Quote from jtw62074 :

Anyway, for sure you can't tell one bit of difference in the handling whether the tires in VRC run at 600Hz or 30000Hz, other than the frame rate drops a bunch. Which is really more accurate? I couldn't tell ya and am not concerned with it. I've changed the frequency of VRC wildly during testing, not told anyone about the changes, and nobody ever noticed a difference, so I'm not too worried about it although it's probably a valid point, however minor in this case.

when thinking about deformation of rubber i guess its natural to assume that the eigenfrequency of it will be well below a 100 Hz, and also that the frequency response of it will be reasonably close to 0 above a 100 Hz (at least that what gut feeling tells me)
therefore a model that runs at about 200 Hz should be able to yield accurate results

however there are two problems with using a sampling frequency that low

1) the difference equation that you use for iteration
most iterations are simply described by a function that only uses the results of the previous step (ie u(n) = f(u(n-1)) ) in contrast to one which uses all previous results or a large but finite set of previous results (u(n) = f(u(-/inf),...,u(n-1)) or u(n) = f(u(n-N),...,u(n-1)) )
in essence this describes filtering (interpolating) with a 2 tap impulse response which itself has a very large spectrum so youll need a high oversampling factor to get accurate results
(frankly ive never seen this approach of describing the effects of iterative models in literature before but im rather confident that at least the basic idea behind my explaination is correct)

2) excitation of the model
obviously if you ever want accurate results your update frequency will have to be large enough to capture the highest frequency in the process that excites your model (mainly the bumps in the road for tyres)
with regard to this id predict that your fractal model will need a significantly higher frequency to either a) produce accurate results at all or b) be beneficial

How can you reach that conclusion while having no idea what the fractal model entails or what specifically it would be used for?

well i was just kind of assuming that you woud use it to model the contact between road and rubber with the fractal feeding into the tyre model in some form or another

That's still way too vague of a description/idea to come to any conclusions about sampling rates. What are the outputs of the function? What exactly does it do? What if it's a closed form system that is not time dependent? You can't really get all into a discussion at that level without breaking out the math and getting into the nitty gritty ins and outs of the whole system. As I said before, this is just a bunch of handwaving really and not meaningful at this level at all...

i believe its mor meaningful than you might think
i assume you lack expierience with frequency domain solutions to really appreciate the meaning and ramifications of this trail of thought

btw on a side note to me the polynomial order of the error in iterative processes confirms that my trail of thought is correct

This topic has never come up when discussing vehicle dynamics modelling with other people that also do this professionally for a living. And nope, I'm not familiar with frequency domain solutions so I may indeed be missing your line of thinking. I've just got a vague idea of what you're talking about.

Anyway, I'll continue to wait for a specific vehicle modelling calculation as an illustration of your point to show us all what we're missing.

Quote from jtw62074 :

Anyway, I'll continue to wait for a specific vehicle modelling calculation as an illustration of your point to show us all what we're missing.

i havent got one simply because i have never worked with such models

what im stating is just the very basics of what happens when you go from differential equations to difference equations

Exactly. It's just a bunch of handwaving at this point.

How about a basic physics math example then? A falling object or something. How does frequency domain and all that fit into the simulated motion of a falling ball or something equally simple?

Quote from jtw62074 :

Exactly. It's just a bunch of handwaving at this point.

seriously this is starting to tick me off just because you dont know anything about it and cant instantly recognise where im comming from without any knowledge of your own in the field doestn change anything on the fact that its the truth about discrete time

ill see what i can come up with

That's fine. A Ph.D. physicist friend of mine just read this thread and had himself a good laugh, and agreed with what I've been saying. This isn't the first time a student has started a discussion of this nature in the LFS or RSC forums and insisted to know more than everybody else about something they've never done Maybe what you're suggesting is simply that if you don't keep the time step small enough the system will blow up. That doesn't take any analysis to figure out though and can be explained in much simpler terms.

Anyway, we'll see what you come up with

I think he is saying that increasing the frequency will not always incease the accuracy of the simulation. Some algorithms will just continue to oscillate instead of converging further towards the correct value. I'm sure you agree with this (Todd) so I don't really see what there is to argue about.

Maybe Shotglass wanted to know an absolute value for a max frequency that you would need to model a tyre correctly, which I think can't be answered without knowing the ins and outs of the model in question.

Quote from jtw62074 :

Maybe what you're suggesting is simply that if you don't keep the time step small enough the system will blow up. That doesn't take any analysis to figure out though and can be explained in much simpler terms.

not accurately ... with systemtheory you can exactly predict how the model will behave for any given frequency

Quote :

Anyway, we'll see what you come up with

have you got a simple model with the continous time differential euqation and its discretization that i could work with ?

Quote from J.B. :

Some algorithms will just continue to oscillate instead of converging further towards the correct value.

nope ... limit cycles is what loopingz was talking about ... the effects im refering to occur without limiting the word length

Quote from student :

I agree, jtw62074, bunch of handwaving. Shotglass either doesnt know what he is talking about or he is bad at explaining things.

let me gues ... kid ?

Hmm, I understand what loopingz means in his example, but I can't uderstand what Shotglass exactly means. Can you give as really simple example of it?

Quote from Shotglass :

nope ... limit cycles is what loopingz was talking about ... the effects im refering to occur without limiting the word length

OK, so I wasn't quite right there. But we are talking about numerical stability in solving differential equations aren't we? Or is this something completely unrelated?

unrelated ... this is about aliasing

Quote from Shotglass :

unrelated ... this is about aliasing

Are you suggesting that for the simulation to be less noisy, the tyre compound should be modelled using a bandlimited algorithm ?

Do you think that aliasing noise would have a noticable effect on the handling of a car in a game/sim, or are we just talking theoretically here?

Quote from col :

Are you suggesting that for the simulation to be less noisy, the tyre compound should be modelled using a bandlimited algorithm ?

no you see any discrete time algorithm is strictly bandlimited

Quote :

Do you think that aliasing noise would have a noticable effect on the handling of a car in a game/sim, or are we just talking theoretically here?

its a very real effect ... for example the whole collision problem can be described by a not band limited excitation (like say a steep curb) aliasing up to infinity (at least if the phase happens to be ill conditioned which it is most of the time) and then feeding into the cars model ... boom

Quote from Shotglass :

no you see any discrete time algorithm is strictly bandlimited

my understanding is that any discreet time algorithm will generate aliasing noise unless it is bandlimited (except when the signal it is generating has a frequency of 'sample_rate/n' where n is a positive integer)

Quote from Shotglass :

its a very real effect ... for example the whole collision problem can be described by a not band limited excitation (like say a steep curb) aliasing up to infinity (at least if the phase happens to be ill conditioned which it is most of the time) and then feeding into the cars model ... boom

seems to me that you just contradicted yourself - the collision detection is a discreet time process, which you have just stated must be strictly bandlimited by definition ?!

btw, don't take these comments the wrong way . I think that you are on the right track. And also believe that you know considerably more than i do on the subject.

col

Quote from col :

my understanding is that any discreet time algorithm will generate aliasing noise unless it is bandlimited

not quite
you see the alias happens when you go from continuous time to discrete time wit a sample rate thats too low (lower than twice the band limit of the process your simulating)

Quote :

except when the signal it is generating has a frequency of 'sample_rate/n' where n is a positive integer

hmmm yes and no

Quote :

seems to me that you just contradicted yourself - the collision detection is a discreet time process, which you have just stated must be strictly bandlimited by definition ?!

yes it is ... but the imput you feed into the collision detection (namely the road surface) is not band limited causing severe aliasing when you sample it

Quote from Shotglass :

...
yes it is ... but the imput you feed into the collision detection (namely the road surface) is not band limited causing severe aliasing when you sample it

right I understand what you mean, so, rather than bandlimiting all the track data (ouch), and the fractal texture generator, build a collision algorithm that uses some sort of bandlimited interpolation filter. Sounds like mucho cpu though.

to my knowledge a way to get around this is a sanity check that generates sampling spots between the usual ones in such cases