Tire loads, weight transfer, CoM and slip angles

[kokalz]

Hi guys!

I've been reading quite a few papers and pages on vehicle dynamics and I think the amount of information I've gone through has just gone over my head.

Could someone please explain on simple terms, how to tyres generate slip angles, how to slip angles generate lateral tyre loads and how do vertical tyre loads affect the lateral tyre load/ slip angle curve. How does the location of CoM affect the slip angles (and thus under/ oversteer).

Thank you very much for your help !!

[Tim.Wright]

You are asking for a simple explanation to a reasonably complex problem. Are you studying this at university or just out of your own interest? What papers and pages have you actually look at? I really find it quite difficult to believe it when people say they have looked for information but haven't found or understood anything. There is a lot of info out there!

There is no getting out of this easily:
Firstly, you need to understand basic mechanics, i.e. Newton laws for linear and rotational systems.
Then you can look at learning about tyres and how they generate forces (grip).
Then in a third step learn about how the tyre forces affect the car's control and stability.

Asking on a public forum is just as likely to send you down the wrong road as it is to help you in any way.

Have a look at books by Milliken, Pacjka, Gillespie, Smith, Dixon and others. If you don't want to buy a book try to at least track down some lecture notes from a reputable uni.

Here are some good book lists:
http://www.fsae.com/forums/showthread.p ... car-design
http://www.eng-tips.com/faqs.cfm?fid=1327

I have Milliken and Pacejka and I still use them often in my work.

There are also numerous seminars being offered by companies on vehicle dynamics, many of them aimed at motorsport and many of them discounted for students if you are in that position. Unfortunately some of them are a bit weak in terms of the theory (old habits die hard) but still they are a very good way to get a lot of exposure to the field in a very small amount of time (e.g. a few days)

But if all that seems like too much work:
1. Tyres generate slip angles by travelling in a different direction to the one they are pointing at
2. CG to the back > OS // CG to the front US

[Greg Locock]

"2. CG to the back > OS // CG to the front US"

But an empty truck oversteers less if you put a coumple of hundred kilos in the back. As in most things to do with vehicle dynamics the simple rules don't always apply.

[Jersey Tom]

Tim's right to say it can be a very involved topic. But let's start simple.

First - and this may make people think I'm a heretic - I'd say forget about the concept of tires "generating" slip angle. In a way, they don't... or at least there's no magic to it. Slip angle (let's call it sideslip angle) is just a ratio of lateral and longitudinal velocities. A tire can have a slip angle, a wooden wagon wheel can have a slip angle, a car can have a slip angle, an airplane can have a slip angle. If I roll a tire straight ahead it has zero slip angle - it's pointed the exact direction it's going. If I were to put a tire on the ground and drag it purely sideways it would be at 90 degrees slip angle. If I were to roll it forward 1 foot while scrubbing it sideways 1 foot, it would be at a slip angle of 45 degrees.

There's no limit to the slip angle a tire can be at (well up to 90 degrees). Doesn't matter the type of tire or the surface. That's a common misconception.

Now let's bring in lateral load. Pretty easy to imagine conceptually. Neglecting all other things, tires like rolling in a straight line. As soon as you start to drag it sideways while you're rolling - it's going to resist you and try to push to go in another direction. There's your force! How much force you get as you start to sideslip / sidestep the tire will vary from one tire to the next with how stiff it is in various direction, how hot it is, etc etc. Then there's a point where it can only generate so much force and that's it. Take the extreme case of dragging a tire sideways - the rubber is just sliding across the ground. Hence why if you look at a typical Fy vs SA chart you have a linear range which then transitions into a plateau where the thing is just sliding.

Let's see how well that makes sense and if you can digest that before moving on.

[olefud]

Slip angles go from the very simple single tire embodiment, i.e. the direction the tire is pointed versus the direction to the very esoteric, i.e. the actual direction the four tires are traveling versus the optimum direction each tire should be traveling to develop optimum thrust and direction of thrust. The latter is a bit of an imponderable and probably not worth worrying about until you run out of other tire idiosyncrasies to ponder.

Just my thought, but understanding roll stiffness and/ or roll moment at each end of the car and the effect upon under or over steer would be the better place to start. Basically a more heavily loaded tire gains traction but a lesser rate than a less loaded tire loses traction. So if you increase the overall transfer at one end of the car it will have less relative traction than the other end with less relative weight transfer. Think antiroll bars, stay rod or springs. Slip angles become dependent variable with this approach. This isn’t intended to be an explanation but rather a suggestion as to a start to your study.

There are numerous other variable and, in the end, the science tend to fade into art

[Jersey Tom]

You can have the lowest CofG but if you just end up with a bucket load of understeer, you've not really gained anything?

If you drop CG, pretty damn good chance you'll make both front and rear work better - not just one or the other. Even if you gained say 5% "grip" on rears and 2% on fronts and moved in the direction of more understeer.. it's still going to be faster.

Plus, it's then pretty easy to get your balance back mechanically or with aero. "Pretty easy" in relative comparison to making significant CG improvements.

[Luke]

You can have the lowest CofG but if you just end up with a bucket load of understeer, you've not really gained anything?

I believe the Question was in regards to the Longitudinal position of CG and the effect it has on front/rear slip angles, not the height.

Simplistically if you move the CG forward the front tyres have to supply more of the % of total lateral load compared to the rear which generally speaking would mean more understeer.

[Greg Locock]

20 million pickup trucks say you are wrong

[Tim.Wright]

Is that because tyres designed for high loads have a lower coefficient of friction when used at a very low load (without the tyre pressured being adjusted)? Or is there something more fundamental.

I can imagine truck tyres which are inflated suitable for a high load, might lose a lot of contact patch area when used a a very low load.

[Tommy Cookers]

tyre drag will be high at high slip angles
throttle-off 'engine drag'(depending on the gear) can be high
both will reduce the contact load ('weight') at the rear
if the contact load is already small the above effects will be relatively large

the old 'hot hatch' scenario, now universal in the form of 'city cars' (small fwd cars with no overhang behind the rear wheels)
TWs point about tyre pressures applies here too, but the manufacturers are in denial mode

[Greg Locock]

I don't think it is the tires particularly, more the suspension rates and friction. Basically adding some weight above the axle gets the suspension to act like a suspension and not a rigid link. If yu go ahead and load the thing up to GVW then it will tend to oversteer more, there is a sweet spot.

Incidentally in this case we may not be talking about pure linear range understeer, it may be more like low amplitude skate, where small surface irregularities bounce the rear axle outwards in a corner.

[thisisatest]

i think unloaded pickup trucks do understeer, with particular situations causing exceptions. first is when trail braking. you get to essentially no load, the rear end will just skate across. another is a bumpy corner, upsetting the heavy-duty live axle rear end. and too much throttle with too much horsepower exiting a corner will bring the rear end around on just about any vehicle as well.

[Jersey Tom]

Pickups are a bit of a unique animal though, particularly the (max) load cases the tires have to be designed around. Easy to fall into some handling pitfalls with poor pattern design, etc.

Beyond that, gotta keep in mind all the typical talk of "move CG forward = more understeer" is for pure cornering, no throttle application... and the limit cornering trim of a pickup is indeed to push. On-throttle behavior is a completely different animal.

[Luke]

20 million pickup trucks say you are wrong

I thought we were talking about racing cars here?
For what it is worth Pickup trucks most likely need more weight in the rear as they have spring rates designed to take a payload. When you dont have said payload the rear bounces across the road.


If you move the CG rearward, the rear wheels have to do more of the cornering,correct? Also there will be a higher % of weight transfer across that axle so more tendency to oversteer mid corner.