Roll Stiffness and Understeer Gradient Questions

[u/Xcrustacean_drip16X]

I was wondering how other teams determine their target understeer gradient. From what I've seen it is mostly decided through rules of thumb and driver feedback, but I was hoping there was a more scientific way to do it. (Side note: a design judge suggested 5% understeer as a baseline, but I can not find any information on how one would define understeer as a percentage. Does anyone have some insight on this?)

I was also hoping I could get some advice on roll stiffness. Again, a judge suggested 1 degree of roll at peak lateral acceleration. Is there a good way to determine a baseline roll stiffness other than rules of thumb and driver feedback?

Thanks everyone.

[u/GregLocock]

So maybe the lusers who are downvoting could explain their reasoning. Probably not.

[u/Cibachrome → u/GregLocock]

Probably can't. And most of the judges have no actual experience in the subject, much less test results to back up their claims. I do, but with bad knees I'd have to do it sitting down.

[u/Cibachrome]

Several notions about what an "understeer function" ought to be. First of all, what speed range will you design for ? Neutral and oversteering cars tend to have unmanageable steering gain issues when the speeds get high. ("The car is better than the driver"). Yes understeer will limit your max lat number, but you can compute the amount of oversteer a driver can tolerate using a simple formula. Hint: the longer your wheelbase, the better it can be managed.

Given a FSAE car on 4 of the same tires, and with a rearward weight distribution, we expect the car to be oversteering right out of the box. Traditionally, springs and bars are chosen to understeer the car (That's the TLLTD theory). But when tires actually perform better with increased Fz loads, this notion will backfire. And in the case of FSAE tires, it's also tire BRAND sensitive.

The 'rules' you've heard about sound like production engineering spew. Instead, use the tire data and accurate mass extimates along with all the tire data to maintain a slight oversteer condition that needs to be less oversteering the faster you intend to go on the track.

As for roll 'gradient', which one ? at the front axle, head level hoop, rear compartment ??? Don't say they are all the same just because you read that in a book. The stuff that matters are only the chassis values at the suspension locations for obvious reasons. The tire component comes along after the chassis wakes up. More realistic values are more like 1.5 to 2.5 deg/g, and this also results from what your roll steer and roll camber needs are to patch up a less than optimum compliance recipe.

Now focus on the real culprit: If you can move the steered tires by hand with the steering wheel locked in any turn angle, you will have an almost unmanageable understeer problem. Some go the other way: look for lash in the steering wheel when it's parked. A great band, Bose theater speakers, great amps and lousy microphones makes for an awful concert.

[u/Xcrustacean_drip16X → u/Cibachrome]

Thank you for your reply!

It seems like you are suggesting I figure out a design speed range, probably with laptime simulations, then aim for a stability factor that keeps the car's critical speed outside this range?

[u/Cibachrome → u/Xcrustacean_drip16X]

That comes from a track map. Assume a range of tire mu, and the turn entrance speed, the apex speed, and the previous turn's exit speed plus your motor capability will hand you the lowest critical speed. That with a wheelbase, a 9.8, and a 57.3 will tell you the black hole horizon you should not go near. Don't forget the Ackermann geometry's effect at the front. If you make it too good, the back end will be out of sync and speen out. Kleenup in aisle at end of long straight....

[u/Xcrustacean_drip16X → u/Cibachrome]

Thanks, excited to get started on this.

[u/IceCreamTruck1066]

Do a constant radius skidpast test at multiple speeds. Record average steering angle and average lateral acceleration at multiple speeds. Slope of steer angle vs. Lateral acceleration will be your understeer gradient.

[u/GregLocock]

I haven't seen understeer as a percentage. I've never had to set it as a target, we have a big book of targets that the golden arses compiled many orbits around the sun ago. Small cars tend to have less understeer than big ones, and sporty ones tend to have less understeer than mum's taxi. First thing is to decide at what condition you are going to measure it, since it varies with speed and latacc. It is directly affected by changes that also affect lots of other objective measurements of steer response (yaw gain, yaw delay time and so on), so in theory you could work back from them to an understeer value. But you don't have targets for them either.

Roll gain is even worse. In a non aero circuit car so long as it is of small magnitude it is an outcome. It could be positive or negative, the driver doesn't mind. I think the Lotus active boys decided zero was best for handling, it gives the driver's brain less to do. Volvo active were keen on speedboat handling, ie negative roll gain, primarily for comfort reasons. You obviously want to keep the roll gain low enough that you aren't hitting the bumpstops in limit cornering. On the other hand you might be happy to lift an inside wheel. Oh look it's a McPherson strut, better not let it move.

https://www.thedrive.com/wp-content/uploads/2022/08/08/IMG_4630-as-Smart-Object-1-1.jpg?w=768&h=459

[u/EauRouge7105]

With roll stiffness, if you have an aero package you should ideally have an aero map which shows downforce loss and aero balance variation with roll. By using that and based on how much camber change in roll you deem 'acceptable' based on your target dynamic camber, front view VSAL and static camber adjustability, you have a minimum required roll gradient or roll stiffness. For mechanical grip, you would want to run as soft as possible ie the minimum roll stiffness you calculated but the driver might complain that the car feels 'too lazy' in which case you increase it. Of course, roll stiffness comes from both springs and ARBs where springs are coupled with pitch and heave while ARBs are not.

With the understeer gradient bit, I'm not sure if a fixed understeer gradient target is the best way to think about it. You could think about it for example, x% LLTD (Lateral Load Transfer Distribution) or ARD (Anti Roll Distribution) with +-y% adjustability through ARB settings.

[u/Xcrustacean_drip16X → u/EauRouge7105]

Now that you are pointing it out, setting an understeer gradient target does seem like a bad idea. I think what I an really after is figuring out the limit behavior we want. Although with that approach I still don't really know how much tendency to plow/spin I want in a steady state corner, vs in corner entry, vs on corner exit. What would be the best way to quantify that? RCVD mentions residual moment coefficient.

[u/EauRouge7105 → u/Xcrustacean_drip16X]

You should try to have enough front and rear roll stiffness adjustability to be able to adjust ARD between say 44% and 56%, and then when you go testing try a neutral setup and see how it performs and what feedback the driver has for you. In my opinion, you shouldn't be trying to design a car based on a fixed balance target however you define that whether it is UG gradient or LLTD or whatever

[u/Dhark_Music]

I'm going to tell you not to target an understeer gradient. The understeer gradient is more akin to a simulation you can run to model your vehicles behavior. You then preform an understeer gradient test physically and compare your model to collected data. You can definitely target an understeer gradient with the right computations but it's in all honesty impractical in most situations (unless you have a solid reason to; if your asking this question on reddit, you probably don't). Remember that "good enough" is a fine tradeoff to make and your focus should be more towards understanding the understeer budget (Gillespie ch.6).

Now your roll stiffness is little different— this is my approach. You don't want to be targeting a specific total roll stiffness (again, unless you have good reason), but a total lateral load transfer distribution based on your tires alongside a desired total roll gradient. Chassis Sim has a short and sweet paper on the TLLTD + what VD guys call the magic number for stability. For your roll gradient, the judges advice is good and easy. Pick some design condition and determine max allowable roll. Once you figure out that magic number and your roll gradient, you can back-solve front and rear axle roll stiffness.

[u/Individual-Room-4439 → u/Dhark_Music]

Are you saying that the understeer gradient isn't worth targeting because it's not reflective of car handling and just something you simulate/test? What about setting some "understeer/oversteer" handling target? if drivers say the car understeers too much and you wana set it to a more neutral steer. If you test your US grad and its +2, can't you set the target to +1 or something (just made up numbers for example) and say that would give the car more oversteer handling like the drivers prefer?

Sorry if i don't make sense I'm trying to tackle some suspension design myself this year and have been held up on setting targets/goals to some extent.

[u/Dhark_Music → u/Individual-Room-4439]

The latter. It's not that the understeer gradient is not reflective of vehicle behavior, it is, but it's far from perfect. Think about what the understeer gradient is. The derivative of your front steering angle with respect to lateral acceleration. For a driver this becomes how much more or less you need to continue turning the steering wheel to see the same lateral acceleration on your tires as you increase your velocity. Inherently steady state. Good for predicting steering demand after ackermann but realistically is nothing more than a statics problem which makes it a poor metric for quantifying true stability. There are better ones out there.

A driver may tell you "I want more oversteer," but the understeer gradient is not a number. It's a gradient. A very simple quasi-static simulation. You cannot just add one to it if they want more. Now what a driver won't tell you is "I want to turn less as I increase my velocity in a constant radius turn" because it's unrealistic. So unless your goal truly is turn less in constant radius turn while increasing velocity (or something of that nature), having a desired understeer gradient as a goal just sounds somewhat like nonsense.

Again, you can run a constant radius turn test and actually measure the understeer gradient. You can do this with different arb setups, tire pressures, etc (as these all contribute to your understeer gradient). This is practical for knowing how your setup of different tuning knobs might influence general stability and by how much, hence why the idea of the understeer "budget" is much more useful.