Chapter 5
Finding the Details
This chapter covers Roll Centers, the Center of Gravity, Wheel Rates, Chassis Frequencies, Front Lift, and Weight Jacking in more detail. In each topic of this chapter, try to relate it back to how it will affect Tire Loading and
Camber and thus the car's Handling Characteristics.
Finding Roll Centers
Figure 8
is a picture of a Roll Center with Non Parallel Arms. In this picture the rounded rectangle is the tire, the dots are the "A" frame pivot points, the vertical dashed line is the center line of the car, the shaded blue rectangle is the chassis/body. This picture is going to help us find the Roll Center of a double "A" frame suspension car. Just draw lines through the pivot points of each "A" frame as shown by the two red dotted lines. These two lines cross at some point, could be on either side of the tire. The blue dashed line from the point where the first two lines crosses through the bottom center of the tire. The roll center, by definition, is where this blue dashed line crosses the center line of the car. A blue circle is drawn around the roll center.
Figure 13: Roll Center with Non Parallel Arms
The chassis/body rolls and bumps. It is a dynamic condition. If you redrew the lines for each bump or body lean, you would see the roll center point change for each new body position. In general, the roll centers move as the chassis/body moves. Technically the roll centers are called
Instantaneous Roll Centers.
The Hand calculations (like the picture we just drew) are very useful for understanding how the geometries change with bumps and body roll. They can also be accurate enough for comparisons. When drawing pictures to see the camber changes of the tire, always keep the "A" arm lengths the same. Also, the pivot points in the tire and the chassis/body must stay in the same relative place in these parts. When the body is redrawn (higher, lower, or rolled) then the tire must be redrawn to meet the criteria outlined in this paragraph. Have fun!
There are many, in fact, an infinite number of points the pivot points could be moved to in both the tire and chassis/body. A few of these combinations are quit common though. This picture is one of them. Relative to the last picture, the top chassis/body "A" Frame pivot point has been moved. Also, the "A" Frame are equal length in this picture. The red dotted lines are again drawn through to centers of the pivots points. They will cross at a point somewhere very far from the car, because they are nearly parallel. If you draw a line back from this point, to the bottom center of the tire, it will be nearly parallel to them. The new roll center is circled at ground level.
Figure 14:
Roll Center with Parallel Arms
Figure 14
is very nearly today's RC10 rear geometry. These ball joint locations will have the following properties. The camber does not change with bumps, but camber does follow the chassis/body roll. For each degree of body roll, the camber will change by a degree. The roll center moves up and down with the body in this case.
Raising the roll center, relative to the ground and center
of gravity, will limit weight transfer as described in
Equation 7
. But raising the roll center, relative to the ground and center of gravity has a disadvantage. It will effect how the camber changes with chassis/body bump and roll. Generally, the higher the roll center is, the more the camber will change because of bumps. But with the higher roll center, the camber will change less because of body roll. The roll center will still move up and down with the body.
Another combination of suspension links that is quit common is this. This is a different type of suspension, it is called a pan hard bar. Real Sprint Cars use it. It features a very high roll center and does not effect the camber in any way. A live axle is used to control the camber of the tire. The live axle is not shown. The picture is totally redrawn to match the new parameters. The dots are now the pivot points of the pan hard bar. The roll center is where the pan hard bar passes through the center line of the car. Again the roll center is circled.
Figure 15:
Roll Center of a Car with a Pan Hard Bar
Figure 15
is not a common Radio Controlled car setup. Although, the Pan Car rear axle acts like a "pan hard bar". The rear roll center of a Pan Car is at axle level. This is one reason Pan Car's corner so well, but also why they are very temperamental.
Finding Wheel Rates
A wheel rate is not simply the spring rate. There are two components of the wheel rates: the spring rate and the motion ratio. The spring rate units are pounds per inch. It expresses the stiffness of the spring. The motion ratio is the leverage factor of the suspension arm that the spring is pushing against. It has no units.
Figure 16
is a picture of a suspension arm with pins in it. The picture also shows a couple of dimensions, D
1
and D
2
. The
motion ratio is D
1
divided by D
2.
The wheel rate calculation uses this motion ration.
Figure 16:
Suspension Arm, Motion Ratio
The
wheel rate is found by solving
Equation 10
.
Chassis Stiffness
Wheel Rate measurements are academic or irrelevant if the frame (chassis) is not 10 times more rigid than any Wheel Rate. If the
frame flexes, spring rate changes will not change the car's handling characteristics they should. The load will still be absorbed by the wheel rates, just not distributed at the wheels as shown by the calculations.
Chassis
Frequencies
When a soft ball rolls over a rock, it will bounce up. A harder ball will bounce up higher. Your car exhibits the same effect because of the suspension stiffness. As you hit a bump, one end (front or rear) will bounce up higher and therefore longer in time and distance. This is a problem if the rear of the car stays up (or light on its tires, possibly reduced
Cts) longer than the front. The front (which in this example still has good traction) will steer, but the back will go straight, spinning you out.
This is a picture to help you understand what
Equation 11
and spring frequencies are all about. It shows a Mass being supported by a spring. If the Mass is pushed down and then released the Mass will oscillate at some natural frequency. The frequency that it oscillates at is dependent on the Mass weight and the Wheel Rate.
Figure 17: Spring Frequency
The formula in
Equation 11
finds the frequency of the Mass. Wheel Rate is in pounds per inch. Mass is the weight supported by a wheel excluding the unsprung weight. It is in pounds. The formula calculates the frequency expressed in
cps (cycles per second) of the Mass. This formula assumes that the wheel is of infinite weight. This is done to enable a simple calculation. The complete math is unnecessary for understanding chassis frequency. These simplified calculations serve this purpose.
Equation 11:
Chassis Frequency
The front chassis frequencies should be set higher than the back chassis frequencies. Then the front of the car will tend to be light longer, thus is easier to drive because the car will tend to push or
understeer. Also, these chassis
frequencies are an indication of how an off-road car will jump. Which end of the car (front or back) has the higher chassis frequency is not intuitively obvious. The end with the highest wheel rates would seem to be the end with the highest chassis frequency, but that end may be heavier, thus a lower chassis frequency could result.
Shock Absorbers
Shock absorbers are used to dampen the oscillations of the car. To stop it from bouncing over bumps and to stop some of the swaying in the corners. Shock absorbers will influence the
wheel rates and thus the chassis frequency and handling characteristics. In theory it should not, but when you use enough
shock to kill the oscillations it will always have some effect. What shock absorbers to use? There is no one hard answer. It will vary with driver style, driver habits, race track conditions and
wh
eel rates.
Unsprung Weight
Unsprung weight is very closely related to chassis frequencies. It probably should have been in that section, but we did not want to confuse that discussion. Unsprung weight is the opposite of chassis frequency. We call it wheel frequency.
With wheel frequency, try to make the frequency as high as possible by minimizing the wheel and tire mass. They can stay on the ground because of their light weight. The math is
Equation 11
, except the Mass is now the wheel, tire, and some portion of the suspension components.
In both cases, wheel and chassis frequency, the Mass we are not using in the calculation is assumed to be infinite. This assumption is done to enable a simple calculation.
Finding Front Lift
Acceleration also changes tire loads. Weight is transferred because of the acceleration. The front lift caused by acceleration is a very considerable amount. The acceleration of a Sprint car can be high enough that the front tires come off the ground under hard acceleration. A NASCAR Cup car also transfers a considerable amount of weight.
To find the new tire loads because of acceleration, apply
Equation 12
. The elements of these equations are pretty self explanatory, except for CG
height
, which stands for the
center of gravity height.
Equation 12
describes the amount of
weight
transferred because of acceleration, it would follow that the front and rear ride heights would change because of these changing loads. This is not necessarily the case though. The rear springs would compress a lot, but
anti-squat is built into the rear suspension geometry. Anti-squat does not prevent the weight from transferring but does limit the amount of chassis travel caused by it. The Anti-squat absorbs the weight transfer mechanically in the suspension components.
Equation 12:
Weight Transferred, Forward Acceleration
Weight Jacking
Remember that cornering force on the
center of gravity is transmitted through the chassis/body via
the roll axis as torque and loads the tires. Another force, because of the cornering force, is between the
roll centers and the racing surface at the bottom of the tire. The net effect is the vertical arrow in
Figure 18
. That's right, this force is trying to lift the car up. This is the force that causes
traction rolls
. The best examples of a
traction roll
are the midget race cars.
Here is the scenario: the outside tire finds a very high amount of traction on the track. It could have been a hole, the cushion of a dirt track, or some other reason. It does not matter. The car crashes. What happens during a
traction roll
is the outside tire gains a lot of traction for some reason and the vertical force on the center of gravity
increases, causing the tire to gain even more traction. This causes even more vertical force on the center of gravity, and so on and so
forth--an avalanche effect. In a short moment this avalanche effect crashes the car. This phenomena, because it happens so quickly, does not really affect handing characteristics, except during the split moment when it happens.
Study the drawing and observe that effect can be minimized by keeping the roll center low. Also driving style, not getting the car sideways, will help. Weight Jacking is just one of the elements of the car which must be considered while setting the roll center heights.
Figure 18:
Weight Jacking
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