Tire Lateral Load Transfer Distribution (TLLTD)

Hi, first time poster here.  I own a 2014 Mazda 3 and no experience in suspension tuning but would like to get the car to have a neutral balance.  Considering that the chassis is relatively new, there is no helpful info on the Mazda 3 forums other than plastidip techniques.  I figured by posting here, you guys can guide me in the right direction.

Assuming that a car's weight distribution is 50/50 and a roll stiffness bias of 50/50, does that mean that under a steady state turn with no brake or throttle at the limit that the front and and rear tires would lose traction at the same time?

With this assumption and the goal of a "balanced" car I came up with this: https://i.imgur.com/fJwJD1c.png (swaybar rate has not been included yet but I will be taking measurements this weekend.)

I talked to an old ME friend and he mentioned that I need to know my chassis' torsional rigidity(~27,000 Nm/deg) and that the TLLTD % is what I should be aiming for and that in his experience 54% balance with a hint of understeer (he states that I should aim for a hint for understeer since it provides more usable feedback to the driver.  Is this true?).

How do I learn more about TLLTD and how do I calculate it?  What other variables do I need?

Thanks,

- Splenda_Daddy

I’m an ME as well and don’t know the answer. You might look into techniques for measuring tire temperature. Once you’re close though, the “ideal” setup tends to depend on your driving style and what type of events you’ll be running.

Have you taken the car out to either an autocross event or track day? Does the front or rear misbehave there? Do you have interest in a staggered tire setup?

If you haven’t done this I’d humbly suggest you may enjoy your car and the journey more if you get out there and try to sort it out, expect to make mistakes, and learn from others who have a different way of doing it. We engineers tend to get theory heavy and run numbers to death, but many folks can feel “the answer” that would take days to calculate by just driving the car for a lap or two around a circuit.

In reply to ace37 :

This. Silly engineers! Y'all overthink things waaaaaaaayyyyyy too much sometimes. 

There are so many other factors that come into play.

Effective spring rates front vs rear.

Camber change differences front vs rear.

Difference in slip angles generated by the tires front vs rear

(if you are going around a corner at constant speed with no accel or brake forces, the front wheels WILL be turned)

etc, etc, etc

It's front wheel , it has about 60% of the weight on the front wheels. it will under steer. usual "fix" is to stiffen the rear roll couple.  Usually with a bigger sway bar.

Learn to drive around the "problem"   A lot of steering can be done with the throttle.

As for TLLD,   fuhgettabout it.      There are more important things.

clshore said:

There are so many other factors that come into play.

Effective spring rates front vs rear.

Camber change differences front vs rear.

Difference in slip angles generated by the tires front vs rear

(if you are going around a corner at constant speed with no accel or brake forces, the front wheels WILL be turned)

etc, etc, etc

He said it had equal roll stiffness front and rear, so there's your effective spring rate. I'm assuming the same roll center front and rear as well.

I'm going to say that yes, with all variables basically zeroed out and an infinite corner radius (and thus infinite cornering speed), you would see equal slip at each end. But the front has to provide the turning force, so that's going to take away some of their traction budget and this effect will likely be inversely proportional to the radius of the corner.  Splenda Daddy, if you haven't read The Physics Of Racing, I suspect that it would be an interesting read for you.

The problem with spreadsheet tuning is that the real world is messy. In the real world, you don't have things like limitless suspension travel so your spreadsheet tends to ignore ugly little corners. It's a fun theoretical exercise, but really you'll get a lot more done with a skidpad and a couple of adjustable sway bars. Then you have to start dealing with transitional behavior. I personally like to set my cars up with a little more oversteer than is sometimes fashionable, but the ideal balance varies depending on what I'm doing - rally is very loose, track less so, autox is most understeery. That's for a RWD chassis, I don't have as much experience with FWD.

In reply to Keith Tanner :

I'll disagree with the first sentence, since real world roll stiffness is never a linear function of roll angle, and the chances of front and rear exhibiting exactly the same transfer curve unless identical suspension is used is nil.

And assuming that the roll centers are the same, or that they remain so with roll angle is likewise unlikely.

So chances of effective spring rates are likewise unlikely to be equal.

To 'break traction', the car will have to at or near it's limit, assume 1G for simplicity, so at 60 MPH on a 242 ft radius circle, roll angle will be significant.

We are basically both saying that in the real world, the OP question is meaningless, the best we can say is 'try it and see'.

In order to understand real world changes, you have to understand the basic mechanics in an idealized system. It's like the frictionless surface often used in teaching physics, we know it doesn't exist but it simplifies the math and the understanding. By coming up with a simplified mental model, it's easier to understand the relationship of the various factors. THEN you can start dealing with the messier real world. When someone's trying to figure out how something works, it's much better to strip it down than to say "it's just too hard". We're not really tuning a real car here, it's a theoretical construct.

I never said that roll stiffness was a function of roll angle. Roll angle does not affect weight transfer*. It's a visible result of it as the suspension reacts to the change in loading. You can have 1g lateral acceleration and the associated weight transfer with zero roll, just ask a kart racer.

Roll centers can certainly stay put with roll, it depends on the suspension type. Check out a Watts linkage. But again, in the simplified idealized system we can just say "it doesn't move" and that serves our purpose.

I definitely never said the original question was meaningless. It's a good question, I might have to go back and do some figuring on what that steering axle will do to the balance in this situation.

* yes, yes, the lateral CG movement may have some effect on weight transfer but it's such a trivially small amount that you can ignore it.

Keith Tanner said:

In order to understand real world changes, you have to understand the basic mechanics in an idealized system. It's like the frictionless surface often used in teaching physics, we know it doesn't exist but it simplifies the math and the understanding. By coming up with a simplified mental model, it's easier to understand the relationship of the various factors. THEN you can start dealing with the messier real world. When someone's trying to figure out how something works, it's much better to strip it down than to say "it's just too hard". We're not really tuning a real car here, it's a theoretical construct.

I never said that roll stiffness was a function of roll angle. Roll angle does not affect weight transfer*. It's a visible result of it as the suspension reacts to the change in loading. You can have 1g lateral acceleration and the associated weight transfer with zero roll, just ask a kart racer.

Roll centers can certainly stay put with roll, it depends on the suspension type. Check out a Watts linkage. But again, in the simplified idealized system we can just say "it doesn't move" and that serves our purpose.

I definitely never said the original question was meaningless. It's a good question, I might have to go back and do some figuring on what that steering axle will do to the balance in this situation.

* yes, yes, the lateral CG movement may have some effect on weight transfer but it's such a trivially small amount that you can ignore it. 

Roll angle does not affect weight transfer*

Of course it does, it's how roll stiffness is expressed, in torque about the roll axis per degree of angular displacement. That torque is the moment equal to the difference in wheel weights times the distance between wheel centers, commonly called 'weight transfer'.

You can have 1g lateral acceleration and the associated weight transfer with zero roll, just ask a kart racer.

On a theoretically perfect kart having an infinitely stiff chassis and solid non deforming wheels, the roll stiffness is infinite.

Ask a kart racer about lifting the inside front wheel, or the relative effects of tire pressures on chassis tuning. The suspension is there, comprising the flex in the chassis and the spring effects of pnuematic tires., as well as the effects of driver movement on the CoG. The roll stiffness is rather high, but it exists and is calculable.

I agree with you that ideal theory can be useful in understanding real world behavior. And as you say, part of that understanding process involves moving from 'ideal' behavior to 'observed' behavior, to gain actionable insights about how and why they differ, that we can apply to making our cars go faster.

In reply to clshore :

The total amount of weight transfer is ONLY dependent upon the CG height, and track width.  That's it.  We use roll centers, springs, and anti-roll bars to determine WHERE the weight is transfered (front vs. rear).  If one end is much stiffer in roll than the other, it will transfer more weight.

So no, the actual amount of roll doesn't change how much weight is transferred.  The amount of roll only matters for dynamic (not static) considerations, driver feel, keeping camber reasonable, keeping your aero package the correct distance from the ground, etc.  The CG does move very slightly during roll, but not enough to matter.

A good read, "Race Car Vehicle Dynamics"  by William and Douglas Milliken.

Matthew Kennedy said:

In reply to clshore :

The total amount of weight transfer is ONLY dependent upon the CG height, and track width.  That's it.  We use roll centers, springs, and anti-roll bars to determine WHERE the weight is transfered (front vs. rear).  If one end is much stiffer in roll than the other, it will transfer more weight.

Exactly. The math is actually very simple. 

The only thing I'd emphasize here is that the stiffer end will transfer a higher percentage of the total weight transfer. It's important to remember that changing total roll stiffness will not change total weight transfer, but the relationship between the front and rear roll stiffness will determine how that weight transfer is distributed. Our original poster knows this already. 

In reply to Matthew Kennedy :

Really? Please reread what I posted.

I never claimed that roll angle affected total weight transfer, only that roll angle was related to weight transfer.

Then please consider this scenario of a car placed on corner weight scales.

Lock the suspension solid. Apply increasing lateral load at the vehicle CoG, recording corner weights vs applied load and measured roll angle (due to tire compression there will be some small but measurable roll angle). As lateral load increases, corner weights change. At some applied load, the tires either break loose, or the tires on one side lift just off the ground, and we stop.

Now unlock the suspension. Apply increasing lateral load at the vehicle CoG, recording corner weights vs applied load and measured roll angle. As lateral load increases, corner weights change. At some applied load, the tires either break loose, or the tires on one side lift just off the ground, and we stop.

Now compare the graphs of roll angle vs 'weight transfer'. You will observe that there is a correlation between the observed roll angle and the 'weight transfer' in both cases. More roll angle, more weight transfer.

Have you performed this experiment? Because I have done some similar tests, and have found exactly the opposite of what you claim. Suspension compression does not cause weight transfer, which is what you're stating.

Roll angle is a visible result of weight transfer. It is not a cause.

In your thought experiment, you're changing one very important factor between your two tests: roll stiffness. Your graph of roll angle vs weight transfer will be an illustration of roll stiffness, of the amount of suspension movement as a result of weight transfer.  You won't gain anything meaningful other than to illustrate that suspensions move when you change the vertical load - which is basically their job.

In reply to Keith Tanner :

I never claimed that roll angle is the cause of weight transfer, I said that weight transfer and roll angle were related, a positive correlation between roll angle and weight transfer. Given the transfer curve, knowing roll angle you can predict the weight transfer, and vice-versa.

The roll angle represents an equilibrium between the force vector at the CoG, lateral traction generated by the tire contact patches, and the resolution of those forces through the suspension mechanical linkages between the tires and the chassis that result in the relative motion loosely termed 'roll angle'.

I have done similar testing. Back in the day electronic weight scales were the stuff of science fiction. But by placing front and rear tires on beams that pivoted at the centerline (a piece of heavy steel pipe), the reaction forces at the end of each beam were easy enough to measure with common scales (300 lb at the end of an 8 foot beam = 2400 ft-lb moment).

Applying a moment to one end by jacking the beam end up, and measuring the moment at the other end while recording suspension deflections made it possible to assess relative roll stiffness.

Admittedly crude, but being young and broke, all I had was my wits and ability to improvise.