Stabilizing/destabilizing moments

[WilO]

Kind of a basic question for the minds here, but I've been wondering about the forces acting on the vehicle as a whole during transient maneuvering (corner entry and exit).

Time to test my understanding...here goes:

The distribution of forces about the vehicles CG must result in some yaw velocity during transients, which implies that the forces develop from zero until the vehicle has gone where ever it has to in order to achieve equilibrium.

I know there must be several contributing factors; wheelbase and CG location, control moment, steering geometry, cornering stiffness, the list surely goes on... and I believe that cornering forces at an axle have to be produced in direct proportion to the mass that axle carries. So far so good?

So what factors determine whether or not the forces produced at an axle will be stabilizing or destabilizing moments about the CG? Again, sorry for asking such basic stuff....

Wil

[Tim.Wright]

Well going on the typical definition of stabilising and destabilising forces that means any torque acting to yaw the vehicle in the understeer direction (or away from the turn centre) is a stabilising moment, and torque acting to yaw in the oversteer direction (into the turn centre) is a destabilising torque.

They are so called because when you consider the extreme cases, a very stable car wants to carry on straight and an unstable car wants to spin out.

So with respect to lateral forces, any force from the rear axle is stabilising because in a RH turn it is acting counterclockwise about the CG trying to yaw the car out of the corner. The front axle is producing a destabilising force. In a RH turn it is trying to yaw the car into the turn.

Again, it helps to think of the extremes. If you blow out a rear tyre mid turn, you loose your stabilising moment and the vehicle spins. If you blow out a front, you loose your destablilising moment and the vehicle goes straight.

Obviously too much of either is bad, but both are require at different times. For turn in (a transient condition), you NEED a destabilising torque to start the yaw into the corner. In the middle of the turn, both should be balanced (what you refer to as equalibrium). In the turn exit, you let the stabiliising force at the rear axle yaw the car out of the turn (again a transient condition).

Next step is to look at some bicycle model theory. The lateral forces at the tyres can be further broken down into different components (eg directional stability, yaw damping, damping in sideslip) which sum together to produce the full axle force. These are very useful to understand if you want a fuller picture of stability.

Tim

[Tim.Wright]

Another thing, it also works with longitudinal forces too. E.g. typical LSD diff locking produces stabilising forces under acceleration because the inside wheel is typically seeing a higher force at the contact patch than the outside. If you sum the torques about the cg, the inside traction force is stabilising, the outside is destabilising. If the inside is bigger, you have a net stabilising torque that needs to be counteracted by a higher destabilising force at the front (e.g. more steer angle) to keep the same trajectory.

Tim

[WilO]

Tim,

Thanks for that excellent response.

Wil

[Tim.Wright]

No worries,

Im sure JT would have something to say on this as well, only problem is the post gets knocked off the front page by people wanting to compare drivers and discuss team politics.

Why the interest in stability? Are you building something for yourself??

Tim

[Jersey Tom]

All pretty much on point IMO.

[Tim.Wright]

That was disappointing...

Tim

P.S. JT, no update on your blog after your win Monday? You know you want to.

[WilO]

No worries,



Why the interest in stability? Are you building something for yourself??

Tim

Studying vehicle dynamics is a sort of 'passionate hobby' of mine I guess....and I do work with some local (and not so local) racers. Once in a great while I even help them go faster.

My difficulty lies in my engineering background, or more specifically, the complete lack of it. I can barely spell 'inverse of the Jacobian', much less know what to do with it. Physics and Calculus were too long ago, and I'm at the age where returning to school isn't an option; at least right now. So I'm stuck with self-study...

Thanks again for the help, and sorry to pollute the board with questions that I should have been able to answer myself.

Wil

[Jersey Tom]

You mean Kurt's win in the Nationwide race at the Glen? Or Brad's win at Pocono the week before? Even his second place at the Glen I was real impressed with. Got some momentum, see if it carries.

[Tim.Wright]

Win at Somona I thought I read somewhere. Maybe not, I actually dont follow it so much so Im showing my ignorance here. Was good to hear Ambrose had a win. Even if he comes from Tassie

Thanks again for the help, and sorry to pollute the board with questions that I should have been able to answer myself.
Wil

I actually thought it was a decent question which is why I answered it. The board needs more questions like these.

When you are learning vehicle dynamics, stability is often forgotten about in the scramble to understand overall grip and load transfer effects.

Like all things in motorsport stability is a compromise. Less stability will give you a more responsive car up to a point where it becomes undrivable.

Tim

[Jersey Tom]

Ohh yeah yeah. Sonoma was a while back. Pretty dominant. I try to keep the blog non-work though.

[GSpeedR]

For typical tires, pneumatic trail will be aft of the center of the wheel center-line, and thus the aligning torques (Mz) from all 4 tires will provide stabilizing yaw moments about the chassis CG. This is obviously proportional to the magnitude of the lateral forces at each wheel.

The front lateral yaw moment and longitudinal drive yaw moments can be thought of as control inputs. As mentioned above, the driver must initially apply a destabilizing yaw moment to generate yaw acceleration, which will be reacted by the rear lateral yaw moment (stabilizing), until the vehicle has reached a steady-state cornering [if it exists] and the net yaw moment returns to zero. Upon exit there will be some combination of a reduction in front lateral yaw moment (stabilizing effect) and an increase in longitudinal yaw moment (stabilizing or destabilizing depending on the differential used). The overall net yaw moment will resemble a sine wave, crossing through zero during the straightaway and during the apex of the corner.

Yaw moments from the differential depend completely on the system used. Open diffs will provide very little contribution to net yaw moment as the torque applied to each wheel will be nearly equal, neglecting diff friction. Locked/spool diffs will transmit torque through load paths in parallel and thus applied torque is biased towards the tire with the max capacity. If a diff creates a significant destabilizing yaw moment then the driver must reduce front lateral control even more so towards an extreme of steering in the opposite direction. LSDs will operate in between those two regimes depending on the conditions and diff type/properties.

[WilO]

Thanks Tim and GSpeedR....

GSpeedR, I had a question about the longitudinal yaw moment; is this moment the result of unequal tractive force from the rear tires (or put another way, unequal drive force across the rear axle) due to the type of diff? This would seem to be the intuitive answer, but I wanted to be sure.

I appreciate you guys taking the time to respond; Tim alluded to the tendency for people to focus on load-transfer effects and grip characteristics, but I've been curious for a while now about the forces and moments acting on the vehicle CG, and their effect on stability and control.

And as GSpeedR touched upon parenthetically, steady state can be a fleeting condition, if it exists at all. Watching Ryan Briscoe negotiate The 90 at WGI during the first Indy test there was telling: he was (really) early on the throttle, and was fast. I found myself watching and enjoying the whole thing with Bob Snodgrass of Brumos, and some guy Bob kept calling Bert......Norbert Singer.

[Jersey Tom]

steady state can be a fleeting condition

"Steady state" can tell you a lot about dynamics.

[GSpeedR]

Thanks Tim and GSpeedR....

GSpeedR, I had a question about the longitudinal yaw moment; is this moment the result of unequal tractive force from the rear tires (or put another way, unequal drive force across the rear axle) due to the type of diff? This would seem to be the intuitive answer, but I wanted to be sure.

For the most part, yes. Passive differentials, when in a locked state, will distribute torque based upon the torque reactions of the tires. So the causal effect is typically the specific tire conditions (affected by load transfer, track surface, grip capacity, etc) rather than the differential type. My logic is that if tire properties and conditions were completely equal then torque distribution will be equal regardless of the diff type (open, spool, LSD, etc). This obviously ignores asymmetric diffs, which add yaw moments any time they are engaged.

And as GSpeedR touched upon parenthetically, steady state can be a fleeting condition, if it exists at all. Watching Ryan Briscoe negotiate The 90 at WGI during the first Indy test there was telling: he was (really) early on the throttle, and was fast. I found myself watching and enjoying the whole thing with Bob Snodgrass of Brumos, and some guy Bob kept calling Bert......Norbert Singer.

I'll agree with Jersey Tom that Steady-state properties are still useful, and are often used to estimate dynamic parameters. However, many people lose track of the assumptions they made (knowingly or not).