Vehicle Dynamics - a layman's introduction

For those with a casual interest in vehicle dynamics but need an introduction that you can understand and doesn't involve huge calculations and derivations I hope you'll find this informative. If you watch motorsport and wish to understand a little more about why commentators bang on about tyres and aerodynamics etc hopefully this will help too.

Tyres

First thing you must know is that the tyres are the only part of the car that can transfer the loads to the ground and therefore are the most important part and limiting factor in a cars performance. So you must understand how they generate these forces and what the limits are to their performance in order to know what the overall limits to your cars performance are.

We can all probably understand that the "grippy" rubber interacts with the ground and the friction between the tyre and the road is what creates the available traction. Newton's equation for friction tells us that the Friction force is equal to the coefficient of friction multiplied by the force that's pushing the two surfaces together (referred to as the normal force, because it's the force normal to (i.e. right angles to) the direction of the friction force. The coefficient of friction is a value that is derived from how "sticky" or "smooth" two surfaces are that are in contact. For most materials this friction coefficient is independent of the normal force, but for a tyre it isn't. More on that later.

So from Newton's friction equation we can see that the more we push the tyre onto the road the more friction we will generate and therefore the more traction we will have for cornering or braking or accelerating.




The above graph shows the relationship between the vertical load pressing the tyre into the road and the amount of traction. Traction for a tyre basically means the amount of force it can generate overall, so you can use this all for cornering, all for braking/accelerating or a combination of both. When you try to go above this force then you have the situation where you lose grip and spin etc.

Slip Angle

The blog link below gives a nice explanation of slip angle. But essentially slip angle is the difference between the direction the wheel is going and the direction where the car is going. Might sound odd at first, as you would hope this is the same, but, to a small degree this is not the case. The wheel during cornering will be at a higher angle than the direction the car is turning. This is because the contact patch of the tyre, is being deflected, the angle difference is referred to as slip angle, and up to a point the greater this angle the more cornering force you can get from the tyre. So on a lot of tyre performance graphs you'll have multiple lines, so you can see the relationship between cornering force and both the slip angle and the vertical load.

http://www.pratperch.com/2011/05/tyre-side-slip-explained/

When you get above the maximum slip angle that the tyre can work at, or that the road conditions will allow then the tyre loses traction. Anyone who drives will likely have experienced this in bad weather conditions, maybe at a roundabout, you turn in and maybe accelerate and the steering feels lighter and less responsive and the car doesn't take the course that you though it would. This is understeer, and it's where you've taken the tyre above it's slip angle limit for those conditions.

Slip angle takes account of speed and steering angle. If you think of a F1 car, it can't take a hair pin bend like the Lowes bend at Monaco at 200 mph, but it can take large radius bends at Silverstone for example pretty much flat out. What will actually happen though is that the slip angle is the same whether it be 30 mph and very tight of 200 mph and very large corner radius. At the tight bend the steering angle will be 20+ degrees but because of the speed of the car the direction the car is taking is close to this steering anlge, and at a high speed corner the steering angle will be much less and the direction of the car also much less but equal as far as the "slip angle" or the tyres contact patch is concerned. So slip angle is important to keep in mind but it allows us to ignore how fast the car is going and the steering angle and equate everything to what the tyre is actually doing.



On a racing tyre like an F1 slick you don't get a lot of warning that you are about to exceed the maximum slip angle of the tyre, and when a driver does go over this limit the tyre's traction rapidly drops off and generally causes a dramatic incident, like a spin. On a road tyre they are much more forgiving and road cars and tyres are designed to give us less competent drivers plenty of warning of impending doom. So the drop off after maximum slip angle is less dramatic. Back to the example of driving a roundabout in wet weather what an inexperienced driver will do is to wind more lock onto the steering in the hope that this will make the car turn more, but, it just makes the situation worse. Big accidents are then caused by the inexperienced driver jumping on the brakes whilst turning more on the steering, and then all control is lost. What should happen is that you wind off some lock so you come back into the usable slip angle range, gently ease off the power until the steering begins to respond again and then you can take back control of the car.

Suspension

So above we have described a little about the performance and limits of the tyres, now the suspension systems job (as far as vehicle performance is concerned) is to keep the vertical load on the tyres consistent. If you were to hit a bump in a very stiffly sprung car the tyre would see a rapid increase in vertical load (and therefore traction) and then the car would bounce on the tyres (because the tyres are very springy) as the tyre oscillates the load will go from very high to very low (low traction) to very high again until after some time the oscillations are damped out and the tyre load goes back to the normal static load from the weight of the car. Obviously if you are cornering, braking or accelerating whilst the tyre is cycling from high traction to low traction the cornering force will cycle from high to low and the cars cornering ability will suffer.

So the job of the suspension is to minimise the effect that bumps etc have on the normal load on the tyre. Just keep this in mind for one moment, whilst I explain about the effect of load transfer as the effect on efficiency is the same.

Load Transfer

When cornering the car will lean (or roll) over to the outside. What happens here is some of the weight of the car stops acting equally side to side on the cars tyres and puts more on the outside tyres and less on the inside tyres. If you were to stand with one foot on one set of bathroom scales and the other on another set, when you stand up straight both sets of scales will read half of your weight. If you then leaned your torso to one side one set of scales will increase and the other decreases by the amount the others increased. Your overall weight hasn't changed just the distribution from one leg to the other has changed. So the same is true with the car, what the outside tyre gains the inside tyre loses.

No problem you would think, we know that the tyres gain traction with increased vertical load, the problem is that it's not a linear relationship. When you look at the first graph above you'll see that as you increase the vertical load, the cornering force goes up, but not as much as it did for the previous increment in load. i.e. tyres are more efficient the less vertical load they have on them. From the first graph at 100 kg's of vertical load we get something like 140 kg's of traction, between 500-600 kg's of vertical load we only add about 50 kg's of traction. So in the case where we are transferring load from one side of the car to another, what happens is we lose more traction on the inside tyre than we gain on the outside tyre and thus overall the amount of traction the cars tyres produce is reduced.

Back to the case where the stiffly sprung car is bouncing on it's tyres and cycling between high and low vertical forces, what we get is less gain in traction at the high load points of the cycle than the loss of traction at the low load points, and therefore overall the tyre is less efficient and less traction is available.

Aerodynamic Load

When you load the tyres with aerodynamic downforce then as above we see that the traction force will increase. With racing slick tyres what you get is tyres that produce more cornering force than the vertical force acting on them. This is where tyres start to defy Newton because Newton says that you can't have a coefficient of friction greater than 1. Whereas racing tyres have a friction coefficient of around 1.5.

'G' we heard talked about a lot on racing commentary and this referred to the number of times heavier an object is whilst cornering or braking than it would be at rest. So a drivers head seems heavier to the driver whilst cornering than it would at rest. As far as the tyres and this blog is concerned "G" refers to the efficiency of the tyres. So a typical Formula Ford on slick tyres and no aerodynamic loads can pull about 1.5 G in the corners. So this means that the cornering force the tyres are generating must be 1.5 times greater than the force of the weight of the car acting on the tyres. Now with an F1 car and it's huge levels of downforce the cars can pull about 4 G in the corners meaning the tyres cornering force is 4 times greater than the normal force caused by the cars weight.

In the last two sentences I've made reference to the vertical force caused by the vehicles weight, because in terms of efficiency and therefore the G pulled during the corner we use the downforce + vehicle weight to determine the tyres cornering force, then divide that by the force caused by the vehicles weight alone, to determine the efficiency and G. So aerodynamic load is free efficiency if you like. I'll totally understand if that's a bit confusing, you might have to just accept it.

Centre of Gravity Height

Weight transfer as mentioned above is not good for a car tyres performance efficiency. The amount of weight transfer you will see is proportional to the cars centre of gravity height (CofG). If you imagine a car has a spot in the middle of it about which the entire cars weight can be considered to act and then when you roll the car over a few degrees this point will move over to outside of the roll. Therefore the weight of the car is now no longer acting perfectly in the middle of the two tyres, and is slightly close to one tyre than the other. Therefore more weight will be acting on that tyre, in proportion to how far this CofG point has moved from the centre point of the tyres.

Now if you lower the CofG, you'll notice when the you roll the car the distance off centre that the CofG moves is reduced, and therefore the amount of weight transfer is reduced.

The pictures above are an extreme view, but, they do clearly illustrate how the position of the centre of gravity moves to one side with roll angle, and how this is reduced the lower the centre of gravity.

There's a lot more to this of course, than I've written above. I'll collect my thoughts together and write more soon on how this relates to suspension geometry, and how CofG relates to other aspects of suspension geometry and vehicle dynamics.