Front-running teams in every...
Front-running teams in every series tend to have developed methods of finding the perfect balanced setup. While trial-and-error has worked fine for years, we have now defined what constitutes a balanced setup and the method for predicting our cars' handling balance. Courtesy of NASCAR
In Part One of this series on racecar dynamics we introduced a new way of looking at the vehicle's suspension systems. We learned that it is important to match the desires of both ends of the car in order to have a truly balanced setup. This balance is what we have always desired when applying trial-and-error methods to tune our setups.
It is important to note here that the methodology, although fairly new in concept, has been applied successfully to stock cars for over 12 years now. Cars representing every class of stock car have had this method applied to them with predicted results. In other words, when the cars were balanced, they became fast and consistent, which showed in the tire temperatures being even front to rear at each side. The lap times became very consistent and the cars handled very well.
Much has been written about how the systems in stock cars work. There are many theories out there, some valid, some not so valid. The great equalizer and final judge is competition. It doesn't take long to discover the validity of a certain theory. A quick trip to the racetrack tells us all we need to know. The problem is that most theories have never been tested. How are we to buy into a particular train of thought if it has never been proven to be correct?
This simple diagram shows...
This simple diagram shows the two ends of the moment arm. The front roll angle is a product of the height of the center of gravity and magnitude of the centrifugal force. The moment center (MC) resists this force. The length of the moment arm influences the amount the front wants to roll.
The primary front suspensions used today in stock car racing are the double A-arm type, the strut-type with the top of the shock acting in place of a top A-arm, and the straight-axle, used mostly in modified and sprint cars. This last system reacts just like a rear differential system, so we will cover that with the rear suspension explanation.
A double A-arm suspension has a moment (roll) center that represents the bottom of the moment arm at the front end. The top of the moment arm is the center of gravity of the sprung mass of the car. As the center of gravity/center of mass tries to continue in a straight line as we turn the corner, a lateral force (centrifugal force) is exerted on the chassis at the center of gravity and that force is resisted by the moment center.
If you stick a shovel blade firmly into the ground, then pull on the end of the handle, your arms represent the lateral g-force, the upper end of the shovel handle is the center of gravity, and the blade at the ground is the moment center. The most efficient way to apply a force to the shovel is when we pull at right angles to the handle. In a AA-arm suspension, this is almost never the case. Usually the resultant force (a combination of the lateral force and gravity) is not perpendicular to the "shovel handle."
A more realistic picture of...
A more realistic picture of what goes on in the front of a stock car as we negotiate a turn takes into account the banking angle of the racetrack as well as the vertical and lateral location of the moment center. The centrifugal force combines with the gravitational force, that exists all the time, to produce a resultant force. It is the magnitude and direction of the resultant force that we use to determine the effective moment arm length.
In a stock car, we really have two forces at work being applied to the top end of the moment arm, the center of gravity. One is the lateral force of cornering known as centrifugal force, and the other is gravity. What many engineers fail to recognize is that the force of gravity is always present, even in a static state. What we have learned in studying the principles of statics and dynamics is that these two forces combine into one resultant force for which we can calculate a magnitude and direction.
By looking at the direction of the resultant force, we can see the true picture of how these forces react in the front suspension through the moment center. The effective moment arm is the result of the direction of the resistant force in relation to the location of the moment center.
The effective moment arm is the right-angle distance between the resultant force line and the moment center. This is a very important concept because we can see that when the moment center is moved to the right or left, the effective moment arm length changes significantly. As in the shovel handle analogy, a longer handle can apply more force to the end, just as a longer effective moment arm applies more roll moment to our stock car.
When the moment center is...
When the moment center is located farther to the left of the centerline, the effective moment arm is relatively long. This promotes a larger roll angle at the front and makes the front more efficient or soft.
Many stock cars have a front...
Many stock cars have a front geometry design that puts the moment center to the right of the center line. As the MC is designed further to the right, the front suspension becomes much stiffer due to the diminishing length of the moment arm.
If we can accurately predict...
If we can accurately predict the roll angles of both the front and rear suspension systems as the car turns, then we can change components so that the two systems are balanced, creating the correct amount of load transfer from left to right. This balance is good for our car and exactly what we attempt to do when we apply trial-and-error methods of chassis setup.
The rear suspension is much...
The rear suspension is much different than the front suspension. The car "feels" the spring base at the top of the springs. The moment center resists the lateral centrifugal force that causes the suspension to roll. Changing the MC height is the primary method used to regulate rear roll.
The magnitude of lateral force and the length of the effective moment arm are contributing factors that help us predict exactly what roll angle the front of our car desires. If the front end of our car was not rigidly connected to the rear, it would roll to a predicted angle and a predictable amount of load would transfer from the left front tire onto the right front tire. But that is not the case. The two are connected and unless we know for sure what each one's desires are, we cannot accurately predict the load transfer at each end of the car, nor can we create a balanced setup.
Both suspension systems of the car are connected by a semi-rigid chassis, however stiff this connection may be. What each system desires to do is influenced by what the other wants to do as the car negotiates the turns. The two ends must work together in harmony in order for everything to work correctly. I have used an analogy in the past that helps to explain this concept.
Have you ever seen a circus act where two people are in a horse suit? The horse moves around fine as long as each end is in sync with the other. When the rear wants to go left and the front wants to go right, it gets comical. In our stock car, when the front moves/rolls differently than the rear, it is not so funny and performance suffers.
In past eras of stock car racing setup technology, the rear usually desired to roll more so than the front. In the more modern setups with soft front springs, large diameter sway bars, and high spring rates in the right rear corner, the front may actually want to roll more than the rear. We can now easily achieve a negative roll angle in the rear with a high enough right rear spring rate and a high rear moment center. This still represents an unbalanced state.
The rear moment center height...
The rear moment center height of a Panhard/J-bar system is the average height of the two ends of the bar. For the purpose of roll-angle prediction, the MC is located laterally halfway between the top of the springs, regardless of where the bar is mounted.
There are seven primary components that combine to influence the amount of roll angle in the front suspension. They are:
1.The weight of the sprung mass of the car supported by the front suspension. This is represented by the weight of the front end measured on the scales under the left front and right front tires minus the unsprung weight of the wheels, tires, brakes, and so on.
2. The height of the center of gravity of the sprung mass.
3. The magnitude of the lateral force measured in g's. One g lateral force would equal the sprung weight of the front end.
4. The dynamic moment center location, both in height and width measured with the attitude of the car as it dives and rolls in the turns.
5. The overall spring stiffness translated to wheel rate as well as the relationship of the two spring rates side to side (i.e., softer right front vs. left front spring).
6. The front sway bar has an effect of antiroll and must be taken into account. The larger the bar, obviously the more resistance to roll.
7. The track banking angle has an influence due to the dynamic downforce when the direction of the resultant force lies between the front tires.
The leaf-spring type of rear...
The leaf-spring type of rear locating device is unique in that the top of the springs are also the lateral locating devices. Therefore, the average heights of the ends are the height of the rear moment center. This system provides a wide spring base and is superior to other suspension systems in some cases.
The rear suspension is a much different system than the front and we look at it much differently. At the front, the spring base is felt by the chassis at the wheels, but a rear solid-axle system (and this relates also to a front straight-axle suspension) has a spring base that is felt on the top of the springs. We should never translate spring rate out to the wheel at the rear. This dynamic model is not a new concept, but was developed and published over 60 years ago. I first read about it while doing research in the Virginia Tech engineering library in 1995, and it has proven to be true beyond a doubt.
The rear suspension model has the center of gravity of the sprung mass of the car representing the top of the moment arm just like at the front. The bottom of the moment arm is the moment center created by the lateral locating device known to us by the terms Panhard/J-bar, metric 4-link, leaf springs, or Watts link. These four devices comprise the majority of lateral restraint systems used for straight-axle suspensions in stock cars. Each restraint system has its own moment center that represents the bottom of the rear moment arm.
The height of the rear moment center is fairly easy to determine, but there have been varying theories on both the height and lateral location. Again, going back to early writings on the subject, the car "feels" the rear moment center laterally halfway between the two springs. Subsequent experiments have proven that regardless of the lateral location of the locating devices, the rolling force remains the same, thus proving the early publications.
The Watts link is mostly used...
The Watts link is mostly used in road-racing cars. The advantage of this system is that as the chassis moves vertically, the rear solid axle does not move laterally. With some rear suspension systems, lateral movement of the rearend would cause rear steer. The Watts system eliminates the lateral movement that creates the rear steer. The rear moment center height also stays very consistent with right- and lefthand turns, such as are encountered with road racing.
There are additional effects created by the Panhard/J-bar angle that tend to leverage and exert influential forces on the suspension that promote load transfer and those effects will be covered in future articles on chassis dynamics. Suffice it to say that excessive Panhard bar angles can have a negative influence on your setup.
There are eight primary components that affect the magnitude of the rear roll angle. These are: 1.The weight of the sprung mass of the portion of the car supported by the rear suspension (scale weights at the LR and RR tires minus unsprung components).
2.The height of the center of gravity of the sprung mass.
3. The height of the rear moment center.
4. The magnitude of the lateral force.
5. The overall spring stiffness as well as side to side spring split (i.e., right rear stiffer than the left rear spring, and vice versa).
6. The width of the spring base, which is the distance between the centers of the top of the springs.
7. The rear sway bar (if used) has a large effect of antiroll and must be taken into account. The larger the diameter of the bar in this system, the more resistance there is to roll.
8. The track banking angle.
Note: The car "feels" the spring base at the top of the springs. In a coilover sprung car, the distance between the tops of the mounting bolts is the rear spring base. For a big spring car, the distance between the centers of the top of the springs is the spring base. In a leaf-spring car, the distance between the centers of the leaf springs is the spring base.
Now that we know something about the cause and effect of roll angle for each suspension system, the key to creating a balanced setup is to change spring rates and moment center locations so that each end of the car will want to roll to the same angle, or what we call "having the same desires."
A typical rear sway bar installation...
A typical rear sway bar installation uses a high mount and arms with several holes to use to adjust the length of the arm, which changes the rate of the assembly. Note that the link between the sway bar arm and the rearend is at 90 degrees off the arm and directly above and inline with the motion of the axletube.
In order to set up our cars, we would need to be able to change component values in order to bring balance to the desires of the front and rear of the car. These changeable components include the spring rates, the moment center locations front and rear, and the static weight distribution.
In Part 3 of this series, we will examine how we can apply this technology to set up some typical types of stock cars. We will show different setups that might apply to your type of racing and why those setups will be better
A sway bar is a device that produces a resistance to roll when used in either the front double A-arm or straight-axle suspension system. Its influence in a AA-arm suspension is much less than when used in the solid-axle suspension.
The sway bar has a stabilizing effect on the AA-arm system and helps control oscillations common with that type of suspension. The sway bar is more effective in a straight-axle suspension when, for reasons of design limitations, the rear roll angle is hard to control, such is the case with big spring/truck arm suspensions.
The tendency in recent years has been to use softer front spring setups and larger diameter sway bars. Racers have found limitations to the usefulness of this trend, but have found that softer springs and larger diameter sway bars help to lower the car and promote a more efficient aerodynamic configuration when the car is at racing speeds. This does not preclude the need to find a balance in the desires of the front and rear.