque to the front and/or rear wheels without simulating the engine, transmission or final drive. The Rear-drive Torque Ratio tells the simulation to apply the appropriate amount of drive torque to maintain speed throughout the simulation. A torque ratio of one represents a rear drive vehicle, while a value of zero causes all of the drive torque to be applied to the front wheels. Any other decimal fraction causes the drive torque to be split between front and rear wheels. The maximum power ensures that the simulation cannot apply unrealistically high levels of torque


— 42 —

to the wheels. In general, the maximum power should not be more than one kilowatt for each five kilograms of vehicle mass. This powertrain is used with all of the speed/acceleration options from the Runs screen. It is most useful for those users who want to run a simulation with the speed controlled, but without the necessity of assembling all the details necessary to describe a powertrain.

Eng

ine

Tran

s

Diff.

2. Front-wheel drive — Choosing this option causes the program to look for a powertrain defined on the Powertrain: Front-Wheel Drive screen. Drive torque is applied only on the front wheels. The program simulates operation of the engine, torque converter, transmission and final drive to determine the appropriate amount of torque to apply to the front wheels. It is necessary to specify a Throttle from Driver input table on the Runs screen to keep the vehicle moving. With no throttle input the vehicle will slow down, with powertrain drag included as one of the retarding factors.

Engine Trans Driveshaft Diff.

3. Rear-wheel drive — Choosing this option causes the program to look for a powertrain defined on the Powertrain: Rear-Wheel Drive screen. Drive torque is applied only on the rear wheels. The program simulates operation of the engine, torque converter, transmission and final drive to determine the appropriate amount of torque to apply to the rear wheels. It is necessary to specify a Throttle from Driver input table on the Runs screen to keep the vehicle moving. With no throttle input the vehicle will slow down, with powertrain drag included as one of the retarding factors.


— 43 —

Engi

ne

TransDriveshaft

Diff.

Diff. Driveshaft Transfer Case

4. 4-wheel drive — Choosing this option causes the program to look for a powertrain defined on the Powertrain: 4-Wheel Drive screen. Drive torque is applied to all four wheels. The program simulates operation of the engine, torque converter, transmission, transfer case and final drives to determine the appropriate amount of torque to apply to the front and rear wheels. It is necessary to specify a Throttle from Driver input table on the Runs screen to keep the vehicle moving. With no throttle input the vehicle will slow down, with powertrain drag included as one of the retarding factors.

Vehicle: Sprung Mass This screen defines the sprung mass dimensions and loading condition for the run. Values for many of these parameters for current production vehicles can often be found on the manufacturer’s web site under the general category of Technical Specifications.

Animation Reference Height (mm) The animation reference height scales the vertical dimension of the image used in the animator. To obtain the correct image size, enter the dimension from the bottom of the vehicle body to top of the roof. If it is desired to adjust the vertical image of an animator shape to represent a larger or smaller vehicle, this data entry can be used to do that.

Wheelbase (mm) Wheelbase is the longitudinal distance from the spin axis of the front wheels to that of the rear wheels when the wheels are aligned (steered) parallel to the longitudinal axis of the vehicle.

In the event you change the wheelbase, several other dimensions on other screens may also need changes, specifically:

� Aerodynamics Screen — the location of the origin for aerodynamic forces as these are usually referenced to the mid-wheelbase position, and the “reference length for moments” which is usually the wheelbase.


— 44 —

� Sprung Mass Screen — The longitudinal position of the sprung mass, as this affects the front-rear weight distribution on the vehicle.

� Also, a change in wheelbase often implies a change in the mass of the vehicle and the moments of inertia. These are not changed by the program, but must be adjusted by you if appropriate. Mass change is generally proportional to wheelbase change. The yaw and pitch moments of inertia change with the square of the wheelbase.

Typical values are:

Small cars 2300 – 2500 mm Intermediate cars 2500 – 2800 mm Large cars 2800 – 3050 mm Small SUVs 2000 – 3000 mm Large SUVs 2300 – 3300 mm

Values for some example vehicles are given in the following table.


— 45 —

Weights and Dimensions of 1998 U.S. Vehicles

Name Wheelbase

Front Track Rear Track Vehicle Mass (kg)

F. Axle to CG

CG Height

Chevrolet Astro 2821 1643 1659 2031 1298 736 Chevrolet Blazer 2718 1445 1405 1963 1216 653 Chevrolet C1500 3340 1610 1646 1932 1418 665 Chevrolet Lumina 2736 1511 1501 1583 1004 561 Chevrolet Metro 2365 1387 1359 879 965 534 Chevrolet S10 2750 1379 1387 1442 1169 604 Chevrolet Suburban 3339 1623 1623 2667 1721 752 Chevrolet Tahoe 2977 1626 1621 2537 1441 722 Chevrolet Tracker 2200 1387 1397 1193 1005 616 Chevrolet Venture 3047 1560 1603 1823 1255 668 Dodge 1500 3518 1687 1699 2265 1478 696 Dodge Caravan 2885 1595 1631 1730 1189 649 Dodge Dakota 3326 1524 1560 1818 1353 618 Dodge Durango 2936 1547 1575 2201 1296 682 Dodge Neon 2642 1458 1455 1244 954 507 Ford Club Wagon 3505 1768 1773 2529 1576 794 Ford Expedition 3025 1664 1664 2637 1459 777 Ford Explorer 2827 1481 1486 2018 1295 697 Ford F150 3517 1656 1651 2039 1465 701 Ford Ranger 2985 1486 1458 1548 1223 666 Ford Windstar 3076 1626 1603 1892 1193 648 Honda Civic 2621 1471 1468 1143 1038 513 Honda CR-V 2616 1534 1529 1545 1180 644 Isuzu Rodeo 2697 1514 1519 1849 1247 633 Jeep Grand Cherokee 2691 1486 1499 1805 1193 695 Mazda MPV 2811 1519 1537 1778 1250 651 Mazda Protégé 2601 1453 1461 1151 1005 522 Mercury Tracer 2494 1430 1435 1224 927 521 Nissan Frontier 2954 1405 1405 1554 1291 601 Nissan Pathfinder 2703 1494 1506 1966 1222 684 Nissan Sentra 2532 1478 1435 1204 959 520 Plymouth Grand Voyager 3040 1593 1621 1899 1288 659 Saturn SL 2598 1450 1430 1127 1044 534 Toyota 4Runner 2670 1499 1509 1906 1226 707 Toyota Tacoma 3101 1425 1438 1436 1356 568 Toyota Tercel 2375 1400 1659 1053 953 502

Source: R. Garrott, NHTSA. All dimensions are millimeters.


— 46 —

Height of Vehicle Sprung Mass C.G. Above the Ground (mm) The sprung mass is the portion of the car supported by the suspensions. It is equal to the curb weight of the vehicle, less the unsprung mass. The CG Heights listed in Table 1 are for the total vehicle (sprung plus unsprung masses). The CG for the sprung mass only, will be about 5% higher than the total vehicle numbers shown in the table.

The CG height is referenced to the Sprung Mass Coordinate System. Although the longitudinal location of the origin for the coordinate system is always the front axle location, you are free to select the vertical position. It could be ground, the wheel center, the bottom of the vehicle body, or the origin for CAD data. Most users will choose ground level, so that all other vertical dimensions (sprung mass CG height, roll center height, etc.) are measured from the ground. However, this feature is provided because it is convenient to vary certain vehicle properties quickly, For example, when the tire radius is increased the vehicle body is raised automatically. The vertical position of the Sprung Mass Coordinate System is also used on the Suspensions, Aerodynamics and Payload screens.

Typical values for the CG height above the ground on typical vehicles are:

Small cars 500 - 560 mm Intermediate cars 500 - 560 mm Large cars 500 – 560 mm Small SUVs 600 – 800 mm Large SUVs 600 – 800 mm

Values for some example vehicles are given in Table 1.

Lateral Coordinate of the Mass Center (mm) This dimension represents the lateral offset (along the y-axis) of the sprung mass center of gravity, a positive value indicating that the load is offset to the left side of the vehicle centerline.

On most vehicles the right to left load balance is within 5%, such that the lateral offset is less than 75 mm. It is normally assumed that the mass center of the vehicle is located on its centerline (zero lateral offset). However, this parameter can be used to explore the sensitivities of the vehicle to side-to-side load imbalance.

Distance of Mass Center Rearward of the Front Axle (mm) This dimension is the longitudinal distance of the sprung mass center of gravity rearward of the front axle (front wheel center). It is assumed that the vehicle is unladen, leaving it to you to add any desired loading to the vehicle in other parts of the program. However, it can be used to represent a loaded vehicle combination if so desired.

The longitudinal location of the sprung mass CG is responsible for establishing the static front and rear axle loads. But since it is often not known, we use the static axle weights to


— 47 —

determine the CG location. These axle weights are measured using scales available at many automotive facilities. Although weights are forces (Newtons), they are expressed in mass units (kilograms). This distance can be found from the following equation:

Distance(mm) = Wheelbase(mm)RearAxleWeight(Kg) − RearAxleMass(kg)

TotalVehicleWeight(kg) − TotalUnsprungMasses(kg)

Designers normally strive for 50/50 weight distribution, which would make this parameter 50% of the wheelbase. However, front engine vehicles tend to be front heavy, and rear engine vehicles rear heavy.

Typical values are:

Front engine, front wheel drive 35 – 45% of wheelbase Front engine, rear wheel drive 45 – 50% of wheelbase Rear engine, rear wheel drive 50 – 55% of wheelbase

Values for this dimension are available in Table 1 for a selection of vehicles.

Distance from Front Axle to Trailer Hitch (mm) This is the longitudinal distance from the center of the front axle to the center of the hitch. It is equal to the wheelbase, plus rear overhang (from the rear axle to the back of the bumper), plus the distance from the bumper to the center of the ball hitch.

Height of Trailer Hitch (mm) This is the height of the pivot point (center of the ball hitch) above the ground before the trailer is attached. The standard height of a ball hitch is 450 mm.

Lateral Coordinate of Hitch This coordinate allows the hitch to have a lateral offset from the vehicle centerline. Normally the hitch is on the centerline and the value is zero. A positive value puts the hitch on the left side of the vehicle centerline.

Sprung Mass (kg) This is the portion of the vehicle mass resting on the suspensions. It is equal to the total mass of the vehicle less the unsprung masses of each wheel. The mass values for some vehicles are given in Table 1. Since the unsprung masses are about 10% of the total mass, lacking any other information the sprung mass can be estimated as 90% of the values listed in Table 1.

Typical values should be in the range as follows:

Small cars 650 – 900 kg Intermediate cars 900 – 1300 kg


— 48 —

Large cars 1300 – 1750 kg Small SUVs 900 – 1600 kg Large SUVs 1600 – 3000 kg

Roll Inertia (kg*m2) The moment of inertia of the sprung mass about its longitudinal (roll) axis through the CG.

Typical values should fall in the ranges of:

Small cars 400 – 650 kg-m2

Intermediate cars 650 – 750 kg-m2

Large cars 750 – 1300 kg-m2 Small SUVs 250 - 650 kg-m2 Large SUVs 550 - 1400 kg-m2

Lacking other information, you can estimate the roll moment of inertia using the following equation from SAE Paper 881767 by Garrott, Monk & Christos:

RollMOI(kg − m2 ) = 0.25 • Mass • TrackWidth • RoofHeight

Roll Radius of Gyration (m) The roll radius of gyration is the effective radius of the sprung mass distributed about the roll axis of the vehicle. Specifying this parameter allows CarSim to estimate the roll moment of inertia. Thus, a value is not needed if the roll moment of inertia is known.

It is approximately equal to the product of one-half the width and one-half the height of the vehicle. CarSim estimates the roll moment of inertia from the following equation:

RollMOI(kg − m2 ) = Mass(kg) • RollRadius2(m2)

Typical values are:

Small cars 0.60 – 0.65 m Intermediate cars 0.63 – 0.70 m Large cars 0.67 – 0.83 m Small SUVs 0.48 – 0.68 m Large SUVs 0.52 – 0.69 m

Pitch Inertia (kg*m2) The moment of inertia of the sprung mass about its lateral axis at the CG location.


Small cars 1600 - 2500 kg-m2

Intermediate cars 2500 - 3800 kg-m2


— 49 —

Large cars 3800 - 6300 kg-m2 Small SUVs (< 1600 kg) 1000 - 3000 kg-m2 Large SUVs (> 1600 kg) 3000 - 8000 kg-m2

Lacking other information, you can estimate the pitch moment of inertia using the following equation from SAE Paper 881767 by Garrott, Monk & Christos:

PitchMOI(kg − m2 ) = Mass • a • b

where: a = Distance from front axle to CG

b = Distance from CG to rear axle

Pitch Radius of Gyration (m) The pitch radius of gyration is the effective radius of the sprung mass distributed about the lateral axis of the vehicle. Specifying this parameter allows CarSim to estimate the pitch moment of inertia. Thus, a value is not needed if the pitch moment of inertia is known.

It is approximately equal to the product of the distance from the front axle to the CG and the distance from the rear axle to the CG. CarSim estimates the roll moment of inertia from the following equation:

PitchMOI(kg − m2 ) = Mass(kg) • PitchRadius2(m2 )

Typical values are:


Yaw Inertia (kg*m2) The moment of inertia of the sprung mass about its vertical axis at the CG location.


Small cars 1600 - 2500 kg-m2

Intermediate cars 2500 - 3800 kg-m2

Large cars 3800 - 6300 kg-m2 Small SUVs 1000 - 3000 kg-m2 Large SUVs 3000 - 8000 kg-m2

Lacking other information, you can estimate the pitch moment of inertia using the following equation from SAE Paper 881767 by Garrott, Monk & Christos:

YawMOI(kg − m2 ) = Mass • a • b


— 50 —

where: a = Distance from front axle to CG

b = Distance from CG to rear axle

Yaw Radius of Gyration (m) The yaw radius of gyration is the effective radius of the sprung mass distributed about the vertical axis of the vehicle at the CG location. Specifying this parameter allows CarSim to estimate the yaw moment of inertia. Thus, a value is not needed if the yaw moment of inertia is known.

It is approximately equal to the product of the distance from the front axle to the CG and the distance from the rear axle to the CG. CarSim estimates the roll moment of inertia from the following equation:

YawMOI(kg − m2 ) = Mass(kg) • YawRadius2 (m2 )

Typical values are:


Product (kg-m2) The product of inertia allows you to specify a vehicle that is not symmetric about its axes. For most motor vehicles this is not significant, in which case a value of zero should be entered here.

CarSim Run Control This screen contains the basic information that defines a run—the vehicle, the control inputs, the test surface (located in the left hand column), and the simulation control information (located in the center column). The right hand column provides options to view the run results as animations or plots. If you are new to CarSim, you should probably look at the introductory material in the CarSim Quick Start Guide or the double-sided CarSim Cheat Sheet.

Speed/Acceleration This option in the Vehicle column lets you select how the speed should be controlled during the simulation. The options are as follows:


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� Initial speed (open-loop control) — This option sets the initial speed at which the run simulation begins. If there is no throttle input (next entry in the column) the vehicle will simply coast while the speed gradually reduces due to aerodynamic drag, rolling resistance of the tires, and scuffing of the tires if the vehicle does any cornering. This option is the preferred choice for braking tests where an initial speed is set and then the vehicle is allowed to brake without any powertrain interactions.

� Constant target speed — This option sets the initial speed and then attempts to hold the vehicle at the specified speed as long as there is no brake application (at which point the speed control would be disengaged). Torque is applied to the drive wheels in an attempt to maintain the speed within the constraints defined by the Powertrain selected on the Vehicle: Assembly screen. If a full powertrain is specified, varying throttle input will control the speed.

� Target speed vs. time — This option allows the vehicle speed to vary with time throughout the simulation. The speed profile (speed/time relationship) is defined in the table accompanying the selection of this option. Torque is applied to the drive wheels to achieve the speed profile within the constraints defined by the Powertrain selected on the Vehicle: Assembly screen. If a full powertrain is specified, varying throttle input will control the speed.

� Target speed vs. station — This option allows the vehicle speed to vary with location along the road. The speed profile (speed/station relationship) is defined in the table accompanying the selection of this option. Torque is applied to the drive wheels to achieve the speed profile within the constraints defined by the Powertrain selected on the Vehicle: Assembly screen. If a full powertrain is specified, varying throttle input will control the speed.

Run Math Model (Action Button) The dark blue box indicates an action button. Clicking on the box causes the math model to run with the simulation parameters from this and all the underlying screens. You have the option to simply run the simulation using CarSim, or to transfer control to a Simulink program.

Start Time (sec) The start time is any number (negative, zero or positive) that you choos to establish the time-base reference for the run. Normally it is set to zero. However, you might choose a non-zero value for reasons such as:

� To offset runs on time-based plots when multiple plots are going to be overlaid.


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� To shift the location on the test surface where a maneuver is performed when controlled by time-base throttle, brake or steering inputs.

� To allow the vehicle to come to equilibrium before starting a simulation at zero time. (Using a start time of –2 seconds will accomplish this.)

Stop Time (sec) The stop time is any number greater than the start time at which the simulation is to terminate. Simulation runs are normally at least 5 seconds long to allow the vehicle to accomplish some dynamic maneuver. Many are 30 seconds or more. Since the computation time is faster than real time on most computers, it is advisable to allow a generous amount of time for the maneuver to be completed.

Note that you can select an option just above the Time/Station entries to have the simulation stop either at a specified time or station. Choosing the “time or station” option causes the simulation to terminate when either the stop time or the stop station is reached.

Start Station (m) CarSim allows the simulation of vehicles driving along a road. Civil engineers define the distance along a road by “stations.” The start station simply tells the simulation the starting point on the road for the run.

Stop Station (m) Although simulation duration is often defined by time, it can also be defined by an end point on the road. The stop station serves this function.

� Depending on the direction of the run the stop station number may be larger or smaller than the start station number.

� On a closed course, once the vehicle completes one lap and arrives at zero station, all subsequent station numbers continue to increment upward (or downward if in the backward direction).

Driving Direction Station When the simulation is set to stop at specified time or station, the stop station displays the option for driving direction. Forward is in the direction of increasing station numbers. Backward is in the direction of decreasing station numbers.


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APPENDIX 1 — EPA Size Classifications Environmental Protection Agency Size Classifications for Motor Vehicles Sold in the U.S., YR 2000

2-Seaters Acura NSX Mercedes Benz SL500, SL600, SLK230 BMW M, Z3 and Z8 Plymouth Prowler Chevrolet Corvette Porsche Boxster Dodge Viper Toyota MR2 Mazda Miata MiniCompact Car (<85 cubic feet of passenger and luggage volume) Audi TT Mercedes Benz CLK320 BMW 323i Porsche 911 SubCompact Car (85 to 99 Cubic feet) Acura Integra Mercedes Benz CLK320, 430 BMW 323Ci Mitsubishi Eclipse Chevrolet Camaro, Cavalier, Metro Pontiac Firebird, Sunfire Ford Escort, Mustang Saturn SC Honda Civic, Prelude Subaru Impreza Hyundai Tiburon Suzuki Esteem, Swift Jaguar XK8 Toyota Celica Lexus Sc300 Volkswagen Cabrio, Beetle

Compact Car (100 to 109 cubic feet) Audi A4 Mazda Millenia, Protégé BMWE 323i, ew8i, 528i, 540i, M5 Mercedes Benz C230, C280, C43 AMG, CL500 Chevrolet Prizm Nissan Altima, Sentra Chrysler Sebring Oldsmobile Alero Dodge Avenger, Neon Plymouth Neon Ford Contour, Escort, Focus Pontiac Grand AM Hyundai Accent/Brio, Elantra Saturn SL Infinity G20 Subaru Legacy Jaguar XJ8, XJR Toyota Camry Solara, Corolla, Echo Lexus ES 300 Volkswagen Golf, GTI, Jetta Mercury Cougar, Mystique Volvo C70, S40

Mid-Size Car (110 to 119 cubic feet) Acura 3.2TL, 3.5RL Mercury Sable Audi A6, A8 Mazda 626 BMW 740i Mercedes Benz E320, E430, C55 AMG Buick Century, Regal Mitsubishi Diamante, Galant Cadillac, Catera, Eldorado, Seville Nissan Maxima


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Chevrolet Lumina, MonteCarlo, Malibu Oldsmobile Intrigue Chrysler Cirrus Plymouth Breeze Dodge Stratus Pontiac Grand Prix Honda Accord Saab 9-3, 9-5 Hyundai Sonata Saturn LS Infiniti I30, QA45 Toyota Camry Jaguar Vanden Plas, X200, Xj8L Volkswagen Passat Lexus GS 300, GS 400, LS 400 Volvo S70, S80 Lincoln LS

Large Car (120 cubic feet or more) Audi A8 Ford Crown Victoria, Taurus BMW 740IL, 750IL Lincoln Continental, Town Car Buick Lesabre, Park Avenue Mercury Grand Marquis Cadillac Deville Mercedes Benz S430, S500 Chevrolet Impala Pontiac Bonneville Chrysler 300 M, Concorde, LHS Toyota Avalon Dodge Intrepid

Station Wagon – Small (Less than 130 cubic feet) Audi A4 Avanti Saturn SW BMW 323i Touring, 528i Sport Wagon, 540i Sport Wagon Suzuki Esteem Hyundai Elantra Volvo V40

Station Wagon – Mid-Size (130 to 159 cubic feet) Audi A6 Avant Quattro Saab 9-5 Ford Focus, Taurus Saturn LW Lexus Rx300 Subaru Legacy Mercury Sable Volkswagen Passat Mercedes Benz E320 Volvo V70

Small Pickup (GVWR under 4500 lb) Chevrolet S10 Isuzu Hombre GMC Sonoma

Standard Pickup (GVWR of 4500 to 8500 lb) Chevrolet/GMC C1500, C2500 Mazda 2500, B3000, B4000 Dodge Dakota, Ram 1500 Nissan Frontier Ford F150, Lightning, Ranger Toyota Tacoma, Tundra Vans- Regular Chevrolet Astro Ford E150 Dodge B150, 2500 GMC Savana, Safari


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MiniVans Chevrolet Venture Nissan Quest Chrysler Town & Country Oldsmobile Silhouette Dodge Caravan Plymouth Voyager Ford Windstar Pontiac Montana Honda Odyssey Toyota Sienna Mazda MPV Volkswagen Eurovan Mercury Villager

SUVs BMW X5 Lexus LX 470 Cadillac Escalade Lincoln Navigator Chevrolet Blazer, Suburban, Tahoe, Tracker Mercedes Benz ML320, 430, 55 Dodge Durango Mercury Mountaineer Ford Explorer, Expedition Mitsubishi Montero, Nativa GMC Yukon, Jimmey Nissan Pathfinder, Xterra Honda CRV, Passport Oldsmobile Bravada Infiniti QX4 Subaru Forester Isuzu Amigo, Rodeo, Trooper Suzuki Grand Vitara Jeep Cherokee, Grand Cherokee, Wrangler Toyota 4Runner, Rav4, Land Cruiser Land Rover Discovery, Range Rover

APPENDIX 2 — Definitions For clarity, several jargon terms commonly used in the automotive industry need to be understood. Some are defined here to help the reader avoid confusion in specifying vehicle properties and parameters.

Axle weight means the total force on the ground from the two wheels at the front or rear axle positions when the vehicle is sitting statically on level ground. The distribution of weight between the front and rear wheels establishes the longitudinal location of the center of gravity for the total vehicle. It does not matter whether the two wheels are on a common axle or independently suspended. It is appropriate to use this term only when there is no reason to distinguish between left and right wheel loads (i.e., the center of gravity is on the centerline of the vehicle). Axle weight is given in units of pounds in the English system, and kilograms or Newtons in the metric system.

Axle load is the total force normal to the ground from the two wheels at the front or rear axle positions either statically or dynamically. Statically on level ground, axle load is the same as axle weight. However, axle load has a broader meaning as it may also be used to describe the force normal to the ground during dynamic conditions. That is, axle load may describe the forces when the vehicle is accelerating, subject to aerodynamic forces, or on a grade.


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Although it might appear that the name axle load could also refer to the load actually carried on the axle, that is not a common use. Rather, load carried on the axle would be referred to as suspension load. The term axle weight might also be used to describe the weight or mass of the axle or axle assembly. Again, that is not a common use, but would be referred to as axle (or unsprung) mass.

The terms wheel load and tire load also deserve comment. While both imply the load at the ground under a tire or tire/wheel combination, there are times they must be distinguished. The distinction is most important in the cases of heavy trucks with dual wheel assemblies. Tire load is best used to describe the load on an individual tire, such that each tire can be treated separately in a dual-wheel assembly. Wheel load is the total load associated with both tires in a dual-wheel assembly. That is, it represents the total load at that wheel position on the vehicle.

Curb weight (mass) is the weight or mass of the vehicle in the unloaded condition with all fluids at their full level.

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