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

1. Originally Posted by BillCobb
Tim. A Datron optical sideslip sensor is the most widely used xducer in the U.S. field. I have seen the telltale Datron lamp beam on the pavement during races when such measurements are forbidden. Oops.
The newer models are infra-red... stealthy....

Regards, Ian

Originally Posted by Z
1. Do you include Yaw MoI, or are you as per the MMM?
2. What are the labels of your axes?
3. What formula did you use to calculate the stability index exactly (I suspect this should give the same as 3 above)?
My model is a time domain bicycle model. So there is yaw inertia . The tyres are linear and there are no tyre lag effects included at the moment. My prameters are:
mass = 335 at 49%F
wheelbase = 1.535
Izz = 150kgm^2

The formula for stability index was one I derived myself from other equations in RCVD:
SI = ( Nb(mV - Yr) + Nr x Yb ) / vYb

Where:
m = mass
V = velocity
Nb = Yaw moment due to sideslip
Nr = Yaw moment due to yawrate
Yb = lateral force due to sideslip
Yr = lateral force due to yawrate

Its possibly written in RCVD as well but I wanted to derive it to understand it better.

If anyone want the excel file its here. Its a bit of a mess but I think its error free now. Basically, column J is a time varying number between 0 and 1 which specifies the steering angle as a ratio of the nominal angle in cell B16. I set it to equal column F for a step steer, col G for a constant sine steer, col G for a sin sweep and col I for the demo corner.

https://skydrive.live.com/redir?resi...OJ8LzxvRWG934I

Originally Posted by Z
1. It seems that this MMM approach is quite simplified (nothing wrong with that!) in that it is a bicycle model in pseudo-steady-state cornering (err..., at very large radius). This means that any Yaw Moment (= Yaw Couple!!!) "N" acting on the car DOES NOT cause a Yaw acceleration. So no Yaw MoI is included in this model, since it does not matter for this type of analysis. So not really good for "looking at transients"...
I'd disagree that its at only showing cornering at a very large radius. What its showing is the behaviour when r = Ay/v which is steady state. However, the fact that the MMM diagram also represents untrimmed conditions (N =/= 0) means that it does have some transient information inside it.

In fact I've shown that even with very dynamic maneuvers, the CN-AY response is bounded by the MMM line.

Originally Posted by Z
3. Milliken's "stability index" seems to be dCN/dAY for FIXED front steer angle, but varying car side-slip angle (= beta), measured at CN = 0.
Yep, this is how I came up the SI calculation and also how I generated the MMM line. This is also the main reason why I have reservations about extracting a slope of N vs AY from track data because the steering angle isnt constant.

Originally Posted by Z
4. The whole MMM map, similar to your last picture of a frequency sweep, gives the maximum "performance envelope" of the car (given the limits of this simple model). The baseline "stability index" at steer-angle = 0, side-slip-angle = 0, CN = 0, and AY = 0, is a diagonal line with similar slope to the one you show, but passing through the origin. The "limit performance" of the car is indicated by the right-hand corner of the diamond shaped map. If this corner is below the AY-axis, then understeer at the limit. If above AY-axis, then oversteer at the limit.
I touched on this before, but my linear model has no limits. I just set the steering angle so it reaches 1g in steady state. I'm not sure the plot made from the frequency response is comparable to the MMM diagram (but at least it looks cool). I think the best way to quantify stabiliy from this simulation is by post processing the data like Bill suggested.

Originally Posted by Z
Finally, I remind anyone doing this MMM sort of analysis that its pseudo-static nature, with no account of Yaw MoI, gives it VERY LIMITED APPLICABILITY in FSAE conditions (which are mostly "transients").
I think it gives quite a lot of information about the transient. Ok, not the full picture but I've at least shown that it has some relationship to a real (ok simulated) transient response.

Tim

PS Are there really no buttons to include links or pictures in this forum?? I might be fluent with Matlab, but I had to login to another forum to remember the BBcode to include a link!

3. Originally Posted by ChassisSim
Moop - I would strongly suggest you double check your numbers. That little equation I put forward to approximate Yaw moment I've seen in use on many formula from V8 Supercars, GP2 and F3. I have lost count of the number of race engineers I know who have used this in anger as a sanity check to tell them what the car is doing . Granted this would break down in extreme cases of structural flexibility but if your at this point your throwing out the car anyway so it's a moot point.
Like I said, it probably works well for bigger cars where most of the mass is located between the wheels, but this is not the case for an FSAE car.

Originally Posted by BillCobb
The goal of your test session would be to measure the tangent speed for every change in trial settings. The highest number speed is the best value.
Is the goal of reducing tangent speed/rear cornering compliance to shorten the yaw rate/lateral acceleration response time or what? Is there a point at which it would maybe be not beneficial to have the car responding faster(say, if the driver couldn't handle it?)?

Also, I thought that cornering compliances were driven by tire stiffnesses, chassis/suspension compliances and geometric steer. Aside from maybe roll steer/camber, what would you be changing at the track that would impact the rear cornering compliance?

Originally Posted by BillCobb
I believe I pointed out earlier that the FFT of Lateral Acceleration - Yaw Velocity phase information ( I call it the "RAY function") graphed vs. frequency will lie on a curve whose initial slope can also produce the vehicle's rear cornering compliance (rear axle axle sideslip angle) metric. Since there may be scale and other instruments snafus in your D.A. box, its pretty hard to screw up the time base, so this phase metric will be pretty freakin' accurate.

Now all you need is a constant radius portion of the track or test area and and a driver able to run a reasonable speed sweep through it. BTW: this is an I.S.O. test procedure. The Math functions for it are printed in the I.S.O. document as I recall.
I thought that this was measured as the difference between the slopes of phase vs frequency at zero frequency for lateral acceleration by steer and yaw rate by steer? What's the FFT for? Unless you're using that to get phase vs frequency instead of calculating the transfer functions from the PSDs and CSDs?

Also, I thought this metric was usually measured in a steering frequency response test? Have you ever seen it attempted with a driver instead of a steering robot? I'm not sure how confident I am in my driver to produce a consistent sinusoid at a given frequency, although I guess I haven't given him a chance yet.

4. Tim

regarding the feasibility of Stability index for on-track studies (data engineer typical work, race engineer as well in many teams), i think it doesn't work as it is.

The assumptions made to produce a MMM diagram make them absolutely fantastic in a design phase and probably also for setup investigations, but as you said, since driver inputs are not constant (above all steering) and are sometimes evolving quite quickly, it could be tricky to apply them for a track side study.

To me, the same is true also for the SI itself. I have tried to calculate it with math channels, but it doesn't show many useful info. To use a X-Y plot with lateral acceleration and yaw acceleration is already better, but still you have to be very careful with the track section you select and it is also difficult to extract a precise number to quantify any tendency.

I normally looked to a slightly modified version of what Danny would call Actual Steer vs Ideal Steer comparison, normalized vs lateral acceleration. I find it useful to quantify understeering tendencies, above all in corner-center (quasi steady state) conditions and it is very repeatable.
It falls down, of course, in corner entry, where it really doesn't give many information about what the car is really doing (or at least less info than in corner center)

I have seen that some info about stability in transients could come anyway from the yaw rate channel itself, which is anyway the one you would use to calculate yaw acceleration. Actually, i guess you could potentially compare the actual yaw rate sensor reading vs an ideal yaw rate value that you could calculate through the other channels you have (see speed, lateral G), above all if you use GPS (although the GPS receivers i have used were a bit slow and they normally showed some delay against the other "in-car measured" channels).

If your measured yaw rate is bigger (at least in its absolute value) than the calculated one, then you should be in an oversteering situation.

Although this method doesn't tell much about the Yaw Moment it could still helps to quantify car stability in transients, at least when used together with the ideal steer vs actual steer one.

I will try to look at it and post something, if it comes out to be a feasible way.

5. Originally Posted by Silente

I have seen that some info about stability in transients could come anyway from the yaw rate channel itself, which is anyway the one you would use to calculate yaw acceleration. Actually, i guess you could potentially compare the actual yaw rate sensor reading vs an ideal yaw rate value that you could calculate through the other channels you have (see speed, lateral G), above all if you use GPS (although the GPS receivers i have used were a bit slow and they normally showed some delay against the other "in-car measured" channels).

If your measured yaw rate is bigger (at least in its absolute value) than the calculated one, then you should be in an oversteering situation.
I think that using yawrate is the right way to go because it contains a component of sideslip velocity.

Slightly off topic, but in my calcs for natural frequency and yaw damping ratio seem to indicate that an FSAE car is highly damped and has a very low natural frequency. Not a good combo for a car that needs a very good yawresponse. This was also backed up in my bicycle model where I saw the yawrate didnt follow the typical magnitude response where from 0Hz it increases in magnitude until it reaches a natural frequency somewhere in the range of 1-2Hz, and then drops down again.

I'd be interested to know if anyone else can confirm this behaviour or if its an error somewhere in my working. I suspect it could be that the cornering stiffness of these tyres (Hoosiers in my case) are in the wrong range for cars of this mass and wheelbase.

If its true, I think there could be some scope to design in some instability to the car to at least give the yaw response a bit of a boost.

6. ## Transfer Function Generation and Appearence.

Controls Engineers (and Vehicle Dynamics fishing addons recognize that it is NOT necessary to use a swept frequency steer input (often called a 'chirp') to generate adequate transfer functions for relatively simple systems such as a vehicle. All that is needed is a pulse of duration width Tf/2, where Tf is the total time response from input to settling out time. The pulse does not have to be perfect, just sufficient to cover the range of interest in the transfer function and its coherence for multiple run segments. The only limitation in this technique is that the system is stationary (That means time invariant). It does NOT mean it must be linear, just consistent with parts and components whose properties do not change over the measurement timespan (like temperature, pressure, wear state and figmosity.

Also, a good FR chirp need not be accomplished with a robot. A human driver properly trained in the methodology can easily produce excellent chirp steer inputs from 0 to 4 Hz if the steering effort is light and the required steer angle amplitude is not too high. A good crutch to train a driver is the use of a CD player with a chirp tone MPEG file. I produced several versions for our test drivers using Matlab. After a few runs with the CD, they no longer need the crutch.

One more thing: As is often the case, a FSAE car can be very low in understeer which is OK for the limited speed range of the tasks, unless it leads to loss of control and major embarrassment(s) involving loss of bodily fluids. Checking your model for a designed in level of understeer or oversteer is one of the first things a design engineer must do. Most of the time, models do not include the elastic chassis compliances in steer or camber either because they can't believe they could be possible or they have no idea their magnitude. That's the eye opening feature of a K&C test. As a result, the low understeer models produce nearly first order FR transfer functions while the road tests produce whooping amounts of peak to steady state yawrate response.

I point out the pulse steer inputs because a 'feeling' driver makes use of this style to read the steered tires aligning moment response to this input type. And driving by moment control is a lot more successful than driving by displacement control IMHO.

7. Hey Guys,

Many thanks for contributing to this excellent discussion on the stability index. A colleague of mine was gracious enough to provide me with some race data for a Ford GT-40 with accelerometers on both axles of the car. This will be the subject of my next Racecar Engineering article. Suffice to say the methods I outlined have for calculating the stability index worked very well in this case. However I will post this in the next couple of days since it deserves a proper treatment and I have some pressing development work I need to be getting on with. There are some big things coming in the pipeline for ChassisSim but I'll let you know about this at the appropriate time.

In other news for those of you in Europe if you want to attend the simulation bootcamp on Nov 20 email me know at info@chassissim.com. Places are starting to fill fast.

In the meantime this is an oldie but a goodie - modern approaches to tyre modelling.

http://www.chassissim.com/blog/chass...tyre-modelling

Enjoy and I'll post that stability index article as soon as I can.

All the Best

Danny Nowlan
Director
ChassisSim Technology

8. Hey Guys,

Here's the latest episode of Dan's Vehicle Dynamics corner outlining what I found with those accelerometers fitted to both axles of the GT-40 racecar.

http://www.chassissim.com/blog/chass...accelerometers

I won't claim this is the last word on the stability index but there is some really good food for thought. I learned a lot in the process and I hope you get something out of it.

Also for those of you in Europe, if you want to come to the simulation bootcamp contact me soon. Places are filling very fast. email at info@chassissim.com . Otherwise if you are based in the U.S I'm looking forward to seeing you at Booth 137 and our Lap time simulation 101 seminars at PRI in Indianapolis.

All the Best

Danny Nowlan
Director
ChassisSim Technologies

9. Hey Guys,

I'm about to get on a plane for Europe and the U.S for tradeshow and seminar commitments. Here's a reminder of where to catch us.

http://www.chassissim.com/blog/chass...rdecember-2013

I look forward to meeting quite a few of you face to face.

All the Best

Danny Nowlan
Director
ChassisSim Technologies

10. Hey Guys,

Sorry for the lack of contact recently. I've had my hands full travelling in Europe and the U.S on business. Here's a quick summary of what we have been up to,

http://www.chassissim.com/blog/chass...es-and-article

Also I've seen a lot of traffic recently on the magic number and lateral load transfer. I've enclosed an old race car article where tyre loads are derived from so I think that will be a great reference for everyone.

Looking forward to meeting a few of year at PRI in Indianapolis on Dec 12-14.

All the Best

Danny Nowlan
Director
ChassisSim Technologies