Optimal thinking – Part 2

by | Jun 27, 2024

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Optimal thinking – Part 2

Theory and good practices on suspension kinematics design part 2: corner weight variation in steering


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Let’s start with a little story. A few years ago, I was invited to attend a demonstration of a high-end simulator, and asked a driver, a multiple winner of the Spa 24 Hours, to accompany me.

The simulator engineers asked me if I could sit in the car and give my impressions. I told them that I thought I was a decent driver on public roads, but did not think of myself as a good racing driver. Nevertheless, they insisted, and I went so I sat in the car.

The car was in the virtual pit lane, and an idea crossed my mind. I asked the engineers if all systems were recording. When they said yes, I turned the steering wheel 90 degrees to the left, and then 180 degrees to the right, before returning it to the initial position with a last movement of 90 degrees to the left. To the surprise of those around me, I then got out of the car and went to the control room, where I asked to be shown each tyre vertical load and front ride height variations.

There were none! After the control room engineers confirmed that every virtual sensor and/or simulation inputs and outputs were properly recorded, I exchanged glances with the driver I came with, and decided to leave.

Now, maybe the simulator hardware was good, but I had real doubts about the relevance of the vehicle dynamics software going with it. If the outputs from a steering wheel cannot be seen with a car at rest, I have all the reasons I need to doubt the outputs of a car at speed.

In other words, if the picture is already wrong, how can I trust the movie?

Four factors

Let me explain. For a given steering wheel input, the design of the front upright will influence four major factors of car performance. Here they are, not presented in order of importance, because that order could be different from one car to another.

  1. Corner weight variation in steering (what will be discussed in this article).
  2. Camber variation in steering.
  3. Ride height variation.
  4. Steering torque variation.

The four design variables that will influence the car outputs are the king pin inclination (KPI), caster angles, the mechanical trail (sometimes called the caster trail), and the scrub radius (sometimes referred to as the KPI trail). The majority of this magazine’s readers know those definitions but, for the sake of comprehension and visualization, they are shown in Figure 1.

Figure 1: Quick reminder of the caster and KPI angles and trails definitions

Due to space constraints, I am not able to display all the graphs and equations in this article as I do in some university master engineering courses, but there are some basic principles to explain, or at least be reminded of.

As a design judge in Formula Student competitions, I often pose this question: imagine that your car is on a set-up pad, each wheel on one scale. You are in the workshop, so no speed, no downforce, no longitudinal or lateral acceleration. You turn the steering wheel 90 degrees to the left, what variation do you notice on the left front (LF) scale?

There are only three answers: the LF corner weight goes up, down or stays unchanged. Additional questions to consider: if the corner weights change, do they change by 0.1, 1.0 or 10kg? Are any of the other corner weights changing at the same time? If so, which one, and by how much? Now, why is it important to know the answer to these questions?

Wrong answer

Worryingly, about 70 per cent of the students give me the wrong answers. If that is the case, I ask them how they are going to answer the following question: How, during the suspension concept phase, did you choose the caster and KPI angles and trails?

Let’s not only blame the students here. Except in a few high-end professional racing series, I have spoken with many so-called racecar engineers over the years who could not answer these questions either.

So, let us start to answer those questions with the simple analogy of a car with each wheel on a scale and a table (Figure 2).

Figure 2: illustration a shows a table on flat ground; b a variation of the diagonal loads if one table leg is longer; c a closer similarity with a racecar as there are springs between the ‘leg’ lower side and the ground (tyre springs) and the ‘leg’ top side and the table lower surface (suspension springs)

When you sit at a table and one leg is too short or too long, or the ground is not flat (Figure 2b), the table will stand on three legs. As soon as one guest puts their elbows on the table, the load shifts onto the three other legs. Unpleasant. One of the guests will invariably then take a paper napkin, fold it, and put it under the leg not in contact with the ground. Problem solved.

Cylinders and cones

On any car, if the KPI axis of one front wheel is perpendicular to the ground (no caster or KPI angle), when the steering wheel is turned, there will be a slight wheelbase and front half-track variation. In themselves, these will create wheel load variations, but no camber variation, nor any variations of the altitude of the wheel centre. With no initial camber, the wheel planes will stay perpendicular to the ground. Their movements will follow the envelope of a cylinder.

However, if there is a KPI, and a caster angle, the wheel plane will follow the envelope of a cone. When the steering wheel is turned to the left, the RF wheel will go up vs the car frame and acquire more negative camber. At the same time, the LF wheel will go down vs the car frame and have less negative camber. This can be easily demonstrated by turning the steering wheel of a Go Kart on stands and observing the movement of the wheels and variations in camber.

On any car, if you turn the steering wheel to the left, because of the KPI and caster angles and trails, the LF wheel will ‘want to go into the ground’. We know this is not possible. The LF wheel load will increase, and the LF ride height will increase, too. Also, the LF wheel will get less negative camber and the distance between the wheel centre and the ground will increase. It is as if we had a shorter ‘RF leg’ and a longer ‘LF leg’.

As with the table example, if one leg (here, the LF) becomes longer, necessarily the table will stand on three legs. Necessarily, RR ‘leg’ load will increase, too. There will also be more load on the LF – RR diagonal. If you know where the center of gravity (c of g) is, you will know which two remaining legs, RF or LR, will be off the ground.

At the same time the RF wheel goes up, its wheel centre will go lower as it acquires more negative camber. Less load on the RF will inevitably mean less load on the LR.

So, if we follow the table example, if we turn the steering wheel, will one of the four wheels be off the ground? That will be the case if you have dummy (rigid) suspensions and wheels, and the frame is 100 per cent rigid.

On a real car, however, we have eight springs: four between the bottom of each leg and the ground (the tyres’ vertical spring) and four between the top of each leg and the table (the suspensions between non-suspended and suspended masses). See Figure 2c. That is why, even with a very rigid frame, all wheels stay on the ground when the steering wheel is turned.

For a given steering wheel input, the design of the front upright
will influence four major factors of car performance

Figure 3: Vertical wheel load variation in steering. Simplified example with no speed (workshop measurements)

Wheel loads

Figure 3 shows an example of each of the four wheels vertical load variation in steering. This simulation has mostly been validated by workshop measurements. I use the word mostly here because the chassis frame is not necessarily perfectly rigid, and there are always some residual frictions in suspension (mostly dampers) and tyres. Also, the slight longitudinal, lateral and steering movements of the contact patch vs the scale centre could induce a vertical load measurement variation.

One good sanity check here is to add all four wheels’ loads. The total must remain the same. You can maybe tolerate an error of one or two kilos, but certainly not 10!

Figure 3 is a simplified example because there is no speed. We are in the workshop, or in the pit lane, as I was on the simulator at speed zero. The steering wheel angle is defined as positive when turned to the left. We can see that the LF load increases from about 2470N to 2630N for a 90-degree steering wheel angle to the left.

That is 160N, or about 16kg. If you know the tyre forces and moment sensitivity to the vertical load, you know that is not negligible. The same increase will occur on the right rear (RR). While on the LF and RR diagonal, the load increases by 2 x 160N = 320N, while the right front (RF) and left rear (LR) diagonal load decreases by 2 x 160N = 320N. That is what we sometimes call the diagonal load transfer.

How does that affect car handling?

KPI and caster angles and trails create an anti-front load transfer and a pro-load transfer

Figure 4: Theoretical load transfer calculation with no steering (all loads expressed in Newtons (N))

Lateral load transfer

Let us first look at a theoretical example of a lateral load transfer, as shown in Figure 4.

The two front-wheel static loads are different. Same for the two rear wheel static loads. These loads were measured on a real car where there is often a bit of asymmetry. There is no braking or acceleration, nor any downforce, and the total vertical load remains the same: 10,110N. The load distribution (48.66 percent front) is also unchanged.

A lateral acceleration of about 1.8g will create a front load transfer of 1950N and a rear load transfer of 2050N. The total lateral load transfer distribution (TLLTD), or ‘magic number’ (this concept has been explained in previous articles) is 1950 / (1950 + 2050) = 48.75 percent. The diagonal load LF + RR is 51.14 percent, the opposite diagonal load is 48.86 percent.

Of course, this is a very theoretical calculation. If we have lateral acceleration, we must be in a corner and, if we are in a corner, there must be some steering…

Figure 5: Theoretical load transfer only induced by steering (all loads expressed in Newtons (N))

Figure 5 shows the effect of the diagonal load transfer induced by the steering. The car is at rest, with no lateral or load transfer, no speed, no downforce, just a steering wheel input of 90 degrees to the left. 320N (2 x 160N) are added to the LF – RR diagonal and are removed from the RF – LR diagonal. It is interesting to note that the change in diagonal load percentage is significantly bigger that the one due to the lateral load transfer. We now start to understand how the design of the front upright can change car behaviour as much, if not more, than springs and ARBs, especially on tight corners with a lot of steering wheel input.

Figure 6: Combined effect of lateral load transfer and steering on dynamic wheel load

To conclude, let us now look at Figure 6, which is the composite of Figures 4 and 5, combining the effect of both steering and lateral load transfer.

The front-load transfer is 1950N – 160N due to the steering. That is 1790N. The new rear load transfer is 2050N + 160N = 2110N. The total load transfer without steering was 1950N + 2050N = 4000N. It has not changed, as 1790N + 2210N is still 4000N. The new magic number is therefore 1790 / (1790 + 2210) = 44.75 percent. Compared to the previous magic number of 48.75 percent, that is a very significant change.

A very simple way to summarize Figure 6 is as follows: KPI and caster angles and trails create an anti-front load transfer and a pro-load transfer. Knowing the influence that 10N of vertical tyre load variation can make on the car balance, it should now be clear that the design of the front uprights has to be very carefully considered.

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