Rear axle sideslip stiffness 3

In the linear range it is part of your understeer budget. It 's the gradient of the curve of rear axle slip angle vs latacc. Strongly related to your understeer gradient and yaw delay time. Less is good. I don't ever remember having a development engineer complaining about too little rear sideslip. Sadly I'm tone deaf when it comes to subjectively evaluating cars for steering feel, I can't tell you what it feels like.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

Well said.
My feeling of going off the road:
Oversteer: 1961 Corvair with brand new rear tires that haven't been worn in yet on a spiral curve off-ramp. In the rain.
Understeer: 240Z in slow, near-full-lock turn. Also in the rain.
Of course it's the rain's fault, and not my driving.

The "rear axle sideslip stiffness" is the generic term for the Rear Cornering Compliance. It is the summation of tire Fz, Fy, Mx and Mz slip and camber effects, rear roll steer and camber, and all sorts of the compliances associated with the rear suspension (which can include multiple axles). It describes this action over the full range of lateral acceleration up to the limit of control. There is a corresponding "front axle sideslip stiffness" named: Front Cornering Compliance, which describes the very same characteristics at the front of a vehicle. Appropriate ISO tests measure Understeer (K) as the derivative of [(steering wheel angle/overall steering ratio)] minus the Ackermann Gradient by lateral acceleration. Then, by means of several techniques including a precision sideslip angle sensor, the sideslip at the rear axle is determined, producing the Rear Cornering Compliance (DR). Adding the Understeer (K) function to the Rear Cornering Compliance (DR) function produces the Front Cornering Compliance (DF). DF = DR + K .

Simple or complex analysis makes it obvious that the lower the DR value is, the lower (better and subjectively more favorable) the lateral acceleration, yaw velocity and body sideslip angle response times are. Think of it in frequency response terms as lower DR produces higher bandwidth. So, DF - DR is the Understeer, while DF + DR is proportional to the damping in the 3 modes (actually Ay response is a combination of yaw velocity and body sideslip states, so its really only 2 modes. Increasing K usually means adding overshoot and longer settling times to vehicle response in order to produce improved response times. But the obvious way to improve the lateral dynamics is to have as low a DR as you can tolerate. This usually means tires with high cornering stiffness. However there is a big price to pay for the ride quality, rolling resistance and the cost of tires in order to get a low DR. This includes very low lateral force suspension compliance etc. meaning hard suspension bushings, oversized tires, cost of replacement tires and other packaging dilemmas. Many vehicles now have much larger rear tires or simply wider wheel rims than fronts if they think they need a 50/50 or more rearward weight distribution. (Think F1, Luxo Rides, big trucks, etc).

A practical handling teaching tool is to make a carpet plot of DF, DR and Ay Response time for any architecture with lines also for constant understeer. DR lines have a steep descent.

Tests (road and simulated) (as in constant radius, step) easily show the DF, DR, and K functions as results to document a vehicle. They help dissolve the lore about whether vehicles are "Oversteer" or "Neutral" since trendy journalistic mouth-breathers are almost always WRONG. Yet, nobody has the data to dispel the myths. Makes for good bird cage lining, though.

BTW: I measured these properties of my outboard Bass Boat (a fish & ski model) using VBOX equipment on a local inland lake. I studied the response for a 3 blade, 4 blade and 5 bladed propeller. The only real challenge was estimating the 'wheelbase' of the hull (to remove the Ackermann effect).

For a very large sample of production cars and light duty trucks, DR ranges from about 1.5 deg/g to 4.0 deg/g (values taken at 0.15 g), with K ranging from 1.0 to 5.0 deg/g. These numbers cover 1 passenger to GVW payloads. For all this you will find Ay response times from about 0.28 sec to 0.50 seconds. These are computed from the 50% steer input to 90% of final response at the 0.30 g's level of a step test sequence.

Short response times from high understeer feel squirelly. From a low DR, feel wonderful!

Excellent stuff. In a typical project with the tires already defined the things we mess about with are roll steer (powerful but unsettling on rough roads), compliance steer (which can feel mushy), tire pressures, and toe in. I'd also have a play with RCH and rear sta bar. I'm not really a fan of rear sta bars, in particular. It's always tempting to increase the rim widths.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

Thank you very much,

i understand corret that is possible to compensate insufficient Rear axle slipangle stiffness with:
a) use widder rear rims with same tires dimension?
b) toe steer in favour toe-in under lateral load?

and
a)"stiffer" rear axle slipangle is ALWAYS better for performance
b)some front versus rear ratio is recommended ?
( as Cibachrome recently said : the front cornering compliance reduction to 1.2 would need a corresponding rear cornering compliance change from 2.0 to, lets say 1.0 to keep the car slightly understeering)
(this in fact represents some "transitient understeer presumptions" ???)

(of course my interest are mainly race cars)

Racing cars deserve special attention to their cornering compliance recipes because:

They tend to go very fast during straightaway segments. And, they consume a lot of their design elements during competition. By this I mean their weight distribution changes as fuel load goes away, their tires lose tread as a function of use and the tire pressures go to new values. Even a limited slip differential can lose capability from wear.

Since their yawrate due to steering is speed dependent and roll is generally not, it is not unusual for yawrate peak frequency to cross over the roll frequency at some higher speed. If roll steer is present, it's sign will change after the crossover and go from desireable to undesireable effects. Early Corvettes and Camaros had this trait. It was addressed by very high damping settings which killed the ride quality and really did not address the root cause.

Since race 'tires' sometimes still have some camber force capability, roll camber and roll caster (camber by steer) are often used but not really effective in a solid rear axle configuration.

Weight distribution is a major player but now you have to choose when you want to get up on the wheel because its a 'knife edged' factor. Good then bad or bad then good.

In ALL cases, getting the rear suspension correct has the highest value for any application. Then you have a steering system to treat and/or bandage up and a rimforce/tierod load to address and its effects on vehicle control.

Funny how you mention tires on, then suspension is adjusted. I was a fan of finding the tire to make the suspension work. BTW, a rear bar often is used to fix a compliance problem rather than change a roll trait. And in a race car, roll is not one of those 'features' you want to entertain.

And in case you wondering, sideslip is kind of important for 'racecars' because the sideslip component of lateral acceleration is very large at high speeds The yaw velocity component is large at low speeds. The speed where this all changes is called the tangent speed. Since sideslip is positive at low speed (let's not debate the signs of all this crap for now), and negative at high speed, there is a magic speed where it is zero. A basic characteristic of low speed sideslip is rear wheels INSIDE the turn path. That's why Grandma knocks down the mailbox when she turns into the driveway. Likewise, at high speed, the body sideslip is negative (positioning the rear wheels outside the turn path. So, the objective of any good race engineer is to get the tangent speed as high as possible in order to get the best (lowest) rear cornering compliance as possible at the max limit of control. Now you don't need a $20K sideslip sensor to help you with this if you are on a limited budget. All you care about is what is the speed at which your sideslip is ZERO. And that situation puts your inside front wheels on the same radius of a path as the rear wheels.

So, when watching or crewing, or driving on a race track, when you see the rear wheels on the line or off the line, you can immediately tell the state of the car. Off the line and outside the turn path (not the racing line) means you are 'tight' (as in understeering state. On the line means the car has about the right balance. You seldom see rear wheel inside the line (oversteering) unless "the driver is better than the car" as we say. So, the goal of any competent team would be to give the car enough understeer to produce acceptable transient response and to keep the rate of change of understeer as small as possible. Many times you hear a driver complain about 'loose' when the sideslip is close to zero. This is usually because the net tire aligning torque peak occurs before the net lateral force peak occurs and the rate of change of steering moment goes to zero or negative. They loose the feel of the turning potential and call it oversteer. The cheap fix is to add enough caster to move the peak Mz effect on the tierods to be coincident with the Fy peak. However this tends to load up the steering system with higher force which creates additional understeer. And that lowers the car's max lat capability. So there you now have the whole enchilada.

Thanks Cibachrome,
so we want (by all means) maximize rear slipangle stiffness,
BUT
only Up to value when front axle can handle understeer
yes?

But it's easy to make the front cornering compliance greater than the rear to have an understeering control situation. Adding compliance (deflection steer or camber) is the way that would be accomplished. Removing a compliance term is very hard. Sometimes this leads to durability concerns because fatigue and fracture are now in the realm of the forcing frequencies. Doing this mechanically involves a time response, damping and settling time quandary.

"Nothing beats a GREAT set of tires".

"it's easy to make the front cornering compliance greater than the rear"

ok, but vice versa?

in fact really not want to get again more rear toe-in (or wider rear tires) before make the front cornering compliance more?

Having trouble following this

So, when watching or crewing, or driving on a race track, when you see the rear wheels on the line or off the line, you can immediately tell the state of the car. Off the line and outside the turn path (not the racing line) means you are 'tight' (as in understeering state. On the line means the car has about the right balance. You seldom see rear wheel inside the line (oversteering) unless "the driver is better than the car" as we say.

Click to expand...

So I'm wondering what it is I might be missing.


Norm

Sierra: If all there was for DR was tire cornering stiffness [CAR, in N/deg] with an infinitely stiff rear suspension and the rear axle weight [ WR ] is specified, then, the required tire cornering stiffness per wheel would be CAR == 9.8*WR/2/DR.

For WR=1000 kg, CAR = ( 1633.3, 2450, 4900, 9800 ) N/deg per tire for DRs of 3, 2, 1, and 0.5 deg/g.
I'm not sure how much you know of tire properties but getting a DR lower than 1.0 takes a remarkable tire construction recipe. Since you mentioned toe changes (roll steer, compliance steer, etc), you must realize that tires just don't listen to steer/slip changes very well as they near peak force levels, so these proposed changes don't do very much for you as a racer. Camber maybe (to minimize Mx).

Norm: Watch cars on the yellow inside pavement line during practice near a constant radius corner. Front and rear inside tires both on this line at the same time in a steady state cornering situation identifies the Tangent Speed. Since sideslip (Beta) per g is zero at this speed, then DR has just a geometric component = 9.8*57.3*b/U^2, where b is distance from total CG to the rear axle and U is the tangent speed in m/sec. It's also the speed where the difference in phase angle between yaw velocity and lateral acceleration are equal. If you are a New School Controls Type (as I am) and can use Big Science to figure it out .

Once in a while (as in a Blue Moon i.e. twice a year), you may observe a car on a track with a light spot appearing under the car near the rear axle. This means they are using a hidden Datron sideslip sensor to measure the rear cornering compliance or just the Tangent speed. Sometimes they forget to turn it off. (Oops).

and only extra static toe adding?
for example if front axle capability was build up, but rear axle improvement already is not possible ??

Front static toe changes (in or out) can improve front grip (reduce understeer) but these settings (including Ackermann steer functions) have other detrimental effects. Same for rear (which could reduce rear cornering compliance by making the pair of tires work better together, but look at how much steer it would take, what mechanism in the rear could do the job, what would it accomplish at max lat and what other penalties do you pay (straight line, aero, tire wear, etc.).

And this requires accurate, specific and appropriate tire test data to determine the proper settings and function values. Changing brands of tires or constructions, wheels and even pressures means you start all over. Otherwise settle for rear or mid-pack positions and enjoy the smell of burned racing fuel !

ciba - what I'm having difficulty with is how the condition where the rear tires are tracking outside the line (and the fronts are on it) can be defined as understeer, or when the rear wheels are inside the line that that's oversteer.


On delayed edit . . . unless it's the rear axle's (wheels' & tires') own understeer or oversteer that's meant.


Norm

I have the same difficulty. In my understanding, if the rear wheels are tracking outside the path of the front wheels, it's an indication of how much rear slip angle is there compared to the trajectory of the car (and it's quite apparent to me that this situation would be more prevalent at higher speed), but it's unconnected with how much slip angle the front tires have at the same time.

"Oversteer: 1961 Corvair with brand new rear tires that haven't been worn in yet on a spiral curve off-ramp. In the rain."

Yeah, I was trying to figure out how oversteer on that old Corvair was supposed to put the tail inside the front wheels. Huh? I should have spun out inwards?

What I'm considering in the edit to my previous post is that rear axle oversteer means it's effectively steering too much, and as a result runs inside. That's not the same as perception of understeer or oversteer of the car as a whole.


Norm

Well, (as I understood Sierra's line of questions), he has a RWD racing car. So, what is the condition and influence of the rear axle's countersteering mechanism when under full power in a turn ? And what would it be ideally (and why)? And what would a be a clever way be to help this situation ?