Wheel frequencies VS track surface

[spacer]

Hi guys,

Regarding wheel rates, or actually, wheel frequencies; I've always tried to set up my car with the filosophy "get the softest springs you can get away with without running into problems somewhere along the track or limiting your setup flexibility". But recently I started having doubts over that assumption. Oh and we don't get any testing sessions so I'm curious about your thoughts and am interested in the theoretical side before throwing away some of the actual race results .

So please enlighten me .

Say we have the following situation:
-FWD car
-no aero whatsoever, all low speed <80km/h corners, mechanical grip is focus
-sharp reaction in transient conditions isn't of much concern, tracks don't have chicanes (mostly ovals) and tracks can often be driven fastest with smooth driving
-car doesn't bottom out anywhere
-coilovers don't end up hitting bumpstops
-I'm quite happy with curent suspension geometry and changes in wheel travel (double wishbone), so body roll is not something I necessarily want to reduce
-car is driven on offroad/gravel/dirttrack type surfaces
-we have enough setup range/flexibility to set up the car well balanced
-front unequal length double wishbone, no ARB. rear trailing arm, with additional ARB

Despite the above, are there any reasons why the softer sprung car is worse than having it stiffer sprung?

Now the reason I'm asking is this: our car is (by some margin) the softest sprung car of all the paddock. At some events we've got the fastest car and are in front, often lapping 0.5sec faster at a 20sec lap than the rest of the field. However, once we get to tracks with a lot smoother surfaces we tend to drop back and fight for P5, struggling for midcorner grip (U/S) and some corner-exit traction. And I mean dirt tracks that are black from begin rubbered in, having the tires squeeling.

This has me searching for what fundamental issue we have at these events, compared to our collegues.
Tyres are the same btw, car weight and distribution nearly identical, and we should have an drivetrain advantage. So this has me looking at the spring rates.

Wheel frequencies our car:
~100 CPM front, ~110 CPM rear
Wheel frequencies competition:
~115 CPM front, ~115 CPM rear

Many thanks for your insights!

-Tom

[SameSame]

Despite the above, are there any reasons why the softer sprung car is worse than having it stiffer sprung?

The goal is always to have your system (car in this case) critically damped. Mathematically, c^2 - 4km = 0. So if your spring rate is the only variable you could possibly end up with a system that is very overdamped with soft springs. This would mean you have a slower than optimal transient response time.

Edit: For clarity, c is your damping coefficient, m is your system mass and k is the spring stiffness coefficient. This is for a simple linear system but the idea still holds for non-linear systems.

[Greg Locock]

Cite please. Sounds like nonsense.

[PhillipM]

Can't say I've ever seen a racecar that was setup to be critically damped. Slightly underdamped, or massively overdamped for body/heave, but not deliberately set for critical.

Given that you're having issues at specific high grip tracks I'd be looking at whether you're under/overheating the tyres first anyway.

[Tim.Wright]

Yea agree, 1. there's no reason to target critical damping. Many methodologies start off with 70% critical as a STARTING POINT then move from there via iterations in testing or simulation. 2. Linear assumptions DO NOT hold for non-linear systems. And there is nothing more non-linear than a racing damper.

Regarding the original post, unfortunately I couldn’t find a short concise way to respond. Mainly because I hate working with ‘rules of thumb’ and prefer a more fundamental approach. I have to say your reasoning/logic is pretty solid. Sounds like a Rallycross vehicle am I right? To explain better you need to go into detail about the pros/cons of hard and soft springing:

Disadvantages of hard springs are primarily the fact that it increases the 'transmissibility' between the wheel and the chassis. This means that the forces passed between the wheel and the chassis are increased in amplitude (for a given road input) and this in turn increases the tyre’s contact patch load variation which causes grip loss through tyre load sensitivity and tyre relaxation effects.

Secondly, stiffer springs (and anti-roll bars!) increase your warp stiffness. All tracks have non negligible amounts of banking, curbs and random asperities during every corner which excite the warp mode of the suspension and here stiff setups cause 3 problems

1. Your roll stiffness distribution becomes MASSIVELY dependent on the road surface. The warp stiffness of the suspension gets effectively ‘superimposed’ over your carefully calculated roll distribution during a corner. To give you an idea of the order of magnitude – a road going sports car’s roll distribution will change by around 10% by driving over a 5mm bump on the track! Consider that a good driver is sensitive to a roll distribution change of around 0.5%... If you don’t believe me stick a small block of wood under one tyre while it’s still on the setup scales and see your cross weights turn to shìt. Below is a calculation showing a warp calculation of a project I’m working on. The blue line is a traditional suspension system with springs and bars and it shows an LLTD sensitivity to warp of 4.6% per mm of warp travel!:
   
2. Banally, and not completely independent of the previous point, the stiffer your warp stiffness is the more likely you are to lift one or more wheels off the ground which is generally throwing grip away for nothing. I’m not just talking about a steady state sense but in transient responses to curb strikes, medium wavelength bumps mid-corner and ‘snap’ corrections made by the driver. As I mentioned before, warp input only need to be tiny to throw a car off balance – even in a straight line:
   
3. Lastly, and always connected to the warp stiffness, your roll distribution will become more dependent on your steering angle especially if you have a lot of caster angle and trail. In this case the act of steering will create a warp input to the suspension and shift your roll distribution to the rear. This can be a useful tuning tool if you understand the effect but it can cause confusion if you don’t.

Essentially stiffer springs makes the car respond to the road inputs more than the driver which in general is not a great thing because the road inputs are uncontrolled.

Conversely, the advantages of hard springs are:
Ability to run a lower ride height which gives you a lower CG, less load transfer, possibly an aerodynamic advantage all of which help grip.

Stiffer springs and bars = less roll which has 2 main influences - one objective (relating to tyre grip) and the other subjective (relating to driver feedback).

• Objectively less roll will mean your outer, dominant tyre, will have an inclination angle more tilted towards the turn centre which for racing tyres typically (not always) means it will have more grip. I know you said you are happy with your roll kinematics but more camber on the outer wheel is almost always an advantage until you run into durability or braking stability problems. How much camber gain are you running out of interest? Also, if you roll centres are high (100mm) I can almost guarantee that your outer wheel camber isn’t what you think it is mid-corner .
• Subjectively harder springs reduce the delay between the roll and yaw movements which all drivers prefer. This phase delay doesn't have a massive effect on the grip to my knowledge but it can be really disconcerting to the driver.

So basically, based on your information, the fact that you are slower on the flatter tracks is likey because the 3 main disadvantages of stiff setups aren’t as present on the flatter tracks. Or in other words the advantages of stiff springs outweigh their disadvantages.

One remedy would be to try and exploit the advantages of a stiff suspension by running the car as low as possible and stiffening the suspension accordingly. I think also that your trailing arm rear suspension might be hold you back here. Why did you choose this type of axle? Rules? I suspect you might be saturating the front axle in order to render the car stable due to a weak rear axle architecture. It would explain your mid corner US and traction problems.

[SameSame]

Yea agree, 1. there's no reason to target critical damping. Many methodologies start off with 70% critical as a STARTING POINT then move from there via iterations in testing or simulation. 2. Linear assumptions DO NOT hold for non-linear systems. And there is nothing more non-linear than a racing damper.

First off, have you ever solved a non-linear differentail equation (and what "assumptions" are you speaking about in solving a linear differential equation)? The tools you use iterate and that should already tell you that it's impossible in most cases. They are OFTEN APPROXIMATED as linear systems in order to be solved, so you have to grasp the fundamentals of a linear system before even beginning to try and linearize a system around a certain operating point.

Is this 70% of the critical value meaning they start iterating from an under-damped case?

I was speaking in the most general sense. I doubt anyone who does not understand a linear system, and the effect that changing coefficients of a simple second order linear differential equation has on the end answer, will understand a non-linear system.

The rest of your post makes good sense and is a very interesting read. +1

[SameSame]

Oh and we don't get any testing sessions so I'm curious about your thoughts and am interested in the theoretical side before throwing away some of the actual race results .

Sorry for derailing the thread, just trying to input some theoretical knowledge about how these systems work. I admittedly haven't modelled/worked with a complex racing setup, I know see there are other better trade off's than having a system respond to an input as quickly as possible thanks to a very informative post

[Tim.Wright]

First off, have you ever solved a non-linear differentail equation (and what "assumptions" are you speaking about in solving a linear differential equation)?

Yes I have actually, it's part of my job. In my experience the part of the vehicle in which linear approximations give you the least insight of the system is damper tuning.

And yes, a typical 'rule of thumb' is to start of at 70% of critical wheel damping because it gives a good balance between response speed and overshoot. In reality it's a massive simplification given that the dampers are controlling an 7 degree of freedom system with each mode having very different stiffness and damping requirements. In addition to that vehicle dampers are typically heavily asymmetric with much more damping in extension than compression.

So when someone tells me a car is X% critically damped it doesn't tell me anything. Is this the wheel mode, ride mode, pitch, roll, heave mode? In extension or compression?

I've personally found that trying to linearise an automotive damper is like a monkey throwing darts. Depending on how you linearise the data, the resulting damping ratios and natural frequencies change wildly to the point of it being practically useless.

This is why dampers are never tuned with linear models. You either use a nonlinear MBD ride model or you put the physical car on a 7 post rig.

[SameSame]

First off, have you ever solved a non-linear differentail equation (and what "assumptions" are you speaking about in solving a linear differential equation)?

Yes I have actually, it's part of my job. In my experience the part of the vehicle in which linear approximations give you the least insight of the system is damper tuning.

And yes, a typical 'rule of thumb' is to start of at 70% of critical wheel damping because it gives a good balance between response speed and overshoot. In reality it's a massive simplification given that the dampers are controlling an 7 degree of freedom system with each mode having very different stiffness and damping requirements. In addition to that vehicle dampers are typically heavily asymmetric with much more damping in extension than compression.

So when someone tells me a car is X% critically damped it doesn't tell me anything. Is this the wheel mode, ride mode, pitch, roll, heave mode? In extension or compression?

I've personally found that trying to linearise an automotive damper is like a monkey throwing darts. Depending on how you linearise the data, the resulting damping ratios and natural frequencies change wildly to the point of it being practically useless.

This is why dampers are never tuned with linear models. You either use a nonlinear MBD ride model or you put the physical car on a 7 post rig.

Thank you that was very informative. This is off topic but I meant that you have to iterate for a solution, it is not like a linear system that has known solutions. I can only imagine how complex an entire car is to model accurately.

Surely the damping requirements change for pitch, roll etc, how do you come up with a solution on which of those takes priority to damp best?

And do setup changes not cause a bit of havoc with the optimal settings?

I didn't mean linearise the data. That is normally a terrible idea that gives rubbish values, the natural frequency of a system is only dependant on the mass and spring stiffness of the system. I meant linearising the system (ie using Taylor expansion for non-linear terms) around a certain system operating point.

[Tim.Wright]

Surely the damping requirements change for pitch, roll etc, how do you come up with a solution on which of those takes priority to damp best?

This is the main problem with objectifying damping setups. There are 7 independent modes to take care of with typically 4 (sometimes 6 in an open wheeler) dampers so the best you can hope for is a compromise. Additionally the dampers have 2 main roles to play - control of the sprung suspension modes (usually low frequency) and control of the wheel mode responses to road inputs (usually high frequency). So in the end its a mess or variables and non-linearities and for this reason its commonly referred to as a black art.

I understand what you mean by local linearising. I use an identical method for calculating lateral handling metrics because the non linearities are a lot more well behaved (at least in steady state). However, local linearising means that you no longer have one 'damping ratio' but rather a damping ratio which changes with the load condition.

Honestly damper tuning is not something I have a lot of experience with but from what I have seen (passively) is that it is done in basically only 3 ways:

1. Track testing with driver feedback
2. 4 or 7 post rig testing
3. non-linear MBD simulation (usually the most difficult to get right with certainty)

[SameSame]

Surely the damping requirements change for pitch, roll etc, how do you come up with a solution on which of those takes priority to damp best?

This is the main problem with objectifying damping setups. There are 7 independent modes to take care of with typically 4 (sometimes 6 in an open wheeler) dampers so the best you can hope for is a compromise. Additionally the dampers have 2 main roles to play - control of the sprung suspension modes (usually low frequency) and control of the wheel mode responses to road inputs (usually high frequency). So in the end its a mess or variables and non-linearities and for this reason its commonly referred to as a black art.

I understand what you mean by local linearising. I use an identical method for calculating lateral handling metrics because the non linearities are a lot more well behaved (at least in steady state). However, local linearising means that you no longer have one 'damping ratio' but rather a damping ratio which changes with the load condition.

Honestly damper tuning is not something I have a lot of experience with but from what I have seen (passively) is that it is done in basically only 3 ways:

1. Track testing with driver feedback
2. 4 or 7 post rig testing
3. non-linear MBD simulation (usually the most difficult to get right with certainty)

Wow, I never thought about all those other variables and even different frequencies to take care of! I guess you use lots of transfer functions to handle the system response to different frequencies? But that would mean having a linear plant which as you say isn't ideal Brilliant information thank you!

[Tim.Wright]

Fitting an overall transfer function may yield something approximating useful (even if it is linear) but this is the point at which my experience is well and truly exhausted.

This is a very good thread regarding the can of worms that is damper tuning:
http://www.f1technical.net/forum/viewto ... f=6&t=8937

DaveW is the guy to pay attention to there. He's done it all, rigs, models and full vehicles.

[bill shoe]

Great thread, great information. Question for Tim or others that relates to SameSame's original post --

Is it generally desirable to dissipate energy at the highest possible rate, but in practice that is very complicated to achieve (is not same thing as 1.0 critical damping for corner mode)?

[Pierce89]

Fitting an overall transfer function may yield something approximating useful (even if it is linear) but this is the point at which my experience is well and truly exhausted.

This is a very good thread regarding the can of worms that is damper tuning:
http://www.f1technical.net/forum/viewto ... f=6&t=8937

DaveW is the guy to pay attention to there. He's done it all, rigs, models and full vehicles.

Its crazy that more people on this board don't know about DaveW. He's literally one of the top.suspension tuners in the entire racing world.

[Jersey Tom]

I'd mirror some other comments that to target "critical damping" and then just leave things be is going to be leaving performance on the table.

There's a lot to balancing "mechanical grip" of the tires versus aero platform. Different tires can want different things at different tracks. And I'd say it's unrealistic to think that - starting from scratch - you're going to come up with the answer through some elaborate analysis in advance. Come up with a few different package options, try them at the track, see what works, and take notes on it.

I still maintain that keeping a good notebook is one of the most important things for any good racing or vehicle dynamics engineer. There are just far more unknowns or things you won't have elegant closed-form solutions to.

Anyway, anything thing to think about as far as springs and such are concerned... I'd say you will hear people say that more stiffly sprung vehicles are overall more responsive, and very soft ones can be a bit lazy. And I would say this is true to an extent.

The limit is effectively a kart, or rigid bicycle model, or whatever. But even then, response isn't instant, it's limited by your tires and the inertia of your vehicle. Adding the dynamics of a sprung platform to the picture is like adding a spring in series. So if on a road car setup you went from 100 lbf/in springs, to 1000, to 10000, there's a limit to where getting more and more stiff does nothing for yaw response...

...unless of course you have a downforce car, in which case the more you pile on the better!