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ANTI-DIVE, AND THE LOTUS REACTIVE RIDE HEIGHT SYSTEM

Current F1 news includes reactive anti-dive front suspension being declared illegal. Why don't they simply employ enough (100%?) anti-dive geometry to do the job. In other words, what are the negative side effects of running high levels of anti-dive geometry in road racing?

Also, can you please verify for me if this is an accurate statement:

With anti-dive the axes of the upper and lower control arms are not parallel. When the suspension compresses, the upper ball-joint moves further negative on the X axis of the car than the lower ball-joint. This leans the spindle rearward relative to the chassis (adds caster). The torque of the brake caliper tries to rotate the spindle forward relative to the chassis (reduce caster) which results in the suspension extending. These countering forces are what makes anti-dive work: compressing suspension adding caster versus caliper torque trying to reduce caster.

Taking the last part first – what makes anti-dive as we know it work – what the questioner is describing is sometimes referred to as torque anti-dive. It is indeed related to the instantaneous rate of caster change with respect to suspension displacement. There is also thrust anti-dive, which relates to longitudinal, or x-axis displacement of the hub or wheel center.

This conceptual framework applies if we think of the forces as acting at the wheel center. I find it simpler to think of the forces as acting at the contact patch. In that case, all anti-dive relates to the instantaneous rate of longitudinal displacement with respect to suspension displacement, for the contact patch center, with the brake locked. This rule covers all cases, even including an inboard brake with drop gears in the upright.

The rule can be expressed by the following equation:

dF_z/dF_x = dx/dz (1)

where:

F_z is jacking or anti-dive force induced in the suspension

F_x is longitudinal force at the contact patch

x is longitudinal displacement at the contact patch

z is vertical displacement of the suspension, at the contact patch

dF_z/dF_x can also be called the jacking coefficient for braking. On a kinematics and compliance (K&C) rig, we can measure dx/dz by cycling the suspension freely with the brakes locked and the sprung mass constrained longitudinally and laterally as it is moved vertically, and measuring longitudinal displacements of the wheel support pad. We can measure dF_z/dF_x by holding the sprung structure at fixed ride height (or a series of fixed ride heights) with the brakes locked, applying rearward force at the contact patch, and measuring change in vertical load at the wheel support pad. Measured results will not follow the equation exactly. The differences between predicted and measured values will give us some indication of the compliances, clearances, and frictional effects in the system.

When we are designing the car, or analyzing an existing car from point measurements, for outboard brakes the car has positive anti-dive if the side view instant center (SVIC) is either behind the wheel and above ground or ahead of the wheel and below ground, or if the SVIC is undefined (side view projected control arms parallel) and the side view projected control arms slope upward toward the rear.

For inboard brakes, assuming no gears in the upright, the rule is the same, with one important change: the car has positive anti-dive if the side view instant center (SVIC) is either behind the wheel and above wheel center or ahead of the wheel and below wheel center, or if the SVIC is undefined (side view projected control arms parallel) and the side view projected control arms slope upward toward the rear. Stated another way, the linkage or control arm system can only have torque anti-dive when torque reacts through it rather than directly to the sprung structure via a jointed shaft.

So anti-dive geometry in the suspension linkage must either create caster change with heave, or make the wheel move forward with heave. In the case of an inboard brake, only the latter of these will produce anti-dive.

It is worth noting that absence of caster change with heave (equal displacement at all four wheels; vertical translation of sprung mass) does not mean the caster never changes. Controlling caster change in both heave and pitch is very much like controlling camber change in both heave and roll: we can’t have zero change in both modes. The best we can do is compromise so we don’t have a lot of change in either mode. One recommendation I often make is to have the side view virtual swing arm length (SVSA) about equal to the wheelbase. That gives similar amounts of caster change per inch of wheel travel in heave (caster increase) and in pitch (caster decrease).

What limits how much anti-dive we can run? Two effects, basically. First, we tend to get wheel hop with large amounts of anti effect, of any kind, mainly at the point of wheel slip. Second, anything that makes the wheel move forward with respect to the sprung mass when the suspension compresses makes the suspension less able to absorb bumps. When the wheel hits a bump, it is best if it can move rearward as well as upward. If it has to move forward to move upward, that makes the suspension less compliant, and increases ride harshness and wheel load variation.

Briefly, that’s how anti-dive geometry as we have known it works. What is this reactive ride height control thing that Lotus came up with, that has been recently in the news for getting banned by the FIA? How does it work? Would it offer advantages over conventional anti-dive? Would it be applicable outside of Formula 1?

The device uses a small hydraulic system, actuated by brake torque, to raise the front end a little bit, compensating for compression under braking. Rather than being attached to the upright in a completely rigid manner, the caliper is mounted to the upright on a bracket that can rotate with respect to the upright – somewhat like a brake floater on a beam axle. The caliper bears against a piston, or pushrod acting on a piston, in a small master cylinder attached to, or built in unit with, the upright. Under braking, the master cylinder sends fluid under pressure through a short hose to a slave cylinder built into the lower end of the suspension pushrod. With sufficient hydraulic pressure, the pushrod extends, raising the front ride height.

An anti-dive effect is thus achieved, without any wheelbase or caster change in heave. If such a system is tested on a K&C rig, Equation (1) will not apply. There can be a positive jacking coefficient without having a locked wheel contact patch moving forward when the suspension is compressed. In fact, if the suspension geometry provides zero anti-dive as conventionally analyzed, the system will show slight rearward motion at the contact patch as the hydraulics work, when rearward force is applied to the contact patch. The system will create a compliance. However, this particular compliance will be accompanied by an increase in wheel load if the sprung mass is not allowed to rise, or a ride height increase compared to behavior without the system if the sprung mass is not constrained vertically.

The FIA banned the system under the rule prohibiting movable aerodynamic devices. Some have suggested that they should have used another rule that prohibits suspension devices primarily intended to influence aerodynamics. Personally, I think either of those is a reach, and the latter rule is highly ambiguous. Claiming that a suspension system is a movable aerodynamic device in the same sense as a movable wing or a sucker fan is baldly absurd. It may be that on a very smooth track, with ground-effect-critical wings and bodywork, the suspension does affect aerodynamics as much as it affects anything. But in that case, anything at all in the suspension is a device that influences aerodynamics. Certainly a third spring in the front suspension is that. Those were introduced after the advent of wings, to limit pitch, and control how far front wings are from the ground. But they’re legal.

Apparently, interpretation of this rule depends on a judgement of what the primary intent of the device at issue is. I would still say it’s a big reach to say that control of aero properties is the

primary function of any kind of passive anti-dive strategy, when cars having no aerodynamic downforce devices at all use various strategies to limit dive, and so do motorcycles. F1 cars had anti-dive before they had wings. This is just a slightly different way of passively harnessing the forces in braking to reduce front suspension compression.

F1 legality aside, does this idea offer functional advantages? Can it do anything that ordinary anti-dive cannot?

Lotus is saying this is all much ado about nothing, because they tested the system and didn’t like the way it behaved, so they weren’t going to race it anyway. That may be so, but I don’t think the matter is as simple as that.

I would expect that, as with so many things, brake-reactive ride height modification can hurt or help the car, depending on the details of how it’s applied and its interaction with other design and setup elements.

Although I would defer to actual experimental results on this, I am inclined to suppose that anything that produces a large jacking coefficient will cause wheel hop or chatter at the limit of adhesion, and also exact some penalty in ride quality and wheel load variation when braking, even if the jacking coefficient is obtained without caster or wheelbase change in heave. I would also expect that this propensity would depend on the overall jacking coefficient of the front suspension system – meaning the total from the brake-reactive elements plus any conventional anti-dive or pro-dive.

Most F1 cars nowadays have little or no anti-dive or pro-dive. If we simply add a reactive anti-dive system to an existing F1 car, we would either end up with a fairly small effect (if the reactive system does not create a large jacking coefficient), or end up with wheel hop or chatter in limit braking.

But since everything in a chassis interacts with everything else, we don’t necessarily get a meaningful read on an idea’s true potential by simply bolting it onto an existing car and seeing if the driver likes it or if the lap times come down. What if we designed the car to have reactive anti-dive, and took advantage of the system’s properties by changing other things?

For example, suppose we designed the front suspension with a side view instant center near the vertical rear axle plane and well below ground. The wheel would then move rearward considerably as the suspension compresses, and the system would have considerable geometric pro-dive. Suppose we then combined this with enough reactive anti-dive to give us just a modest amount of net anti-dive. We would then have improved ride and reduced wheel load variation most of the time, with braking behavior about like other cars.

We would get this without the disadvantages of compliance struts as used in passenger cars to allow the wheel to move rearward on bumps. Compliance struts allow compliance caster change in

braking and also in cornering due to the rearward force the tire generates when it is steered and running at a slip angle. This in turn results in compliance camber change. Those effects are the reason compliance struts are not used on race cars. Even for a passenger car, where the benefits of compliance struts are deemed worth the penalties, the combination of pro-dive geometry with reactive anti-dive could allow really low impact harshness, and/or allow lower control arm compliance to be reduced, resulting in a handling improvement without ride penalty.

Reactive anti-dive is just as suitable for inboard brakes as for outboard ones. Ordinarily, the only way to get anti-dive with inboard brakes is to make the wheel move forward when the suspension compresses. With reactive anti-dive, we can have a wheel that moves rearward in compression, and any amount of anti-dive we want. In many cases, we might even be able to dispense with hydraulics. Hydraulics are pretty much inescapable if the brake has to steer with respect to the suspension, but if the brake does not steer and is part of the sprung mass, in many cases we will be able to get the effects we want with purely mechanical actuation.

Compared to conventional anti-dive, reactive anti-dive is a roundabout way of getting the job done, and it does inevitably involve using more parts. However, as with other roundabout ways of doing things (e.g. pushrod and rocker suspension), the extra bits afford a convenient way of introducing intentional nonlinearities into the system’s behavior. With either hydraulic or non-hydraulic actuation, we can use preload springs, limiting springs or stops, and linkages with rising or falling motion ratios to get all sorts of non-linear anti-dive. We can, for example, have anti-dive that is extremely aggressive for small amounts of brake torque, then drops away to near zero or even goes negative for the high ranges of brake force where we are likely to encounter chatter or wheel hop.

Therefore, it is my opinion that brake-reactive anti-dive has a future, perhaps most of all for street use. In outlawing it for F1, the FIA is passing up an opportunity to have racing justify its existence by improving the breed.