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suspension lateral compliance

suspension lateral compliance


Hello experts,

I am very interested about suspension lateral compliance data,

exist some database or real examples toe and camber lateral stiffness for modern passenger cars or racing cars?

or can we determine some ussual target values we want to achieve?

Thanks for the answers

RE: suspension lateral compliance

You'll struggle to find data I think for modern cars, unless it is mentioned in passing in an SAE paper.

Both are important. I usually try to set the rear suspension as stiff as possible in camber, and neutral to slight understeer in toe.

The front suspension is far more complex. Again I usually have to dial in toe compliance understeer, but I don't like doing so, and again as stiff as possible in camber.


Greg Locock

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

RE: suspension lateral compliance

By "toe and camber stiffness", do you mean steer and camber stiffness for Mz and Fy inputs (as in K&C data) ?

Front or rear? Cars or trucks ? Red or white vehicles ?

RE: suspension lateral compliance

I don't use "stiffness" for these kinds of terms, I use "compliance". "stiffness is "good", "compliance is "bad".

So, for example: Typical statistics for production vehicles of all types. Yes, there is a trend here because toe (steer) compliance has a component due to Mz as well as a component from Fy due to caster angle and offset. But, most of the toe compliance is from steering gear mounts, steering gear rack to pinion "push-away" (They don't like each other} and power steering torque sensing elements (in hydraulic power steering systems, something usually has to move in order to know how much assist to generate).

Camber compliance is primarily due to wheel bearing and spindle flex. If you have bending struts, buy them more protein.

RE: suspension lateral compliance


The toe/SAT figure is a trap for young players, engine on or off, in phase for the two wheels or out of phase? The 4 possible combinations measure quite different things. I think that plot must be engine off, in phase. This confusingly includes the T bar and steering column stiffness. it's a useful diagnostic but for understeer budgets or steering feel you need the PAS to be working.


Greg Locock

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

RE: suspension lateral compliance

The Toe/SAT figure is for in-phase, 2 wheels, engine on (or aux-P.S. pump at specified flow rate for 100 kph), steering wheel clamped. For speed sensitive steering controls, a simulated transmission signal provided by the vendor is also necessary. This is the 'on-center' compliance) for which other terms roll off the value for data fitted to a log function (an excellent 3 term data model, btw). These factors + quite a few others, + tire data (nonlinear) deliver the understeer budget of all these cars which always get accompanying road tests for verification using ISO procedures (step in and out, Frequency Response , Constant Radius (constant speed), etc. Yes, out-of phase data tends to eliminate the steering system, but is not really useful for any other purpose other than to flag unwanted out-of-spec asymmetries. The steering system compliance contribution (gear, mounts and I-shaft) are all measured individually again on other test equipment and this is done to audit design specifications for these parts.

BTW: The rather LARGE values for vehicles on these plots can surprisingly come from vehicles which might be puffed up as world class state of the art right brained fantasies, but in fact are almost entirely saved by way oversized tires which have very high cornering stiffness used to minimize the overall impact of the required soggy steering system. And which have high rolling resistance and poor wet and/or snow traction. Otherwise, the forseeable loss of understeer budget due to large payload increases, worn tires, aftermarket tires, low pressure tendencies and spare tire use make those cars exciting, especially in a courtroom filled with vehicle dynamics 'expurts', non-technical jury members, and a few vegetables or a widow.
I've seen it all.

RE: suspension lateral compliance

The devil is in the details. It was a surprise to many when it was revealed that BMW used a soggy piece of rubber, in the 90s, in the steering column to 'add' understeer (it will not be much apparent in engine on graphs). Even if the numbers said I'd have to do it I don't think I would. There again I don't have to tune for runflats, about which I know nothing. Thanks for the graphs.


Greg Locock

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

RE: suspension lateral compliance

Thank you very much, are useful responses all ,
very nice graphs

my main interest is front also rear axle for race use, then modern cars data can serve like some guidance how much still is good and how much already becomes really bad

for explanation, i trying build easy tool for one wheel laterally loading in garage conditions when powersteering is excluded (steering rack is blocked)

few first measure show very interesting results, that this tool seem like very useful helper to find structural problems (and yes main deflections comes from bearing and spindle flex and strut bend also steering rack mounting)

(please excuse my bad english and inaccurate terms)

RE: suspension lateral compliance

Always tricky with race cars. Despite what Team Hoon will tell you, you need linear range understeer, otherwise you'll get control reversal at high speeds on the straight. Sadly, you almost certainly don't know your tire characteristics so building an understeer budget is impossible. If you could it would look like this


Greg Locock

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

RE: suspension lateral compliance

The understeer budget for a race car is actually very easy to do because:

They have very stiff chassis parts and very little rubber anywhere (fan belt and hoses ??).
They don't roll very much (1.5 to 2.0 deg/g is mostly from tire deflection).
They have weight distributions close to ideal (whatever that means to you, could be 50/50 or 40/60).
The tires they use are VERY large from a load capacity rating, so they have high load sensitivity (i.e. They like load on them). That can cause confusion to race engineers because adding a front bar can reduce understeer and adding a rear bar can increase it. True now with many street cars in the high performance class.
Race tire characteristics are not 'scaled' versions of street tires. More like 'extended' tires. Yes they have above average cornering stiffness at low slip angle, but so do some street tires now. The 'extended' characteristics are a result of carcass structure, wide rims, sidewall stiffeners and gummy-bear tread compounds. Oh, and they usually don't have groovy designer treads.

This all make the steady-state and transient analysis very easy except for ONE major problem: Race tires don't lend themselves to modeling using Pacejka formulations (always curvature somewhere). There is no capability for representing the 'non-curved' sections of the tire properties. So, you can try to use strong weighting functions to do a decent fitting job in 2 of the 3 sections of the race tire (on-center, mid-range, or limit). You can only do 2 of the 3). Other tire models are necessary. Good, fast, cheap, pick only 2.

Your Bundorf analysis is pretty standard ops for me and many others now, but the numbers in your reference are for an early '60s B-car barge. These days, front values for any decent car are 3.5 to 4.5 deg/g and rears are 2.0 to 3.0 deg/g. This is a result mainly of tire evolution, reduced dependence on roll steer, stiffer steering parts and chassis synthesis (demanding quick response times AND yaw rate damping with only moderate gain changes with speed). However, a survey of the K&C parameters of a few Drool Cars shows a complete lack of understanding their science because having 15% roll understeer in a super-car, which doesn't roll, which has large tires and no longer listens to slip angle changes at limit handling, and goes very fast (where yawrate peak frequency crosses over the fixed roll peak frequency) makes no performance sense other than to patch a poor design for their customers who will never pull greater than 0.25g cornering without a diaper change.

Did I mention that Tom Bundorf was my first boss (I still see him occasionally).

RE: suspension lateral compliance

Here's a demo analysis for a hypothetical RACECAR (spelled backwards is still a RACECAR) I put together for the FSAE tribes (Open source Matlab). The tire model is a decent 4 term Pacejka-light formulation for which students are able to manipulate the coefficients using their purchased TIRF test data (Tire Test Consortium run by Doug Milliken, et. al.). The tire coefficients shown are close but no cigar. The flaw in these car's analysis is usually the steering system (off the chart I posted), but when they fix it, shit happens because of the control issues inherent in the layout). Yes the tire model lacks the linear midsection regime, but who really cares at this stage of your career as a future Trophy winning Formula 1 Chief Engineer ? Then they find out that "Racing Radial" are actually bias tires, so the fraud notion starts early.

I really enjoy all their discussions about having the 'optimum' camber curve, 'working all 4 tires at their peak force levels', and then watching for the disappointments. (These tires have little or no camber stiffness).

Now let's have some fun !

RE: suspension lateral compliance

Yes, I'm familiar with Bundorf analysis,and thank you
so how much can be considered like "good" values (Deg/kN)for example for BTCC racing car if power steering effect is exclude?
sorry if my ask is stupid ..............i am not expert, only enthusiast

RE: suspension lateral compliance

In racing, there is no such thing as "Too Much Stiffness". You have gone well above many race engineering procedures by utilizing a compliance rig. BTW: a wheel aligner is a good platform for studying these issues. Just add two cylinders (air or hydraulic) to the wheel plates to apply lateral force (cylinders in-phase) and aligning moment (cylinders out-of-phase). Many aligners now have digital signals out of the wheel pales so you can read the compliance steer values. A calibrated cylinder pressure gauge can give you close applied force readings. It will boil down to what you can invest in software (to get you the bare minimum based on solid metal parts with perfect joints) and what's moving that should not be (frame rails, strut towers, strut rods, wheel rims, engine cradle, front of dash, tie-rod buckling, wheel bearings, spindle and uprights. A simple video often tells the whole story. You will also need some calculated peak loads to apply so your braces and structures don't need to support unrealistic loads.

You will know you are close when stuff starts breaking. Best car would be one one with tire only cornering compliances, a hint of understeer at full fuel load, enough caster to align the net front aligning moment peak with the lateral force peak slip angle, and most likely anti-Ackemann to keep the inside tire from fighting the outside tire (which is usually the case at max g). The amount depends on the tire, rim width and pressure. BUT, and this is a BIG BUTT, good Ackermann produces a looser car, so corresponding changes have to be made in the rear because it reduces understeer, Also, Your 'camber curve' needs to track the tire Mx to keep your active scrub radius from going berserk ('snapping through' when the sidewall gives up and can't hold the tread under the wheel any longer). If you could get on a tire tester (or make one up from a LARGE wood working belt sander), you could see some of the tire effects in play.

RE: suspension lateral compliance

Thanks for tips with pressure loading,is excelent idea
in fact also i use wheel plates but mechanical loaded and measure wheelcenter deflection with laser projectors

if you are interested
with my tool on my racecar was found 0,26 Dg/kN camber and -0,16 Dg/kN !!! toe change(with steering rack blocked) on front McPherson and 0,35 camber and -0,03 on rear semitrailing axle
(car feels very understeer and stable and must be compensate with rear toe out)
(main deflection happens in bearings and rear arm bend on front in bearings, knuckle, damper bend crossmember lateral shift and mainly steering arm twist due to long bumpsteer extension)

now i know how much my car is bad,
seems like a good potential to improve and lot of work for me in the future censored

RE: suspension lateral compliance

Of course also thanks for other setup tips with Ackerman etc.
now i prepare new superstiff knuckles with better bearings and Ackerman correction future new upsidedown dampers, also adding crossmember lower support to main rollcage,

What did You mean "so corresponding changes have to be made in the rear because it reduces understeer" ?

For rear axle want reinforced trailing arms then will be restored slight rear toe-in to maintain stability

i hope understand all correct

RE: suspension lateral compliance

What I mean is this: Let's say (just for the sake of because) that your car has a front cornering complaince of 2.5 deg/g from the sum of tires (.75), steering (.5), roll (.25), lateral force steer and camber contributions + rigid body Mz (.5). Now you fix the steering to .1 and other stuff from .5 to .1. and you were to flip the front roll understeer from +.25 to -.25 with a shift in the gear height. Your new front cornering compliance is 1.2 deg/g (2.5 -.4 -.4 -.5). Meanwhile your rear cornering compliance was 2.0 deg/g (tires + some roll steer - some deflection oversteer. Without a change in the rear, your new understeer is -.8 deg/g oversteering. This may not be unstable in open loop control (there is still an Ackermann gradient to save you at low speed (9.8*57,3*wheelbase/speed^2, but at a very high speed its gonna spin no matter what as the stbilizing Ackermann component diminishes. Meanwhile, your transient response is first order (exponential no overshoot), your bandwidth is low (long response times), and the control sensitivity (g/100 deg steering wheel angle) is higher than you can probably control without a major steering ratio change. If you do that (probably steer arm length) it will be a slug in the pits requiring lots of hand motion.

So, 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. (1.2 - 1.0 = .20 deg/g). OK, so just emptying the fuel tank or filling it can really change the car (trim heights and weight distribution). AND there aren't a lot of ways to drop the rear without a tire property change (different construction, wheel, brand) or a roll understeer increase, or a track/panhard bar position change (if you have one). So, fixing the front loosens the car, gets you more side grip, but worsens the driver control load and makes the tire property changes during the race a rat's nest to figure out. When the understeer is very low, any fart in the wind has a big effect on performance and controllability. The car is often referred to as 'knife edged' which is good for a few laps, then it falls apart.
That's what I mean.

RE: suspension lateral compliance

but i think , I can changed rear wheel alignment (i have semi-trailing arms there with wide adjustable range) have panhard bar

also get more rear wing angle of attack (now run low angle)

this all to keep some necessary understeer

i have right?

RE: suspension lateral compliance

You need to set rear toe for maximum cornering capability, too. Just like the front. It's probably not toe-in. Compromise between straight line stability and max rear grip. You have plenty of work on your plate now !

RE: suspension lateral compliance

but I like this work to find new limits!!

i think we can say my car lateral compliance in this time not achieves average modern passenger car level (although he use rose joints everywhere) so can be assessed as totally inadequate for racing ,then especially front steering

Alhough car in fact not really slow already now,
it will be quite easy to get half values all around and front steering even better, because i know where deflections happens

Thank You Cibachrome also Greg

RE: suspension lateral compliance

Supplementing and specifying

if in fact some rear compliance will be replaced with wheel alignment to achieve necessary understeer
what is the real impact on performance and resultant effect on driving feel?

Thank you for explanation

RE: suspension lateral compliance

There is not really a lot that wheel alignment can do for you to increase understeer. This would mean reducing the rear cornering compliance (oversteer) somehow. Instead, the sources of rear cornering compliance are tire slip, roll steer, lateral force steer, camber, and aligning moment (toe) compliance and rear weight (again tire load sensitivity). Unfortunately, almost all these things are oversteering, so you need to stiffen them. Changing roll steer to increase roll induced understeer is not good because as you near max lateral capability, tires don't 'listen' to slip angle changes very well. Reducing roll induced camber oversteer could be useful, but you need tires with camber stiffness to generate effective force levels. And, some race tires Slicks)have little or no or NEGATIVE camber stiffness. Changing camber alignment might get you something (again if the tires have such stiffness). You could alter toe alignment or if really clever alter roll steer side to side symmetry to mimic Ackermann or anti-Ackerman) to increase the net rear sideslip stiffness but there are additional side effects and this tactic introduces problems with compatibility with track curvature, track speed and straightaway drive ability. A wider wheel often helps and finding the optimum hot tire pressure does, too.

RE: suspension lateral compliance

I was thinking (just from Bundorf table) can be get some understeer from the rear toe-in ,
but seems (for dynamic events) no exist appropriate equivalent to structural stiffness.

i understand correct?

(wider wheel can helps because increase cornering stiffness?)

RE: suspension lateral compliance

If you had a twist axle with Panhard Bar for lateral support, placement of the Bar behind the wheel centerline can get you some deflection understeer if the control arms are flexible laterally (blades).
Keep in the back of your mind that NOTHING beats a great set of tires (or sets of tires if the front axle and the rear axle should just happen to have different tire constructions).

RE: suspension lateral compliance

i was doing short test in my Dynatune-XL smile , here is Step steer result
if my car have improved front axle
car 1 use extra rear toe (dark blue curve)
car 2 have stiffer rear axle (light blue curve)

i think difference is evident

(car with softer rear axle but with more rear tire cornering stiffness can get same result like car 2 )

i hope i understood

RE: suspension lateral compliance

Your DynaTune is actually a Dyna-Tuna because something is fishy.

First of all, your 'Yaw Gain' is actually 'Yaw Velocity Response Due to 20 Deg SWA Input at (I'm figuring) 120 kph'. Same for Lateral Acceleration. The 'Gain' terminology would/should be put on the ratio of Output to Input. For this metric, the Gain is about 4.6 g/100 deg (to use an industry standard). This is a rather high number, BTW.

Second, Lateral acceleration for the constant speed conditions you have created consists of a yaw velocity component and a body side-slip component (probably the one labeled 'Slip Angle' and rightly so). Notice that the 'Slip Angle' figure contains a response trait at Time == 0+ due to the thrust of the steered axle. This is the normal signature of the side-slip characteristic. So... Where is this signature in the Lateral Acceleration graph ?? It's missing. That tells me that the software is not presenting true transient response, but is simply the yaw velocity channel multiplied by the set speed . Your 0.91 g (steady State) translates to about 120 kph in this case. The steady state is correct, but everything up to the steady state value is false (as in your response time and overshoot numbers are SNAFU). The 'glitch' (as we call it) in the initial Ay transient is a player in road feel.

Third, I don't know which coordinate system Dyna-Tuna is using, but it indicates a +Steer Angle produced a +Yaw Velocity' (not 'Yaw' as in Yaw Angle) a +Lateral Acceleration (both correct) but a +Side-slip Angle (say it ain't so). My Side-slip Angle transducer would produce a negative steady state value, not a positive one. Besides, my sideslip angle would be positive at low speed, negative at high speed (certainly at 120 kph) with it being ZERO at the so called "Tangent Speed". The goal of producing a high Tangent Speed is usually on everybody's To-Do List. A constant radius ISO4138 Test Procedure can hand this to you.

The middle Figure says that the light blue line Sideslip Angle is lower for the same steer and same speed and that the lateral acceleration achieved is also about the same, so the Gain is the same so the understeer is about the same, meaning the Front and Rear Cornering Compliance DIFFERENCE is still about the same. It looks to me like are merely seeing the effects of stiffer tires ALL AROUND.

Post some car details: Weights, wheelbase, steer ratio, estimated tire properties (at least some cornering stiffness info) maybe some tire aligning moment values and I can demo what you should be expecting. Stick to the steady state analysis with this program. Response times are clearly of high value to a driver, but not ones from this program.

RE: suspension lateral compliance

I do not know,
maybe my input data are bad?
maybe is software limitation?
also it's very likely that I'm doing this test wrong?!!
then my result can be incorrect?

difference is small because changes are small also ? (rear toe change from 0,3 Dg to 0,4 Dg total)(also rear stiffness change is small)

car weight 1055kg (56% front)
wheelbase 2610 mm
steering ratio 12
tire cornering stiffness 2000 N/Dg
tire aligning torque stiffness 200 Nm/Dg
(these tire data are only estimated............i do not know if are have real tire data)

RE: suspension lateral compliance

Well, now we can all have a little bit of fun. With the info you provided, let's throw a Hoosier 225/45-R17 tire on your ride (250 kPa on a wide wheel. At your loads, these tires spit out cornering stiffnesses of about 1390 N/deg front and 1256 rear. Aligning moment stiffnesses are a meek 34 Nm/deg front and 23 Nm/deg rear.

Rubbing your emerald slippers together should give you a front cornering compliance of 2.11 deg/g and 1.78 deg/g at the rear. This recipe was lightly sweetened with a bit of steering compliance. Turning the crank gets you an Ay response time of 0.29 sec at 120 kph and with a constant radius test sim I get a tangent speed of about 77 kph. Your 12:1 gear gets you a steering gain of 3.74 g/100 deg-swa at 120 kph. A bit quick if I do say it. In a nutshell, here is what Dyna_Tuna should get you: (more to follow).

RE: suspension lateral compliance

And with a little more software grunt, you can get serious enough to go racing. BTW: These programs are open source Matlab. I provide them for entertainment to FSAE and its Tire Test Consortium members in order to embarrass the Design Judges who often know less about the subject than my 3 dogs.

RE: suspension lateral compliance

Thank you Cibachrome,
although i do not understand all ,i think your responses was useful
so we can say total compliance is crucial for race car manipulation
as in steady states ALSO during transitient maneuvers, that seems really NOT the same in terms of understeer level

RE: suspension lateral compliance

BTW: i am stay with Dynatune smile
is Great tool!!

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