"The Black Art Dynamics Guide to Suspension Tuning"

Part 1 - Tyres and Load Transfer

This is the first of several articles where I will attempt to sum up the basics of vehicle handling balance. Pretty much every aspect can be expanded on, however in the interests of keeping it simple I'll only include the essential parts needed to understand the whole process and not concern you all with the full array of nuances and equations used to calculate everything, however in sections there will be variables you can change to see the resulting effects. These inputs are in cyan, you can change them then hit enter within the text field to submit the value and update the results.

Tyres, it's all about the rubber!

We'll start at the beginning with tyres. Tyres are the single most important aspect of the vehicles suspension system. They are the only point of contact between your car and the road, without them you cannot transfer force to the road to accelerate, brake or turn. Everything we do with suspension and chassis tuning is to optimise the conditions for the tyres to produce as much grip as possible.

Tyres loosely adhere to the laws of dry sliding friction, which dictate that lateral force (Fy) is equal or less than the vertical load (Fz) multiplied by the co-efficient of friction (μ), a constant for the pair of materials in contact.

So the basic formula for dry sliding friction is: $$Fy = Fz \cdot \mu$$

(Note how theoretical grip at this stage is independent of surface area and so contact patch of the tyre.)

We can see that lateral force increases proportionally with increased vertical load, given a constant friction coefficient. However, rubber is a soft, deformable material, and as such it’s co-efficient of friction is not constant. What in fact happens is that as vertical load increases, the μ drops. The end result of this is that as vertical load increases, lateral force increases but at a decreasing rate. So (as an extreme, illustrative example) if 100lbs vertical produces 100lbf lateral force, 200lbs vertical only yields 150lbf lateral, 300lbs vertical yields 175lbf lateral and so on.

This diminishing relationship between vertical and lateral force is called load sensitivity. Load sensitivity varies greatly between different tyres, some may not be very sensitive over wide range of loads and temperatures, others may be more sensitive over certain temperature/load margins etc. The general trend is summarised by the following graph, we can see that grip tails off as load increases, eventually to a point where further increases actually reduce grip.

Lets now look at this with relation to a pair of tyres on an axle with 400lbs static vertical load, 200lbs on each tyre. Going on my basic example above, our maximum potential lateral force in this condition is 150 + 150 = 300lbs potential grip.

Now lets transfer 100lbs from one side to the other, simulating a car in a corner, so we have one wheel on 300lbs vertical and one on 100lbs.

We get 175 + 100 = 275lbf potential tractive force from the tyre pair, a drop of 25lbf from the static condition

We can see from this that a pair of tyres makes the most grip when equally loaded, as the unloaded tyre will always lose grip faster than the loaded wheel gains it.

Breaking down the mu

The friction property μ of tyre grip is the adhesive property of the rubber compound. Adhesion comes in two forms, chemical and mechanical. Chemical adhesion is a complex molecular property which is beyond the scope of this article, but think of it as the stickiness of the rubber.

The mechanical aspect is the action of interlocking between small peaks and troughs in the contacting surfaces. An easy example to imagine is moving to pieces of sandpaper over each other. The friction is generated as the individual grains on each sheet interlock with the grains on the opposing sheet. In terms of tyres, this manifests itself as the soft rubber deforming around asperities in the road surface. This also exposes one of the reasons that adding load reduces the friction co-efficient, as you add load the depth of the interlocking features increases adding to the friction, but in doing so also reduces the amount of further interlocking available with additional load. Eventually, the tyre is pushed into the road surface so hard that no additional interlocking is possible, and the tyre quickly loses grip.

Both of these types of adhesion DO rely on contact area, obviously using a larger blob of glue, or a larger patch of Velcro, can support more weight than a smaller area.

One easy way to get an idea of a tyre’s adhesive properties is to look at the UTQG ‘Wear Rating’, visible on most tyre sidewalls. A lower number usually indicates a higher level of adhesion, by virtue of the rubber being a softer compound. Bear in mind that this is not a reliable indicator however, one brands 180 rating is not necessarily the same as another brands.

Member NickD on MX5Nutz provides this useful insight on the matter.
"I know there is a calculation that is supposed to relate the tread wear number to the frictional coefficient of the tyre however this makes the assumption that all rubber compounds are the same and have sliding scale properties based effectively on Shore hardness. It is a bit like saying a steel's having the same hardness all have the same properties.

First up the compounds are not the same. Modern Silica technology rubbers have much greater wear resistance that the older organic compounds without sacrificing any grip. To test standards these would record higher life numbers and so to the calculation be considered to have less grip.

The test is only a wear rate ratio against a test tyre and the manufacture does not have to report the test accurately so long as long as they do not claim a higher number. It is quite legal for a tyre that recorded a wear rate of 500 to be listed as 50 if there is a marketing requirement to do so. The advent of the concept that this wear number relates to grip is one such reason for this.

The tests are carried out in Texas where even in January the average day time temperature is 17C compared to around 6C for Birmingham. The calculation again makes no allowance for rubbers that have better (or worse) properties at higher temperatures and equally rubbers that perform better (or worse) at certain weights. The mechanical grip part again is hard to calculate as the better tyres tend to be softer and so report lower wear figures, however when thinking of sustained ultimate grip these tyres can "go off" rapidly and so the tyre may develop good mechanical grip to the road, but the thermal breakdown of the construction of the rubber means it does not have the internal strength to use it. And all the "grip" figures reported on tyres are for straight line tests and lateral cornering grip can be vastly different.

Bottom line is we have all driven on tyres that have the same side wall figures but behave and feel totally different. I believe the Pirelli P6000 and Toyo T1R are both classed as 280 on the UTQA system, it is generally what happens to the tyre and how it responds once it has gone over its "standard" level of friction that we want to know about."

Make of it what you will. It's not a perfect system, but it's the probably the best indicator we have to compare!

With tyre basics covered, we now move onto the next aspect of handling; load transfer. Load transfer is the shift in vertical tyre load from the inside wheels to the outside wheels as a vehicle experiences lateral (sideways) acceleration in a turn.

The vast majority of the weight of a vehicle is a 'sprung mass' and for the purposes of load transfer we are talking about the sprung mass of the vehicle and not the unsprung transfers.

Load transfer is a result of a few basic variables in the vehicles design: track T, height of the centre of gravity CGz,vehicle mass M and lateral acceleration A. These four variables alone dictate how much load transfer a vehicle experiences and are difficult to change aside from the mass, although small changes in CGz can be made with ride height changes.

The equation for load transfer is: $$\text{Load Transfer} = A \cdot \bigg({CGz \over Track}\bigg) \cdot Mass$$

Let’s try that out!

Hit enter within any of the input fields to register a change.

 A CGz (in) T (in) M (lbs)

The math engine has not been started, please change an input.

So in the case above that’s transferred off the inside tyres and onto the outside tyres when cornering at .

What is important at this point is to differentiate between load transfer and roll. Load transfer is engineered into the vehicle, it cannot be drastically changed other than by changing the accelerative force acting upon the car. Since we are interested in going faster, what we actually want is more load transfer! Roll, as we will get onto later, is not so good. It is a product of load transfer, but it is easily changed by altering spring rates and anti-roll bars.

Next, let’s have a look at some tyre loads.

 Front Weight % Vehicle Mass lbs

The static tyre loads for this car at rest are:

 Nearside Offside Front Rear

Now let's apply some lateral acceleration:

 Lateral Acceleration

The dynamic tyre loads are then:

 Nearside Offside Front Rear

As stated earlier, rate of load transfer is engineered into the vehicle and cannot be changed without adjusting the vehicle weight or ride height; however the front/rear distribution of this load transfer can be altered, and is what we change when we alter spring rates and anti-roll bars. As you make one end proportionately stiffer than the other, you increase the amount of the total weight transfer that that axle sees, and reduce the transfer the other sees.

This is where the relationship with the tyres comes in to play to form the 'balance' of the car with regards to over/understeer. You will recall how a pair of tyres makes most grip when equally loaded, and how the more load is transferred the less grip they can produce in total, well now we can work out the balance between front and rear load transfer to see which end is delivering the most grip and thus pushing towards understeer or oversteer.

At this point, I'll introduce the idea of 'front diagonal', a way of expressing the balance in load transfer between front and rear. Front diagonal (properly called Front Lateral Load Transfer Distribution, or FLLTD) is calculated as the load on the front outside tyre NSFz plus load on the inside rear OSRz, divided by the total Mass.

$$\text{FLLTD} = {(NSFz + OSRz) \over Mass}$$ So given the details above:

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Since we split the load transfer equally between front and rear axles, this is reflected in the 50% front diagonal. If we remember that a tyre pair loses grip with load transfer, this would translate into a neutral balance of front and rear grip as lateral acceleration increases, as both axles will lose grip at the same rate.

Let's say the front axle has stiffer springs, or a bigger anti-roll bar, so the roll stiffness distribution is no longer 50%.

 Front Roll Stiffness %

The tyre loads would then be:
 Nearside Offside Front Rear

The front diagonal is then:

The math engine has not been started, please change an input.

In this case, there is a bigger load differential at the front than there is the back, and since a bigger load differential means less grip, we can see that this car will tend towards understeer with the front making less grip than the rear. Of course, this does not paint the whole picture of balance, but it is a start. Managing load transfer is the primary mechanism for setting up the balance of a four wheeled vehicle, so it is important to know these basics from which to build upon.

In the next article we’ll look at how to apply this theory to spring rate selection. Read Part 2

Don't forget to check out the Load Transfer App, which is what this series will be working with and explaining.

I hope you've enjoyed this article, don't forget to follow Black Art Dynamics on facebook to stay tuned for the next issue if you haven't already! The Twitter button is inactive at present but I will get that sorted out soon.