Ackerman Redux

[olefud]

Though the subject of Ackerman is rather involved, it may be useful to develop one aspect of a theory of Ackerman. With a fairly complete but limited rationale, perhaps this will develop an informed discussion.

Tires

Tire performance is often reported in a first classical three-axis format with, slip angle, cornering thrust and load plotted. I’m assuming that cornering thrust is measured parallel to the wheel axel. Also, though not universal, an important common tire characteristic is the ability of a more lightly loaded tire to maintain a flatter, near maximum cornering thrust over a larger slip angle range than a more heavily loaded tire..

Not often seen is a second similar graph with drag replacing cornering thrust. In this plot, the more heavily loaded tire develops greater drag that also increases with greater slip angle. To be clear, this second plot has not, to my knowledge, been published by tire companies and is inferred from observations.

Pointing Couple

To turn, a car must first point in a new direction. Of course, the car wants to travel in its established direction and exerts a centrifugal force attempting to maintain the original direction when forced to turn (accelerate) from an established direction. The turning centripetal force is developed by pointing the front tires to obtain the desired new direction thus developing the needed front tire slip angles and the thrust as referenced in the above-mentioned first plot.

Two phenomenons are involved with entering (turn in) and maintaining cornering. First, the car must overcome its own inertia to rotate around its own polar axis to point in the desired direction; and then it must generate a cornering thrust towards its instantaneous turn center. Thus, on turn in, a turning or pointing couple is developed to redirect the car in order to develop the required slip angles that, in turn, generate the tire thrust through the instantaneous turn center. However, the turn itself transfers weight from the inner to the outside tires. As stated in regard to the second graph, the outer tires develop greater drag than the inner tires. This unbalance results in a pointing couple tending to redirect the car out of the desired turn. Thus the car wants to away from the desired turn as a result of asymmetrical lesser inner and greater outer tire drag.

Ackerman

The undesirable pointing couple can be offset by generating offsetting tire drag at the inner steering tire by either pro or antiAckerman. The turning thrust of the lightly loaded inner tire is not materially diminished in view of the flat nature of such thrust over fairly broad slip angles.

There are a number of other important considerations involved in Ackerman, but the discussion gets involved. So this thread is (hopefully) specific to the pointing couple

[ubrben]

http://forums.autosport.com/index.php?s ... l=response

Happy reading - I started that thread and haven't got the energy to re-type :-p

Ben

[olefud]

http://forums.autosport.com/index.php?s ... l=response

Happy reading - I started that thread and haven't got the energy to re-type :-p

Ben

Can’t open, could you post a synopsis –particularly anything that differs.

[Tommy Cookers]

Didn't Colin Chapman introduce anti-Ackerman, though apparently to gain centripetally by having both steered wheels at optimum angles ?

Bends are tighter these days though.

[Caito]

This days they run with anti ackermann because maximum force slip angles increases as load increases.

[olefud]

This days they run with anti ackermann because maximum force slip angles increases as load increases.

JMO, but I suspect that with high aero downforce the tire drag is relatively equal side to side. Also, at high speed, the steering inputs are small. However, at almost-parked 180’s, the opposite is true. The cars really struggle at Monaco. That’s where large steering inputs and greater side to side weight transfer would generate “pointing” problems.

I didn’t touch that much on the centripetal situation since it gets to be a hairball fast. But I think the key is that the tires don’t freely assume an optimum slip angle since they’re connected by the chassis. Also, the instantaneous turn center isn’t where the axels point but perpendicular to the tire’s direction taking into account slip angle at each tire. Also, over/understeering shifts the instantaneous center, ect.

[GSpeedR]

The yaw moment contribution from steer can be quite significant in situations where the turn radius is of a similar order to the vehicle track-width and wheelbase (think autocross car). There are two distinct geometric effects (ignore the tire data for a moment):

1.) Geometrically, the yaw moment arm between a tire's resultant force (lateral force, drag, drive) and the vehicle CG is not equal once an axle is steered. The outside front moment arm is at a maximum with zero steering angle and it reduces to zero when the force vector points to the CG. The inside front will change with steering depending on the ratio of 1/2 track to 1/2 wheelbase (hence it will increase slightly for nearly all vehicles but never go to zero).

2.) As mentioned by olefud, the longitudinal component (in chassis coords) of the resultant tire force will provide yaw moments about the CG. The inside tire provides a moment into the turn and the outside front tire provides a stabilizing moment. This effect is distinct from slip angle drag, it is purely geometric caused by a wheel steered relative to the chassis. In tight turns, steer is much larger than slip angle. Ackermann will change the proportion of steer and thus the proportion of this longitudinal component.

So from these (simple) effects, we can generate very different yaw moments simply by our proportion of inside/outside wheel steering; the effects become huge in very tight turns. Olefud is certainly correct that the tire slip angles are dependent upon the overall dynamic state of the vehicle. With this in mind it is important to set steering/Ackermann such that it is possible for each tire to achieve its optimal slip angle...it is certainly possible to have a steering geometry that makes this impossible. It may be necessary to use less or more anti-ackermann than what the tire data suggests.

[WilO]

GSpeedR,
if I could, I'd give you a positive rating for the above post (amongst others). Thanks for that.

Wil

[GSpeedR]

GSpeedR,
if I could, I'd give you a positive rating for the above post (amongst others). Thanks for that.

Wil

That would only soften the blow when I start to rack up negatives.

[Jersey Tom]

Didnt we have an Ackermann discussion not long ago?

I still don't buy the slip drag yaw moment thing, as discussed earlier. But that's just me.

[olefud]

2.) As mentioned by olefud, the longitudinal component (in chassis coords) of the resultant tire force will provide yaw moments about the CG. The inside tire provides a moment into the turn and the outside front tire provides a stabilizing moment. This effect is distinct from slip angle drag, it is purely geometric caused by a wheel steered relative to the chassis. In tight turns, steer is much larger than slip angle. Ackermann will change the proportion of steer and thus the proportion of this longitudinal component.

So from these (simple) effects, we can generate very different yaw moments simply by our proportion of inside/outside wheel steering; the effects become huge in very tight turns. Olefud is certainly correct that the tire slip angles are dependent upon the overall dynamic state of the vehicle. With this in mind it is important to set steering/Ackermann such that it is possible for each tire to achieve its optimal slip angle...it is certainly possible to have a steering geometry that makes this impossible. It may be necessary to use less or more anti-ackermann than what the tire data suggests.

Beautifully put!! Rather than looking at the combined vector, I resolved the forces into the centripetal force vector through the through the instantaneous center and the orthogonal drag vector. The idea was to separate the centripetal tire thrust, which is instinctively appreciated, in order to develop the less recognized pointing –or, as you more accurately describe it, yaw moment. IMO much more performance is left on the table because a car won’t point into the desired than due to the centrifugal force overcoming the centripetal force –though maybe not so much in F-1.

As to each tire obtaining its optimum slip angle, this gets difficult with each tire running at a different and changing slip angle imposed by the other three tires. But I take your statement as relating to a relative rather than absolute optimum.

[GSpeedR]

Didnt we have an Ackermann discussion not long ago?

I still don't buy the slip drag yaw moment thing, as discussed earlier. But that's just me.

I agree with you in regard to toe settings, which is the discussion I think you are referring to. With high steer and small turn radii I believe the effects are large. You still obviously have to use the tire data, but many ignore the track geometry.

[Jersey Tom]

Ah true, good call. It was toe indeed.. my bad.

[olefud]

Didnt we have an Ackermann discussion not long ago?

I still don't buy the slip drag yaw moment thing, as discussed earlier. But that's just me.

We did (Anti-Ackerman Steering at Similar Topics, below), but we never developed the issue. Without setting forth the basis for various assumptions and beliefs, it’s hard to get to a meaningful discussion.

The weak point in my position is the magnitude of tire drag with load. I’ve never been able to get anything from a tire engineer on this. It’s either proprietary or they don’t know.

If I understand your view, it’s the same as that of Steve Smith in his book on the Stock Car Chassis, i.e., that neutral Ackerman vectors the cornering thrust through the instantaneous turn center. My problem with that is that slip angles determine the instantaneous center and, depending on under/oversteer, the instantaneous center wanders rather far from that of classical Ackerman. I don’t think you’re saying that there is no yaw couple effect, just that it’s not that important in the scheme of things