Anti-Roll Bars or ARB for short are a great device to change the cornering balance of a car. ARBs are one of many tools you can leverage in your tuning strategy. Before we talk about how to setup a car with ARBs in mind, we first need to discuss the science behind them.
There are many suspension design variants in use today. However, all of them share one common goal, and that is to minimize CPV (Contact Patch Variation). Most race cars utilize a suspension design that falls under the suspension category of independent, an independent suspension is a suspension that not only allows wheels to move independent of the chassis, but each wheel can move independent of one another. One of the advantages of an independent suspension design is the improved ability to drive over curbs and bumps vs a dependent (solid axle) suspension. However, a huge disadvantage of allowing the wheels to move independent of one another, is now the chassis is free to roll about its longitudinal axis due to lateral load transfer. Using RST Software, we can directly quantify the roll behavior of a car by using a graph called the “Roll Gradient” this graph will tell us how much the car is rolling in degrees per unit of G. An example of a car without an ARB is given below, notice how much the car rolls in respect to the road and observe the high Roll Gradient.
Let’s talk about what the ARB tries to accomplish, the ARB connects the two wheels so that the two wheels (aka unsprung mass) are coupled again. I know you may be saying, “But Zach, aren’t we defeating the whole point of an independent suspension?”. The answer to that question is not exactly. In a dependent suspension (single axle) the lateral stiffness is equivalent to the bending stiffness of the axle, which is very high. With an ARB we can adjust the lateral stiffness as we see fit, which means we can allow the wheels to move independent of one another but also regain some lateral stiffness which reduces the roll of the car. An example of a car with an ARB is given below, notice how little the car rolls compared to the image of the same car without an ARB, the affect can be measured by the RG which is less than half!
USING ARBs TO CHANGE CORNERING BALANCE
At the beginning of this blog I mentioned ARBs can be a great way to fine tune cornering balance of a car. This is because as the car rolls, the outside tires will go into compression and the inside tires will go into rebound, this difference in wheel ride height will cause the ARB to load up. The ARB will now affect our lateral load distribution because the outside tire (tire in compression) will GAIN normal load, and the inside tire (tire in rebound) will LOSE normal load. This is a direct result of increasing the lateral stiffness for the axle we are adjusting the ARB on. As we increase one axles lateral load transfer we decrease the other axles because the Total Lateral Load Transfer is conserved.
But how does this relate to cornering balance? To answer that question, we need to understand a concept called “Tire Load Sensitivity”. Every tire has a coefficient of friction, this coefficient of friction is defined as the Cornering Force / Normal Force. Rearranged it means our maximum cornering force is given as:
The coefficient of friction behavior of µ is a factor of several things such as tire compound, tire temperature, etc. However, as you increase normal load (Fz) the coefficient of friction will go down. An example of a typical graph is given below:
Using the graph above let’s consider two cases:
A Car without an ARB on the Front Axle.
A Car with an ARB on the Front Axle
Before we look at the two cases above, lets investigate the total lateral force capability of the tire statically. If we have 800 lbs. of load on each tire.
Looking at the graph above we can see our coefficient of friction for 800 lbs. is approximately 1.65, our Grip becomes:
Fy (front) = (800*1.65) + (800*1.65) = 2640 lbs. (lateral grip)
Fy (rear) = (800*1.65) + (800*1.65) = 2640 lbs. (lateral grip)
Case 1: (No ARB)
As a car corners we begin to see Lateral Load Transfer where some of the load from the inside tires is transferred over to the outside tires. Due to most car designs factors such as Rake, and the Roll Center location, the rear will see more lateral load transfer than the front. If our front has 100 lbs. of lateral load transfer and our rear has 300 lbs. and our car doesn’t have an ARB, we have:
Fy (front) = (900*1.6) + (700*1.7) = 2630 lbs. (lateral grip)
Fy (Rear) = (1050*1.5) + (550*1.79) = 2559 lbs. (lateral grip)
From the example above we can see that the Front axle has MORE lateral grip than the rear, this means this car will most likely experience oversteer while cornering. This is because the rear axle will exceed maximum cornering force before the front. To correct this oversteer tendency of the car we can add ARB to the front.
Case 2: (with ARB)
If we add an ARB to the front axle and assume it contributes 100 Lbs. of lateral load transfer, we get the following:
Fy (front) = (1000*1.5) + (600*1.79) = 2574 lbs. (lateral grip)
Fy (front) = (950*1.5) + (650*1.75) = 2562 lbs. (lateral grip)
After adding the ARB on the front axle, we can see that the total lateral grip of the front axle is very close to the total lateral grip of the rear axle. This means that both front and rear axle will exceed maximum lateral force at approximately the same time. As a result, the car will feel very neutral during cornering. If the driver preferred a car that had slightly more understeer, we could increase the front ARB further.
Analyzing ARBs with RST Software:
Now that we understand what the ARB is and exactly how it affects corner balance of a car. Let’s talk about how you can analyze it in your sim. Using the “Lat. Stiffness Distribution Tab” in the RST Software we can see what the ratio of front load transfer compared to the rear load transfer is. This ratio will tell us the cornering balance of the car for each corner. As we increase front lateral stiffness either with Springs or ARB the graph will be higher because the lateral load transfer on the front will be higher than the rear. As we decrease the front lateral stiffness the graph will go down. Additionally, the Race Engineer feature within the RST Tool will tell you what the corner average is, (if you don’t fancy trying to read all the graphs).
Using the R8 Audi GT3 I made the Front ARB and Rear ARB both 50 N/mm. Scrolling the graphs to turn 3 and zooming into the graph and looking at the Top Graph we see the image below,
From the data above you can see the line oscillates around the 50% marker on the y-axis. This means the car is very balanced, which I also felt while driving the lap. To see exactly what the corner average was I can look at the Race Engineer who tells me the average is 54.42, which can be seen below.
I then Increased the Front ARB to 180 N/mm. Increasing the ARB stiffness will increase our front lateral stiffness, and as a result we will see a shift in the lateral stiffness distribution. After running a lap with this increased ARB setting on the front of the car, we have the following graph.
From the data above you can see overall the graph shifted upwards. This is because the Lateral Stiffness Distribution has shifted forward, and as a result the Front Increased in Lateral Load Transfer, and the Rear Decreased. Looking at the race engineer, he tells us the average for this corner is 62.66, the race engineer also gives us a suggestion warning us that the lateral load distribution is too far forward and is causing us understeer.
Comparing the two laps we manage to shift the Lateral Load Distribution by nearly 10%. This is quite a large adjustment and was felt while driving the lap.
ARBs can be a great tool when tuning a car. They can help reduce body roll which can improve aerodynamics and responsiveness of the car, additionally they can be used to change the cornering balance. The distribution of front ARB and rear ARB needed on a car setup will depend on the driver, car, and track that is being analyzed.