# Thread: A new free vehicle dynamics resource - Dan's Vehicle Dynamics Corner

1. Hi Danny,

You up for a discussion about the stability index you mentioned in your video blog? Just to clarify, I'm speaking of the equation used by yourself and Milliken:
SI = (dN/aAy)(1/mL)

I've been stuffing about with the stability index calculations with a mix of FSAE and non FSAE data in both simulation and from track data. I thought it would be appropriate to discuss here and hopefully it can develop into a useful discussion for everyone.

So... Milliken (if I understand correctly) describes the SI as a representation of the static stability moment (dN/dß)ß and the yaw damping moment (N_r x r) for a constant control moment (dN/dδ)δ.

Myself and another aquaintance are trying to get our heads around two things:

1. Theory: how applicable is this linear, steady state calculation to non linear/transient track data
2. Practice: how do you filter/calculate this without ending up with nothing but noise?

On my first point, I'm a bit skeptical about how valid it is to calculate dN/dAy from track data considering that its definition comes from a condition of constant steering angle (not to mention trimmed steady state).

For me, the fact that the driver is continuously correcting the steering on track means that the yaw acceleration (and therefore yaw torque) is not a function only of the static stability moment and yaw damping moment but also the control moment. In fact I'd guess that most of the yaw dynamics of the car in a turn are coming from the driver's steering inputs rather than the yaw damping and static stability moment.

My second point is about implementing this on track data. With dAy in the denominator of the formula, the resulting signal is constantly going to +-infinity. When I've put the first equation above into my track data, the result looks like white noise. I don't want to filter out high frequencies because I feel that these higher frequency (ca. 10Hz) movements are exactly what we are trying to measure. Am I going about this the right way?

I hope I've explained myself properly. Would be interested to hear anyone elses comments on this...

T

PS, this forum needs an equation editor!!

2. ## A simple and elegant method for you to try.

In deference to Doug Milliken's observation on my presence here, I will say that the best answer for you has to do with holding circus tents up and also famous Japanese WWII warplanes...

I will explain once all the verbosity is infiltrated...

3. i am totally with Tim...

I tried to take out the same channels both on sim and real data, but no success on really using it for stability evaluation. Sometimes, a part from the noise mentioned by Tim (which makes very difficult to use this metrics), i also noticed that results from SI calculations seem to be contrary to what is shown by comparing "actual Steering angle" to "Ideal Steering angle".

4. Hey Guys,

It's fantastic to see a genuine high level technical discussion on this forum. Tim many thanks for kicking this off.

Firstly I think it would be wise to step back a bit and discuss where the stability index comes from. The stability index has it's origins in Longitudinal aircraft stability analysis. Aeronautical engineers came up with something called the static margin. What this represents is a non dimensionalised moment arm between the centre of aerodynamic forces and where the centre of gravity is. Effectively the highlights are,

*When the static margin is less than 0 the aircraft is stable. You give it a disturbance be it a gust or control input and it will stabilise itself.
*When the static margin is 0 the aircraft is Neutral. That is given an input it will just keep on going.
*When the static margin is greater than 0 the aircraft is unstable. That is you give it an input and it will swap ends.

Also the magnitude of this number gives you a direct measure of the ability of the pilot. Bottomline the closer they get to 0 the better the pilot is. Mathematically the definition of this is,

SM = (dCm/dCL)/mean chord

Effectively it's measuring the change in ptich moment vs change in lift co-efficient.

The motorsport incarnation of this is,

SI = (dN/day)/mt*wb

The derivation for this is covered in both Milliken's book and my book the Dynamics of the RaceCar. I actually dedicated a whole chapter to this. As per the aerospace definition we are measuring the change in Moment about the centre of gravity as a function of Side force. A very effective way of measuring this is lateral acceleration. Tim I trust this resolves your question because what we are measuring here is not just a control slop for a given input. The Stability Index is a leaving breathing animal that is a direct measure of the stability or otherwise of the race car.

Let me show you a little party trick that will measure the stability index. Tim and Silente should answer your question. What you need to do is simply put an x-y plot of Yaw Moment vs lateral acceleration. Yaw moment is in N, lateral acceleration in g. To instrument this to your car is easy. You put lateral accelerometers on the front and rear axles and the Yaw Moment you are plotting becomes,

N = wdf*mt*ay_front*a - wdr*mt*ay_rear*b

We have

N = Yaw moment (Nm)
wdf = Weight distribution at the front (%age/100)
ay_front = Front lateral acceleration (g)
wdr = Weight distribution at the front (%age/100)
ay_rear = Rear lateral acceleration (g)
a = moment arm from front axle to c.g (m)
b = moment arm from rear axle to c.g (m)

Here's the trick, make the vertical axes Yaw Moment (N) and the horizontal axis lateral acceleration. Filter the signals and the slope is the stability index. On this one you might have to do some work. Just don't do a curve fit. Look at what it is telling you. Silente in answer to your question I gave an analysis in a racecar article and my book comparing actual vs neutral steer and correlating that to the stability index.

I trust this gets you all thinking. By all means keep the comments and questions rolling in, but I'll give you all the heads up about something. At the end of the year you can ask me this in person. If your in Europe I'm giving a simulation bootcamp on Nov 20 at the ORECA factory in Signes France. If your in the U.S We'll be at PRI booth no 137 on Dec 12-14 in Indianapolis and I'm given a series of free seminars at the show.

I trust this has given everyone some good food for thought.

All the Best

Danny Nowlan
Director
ChassisSim Technologies

5. Hi Danny, thanks a lot for the answer. I will need a bit of time to digest the theoretical part...

On the practical side, I've messed around with some track data and its looks a bit more useable when I represent it like you said. Still not perfect but I will experiment with the filtering when I get some spare time this week.

I have seen already that long steady state corners will give you a trendline gradient of zero because you have a lot of points in the steady region and not so many in the transient region. I'm beginning to think maybe the useful information here is only in the transient regions.

I will come back when I've got something useful to share.

Tim

6. Tim,

Good hunting my friend. One thing I will say it is best used as a transient tool which is what it was set up for in the first place.

Good Luck!

Danny Nowlan
Director
ChassisSim Technologies

7. Originally Posted by Tim.Wright
In fact I'd guess that most of the yaw dynamics of the [FSAE] car in a turn are coming from the driver's steering inputs rather than the yaw damping and static stability moment.
Tim,

Not enough time for details, but I agree with your above quote. With the low speeds and constant changes of direction in FSAE I reckon a car could be highly UNstable, but nevertheless be quite fast around a typical FSAE track.

I reckon all 2nd year+ teams should be testing these sorts of things with their previous year's car. Take ~50 kg of barbell weights and bolt either to nose of car, or under driver's seat, or to rear jacking bar (or rearward extension). Bolt to car at same height, so same total mass and same CG height, but different "Static Margin". Then do some hot laps to find out just how important is a stable, or neutral, SM. Or not...?

(Splitting the 50 kg so it is half-at-front + half-at-rear (for bigger Yaw MoI), or all under driver's seat (for original Y MoI), and then some hot laps gives an indication of how important is a low Y MoI. Or not...?)

Z

8. Hey Guys,

Just some updates on what is going on with our seminars.

Firstly the bootcamp in Europe on Wednesday Nov 20, will be at the ORECA factory in Signes France,

http://www.chassissim.com/blog/chass...-oreca-factory

Also for those of you who are based in the U.S we have some format changes coming to the Lap Time Simulation 101 seminar at PRI. You can find out the details here,

http://www.chassissim.com/blog/chass...01-at-pri-2013

Also any sensible/in-depth questions about the Stability Index keep them coming in. Given the interest this has generated I might run a mini seminar about this at the Booth. We are at Booth no 137. However we'll see how busy we get!

All the Best

Danny Nowlan
Director
ChassisSim Technologies

9. I intend to keep the discussion going. I'm trying to get a hold of some data that I'm allowed to share to use in the discussion.

Tim

10. Originally Posted by ChassisSim
Let me show you a little party trick that will measure the stability index. Tim and Silente should answer your question. What you need to do is simply put an x-y plot of Yaw Moment vs lateral acceleration. Yaw moment is in N, lateral acceleration in g. To instrument this to your car is easy. You put lateral accelerometers on the front and rear axles and the Yaw Moment you are plotting becomes,

N = wdf*mt*ay_front*a - wdr*mt*ay_rear*b
I sat down and worked out that calculating the yaw moment on the car this way is equivalent to calculating the yaw acceleration and assuming the car's yaw inertia is total mass * a * b. This may be a reasonable yaw inertia estimate for a production car or cars where most of the mass is sitting far from the CG and in between the wheels. But it's not a very good estimate for an FSAE car, where the two heaviest parts of the car, the driver and the engine, are sitting right next to the CG.

To check this, I dug up a published FSAE car yaw inertia and also calculated the yaw inertia with this estimate. The estimate was nearly twice as big as the published value.