The basics of Weight Transfer

Weight transfer is one of the more commonly misunderstood terms in vehicle dynamics. In reality, this topic gets pretty complicated once we factor in more physics, kinematics, considerations for sprung and unsprung masses, geometric and elastic differences, damping, tire characteristics including slip angles, etc. The whole story gets a little too long. Today, we will try to cover the basics and the common misconceptions with weight transfer.

One of the first things to clarify is that weight transfer is not related to what the driver feels, but rather what the tires feel. The opposing forces we feel in the car pushing us in the opposite direction of the turn, throwing us forward as we brake, and pushing us into the seat as we accelerate, are primarily due to inertia and other references or feedback such as roll angle and forward dive. However what eventually connects the car to the road are the tires, or more accurately the 4 tire contact patches.

Most of us would be familiar with the classical friction theory which shows that the amount of friction (or sideways resisting force) is directly proportional to the vertical load as follows:

Where the friction coefficient (mju) is static assuming a no slip condition between both surfaces. What this suggests, is that the larger the vertical load, the larger the amount of sideways force that would be generated. This sounds pretty good, especially since rubber is one of the few materials to have a friction coefficient much greater than 1. Right? Except not. When something sounds too good to be true, there is always a catch. Sure, it's difficult to push a stationary car from the side into a parallel lot for example. The key difference between the stationary 'tire model' block above and a real tire is that real tires rotate.

The mechanisms in which a tire generates grip is quite complex as well, but is generally thought to be the result of 3 main factors: molecular adhesion, deformation and wear/tear. A whole book could be written on tires alone (Hans B. Pacejka), but what we can take from this is that a tire needs a slip angle to generate grip. We'll leave it at there now and get back to weight transfer.

Weight transfer is the transfer of weight from the inside to the outside tires of the car (for example from the left to the right of a car that is turning left), from the rear tires to the front when the car brakes, and from the front to the rear as the car accelerates. The following describes in general (without consideration of suspension geometry and sprung/unsprung mass), a simplified 2 dimensional illustration of the factors that affect weight transfer:

In the car above (without suspension apparently, jacking up the inside wheel as it turns to its left), weight is transferred to the outside tire (Fz), which is responsible for generating the resultant grip or Fy required to keep the car in its intended path. The weight transferred to the outside wheel is a function of the CG height and track of the car in 2 dimensions, which leads to a common misconception that stiffer springs allow you to transfer more weight. The spring rate is not part of this equation, thus does not influence the steady state weight transfer during a corner.

But some of what stiffer springs offer are:
- Reduced time for the load to be transferred, thus increasing the response of the car.
- Reduced body roll, dive and pitch giving the driver more confidence in the car's capabilities.
- Reduced height (usually), which lowers the CG height and reduces weight transfer.
- For custom springs, the ability to adjust the front/rear distribution of roll stiffness

wait, reduce weight transfer?

Another misconception about weight transfer is that it is good, that stiffer springs transfer more weight so we get more grip. We've seen from the above that the Fy (what we are ultimately interested in), is a linear function of Fz, which means the greater the amount of weight transfer, the greater the amount of Fy or sideways grip we get. However, due to the visco-elastic properties of the rubber compound in the tire, the increase in sideways grip is not linearly proportional to the increase in downward force or weight transfer (Fz), a property known as 'Tire Load Sensitivity'. If we revisit the 3 mechanisms that contribute to tire grip, a major contributor would be the deformation of a tire as the rubber tries to 'wrap around' the irregularities in the road (which are vast valleys under a magnifying glass). As the load is increased past a certain limit, the valleys in the road would be pretty much filled up, leaving only 2 mechanisms left for grip.

Source: Milliken & Milliken

We can non-dimensionalize the sideways grip with the vertical load or weight transfer by removing the effect of the weight of the car for different kinds of cars and setup to give the term 'lateral force coefficient'. What is then seen, is a reduction of maximum sideways grip as the amount of vertical load increases. The slip angle required to achieve the maximum is also increased.

If we consider the fact that the inside wheel sees a reduction in vertical load, and hence a reduction in sideways grip, then what Tire Load Sensitivity suggests is that we lose more grip than we gain with weight transfer.


To reduce sideways weight transfer, here are some options:
- Reduce the mass of the vehicle
- Lower the centre of gravity height
- Increase the track of the vehicle (via wheel spacers or wider tires in production cars)

This pretty much sums up the basics of weight transfer. Note that the above was a simplified 2 dimensional explanation without the considerations for suspension kinematics, sprung/unsprung masses and transient effects. Hope it was useful. :)

The Effect of Weight Distribution on Steady State Handling

Well since we are in a lull period, lets review something quite fundamental to vehicle handling - weight distribution. For those who know, please bear with me.

The entire weight of a car is carried by its 4 wheels, or more accurately its 4 tire contact patches. Assuming symmetry on the left and right side of the car (which is often not especially if there is a driver but no passenger), the fore-aft weight distribution determines the vehicle's centre of gravity. Weight distribution or centre of gravity location, is a key consideration in car design. It is the reason why manufacturers select different engine layout configurations, and why race teams do their best to create the lightest car as possible to have the freedom in positioning their ballast weight to meet minimum weight regulations.

Why is it important? The two most important considerations for CG location are its fore-aft location (or x-axis in SAE terms), and its vertical location (z-axis). It's lateral or y-axis position is normally assumed to be in the centre.

The fore aft position of the CG primarily influences the steady state stability of the vehicle. By steady state we do not mean 'not moving', but rather when the yaw moment of the vehicle approaches zero, or when the vehicle reaches its maximum lateral acceleration. This is typically when the vehicle is close to the apex of a turn. If we define the position of the CG relative to the front and rear axles in the following diagram, a1 and a2 are the distances between the front and rear axles to the CG respectively.

From the above, we can see that the sum of a1 and a2 is the vehicle's wheelbase. Instead of explaining it in a way such as front weight bias will result in understeer or vice versa, etc. lets look at it from a more quantitative point of view. The steady state stability factor for a vehicle is represented in the following equation:

Where m is the mass of the car, l is the wheelbase, Caf and Car are the tire stiffness of the front and rear tires respectively (or more simply the amount of 'grip' of the tires). The tire stiffness of the front and rear are said to be equal if they are of the same width and construction. From the above, we can see that a front heavy car with a1 being lesser than a2, would result in an understeering car, all things equal. Similarly, we notice that a rear heavy car (eg. rear engined car) would require a higher rear tire stiffness (often with larger rear tires) in order to reduce the second term to reduce the overall value of K.

Should the CG position be central, forward or rearwards of the vehicle with respect to the middle of the vehicle's wheelbase? In other terms, is a 50:50 weight distribution ideal? It may or may not be, depending on the vehicle's design, purpose and capabilities. For a high performance car, eg a formula single seater, it is usually more desirable to have a slightly rearward biased CG, giving a front/rear weight distribution of something like 45/55 or 40/60. This gives a slight oversteer characteristic to the vehicle, allowing for better response for quick transitions such as those seen in autocross. It also allows for better braking performance as weight is shifted to the front, making better use of the capabilities of the rear tires. Also, the slight rear bias gives an advantage grip when the vehicle accelerates.

A sporty or fun car would more likely benefit from a 50:50 weight distribution as much of its driving pleasures come from winding roads in which a car with neutral handling characteristics would be the easiest to drive in. A passenger car rarely sees more than 0.7Gs of lateral or longitudinal acceleration with a maximum seldom more than 1G with street tires, thus there is no need to largely 'offset' this CG location to take advantage of that.

An everyday car for anyone would benefit from a front biased car, eg a front wheel drive with a typical front/rear weight distribution of around 60/40. This gives the car an understeer characteristic, which is easily recognisable and instinctively corrected (reduce speed and increase steering depending on which portion of the tire curve the driver is at). Moreover, safety systems in the car, both passive and active, are most effectively designed for a front on collision than a sideways collision into a tree.

The vertical position of the CG is important as well, but it is not changed by weight distribution. We'll cover it in another post. While we are on the subject of weight distribution, consider the following very simplified car model:

It can be agreed that in both cases, the weight under each wheel would be 200kg excluding the mass of the car obviously. But the location of the weight relative to the car's CG is another important consideration, a term known as Moment of Inertia. The moment of inertia equation varies according to the geometry of an object. For simplicity, we shall assume the car is a giant cylinder with the following equation:

Where 'r' can be taken as a1 or a2 if the CG is exactly in the middle of the wheelbase, and d is the offset distance of the masses. The above equation is what's known as the Parallel Axis Theorem, which suggests that the influence of distance of overhanging masses from the centre of rotation is exponential. In fact all distance related factors are exponential (squared). What this means is that distance of the mass from the centre is a more important consideration than the actual mass itself for reducing the MOI.

Why reduce MOI? Similar reason to why divers tuck themselves in, or why a figure skater brings her arms close to her body, a car with lower MOI would be more agile and respond quicker to direction changes. Another extreme end would be a tightrope walker, who would want a larger MOI for greater stability on the rope. Examples of reducing MOI would be selecting a hatchback over a sedan, choosing a smaller wheelbase and shifting the positions of the engine and driver closer towards the vehicle's centre of rotation.

From the above, we can see that not only is the weight distribution of a vehicle important, but also the location of placement of the masses that greatly influence the steady state handling characteristics of a car. :)

Analyzing the data

Well.. pardon me for the long delay, it has been a difficult time for me the past month.

The following is a short or summary analysis of the data taken during the track day. It would hopefully show the capabilities of the system and data acquisition, and also hopefully enable amateur drivers starting out circuit racing to see a potential in this as a tool to gain feedback and improve their lap times.

First of all we have the GPS plot, which when overlaid on Google Maps, gives a rather impressive pictorial description.


Although positional data has an error of up to 3m, which means actual racing lines cannot really be taken literally, the overall data as a whole gives a rough idea on the lines taken.

The lap is broken down into sectors, with each sector comprising of an entry, corner and exit. Naturally, there would be 15 sectors since Sepang has 15 turns. The sectors are not 'official', but their collective times add up to the overall lap time. Sector times allow a more detailed, quantified section of a track serving as a constant to compare the performance of multiple laps against.


The sector times are what every driver is interested in reducing eventually. But how and where the times can be reduced is what this is all about.

Next important bit would be the speed of the car through the entire track.


The speed is fundamentally what all drivers try to maximise throughout the entire circuit. By laying out multiple laps over one another, the first thing we notice is consistency. Whether the driver reaching the same speeds at the same points of the circuit. Whether he is braking at the same point in the circuit as well.



This is an example at Turn 4. Firstly, we can tell the maximum speed reached just before braking. In the above example, the difference in speed between the laps was caused by the difference in exit speed for Turn 3, which is a long right hand sweeper. As a bonus, the drop in speed is caused by shifting the gears, and through that, it is possible to estimate the shift time, as well as mis-shifts or other shifting errors. In the red lap, the shift took a split moment longer than the rest, which suggests uncertainty later confirmed by early release of the throttle.

Next, we can tell the delay the driver takes in lifting his foot off the accelerator and applying the brakes. If this is done well, the speed would peak and drop sharply similar to the green lap. The blue and red laps show a noticeable lift off, as if he applied the brakes too early and later realised it. The rate at which the speeds drop are almost constant, suggesting that the brake pressure of the driver is consistent.



The next example is lateral Gs. This is the measure of the car's lateral acceleration throughout the circuit. In this analysis and convention we will be using, negative values are turns to the right, while positive values are turns to the left. You might observe that the readings when the car is supposed to be travelling in a straight line are not zero. This was due to an installation oversight which resulted in the unit being slightly tilted. so what can the lateral G plot tell us?

Besides showing the cornering capacity of the car (maximum lateral Gs the car can produce), it shows us the rate that the lateral G is building up for every turn, and whether it remains constant, increases, or falls through the turn. This gives an indication to whether the car is over steering, under steering, or a change in line has taken place.


An example of a lateral G plot for a corner (Turn 15) is shown above. For example, corner entry understeer shows as a slower buildup of lateral Gs after the initial rise.

Sepang Test

Apologies for the delay, it's been one hell of a month. The original post was just screenshots as I had intended to write about it later, plus do up a report also, so the initial posts were just to 'park' this slot.

The test at Sepang was an eye opener which raised other thoughts about this whole project and the scope and direction to where all these are heading to. It's still beyond myself for now, so I shall pen it when I've got it all sorted out.

To sum it up, the test car was a Honda Civic Type R (FD2R), pretty much stock with normal tyres.

Only managed to take a couple of pictures:


Not a very happening atmosphere as it was pretty much an 'own time, own target' day. Quite a few exotic cars including Lotus, Porsche, BMW, Lamborghini, Ferrari, an Ariel Atom... and the usual Civics, Rex and Evos.

This is the GPS antenna placed on the roof of the car. It's magnetically mounted with a plastic-cover for the base so it does not scratch or damage the painted surface. The wire is run through the seal of the door, at the corner which has plenty of excess rubber and doesn't damage the seal or the wire.


This is the basic unit - the data logger with built in gyroscope and acceleromters. GPS data is logged at a post processed frequency of 20Hz (normal loggers usually do 5Hz for GPS), with speed having additional information from accelerometers. Other inputs are logged up to 100Hz. The mounting strategy of the logger could be improved for future runs as later it was discovered that the unit was mounted slightly tilted which affected the readings.

A total of 3 runs were made, with about 4 laps each. Unfortunately one of the runs was compromised, so there was only 2 runs worth of data.

Other points to note would be made out on future posts.

Laps Testing at Tuas

This test was done on the night of 30/8/2011, which was a wet and rainy day. The main objective was to test out the lap functions and to try and overlay the results to compare. The car was a toyota corolla, so naturally the figures would be very conservative. Because the run is sampled as a continuous drive, one needs to break up that continuous drive into laps, or consecutive single runs, in order to overlay them and compare.


The above diagram shows the typical main screen displaying speed, longitudinal and lateral acceleration. The drive was fairly consistent except for the first lap, which was a 'Reece' lap.


Further screenshots showing the positional data overlaid on Google Maps. The blue arrows denote markers which are used to determine sectors.


Overall, it was a simple rectangular left handed circuit. It was a learning experience trying to explore and utilise the software in greater detail. The potential for this is literally limitless once one knows how to manipulate, create and present the required data. :)

Tests lined up

A couple more days before I can dedicate my 100% into this interest.. and we've got a couple more tests lined up to familiarize myself with the system and it's capabilities before we test it on the actual field. Currently, there are no confirmed dates although the nearest 'confirmed' one is a go-kart test somewhere in September, and probably one at Sepang around then too. Btw, we're looking for volunteers to test this system out. Volunteer = no monetary gains obviously, but the driver would be rewarded with detailed information and feedback on his driving and if possible, his car's capability and setup. If this plan works out, he would have other perks and priority as well.

First up we've got the OBD (On Board Diagnostics) to Serial adaptor which we will test to see if it able to read and record ECU data and synchronize it with the other data. I have a feeling that we can only either record both logger and OBD or view OBD alone only, and not both together. We'll see how it goes.

The next test would be trying out laps. I haven't had the chance to use the lap function in the software, with sector markings, split times and all. It would be interesting driving around my block round and round. =)

Hopefully, will get these two tests sorted out by the end of this week cuz Murphy's Law always stands. Something will go wrong. If it doesn't, then you're doing it wrong.

oh. Look what's cooking

This little test was done on the 18th of Aug so it's another backdated entry. Before that, I was having troubles with the live data display function of the logger. It turns out that I have been using the wrong cable - a straight through serial cable instead of a null-modem or cross over serial cable. Basically, the former is a one-way street, and the latter is a two way street. Another D'oh moment.

Although we know that the sensor from the manufacturer would be pretty much calibrated and ready to be installed on the car, I just wanted to see it working for myself under controlled and known conditions. The purpose of testing was also to see how close both sensors were in the temperature readings, which was more important as it is the difference between the two temperatures which would be used in calculations for the radiator test.


This was the very impromptu test setup that I made on my kitchen stove top. The tripods prevent the wires and sensors from touching the pot directly. Also there is a reference temperature probe for a '3rd party' point of view.


I used the lowest heat settings to reduce the heat coming from the sides of the pot. Thus it took a very very long time for the water to boil.


The temperature plateaued off at around 97 degC, not too far off from the reference temperature of about 98 degC. The difference between both sensors was also around +-1.5 degC. The graphical results are shown below.


You can see the very slow climb to the top, till it reached a small plateau. This was when I added a little more heat to give it a 'boost'. Then the heat was shut off and the pot allowed to cool on its own. The sharp drop was when I added extra water at room temperature to bring the temp down, and the final drop was when a couple of ice cubes were added in.


This graph shows the difference between both temperature sensors. If both were reading exactly the same, it would be a single straight line. The increasing thickness of the line shows that the difference between both sensors increase as the temperature increases. Still, they were not that far off each other.

This concludes the test. Hopefully next time, we will get to do some real testing.