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# Optimal thinking

by | Apr 25, 2024

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## Optimal thinking

Theory and good practices on suspension kinematics design, part one

BY CLAUDE ROUELLE

Download the original PDF from RaceCar Design Magazine!

Content - 2024 - Article download - Optimal thinking

### Give me a lever long enough, and a fulcrum on which to place it, and I shall move the world,’ said Archimedes

We have learnt in our engineering courses that a force is defined by an application point, a direction and an intensity. So worry first about the force application point, and its direction, before you consider its intensity.

Now apply this thinking to racecars. Sometimes, when a car cannot get into ‘the zone’ of performance, even after having changed ride heights, springs, ARBs, dampers, camber, caster, toe, tyre pressure… you name it, changing some inboard or outboard suspension pick-up point coordinates by a few millimeters can make the car more controllable for the driver, and more sensitive to set-up changes.

What will follow over the next few OptimumG columns is a proposed approach for suspension kinematics design in 12 steps, which we will then look at individually:

1. Wheelbase and tracks
2. Scrub radius and mechanical trail
3. Caster angle and KPI angle
4. Outboard pick-up points
5. Front view VSAL, front view IC height, roll centre height
6. Side view VSAL, side view IC height, pitch centre height
7. Inboard wishbone pick-up points
8. Steering rack position, inboard and outboard toe link position
9. Spring motion ratio
10. ARB motion ratio
11. Integration with vehicle design
12. Suspension kinematics optimisation and conclusions

For years, WRC teams have been exploiting short wheelbase cars by turning small hatchbacks into very competent off-road racers

## Tracks and wheelbase

For most passenger cars, the wheelbase and the tracks are largely defined by the segment the car manufacturer wants to compete in and the consequent packaging of all parts.

For racecars, however, things are different. Several additional factors must be considered: inertia, type of circuit the car will be running on, driver skill, tyre characteristic, rules, weight target, downforce target and risk of roll over.

Figure 1 shows various racecar wheelbases. We know that in Formula 1, for example, the biggest part of the downforce is generated by the underwing. If well designed, the longer the underwing, the more downforce. However, a longer car will necessarily be heavier, so a compromise has to be found between how much you gain in downforce against how much you are prepared to give away in weight. With a new standard part for 2022, several F1 teams are finding themselves unable to reach the minimum weight.

Figure 1: Different wheelbases for different reasons

Also, a longer wheelbase will create a higher yaw and pitch inertia, which is good for stability in high-speed corners but detrimental to response and agility in short radius corners, such as in the streets of Monaco. Because of the parallel axis theorem (also called Huygens or Steiner in different countries), the longer the distance (in fact the square of that distance) between each car part center of gravity (c of g) and the car c of g, the higher the inertia. In fact, non-suspended masses and wings will create more yaw and pitch inertia than the engine and gearbox.

Roll inertia plays a role in performance too, but to a lesser extent because a car width is always shorter than its length.

In some racing series, cars are built under the minimum weight, and ballast must be added. Even with an imposed weight distribution, putting ballast in the nose and near the gearbox will help stability in large radius corners, while putting them near the car’s c of g will help response in small radius corners.

In series where ballast position is not mandated, engineers will use it in different places depending on track

The type of circuit helps engineers decide on which side the compromise is made.

In Formula 1, most of the drivers have very similar skills, but in some racing series there could be a large driver skill spectrum.

If we look at the man / machine control loop, a professional driver that has excellent sensing, as well as quick and proportioned reactions, could drive a car with less yaw inertia, while an amateur driver will want a less responsive but more stable (‘calm’) car.

## Tyre influence

The tyres’ grip will influence the yaw inertia target, too. On a wet surface, the difference between the ‘ideal’ inertias in slow and fast corners will be bigger than on a dry surface.

With the many hairpins encountered in a special stage, it is obvious a World Rally Car could not be run with a 3.6m wheelbase. WRC engineers, therefore, have the chance to distribute their ballast in different positions, and often locating it close to the centre of the car gives the best results.

The extreme case is Formula Student. For the type of circuits and corners used in this competition, if well designed, and if with good drivers, a Formula Student always has too much inertia. Because of the low-speed corners, though, stability is rarely a problem. Lack of response is. The best proof of this is that go-karts are lighter, smaller and have way less inertia, yet good drivers can still manoeuvre them in all corners.

In a relatively low speed competition like Formula Student where inertia is high, response is the most critical factor, so wheelbase and track are kept deliberately small for maximum agility

There is also no minimum weight in Formula Student, and we all know the best way to get a light car is to design a small car. I do not understand, therefore, why any Formula Student team would design a car with a wheelbase much longer than the 1525mm minimum imposed by the rules.

If we consider the risk of possible roll over, larger tracks are obviously better. However, I have seen Formula Student cars with tracks as little as 900mm. These cars did not overturn because they were light (less mass = less load transfer), had a low c of g and, even at low speed, produced enough downforce to counteract the load transfer. The attendent gain in agility was consequent, and the risk of high overturning moment was low.

In the next article, we will discuss the importance of upright design, especially the front one, and the influence steering has on corner load variation, camber variation, ride height variation and steering torque.

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