Car Dynamics in a Corner

It's important to understand what the car undergoes during a corner, or while driving  in general, so that we can understand how to drive with the car and not against it. The right technique will give us a greater reserve of grip, speed and the potential for good lap times and a reduction of mechanical wear and tear (along with gas milleage).

It all begins with Tyre Grip

For a while now I've been talking about the significance of Tyres as if they exceed the importance of the chassis and suspension. Well, they do. The reason they do is that they are the ones in contact with the ground and all the improvements and performance of the chassis, suspension, steering, engine, drivetrain and even aerodynamics, have to be realized by applying a certain force through the tires and onto the ground. What's the worth of a incredible Formula 1 Chassis if you fit it with bike tyres that can't convey it's performance to actual speed?

The tyre only contacts the ground in a little patch, about the size of an average size 9 shoe. Try stuffing two pieces of paper on both sides of the a tyre and you will see what little distance is left between them. This is the contact patch. The rubber inside the contact patch generates grip by squeezing into fybers into the little undulations of the tarmac surface. Each rubber element twists down under the weight of the car and into the surface, generating grip. The formula used to present this is:

Fs=Nμ

Fs is the force of static friction (grip) and N is the Normal force, which is the vertical loading of the rubber fyber. μ is the coefficient of friction: Softer rubber or grippier pavement hold a higher μ value. The fyber distorts and squeezes into the earth, but it also has to do things: Make the car accelerate, decelerate or turn. For the car to accelerate, the gripping elements must distort not only downward but to the back as well. For deceleration, tire rubber distorts forward, and for cornering it distorts laterally. Overall, there is so much twisting and deforming that the fyber can take, one extended too far it will start tearing apart and slide.

This can be expressed mathematically as F=√(L²+T²) and can be intuitivelly expressed like this: Every tire can only give you 100% of performance. Spend 80% on cornering and you have 20% left for either braking or accelerating. Decrease it for 50% cornering, and you've freed the extra 30% for braking/accelerating, and if you spent 100% on braking, you have zero left for steering! This is expressed in the "Friction Circle," which is an oval-shaped circle which expresses how much a car can corner, brake, accelerate and/or combined, without exceeding the limit of grip. According to this modell, you need to steer while keeping the car moving at a constant speed, which is done by sensitivelly using the throttle.

However, there is more to it than that. When the car accelerates, decelerates and/or turns, it experiences changes of balance. When we brake, we apply a "negative acceleration" vector while pulls backwards, while the force of inertia is pushing forward. The grip of the wheels when they brake and slow down resists this force. So the force tries to trick the tires. Instead of pushing straight on against the decelerating tires, it disguises itself as torque -- a force that works around in a twist and trying to roll the car forward instead of pushing it. This is why you feel the car nosediving when you brake and it is called a forward weight transfer. It changes the weight distribution of the car to cause the front axle to be pushed down against the road, while the rear axle is slightly elivated. 

Remember the first formula? Fs=Nμ? If the forward weight transfer pushes down against the tires, it increases the normal force N and increases grip in the front, on the expense of the rear. The same would happen when steering, where the wheels on the "outside" of the corner get loaded, and the rear wheels under acceleration. Weight transfers somewhat obstruct proper driveability and can reduce grip. However, a good driver can use weight transfers in a clever, accurate way which allows for faster and/or safer driving.

Weight transfers can help during transients. One transient is when we enter a corner. We turn the wheel which, through the steering mechanism, tilts the front wheels in the direction of the corner. The rubber fybers wish to continue going straight, so they twist aside in an attempt to remain perpendicular to the road. The result is a "Slip angle" which makes the tire point (and turn) at an angle slightly smaller than the angle in which you turned it. The slip angle allows the tire to use it's grip to turn the car and create a cornering force (Centripetal force), but also subjects the car to external forces.

Remember the force of inertia? It is the force that, based on Newton's first law, pushes the moving car forward. It is described as F=mv²/2. M is the car's mass; v is the car velocity or speed. The force of inertia is pushing the car forward while the grip generated by the tires is pulling it into the the corner. This turns the inertia into a side force (lateral force) which pushes the car out. The force is in part turned into torque and creates the weight transfer we talked about earlier. The side force, which originates from the inertia, is expressed as:

F=mv²/r

F=mgμ           

mv²/r = mgμ

v=√g μr

r is the radius of the corner and g is the force of gravity (downward acceleration of ~9.8m/s). If the cornering speed v exceeds the speed allowed by the variants of grip levels (μ) and the corner radius (r), the car will slide forward and out of the corner, as if it is refusing to turn. The way to reduce this possibility is:

1. Reduce speed

2. Increase grip: By investing in good tyres, tyre pressure, wheel alignment, etc...

3. Increasing radius: Taking a line through the corner (look in the article about cornering lines) that will increase the radius

4. Being smooth and percise with your steering input

5. Using a forward weight transfer 

The different ways are listed according to priority. The effect of proper corner entry speed is much larger than that of a line that allows to take a greater radius. Being smooth is also important, because the effects of tire element deformation and suspension movement takes some time, which is why we need to load the car with forces  progressively. 

A forward weight transfer is an important element in proper corner entry. When you brake, steer or accelerate, the car's center of gravity moves. When you brake, the wheels generate deceleration that slows down the car. The force of inertia (K=mv²/2) seeks to keep pushing the car forward, resisting the deceleration. This resisstence makes some of the inertia turn into torque that tries to push the car in a circular motion and basically roll it foward. This can be felt as the car nosediving during sudden braking. This movement creates an additional downforce which pushes down against the front tires, giving them more grip, while proportionally reducing grip to the "elevated" rear wheels.

It's important to understand this weight transfer: If we look at the formula for cornering speed, we see that it carries two contradicting effects: A heavier car produces a greater side force pushing it out, but also produces greater friction that keeps it in the corner. We can see that eventually the parameter M is canceled out of the formula, which might lead us to the conclusion that it carries no effect. This is not true. Because of the deformation of the tire's elements under load, it is custom to say that the coefficient of friction reduces slightly under additional load, so the net result of additional weight reduces the overal grip/turning speed.

However, with a proportional increase of tire pressure, the effect of weight on the tires' grip is reduced and the grip will, up to a certain point, be increased. The car will still suffer, though, from dynamic disfunctions like slower transients coming into the corner. 

However, this disscussion refers to actual weight or load. Weight transfers are a result of an application of torque, not actuall mass. The result is that a forward weight transfer will categorilly increase the front grip and reduce rear grip, making the rear of the car slide out. This reduces the overall cornering speed, but increases the speed that can be carried through the transient. 

When the car is turning into the corner, it does so by relying more on it's front wheels (which are the ones tilted into the corner) that on it's rear wheels. Once turned, it achieves a steady state of cornering where it relies on both outside wheels, and when it straightens out of the corner it relies on the rear wheels. Hence, turning into the corner we seek to increase the front tires' grip by gently loading them with additional downforce by slowing down very gently. Of course braking would mean using some of the tires' grip for deceleration instead of cornering, but with feel it's possible to achieve a positive influence. There is a slight trade-off is the immediate responsiveness of the steering, where the tire takes slightly longer to develop the front slip angle, so there is a slight (unnoticable) hesitation before the car responds, but than it reacts more sharply and the transient is overall quicker and can be performed at a higher speed. 

After the turn-in is finished, the braking force is smoothly removed and replaced with steady-state acceleration, where the car is not slowing down or speeding up. This allows the fastest possible speed through the corner. when coming out, we increase the throttle to accelerate, which helps the rear wheels to straighten us out. This procedure is relevant mainly to slow-speed corners. In the faster corners, there is no problem in rotating the car into the corner and "trail braking" is not nessecary.

Another point, to be mentioned after smoothness and weight transfers, is that of decisiveness. Clearly a smooth steering input is not effective if it's too slow. The subject of how quickely to turn the wheel is debated amongst many performance drivers and is perhaps the most dramatic difference in driving style betweent different drivers. It is true that being smooth is crucial, but it so happens that some professional drivers (on tarmac) are not so very smooth and reach identical and sometimes superior results as smoother drivers.

The reason is that some drivers are too smooth, while others are to "jerky" and a selected few know to achieve the right balance. The "right balance" changes depending on the corner and the car. Slow, sharp corners, where you take a very late line (the "last apex line") require a decisive steering input where the weight of the car is on the front wheels. The quick steering input is required to enable the car to change directions quickely enough, as the required line obligates.

Another situation is a fast corner, where for some reason the car has an increased understeer tendency that makes it "refuse" to take the right line. The understeer tendency can be a result of car setup (usually in powefull front-wheel drive) and of the corner (usually an uphill incline or side slope that increases understeer). In this case, we do not want to reduce the throttle input, so we compensate by a quick steering input that turns the car in the right direction.

Effect of car setup

The basic rules of effective driving are paramount for every car and every driving environment. However, slight differences of driving styles remain, and they have to fit the car being driven. A professional race car is the most extreme example. It has a low ride height and center of gravity, reduced weight and stiff suspension. The result: A sharp car that has to be driven very smoothly and without much of weight transfers. Being low and light, the car's weight transfers are smaller. A small weight transfer can occur faster, and the stiff suspension make it happen faster still. Because the car is sharp, the driver must compensate by being smooth and carefull around the limit.

Road racing cars and especially rally cars are set up differently. They are a tad softer, ride higher and with less grippy tires. They therefore generate larger weight transfers and react more progressively. These cars require a driving style which is a bit more "decisive" and not quite as smooth as a proper race car. 

Road cars portray a wide arc of handling characteristics that might be similar to one of the above and be a symbiosis of each of the prototypes. Some cars will require a smooth and accurate driving style, but others might perform better in a driving style that is a bit more "messy." A short and relativelly stiff car with a relativelly balanced weight transfer will be more responsive to a decisive driving style. Where a stiffer car with a larger wheelbase and and maybe a heavier front, will not tolerate such a style. 

It's important to understand that the difference is mainly in the approach, and the actuall changes in the driving style are much more subtle than they might appear from reading. All cars require smooth and percise inputs, which are also as decisive as necessary.

 

Car Setup

Knowing your car is usefull knowledge in the realm of driving. Understanding the effect of changes in car design and setup allows the driver to be more knowledgeable at acquiring a "feel" for cars, whether in comparing different cars (as journalists) or simply at driving them effectivelly, as a driver; Verily, this article is also usefull for drivers who want to change the setup of their car, even though this is not the primary purpose of the article. For those, I issue the following rules of thumb: First, remember that a car is an object. Changing one aspect of the car carries it's effect on other parts. This also dictates that changes must be done scientifically, with one little change at a time. The second rule is that tuning always begins with driver's skills, continues in driveability, follows in grip (starting with tyres) and ends with the engine.

As an article for drivers, and within the knowledge limitations of the author, this article will deal with dynamic aspects of car setup: Tires, Suspension, Steering and Chassis. These components create a car that works as one piece, but still grips the road at two axles: Front and Rear. This is crucial to understand because all of the changes below: Tire improvements, suspension setups, chassis bracing, etc -- can all be applied on different amounts on the front and rear.

Making adjustments to increase the grip of the front will make the front lose grip (=slide) at a higher limit relative to the rear. If the front breaks away before the rear, the car's handling is said to be of understeer. Sliding the front wheels, which turn the car into corners, make them skid forward and out of the corner, as if they refuse to turn-in, hence under-steering. However, if the rear breaks-away, it is said to oversteer. The rear sliding wheels can no longer keep in line with the front wheels, making them swing aside in corners and rotate the car "too much" into the corner -- thus over-steering. A car can also achieve neutral handling, where both ends slide simultanosuly. 

We measure a car's handling by taking a turn on the limit. We need to keep the right foot on the throttle with sensitivity to keep the car at a constant speed through the whole corner -- not slowing down or speeding up, just turning. This is the natural balance of the car. If this makes the car understeer, the car is said to naturally understeer. If the rear is sliding, it is said to naturally oversteer. If both ends slide symmetricaly, it is said to behave neutrally.

Unlike what some people think, ALL cars are set to understeer -- Front-Wheel Drive, Rear-Wheel Drive, All-Wheel drive; Road car, Race car (Saloon/Single Seater), World Rally Car,  Drifting car or Off-road car -- Based on the laws of physics, when you first turn the wheel, you fight against the inertia that keeps on pushing the car forward, hence generating understeer. Also, understeer allows to feel the slide through the steering mechanism, and feel your way when driving on the limit. Recovering from understeer is more simple and intuitive.

Oversteer is often looked upon as "quick" because it allows the car to change direction more quickely. This leads to the false notion that race drivers set their cars to oversteer while in fact the amount of understeer in professional race cars can be surprising! Understeer allows the driver to brake as late as possible and as hard as possible before the corners and into them, while keeping the car stable. Since professional race-cars are rear-wheel driven, setting them to understeer in the apex means that there still is grip in the rear wheels, and allows to commence acceleration out of the corner earlier.

Understand that a driver can make the car do anything: Understeer, Oversteer and Neutral-steer. However, if he just turns the wheel, without adding acceleration or deceleration, it would generate understeer. If he would do the same turn and brake with feel, he might get "over" the natural understeer tendencies and create neutral handling or even oversteer. Applying throttle could either increase the understeer or reduce it and even generate neutralsteer or oversteer again. 

Tires

Tires are always the most substantial aspect of automotive design. They form the actual contact with the road. It is only through that fragile contact, that the capabilities of the driver, suspension, steering, chassis and engine can be "put down" onto the road and generate performance. The tire is round, but it contacts the road through a flat contact patch at the bottom. Looking at that contact patch in magnitude tells us that the seemingly solid rubber is in fact bulit out of a collection of polymeric rubber fybers. Likewise, looking at the same magnitude on the road under the contact patch shows us that the seemingly smooth road surface is in fact rugged.

This combination gives us grip. Imagine a rolling tire. Focus on one fyber on the tire's radius. While the tire rotates, it eventually brings the fyber to contact with the road. The fyber is than crammed against the road by the downward pressure of the car's weight. This pressure makes the elastic fyber squeeze into the little undulations of the road and grip into the them, pulling the car forward. As the fyber distorts more and squeezes deeper into the road, it will produce more grip, up to a point where more bending of the fyber would threaten it's integrity. 

The way to improve tire grip can be achieved in one of several ways: The first is to use softer rubber that allows more flexing to take place. The compromise here is that the tire wear out sooner. The second method is to change the amount of downward force ("Vertical Loading") by using a wider tire that distributes the same weight over more fybers. The disadvatage here is that this tire will be heavier and will be less effective on wet surfaces.

However, the tire's job does not end with the contact patch. The sidewalls also have a job. When turning, a lateral force is working on the car and tries to push it's components away from the corner. This force takes a toll on tires. It makes them bend aside and twist. This twisting changes the contact patch: It creates folds in it, retracting some of the rubber from the road. By use a lower-profile or a stiffer tire construction (regardless of how soft the rubber compound is), a tire is made to be less distortive and more grippy. 

Additionally, stiffer components make for sharper responses. The car reacts to the driver's inputs faster. The disadvatage is that if the driver makes an input that is above the car's ability to perform (above it's limits of grip), it will still give us a sharp response, so the transient from grip to sliding is more sudden and with less warning. However, once sliding, the car will also respond more sharply to the corrective input, making the slide more controlable. 

Stiffening the tire is also made possible by use of air pressure: More air makes a stiffer tire and less air makes for a softer tire. But air also has another effect, unlike the size of the tire, which effects the tire's shape. Low air pressure makes the tire recieve a convex shape where the inside of the tread folds away from the road, which remains in contact with the corners of the tread (which are less grippy in general) and denser air pressurs make it recieve a concave shape which orginates grip from the center of the tread. The goal of proper air pressure is to keep all of the tire flat against the ground as well as possible.

Wheels

The goal of the wheel (rim) is to provide a stable mounting for the tire. For performance, lighter alloy rims are used to substruct unnessecary weight. Removing weight from the wheels (unsprung weight) is crucial. Of course, the rim also dictates the radius of the tires. A greater radius of tires does not increase performance, it again increases the weight under the suspension, but it might be nessecary to host large brakes in performance cars. Off-road cars also need to the rims to be rigid enough to sustain blows.

Weight

More weight presses down on the tires to generate more grip, but also places more weight for those wheels to handle with. The graph of grip/weight is none-linear: As weight increases, the grip levels increase, but not parallel. Eventually, the tire reaches a point of "saturation" where more weight reduces it's grip levels. Additionally, a heavier vehicle -- while it will generally grip more -- will have isssues with driveability and with using the grip it has. The heavier weight will make it harder to accelerate and slow down. In the corners, the car will have trouble with direction changes, particularly fast or repititive ones. Ultimately, substructing weight will indeed make you "faster everywere."

However, looking at a car's static overall weight does not give us the full picture. When the car moves, it experiences weight transfers. You accelerate, and the wheels start rolling faster and try to get ahead relative to the car's body which is constrained by it's weight and aerodynamic drag. This makes more "weight" to work on the rear wheels and push them down. In reaction, the car's body will seem to squat. Under braking, weight is transferred from the rear wheels to the front, and all cars other than trucks will thus have larger front brakes. 

Weight transfers does not change the car's mass. It only changes the downforce on the wheels and their grip levels. This can help the driver but also carries negative effects on driveability: Every weight transfer disturbs the car's balance and successive weight transfers tend to create a resonance that intesifies the effect of the second weight transfer, and the third weight transfer will be even harder. 

Our goal in engineering is to reduce the car's weight transfers. We can achieve this by substructing weight, chaging the car's  weight distribution and ride height. We cannot achieve it through suspension design: Stiffer springs don't decrease the weight transfer, they only make it more rapid and create less body roll in response to it. On the other hand, lowering a car and making it wider, will evidentially make it more "stable."

One important aspect here is the wheelbase. A good car (dynamically) has its wheels at about the very corners of the car's body. The closer the wheels are to the corners, the better. If the wheels are closer to one another, they work like one big wheel instead of four wheels, making the car less stable. The areas of the body that protrude from the line of the front and rear axles would create a load that decreases grip, especially if it's heavy. Look under the hood of most Audi models, and you will see the engine sitting mostly in front of the front axle, generating understeer. 

A car with an engine mounted on the rear would therefore be more likely to oversteer, because the center of gravity is placed further to the back. Placing the center of gravity closer to the middle and lower helps in achieving balance.

Springs

Besides the little undulations, that allow the tire to grip the road, there are also larger undulations that shock the tire. The tire is moving forward as it hits a bump, making some of it's forward movement turn into upwards of downward acceleration and bouncing it off of the surface, aside from making it uncomfortable inside the car. The springs are made to negate this phenomena by absorbing the bumps and keeping the tires against the ground. A softer spring absorbs more energy and allows to keep the tire against the road.

However, the springs also have to carry the car's body. This gives them another task, which is to control the body movements of the car. When weight transfers occur, the car's body moves with it. This can be seen and felt as a nosediving of the car under braking and "leaning" towards the outside of the bend during cornering (called "body roll"). Contrary to what some believe, body roll has both a positive and a negaitve influence. The negative influence is that moving the car's body in an angle moves the tires in an angle, and changes the way they contact the road. You turn right, the car rolls left, so the wheels are forced to contact the road with their left shoulder and less with the center of the contact patch, not to mention the right corner.

However, it is custom to speak of stiffening the suspension as a move that decreases grip levels. First, because too stiff a suspension will fail in the original task of keeping the tires flat against the road but also, because a soft spring "absorbs" some of the cornering energy instead of the tire. If you force the car not to lean on it's side,  you force it to slide laterally. This returns to the point of viewing the car as a singular object: To benefit from stiffening the car, all parts must be stiffened, begining with the tires, through the springs and coming up to the chasis. If you just stiffen the springs relative to the chassis and tires, they will become the "weak" links of the combination.

Under the conditions of a stiff chassis and stiff, grippy tires, stiffening the suspension helps in reducing the roll angles, and keep the car and the tires flat against the ground. Since the car is stiffer, it will also have all the other aspects of a stiffer vehicle: A sharper response, including a sharper lost of grip, but also more control on slides and weight transfers. On the track in particular, we also assume well-paved tarmac, so we can stiffen the car quite a lot to reduce the roll angle and not suffer from a car that bounces over the surface.

In road cars, one of the solutions is to apply progressive springs, that are not as stiff across their whole length. The are softer at first to absorb little bumps, but becomes stiffer as the driver pushes them harder, to restrain the roll angle. Another solution is coilover springs, which allow the driver to personally configurate the ride height, which is also a function of the springs.

Old cars, and many of the modern trucks as well, don't have coil springs, but rather have leaft springs, made out of "leaves" of elastic metal. The advantage of these leaves has to do with simplicity, and they also have advantages in requiring less rubber bushings to connect them to the chassis, and the ability to make them progressive by fitting different layers with different thickness and stiffness. However, they reduce the ride height near the wheels, they have a problem when they reach for compression, and they cannot hold the axle in place, so that the axle itself swings around and moves laterally under cornering forces.

Another type of spring is the Torsion Beam. In your everyday family car, the rear axle usually hosts such a suspension, which consists of a beam stretched between the two wheels and connected to them on special arms. When the wheel hits a bump, the wheelarm rotates and "twists" the beam. The force of torsion than twists the beam back to push the wheels back unto the road surface. The advatage is mainly in space management, because the beam that actuates as a spring is placed across the car, the dampers can be placed in very flat angles, opening space for the back seats or trunk.

Dampers

Mistakenly called "shock abosrbers", the dampers provide resistance to the spring. They are brakes that stop the springs from osciliating. When you press on a spring to compress it, letting go will make the spring saw back and forth before returning to it's original form. This motion is called osciliation and it is measured in cycles. The task of the dampers to ensure just a single cycle of osciliation. Dampers allow enable the spring to compress differently at different rates. When a spring hits a bump, it generally compresses quickely, so dampening the road bumps is a task for a function known as "fast bump", whereas restraining the movement of the car's body is done more slowely, thereby being under the slower movement of the suspension (slow dump). Dampers allow to have springs that are soft enough to grip the road surface and provide road isolation, and still stop the car's body from rolling too much.

Anti-Roll Bar

To differ from the torsion beam, and from the tower strut which will be disscussed later, the anti-roll bar (mistakenlly called a "sway bar") is meant to enable a reduction of body roll, without damaging the ride. Stiffen the springs to reduce body roll and your make a harsher ride over bumps, but if you take a stiff bar and use it to bind both sides of the car toghether, you achieve this reduction of roll angle, without interfering with how the springs dampen the bumps.

The drawback of the anti-roll bar is that it limits the abilities of the suspension. Once again we need to remember that the suspension is one big organ, and changing one element changes another. Just like reducing the roll angle of a car with a soft chassis and tires would reduce it's grip levels, applying too stiff a roll bar unto too soft a spring, will turn the spring into the "weak link." This means that under heavy cornering, the body roll will result in the stabilizer bar forcing the spring and wheel to lift and swing in the air. This does not mean that the car is anywhere near to rolling over, but it does not do good to performance.

Chassis

The Chassis is the car's body. In older cars the chassis was only the lower part of the vehicle (usually in the form of a ladder chassis). In modern cars, the chassis and body are one. The chassis, like all other parts viewed so far, also endures the forces working on it and twists somewhat. This is not the body roll, but an actual twisting of the elastic metal parts. 

Different manufacturers design the chassis of their cars with different technologies, offering various levels of stiffness, which also carries an effect on safety. Porsche invented a chassis that is also at one with the engine, which contributes a lot to it's stiffness, while Opel and BMW use hydralic pressure to create the metal work of their chassis (in the Astra and M-3), leading to more stiffness in the corners of the tin. Improving the chassis stiffness can be achieved by means of struts that connect both front wings over the damper housings, and by the safety installement of a roll cage inside the car.

Bushings

The rubber bushings connect the suspension to the chassis. The amount, formation and compounds of bushings carry an effect because they too have to face the loads working on the car. As the bushings twist, they can move the whole suspension from it's original alignment. They also create frequencies of noise as the suspension under them moves. The first solution is to install stiffer bushings, usually made out of materials such as polyorithane. Another solution is to include a sub-frame which provides extra isolation from the noise.

Suspension Types

The same suspension can be placed in different ways. Three main ways are the Mc'Pherson strut, Double-Wishbone/Multi-link, and Trailing arms. The Mc'Pherson strut is the most simple of the three, and is used as a cheap and compact solution in the front of many cars today. It consists of a damper mounted inside the coil spring. This saves room, but also makes the damper support the spring and allows to design the coil of the spring differently. 

The Double-Wishbone is more complex, but yields better results. It consists of placing the wheel, with the spring and damper, clanched between two A-shaped arms, one above the other. This gives the wheel itself a certain freedom of motion. This freedom of motion helps avoiding something we mentioned earlier which is the interference of body roll. Turn the car and you will make the car's body roll, but when the car's body rolls, the wheels do not have to tilt also. With the double wishbone formation, even when the wheels hit a bump or when the car's body rolls in an angle, the tire can remain flat against the road, straight up-and-down and vertical against it, maintaining grip.

This designed can be changed by altering the formation of the arms. The popular way is to make the upper arm shorter. The result is that while the wheel is pushed up by a bump it does recieve a slight angle, but it recieves no change of angle over body roll. A multi-link suspension is an elaboration of this concept. By adding even more arms it allows the wheels to be even more independant or to "program" them intentionally to recieve a certain angle during a certain situation.

In professional racecars, the multi-link setup also allows to change the angle of the springs and dampers. When the wheel hits a bump, the upward movement is turned into a lateral movement of the wheelarms, so the springs can be placed horizontally, allowing to reduce the ride height.

The trailing arms are a different story. They are a more simple suspension, used in the rear of some car, especially with a torsion beam spring, where each wheel is connected to an arm that runs longitudally under the car, and hangs unto a pivot. When the wheel hits a bump, the arm pivots up and back down to keep the tires flat against the road. The problem is that when the body rolls, the arms and wheels roll just as much. To reduce this effect, the Semi-Trailing Arms have been invented. These arms are assentially the same, but their pivots are placed in an angle that makes it pivot in an angle that allows the wheels to stay flat against the road even when the car's body begins to roll.

One shortcoming of both trailing and semi-trailing arms has to do with braking. When you brake, the bushings of the arm and pivot would twist as to change the angle of the wheels so that they are turned away from the car. When this happened in the rear of the cars with this suspension, the result was lack of stability. The solution was to split the links of the arm into two bushings, so that the movement of each cancels the movement of the other, keeping the wheel static or even turning it towards the body of the car. This is known as the "Weissach" formation and it was the first installment of passive rear steering.

Ackerman Steering

When the car turns, the outside wheel takes a wider radius. When we turn the wheel, we tilt both front wheels into the corner. However, with Ackerman steering, the inside wheel is turned more than the outside wheel, because it takes a tighter circle. On professional race-cars, this fucntion is removed because the cars function at the maximum slip angles that allows to maintain grip, and therefore having the inside wheel turned more (in some race cars it's even turnd less) will make it go over the limit.

Rear Steering

Rear steering is the tendency of the outside-rear wheel to be titled when faced with a certain load. Active rear steering systems allow for the rear wheels to turn into the corner in slow speeds, which helps in turning the car more tightely, and turn them away from the corner at a high speed. Passive rear steering is a function of the rear suspension, and usually performs the latter action. In some cars (Like the Volcan ZX) turning the wheel away from the car helps in reducing the risk of oversteer. An attempt to oversteer the car would only generate a so-called "Cynical oversteer" that begins and ends with a momentary wiggle of the back-end.

Other cars, to name the new Fiat Abarth or Clio, use the same tendency to make up for understeer. The rear suspension is set to create a steering angle under a load greater than what the front can take. I.E. The front of the car starts sliding (understeer) and than the rear wheel is turned and rotates the car around the corner. Again, this feels like a momentary oversteer: The back of the car swings around, but just for a moment, before going back into line. It's important to understand that this is NOT oversteer! Neither of these situations is desired in setting up a true race-car.

Bump steer

Changing components in the suspension does not merely carry an effect on other parts of the suspension, it carries an effect on the steering mechanism. Under pressures such as a bump or under body roll, the steering tie-rod and the suspension needs to move symmetrically. If a wheel hits a bump that makes it swing, and the suspension swings more than the steering arm, it will make the suspension turn the wheel. This happens in road cars, but must be minimized in a serious race-car design. One way to reduce bump steer is to change the connection of the steering tie-rod to the wheel, by applying so-called "hi-steer", where the steering arm connects to the wheel from above rather than from below.

Kingpin inclination

The Kingpin inclination is the inclination between the the nuts that connect the wheel-arms to the wheel. The upper nut will be typically further from the tire than the lower one. If you draw an imaginary line between them, you recieve the kingpin inclination. This creates a steering offset. Draw the imaginary line all the way down untill it contacts the tarmac, and you will see that it in an offset relative to the center of the tire. This offset creates steering feel, but in a front-wheel-driven car, it will create torque steer (where the torque of acceleration "fights" with the turning of the wheel and tries to set the wheel straight). 

Reducing the Kingpin inclination in a Front-Wheel driven car is impractical with a Mc'Pherson strut, which must be placed vertically (because it's kingpin is the spring and damper), and adds yet another advantage to front double-wishbone suspensions.

Camber

We said we need to reduce body roll in order to keep the wheels straight up-down and flat against the road. If the wheel is tilted in an angle relative to the road it is cambered. Because cars naturally have body roll, the wheels are intentionally cambered. They are placed in an angle towards the road surface, leaning against it with their inside corner. Under body roll, this negative camber cancels the positive camber created by the body roll, and the tire is placed straight and vertial against the road.

Of course, stiffening the suspension reduces body roll, so we can reduce the camber. Camber changes at the front as the front wheels are turned, and also changes at any wheel when the suspension is compressed over a bump. Multi-link suspensions reduce the the camber changes over bumps.

Castor

Castor is the inclination of the wheels when you look at them fron the side. A negativelly castored wheel is titled backwards, like a supermarket trolley's wheel. This places the grippiest point of the contact patch further back. The effect is for negative castor in the front wheels to make the steering sensitive, but heavy to turn. Flick it into reverse, and the car will be moving in the other direction, so that the castor will be as if reversed, so you will suddenly have a lighter steering, which will even not turn back to straight when you let go of it.

Toe

Toe is the steering angle. A wheel that has toe-in is turned towards the car itself. A wheel that toes-out is turned outside and away from the car. Having the wheels aimed for toe-in and towards one another, makes it stable in a straight line, but also stable when turning into corners, making it harder to change direction. Toe-out makes the car unstable over the road, but more compliant in turning in.

Steering methods

How to steer your vehicle? does steering have an effect on the ability of a motor-vehicle driver to control his car? While not being the most important chapter in car control, steering techniques do make a difference, and can save time, effort and even help maintain the direction of travel where it would otherwise be impossible. Most big institutions in the advanced driving and racing world tend to teach one steering style or the other, out of nearly two-dozens of styles that exist! A steering technique can help turn more steering faster and with more feel and finesse, while investing minimal effort into the movement. 

There is a vast variaty of styles, which we will not explain here. I wish to move directly into the explaining the technique I advocate and it's advantages. One could view it as one technique, a combination of some "tools" or a technique with several variations, and I explain:

First, the basic grip of the wheel. Having set the seating position, we now grip the wheel at 9 and 3, which are both edges of the wheel. The palms should be cupping the outside of the rim, and whenever driving on normal tarmac roads, the thumbs should be hooked lightly into the sockets created by the crossbrace of the wheel. The grip of the wheel is ought to be soft, just strong enough to keep the wheel controlled. There are various ways that help deal with the phenomenon of "squeezing" unto the wheel:

- A proper seating position

- When cornering or braking hard, applying support with your left foot, so that you do not need to lean over the wheel.

- Take deep breathes before a high G-force corner. Wiggle the fingers on straights, one hand at a time.

- Feel the wheel mainly through your fingertips, the most sensitive part of your body, save the lips. It's not that you cannot use the palms and thumbs too, it's just that the main sensory input should be the fingertips.

With many cars, adjusting the seating position right for 9 and 3 allows for a vigilant and comfortable posture. If we look as the steering grip apart and assume a driver might get his hands right without setting the seating position appropriately, or if we assume the car does not allow that person to reach an adjustment close enough to optimal, this position might become somewhat inconvenient over long periods of time, but it's nothing too bad and the hands can be momentarily moved to a higher position (the tradition 10 and 2). Move the hands one by-one and not both toghether.

This position is our "homebase" for car control and it should be maintained for as long as possible, and this is part of what a good steering habits seeks to achieve. This position allows us to, at will or when surprised, to turn the wheel up to 270 degrees with both hands, to each direction. While the crossing of the forearms appear odd to most drivers, there is nothing seriously wrong with it, when you need it, and it suffices greatly for when you need to avoid an obstacle or make steering corrections to your traejectory.

However, when we do encounter a corner, we see it and plan it, do we simply turn the wheel like this? Not nessecarily. If the steering input is relativelly small. I.E. a very slight curve, you simply move the wheel somewhat with both your hands, no need for any excerise of arm-acrobatics. But, when you turn the wheel to an amount of say 90 degrees -- when one of your hands reaches the topmost point of the wheel and your other reaches bottom, do you keep both hands turning like this?

Otherwise, what happens if, in exactly that corner, you slide your right hand (assuming it's a righthander) to the top of the wheel (12 O'Clock) and than pull it back down, untill the hand gets back to where it started in  (3 O'Clock, the right-end of the wheel). What happens than? You have the wheel turned to the same amount, but your hands are on both sides of the wheel: 9 and 3. So? Your hands are holding the wheel as if your were driving straight ahead, which allows you both to grip the wheel in a more vigilant and relaxed manner, but also be able to make little corrections easily or even make a large correction for a miscalculation, a tightening corner, a pit or stain of oil mid-corner, an obstacle, a skid, etc. And this amount of steering should suffice greatly.

Let's recap: You reach a righthander and you assume you need to turn the wheel one-quarter of a turn of lock, or 90 degrees. So you slide your right hand to the top of the wheel and pull back down to the right end of it, all while the wheel is sliding under the fingers of the left hand. You have turned the wheel 90 degrees and behold! your hands are again in the static posture, a magic! It can also be described like this: You see a corner, you assume you need to turn the wheel 90 degrees right, you move your right hand 90 degrees left so that when you pull back, your hand gets back to where it started.

What about tracking-out of the bend? Let the wheel straighten-up, maybe just turn it back by feel? No. We do the same thing we did going in, in reverse action. We relocated the right hand before the corner to the top of the wheel and pulled down. Now, we relocate the left hand to the top of the wheel and pull back down, and again, we find ourselves instantly at 9 and 3. With these two movements, going in and out, we kept the hands in 9 and 3 for a substantially larger time overall.

This might sound kind of complex, but in fact it becomes quite natural and simple once you get used to it. The main point here is to apply steering predictivelly. Instead of starting at 9 and 3 and than commencing the steering movements, so that in the corner your find yourself in an awkward hand position, you predict how much steering you need to turn, than you relocate your hands before the turn so that, we you turn, your hands return to 9 and 3. Than, you do the same going out, so that your hand movements mirror one another. Just like this:

You will quickely learn that wide-radius turns at intersections and junctions tend to require about this amount of steering rotation, but what happens if you need to turn the wheel more than that? Let's assume we are driving on the right (as opposed to places like the UK) and we need to turn right into a relativelly sharp corner in an urban area. This type of turn requires twice the amount of steering: a half-turn of lock (180 degrees). I have witnessed an interesting variation of this technique where you turn  the wheel just 90 degrees and than make the extra 90 with both hands, but I do not like this style. Here's the classic way of doing it: Pulling the wheel a full 180 degrees.

This might feel a bit odd at first, but it requires you to slide your hand (right hand in the case I stated above) and pull the wheel all the way across, and the left hand is just staying in place and letting the wheel slide under it's fingers with control. Like I said, this might feel a bit odd but it carries the great advantage of being able to perform a relativelly sharp turn with no more than one hand motion. A little tip of my own: When you cross the hand, hook the thumb under the spore of the wheel, just below the fingers of the other hand, so that you can pull a full 180 degrees.

But what if it gets tighter than that? Well, you will be surprised to learn it is no different. If the turn requires 90 degrees right you relocate the right hand 90 degrees left. If the turn requires 180 degrees left you relocate the left and 180 degrees right. If the turn requires 270 degrees left (3/4 of a turn of lock), you can actually relocate your (left) hand 270 degrees to the right, which means placing it on the bottom of the wheel. No, not with your palm, you actually grip the wheel with the hand upside-down (palm pointing up). This might feel really awkward but it becomes natural quickely, and enables you to turn an insanly large amount of steering in one "go", and than get back to 9 and 3, effective!

Remember though, that the opposite palm should always remain in position and let the rim slide under it with control. Also remember to mirror your hand movements: Turn-in by one hand that is relocated to pull the wheel as much as nessecary, and exit the turn by pulling back with the opposite hand -- and here's where a lot of  people go wrong.


The Steering Action
The steering action performed by turning the steering wheel, utilizes the steering mechanism to tilt the front wheels into a corner. Turning the front wheels gets them to roll towards the corner and direct the car into it. This discription is actually very simplistic. First, we must understand that the tire does not want to roll aside like this. The rubber wants to keep on going straight, and so does the whole car. The rubber in particular is elastic, which actually allows it to do that.

You turn the wheel, but the actuall patch of rubber on the road, twists aside in order to keep on going straight. Since rubber does not have an actuall will of it's own the actuall result is that the wheel is actually turning a bit less than the amount it is turned. This difference is measured in the angle between where the wheel is pointed and where the tire is actually going, and that's a "slip angle".

In fact, it becomes even more complex when talking about tire sidewall cramming, chassis twisting, rear-wheel slip angle, weight transfer and weight distribution, steering drag, body roll, longitudinal forces and speed, but what you need to know is that steering should be smooth and progressive but never slow. The more steering required, the faster it can be turned to result in a smooth output. "Sharp" steering movements might be required in times, but they are situations forced unto the driver due to the required driving line. They are not a desired input.

Other Techniques -- Extremities
Should we limit ourselves to one steering style, or should we use multiple techniques to serve different causes?  Is our very thought in terms of applying one method and/or the other is misintended? The short answer is yes and no. Yes, because no one technique can always work for all situations. No, because most "normal" situations can be negotiated very well by use of a one, uniform method.

It's not that there are no other techniques to learn, it's simply that the cases requiring their application should not be considered exceptional or, in the professional terminus technicus, an "extremity". With reference to steering styles, there are several extremities.

The first is where the car is old and has a heavy steering mechanism with no hydraulic support (i.e. no power-steering). In very low-speed manouvering, mainly parking, the steering tends to become very heavy. Here, we need to "shuffle" our hands, which carries some resembelence to the above technique: You relocate your one hand to the top of the wheel and pull down towards 7 O'Clock on the wheel, and than push up with the oppposite hand back towards 12O'Clock, reaching the required amount of steering rotation with such hand movements of about 120 degrees each. With practice, both hands mirror each other and it seems that the driver is "milking" the steering mechanism. This is only relevant to these types of cars in this particular situation.

The same situation (low-speed) parking, will in times be considered an extremity also in modern cars. When we are talking about a seriously slow steering manouver, or perhaps steering performed in a fully stop, we can let ourselves press the palm of the pulling hand against the wheel and turn it like this as much as we need. Still, we should keep our opposite hand in place to support the movement, and -- having turned the wheel to the required amount -- slide the hands to the right spots on the wheel. Rather than being another technique, this is simply a variation of the standard technique where you use the palm of the wheel and not the fingers.

Another extremity is when you turned the wheel with both hands to the point where your forearms became completly entangled and more steering cannot be applied, and you actually do not some extra extention of steering. For the sake of disscussion let's say you turned the wheel 270 degrees left with both hands to avoid an obstacle. Now, you need a bit more steering, but your hands are completly entangled, right hand on the bottom of the wheel (6 O'Clock), left hand ontop of it. So, you pull your right hand back and place it back ontop of the wheel, and than you open the right hand and press the palm against the wheel and turn the extra 90 degrees, and your hands return to 9 and 3 after turning a full 360 degrees.

A similar course of action is where you relocate the hand to pull the wheel to a certain quantity in one direction and, while pulling the wheel into the corner, you find it nessecary to turn the wheel away from the corner and all the way to the other direction. Say we relocate the right hand to the top of the wheel to pull 90 degrees right. Just as we start pulling, a car rolls into our direction, forcing us to steer sharply to the other direction. We push down with the hand that's doing the steering, under the stationary hand if required. It's range of motion is all the way down to the bottom of the wheel (6 O'Clock).

If it gets there and we actually need a bit more extention, we relocate our other hand to the top of the wheel and palm the wheel with our opposite palm and we have now returned to 9 and 3. To know how much we turned, we think about how much steering we initially wanted to apply. If I relocated my hand to pull 90 degrees right, pushed all the way down and than an extra 90 degrees, we do 360, minus the amount we wanted to turn, which is 90 degrees, which adds up to 270 degrees.

The last extremity is what I like to call "a situation where you need to turn as much steering as possible as quickely as possible". The normal steering technique normally suffices both for slow inputs and for large and quick inputs, but sometimes you need to turn the wheel an awfull a lot very very quickely (say, from lock to-lock), and this becomes more effective when a different style is adopted. Let's say I need to turn the wheel all the way right from lock to-lock. My hands are at 9 and 3. I push with the right hand all the way over (180 degrees) and than cross the other hand that pull the extra 180 degrees. A full 360, hands again in 9 and 3. Three sequences like this actually suffice in turning the wheel from one edge of the rack to the other!

Other Techniques -- Why not

The goal of this section is to specify the advantages of this technique over the others:

1. Range of Motion: This steering technique allows to turn the wheel 270 degrees in one hand motion, and a full 360 degrees by a more complex manouver, and than return to a hand position that allows to turn an extra 270 degrees, and further if nessecary. This also helps with turning the car, because you get a single hand movement, which is easier, smoother and yet decisive as nessecary. It is particularly effective during a set of successive corners.

2. Maintainence of the basic hand position for maximal amount of time: In this technique, you keep the hands in 9 and 3 for the maximal amount of time possible: Before the corner, in the corner, after the corner. In the timespawn in which the hands are not in 9 and 3, at least there is one hand in the right spot. This proves superior over the technique where both hands are relocated before the corner. In that technique, you have to perform the hand relocation ealier before the corner and place both hands in the wrong posture, just in order to have them in the right position somewhere within the corner, and unwind it and than finding yourself replacing the hands at track-out.

3. Maximal sensitivity: Pulling the wheel is done with greater sensitivity and ease than pushing, especially since the hand does not does not go below 9 or 3, and due to the extra sensory input of the opposite palm.

4. Symmetry:  One hand turns the wheel while the other is letting the wheel run under it, and than tracking-out by the opposite hand pulling back and the other in "supervision". This contributes to elegance, smoothness in turning-in and tracking-out and to the points mentioned above.

5. Sense of turning: With this technique, you are aware of how much you turned and where the wheels are pointing, making it easy to control the car on the limit.

6. Ability to steer one-handed: In rallying and road driving, this technique is friendly for one-handed steering, and hence allows to operate the gear lever and handbrake, and perform manouvers like double slides, handbrake turns and J-turns.

7. Two handed-steering: There are always two hands on the wheel and always at least one hand gripping and guiding the steering wheel.

All about Cornering lines

By now, you probably know that attention to details while driving improves the net result. This is again true to all types of driving: Road, Track and Stage -- and to all drivers and driving styles within them. One very important detail is how we turn through the corners. This has various aspects to it and it's the core of performance driving -- the ability to corner at the limit. 

The Basic Racing Line Formula: Outside + Inside + Outside = The Racing Line

Cars don't like turning. It puts each and every component of the car (as well as the driver) under lateral loads that threaten it's stability and distrube it's otherwise plane intercourse with the road. Some drivers try to "help" the car turn by making the turns shorter and take a sharp line to the "inside" of the corner, which makes the corner very short but also very sharp and narrow. 

Others prefer the "highside" -- they turn the car through a very wide arc around the turn, otherwise known as a "rimshine" line. This line suffers from making the corner very long. The real line is a combination of both. Let's take a left-hand, 90-degree angle corner as an example: We approach from the right, "dive" into the corner to "cut" it in the inside (left side) just in the middle of the turn, and than let the car run wide and back towards the right shoulder at the exit of the turn. This allows to make a very straight line because, unlike the two former lines, this line considers not only the length of the track, but also it's width.

On this line we mark three key points: The turn-in, which is obviously where we start turning the car into the corner. The second point is the APEX -- the "peak" of the turn. In every turn, in every line, there is a "peak" where the car is under the greatest load/steering input -- in the racing line, this point is inside the turn, just in the middle whereas in a tight line it would be at the end of the turn. The Third point is the Exit point, where we are after the cornering settle for the next straight.

This line offers to fastest possible speed in the corner. Even if you don't plan to attack the corner at speed, this line keeps you further from the limit and reduces the jerking of the car through the turn. However, it does have cons. I said it was the fastest possible line, but it also isn't. The key is the definition of a corner.

Physically speaking, this line allows for the fastest speed in the corner. However, in terms of driving, real-life corners appear as part of a more complex road: There are preceeding and following straights (or other corners...). In this respect, this line is not the fastest one available. 

The Basic Driving line: In Late, Out Early

The racing line is theoretical, the Driving line is practical. Before a standard turn, say, at the track, we normally have to slow down. When we slow down for the corner, we want to squeeze as much braking as possible into as little space and time. By braking very hard, we are able to keep the throttle full untill the last possible moment and than brake just enough before the turn.

In the theoretical racing line, we would have to ease off of the brake pressure to allow the car to turn into the corner at the required turn-in point. But, if we would place the turn-in point slightly later, we could also brake later and keep full throttle a bit longer on the straight before the corner. The trade-off is that once you turn you have to make a sharper and slower turn. This is worthy because brakes are the strongest means of car control. Since they are stronger than the steering, they produce a greater change in performance.

But, this is still not the essence of the driving line. You brake a bit later and turn a bit later, but you also clip the APEX later, a bit after the geometric center of the turn. Again, this makes you make a tighter, slower turn from turn-in to APEX, but sets you up for a nearly-straight path from the APEX to exit, so you can put more power down more quickely and begin accelerating before the APEX. 

This trade-off is very effective because instead of gaining a few tenths of-seconds in the few metres between turn-in and APEX, you gain several seconds over the several houndrends of meters of the following straight by accelerating into it earlier. This "cornering philosophy" also dictates a very important rule: "Slow-in, Fast-out." You take a sharp line going into the corner, to take a straight line out of it, so you have to weigh corner entry speed AGAINST corner exit speed, in which case the latter almost always wins. Slow corner entry speed + Fast corner exit speed = Cornering efficiency.

This trade-off is very clear in sharp corners. Ameatures are often surprised to find out just how slowly Rally drivers and Track drivers go into the really sharp turns. These ameatures are under the false belief that a skilled driver can enter a sharp corner in a fast speed and this is not true. The limits of cornering speed are the limits of physics, not the limits of a driver's skill.

Another thing to mention here is that sliding the car is not taken very kindly. Any serious sliding makes the tire work in a "slip angle" that it was not planned to function in, and this slows the car down. Sideways is slow-ways. It sometimes happens in rallying that drivers almost can't manage to make it through a slippery gravel turn without sliding, so they prefer to initate a slide intetionally and early, than try to drive without sliding only to slide more sharply later inside the corner. This is a compromise, not a desired situation.

The Last APEX line

The "Theoretical" racing line is called a "geometric APEX" line because it's based on clipping the apex directly in the geometrical center of the turn. The basic driving line is known as a "late APEX line". However, sharper corners demands a later APEX and very sharp corners, especially off of the track -- often require taking a very late APEX which I call the "Last APEX". This apex should be late enough to provide an almost straight driving line through the exit of the turn.

The last apex is not your usuall line because it makes turn-in so sharp that it's often not desirable in spite of the fast exit speed. This line forces you to "rock" the car into the corner by a relativelly rapid turning of the wheel to make the car to change it's direction at once (where in the other lines the car is progressively eased in towards the apex) from turn-in towards the APEX. However, it is advantagous in very slow bends, and in other conditions when it's required -- it keeps you prepered for what's coming next by allowing you to have a better look around the turn in advance and by giving a slow and safe turn-in and a steady state inside the corner.

This is a good place to define the relationship of the three points that make up a cornering line: Turn-in, apex and exit. We have already attributed the greatest importance to the exit -- it has the greatest effect on performance. The apex is significant for being the place where the greatest load is placed on the car. The turn-in is important because it initiates the turn. In order to exit a turn properly you first need to enter it, and properly.

In fact, we can say that the first 20% of the corner (=turn-in) make up for 80% of the cornering, but that the results of those critical 20% are only discovered half-way through the corner (at the APEX) and the net result is only experessed after the exit. Races are won over the straightaways.

The error line: Early APEX

The problem with "Slow-in, Fast-out" is that you first reach the corner's entry before you do the exit. Without planning in advance (by looking ahead), a driver is going to prefer fast entry speed anyhow. Because of the high straight-line speed the car is in, the driver is likely to try and smooth the corner by turning in from an earlier point and in a line even more straight than the geometric apex. However, cornering lines have some sort of "racing karma" to them -- a earlier, smoother and faster line at corner entry, will become into a tight and slow line at the corner exit. You will simply clip the apex too soon, and the car will not be in one line with the exit point, and would instead be facing the edge of the roadway, forcing a slow down.

If the driver's attempts to slow down are succesfull -- the real trouble begins. The driver might interprate this as a succesfull corner, without noticing that trying to be fast in entering the corner have made him to slow and brake on the straight where he should have been on full throttle.

A summary of Driving Lines:

1. Early apex: This line is normally an error. The driver turns-in too early, which lines the car up towards the edge of the turn after the apex. This sort of line sacrifices corner exit speed for corner entry speed, which is foolish.

2. Geometric apex: This line is fast but not very commonly used. It offers a very smooth line by clipping the inside the corner directly in it's middle, but it does not offer a very good corner exit speed.

4. Late apex: This is the normal driving line. You turn-in and apex later to achieve both later braking before the turn and earlier acceleration out of it. You sacrifice corner entry speed for corner exit speed, which is the best tradeoff there is.

5. Last apex: Popular in road driving because it enables to have a better look around the turn. Might require turning the wheel somewhat sharply in racing.

"Taking a Set"

At the Apex of the turn, the car essentially becomes a bike. After turning the wheel, the car's weight is being transferred to the outside wheels so they provide almost all of the cornering force. This is important because the "inside" wheels often become nearly fully neglectable. This enables to cut the inside of the turn so much that you drop the inside wheels off of the pavement. On the track, this helps in making a faster turn. On the road, the same ability can be used to avoid a car that strayed into your lane or to get around slippery parts of road that you find inside the turn (a puddle, a sheen of ice, an icy patch).

Sometimes, especially when you take a "last apex" into a very sharp corner, a relativelly sharp steering input should be made to make the car respond by "taking a set" earlier. This rapid turning of the wheel rocks the car somewhat, distributing the weight of the car on the outside wheels when slightly more biased forward. Another place where quick steering inputs are required is in some of the fast curves on the track. Some curves of the track are very fast and you accelerate all the way through them, but sometimes they are performed at a speed and/or over a surface/incline that makes the car push too much out of the turn, in which case rapid steering helps.

Camber and Castor

Camber and Castor are two principles in wheel alignment. Both of them change the way in which a given tire faces the road. However, the road also has a Camber and Castor. The Camber of the road, is a side-slope while the Castor is the uphill/downhill incline. Each of the two carries an effect on the driver, car's grip and car's handling.

Negative Camber is the classic example and it is seen on the road and track, particularly oval tracks, where the corner appears to be "banked" and inclined towards the inside. This is "negative camber" which helps increase the car's lateral grip. Think, if the corner was banked at 90 degrees, we would not have to turn the wheel at all. It keeps the car's weight lateally stabilized. In a negative Camber corner, it's vital to be smooth and gentle because the effect on car handling is a reduction of understeer. This also dictates that the driver should take the geometic line and sometimes even an early apex line.

An uphill incline has a similar effect on grip, but increases understeer by causing a weight transfer to the rear. A downhill incline would decrease the grip levels. The problem is that Camber and Castor are not nessecarily identical all the way through the corner. Some corners have an increasing Camber that makes the driver turn-in early, while other corners have a decreasing camber, where you want more turning effort done in the early, grippy part of the corner, and less in the final part of the corner. 

Banking also carries an effect on the effect of grip reducing agents. If a part of the road is inclined, water and foliage would drain downwards, forcing the driver away from the inside edge of the corner. In fact, the road always have some camber that drains water sideways, so the edges of the road are categorily more slippery, and it often makes the driver adjust the line so that he does not turn so far from the edge of the track.

Corner prototypes

The track has three corner prototypes: A fast curve, a moderate bend ad a slow corner. The fast curve is the most simple but treacherous sort of corner. The line is normally geometric: You turn in and apex just in the center of the turn. Usually, some acceleration takes place all the way through the corner. The driver has to turn the wheel smoothly and once a steering angle is established, the driver controls the line by throttle maintainence -- more throttle will induce more understeer and a wider line. Less throttle would make the car tighten up the line.

Lifting-off completly usually undermines the car's stability and can lead to terminal understeer that has to be coped with by strong and instantanous acceleration without significant steering corrections. Steering corrections will rock the car, but the speed reduces the engine torque enough so that, in all drivelines, it's possible to use more engine power for recovery and less steering. In a fast corner, staying "at one" with the car obligates that the driver keeps his eyes high, usually all the way through the corner.

Sometimes, fast curves are very fast but due to the line, incline and/or car -- create too much understeer that threatens to push the car off of the right line. These turns might also require a quick turning input for "taking a set" earlier.

The moderate-speed corner is the normal racetrack corner. It is slower than the fast curves and does not allow to accelerate all through it and usually requires braking before it. The line is therefore -- the basic late APEX line. This corner requires finesse like the fast curve -- and a minimum of weight transfer -- but requires some decisiveness to get around nicely. You brake to reduce your speed in a straight line. As you turn in, you remain with brake pressure applied and "share" the tires' traction between cornering force and braking force. This is known as "brake-turning."

You start easing the steering into the corner as you start easing the braking force off -- the more steering, the less braking. from full 100% braking, you switch to 90% braking and 10% cornering force, and than to 75% braking and 15% cornering force. Once the full steering angle is achieved and the maximum cornering force is established -- you have to seemlessly lift off of the brakes and roll onto the throttle just enough to keep the car at a constant speed so that it's just cornering. This is called "Balanced Throttle." 

Just before the apex, the car is lined up so that you increase balanced throttle to some acceleration and than, at the apex -- start to unwind the steering as you accelerate. This is the exact opposite of what you do with the brakes as you turn in -- the more steering you unwind, the more throttle you can apply. From 100% cornering, you go to 95% cornering and 5% acceleration, 70% acceleration and 30% acceleration up to full acceleration even before the straight. 

Throughout the corner, the car has to behave around neutral -- either fully neutral or with slight understeer. If the car understeer, the driver needs to reduce speed and/or acceleration. Just slightly back-off of the throttle or brakes while you undo some steering. The car would regain grip faster and more smoothly if it only has to make up for extra 3 degrees of steering instead of 5 degrees, so straightening the wheel slightly helps. Once regripped, you can turn back into the corner. You actually saw the wheel slightly out of the corner and back inside. 

If the car oversteers, the corrective input has to be faster and car-dependant: In a Rear-wheel drive and/or four-wheel drive, you will need to apply constant throttle and use the steering to balance the car. You actually need to reduce the steering angle and probably turn the wheel away from the corner (countersteering) and than straighten the steering back once the car is balanced. In a front-wheel drive, you need to recover early enough that you don't need to countersteer -- you just accelerate forward and start to straighten the wheel. The key in both cases is to to keep the eyes up to the next reference point.

A Sharp corner is not very common on the track. They are more common in rallying, especially road rallying, as well as in normal road driving. The apex here is even later and the braking is drawn ever deeper into the corner. You keep the car braking in a straight line a bit later and than begin to turn the wheel quite sharply into the corner while lifting off of he braking a bit later but less progressivelly. You set-up the car for the "last apex" and keep the constant throttle towards the apex, and accelerate just through it and out of the corner towards the outside. 

Understeer and oversteer recovery are quite similar, except that some front-wheel driven cars can have enough torque in such a turn, that it can be utilized to help straighten the car out of oversteer. You start straightening the wheel while momentarily accelerating hard to spin the front wheels slightly. This spinning still allows some acceleration to take place, so there's still a rearward weight transfer that helps the rear grip again, but the sliding of the front wheels will cause them to slide outisde and straighten the car instead of countersteering. Once the car is straight, you reduce the amount of throttle to get you around the turn.

Successive corners

Let's assume a place on the track with one righthander followed directly by a lefthander. You stick to the left before the first corner, turn right and into the corner, apex and track out to the left again -- this would place you on the "inside" of the next corner and off of the right line. This is particularly bad because our priority is for corner exit speed, so the speed coming out of the last corner in the corner-set is most crucial.

The choice is to "prioritize" the second corner. You take the "last apex" line into the first corner, which enables you to keep the car "pitched" on the inside after the apex, allowing you to take the correct late apex line towards the next corner. Alternativelly, if you have two right-hand turns one after the other, you can take the first corner with a geometic apex and than track-out to the far left-end of the road so that you can carry a late apex into the next corner.

This is just theory. In real-life you sometimes don't track-out all of the way, and negotiate the following corner somewhere from the middle of the track. This is mainly true for the faster curves that are in times very easy to get around even when you don't use the whole track width.

On the road

Driving lines on the road can be used in one of two causes: To increase safety, or to increase speed while practicing racing lines in winding roads. The system is preety much like the lines used in a race. Fast curves normally have a field of vision which is open and wide around the corner. This enables to use the geometric apex to make the corner as smooth and grippy as possible. Of course, the line on the public road should be restricted to the bounderies of your own lane.

A moderate bend is the type of corner you might negotiate on the countryside rural roads and in winding mountain roads. On the road, we need to drive well within the car's grip limits, so the main problem in such corners is not the grip that gets us through it, but the limits of vision. This is why a late apex is very effective here. In fact, it's best to take an even later apex -- just like the last apex. Still, because we drive on the public road, we need to avoid the sharp steering input which is used in that line: You turn the wheel a bit earlier and bit more smoothly, but aim for the same "last apex." Sharp corners are negotiated in urban districts and in mountain roads. These corners are negotiated much like the moderate speed bends: You enter it very slowely, wait to a very late stage and turn the wheel into the corner. You try to be smooth, but sometimes smoothness has to be compromised for a clasic "last apex" line. 

On the road, it's important to reduce the overalp between braking, steering and acceleration. Some overlap helps in achieving a weight transfer that makes for a bit of extra responsiveness of the car during transients. However, less overlap makes for easier, safer cornering and a larger grip reserve: You brake with feel in a straight line, turn the wheel smoothly (but as decisivelly as required) and ease off of the brakes. You than establish balanced throttle all the way through the turn. Even when you start winding the car through the corner, you don't accelerate much -- just a little bit of acceleration to help straighten the car.

On the road, very fast curves and very sharp and slow corners often require a different line than the above prototypes: Let's say you drive on the righthand lane of the highway and you follow a slight curvature of the road to the right.  Moving to the left-edge of the lane is going to be really unnessecary. It's going to put you out of the normal position you should keep on the road -- so it's best to stay on the right or maybe move just a bit towards the middle of the road as you turn. The same happens in slow, sharp corners in the city -- you keep a tight line to avoid posing a hazard for motorcycles.

Even in corners where you do take a wide driving line you don't nessecarily use the whole width of the lane. In a righthander, you want to keep a short distance from the divider line to keep a certain gap from oncoming traffic. Even on lefthanders (in countries where you drive on the right) you can't always set-up from the rightmost edge of the lane, because it can be slippery due to dirt and especially when wet. 

Eyepath

The eyepath is a major element in taking a corner properly. First, you need to drive straights with your eyes UP. This way, you will see the corners in advance from the largest possible distance. Once you see a corner, you need to to glance into it and as far as possible through it. You need to assest the corner's type: What type of corner is this? The next step is to visualize the cornering line you want to car to take through the corner. Once you established the line you want to take, you mentally draw the turn-in, apex and exit points on it.

While glancing around the corner, look out for the convergence point. This is the furthest point of the corner you can see. This point appears as an arrowhead that seems to "unwind" and get away from you as you get closer. Adjust your pace to fit to that of the convergence point - so that you can match the right speed, gear and pace for the corner. 

Once you enter the corner, you use your eyes to guide you through the right line which you planned and visualized in advance. In fast curves, you just treat the corner as a twisting of the straight, and keep on looking through it. You don't even need to use the convergence point. On slower corners, however, a more advanced eyepath is used. You start driving towards the convergence point. You set the right speed and gear to the corner and adjust your position in your own lane so that you are ready for the line you want to take.

When you reach the point which you designated in your imagination as the point of "turn-in", you should evert your eyes and look towards the next point -- the designated apex. You should gauge the exact turn-in point through the corner of your eye, through your peripheral vision. As you start lining up towards the apex, you look through it and down the following straight. You gauge the exact clipping point based again on your peripheral vision.

On the track, you improve this system by using a system of reference points: You set permenant visual details as points where you want to turn-in, apex and track-out. Apart from the fixed points, you use you judgement to gauge when you brake, when to let up the brakes in a corner and when to begin accelerating out of the corner. The driver can also use his steering and engine/exhaust tone as points of reference. 

Lesson learned:

For the next month, try and practice the effective driving lines: Both road driving lines and race driving lines. You can also practice racing line on the public road too. They are best practiced on deserted winding mountain roads. You first make a slow run and inspect the whole road and decide what is the right driving line and if there are any surprises to avoid. Than, you do a faster run with the right driving lines.