I'll add that it seems that Mark Ortiz prefers to transform tire forces from the wheel coordinates to the vehicle coordinates: this means that a tire that is steered 45 deg and producing only lateral force (perpendicular to the wheel plane, or parallel to the wheel spin-axis if you like) produces a equal lateral and longitudinal force in the vehicle coordinates. It's the same thing. To be honest it is generally easier to work in vehicle coordinates, especially regarding yaw moments.
If u reach the same bit of track at the same time then turn the wheel at the same rate then the inside tyre of a 1 degree toe-out car will have one more degree of steering angle and the outside tyre one less compared to a zero-toe set-up... So I don't think that's it...
Against my better judgement (I really should have been doing something more productive) I added the weight transfer effect to my little sim and concur with JT's thoughts...
So either there's some other effect or it is simply 'feel' that toe-out affects that would people report as 'better turn-in'. Using computer games can be dangerous as they generally have really simple physics models...
One thing I've thought of is that with toe out on both fronts won't they both try and self-centre... would that give the driver a different feel...?
So basically; when the '1 degree toe out car' turns into the corner its outside wheel crosses the 'straight ahead' portion but it is actually already slipping at this point (creating lateral force) and is perpendicular to the CG and therefore greater yaw moment?
Basically, my larger post (end of page 2) is the same argument made my Mark Ortiz. There was some confusion about "drag" force but I believe Ortiz is referring to the longitudinal component of the lateral tire force (due to tire steered relative to chassis), and not "slip angle drag".
Vehicle response and feel are very much aligned with the derivative responses of the car. You will find the bicycle model derivation of these in Race Car Vehicle Dynamics - all 6 of which are a function entirely of front and rear axle cornering stiffness (for a given speed, and set of inertial properties). Front and rear axle cornering stiffness are the first order, primary dominant factors of response, stability, and feel of balance.
However, these are only valid for cars that behave similar to a bicycle model. If you were to extrapolate a 4-corner model and add toe to the front or rear axles, since you're still within the linear range of the tires there's no really no change to the yaw response of the tires. Despite this, we know that it DOES have an effect. Incidentally, since these bicycle model derivatives are a function of CS only, there would be no predicted change in response if you were to add a huge front bar, etc. So what are we missing?
Load transfer is the key, and cannot be neglected. The argument, "well the slip angles and forces and load transfer are small" does not mean that they can be forgotten. It's the rate of change that's important, rather than the absolute value. When you add toe out to the front end, there's an introduction of vertical load transfer sensitivity, in addition to just yaw sensitivity. The result is that you have a self-REDUCTION of into-corner yaw moment, with front toe out and with load transfer in the appropriate direction. This REDUCTION of yaw moment is key, and lets the car reach a steady state condition quicker, with less lag, albeit at a smaller steady state value (of course this can be changed by just adding more steering input to begin with). Similarly, as you increase understeer you will also make response faster.
As I said earlier, this all plays on feel. Sometimes, adding that front toe out will help. Other times if the car is so damped that it feels like it won't rotate at all.. some front toe in may do the trick. Have to know which side of the fence you're on, as with many aspects of handling there are few absolutes.
Don't believe me? Prove it yourself. Like I've been hinting at, open up RCVD, and in MATLAB write a 2DOF bicycle model simulation, then expand it out to 4-corners with some brute force lumped parameter load transfer coefficient. Do some simulations. Run some with a CG height of zero (where the only effect is the slip angle drag Ortiz speaks of), and run some with a non-zero CG height. Axle height should be appropriate. Should be plain as day that load transfer and tire sensitivity is what has the primary effect by a large margin.
But like I say, these are just the basics.
Grip is a four letter word. All opinions are my own and not those of current or previous employers.
The "alright fine I give in" post was really superb. It took my big-picture understanding of vehicle dynamics up a step.
The best technical writing seems to come from people who have enough frustration/angst to break through their normal filters and just throw some wisdom on the screen without thinking too hard.
Incidentally, as can be gathered this is all contingent on tire properties. Could certainly have situations where the car is pretty numb to toe adjustments in which case you can spend all sorts of time playing with it to no end. This is why I don't like these "generalized" statements of X does Y without taking the time to truly understand what's going on.
Gotta start thinking big picture...
Grip is a four letter word. All opinions are my own and not those of current or previous employers.
Jersey Tom wrote:
However, these are only valid for cars that behave similar to a bicycle model. If you were to extrapolate a 4-corner model and add toe to the front or rear axles, since you're still within the linear range of the tires there's no really no change to the yaw response of the tires. Despite this, we know that it DOES have an effect. Incidentally, since these bicycle model derivatives are a function of CS only, there would be no predicted change in response if you were to add a huge front bar, etc. So what are we missing?
Load transfer is the key, and cannot be neglected. The argument, "well the slip angles and forces and load transfer are small" does not mean that they can be forgotten. It's the rate of change that's important, rather than the absolute value. When you add toe out to the front end, there's an introduction of vertical load transfer sensitivity, in addition to just yaw sensitivity. The result is that you have a self-REDUCTION of into-corner yaw moment, with front toe out and with load transfer in the appropriate direction. This REDUCTION of yaw moment is key, and lets the car reach a steady state condition quicker, with less lag, albeit at a smaller steady state value (of course this can be changed by just adding more steering input to begin with). Similarly, as you increase understeer you will also make response faster.
Correct me if I'm wrong, but it seems that you are stating that this reduction of into-corner yaw moment (which is due to a reduced overall front axle load) is because of the reduced cornering stiffness of the inside, more lightly-loaded tire. This creates more optimal slip angles for both tires, and is the typical argument for anti-ackermann steering on racecars. However, I would point out that many racing series have differing tire compounds and constructions between LS and RS tires and thus have very different cornering stiffness relationships between the inside and outside tires. Toe-out in this case may not reduce into-corner yaw moment.
I admit that I want to take back the last sentence of my post from page 2, as most racecars will not run large amounts of front toe-in or toe-out and thus the effect is small in such cases. However, if the poster is looking for a universal reason why toe-out aids response, only the geometrical effect is present for all 4 wheeled vehicles. However, I'll agree that tire characteristics dominate.
In my experience, drivers seem to be more sensitive to directional response (yaw accel / steering), which is obviously proportional to net yaw moment. Directional control isn't relative to a steady-state value unlike the transient response in Milliken's control derivative approach.
In the end what everyone is really saying that in the usual doses,,toe out..toe in...It all comers down for the most part, to driver feel and what he likes.
To achieve anything, you must be prepared to dabble on the boundary of disaster.”
Sir Stirling Moss
We've always been talking fundamentals here - basics - e.g. assuming same tire left and right and a pure steering input. This entire discussion becomes moot if we're talking about radically asymmetric setups, tires, running on banked ovals, combined loading entry, etc etc... because then we can arbitrarily make the situation whatever we want to fit the argument.
In any event, my point is still that the slip angle drag is far from the dominant effect on turn-in and is drowned out by everything else going on. Or, even if there was nothing else present, the effect is going to be so small I don't think the driver would even notice it. Yes it's always present, but so what? Doesn't mean it is really going to show up. I agree though that it's silly to talk in generalities of X does Y because there are few absolutes and gospels.
Anyway, still not really not so much a "slip angle optimization" thing since we're talking about linear range. Just manipulating what you have in that range.
Grip is a four letter word. All opinions are my own and not those of current or previous employers.
"More optimal slip angles" meant more slip angle on the tire with the greater cornering stiffness. Linear range tires meaning linear cornering stiffness, but not necessarily linear friction coefficient, which I assume you also meant, otherwise vertical load sensitivity wouldn't be a factor.
I am not referring to "slip angle drag", which is defined as the portion of lateral force parallel to the path velocity [drag = Fy*sin(slip angle)], but the longitudinal component of a steered wheel in vehicle coordinates [Fx = Fy*sin(steer angle)]. Both will be very small for a vehicle at turn-in, but I only make the distinction as vehicles negotiating turn radii of the same order as the track widths (high steer), the effects are very significant. I don't consider this making the situation arbitrary, but I think you've made good points in any case.
thisisatest wrote:
also, as often is said that toe out helps with turn in, it is also said that too much toe out can lead to understeer. i think this is part of the picture. if the end result is some understeer, then the transient turn in behavior will feel more aggressive.
