Cornering Speed

1) Tire's Grip

Most obviously, the selection of tires is decisive to cornering grip. Car engineers have nothing to do with the friction of the tires, which is determined by the compound and texture. However, they can choose the most suitable tires for their cars.

In the past decade, increasing tire's diameter and width is a common trend shared by all car makers. Do you still remember the Lamborghini Countach employed 15-inch tires ? Today's most exotic Ferrari, Porsche and Viper have 18 to 19-inch rubbers! Larger diameter accompany with larger width increase the contact patch area (that is, the area of the tire contacts with the ground), thus result in more grip. However, this also result in poorer wet road grip because the pressure acting upon the contact patch (that is, the car's weight divided by contact patch area) is reduced thus the tire becomes easier to "float" on the water. Therefore the texture also need to be improved for better water clearance.

Low profile tires are also fashionable in these days. Since the thickness becomes thinner, it is more resistant to side wall deflection under substantial cornering force. However, this is not much related to grip.

It must be mentioned that wide tires are not always good. Especially are front tires, the wider they are, the more resistance generates when they are steered. This create a heavy and insensitive steering feel, also more tire roar and wear. If you want to modify your car by using wider tires, always consider the drawback first. In my opinion, most well-sorted production sports cars have already equipped with the most suitable tires.

2. Suspension Design

To maximize cornering grip, the suspension must keep the tires perpendicular to ground under all conditions such as bump and body roll so that the contact patch area remains maximum.

Generally speaking, double wishbones suspension does the best job to keep the tire perpendicular to ground. The below figure shows how the conventional double wishbones suspension deals with bump and body roll. You can see there's no camber change at all under bump.

But the scene changes very much under body roll - camber changes for the same degree as the body roll. Track width also increases. Camber change reduces the contact patch area thus grip, and also introduces non-neutral steering (we'll discuss this later). Track width variation forces the tires to slip thus also reduce grip.

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Therefore engineers invented unequal length double wishbones. As shown in the below figure, the variation in camber and track width are largely reduced under body roll, although there is a small trade-off in wheel control under bump.

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Unequal length non-parallel double wishbones (below) is even more impressive, whose camber angle at the heavy-loaded outside wheel is nearly unchanged, although it is less good under bump.

3. Weight Transfer due to lateral force

When a car is cornering at speed, the car's weight transfers from the inside wheel to the outside wheel. The rate of change is proportional to the height of center of gravity (CG), the lateral acceleration ( in g ) and inversely proportional to the track width. As this :
 
Weight transfer = ( Lateral acceleration  x  Weight  x  Height of CG ) / Track width
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For example, a Factory Five Roadster is cornering at 0.85 g. Assuming its track width is 1600 mm, height of CG is 500 mm and it weighs 1250 kg, then we can calculate the weight transfer is 332 kg. Assuming the car has a perfect 50 / 50 weight distribution between front and rear, then we can see each inside wheel takes 146.5 kg while the outside 478.5 kg. What a big difference! Therefore you can see the outside wheel has far more influence to handling than the inside wheel. This explain why we prefer unequal length non-parallel double wishbones, because it has the least camber change on the outside wheel.

If the car corners at extremely high g-force, our calculation may find the weight transfer approaching half the weight of the whole car, this means the outside wheels take all the load while the inside wheels are virtually unloaded! Then the car is going to roll over! Don't worry, this is almost impossible in reality, as it requires impractically high lateral acceleration. In our FFR Roadster example, that equals to 1.6 g. Before that, the tires would have already run out of its traction limit and slide.

However, if the car is the elk-freightening Mercedes A-class or a high center of gravity SUV, with their exaggerate high center of gravity versus narrow track width, roll over might occurs even at a leisure cornering speed.

We've discussed the properties of weight transfer, but how does it relate to grip ?

Look at the following graph. It illustrates the Grip - Load characteristic of a typical tire.

As you can see, as the load increases on the tire, the grip generated by the tire increases, but at a declining rate. This says, when weight transfer to the outside wheel, the grip on the outside wheel is increased, but not increase as much as the grip loss on the inside wheel.

Therefore the total grip decreases as weight transfer occurs. The more weight transfer, the less the total grip becomes.

Now can have some conclusions : to maximize the cornering grip, we must minimize the weight transfer. We can achieve this by lowering the CG, by reducing the weight of the car or by enlarging the track width. The first could be implemented by placing the heavy engine and transmission as low as possible, by using a wide V-angle or even boxer engine, and by lowering the seats. The second can be implemented by using lightweight materials and better chassis structure, and reducing the size of the car, but this seems to conflict with the third method. Therefore I don't recommend to increase the track width to as wide as Lamborghini Diablo. It won't help making the car nimble too. Another advantage of weight reduction is obvious: quicker to accelerate and to stop.

These are no secret. Any one interested in motor racing already knows them.

Weight versus Downforce

But then you may ask a question: reduce the car's weight also reduce the grip generated by the tires, so what's the advantage ?

Firstly, because the car is lighter, centrifugal force acted on it is smaller. In theory the reduced grip could exactly withstand the reduced centrifugal force. Secondly, we could use aerodynamic downforce to increase the grip without increasing the centrifugal force. As a result, the car can corner faster.

4. Weight Transfer due to body roll

Body roll also introduces weight transfer thus reduction of total grip. Let's see the following drawing :



The lateral displacement of center of gravity (CG) is d. If we again use the Factory Five Roadster example (track width 1600 mm, height of CG 500 mm, weight 1250 kg), if it rolls 10 degrees when cornering, d will be 500 x sin10° = 86.8 mm. Then the load of the outside wheels can be calculated as: ( 1250 x ( 800 + 86.8 ) ) / 1600 = 693 kg while the inside wheels take 557 kg. So there is 68 kg weight transfer. Although it is not a great amount compare with the weight transfer due to lateral acceleration, its influence should not be ignored because camber change exists in this case.

We want to keep the body roll to an adequate level. We can use stiffer spring and anti-roll bar to reduce roll in the price of ride comfort. We can move the roll center, which is determined by the suspension geometry, as close to the CG as possible so that the roll moment is largely reduced, but this has a very bad drawback - a large jerking force will be generated and jerk up the body thus raise the CG. Alternatively, we could leave the body roll alone and try to lower the CG, so the weight transfer is also reduced.

After all, I don't recommend to eliminate body roll, since it is an important signal to tell us how well the car enters a corner and how close it approaches its limit. Body roll is a kind of feedback.

5. Four-Wheel Drive

Finally, 4WD can maximize the total grip of the car, both in straight line and cornering. The former case is easier to understand: compare with RWD and FWD cars, 4-wheel drive cars distributed less tractive force to each of its driving wheels, so it is less likely that the tractive force exceed the frictional force generated between tires and ground. In other words, the driving wheels are less likely to slide. However, since we are talking about handling, straight line grip is not our interest.

For cornering grip, whose direction is perpendicular to the wheel's tractive force, the above mentioned theory is completely useless. The actual theory is quite complicated, it requires the concept of Slip Angle, which will be introduced in later sections. We will continue this discussion later.

Steering

Surprisingly, steering mechanism is not in our scope. In fact, most good cars today use rack-and-pinion steerings whose designs are more or less the same. What makes one car's steering superior to another is the weight distribution, drivetrain system and suspension geometry etc.

Steering Response

I always said mid-engined cars are superior in handling. Some ignorant auto journalists interpret as "because the heavy engine is placed in the middle of the car, it is easier to achieve 50 / 50 weight distribution between front and rear. In other words, the car is more balanced."

Wrong ! Most mid-engined sports cars have about 60% weight bias towards the rear, thanks to the engine, gearbox and differential are all located at the rear half of the car. In contrast, a Factory Five Roadster has the engine in front and the transmission mid mounted (right behind the motor), so it could actually achieve the perfect 50 / 50. Other good front-engined cars such as BMW 3-series and Honda S2000 also achieve 50 / 50, thanks to the lay-back engines.

The reason I prefer mid-engined cars is, instead of better balance, mid-engined cars have superior steering response. This is because they have lower polar moment of inertia. Considering the two system shown in below.


Both of them have equal front to rear weight distribution. The one having the mass concentrating near the CG (in other words, lower polar moment of inertia) is easier to rotate about the CG. This could be easily verified by our experience. Applying the same steering force, the mid-engined car steers more quickly. The same for countering a steering action. This means it is responsive to steer and correct.

There is another advantage: since less effort is required to steer the car, we can reduce or even discard power steering, which always filter the feedback from the road thus downgrade the steering feel.

Dynamic Balance

Another reason I prefer mid-engined car is actually the slightly rear-biased weight distribution. In acceleration, we need more weight on the rear wheels to generate more traction for better launch. Obviously, FR cars are inferior in this respect. (FF cars, however, might be even better, but we shall see FF’s disadvantages later)

If acceleration is not much related to handling, braking must be very decisive. When braking into a corner, weight transfers from the rear to the front, hence actually creating unbalance to a car which achieves 50 / 50 in static condition. In contrast, a 40 / 60 mid-engined car may achieve a real dynamic balance under braking.

 

>>> Continued here...

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