output of suspension analyses

Running Analyses > Output of Suspension Analyses

Output of Suspension Analyses

Adams/Car analyses output the following general suspension characteristics for all suspensions:

• Aligning Torque - Steer and Camber Compliance

• Camber Angle

• Caster Angle

• Dive Braking/Lift Braking

• Fore-Aft Wheel Center Stiffness

• Front-View Swing Arm Length and Angle

• Kingpin Inclination Angle

• Kingpin Location

• Lateral Force - Deflection, Steer, and Camber Compliance

• Lift/Squat Acceleration

• Percent Anti-Dive Braking/Percent Anti-Lift Braking

• Percent Anti-Lift Acceleration/Percent Anti-Squat Acceleration

• Ride Rate

• Ride Steer

• Roll Camber Coefficient

• Roll Caster Coefficient

• Roll Center Location

• Roll Steer

• Side-View Angle

• Side-View Swing Arm Length and Angle

• Suspension Roll Rate

• Toe Angle

• Total Roll Rate

• Wheel Rate

For steered suspensions, Adams/Car analyses also output the following steering characteriscs:

• Ackerman

• Ackerman Angle

• Ackerman Error

• Caster Moment Arm (Mechanical Trail)

• Ideal Steer Angle

• Outside Turn Diameter

• Percent Ackerman

• Scrub Radius

• Steer Angle

• Steer Axis Offset

• Turn Radius

Aligning Torque - Steer and Camber Compliance

Note: This help file is shared by several Adams products.

Description The aligning torque steer compliance is the change in steer angle due to unit

aligning torque on the wheel. The aligning torque camber compliance is the

change in camber angle due to a unit aligning torque on the wheel.

A positive aligning torque acts to steer the wheel to the left. For a positive

steer angle, the wheel turns to the left. For a positive camber angle, the top

of the wheel tilts away from the body.

Units Angle/(Force*Length)

Request Names• alt_steer_compliance.left

• alt_steer_compliance.right

• alt_camber_compliance.left

• alt_camber_compliance.right

Method alt_steer_compliance.left = C(6,6) + C(6,12)

alt_steer_compliance.right = C(12,6) + C(12,12)

alt_camber_compliance.left = C(4,6) + C(4,12)

alt_camber_compliance.right= -C(10,6) + C(10,12)

Figure 1 Aligning Torque Loading for Steer and Camber

Compliances

Camber Angle


Description Camber angle is the angle the wheel plane makes with respect to the vehicle's vertical axis. It is

positive when the top of the wheel leans outward from the vehicle body.

Note that the inclination angle, a measurement available in full-vehicle analyses, is the angle the

wheel plane makes with respect to the road surface. The inclination angle is used for tire

calculations.

Units Angle

Request

Names• camber_angle.left

• camber_angle.right

Inputs Wheel-center axis (spin axis) unit vectors, left and right

Methodcamber_angle = -arcsin

Figure 2 Camber Angle

Caster Angle


Description Caster angle is the angle in the side elevation (vehicle XZ plane) between the

steering (kingpin) axis and the vehicle's vertical axis. It is positive when the

steer axis is inclined upward and rearward.

Adams computes the steer axis using the geometric or instant axis method.

Units Angle

Request Names• caster_angle.left

• caster_angle.right

Inputs• Steer (kingpin) axis unit vectors - left and right

• Road vertical unit vector (z)

• Road longitudinal unit vector (x)

Method Adams uses the direction cosines in the x- and the z-directions of the kingpin

axis to calculate caster angle, such that:sx = steer_axis road_x_axis

sz = steer_axis road_z_axis

caster_angle = rtod * arctan(sx/sz)

Figure 3 Caster Angle

Dive Braking/Lift Braking


Description Dive braking is the amount of front suspension compression per G of vehicle

braking. Included in dive is suspension compression due to weight transfer plus

suspension extension due to brake forces. Positive dive indicates that the front

suspension compresses in braking.

Lift braking is the amount of rear suspension extension per G of vehicle

braking. Included in lift is suspension extension due to weight transfer plus

compression due to brake forces. Positive lift indicates that the rear suspension

extends in braking.

Units Length

Request Names• dive.left

• dive.right

Inputs• Compliance matrix

• Fraction of braking applied at this axle

• Loaded tire radius

• Tire stiffness

• Whole vehicle CG height

• Total vehicle weight

• Wheelbase

Method Adams first computes the longitudinal force percentage due to braking:Fleft = Fright = Brake Ratio / 2.0

and then the vertical force percentange due to weight transfer:Wleft = Wright = Whole vehicle CG height/ (2 x

Wheelbase)

For rear anti-lift, the weight transfer is a negative value.

These are forces at each wheel per unit total braking force.

Vertical deflections due to the vertical force are:Zwleft = Wleft x C(3,3) + Wright x C(3,9)

Zwright = Wleft x C(9,3) + Wright x C(9,9)

Vertical deflections due to tractive forces are as follows, where Rl is the loaded

radius of the tire:ZFleft = Fleft [C(3,1) - Rl x C(3,5)] +

Fright[C(3,7) - Rl x C(3,11)]

ZFright = Fleft [C(9,1) - Rl x C(9,5)] +

Fright[C(9,7) - Rl x C(9,11)]

The dive is:dive.left = (ZFleft + ZWleft + Wleft / Kt)

Vehicle Weight

dive.right = (ZFright + ZWright + Wright / Kt)

Vehicle Weight

Fore-Aft Wheel Center Stiffness


Description The stiffness of the suspension in the fore-aft direction is relative to the body,

measured at the wheel center.

Units Force/Length

Request Names• fore_aft_wheel_center_stiffness.left

• fore_aft_wheel_center_stiffness.right

Inputs Compliance matrix

Method Adams applies equal unit forces acting longitudinally at the wheel centers. It

calculates the fore-aft wheel center stiffness as follows:fore_aft_wheel_center_stiffness.left = 1 /

C(1,1)

fore_aft_wheel_center_stiffness.right = 1 /

C(7,7)

Front-View Swing Arm Length and Angle


Description The swing arm is the imaginary arm extending from the wheel's front elevation

instant center of rotation to the wheel center. The swing arm has a positive

length when the instant center is inward of the wheel center. The angle of the

swing arm is the angle it makes to the horizontal. A positive angle is when the

arm slopes outward and upward from the center of rotation to the wheel center.

The magnitude of the swing-arm length is limited to a maximum of 1000

meters.

Units Length; Angle

Request Names • fr_view_swing_arm_angle.left

• fr_view_swing_arm_angle.right

• fr_view_swing_arm_length.left

• fr_view_swing_arm_length.right


Method The change in vertical and lateral position and the front view rotation of the left

wheel center due to a unit vertical force at the left wheel center is:

The left front view swing arm length and angle are:

fr_view_swing_arm_length.left =

fr_view_swing_arm_angle.left =

The change in vertical and lateral position and the front view rotation of the

right wheel center due to a unit vertical force at the right wheel center is:

The right front view swing arm length and angle are:

fr_view_swing_arm_length.right =

fr_view_swing_arm_angle.right =

Figure 4 Instant Center Front View (Lateral, Vertical)

Kingpin Inclination Angle


Description The kingpin inclination angle is the angle in the front elevation between the steer

axis (the kingpin axis) and the vehicle's vertical axis. It is positive when the steer

axis is inclined upward and inward.

Units Angle

Request Names• kingpin_incl_angle.left

• kingpin_incl_angle.right

Inputs Kingpin axis unit vectors - left and right

Method Adams uses the direction cosines in the y-direction and the z-direction of the

kingpin axis to calculate the kingpin inclination angle:

kingpin_incl_angle.left =

kingpin_incl_angle.right =

Figure 5 Kingpin Angle (Ø is the Kingpin Angle)

Kingpin Location


Description The kingpin location is the location in global coordinates of the intersection of the

steer axis (the kingpin axis) and the wheel-center (spin) axis.

Units Length

Request Names• kingpin_location.left_X

• kingpin_location.left_Y

• kingpin_location.left_Z

• kingpin_location.right_X

• kingpin_location.right_Y

• kingpin_location.right_Z

Inputs • Compliance matrix or kingpin axis markers

• Wheel center position

Method Adams uses one of two methods to compute the kingpin location. Ideally, if the

user selects the Steer Axis Calculation method Instant Axis, Adams will use the

compliance matrix to find the kingpin location. This method uses a small steering

input and finds the location on the wheel that doesn’t translate when steering

about the kingpin axis.

T = wheel center translation vector

A = wheel center orientation vector

R = vector from wheel center to kingpin axis

wcpos = wheel center position

kpps = kingpin position

A point on the kingpin axis will not translate due to a steer input. To find this

point relative to the wheel center, compute a radius vector from the wheel center

to the kingpin axis such that:0 = T + R X A

Solving this equation for R yields:R = -T X A / (|A|*|A|)

To locate the Kingpin axis add R to the wheel center position:kppos = wcpos + R

Alternatively, if the user selects the Steer Axis Calculation method Geometric,

Adams will use the I Coordinate Reference as the kingpin location. This method

relies on the user to select an appropriate location. Due to suspension compliance,

the resulting location may be slightly different than the input location.

Lateral Force - Deflection, Steer, and Camber Compliance


Description The deflections at the wheel center due to unit lateral forces applied simultaneously at

the tire contact patches. The forces are oriented as if in a right turn. Adams reports the

lateral translational deflection, steer deflection (rotational deflection about the vertical

axis), and the camber deflection (rotational deflection about the longitudinal axis).

Positive deflection indicates a deflection to the right. Positive steer is a steer to the

left. Positive camber compliance is when the wheels lean outward at the top.

Units Deflection - length; Camber and steer - angle

Request

Names• lat_force_defl_compliance.left

• lat_force_defl_compliance.right

• lat_force_steer_compliance.left

• lat_force_steer_compliance.right

• lat_force_camber_compliance.left

• lat_force_camber_compliance.right

Inputs • Compliance matrix

• Tire radius - loaded

Method When the force is applied at the tire contact patch, Adams computes the deflection

due to both the lateral force at the wheel center and the moment created around the

wheel center. The total compliances are:

lat_force_defl_compliance.left = +[C(2,2) + Rl x C(2,4) + C(2,8) + Rl x C(2,10)]

lat_force_defl_compliance.right = +[C(8,2) + Rl x C(8,4) + C(8,8) + Rl x C(8,10)]

lat_force_steer_compliance.left = +[C(6,2) + Rl x C(6,4) + C(6,8) + Rl x C(6,10)]

lat_force_steer_compliance.right = +[C(12,2) + Rl x C(12,4) + C(12,8) + Rl x C(12,10)]

lat_force_camber_compliance.left = +[C(4,2) + Rl x C(4,4) + C(4,8) + Rl x C(4,10)]

lat_force_camber_compliance.right = -[C(10,2) + Rl x C(10,4) + C(10,8) + Rl x C(10,10)]

Figure 6 Lateral Force Loading for Deflection, Steer, and Camber

Compliances

Lift/Squat Acceleration


Description Lift is the amount of front suspension extension (rebound) per G of vehicle

acceleration. Squat is the amount of rear suspension compression (jounce) per

G of vehicle acceleration. Lift and squat arise when the suspension reacts to

longitudinal tractive forces, weight transfer forces, and, in dependent

suspensions, to the differential input and output torques.

Units Length

Request Names Front suspensions:

• lift.left

• lift.right

Rear suspensions:

• squat_acceleration.left

• squat_acceleration.right


Suspension parameters array:

• suspension_type (independent/dependent)

Vehicle parameters array:

• sprung_mass

• cg_height

• wheelbase

• loaded_tire_radius

• tire_stiffness

• axle_ratio (final drive ratio, pinion ring gear ratio)

• drive_ratio (fraction of total drive torque directed to the suspension)

Suspension geometry:

• Track

Acceleration due to gravity (Ag)

Method The suspension lift or squat during acceleration arises due to the tractive

forces, weight transfer, and, in live axles, due to the differential input and

output torques, as well. The longitudinal tractive forces at the tire contact

patches are:Fleft = Fright = -drive_ratio / 2.0

The vertical forces at the tire contact patch due to weight transfer are:VWleft = VWright = - cg_height / (2 *

Wheelbase)

Live axles also react to the drive torques (input torque to the differential

pinion and the left and right output torque from the differential). Given the

longitudinal tractive forces, the input torque (TI) to the differential is:TI = tire_loaded_radius * abs(F

left + F

right) /

axle_ratio

And the vertical force at the tire contact patches due to the drive torque is:VTleft = -VTright = TI / Track

The left and right output torque from the differential is:TOleft = - tire_loaded_radius * Fleft

TOright = - tire_loaded_radius * Fright

The vertical deflections of the suspension due to drive torque are:ZDleft = VTleft * C(3,1) + TOleft * C(3,5) +

VTright * C(3,7) + TOright * C(3,11) + VTleft /

tire_stiffness

ZDright

= VTleft

* C(9,1) + TOleft

* C(9,5) +

VTright

* C(9,7) + TOright

* C(9,11) + VTright

/ tire_stiffness

Independent suspensions do not react to the drive torques. Therefore,ZDleft = ZDright = 0.0

The vertical deflections of the suspension due to tractive forces are:ZFleft = Fleft * C(3,1) + Fright * C(3,7)

ZFright = Fright * C(9,7) + Fleft * C(9,1)

The vertical deflections of the suspension due to weight transfer forces are:ZWleft = VWleft C(3,3) + VWright C(3,9) +

VWleft / tire_stiffness

ZWright = VWleft C(9,3) + VWright C(9,9) +

VWright / tire_stiffness

Finally, the lift/squat per G of acceleration is:

lift.left / squat_acceleration.left = (ZDleft + ZFleft + ZWleft) * sprung_mass

* Aglift.right / squat_acceleration.right =

(ZDright + ZFright + ZWright) * sprung_mass *

Ag

Percent Anti-Dive Braking/Percent Anti-Lift Braking


Description Percent anti-dive braking for a front suspension and percent anti-lift braking for

a rear suspension are the ratio of vertical suspension deflections caused by

braking forces and torques to the deflections caused by weight transfer. During

braking, the vertical deflections in a suspension from weight transfer can, in

part, be cancelled by the vertical deflections caused by braking forces and

torques in the suspension. Suspensions that exhibit this characteristic are said to

have anti-dive or anti-lift geometry.

For front suspensions, percent anti-dive braking is positive when deflections

caused by braking forces and torques act to extend or rebound the suspension.

For rear suspensions, percent anti-lift braking is positive when the deflections

caused by the braking forces and torques act to compress or jounce the

suspension.

Units %


• anti_dive_braking.left

• anti_dive_braking.right

Rear suspensions:

• anti_lift.left

• anti_lift.right



• sprung_mass

• cg_height

• wheelbase


• tire_stiffness

• brake_ratio (fraction of braking done by the suspension)

• acceleration due to gravity (Ag)

Method The brake forces at the tire contact patch per G of longitudinal deceleration are:Fleft = Fright = sprung_mass * Ag * brake_ratio

/ 2

The brake torques reacted that the suspension reacts to are:BTleft = loaded_tire_radius * Fleft

BTright = loaded_tire_radius * Fright

The weight transfer forces that the suspension reacts to are:WTleft = sprung_mass * Ag * cg_height /

wheelbase / 2

WTright = sprung_mass * Ag * cg_height /

wheelbase / 2

The brake forces and torques that cause the suspension deflections are:ZBleft = Fleft * C(3,1) + Fright * C(3,7) +

BTleft * C(3,5) + BTright * C(3,11) + Fleft /

tire_stiffness

ZBright = Fleft * C(9,1) + Fright * C(9,7) +

BTleft * C(9,5) + BTright * C(9,11) + Fright /

tire_stifness

The weight transfer forces that cause the suspension deflections are:ZWleft = WTleft * C(3,3) + WTright * C(3,9) +

WTleft

/ tire_stiffness

ZWright = WTleft * C(9,3) + WTright * C(9,9) +

WTright / tire_stiffness

Finally, the percent anti-dive and percent anti-lift are:anti_dive_braking.left = anti_lift.left = 100 *

ZBleft / ZWleft

anti_dive_braking.right = anti_lift.right = 100

* ZBright / ZWright

Percent Anti-Lift Acceleration/Percent Anti-Squat Acceleration


Description Percent anti-lift for a front suspension and percent anti-squat for a rear

suspension are the ratio of vertical suspension deflections caused by

tractive forces and drive torques to the deflections caused by weight

transfer. During acceleration, the vertical deflections in a suspension from

weight transfer can, in part, be cancelled by the vertical deflections caused

by tractive forces and drive torques in the suspension. Suspensions that

exhibit this characteristic are said to have anti-lift or anti-dive geometry.

Note that a suspension that does not transmit tractive forces and drive

torques (drive_ratio = 0.0) has zero anti-lift or anti-squat.

For front suspensions, percent anti-lift is positive when deflections caused

by tractive forces and drive torques act to compress or jounce the

suspension. For rear suspensions, percent anti-squat is positive when the

deflections caused by the tractive forces and drive torques act to extend or

rebound the suspension.

Units %


• anti_lift.left

• anti_lift.right

Rear suspensions:

• anti_squat.left

• anti_squat.right


Suspension parameters array:

• suspension_type (independent/dependent)


• sprung_mass

• cg_height

• wheelbase


• tire_stiffness

• axle_ratio (final drive ratio, pinion ring gear ratio)

• drive_ratio (fraction of total drive torque directed to the suspension)

Suspension geometry:

• Track

Acceleration due to gravity (Ag)

Method The longitudinal tractive forces at the tire contact patches are:Fleft = Fright = -drive_ratio / 2.0

The vertical forces at the tire contact patch due to weight transfer are:VWleft = VWright = - cg_height / (2 *

Wheelbase)

Live axles also react with the drive torques (input torque to the differential

pinion and output torque from the differential). Given the longitudinal

tractive forces, the input torque (TI) to the differential is:TI = tire_loaded_radius * abs(Fleft + Fright)

/ axle_ratio

And the vertical force at the tire contact patches due to the drive torque is:VTleft = -VTright = TI / Track

The left and right output torque from the differential is:TOleft = - tire_loaded_radias * Fleft

TOright = - tire_loaded_radias * Fright

The vertical deflections of the suspension due to drive torque are:ZDleft = VTleft * C(3,1) + TOleft * C(3,5) +

VTright * C(3,7) + TOright * C(3,11) + VTleft

/ tire_stiffness

ZDright = VTleft * C(9,1) + TOleft * C(9,5) +

VTright * C(9,7) + TOright * C(9,11) +

VTright / tire_stiffness

Independent suspensions do not react to the drive torque. Therefore,ZDleft = ZDright = 0.0

The vertical deflections of the suspension due to tractive forces are:ZFleft = Fleft * C(3,1) + Fright * C(3,7)

ZFright = Fright * C(9,7) + Fleft * C(9,1)

The vertical deflections of the suspension due to weight transfer forces are:ZWleft = VWleft C(3,3) + VWright C(3,9) +

VWleft

/ tire_stiffness

ZWright

= VWleft

C(9,3) + VWright

C(9,9) +

VWright / tire_stiffness

The left and right percent anti-lift for front suspensions and percent anti-squat for

rear suspensions are:

anti_lift.left / anti_squat.left = 100 *

(ZFleft + ZDleft) / ZWleft

anti_lift.right / anti_squat.right =100 *

(ZFright + ZDright) / ZWright

Ride Rate


Description Ride rate is the spring rate of the suspension relative to the body, measured at

the tire contact patch.

Units Force/Length

Request Names • ride_rate.left

• ride_rate.right


• Tire stiffness

Method Adams computes ride rate as the equivalent rate of the wheel rate and tire rate

in series.Ks = Wheel rate (see Wheel Rate)

Kt = Vertical tire rate

Ktotal = Ks x Kt / (Ks + Kt)

Ride Steer


Description Ride steer is the slope of the steer angle versus the vertical wheel travel curve. Ride steer is the change

in steer angle per unit of wheel center vertical deflection due to equal vertical forces at the wheel

centers. Positive ride steer implies that the wheels steer to the right, as the wheel centers move upward.

Units Angle/length

Request

Names• ride_steer.left

• ride_steer.right


MethodChange in Wheel Orientation

Using the compliance matrix, Adams first calculates the change in wheel orientation (W) due to unit

forces applied at both wheel centers:Wl/dF = C(4, 3) - C(4, 9) , C(5, 3) - C(5, 9) , C(6, 3) - C(6, 9)

Wr/dF = C(10, 3) - C(10,9) , C(11, 3) - C(11, 9) , C(12, 3) - C(12,9)

Change in Wheel-Center (Spin) Vector

Orientation

The change in the left wheel-center (spin) vector (d(wcvl)) and the right wheel (spin) vector (d(wcvr) are

vectors of partial derivatives given by the cross product of the change in wheel orientation with the

wheel-center vector:d(wcvl)/dF = Wl x wcvl

d(wcvr)/dF = Wr x wcvr

Change in Steer Angle

The change in steer angle due to a change in wheel-center vector orientation is also a vector of partial

derivatives given by:d(steer_anglel)/d(wcvl) = (-1.0 / ( syl**2 + sxl**2 ) ) { syl,

-sxl, 0 }

d(steer_angler)/d(wcvr) = (-1.0 / ( syr**2 + sxr**2 ) ) { syr,

-sxr, 0 }

where:

sxl = wcvl o x; The x component of the left wheel-center (spin)

vector

syl = wcvl o y; The y component of the left wheel-center (spin)

vector\sxr = wcvr o x; The x component of the right wheel-center

(spin) vector

syr = wcvr o y; The y component of the right wheel-center (spin)

vector

The change in steer angle due to unit vertical forces at both wheel centers is computed by the chain rule:d(steer_anglel) /dF = ( -d(steer_anglel)/d(wcvl) ) o ( d(wcvl) /

dF )

d(steer_angler)/dF = ( -d(steer_angler)/d(wcvr) ) o ( d(wcvr) /

dF )

Change in Wheel-Center Vertical Travel

The change in wheel-center vertical travel (dz) due to unit vertical forces applied at both wheel centers

is:dzl /dF = { C(3,3) + C(3,9) }

dzr /dF = { C(9,3) + C(9,9) }

Using the chain rule one final time, the ride steer is:

ride_steer.left = d(steer_anglel)/dzl = d(steer_anglel)/dF

/(dF/dzl)

ride_steer.right = d(steer_angler)/dzr = d(steer_angler)/dF

/(dF/dzr)

Nomenclature • Bold, uppercase text, such as Wl, are vectors.

• Bold, lowercase text, such as wcvl, are unit vectors.

• X is the vector cross product operator.

• o is the vector dot product operator.

• * is the scalar multiplication operator.

Roll Camber Coefficient


Description Roll camber coefficient is the rate of change of wheel inclination angle with

respect to vehicle roll angle. Positive roll camber coefficient indicates an increase

in camber angle per degree of vehicle roll.

Units Unitless

Request Names• roll_camber_coefficient.left

• roll_camber_coefficient.right


• Tire stiffness

• Track width

Method Adams applies opposing unit forces acting vertically at the tire contact patches.

The height difference between the tire contact patches is the following, where Kt

is the vertical tire rate:DZ = C(3,3) - C(3,9) - C(9,3) + C(9,9) + 2/Kt

The vehicle roll angle is the rotation of the line through the tire contact patches:Av = DZ / track

Adams measures the wheel inclination with respect to the line through the tire

contact patches, which has two components. The first is from the vertical

movement of the tire contact patch and is the same as the vehicle roll angle. The

second is from the rotational compliance at the wheel center due to the vertical

force:Ac = - C(4,3) + C(4,9) (left side)

= - C(10,3) + C(10,9) (right side)

The total wheel inclination is then:Ai = Av - Ac

The roll camber is then:roll_camber_coefficient = (Av - Ac) / Av = 1 - Ac / Av

Figure 7 Roll Camber

Roll Caster Coefficient


Description Roll caster coefficient is the rate of change in side view steer axis angle

with respect to vehicle roll angle. A positive roll caster coefficient

indicates an increase in caster angle per degree of vehicle roll.

This calculation assumes that the steer axis (kingpin) is fixed in the

suspension upright as in a double-wishbone or MacPherson strut

suspension. The calculation, however, is not valid for suspensions where

the steer axis is not fixed in the suspension upright, for example, a

five-link front suspension used in Audi A4.

Units Unitless

Request Names • roll_caster_coefficient.left

• roll_caster_coefficient.right


• Tire stiffness

• Track width

Method Adams applies opposing unit forces acting vertically at the tire contact

patches. The height difference between the tire contact patches is the

following, where Kt is the vertical tire rate:DZ = C(3,3) - C(3,9) - C(9,3) + C(9,9) + 2/Kt

The vehicle roll angle is the rotation of the line through the tire contact

patches:Av = DZ / track

The rotational compliance at the wheel center due to the vertical force is:Ac = C(5,3) - C(5,9) (left side)

= C(11,3) - C(11,9) (right side)

The roll caster is then:roll_caster_coefficient = Ac / Av

Roll Center Location


Description Roll center location is the point on the body where the moment of the lateral

and vertical forces exerted by the suspension links on the body vanishes.

Units Length

Request Names• roll_center_location.lateral_from_half_track

• roll_center_location.vertical

• roll_center_location.lateral_to_left_patch

• roll_center_location.lateral_to_right_patch

Inputs • Compliance matrix at contact patches

• Contact patch location

Method Adams applies unit vertical forces (perpendicular to the road) at the tire

contact and measures the resulting contact patch displacements in the vertical

and lateral direction (front view). Adams projects lines perpendicular to the

contact patch displacements for both the left and right patches. The roll center

lies at the intersection of these lines.

Adams reports errors when the motions of the left and right patches are

parallel (just as it occurs with a fully trailing arm suspension). Therefore, the

projected lines have no intersection. Adams also reports an error when the

motion of the left and/or right patches is very small for a unit vertical force

(for example, the suspension is very stiff).

Finally, Adams limits the distance from the roll center to the left and right

patches to +/- 1000 meters.

Figure 8 Roll Center Location (Front View)

Roll Steer


Description Roll steer is the change in steer angle per unit change in roll angle, or the slope of

the steer-angle-verses-roll-angle curve. Roll steer is positive when for increasing

roll angle (left wheel moving up, right wheel moving down) the steer angle

increases (wheels steer toward the left).

Units Unitless

Request Names • roll_steer.left

• roll_steer.right

Inputs • Wheel center spin axis unit vector (wcv) left and right

• Track

• Tire stiffness (Kt)

• Compliance matrix

Method Using the compliance matrix, Adams first calculates the change in roll angle and

the change in the wheel-center vector orientation due to a roll moment (the roll

moment is a unit vertical force upward at the left contact patch and a unit force

downward at the right contact patch). Then, Adams calculates the change in steer

angle due to the change in wheel-center vector orientation. Finally, Adams

applies the chain rule to calculate the roll steer.

Change in Roll Angle

The change in roll angle is:d(roll_angle)/d(roll_moment) = ( C(3,3) - C(3,9)

- C(9,3) + C(9,9) + 2.0/Kt ) / Track

Change in Wheel-Center Spin Vector Orientation

The changes in orientation of the left wheel (Wl) and of the right wheel (Wr) due

to a unit upward force at the left contact patch and a unit downward force at the

right contact patch are:Wl = { C(4, 3) - C(4, 9) , C(5, 3) - C(5, 9) ,

C(6, 3) - C(6, 9) }

Wr = { C(10, 3) - C(10,9) , C(11, 3) - C(11, 9) ,

C(12, 3) - C(12, 9) }

The change in the left wheel-center (spin) vector (d(wcvl)) and the right wheel

(spin) vector (d(wcvr) are vectors of partial derivatives:d(wcvl)/d(roll_moment) = Wl x wcvl

d(wcvr)/d(roll_moment) = Wr x wcvr

Change in Steer Angle

The change in steer angle due to a change in wheel-center vector orientation is

also a vector of partial derivatives given by:d(steer_anglel)/d(wcvl) = (-1.0 / ( syl**2 +

sxl**2 ) ) { syl, -sxl, 0 }

d(steer_angler)/d(wcvr) = (-1.0 / ( syr**2 +

sxr**2 ) ) { syr, -sxr, 0 }

where:

sxl = wcvl o x; The x component of the left

wheel-center (spin) vector

syl = wcvl o y; The y component of the left


sxr = wcvr o x; The x component of the right


syr = wcvr o y; The y component of the right


The change in steer angle for a change in roll moment is computed using the

chain rule:d(steer_anglel)/d(roll_moment) = (

d(steer_anglel)/d(wcvl) ) o (

d(wcvl)/d(roll_moment) )

d(steer_angler)/d(roll_moment) = (

d(steer_angler)/d(wcvr) ) o (

d(wcvr)/d(roll_moment) )

Roll Steer

And applying the chain rule one last time, the roll steer isroll_steer.left = (

d(steer_anglel)/d(roll_moment) ) / (

d(roll_angle)/d(roll_moment) )

roll_steer.right = (

d(steer_angler)/d(roll_moment) ) / (

d(roll_angle)/d(roll_moment) )

Request

Statements

REQUST/id, FUNCTION=USER(900,17,characteristics_input_array_id)

Nomenclature • Bold, uppercase text, such as Wl, are vectors.

• Bold, lowercase text, such as wcvl, are unit vectors.




Side-View Angle


Description The side-view angle is the wheel carrier side-view rotation angle. It is

positive for a clockwise rotation, as seen from the left side of the vehicle.

Units Angle

Request Names • side_view_angle.left

• side_view_angle.right

Inputs Wheel bearing I marker and origo_y

Method side_view_angle = az, marker I, marker J

Side-View Swing Arm Length and Angle


Description The swing arm is an imaginary arm extending from the wheel's side elevation

instant center of rotation to the wheel center. For front suspensions, the sign

convention is that when the instant center is behind the wheel center, the swing

arm has a positive length. For rear suspensions, the sign convention is the

opposite: when the instant center is ahead of the wheel center, the swing arm

has a positive length.

The angle of the swing arm is the angle it makes to the horizontal. A positive

angle for a positive length is when the arm slopes downward from the wheel

center. A positive angle for a negative length arm is when the arm slopes

upward from the wheel center.

The magnitude of the swing-arm length is limited to a maximum of 1000

meters.

Units Length, Angle

Request Names• side_view_swing_arm_angle.left

• side_view_swing_arm_angle.right

• side_view_swing_arm_length.left

• side_view_swing_arm_length.right


Method The change in vertical and longitudinal position and the side view rotation of

the left wheel center due to a unit vertical force at the left wheel center is:DX left = C(1,3)

DZ left = C(3,3)

DØ left = C(5,3)

The left side view swing arm length and angle are:

side_view_swing_arm_length.left = (DX left 2 + DZ left

2)1/2 / DØ left

side_view_swing_arm_angle.left = tan-1 (DX left / DZ left)

The change in vertical and longitudinal position and the change in side view

rotation of the right wheel center due to a unit vertical force at the right wheel

center is:DX right = C(7,9)

DZ right = C(9,9)

DØ right = C(11,9)

The right side view swing arm length and angle are:

side_view_swing_arm_length.right = (DXright 2 + DZright

2) 1/2 / DØ right

side_view_swing_arm_angle.right = tan-1 (DXright / DZ right)

Figure 9 Instant Center Side View (Fore and Aft, Vertical)

Suspension Roll Rate


Description Suspension roll rate is the torque, applied as vertical forces at the tire contact

patches, per degree of roll, measured through the wheel centers.

Units Force-Length/Angle

Request Names • susp_roll_rate.left

• susp_roll_rate.right


• Track width

Method Adams uses opposing unit forces as the applied torque:T = F x track = track

The resulting vertical distance between wheel centers is:

The rotation of the line through the wheel centers is:

The roll rate is:

susp_roll_rate = T / Ø =

Figure 10 Roll Rate - Suspension

Toe Angle


Description Toe angle is the angle between the longitudinal axis of the vehicle and the

line of intersection of the wheel plane and the vehicle's XY plane.

Adams reports toe angle in radians. It is positive if the wheel front is

rotated in towards the vehicle body.

Units Angle

RequestNames• toe_angle.left

• toe_angle.right

Inputs Wheel center axis unit vectors - left and right

Method Adams uses the direction cosines in the x- and y-directions of the wheel

center axis relative to the road to calculate toe angle, such that:

toe_angle.left = tan-1 (DCOSX/DCOSY)

toe_angle.right = tan-1 (-DCOSX/DCOSY)

Figure 11 Toe Angle

Total Roll Rate


Description Total roll rate is the torque, applied as vertical forces at the tire contact

patches, per degree of roll, measured at the tire contact patches.

Units Force-Length/Angle

Request Names• total_roll_rate.left

• total_roll_rate.right


• Tire stiffness

• Track width

Method Adams uses opposing unit forces as the applied torque:T = F x track = track

The resulting vertical distance between wheel centers is the following, where

Kt is the tire stiffnesses:

The rotation of the line through the tire contact patches is:

The roll rate is:

total_roll_rate = T/Ø =

Total Track


Description Total track is the distance measured along the line passing through the left

and right tire contact points with the left and right road parts (pads) and

then projected onto the right road plane.

The tire contact point lies at the intersection of two lines:

• The first line is formed by the intersection of the wheel plane with

the road plane.

• The second line is perpendicular to the first and passes through the

wheel center.

The wheel plane is perpendicular to the wheel spin axis and passes through

the wheel center.

The left and right road planes behave differently, depending on your

coordinates:

• In vehicle coordinates, the left and right road planes remain

perpendicular to the vehicle's vertical axis, but lie at different

heights. If you run an opposite wheel-travel using vehicle

coordinates, the left and right road planes remain un-rolled (flat)

relative to the vehicle body (ground in a suspension analysis).

• In ISO coordinates, the left and right road planes form one plane

that rotates about the vehicle's longitudinal axis to simulate rolling

of the suspension relative to the road. If you run an opposite wheel-

travel analysis using ISO coordinates, the right road plane and left

road plane are identical, as if the suspension was rolled relative to a

flat road. The total_track (distance between tire contact points)

projected onto the right road plane is foreshortened, and therefore, is

less than the total track output.

Also, the distance from the road plane to the wheel center depends on the

tire deflection, which depends on the tire stiffness and the force required to

deflect the suspension to a given position.

Units Length

Request Names • total_track

Inputs • Contact patch positions

Method The following is the equation used to compute total track:T = ABS (ROAD (COMP, CPPLEFT) - ROAD (COMP, CPPRIGHT))

where:

• ROAD is a data structure filled with a series of kinematic

characteristics of the suspension. ROAD (Y,CPPLEFT) returns, for

example, the Y component of the left contact patch position.

• CPP represents the instantaneous coodinates of contact points

obtained as described above.

Wheel Rate


Description Wheel rate is the vertical stiffness of the suspension relative to the body,

measured at the wheel center.

Units Force/Length

Request Names• wheel_rate.left

• wheel_rate.right


Method Adams computes suspension wheel rate as the inverse of the z-axis

displacement at the wheel center due to the vertical forces applied at both wheel

centers simultaneously.wheel_rate.left = 1 / (C(3,3) + C(3,9))

wheel_rate.right = 1 / (C(9,3) + C(9,9))

Ackerman


Description Ackerman is the difference between the left and right wheel steer angles. A

positive Ackerman indicates that the right wheel is being steered more to the

right than to the left.

Units Angle

Request Names • ackerman.left

• ackerman.right

Inputs Steer angle (see Steer Angle)

Method Adams/Car computes Ackerman by subtracting the right steer angle from the

left steer angle:ackerman = Right steer angle – Left steer

angle

Ackerman Angle


Description Ackerman angle is the angle whose tangent is the wheel base divided by the turn

radius. Ackerman angle is positive for right turns.

Units Angle

Request Names • ackerman_angle.left

• ackerman_angle.right

Inputs • Turn radius (see Turn Radius)

• Wheelbase

Method ackerman_angle = tan-1(Wheel Base/Turn Radius)

Figure 12 Ackerman Angle

Ackerman Error


Description Ackerman error is the difference between the steer angle and the ideal steer

angle for Ackerman geometry. Because Adams/Car uses the inside wheel to

compute the turn center, the Ackerman error for the inside wheel is zero.

For a left turn, the left wheel is the inside wheel and the right wheel is the

outside wheel. Conversely, for a right turn, the right wheel is the inside wheel

and the left wheel is the outside wheel. Positive Ackerman error indicates the

actual steer angle is greater than the ideal steer angle or the actual is steered

more to the right.

Units Angle

Request Names• ackerman_error.left

• ackerman_error.right

Inputs• Steer angle (see Steer Angle)

• Ideal steer angle (see Ideal Steer Angle)

Method ackerman_error.left = (left steer angle - left ideal steer angle)

ackerman_error.right = (right steer angle - right ideal steer angle)

Caster Moment Arm (Mechanical Trail)


Description Caster moment arm is the distance from the intersection of the kingpin (steer)

axis and the road plane to the tire contact patch measured along the

intersection of the wheel plane and road plane. Caster moment arm is positive

when the intersection of the kingpin axis and road plane is forward of the tire

contact patch.

Units Length

Request Names• caster_moment_arm.left

• caster_moment_arm.right

Inputs• Kingpin axis position, a point on the kingpin axis (Rs) - left and right

• Kingpin (steer) axis unit vector (s) - left and right

• Tire contact patch position (Rp) - left and right

• Wheel center axis unit vector (w) - left and right

• The road normal unit vector (k)

Methods Adams/Car first finds the intersection of the kingpin axis and the road plane.

Note that by convention, the kingpin axis unit vector is directed upward,

away from the road, and the road plane has zero height. The intersection of

the kingpin axis and the road plane (Rkr) is:

Rsr = Rs - (Rs o k)/(s o k) s

Next, Adams/Car finds a unit vector (l) directed rearward along the line of

intersection between the wheel plane and the road plane:l = k x w / | k x w | (left side)

l = k x -w / | k x -w | (right side)

The distance along l from the contact patch to the intersection of the kingpin

axis and the road plane is:caster_moment_arm = (Rp - Rkr) o l

Figure 13 Caster Moment Arm and Scrub Radius

Ideal Steer Angle


Description Ideal steer angle is the steer angle in radians that gives Ackerman steer

geometry or 100% Ackerman. For Ackerman steer geometry, the wheel-

center axes for all four wheels pass through the turn center. Note that

Adams/Car uses the steer angle of the inside wheel to determine the turn

center for Ackerman geometry. Therefore, the ideal steer angle and the steer

angle are equal for the inside wheel. When making a left turn, the left wheel

is the inside wheel. Conversely, when making a right turn, the right wheel is

the inside wheel. A positive steer angle indicates a steer to the right.

Units Angle

Request Names• ideal_steer_angle.left

• ideal_steer_angle.right

Inputs• Turn radius (see Steer Angle)


• Wheelbase

Method ideal_steer_angle.left = tan-1 [Wheel Base/Turn Radius - Rp(left) o )]

ideal_steer_angle.right = tan-1 [Wheel Base/Turn Radius -Rp(right) o )]

Note • Right turns give positive angles and turn radii

• Rp(left) o < 0

• Rp(right) o > 0

• |Inside wheel's ideal steer angle| > |outside wheel's ideal steer angle|

Outside Turn Diameter


Description Outside turn diameter is the diameter of the circle defined by a vehicle's

outside front tire when the vehicle turns at low speeds. Adams/Car determines

the circle by the tire's contact patch for a given steer angle. For a left turn, the

right front wheel is the outside wheel. For a right turn, the left front wheel is

the outside wheel.

Units Length

Request Names • outside_turn_diameter.left

• outside_turn_diameter.right

Inputs • Turn radius (see Turn Radius)

• Track width

• Wheelbase

Method outside_turn_radius = 2.0 [(| Turn Radius | +Track/2)2 + (Wheel Base) 2]1/2

Percent Ackerman


Description Percent Ackerman is the ratio of actual Ackerman to ideal Ackerman expressed

as a percentage. Percent Ackerman is limited to the range from -999% to

999%. Percent Ackerman is positive when the inside wheel's steer angle is

larger than the outside wheel's steer angle.

Units %

Request Names • percent_ackerman.left

• percent_ackerman.right

Inputs • Steer angle (see Steer Angle)

• Ideal steer angle (see Ideal Steer Angle)

• Ackerman (see Ackerman)

Method ackerman = Right steer angle - Left steer angle

ideal_ackerman = Right ideal steer angle - Left ideal steer angle

percent_ackerman = 100 x Ackerman/Ideal Ackerman

Scrub Radius


Description Scrub radius is the distance from the intersection of the kingpin (steer) axis

and the road plane to the tire contact patch measured along the projection of

the wheel-center axis into the road plane. Scrub radius is positive when the

intersection of the kingpin axis and the road plane is inboard of the tire

contact patch.

Units Length

Request Names• scrub_radius.left

• scrub_radius.right

Inputs• Kingpin axis position (Rs) - left and right

• Kingpin (steer) axis unit vector (s) - left and right


• Wheel-center axis unit vector (w) - left and right

• The road normal unit vector (k)

Method Adams/Car first finds the intersection of the kingpin axis and the road plane.

Note that by convention the kingpin axis unit vector is directed upward, away

from the road, and the road plane has zero height. The intersection of the

kingpin axis and the road plane (Rkr) is:

Rsr = Rs - (Rs o k)/(s o k) s

Next Adams/Car finds the projection (m) of the wheel-center axis (w) onto

the road planeM = (k x w) x k

m = M / | M |

The distance from the contact patch to the intersection of the kingpin axis and

the road plane along m is:scrub_radius = (Rp - Rkr) o m

Figure 14 Caster Moment Arm and Scrub Radius

Steer Angle


Description Steer angle is the angle measured from the vehicle heading to the line formed

by the intersection of the wheel plane with the ground plane. Steer angle is

positive when a wheel is rotated to the right as if the vehicle were making a

right turn.

Units Angle

Request Names • steer_angle.left

• steer_angle.right

Inputs Wheel-center axis unit vectors - left and right

Method Adams/Car uses the direction cosines of the x-direction and the y-direction

of the wheel-center axis constructed from the wheel-center orientation to

calculate steer angle:

steer_angle.left = tan-1 (-DCOSX/|DCOSY|)

steer_angle.right = tan-1 (DCOSX/|DCOSY|)

Steer Axis Offset


Description The steer axis offset is the shortest distance from the steer (kingpin) axis to the wheel

center. The steer axis offset is measured in the plane perpendicular to the steer axis and

passing through the wheel center. The steer axis offset is always positive.

The steer axis offset-longitudinal is the component of the steer axis offset along the

intersection of the wheel plane with the plane perpendicular to the steer axis and passing

through the wheel center. The steer axis offset-longitudinal is positive when the wheel

center is forward of the steer axis.

The steer axis offset-lateral is the component of the steer axis offset along the projection of

the wheel-center axis into the plane perpendicular to the steer axis and passing through the

wheel center. The steer axis offset - lateral is positive when the wheel center lies outboard

of the steer axis.

Units Length

Request

Names• steer_axis_offset.off_left

• steer_axis_offset.off_right

• steer_axis_offset.lon_left

• steer_axis_offset.lon_right

• steer_axis_offset.lat_left

• steer_axis_offset.lat_right

Inputs• Wheel-center position (WCP) left and right

• Wheel-center (spin) axis unit vector (wcv) left and right

• Kingpin (steer) axis position (KPP) left and right

• Kingpin (steer) axis unit vector (kpv) left and right

Method First, define longitudinal and lateral directions in a plane perpendicular to the steer (kingpin) axis

using the kingpin axis vector and the wheel-center (spin) vector.

u_lon = ( wcv x kpv ) / | wcv x kpv |

and:

u_lat = ( kpv x u_lon ) / | kpv x u_lon |

Note that u_lat is the projection of the wheel-center vector (wcv) onto the plane perpendicular to the

kingpin axis.

The displacement vector (R) from a point on the kingpin (steer) axis to the wheel center is:

R = WCP - KPP

The steer axis offset-longitudinal is:

steer_axis_offset.lon_left = -R o u_lon

steer_axis_offset.lon_right = R o u_lon

The steer axis offset-lateral is:

steer_axis_offset.lat_left = R o u_lat

steer_axis_offset.lat_right = R o u_lat

Finally, the steer axis offset is:

steer_axis_offset.off_left = sqrt( lon_left2 + lat_left2 )

steer_axis_offset.off_right = sqrt( lon_right2 + lat_right2 )

Figure 15 Steer Axis Offset (Top View)

Request

Statements Offset:

REQUST/id, FUNCTION=USER(900,44,characteristics_input_array_id)\

Longitudinal offset:


Lateral offset:


Nomenclature • Bold text in uppercase letters, such as R, shows vectors.

• Bold text in lowercase letters, such as u_lon, shows unit vectors.




Turn Radius


Description The turn radius is the distance measured in the ground plane from the

vehicle center line to the turn center along the y-axis (see the figure for

Ackerman Angle). Turn radius is positive for right turns and negative for

left turns.

Units Length

Request Names • turn_radius.left

• turn_radius.right

Inputs • Steer angle (see Steer Angle)

• Track width

• Wheelbase

• Wheel-center orientations - left and right

Method Adams/Car determines the inside wheel by checking the sign of the steer

angles. It computes turn radius using the inside tire orientation.

Left turn:turn_radius.left = - [Wheel Base (DCOSY/DCOSX) +

Track/2]

Right turn:turn_radius.right = [Wheel Base x (DCOSY/DCOSX) +

Track/2]

output of suspension analyses

Documents

description camber angle

positive camber angle

view angle

positivesteer angle

left camber

description caster angle

camber anglecaster angle

camber compliance note