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I am going to post some of a short report I had to recently write on weight transfer and the effect of fitting an ARB to a car. If you have any questions what so ever ask away.

Matlab Script Writing and Vehicle Simulation
For the purpose of dynamic analysis during cornering of the 2004 FSAE Brookes Formula Student car, Matlab will be used to simulate the impact of cornering a 1.41g corner on the contact patch load of the individual tyres and the overall vehicle roll. An important aspect of the analysis is that the car is a rear biased car with a front/rear weight distribution of 46/54. This will be seen to have an important effect on the analysis of the car and will be discussed below.
Following writing a Matlab script the results obtained are shown in figure 1.

Fig.1:
Standard Set-Up
Front ARB Stiffness (N/mm) 0 Rear ARB Stiffness (N/mm) 0
Wheel Reactions
Front Inner (N) 71.87 Front Outer (N) 1371.70
Rear Inner (N) 200.92 Rear Outer (N) 1493.70
Maximum Roll Angle (deg.) 1.4985

Wheel reactions and their impact on tyre performance
The vertical weight of the car pushing down on the tyres determines the maximum lateral (cornering) force achievable by the tyres, defined by the following equation:
Fy=Fz×μ
Where Fy is the lateral force created by the tyres, Fz is the vertical weight of the car, and µ is the tyre’s co-efficient of friction. Hence the cornering capability of the vehicle increases with increased co-efficient of friction (this is why “sticky” high friction tyres give greater performance), and also with increased vertical load (why heavy vehicles do not tend to loose traction). However the relationship between vehicle load and cornering force is not truly linear and if we double the vertical force on the tyres we do not gain double the cornering force (see figure 2).

Fig.2:


The reason why the relationship is not linear is due to the degradation in tyre friction co-efficient with increasing vertical load (figure 3). It becomes apparent then that designing a car with a high vertical load (with the aim of increasing lateral force) is not optimal since as the vertical load is increased the maximum lateral force will decrease due a drop in friction co-efficient. This effect also has important repercussions during weight transfer since, as the outer wheels becomes more highly loaded, their friction co-efficient will decrease, leading to lower cornering capability. Hence it becomes obvious that the most important factor in creating a high cornering capability vehicle is to maximise the cornering force generated by the tyres by keeping the load on the tyres as stable as possible, i.e. minimising weight transfer (1).

Fig.3:


Weight Transfer and the Effect of an Anti-Roll Bar
Weight transfer is an inevitable effect of turning a corner and can never be completely removed. However there are methods of reducing the negative effects of weight transfer, or rather using the fact of weight transfer to remedy other handling issues. A vehicle that tends to either understeer or oversteer (due to a forward or rearward centre of gravity respectively) can be remedied to some degree by the introduction of an anti-roll bar (ARB) to the chassis. A vehicle with a centre of gravity either for or aft of the geometric centre of the vehicle will exhibit increased weight transfer on the axle with the most weight situated upon it e.g. on a heavily rear weight biased car the majority of weight transfer will occur at the rear, this will make the vehicle tend to oversteer in a corner, and the opposite is true for a front weight biased car. To remedy this issue, it is possible to increase the amount of weight transfer at the other end of the vehicle through the introduction of an ARB at the opposite end of the chassis, thereby decreasing weight transfer of the vehicle on the previously more heavily loaded axle during cornering and increasing the overall lateral force generated by the tyres.

For example in a vehicle that is heavily front biased (most front-engine front-wheel drive cars) the introduction of an ARB to the rear axle will increase the proportion of overall vehicle weight transfer that occurs at the rear due to a stiffer chassis, hence it will minimise the transferred load at the front axle and increase it at the rear. This acts to keep a more stable amount of load on both inner and outer tyres thereby maximising the tyre co-efficient of friction (from figure 3) and cornering capability.

Evidence of this Affect shown in Matlab
Using the Matlab script created for this report it was possible to analyse the effects of changing the weight transfer distribution at the front and rear axle, by adding an ARB, and the results have been displayed in figure 4.

Fig.4:
Standard Set-Up
Front ARB Strength (N/mm) 0 Rear ARB Strength (N/mm) 0
Wheel Reactions
Front Inner (N) 71.87 Front Outer (N) 1371.7
Rear Inner (N) 200.92 Rear Outer (N) 1493.7
% Weight Transfer at Front 50.14% % Weight Transfer at Rear 49.86%
Maximum Roll Angle (deg.) 1.499

Front ARB Set-Up
Front ARB Strength (N/mm) 5 Rear ARB Strength (N/mm) 0
Wheel Reactions
Front Inner (N) 38.98 Front Outer (N) 1404.6
Rear Inner (N) 236.08 Rear Outer (N) 1458.5
% Weight Transfer at Front 52.77% % Weight Transfer at Rear 47.23%
Maximum Roll Angle (deg.) 1.359

Rear ARB Set-Up
Front ARB Strength (N/mm) 0 Rear ARB Strength (N/mm) 5
Wheel Reactions
Front Inner (N) 110.13 Front Outer (N) 1333.4
Rear Inner (N) 161.91 Rear Outer (N) 1532.7
% Weight Transfer at Front 47.16% % Weight Transfer at Rear 52.84%
Maximum Roll Angle (deg.) 1.369


It can be seen that adding an ARB to the suspension affects the vertical load on each tyre and therefore the cornering performance of the vehicle as a whole. The results show that adding a small front ARB creates more weight transfer at the front axle (for the reasons described above) hence less of the overall weight transfer will occur at the rear; leading to more balanced contact loads on the rear tyres (at the expense of the front). However in a car with a rear biased weight distribution that has an inherent tendency to oversteer this could go some way to remedying this situation and providing a more neutral steering car. In the case where a rear ARB was added, the rear suspension is stiffer and so suffers from increased weight transfer; this would increase the vehicles tendency to oversteer further and is inadvisable. Thus we can conclude that the addition of a small anti roll bar to the front of the vehicle may remove some of the vehicles tendency to oversteer and provide us with a more neutral steering vehicle; however, since more weight transfer will occur at the front it will be important to confirm that the front tyres are not already near their limit and can handle the increased weight transfer that will occur on them. It is important to note that there are many interrelated factors at play in vehicle suspension and the supposed remedying of one problem can lead to others, this highlights the benefits of simulation through programs such as Matlab where changes to a vehicle can be tested before they are fitted to a vehicle.

Quick summary: Vertical force on tyres (vehicle weight) is what creates the lateral force (that turns your car round the corner) through the tyres co-efficient of friction. Tyres a speciall because their friction co-efficient is above 1 (about 1.5 for normal tyres and up to 3 for race tyres), this basically means that if you put 100 N of force on the tyres it will create 300 N cornering force (yay!). When a car turns a corner load is moved from the inside wheels to the outer ones, thus, the outer wheels now have to produce more cornering force and the inners less (otherwise a slip angle will be created (a lesson for another day)) essentially this slip angle is what causes oversteer or understeer depending on the front/rear weight distirbution of the car. E.g. if you have a front biased car (like our civics) more weight will be transferred over the front tyres (from inner to outer), if the tyres cant handle this extra loading a slip angle will be created and the car will understeer (since the slip angle is largest at the front in this case).

If you understood that then you can now imagine what an ARB does. Adding a ARB to the chassis will cause more weight to be transferred at the axle it is fitted on, because the chassis is now stiffer. So this means if you add a front ARB more weight will be transferred at the front than at the back (however the overall amount of weight transferred in the vehicle will always total the same). So, if we add a ARB to the front of the car more weight will be transferred there and so if the tyres cant handle this extra weight then there is a potential for a slip angle to be produced and thus understeer, sounds bad right? Not exactly, because if we used this knowledge and purposefully made more weight be transferred at the rear (by adding an ARB) then we know less weight will be transferred at the front and we can remove the vehicles tendency for understeer (again im using the example of a front weight biased car (like our civics)). It is important to note here that an ARB is not an ANTI-ROLL device, that is a misnomer, it is a chassis stiffenening device that increases weight transfer at the axle it is fitted on. A by-product of this is usually decreased vehicle roll but that is not always the case, vehicle roll is dictated by the stiffness of the suspension springs and chassis torsion resistance, not ARB choice. This is something that 99% of people get wrong, myself included before I came to uni.

So if you want to make your car roll less fit stiffer springs, if you want your car to be faster round a corner fit an ARB to correct the effects of imperfect weight balance (understeer and oversteer). You can only really know wether to fit one (or how stiff is should be) through proper testing (or in our case trial and error). I would suggest for our cars (prone to understeer) fitting a small rear ARB would be beneficial.

If this doesnt make sense or you have questions, ask away.

I apologise for spelling mistakes, I can't be bothered to read over it now...

Very nice tech article you set out there Owen! I like it, and in my opinion 99% of it is entirely correct when starting with the basics of car handling (this bad 1% is not important, will tell it later what I think is wrong).

But first, Matlab in the house! Way to go, I myself eat, drink, sleep and dream it... at my work PC Matlab is almost always open as is it now while I am at home. Tomorrow morning an automated script (actually compiled into executable) will start itself around 6 or 7 in the morning as does it each day and provides me with that days fresh statistics. So if you have any Matlab programming questions, I am always willing to help. I am one of few people who maintains, supports and develops a fully functional User Interface application based on Matlab. Often people set Matlab in the corner of programming languages only to use for quick and dirty prototyping, but I like to convince people they should actually use it in their end products as well. Apart from 'standard' Matlab, the optimization toolbox, Simulink and Object Oriented are all on my lists of interests.

Then the article itself, very well told and it's true. My track coupe should have a rear ARB... unfortunately it still can oversteer especially in the rain. Reason for that is it's slight toe-ed out at the rear and toe-ed in at the front, making a very nimble car at the track. But when driving and tuning RWD cars like S2000, Supra or MR2 you really should pay attention to the info you put.

Now this 1% bad? I think you should reconsider this piece: (why heavy vehicles do not tend to loose traction). I think you meant: (why vehicles with more downforce do not tend to loose traction). Heavier vehicles are with all 4 tires in a degraded region of friction compared to lighter vehicle assuming same tires and will therefore produce less G. Heavy vehicles only have more traction in rain when aquaplaning is an issue for light ones, agreed?

I agree, the sentence was thought up quickly and was more of a reference to heavy vehicles which are fitted with tyres that match their weight. I.e. not sticking "light vehicle" tyres on a heavy vehicle. So what I mean is, if you have a heavy vehicle (with correct tyres) you have the potential for a high lateral force. Obviously if you are a light vehicle you dont need that much lateral force to get you round the corner in the first place though so my point is kind of null... :p

You seem to be a Matlab king =P I don't use it that much so most of what you have said has gone straight over my head However it is a powerful program and one that I wish I knew how to use better. What do you mean by daily statistics? Energy expenditure during the day? Average time between toilet breaks?

Great indeed. So how you would comment on the choises of honda in swaybar sizes?
Civic ej9 none front or rear
Civic ej9/ek3 26mm front no rear
Civic ek4 26mm front 12-4 rear
Civic ek9 26mm front 22rear
Int. dc2 26mm front 23 rear?

It has come to my intention that the jdm versions when equipped with lsd use bigger rear swaybars.

To be honest I havn't really thought about it; if someone knows the front/rear weight distribution of a Civic and some other info we could work out the contact loads on each tyre and from there work out whether we could add a ARB to combat understeer (as I assume this would be a problem) however since these are road cars I'm sure Honda has balanced up the pros and cons themselves and decided for and against ARBs for a reason. I would like to know the logic behind their decision though.

Getting the balance right is influenced by a lot more stuff. In the end each individual Civic will have it's own handling issues. So don't go guessing which ARB is best for which car... especially things like toe can totally screw up any analyses.

In the end it comes down to how a certain car feels and how you would correct it's handling. From there you can pick those guidelines and see if you can improve with ARB tuning. So with an understeering civic one might consider getting a (bigger) ARB at the rear. But perhaps an oversteering car might be helped by simply removing the ARB at the rear if one is installed.

About my daily statistics, it's the usage info of fore-mentioned user interface. It is logged into several logging files and each morning a report is written of it. Just checked it a few hours ago hehehe.

I will be performing this analysis on our EJ9's soon and I need your help! Please read my latest newbies topic post for information:
viewtopic.php?f=3&t=139&p=13432#p13432

Also Polyvios, in reference to your previous question: it confuses me that Honda would choose to add a front ARB to our naturally understeer prone vehicles (hence increasing the tendency to understeer) however now that i think about it, it was probaby done for saftey reasons. As we all know cars are designed to understeer so they are safer, however in the rain/snow our previously already understeer prone cars can easily oversteer (dangerous) so I presume Honda have added a big front ARB not to make our cars handle better, but to make them safer under high speed or treacharous conditions.

One important thing that my previous article did not highlight was the importance of contact patch load (CPL) variation and how ARB's affect this. I'll go over this quickly here:

Looking back to the matlab results from fitting a front/rear ARB we can see that it affects the load on each tyre. If we add a rear ARB the outer tyre now has a lower force on it and the inner has a higher force on it than if we had no ARB. This is a positive affect of fitting an ARB since now the outer tyre (which previously had amost all the load on it) requires a lower slip angle to create a cornering force and thus is less likely to go over the limit (slip angle too large), and the inner tyre (which had a really low load on it) can assist more to the cornering (because it has increase load on it, remember cornering force = vertical load * coefficient of friction (see above!!)). This evening out of the load on each tyre means that less is reuqired of the outer tyre (phew!) and more is required of the lazy inner tyre! Great news. So Honda may have added a front ARB to reduce CPL variation on the front axle since the outer tyre may be prone to locking up (which is definitely is).

In conclusion fitting an ARB to an axle improves its CPL variation which makes the tyres better performing, however it also increases the amount amount of (total vehicle) weight transfer that occurs at that axle increasing that axles propensity to under/oversteer. SOOOOOO when fitting an ARB you need to fit it in pairs, one on front one on rear, and you need to tune the diameters so that CPL variation is reduced but also you do not create a under/oversteering vehicle, indeed you can fix a vehicles tendency to under/oversteer as described in my big post above but this may come at a disadadvantage to ability to reduce CPL variation. THUS when designing a car you want to design it to have central centre of gravity so by nature it is a neutral car, then you can fit ARB's to reduce CPL variation and then you have an F1 car round the corners!! This is why all good race/sports cars are MR so that they fly around corners with a neutral centre of mass, and also why drifting is silly! The fastest way round a corner is neutrally!

As Joris mentioned above there are lots of interelated factors and other aspects of steering geometry can affect handling, especially at the limit or in wet conditions. So be careful! This information is meant for small improvements instead of wham bam thank you ARB.

Any questions please ask, and also make sure to visit my topic to help me out

I am kinda suprised of what Saxo said...how come Ej9's don't have arb?
From what i know ej9 before 1998 don't have ARB installed, the same goes for the 1.4i/d14a3 models. After 1998 the front ARB is there. At least my car has front arb for shure, and i am pretty happy with cornering on mountain roads. Understeer is felt on higher speeds only...I've seen a friends d14a4 from 1997 wich didn't have it underneath.Or my car could be a Frankenstein of some sort