5 replies to this topic

[Ben]

I mentioned on a thread many years ago:

http://forums.autosp...t=ground effect

The idea of using the gradient of the aero map as an additional stiffness in a ride analysis. Now it looks like I might have been on to something:

http://www.mscsoftwa...on_week4602.pdf

This paper shows a ride model specifically modelled using a spring between the sprung mass and ground representing the aerodynamics. They also have "anti-damping".

Now as I mentioned I assume that the aero spring is the gradient of the aero map - i.e. if for a given attitude I generate 1000N downforce and at 1mm higher I generate 1500N downforce then my aero stiffness is 500N/1mm i.e 500N/mm. I'm not saying that's right - but that's how I'd start defining that value.

The aero damping (or anti-damping apparently) is a bit more confusing - I can't see how that can be defined from a steady-state aero map.

Any thoughts?

Ben

[murpia]

Hi Ben,

I can see what they're getting at, that the aero behaviour introduces a positive feedback effect in the ride dynamics. Representing it in the diagram as a spring seems a bit misleading, the force-displacement graph would not be that of a spring... Maybe a magnet symbol would be better? As the distance to the ground decreases the force increases.

It looks like they're treating the front and axle rear ride height / aero force relationships as independent. I'm not sure about that assumption...

Aerodynamic pitch sensitivity and the associated 'porpoising' car instability is a tricky subject. Probably has as much to do with vortex shedding and the like as vehicle ride dynamics.

Still, it could be that after they have validated the model against track data, it proved to be a better model with these terms included the way they have done.

Regards, Ian

[DOHC]

Originally posted by murpia
It looks like they're treating the front and axle rear ride height / aero force relationships as independent. I'm not sure about that assumption...

Aerodynamic pitch sensitivity and the associated 'porpoising' car instability is a tricky subject. Probably has as much to do with vortex shedding and the like as vehicle ride dynamics.

The way I understand their model (p 15 in the pdf presentation) is that front and rear are not treated as independent. Front and rear are coupled via the chassis in an equation system that represents the interaction. (That's like when you have "independent" suspensions, there will still always be an interaction as long as the wheels are attached to the same car.;) )

Anyway, as downforce depends on ride height as well as on rake, two state variables (minimum) are necessary to model the aero force as a function of the ride state.

Modelling downforce in steady state as a function of ride height as a linear spring with a (speed-dependent) spring constant appears sound as long as downforce is proportional to ride height. Dependence on rake is obviously much more complicated.

Accounting for dynamics (rather than for steady state) is another complication, and it's not transparent to me how the "aero damping" characteristics are obtained from real aero data -- using 2nd order differential equations in a model with a finite number of degrees of freedom implies "lumping" real aero forces into the model.

As the model is linear throughout, it would only be valid for rather small displacements. On the other hand, they aim at a frequency analysis based on the conventional approach of using linear transfer functions, so they have to, for mathematical reasons, to stick to a linear model.

I see two limitations with the model: 1) linearity basically implies that displacements must be small (towards the end they mention nonlinear spring/damper characteristics in the suspension); 2) the model is basically a steady state model, so its relevance when dynamics become significant is not so clear.

[Ben]

Originally posted by DOHC




Anyway, as downforce depends on ride height as well as on rake, two state variables (minimum) are necessary to model the aero force as a function of the ride state.

Modelling downforce in steady state as a function of ride height as a linear spring with a (speed-dependent) spring constant appears sound as long as downforce is proportional to ride height. Dependence on rake is obviously much more complicated.

If a manufacturer supplies aero data it's generally got an overall downforce map vs. front and rear ride height and a balance map vs. front and rear ride height - this would allow you to create two maps - front and rear ride height both vs front and rear ride height. I think the Audi model is taking the gradient of those maps and using it as the "aero spring rate" in the model they present.

Ben

[murpia]

Originally posted by DOHC
The way I understand their model (p 15 in the pdf presentation) is that front and rear are not treated as independent. Front and rear are coupled via the chassis in an equation system that represents the interaction. (That's like when you have "independent" suspensions, there will still always be an interaction as long as the wheels are attached to the same car.;) )

Anyway, as downforce depends on ride height as well as on rake, two state variables (minimum) are necessary to model the aero force as a function of the ride state.

Just to clarify: What I meant was that on that P15 diagram the CLV and CLH 'springs' look to me like independent components of the model. I could not see evidence within that diagram or the text that they relate front or rear downforce to anything other than single axle ride-heights. As we all agree you need either front and rear rideheights or a rideheight plus rake combination to get a true axle downforce (for most racecars anyway). But maybe not the aero map gradient? It's possible that in the Audi's case this is independent front and rear, but I would not make that generalisation without evidence.

The ride model clearly couples the axles via the chassis, as it should.

Regards, Ian

[DOHC]

Originally posted by murpia

Just to clarify: What I meant was that on that P15 diagram the CLV and CLH 'springs' look to me like independent components of the model. I could not see evidence within that diagram or the text that they relate front or rear downforce to anything other than single axle ride-heights.

I see what you mean. But I think there is still a coupling. In fact, it appears to me that the model contains redundant (or "auxiliary") variables, so that there are algebraic relations between some of the variables. This is often done to simplify the modelling and the programming.

For simplicity, if we suppose that the car runs on a perfectly flat track, then we can put zBV=zBH=0, which implies that front steady state downforce is CLV*(zAV-zAVref) and rear is CLH*(zAH-zAHref). But from chassis geometry (assuming no chassis flex) we have

zAV = z + lV*sin(theta)
zAH = z - lH*sin(theta),

so if the actual variables used in the model are z ("nominal ride height") and theta ("rake"), then you have to insert the expressions above into the downforce expressions. Then you see that both front and rear downforce only depend on nominal ride height z and rake theta as follows:

Front steady state downforce = CLV*(z + lV*sin(theta) - zAVref)
Rear steady state downforce = CLH*(z - lH*sin(theta) - zAHref)

(Give or take a few minus signs; I'm not sure what their sign convention is -- for example, theta seems to be positive going the "wrong" way compared to mathematical standards, but I have used their sign in the equations above.)