# How it Works

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## + Terminology

Here you'll find the terminology we use.

The Sacli suspension prototypes worked with promising results. But the Sacli suspension is a new and complicated design and it hasn’t been completely understood or optimized yet. There are many factors affecting the vehicle’s performance and there is still much more to be tried before we know how it works at its best. Our testing and development has taught us quite a lot about the Sacli system and the Sacli cars are evolving accordingly.

Here you’ll find the terminology and simplified analytic methods we use during our design stages. These help put together different parts of Sacli suspension design such as kinetics and kinematics designs for roll and dive suspensions. Since there is no prior analytic method and terminology associated with the Sacli suspensions, it was necessary to establish certain definitions and equations that allow for analytical calculations.

These equations are for steady state and testing shows that they are accurate as long as the difference in jacking forces between the two sub suspensions is relatively small. If each of the sub suspension systems of the vehicle experience significantly higher jacking forces over the other, then the resultant camber based these equations will not be accurate. This is the same for commonly used equations in conventional suspension systems and like the conventional suspension systems this jacking effect can be minimized by keeping the roll centers closer to ground and close to each other.

However testing also shows that unlike the conventional suspension systems, Sacli suspensions could benefit from jacking one sub-suspension over the other without jacking the vehicle sprung mass. This effect is not covered in the equations below as they are simplified and provided to help understand how Sacli suspension works and behaves as a combination of existing suspension systems. You can check out the development notes for more information on the jacking force related interaction of the two sub suspension systems with each other.

DIVE SUSPENSION = A suspension design that has good camber control at dive and bump and bad camber control (camber losing) at roll.

ROLL SUSPENSION = A suspension design that has good camber control (camber recovering) at roll and bad camber control at dive and bump

TIRE SUSPENSION = Tire as a suspension

CG = Center of Gravity.

LGs = Desired/Max Lateral Gs the vehicle can handle/ Limited by CG height/track ratio.

CAMBER RATE = (CAMBER CHANGE AT WHEEL/BODY ROLL) x ROLL RATE. CAMBER RATE is with respect to the ground. Units for CAMBER RATE are, DEGREES/Gs

R1 = Roll rate for DIVE SUSPENSION

R2 = Roll rate for ROLL SUSPENSION

RT = Roll rate for TIRE SUSPENSION

RR = Resultant roll rate. RR = R1 + R2 + RT.

RC1 = Roll center for DIVE SUSPENSION only.

RC2 = Roll center for ROLL SUSPENSION only

RCT = Roll center for TIRE SUSPENSION only (estimated on ground, center of track).

RC = Roll center for DIVE SUSPENSION, ROLL SUSPENSION working together.

ROLL1 = Total roll over DIVE SUSPENSION

ROLL2 = Total roll over ROLL SUSPENSION

ROLLT = Total roll over TIRE SUSPENSION

ROLL = Total roll. ROLL = ROLL1 + ROLL2 + ROLLT.

CC1 = Camber change/loss at wheel due to ROLL1

CC2 = Magnitude of the camber change/gain at wheel due to ROLL2

CCT = Camber change/loss at wheel due to ROLLT

CC = Resultant camber change at wheel due to ROLL. CC = CC1 - CC2 + CCT.

LF = Lateral Force acting on the CG

WR = Effective wheel rate at roll including all factors such as anti-roll bars or swaybars if there are any.

TRACK = width of car from center of one wheel to center of another wheel.

WR1 = Effective wheel rate of the dive suspension at roll including all factors such as anti-roll bars or swaybars if there are any.

WR2 = Effective wheel rate of the dive suspension at roll including all factors such as anti-roll bars or swaybars if there are any.

## + Equations

In this section are equations used in our analytical calculations.

### For Wheel Camber Behavior at Roll

The wheel camber versus body roll behavior of each suspension can be analyzed with the existing methods for each suspension. First the design parameters, such as roll center locations, roll center movements, roll rates, wheel camber versus body roll curves, for each suspension can be found by use of the existing geometric and analytical methods. Then those parameters are combined with the following relations to analyze the resulting wheel camber versus body roll behavior of the inventive suspension

The analysis starts with the following relations and definitions:

(1)ROLL1 = R1 x LGs

(2)ROLL2 = R2 x LGs

(3)ROLLT = RT x LGs

Camber rate at wheel due to DIVE SUSPENSION is:

(4)C1 = CC1/LGs = (CC1/ROLL1) x R1

Camber rate at wheel due to ROLL SUSPENSION is:

(5)C2 = CC2/LGs = (CC2/ROLL2) x R2

Camber rate at wheel due to TIRE SUSPENSION is:

(6)CT = CCT/LGs = (CCT/ROLLT) x RT since CCT/ROLLT = 1 at all times, then CT = RT at all times also.

### Camber Factor

A Camber Factor (CF) is defined as,

(7)CF = (R2 x C2) / ((R1 x C1) + (RT x CT))

(8)CF = (R2 x C2)/ ((R1 x C1) + (RT^2)), since CT = RT

This Camber Factor is a useful parameter that links the suspension kinetic and kinematics with the camber response of the suspension. When CF = 1 the wheels will stay at a fixed angle with respect to the ground at roll. When CF > 1 the wheels will camber into (camber gain) the turn at roll. When CF < 1 the wheels will camber out (camber loss) of the turn at roll.

### Simplified Camber Factor

For simplification of the design process, as it is commonly practiced, the tire suspension (deflection due to tire) can be neglected. This is only done to make the complicated design and analysis process simpler. A Simplified Camber Factor (SCF) that does not include the effects of the tire is as follows,

(9)SCF = (R2 x C2) / (R1 x C1)

SCF > CF at all times since it ignores the tire roll and camber loss due to that roll. Overall SCF can relate the dive suspension and the roll suspension directly to each other without the effects of the tire.

Again for simplification, a common practice is the process of dividing the suspension design into two main sections: kinetics and kinematics. Where kinetics focuses on the dynamics of the system and kinematics focuses on the geometry of the system. Thus in an attempt to link the two suspensions for resultant wheel camber at roll, the following Dynamic Camber Factor (DCF) and Kinematic Camber Factor (KCF) are defined:

(10)SCF = DCF x KCF

### Dynamic Camber Factor

Substituting the camber rates (C1, C2) into the equation for Simplified Camber Factor (SCF) yields,

(11)SCF = (R2^2xCC2/ROLL2) / (R1^2xCC1/ROLL1)

Since CC1 and CC2 are defined by the suspension geometry (kinematics) if the terms in equation (11) are reorganized to separate the geometric terms we get:

(12)SCF = [(R2^2 /ROLL2) / (R1^2 /ROLL1)] x (CC2/CC1)

Plugging in equations (1), (2) and (3) and simplifying yields,

(13)SCF = (R2 / R1) x (CC2/CC1)

The first term in this equation relates to the roll rates and is included in the kinetic design and analysis. Thus, to describe and identify the kinetics effect on the Simplified Camber Factor (SCF), we define the first term in the equation (13), the Dynamic Camber Factor (DCF).__ __

(14)DCF = R2 / R1

With the Sacli suspension the camber curves can be modified kinetically by changing the ratios of the two suspension roll rates. At the practical level this would allow the suspension tuner to change the camber curves of a vehicle significantly by changing spring rates, torsion bar rates, swaybar rates and/or dampening rates.

The kinematics of the system could still limit the designers’ choice of roll rates and camber curves. A vehicle with a proper kinematics design that has the roll centers for both suspensions balanced with each other and moving very little through dive and roll could be adjusted over a wider range of roll rates and camber curves without causing instability.

### Kinematic Camber Factor

The second term in equation (13) relates to the camber curves and is included in the kinematics design and analysis. Thus to describe and identify the effects of the kinematics on the Simplified Camber Factor, we define the second term in equation (13) the Kinetics Camber Factor (KCF).

(15)KCF = CC2 / CC1

The Dynamic and Kinematic Camber Factors are based on ignoring the tire deflection, thus they can only be used with the Simplified Camber Factor, which is also based on ignoring the deflection in the tire.

Plugging back into the Simplified Camber Factor (9),

(16)SCF = DCF x KCF = (R2/R1) x (CC2/CC1), which proves equation (13) is true to the definition of Simplified Camber Factor (SCF) and the related equation (9).

### Equations For Body/Chassis Behavior at Roll

Although the body roll can be calculated individually for each suspension and combined as the sum of both, the location of the effective geometric roll center is still very important to know. This is calculated as follows.

(17)Roll Moment = [Distance RC to CG] x LF

(18)Roll Resisting Moment = ((WR x Track^2)/2) x ROLL

At equilibrium Roll Moment is equal to Roll Resisting Moment thus,

(19)ROLL = (2 x [Distance RC to CG] x LF) / (WR x Track^2)

This can be written separately for both roll and dive suspensions combined in series,

(20)WR = (WR1 x WR2) / (WR1 + WR2) and

(21)ROLL = ROLL1 + ROLL2

Combining these equations, and excluding the tire suspension and other factors as it is done with the existing geometric roll center calculation methods, the effective combined roll center location with respect to the center of gravity is:

(22)[RC to CG] = (WR1 x [RC2 to CG] + WR2 x [RC1 to CG]) / (WR2 + WR1).

All of these equations are based on the initial simplified model. The dampening rates have been excluded due to steady state assumption.