Plotting Cn-Cy and Cn-Ay Graphs.

[apoorv]

Hello this is Devansh from Srm university,chennai. I am working on vehicle dynamics for our 2nd vehicle for FSAE 2016. We have been plotting force moment diagrams for our vehicle. We first created Cn-Cy diagram on Matlab in which for each delta and beta ranging from -5 to 5 in steps of 0.5 we iterated Ay based on slip angles and verticle loads (considering lateral load transfer with new Ay for each iteration). All the Fy data was imported from pacejka tire model.In Cn-Cy Ax=0.2

Then we plotted Cn-Ay in which we first assumed intial yaw rate and iterated yaw rate along with Ay similar to Cn-Cy but this time slip angles were calculated for each iteration(as yaw rate varies).

The Cn-Ay and Cn-Cy graphs looked almost similar. The constant steer lines of Cn-Ay are intersecting 0 yaw moment(Cn=0) line almost at max acceleration. Which makes this graph similar to Cn-Cy.Even when I change my CG location close to front axle in both the graphs the lines now intersect Cn=o before max Acc. which again makes both the graphs look similar.

I guess my understanding of the difference between Cn-Cy and Cn-Ay is not fully clear. In RCVD its mentioned that the most significant difference between Cn-Cy diagrams and Cn-Ay diagrams is that in Cn-Cy the total lateral force generated is not assumed to resist the acceleration of the vehicle mass. Instead, some portion could be used to resist an outside disturbance. whereas in Cn-Ay all lateral force created by the tires is used to hold the vehicle in steady state equilibrium without any outside disturbances.

Does this difference b/w the 2 diagrams change the way in which Ay iterations are done? Am I missing something or this behaviour of graph is acceptable?

I have attached respective images of the plotted graphs778779780781

[Adam Farabaugh]

The difference:

CN-Ay
- all lateral force goes to lateral acceleration
- diagrams are typically drawn at constant velocity
- thus since velocity is known, and lateral acceleration is known, radius is known
- note that instantaneous radius varies across the plot
- can also do this with constant yaw rate

CN-Cy
- some lateral force may not go to lateral acceleration
- for this reason it's possible to generate the plot at a constant radius
- this diagram should be asymmetric, since negative lateral acceleration on a positive radius is different than positive lateral acceleration on a positive radius


Looks like you have some problems, your CN-Ay is not totally symmetric, also the zero beta/delta point is not on the origin for some of your plots. Is the car setup symmetric?

[Claude Rouelle]

Devansh,

This is not answering your question but here is an observation: there are no legend on your graphs so we do not know what the values of the beta and delta isolines of your graphs are.

In any case, as Adam just mentioned, it seems that the isolines of beta = 0 and delta = 0 are not crossing at the graph origin of coordinates CN = 0 and Ay = 0

If you car is symmetrical and you are going straight (beta = 0) and you do not have any steering input (delta = 0) you can't have any yaw moment or any yaw acceleration.

When students try to create a yaw moment Vs Lateral acceleration graph 99% of them face this issue. If you want a hint, have a look at your tire and car system of coordinates.... You cannot look the whole car and the tires in 2 different systems of coordinates.

[apoorv]

Sir, we followed your advice and multiplied the lateral forces(Fy) at the rear by cosine of the body slip angle(beta) and then multiplied the front tire lateral forces by both the cosine of steer angles(delta) and cosine of body slip angles (beta) to change them in velocity frame coordinates which is aligned at Beta to the vehicle axis system.

So my "Fynew at rear" = Fy*cos(beta) and "Fynew at front" = Fy*cos(beta)*cos(delta).

But still my Cn-Ay graph look similar to the previous graphs as the constant Beta=0 and constant delta=0 lines are not intersecting at the origin. In the attachment below Z=0 is the constant beta line intersecting the constant steer line = 0 at Cn=0 and Ay around 0.24(both are Cn-Ay). So I still am confused as to how, despite of factors such as conicity and plysteer these lines would intersect at the origin.

Have i changed the coordinates correctly? Am i missing something else here? Should converting coordinate system give Ay=0 or not? Is it the solution to my previous problem? 792793

[Adam Farabaugh]

What is the output of your tire model at zero slip angle at various loads?

What other effects are you modeling? Inclination angle? Ackerman? Change of inclination with ride and steer? Compliances? Hard to tell what the problem is without knowing how complicated your model is. Would suggest that if you do have any of these things modeled you turn them off until you can get symmetry with the simplest possible model (tire model + weight transfer)

[apoorv]

At zero slip angle tire is producing some lateral force. The inclination angle is 0, no ackerman, no compliances. The minimum slip angle in the lookup table exported from tire data is +0.0502 and -0.0502 which matches with 0 slip angle in matlab calculations. Can this be the cause of asymmetry ?

[Claude Rouelle]

Devansh,

Let me repeat the same thing but with other words.

No tire is perfectly symmetrical. Even with no slip angle and no camber it could be that your tire will produce a side force. OK, now imagine your beta and delta are both = 0 and your car has a symmetrical setup (in other words you are in straight line) and you have no camber and not toe. If in these conditions, your LF tire and RF tires both pull a force in the same direction (pulling the car to the left of the right) there will be a lateral acceleration and most probably a yaw moment (unless your weight distribution is exactly 50-50 and you have exactly the same front and rear tires and a=b). Something is wrong....

Most of the time students do not adapt their tire coordinates system to the chassis coordinate system. I remember having clearly explained this in the last seminars I taught for at least the last 5 years.

Is this helping or not?

[Adam Farabaugh]

Hint at the solution, look in the mirror (while holding a plot of lateral force vs slip angle)

[BillCobb]

Instead of trying to use a model which has a hint of extra complexity, try creating a simple tire model formulation using a 2 term exponential slip sensitivity and a linear load sensitivity. Once that seems to be working go ahead and add some nonlinear load sensitivity.

If all that makes sense, add the aligning moments and perhaps some non-zero slip responses. After that, you can open the throttle with some real tire data.

[Claude Rouelle]

Nice and simple way to present the perspective (literally!) Adam.

In the seminar I show it with another visual trick: in the Adapted SAE tire coordinate convention system, I take the graph the RF tire Vs its slip angle then flip it once around the X axis (slip angle axis) and then one more time around the Y axis (force axis). From there you see the 2 side forces at 0 slip angle are in opposite direction and there ore no resulting chassis lateral force in a straight lime.

[apoorv]

thanks sir I will look into this and reply ASAP.

[Tim.Wright]

I agree with Claude and Adam, that the problem is in the static offsets of the tyre curves. However, with no labelling on your plots its impossible to say much more.

Try switching off the horizontal and vertical shifts in the tyre model (by setting their scaling factors to zero) and see if it fixes the problem.

If the tyre has a different (mirrored) construction for the left and right side, you need to first understand which tyre you have the data for (left or right) then in your calculations incorporate a mirroring function which inverts the X and Y axes.

If your tyres are interchangeable left and right and have single specified rotation direction, that means that any static force offsets are going to add together instead of cancelling each other out. In other words the staic offsets in the tyre curves will make the car asymmetric and you just have to live with it.

[apoorv]

Hello everyone,
First of all thanks Claude, Tim, Bill Cobb and Adam for explaining us the differences between both the diagrams and about the assymetry that we got as we didn't adapt the tire coordinate system to chassis coordinate system.
From Fy vs SA graph we can see the forces cancelling out as we mirror about the axes. So in the images attached below we rectified the Assymetry problem and as well as we were able to figure out the problem with Cn-Ay constant steer lines. There was a problem with the yaw rate calculation in the matlab which we rectified as we did a sanity check on our code.
Below I am attaching both Cn-Ay and Cn-Cy graphs. These are the final ones. The green ones are the constant steer lines. I hope these are correct but I still want u to have a look at it and any comments are welcomed.
We are also going to add some other factors such as rollstiffness, camber angles etc.
Once again Thank You
798797

[Claude Rouelle]

What about a legend?
What about color that would help the reader to easily identify what the values of CG slip slip angle and what the value of steering angle are?

[apoorv]

Sir,
Here are the images with Legends and markings!


804805

[Claude Rouelle]

What is CN positive? Left or right hand corner?

Same question for the sign of the X axis.

How do you define a postive and negative Beta?

What is a positive steering? Turning left or turning right?

Is the steering angle the steering wheel angle or one wheel angle (if so which one?) or the average of the LF and RF steering angle?

Is this a simplified 2 wheel or 4 wheel model?

CN Vs lateral acceleration is a constant speed correct? What is that Speed? Why is that speed not on the graph legend?

CN Vs CY is a constant radius correct? What is this radius?Why is that radius not on the graph legend?

[Claude Rouelle]

What is CN positive? Left or right hand corner? Or less confusing: clockwise or anticlockwise?

[apoorv]

CN clockwise is positive, front wheels steering is +ve for right side. Its not steering wheel angle so no steering ratio and average angle of both wheel. Fy is positive for right side! Beta postive for right side. cn-cy at 16.75m constant radius and cn-ay is at 17m/s constant speed.

[Claude Rouelle]

There is a part of me that will play dumb because your explanations are not precise enough and I am sure other readers have similar questions and the other part that will ask because simply your best definition are not good enough

1. Is this a simplified 2 wheel or 4 wheel model (with weight transfer)? You did not answer that question

2. CN clockwise is positive, OK got it!

3. front wheels steering is +ve for right side. What the heck does that mean? The right side of what compared to what? What is "+" ve? What about the forces sign convention? Is it the same? Please make a sketch!

4. Its not steering wheel angle so no steering ratio and average angle of both wheel. The "and" is confusing! What is it at the end? You could be going into a left hand corner and turning the wheel(s) or the steering wheel to the right because you have oversteer.... Can you simply tell us if its clockwise or counter clockwise from the driver perspective?

5. Fy is positive for right side! Again right side of what compared to what? Pointing towards the right side of the tire, the screen, the corner center?

6. Beta postive for right side. The right side of what? Again a clockwise and counterclockwise definition would be better

7. cn-cy at 16.75m constant radius and cn-ay is at 17m/s constant speed. Got it, thanks but why in the hell didn't you say so!

You think inside your own box. You understand yourself but your explanations for the information for the newcomers are not clear enough. Too much time wasted making sure we speak the same language instead on focusing on the core issue of your questions. If we would be side by side that would be easier but here we are working via a forum posts so we need to have precise definition of our sign convention.

Fix that first and then we will go ahead.

When we will all use the same language we will continue to work but I can tell you already that I see some issues in your graphs. It is about control and stability that are the most powerful and useful part of this graph.


Claude

[apoorv]

1. This is a 4 wheel model with weight transfer (for right hand cornering).
3. Steering angle front wheel is positive for clockwise direction.(It's a right hand cornering ). The lateral forces are positive for the right hand turn.
4. Basically we are referring to a parallel steering here and the delta mentioned is actually front wheel's angles which is +ve for right hand turn.(clockwise with respect to driver).
5. Fy is +ve for right side of the Tire i.e. towards right hand cornering centre Fy is positive.
6. Beta is positive for clockwise direction.
7. By mistake I typed speed as 17m/s but it is actually 27m/s.

PS: All the sign conventions followed are from "Race car vehicle dynamics".

Here is a screenshot of the table that includes all the sign conventions we followed.

807

[Claude Rouelle]

OK that is better

3. The lateral forces are positive for the right hand turn. How do you define positive? Which direction? If possible please provide a sketch, not only a list, for all these sign convention.
Most to the people who can help you are too lazy or too busy (at least I am) to take the time to get back to RCVD to re-learn that specific sign convention.

Claude

[Claude Rouelle]

Can you show us a Cn Vs Ay at 8, 10 and 12 m/sec?
Can you tell what your wheelbase is?

[Claude Rouelle]

What is the tangent speed for your car?

[apoorv]

The earlier graphs I posted are at 27m/s not at 17m/s, which I typed mistakenly. Our tangent speed is at 19m/s. Wheelbase is 1.525m

Here I am attaching images at speed 18, 19, 20 m/s
810811812

[apoorv]

To plot graphs below 15m/s I had to use relaxation parameter(0.7) in order to converge the solution but this changes my tangent speed to 11m/s. For 8m/s the solution does not converge unless I change my convergence criterion and and high relaxation parameter to around 0.9 (which again changes my graph behaviour).
Here are the images813814

[Claude Rouelle]

Labels for beta and delta values please!

[apoorv]

Its same as previous one!

[Claude Rouelle]

So to remember the beta and delta value you use, the reader has to look at the previous post? Who is trying to help who here? Just post these values and labels on your graphs!!

I know I act as a bit as teacher here (or a customer or a design judge for this kind of exercise, that is the same) but just try to be consistent!

Anyway I think something is quite inconsistent in your graphs

1. At 10 m/sec your control is negative, at 12 m/sec positive and at 18 ms/ negative and at 19 m/sec positive again..... I do not know how your calculations were made and I do not know your car, tires, weight distribution, roll stiffness distribution, aerodynamics properties etc...but I have serious doubts about these calculations.

2. At any speed it seems that the yaw moment at the limit (max G) is always zero: no understeer, no oversteer.... Too good to be true I think.

3. What is the relaxation parameter; how do you define it? What is the unit? What is the meaning of it?

4. Same question for your convergence criteria.

Many questions and a few criticisms from me but I have to say that not a lot of guys in this forum went that deep and that quickly. that is encouraging.

However, you are only at the beginning: the goal is not to make a simulation that works: it is to make a simulation that is pretty realistic and useful to design and tune your FS car.

[apoorv]

1. When I plot my Cn-Ay diagram it gives me tangent speed at around 19m/s. When I try to plot the graph below 15m/s the solution does not converge as my yaw rate values become very Large. Therefore to Converge the solution for speeds below 15m/s I use a relaxation parameter to calculate more stable value of yaw rate on each iteration.

w3=w2(1-Pr)+w1*Pr
Pr is relaxation parameter (0.5 for low speeds)
where, w1 = previous yaw rate estimate(initial value)
w2= new yaw rate estimate(after 1st iteration)
w3=more stable yaw rate estimate(value for 2nd iteration)

so when I don't use any relaxation parameter the tangent speed is 19m/s but when I try to plot for speed below 15m/s I have to use Relaxation parameter and it gives me different tangent speed.

2. The weight distribution is very close to 50:50 and same front and rear cornering stiffnesses and no aero.

3. Relaxation parameter is basically a mathematical tool that allows me to estimate value of Yaw rate on each iteration that allows to converge the solution at low speeds. No units just a number.

4. The convergence criteria is that for each iteration the AY values must be within 2% range
i.e. Ay(new)-Ay(old)<2%

[Adam Farabaugh]

I find it odd that you only need +/- 3 degrees of steer and body slip to saturate the tires

Edit:
A "relaxation parameter" as I understand it is just an IIR low pass filter applied to some of your converging values. This helps avoid gradient based (which basically is what we all use to solve problems like this) methods from diverging. It should not affect the actual result that much, just whether or not convergence is reached. Personally I generate all my plots with the same low pass cutoff, and now that I have a good one chosen, I never have to change it.

[apoorv]

Adam whatever other graphs I have seen for FSAE cars they all go almost up to +/-3 to +/-4 degrees of steer and body slip. Which even my vehicle is also giving so I am assuming to be correct. Other than that there is not much data available to compare!

About relaxation parameter u are right that it should not affect the actual results. I will look into this once more and try to correct the code or may be use some other function such as fminsearch to converge at slow speed

[BillCobb]

But if you are at 27m/sec and (you say you are) 'above' the tangent speed, your sideslip should be -ve. Run it at "the" tangent speed and see if your sideslip is zulu oscar.

[apoorv]

Yes its zero at tangent speed (19m/s) above that speed positive and below that speed negative. Is this incorrect?
815

[BillCobb]

Yes its zero at tangent speed (19m/s) above that speed positive and below that speed negative. Is this incorrect?
815
The expectation (and convention) is for sideslip to be negative above the tangent speed. Positive below it.

You have a vehicle that is pretty much neutral steer without any realistic compliances or geometric steers and cambers. Depending on what tires you are using, any roll stiffness distribution may not alter this trim that much. The +- 3 degrees of reference steer angle is just about what I would expect and what I calculate.

Max lat at about 2.0 g for a tire I chanced to pick. However, the yaw rate and lateral acceleration transient responses are pretty slow/sluggish as would be expected from a neutral steer (i.e. first order response behavior) vehicle.

If you are going through all the hoops to simulate your car, why don't you just run a ramp steer or series of step steers into it and calculate some system engineering metrics (like gain, damping, and response time) ??? Then add some nonlinear steering compliance, some roll steer and camber, deflection steer and camber at both ends. Now you have a vehicle model grounded in laboratory and road test regimes.

[apoorv]

Bill,
When I said its zero at tangent speed (19m/s) above that speed positive and below that speed negative. I meant to say the slope of the line Beta=0(side slip angle).
I am not sure if both of us are talking about the same thing or not. Correct me if I am wrong sir. What exactly did you mean when u say side slip is zero.

Adam,
I have corrected my relaxation parameter code and now it does not affect the tangent speed as earlier. But I am only able to plot at minimum of 13m/s speed even after using the relaxation parameter. What was the minimum speed that u were able to iterate for with relaxatn factor????

[Claude Rouelle]

Bill,

The yaw moment Vs Lateral Acceleration method is a quasi steady state basic simulation.

You are right about the importance of compliance and transient and response but if most of the students do not fully understand the picture (steady state) how can we push them to get straight to the movie (transient)?

In the passenger car industry you can learn a lot by doing frequency, steering response tests etc... because you have all the sensors, the available track, the time, the money, the organization and most of all a few reliable cars. Most of the students are not organized enough to finish a car that they can test extensively. And that is if they do they face any reliability issues. Most of them are struggling to get their car ready on time and do not have the luxury to test and therefore experience, analyze subjective and objective data.

Most of them barely understand what compliance is and even more the bad effect that compliance has on their car (and driver!) behavior. If most of them would, we would not find so many bad FS / FSAE chassis and suspension design with suspension pick up points in a middle of a tube or too short rear toe base.

This thread was going the right direction and then suddenly we go (in my opinion) in stratospheric perspectives. I was hoping that "apporv" (who has the gust to ask the right questions) would come with a decent working useful Yaw Moment Vs Lateral Acceleration diagram and, within other challenges", overcome the low speed convergence and simulation issue with the help and/or hints of others. Then at that time and only at that time we could have asked the "what if we add compliance" and what if we look at this in transient?

Simple then complicated, not the other way around. The basement, the walls and then the roof, not the other way around.

You know how much I respect you and how much I learned from you but here I had to give my perspective. I sure will not disagree about the importance of transient measurements, simulation, testing and analysis which at the end is everything (and if fact way underestimated by the majority of the racing teams including the professional ones) but I feel we are out of the "one thing at a time" sequence.

Maybe am I wrong, the other readers of this thread may have a different opinion...

For now I would like to get back to the (good) questions that "apory" came with.... He is onto something.

Cheers,

Claude

[Claude Rouelle]

Devansh,

A hint....maybe...

At the corner entry where the beta is still = 0 degree and the delta is minimal, let's say 0.1 degree the turn center is on the rear axle axis. From there, as the car slip and yaw, the turn center Vs THE CAR is itself moving: the turn radius decreases an the turn Vs THE CAR is moving forward center it moves forward (again Vs the car). That is an intermediate calculation that has to be taken into account too.

In the simplified sketch I show in the seminar the Turn center is right "under the car CG" (in top view). The turn center is also right as the center of a circle and this circle is the car trajectory. That is a bit simplified. That is one of the picture; you need to look at all the other pictures from the turn entry and the very first steering input.


We are back to the yaw center definition. You will have to mix both kinematic and force aspects together. To do that you need a realistic tire model.

[Goost]

In the simplified sketch I show in the seminar the Turn center is right "under the car CG" (in top view). The turn center is also right as the center of a circle and this circle is the car trajectory. That is a bit simplified. That is one of the picture; you need to look at all the other pictures from the turn entry and the very first steering input.

We are back to the yaw center definition. You will have to mix both kinematic and force aspects together. To do that you need a realistic tire model.


Claude,

Can you please explain this again, maybe in a different way? I never quite catch onto what you want from this when you explain it as a 'yaw center'.

I am confused if you mean

1) the center of the turn (which we are claiming is a fixed point in space) changes
laterally (Do you call this distance in the vehicle y-direction from the CG 'radius'?) and
longitudinally (Do you call this distance in the x-direction from the CG 'yaw center'?)

2) or is radius the magnitude of the distance from the CG? and therefore 'lateral' force is in Path coordinates, not Vehicle coordinates?
Perhaps 'turn center' and 'lateral' can be found more easily from the intersection of lines perpendicular to front and rear slip-angle

3) or is it that we assume the vehicle moves in a straight line, 'lateral' is just perpendicular to the (straight) path, and 'turn radius' is kinda meaningless anyway?
In this case, for instance, steer angle would not affect the direction called 'lateral' only body slip.

It is bothering me because of a practical component - If I were to Measure the lateral acceleration to construct a moment diagram, what would I use?
Sounds like a vehicle mounted lateral accelerometer at the CG is not the same as the lateral acceleration you would have on a moment diagram?
If that is true, then what is?

Perhaps I misunderstand completely but this has come up several times and I still don't follow which components of each you keep when you
"mix both kinematic and force aspects together"

Thanks!

[Adam Farabaugh]

This is turning into a great thread.

Backing up a little bit (not to detract from the discussion of yaw center), I am confused as to why it's expected to have such small delta and beta ranges to saturate the vehicle completely. Even looking at the tires we've used in the past, we see peak lateral forces in the ~5 deg area (lateral-only tire model) and need to sweep beta and delta at _least_ +/- 10 deg each to saturate our diagrams. With other tires we need more. Obviously this is a function of the quality of the tire model.

See rather large slip angle/steer angle especially in the slaloms:
https://www.youtube.com/watch?v=MQwQsAhAjVY

[Claude Rouelle]

Adam,

It is not because you peak slip angle is in the 5 degree area ("guessed" from the tire model) that the driver the car and use the tire at that slip angle.

In fact look at WRC cars on tarmac; their slip angle peak is also in the 5 or 6 degree peak area. But they are often driving the tires above that limit.

One of the reasons (but not the only one) is that passed the peak slip angle the cornering stiffness (the "slope" of the FY Vs alpha) is negative but it is also smaller. Each slip angle variation from the steering (delta) and/or the "throwing the car in yaw" (beta) gives you less lateral grip variation, therefore more drive-ability. Grip is one thing, Balance, Stability and Control are others.

I have been lucky to measure car and tires slip angle (they are often bigger than the peak one you measured on the tire testing machine.

https://www.youtube.com/watch?v=Q4t-EoVxyds&feature=youtu.be

[Claude Rouelle]

Austin,

It is just an out of the box usual perspective.

Try to look at the same thing but in a different way.

Instead of looking at the car steering, side slipping, yawing Vs a given fixed point of a circuit....try to imagine a car in 2 D top view and a front and rear chassis slip angle. Draw the perpendicular to the direction in which the front and rear of the chassis are moving. The intersection of these 2 perpendiculars is the point around which the car is rotating, correct? Now try to imagine the "trajectory of this "turn center" Vs the car itself. That is all

The reality is that if there is a slip angle there is a force. Pure kinematic is approach one thing, force and moment is another and you need to put both together.

***
Of course

1. The lateral acceleration calculated on an axis going from the CG to the turn center or the one measure perpendicular to the chassis in not the same because the yaw angle

2. This is confusing for some students: you can have a lateral acceleration without being in a corner. You can have gust of wind that makes your car side slip and still no signal from your gyro or your steering senors. If you have side slip speed VARIATION there will be a lateral acceleration measured by your lateral accelerometer. Lateral acceleration = dVy/dt + (V squared / R)

***

[Goost]

Instead of looking at the car steering, side slipping, yawing Vs a given fixed point of a circuit...
try to imagine a car in 2 D top view and a front and rear chassis slip angle.
Draw the perpendicular to the direction in which the front and rear of the chassis are moving.
The intersection of these 2 perpendiculars is the point around which the car is rotating, correct?
Now try to imagine the "trajectory of this "turn center" Vs the car itself. That is all



I'm OK with this, it's a neat idea, curious how it makes it into the diagram.
For my 'lateral accel'/'lateral force' axis on your version of the YMD, would I only keep forces that are radial to this center point and the 'yaw center' helps define the line?

I still don't see what is the definition of 'yaw center' and how it should be used?
Part of my confusion comes from discussion with a teammate who understood your notes to say negative slope 0-beta lines are inherently bad.
For instance; here is a simple 'top-view' Moment diagram that just uses a Pacejka '93 tire and rough FSAE dimensions.
Is the first plot (at low speed) inherently wrong since 0-beta slope is negative? or just not the way you like to see it?
If I used your 'yaw center' concept would this be eliminated? is that different than simply adding the ackerman steer angle to my delta values?

I may miss your point completely.

[Claude Rouelle]

Austin

If you have, in the chassis coordinates, a front chassis slip angle you have a front lateral slip speed Vyf, correct? Same thing for the rear of the chassis, Vyr, correct? Draw these 2 vectors on the chassis. They are perpendicular to the chassis. They do not necessarily have the same direction and intensity, correct? Their values only depend on your side CG slide slip and your yaw speed sign and intensity, correct?

If you have 2 speed vectors, can't you find a point on your drawing where the speed is zero?

****

When you will have to calculate the control (yaw moment due to a steering input for a given fixed beta, this beta being zero at the corner entry) there will be in "quasi steady state" a front chassis slip angle and yet no rear slip angle. Your yaw center will be on your rear axle. That will change the shape of your yaw moment diagram. But as you go into the corner not only the yaw center but the turn center VS THE CAR do move too. Just worth to look at it in the chassis coordinates, not only the circuit coordinates. Again, same thing but different perspective.

***

I do not think I said that negative slope of beta was "bad". I remember saying that it initially looks unusual and not logical but you had to think about it. It seems to mean that the car will yaw towards the left while you will be steering to the right. But if it is the reality or is it that your calculations are missing something? What if the missing part is related to the 1st paragraph of this post? It is not about what I say: it is about what the car needs and how you understand an calculate it.

Let me help you and give you a hint: can you draw a simple intuitive graph of the beta Vs speed. Beta is 0 at 0 km/h, obviously, correct? But it will be zero at the tangent speed too (that is the definition of the tangent speed), correct? So what is the Beta Vs Speed curve shape starting from 0 and before and after the tangent speed?

****
Print your yaw moment diagram (the one at constant speed, which is a bit theoretical, but that is another story) and use a pen to describe which isoline you first follow and then, one by one, to which isoline you switch to as you enter the corner.

****

Also Imagine you had to create a yaw moment diagram where you would have to display not only the beta (CG slip angle) but also the front and rear chassis slip angle....

***

The issue of the negative beta slope at low speed is an mathematical issue that Devansh is facing too. it is a convergence issue. If you can solve it and you can use it you will have a very, very quick car on the skid pad!

[Z]

Austin (Goost) asks Claude,


Can you please explain this again, maybe in a different way? I never quite catch onto what you want from this when you explain it as a 'yaw center'. ... I am confused if you mean...

Austin again asks Claude,


I still don't see what is the definition of 'yaw center' and how it should be used?

One part of Claude's many cryptic replies is,


If you have, in the chassis coordinates, a front chassis slip angle you have a front lateral slip speed Vyf, correct? Same thing for the rear of the chassis, Vyr, correct? Draw these 2 vectors on the chassis. They are perpendicular to the chassis. They do not necessarily have the same direction and intensity, correct? Their values only depend on your side CG slide slip and your yaw speed sign and intensity, correct?

If you have 2 speed vectors, can't you find a point on your drawing where the speed is zero?
~o0o~

Austin,

Other than Claude's explanation above of his "yaw center" being very poorly worded (!*), and with many key parts of what should be in a good explanation missing, this concept of a "Yaw Centre" is, for all practical purposes, meaningless.

I am pretty sure I know what Claude is getting at here. Claude' version of a "Yaw Centre" is quite easy to explain, but it requires clear descriptions of at least three different reference frames, which so far Claude has refused to give. In fact, I reckon the key reference frame here is a rather useless one, but it is the one in which "you find a point on your drawing where the speed is zero", which is Claude's "Yaw Centre". An apt name for that reference frame might be the "Wishful Thinking" frame.

Anyway, I will wait a few days to see if Claude wants to give a better explanation (ie. in return for your money!), before I spell it out more fully.

Z

(* "If you have, in the chassis coordinates, a front chassis slip angle you have a front lateral slip speed Vyf, correct?"
NO! Not unless the car is undergoing a major collision. In "chassis coordinates" the "front chassis" should NOT be moving at all!)

[Goost]

Claude,

Thanks for helping but your answer was confusing again; I think that is your teaching style though, you would rather people discover these things 'on their own', which is fair if you think overall that is more effective.

So I still don't know which coordinate systems you use and what you mean by 'yaw center', but could you tell me if this is a good summary:

A) the 'Milliken Moment Method' is about 'constrained' force and moments. You take a car on a (generally) straight path, and measure the forces/moments that it generates. Sometimes we would rather think of lateral force as meaning some amount of 'cornering' ability, so we hack up the force into something with units of accelerations based on an imaginary 'turn center'.

B) the Claude 'Yaw Moment Diagram' is about the cornering sequence. You take a car and change the 'path' it is on to correspond with the way it would get around a corner. This means the diagram in some ways no longer tells us the same stability and control (a dynamics/traction control guy might wince at this change),
BUT it tells us a lot about the cornering sequence. Which, for a race-car, you find more instructive in designing and tuning a car. You must let the 'turn center' move both lateral and longitudinally relative to the vehicle to think of it this way

Is this fair?

~~~

Z,

True, I recognize that there are multiple coordinate systems being used too, that's part of why I asked to start with. I think Claude would draw a 'yaw center' on the chassis center-line, which seems a bit misleading, even if useful.
Perhaps it would be better if we could get a clear definition to at least agree on the terms, Then we could discuss better how to use the concepts?

'turn radius' - lateral distance from vehicle CG to the cornering center (in chassis coordinates)
'yaw center' - the longitudinal distance from vehicle CG to the cornering center (in chassis coordinates)

Or something like that.

~~~

So then my original question comes back again - If I want to make a 'Yaw Moment Diagram' not a 'Milliken Moment Diagram',
what forces do I consider 'lateral' forces? The ones that face the turn center (PATH coordinates) or the ones that face the side of the vehicle (BODY coordinates), or something else entirely?

The only reason I commented in the thread was poor apoorv isn't making progress because we can't get a silly definition lined up for yaw center - so how can we criticize his diagram that doesn't use the 'right' method?

[DougMilliken]

... A) the 'Milliken Moment Method' is about 'constrained' force and moments. You take a car on a (generally) straight path, and measure the forces/moments that it generates. Sometimes we would rather think of lateral force as meaning some amount of 'cornering' ability, so we hack up the force into something with units of accelerations based on an imaginary 'turn center'.
RCVD Table 8.4, pages 310-311 lists some of the possible ways to run MMM simulations and the corresponding road tests (when applicable). Note that these road tests (aka control response tests) are often mentioned by Bill Cobb, used to quantify street-car behavior. Nearby pages have more discussion.
In the 20+ years since Chapter 8 was written, we have also looked at some other "modes" (first column of Table 8.4) to help illustrate or understand specific problems.


B) the Claude 'Yaw Moment Diagram' is about the cornering sequence. ...
Q for Claude -- does this relate to the the Qualitative Transient Description given (with figures) in "Chassis Design", section 4.3, starting on page 232? Olley's group did this work before the (linear) equations of motion had been written, so it is quite remarkable what they were able to deduce from their proving ground tests, in the 1930s..


... apoorv isn't making progress because we can't get a silly definition lined up for yaw center - so how can we criticize his diagram that doesn't use the 'right' method?
Oddly enough, I remember working with an F1 team (nameless to protect the guilty!) in the mid-1980s. They were calculating a "yaw center" value with what are now called "math channels", inside their data acq system. We tried to pin them down on how this was calculated and were never able to get a satisfactory answer...someone coded it and no one else was willing or able to decode the formula and define it. The "yaw center" in their scheme was located on car centerline, a calculated length from the CG location.

[Silente]

question for all of you:

being this Yaw Center on car center line, shouldn't it only tell how much of the overall Yaw moment is coming from the front and rear axle? considering also Yaw Moments' signs?

Anyway i back Goost on the lack of clear definitions here. clear definitions would make the discussion much easier. On this side i really appreciated the sketches from Z in the other Yam Moment diagrams discussion.

[DougMilliken]

being this Yaw Center on car center line, ...
What you describe sounds a lot like "static margin", see RCVD page 166-7.
There are other discussions also, the Index entry for "static margin" is a sub-heading under the main (and long) index entry, "Stability and control, steady-state".

[Z]

Austin,


Claude, ... your answer was confusing again; I think that is your teaching style though, you would rather people discover these things 'on their own'...

It is beyond me why students pay good money to go to seminars where they have to "discover things on their own". Just how far down the crapper has the concept of "teaching" gone!?

Anyway, given that Claude is refusing to clarify where his "yaw centre" is, here is my shot at explaining it.
~o0o~

Firstly, here is a cut-and-paste (plus some extra emboldening) from one of my old posts that I just linked to on another similar thread. This was written two years ago, but it seems that many people, Claude included, still do not get it.

"... when studying MOTIONS you MUST consider at least TWO DIFFERENT BODIES (or, equally, two different reference-frames). It is completely pointless to try and describe the motion of a single body with respect to ... itself (?), or with respect to ... nothing much at all (???). A motion is always that of BODY-A WITH RESPECT TO BODY-B (or reference-frame-A wrt frame-B, etc.)..."

So when Claude starts his explanation with, "Austin, If you have, in the chassis coordinates, a front chassis slip angle you have a front lateral slip speed Vyf, correct?...", then you know that what follows is going to be pure poppycock... Claude!!!

(In case any students still don't get this:
For any analysis that assumes a reasonably rigid chassis, anything that starts out in "chassis coordinates" as "the front chassis", should bloody well stay forevermore at that same place, UNMOVING in "chassis coordinates", regardless of where the car goes on track!
Once again. When measured in "chassis coordinates", the X,Y, & Z of "the front chassis" should remain CONSTANT (ignoring small frame flexing and catastrophic collisions)!)
~o0o~

My guess for finding Claude's "yaw centre" is this.

Claude starts by considering the velocity-vectors of points on the Car-Body, WITH RESPECT TO THE GROUND-BODY (<- important!). To repeat, this discussion is about the motion of points, or particles, that are part of the CAR-Body, and their motion is taken WITH RESPECT TO (or "relative to", or "with reference to"...) the GROUND-Body (or "the-track-XYZ-reference-frame", or "the-Earth's-global-coordinates-of-latitude/longitude/altitude", or "relative-to-the-fixed-stars", etc.).

Claude then decomposes each such instantaneous velocity-vector (of Car-Body-point, WRT Ground) into two components aligned longitudinally and laterally to the instantaneous car-centreline. Then, without telling anyone, he SUBTRACTS the longitudinal-velocity-component of the car-centreline from all the Car-Body-points' velocity-vectors (... with all these velocities WRT Ground).

In effect, Claude is considering the motion of the Car-Body WRT a "Virtual-Reference-Frame", with this VRF itself moving WRT the Ground-Frame with a uniform translational velocity equal to that of the car-centreline's longitudinal-velocity-component (... WRT Ground!). (Edit: Add Claude's velocity field of "Car wrt VRF", to uniform translational velocity field of "VRF wrt Ground", and you should get velocity field of "Car wrt Ground".)

So, in Claude's picture the whole Car-Body can be seen to be yawing WRT this VRF, and the Car-CG (assumed here to be on car-centreline) can also have a pure lateral "side-slip-velocity" WRT this VRF. The pattern of velocity-vectors of points of the Car-Body, wrt the VRF, will have a point where the velocity magnitude is zero, and Claude calls this his "yaw centre".

But (?), it may be that Claude's mysterious and undefined Virtual-Reference-Frame is also ROTATING wrt the Ground-Frame. This would make it the "Wishful-Thinking-Frame" I mentioned earlier, because this is the frame you might want the Car-Body to "stick to" as it goes around the corner. Any CG-side-slip, or Car-Body yawing, wrt this Wishful-Thinking-Frame, might be seen as the car not following its ideal line.

But I doubt we will ever know for sure. Only one person can really explain where Claude's "yaw centre" is. Claude???

Also, I see NO benefit from this "make it complicated first..." approach.

Even worse is that all this conjuring-up of mysterious and undefined "centres" can be multiplied indefinitely. Having difficulty explaining a car's behaviour? No problem, just pull yet another "roll, pitch, or yaw centre" out of your hat!

Z

[Claude Rouelle]

Guys,

If you are interested you can download from the OptimumG website four articles on the yaw moment Vs lateral acceleration simulation method that I wrote for the Race Car Engineering magazine. That is, of course with the authorization of Race Car Engineering.

http://www.optimumg.com/technical/technical-papers/

[BillCobb]

Claude:
I have enjoyed reading these articles very much. Most of my career was targetted on the 'pleasability' and 'safety' aspects of vehicle dynamics. Your talking points show that the racing focus demands attention almost entirely to the balance and ultimate/max limit control regimes.
Great stuff ! (Check your e-mail).

I remember way back in time (1969) as a Summer Co-Op at GMPG, we had a car equipped with front and rear rocket engines mounted on the front and rear axle locations on the body (powered by hydrogen peroxide) that could 'augment' yaw moments by a rear seat operator that could surprise a driver or help them through a course.

I still have a few pieces of that system in the barn and the a pyrex bottle that held the peroxide that I smuggled out many years later.

[DougMilliken]

Bill,

Looks like that rocket motor setup goes back pretty far, https://www.sae.org/publications/technical-papers/content/640001/ "Vehicle Handling Response to Aerodynamic Inputs", 1964. Did you ever talk to Tom Bundorf about this bit of history? CAL/Calspan had something similar used for crosswind simulation around the same time, but I'm not sure where it came from.

RCVD Chapter 8 has quite a bit of detail on racing applications of MMM, for anyone thinking of rolling their own.

-- Doug

[BillCobb]

Doug, the best aerodynamic wind gusts came from 2 full blown Continental piston airplane engines, props and all with wire guards. Mounted on steel frames painted yellow as I recall. They would be placed along side a road course and you would drive by them. By today's OSHA standards, it would never 'fly', so to speak.

[DougMilliken]

the best aerodynamic wind gusts came from 2 full blown Continental piston airplane engines, props and all...
We made a survey of these types of facilities, c.1980. From memory, there were nearly a dozen around the world, some had several big prop fans as you described, up to six(?) in a row. Many had been used for a few years until test work dried up and were no longer operating. Judging by the crosswind handling of some current cars, it might be a good idea to resurrect this testing in some form.

We did some low-buck projects to look at crosswind effects on single track vehicles (2-wheelers). One used a solid propellant model rocket engine (not much thrust) and another used a Cessna taildragger. Before the USA went nuts about airport security, it was relatively easy to set up in a corner of the Buffalo airport. The little plane was tied down so the propwash blew across an unused taxiway and we rode through the sharp-edged "gust".

The most elegant (and lowest cost) setup used a string--which could be attached at different places to simulate different locations for the center of the aerodynamic sideforce (simulating different types of streamlined bodywork)...a second vehicle rode/drove alongside the test bike and the experimenter tugged on the string.

[Claude Rouelle]

Bill, Thank you for your remarks. From you, I take them as a big compliment.

At OptimumG we always focus on balance more than grip for one simple reason: Drivers can feel the balance not the grip.

I defy any driver to feel the difference between 3.1 and 3.2 G of lateral acceleration. Some will tell you that the car has more grip simply because they look at the lap time. 0.1 G difference in each corner will make a huge lap time difference

If you remove the lap time from the dashboard some rare drivers will tell you that the car has more grip "because I shift from 2nd to 3rd 20 meters earlier at the corner exit" But that is it.

But give them a very small difference of front and rear cornering compliance and they will fell it.

Put a big guy of 100 kg 1 meter away from the center of a swing and another small guy of 50 KG 2 meters away of the swing center. The swing is horizontal, balanced. Put a ballast of 1 Kg under the seat of the guys. The swing angle will change. Both guys will feel and see it.

Give 1 Kg under the seat of the big guy and 2 Kg under the seat of the light guy. What do they feel?

OK that is not the perfect comparison because mass and force is not the same thing: we should do the same experience on the earth and on the moon.

It is true that the driver will feel in his shoulder, hips, ribs, head/ helmet a different acceleration. But can he feel the difference between 3.1 and 3.2. G? At 100 or 200 or 300 Km/h with the noise and vibration of the track and the car? I doubt it and my experience has shown they don't.

But if they miss the apex by 1 meter they will complain about understeer.

[rory.gover]

I have always found it interesting that most dual-axis acceleration diagrams (e.g. Cn-Ay etl al) ignore body slip angle rates (see below). While not a huge concern when the diagrams are being used to look at max planar accels, it is especially of concern when using the diagrams to 'control' and 'stability' derivatives.
https://i.imgur.com/m2q1gy4.png
(N.b X-Y is the ground frame fixed to the CoG of the vehicle, x is the chassis heading, y is orthogonal to x, t is the heading of the velocity of the CoG, n is orthogonal to t, the box is a rendition of a vehicle and the shoe is on the other foot just FYI)

So it's obvious there is a coupling between normal acceleration, body slip velocity and chassis yaw velocity (and from chassis yaw velocity, there is an influence on the effective slip angles of each tyre). Side note: I think there is a great benefit to thinking in terms of normal acceleration {n-direction} rather than lateral acceleration {y-direction}, insofar as the math is actually correct when using nt-coords. Similar point with using yaw acceleration (Az) rather than net yaw moment (Cn); why compare moments with accelerations when you can compare accels with accels (perhaps I am missing something)?

Well it will obviously depend on the magnitude of the body slip angle velocity, and body slip angle velocity (betaDot) depends on a bunch of stuff, but crucially, depends on slip velocity. For a typical FSAE vehicle, Slow steer speed, betaDot <10 deg/s; steer velocity greater than full lock in less than 0.2 sec, betaDot > 50 deg/s. This is obviously dependent on a huge array of factors, including yaw inertia. Anywho, Az-An diagrams below for betaDot = [0; 30; -30] deg/s.
https://i.imgur.com/ArpfJ7Y.png
https://i.imgur.com/kY77p05.png
https://i.imgur.com/3xUevu6.png
(N.b. Body Slip Velocity is betaDot, just FYI)

So, as I said, the magnitude of accels not much altered, but the control and stability derivates are reasonably different at the limiting accels. Side note mk2: I see a lot of CnAy diagrams developed for arbitrary chosen steers and body slip angles, this will give you arbitrary limits of your diagrams. The above diagrams determine the limits by looking for saturation of the tyres on each axle, limiting load transfers, steering and slip bandwidths etc.

Lastly, even though I know the bounds of the above diagrams are reasonable, I still don't know if the steers and body slip angles provided to generate the vehicle responses are actually achievable for the stated velocity and betaDot (as ya'll know, the driver only has input actuation for steer angle, not so much over body slip). I think it would be reasonable to say that some sort of transient, Lagrangian assessment (whether through modelling or experimentation) would be useful to examine the actual space of steer, slip, slip rate and speed acheivable by a particular vehicle before placing full, unconditional trust into these Eularian models.

[BillCobb]

Hence the conundrum: "Racing is all transient", but racing analysis is apparently all steady state.

[Claude Rouelle]

At OptimumG we always take r into account

[Claude Rouelle]

Racing is nothing else than transient but racing analysis could be QUASI steady state

[BillCobb]

Racing is nothing else than transient but racing analysis could be QUASI steady state

That would be pages 308 and 309. Beat ya to it, Doug !

Besides, smooth (smoove) is fastest, with minimal r-dot. Tires like to be in a momentary steady state. The fastest drivers look slow. When you see a driver sawing at the wheel, its not gunna be a good day.

[rory.gover]

At OptimumG we always take r into account

Yeah, r is taken into account. But I guess the point of my input was to highlight that r (chassis rotational velocity) does not equal ay/V, or even an/V. Omega (the rotational velocity of the velocity tangent direction) does is equal to an/V, and to find r from omega you need to remove the body slip velocity. So yeah, you can take r into account, but you need to ensure you have the right value of r.

Also, while small angle approximations might make sense if calculating the slip angles once or twice, I would hazard to suggest that if you are going to determine a Cn-Ay or Az-An diagram it may be worth the extra computational expense to make use of proper cosines et al.

[BillCobb]

Steady State: Beta-dot ~ zero. Race tires: Mu max ~ 3-4 degrees slip. Cosine / Sine inclusion should not be costing you that much extra computational overhead.

If you use Matlab, ask the PROFILE and PROFILE VIEWER functions to show you where all the cycles are being spent. Then 'fix' the heavy hitters.

For example, I use Watcom Fortran modules to do the heavy lifting in Matlab, driven by a pre- and post- processing GUI foundation.

[Claude Rouelle]

Yes many students (and engineers) mix yaw velocity and slip angle velocity (Beta dot)
Yaw velocity r = V/R is correct because the slip angle speed (beta dot) is = 0 because in steady state Beta is constant
The gyro captures everything: the total of V/R AND Beta dot but doesn't tell you what part if yaw velocity due to V
/R and what part is from Beta dot. To do that you need a slip angle sensor.

[Claude Rouelle]

In the last FSG Electrical design final I judged half of the cars did have slip angle sensors.

[Claude Rouelle]

Bill,

Answering your question that was posted in the wrong thread (Mumbai seminar)

Most of the teams used the slip angle sensor either to validate their vehicle simulation and/or use its signal in the control loop of their 4WD torque vectoring / traction control / launch control .
In one hour of judging I could not go in the details of each team use of theit slip angle sensor.
I would say that for one third of them the slip angle sensor was used as a BS smoke bomb, just a kind of show off with no substance (but I bet they will be much better this year - you always need a first time), one third was REALLY good - the guys know what they are doing - and the rest was in between.
I know that is a generic answer but for more we would need more than a FSAE thread: a seminar, a webinar or a complete PDF report - which most FS teams are not good at.

Claude

[BillCobb]

I posted my question on the Mumbai thread so as to not bump your seminar announcement.

Since as you say, there are some teams with a sideslip sensor, there should be a subset of them who can also sense yaw velocity and forward speed: all the elements of a perfect storm of test data suitable for evaluating their handling models on a professional level. Maybe even steering shaft angle.

Add a few slides on how and where to mount these devices, sample rates, power needs and an example test procedure. THEN the seeds you plant now will flourish and be ripe and ready for picking next year, too. It's long overdue. I can see why some teams would not want to publish their results, but all it takes is ONE and the gates will open up.

(Maybe you already have this in the Program, but it sure would be nice to have a Forum thread with some meat in it for once instead of just bones and half baked bread).

[Z]

Claude and Rory,

Both TOO SLOPPY!!!

NO DEFINITIONS!!! Why such negligence?

Too much alphabet-soup, with too much of the extra-strong Cottage-Industry flavouring, and negligible attempt to give even the vaguest hint of what the little noodles represent. (Rory, should the noodles spell "BSAV", or "BVAS", or "BodySlipVelocity" as in the graph-headers???)

No wonder the students struggle with this.

Quite obvious that the students should struggle, given that both descriptions (C's and R's) are conflating Point-Mass-(or Particle)-Mechanics with Planar-Rigid-Body-Mechanics, with nary any attempt to explain which noodles apply to what Mechanics.

For example, it should be abundantly clear that a point-mass CANNOT HAVE A YAW-VELOCITY (as was suggested in C's RCE1 article), let alone a Yaw-Angle or Yaw-Acceleration. (Read Euclid's "Elements", Book 1, Page 1, Definition 1, to find out why.)

So why mix the noodles from the two different fields of Mechanics into the same equation, and then pretend that this is in any way helpful to understanding? Oh yes, I know. It is because stirring the noodles in the alphabet-soup is FUN, and you can keep doing it forever, without going anywhere...

Moving on, from Claude in an earlier post:


The gyro captures everything: the total of V/R AND Beta-dot, but doesn't tell you what part is yaw velocity due to V/R and what part is from Beta dot. To do that you need a slip angle sensor.(My added punctuation and spelling correction.)

Geez, I explained this to you 15+ years ago! YOU DO NOT NEED A GYRO, OR A SLIP-ANGLE SENSOR, to track the full 3-D motion of the car-body, WRT "the fixed stars", or wrt an approximate "ground reference frame", or "the track", or possibly Rory's "X,Y frame", but I can only guess at that last one because it was never DEFINED.

I have to wonder if Claude has shares in the company that sells those EXPEN$IVE $en$or$. It can all be done much more cheaply, more easily...

Z

[Claude Rouelle]

If you can do a cheap and accurate slip angle sensor then just do it, Z!

And no I do not have any ownership in any slip angle sensor companies.


What I can tell you is that no one of these teams in FSG E did pay for their slip angle sensor: they make a technical partnership and a knowledge exchange. Companies that manufacture such sensor do like to have students telling them what they do not understand and they like out-of-the-box most of the time very useful observations.

I just know the benefit of using it. Just think as an example about traction control and the exact measurement of slip ratio.

I also know that most OZ teams even if they had one free of charge won't know what to do with it.
Most of them have much bigger and simpler challenge like reliability just to name one.
The top OZ teams could use it if they had the sense of the level of competition of excellence that is now required in the international world of FS competitions

On that perspective: on one hand you help - very well- students getting back to the more than necessary basics but on the other hand with your ideal ultra simplistic car, your lack of international experience, your lack of proven records on the race car engineering international scene, you discourage them to be a touch more sophisticated and competitive on the knowledge and on the tracks outside Australia.

OZ FS team have lost the competitive advantage they had 10 years ago and I have to wonder what part you played in that loss.

[maxay1]

That was kind of an unfortunate response, Claude. Insulting OZ student teams with the hope of blaming Z for their perceived lack of success does not speak well of you. You could have just as easily engaged Z in a more positive manner, and those following this thread
would benefit from the resulting discussion.

[BillCobb]

experientia magistra est difficile.

And from 1999: 1294

we are looking at sideslip angles on the order of 1.5 to 2.5 degrees per g, read at this mounting location between 0 and 2 g. Things are a better now, but this Datron was state of the art 20 years ago.

[Tim.Wright]

Claude,

Out of interest, how many of the teams using a slip angle sensor have built it themselves?

Has anybody else figured out that a caster wheel will do the trick?

[Claude Rouelle]

Tim, I am going to look stupid but I have to ask: what is a caster wheel? Do you have picture or a simple sketch?

[BillCobb]

A caster wheel type sideslip sensor is essentially a tiny single axle trailer with 2 'tires' on it. It is configured to follow the roadway such that it stays aligned with the vehicle velocity at the mounting point and is zeroed at the vehicle's longitudinal centerline.

The suspension arms are hinged so that body ride motions do not interfere with the measurements. Same for roll by the use of 2 wheels. We used such a device very nicely to directly measure rear cornering compliances when the transducer was hung from a rear axle mount. Easily calibrated with a belt sander and an engine lathe rotary index vice.

Nowdays, you would use multiple digital encoders to measure the 'tow' angle and also the wheel speed to get vehicle velocity. The trailer tires had negligible slip or it could be compensated for during calibration for the hard-noses of the day. Pretty simple, elegant and accurate for the kind of rear cornering compliances of the day (4 - 8 deg/g) All it would take is a redundant test with a Datron to end the suspicion. Ours used treadless aircraft slicks about 10" in diameter, tongue length about 16" as I recall.1295

[DougMilliken]

Mine used 3" OD tires that I made from 1/4" thick sheet rubber, sandwiched between two 1/16" thick aluminum disks... a more robust version of the model tire in RCVD on page 16. I was able to sneak the caster wheels and trailing arm suspension under the street car, so the caster wheels were under the CG. For that job we wanted to measure vehicle slip angle, not rear axle slip angle. The two little tires were separated laterally on an axle with roll degree of freedom, so as well as beta, it also measured chassis roll angle directly to ground.

Then a macho test driver decided that the short way back from the skid pad (VDA) was through some 2" gravel. The stone impacts ruined all my nice machining.

This was early 1980s -- but before I built mine, I read an earlier GM paper that used a single castering tire for a slip angle sensor.

[Z]

Rory,

I wanted to comment on why there is a "...coupling between normal acceleration, body slip velocity and chassis yaw velocity...", but I guess I should attend to the usual distractions first.
~~~o0o~~~

Claude,

I agree, FSAE-Oz is going down the crapper. More on that below. But who is at fault?

Your "Claude-Logic" suggests:
1. If a race team that you, Claude, are doing some work for is successful, then clearly you are the reason for such success, and you can spruik that success as your "...proven records on the race car engineering international scene...".
2. Of course, if any such team is a miserable failure, then this failure is NO way your fault.

And similarly, but the other way around:
3. If any FSAE-Oz team is a miserable failure AFTER I have talked to them, then obviously it is a miserable failure BECAUSE I talked to them. (BTW, this type of thinking was well known to all Mediaeval school-boys as "Post hoc ergo propter hoc" thinking. Namely, NONSENSE!)
4. And all the successful FSAE-Oz teams must never have payed any attention to anything I have ever said, at all, ever.

5. And, by similar logic, Paris Hilton enjoys her jet-setting, A-list, lifestyle because she is such a clever and hardworking business woman, and her "success" has nothing to do with daddy's money.

Fact is, all the FSAE-Oz teams near the top of the ladder have at least "considered" the many suggestions I have made over the years. They have then discussed these ideas amongst themselves, mulled them over, analysed them qualitatively, and then quantitatively, putting numbers to them, and eventually they have come to a conclusion based on these, frankly, very long and boring reasoning processes.

On the other hand, the teams at the bottom of the ladder have just charged ahead and built a mini-F1 car, like their testicles, and all the experts, told'em to. NO BORING DISCUSSIONS REQUIRED!
~o0o~

So, Claude, are you open to some discussion?

For example, in your RCE2 article, linked by you earlier in this thread, you write:

"The yaw moment equation is as follows: (FyLF cos dLF + FyRF cos diRF)a- (Fy LR + Fy RR) b + FxLF Tf /2 + FxLRTr /2 – FxRF Tf /2 + FxRR Tr /2 - MzLF –MzRF - MzLR – MzRR = Izz (dr/dt) ... This equation is made in the chassis coordinate system, which is why the cosines of the inside and outside front steer angle are used." (My emboldening.)

The same equation is repeated in Figure 1 of that article.

Let our "dialogue" begin this way:

I say that your above equation is seriously wrong. I say that a whole lot more "cos-delta"s, and even more "sin-delta"s, are required for the equation to be at all useful. And some of the +/- signs also need changing.

Now, perhaps these errors were introduced by the editors at RCE, and so are the editor's fault? A very likely thing! But if so, then why have you not corrected the errors in the .pdfs on your website?

What do you say??? (<- Your turn to continue the dialogue...)

Or are you now going to refuse to enter into this dialogue? Much like your previous NON-discussions of the subject of Direct-Acting-Spring-Dampers? And to hell with the student's understanding of these subjects!???
~~~o0o~~~

This is not really the place to discuss the falling standards of FSAE-Oz, but while I am here...

Recently it has become quite clear to me that the current management of FSAE-Oz are in a frantic race-to-the-bottom. Everything is being done to reward the no-hoper teams, and this is coming at the expense of the better teams. There have even been, to some degree at least, attempts to "nobble" the top teams.

An increasing number of the top teams are now not even bothering to come to the Oz-event. They prefer to fly directly overseas for their comps. Monash still attends Oz-comp because, by my guess, the event is in their backyard, and it is as good as any other practice session.

Over the last few months (and, indeed, years) I have tried to engage in a dialogue with the FSAE-Oz organisers to address this issue. But so far this has been as succesful as trying to openly discuss DASDs with Claude. Or trying to have a pleasant chat with the statues on Easter Island!

In short, the way that these people "manage the troublemakers", such as myself, is to turn them into UN-persons. Read Orwell's "1984". That is, NO DISCUSSION REQUIRED!

So, unless there are big changes upstairs, I confidently predict that all the third-rate Indian teams will be flooding into FSAE-Oz, ... because we have a swag of trophies waiting just for you!
~~~o0o~~~

Finally, for now, students might like to compare Claude's apparent dislike of the idea of an "...ultra simplistic car" with this quote from Newton's Principia, under "Rules of Reasoning in Philosophy".

"...more is in vain when less will serve; for Nature is pleased with simplicity, and it affects not the pomp of superfluous causes."

Of course, Newton had an even greater "...lack of proven records on the race car engineering international scene..." than Z, so what would he know!? :D

Z

(PS. Tim,
Or an "L-shaped" bit of fencing-wire. End of horizontal bit drags on ground. Vertical bit pivots on chassis and can slide up-down. Maybe an elastic-band pulling down for good road contact. TPS on top of vertical bit. Or just a pointer-and-protractor-scale on top of vertical bit, viewed with a Go-Pro camera.)

[DougMilliken]

...Or an "L-shaped" bit of fencing-wire. End of horizontal bit drags on ground. Vertical bit pivots on chassis and can slide up-down. TPS on top of vertical bit. ...
Z -- while I appreciate your minimalism, please elaborate. I just tried this with a bit of L-shaped wire on my smooth table top and found: as soon as the vertical bit leaned (even very slightly) away from "square with the table," there was a large error in the direction-sensing of the dragging horizontal bit.

[Z]

Doug,

Yes, I know what you mean (= "KPI effect").

I made it TOO COMPLICATED. It could be simplified to a straight bit wire, dragging behind the car from a simple hook. There are also some other issues that need "fine tuning". But hang the L-shaped wire off a beam-axle and you have cheap 90% accurate answer right now, rather than an expensive 99.99% accurate answer "...err, when we can afford it...".

Also, my current thinking for replacing both gyros and slip-angle sensors would not even bother looking at the ground. Mostly solid-state stuff, plus good software.
~~~o0o~~~

Rory,


https://i.imgur.com/m2q1gy4.png
... So it's obvious there is a coupling between normal acceleration, body slip velocity and chassis yaw velocity...

What is perhaps not so obvious is that the above "coupling" is NOT in any way necessary, or intrinsic, to the Mechanics of the situation. The "coupling" is in fact nothing more than the result of some arbitrary decisions made by some Cottage-Industry workers many generations ago, and modern students are simply, and perhaps blindly, following that lead.

As a first step to understanding this, remember that the noodle-equation of "An = V^2/R" comes from the Kinematic sub-field of Mechanics that studies a POINT moving along a space-curve. (On this thread the space-curve is in its 2-D-Lite, or Flatland, form of a plane-curve.) The "An" represents the Acceleration of the point Normal to the space-curve, the "V" represents the point's Velocity along the space-curve, and the "R" represents the instantaneous Radius-of-curvature at that position along the space-curve. So far all this is pure Kinematics, but you can move into Dynamics by multiplying the RHS of the equation by Mass to get the Force required to cause said Acceleration.

The very important point here is that the word "Yaw" should NEVER appear anywhere in the above Mechanics. To suggest that the above "point" has any sort of Yaw-angle, or Yaw-velocity, or Yaw-acceleration, is utterly meaningless!

So how did the "r", namely the car's rate-of-change-of-Yaw-angle, or its Yaw-velocity, get "coupled" into the equations (ie. in above image)?

Well, you, or those Cottage-Industry workers from years ago, put it there!

That is, the curvature of the space-curve is defined, in this Cottage-Industry approach, as the angle-of-the-space-curve, "Beta", WITH RESPECT TO a somewhat arbitrary reference-frame "x,y". Unfortunately, this frame "x,y" keeps changing its orientation WRT the ALL-IMPORTANT INERTIAL reference-frame "X,Y". (Note that "A=V^2/R" is nonsense in a NON-inertial frame. For example, a reference-frame fixed to the surface of the Earth, such as "the ground or track", which is spirallng through space! But how much error comes from using this non-inertial ground-frame? Easy to calculate, and fortunately not much.)

Now, the intermediate-frame "x,y" is perhaps not so arbitrary, because it was specifically chosen to track the "heading", or "rotational direction", or "Yaw-angle", of a thing that is extended in space, and that is considered to be Kinematically perfectly rigid, and is meant to represent the "Car-body".

So what has happened is that the movement of a POINT along a space-curve has been defined in such a way that it is is built on, and must include, the orientation "Theta" of a RIGID-BODY, namely the intermediate-frame "x,y", WRT the inertial-frame "X,Y"!

So there has been, for 50+ years now, a thorough mixing of two different fields of Mechanics, namely that of "points", which CANNOT "YAW" (!), and that of extended "rigid-bodies", which can yaw. The unfortunate part of all this is that the alphabet-soup nature of the presentation makes it hard to distinguish which noodles refer to the Point-Mechanics, and which refer to the Rigid-Body-Mechanics.

Of course, you could start by defining the space-curve DIRECTLY WRT the inertial-frame "X,Y", say by using a noodle called "?", which when dotted becomes the "W" or "Omega" that you have above. Easier calculations, with only one angle to track. Well, at least for the Point-Mechanics stuff.

But what happens when you want to track the "yaw" behaviour of the extended rigid-body that represents the "car-body"? Well, now you could reference it wrt the direction that the "point" is moving at that instant, namely the V-vector, WRT "X,Y" (!). So something like a minus "Beta", or choose your sign to suit. Then call it "Yaw-angle-wrt-path-direction".

Alternatively, you might want to know the "heading-angle" of the extended rigid-body wrt "X,Y"? So now you have something like "Theta" = "?" + (or -) "Beta", and you can call it "Yaw-angle-wrt-fixed-stars".
~o0o~

Anyway, all this becomes very clear when you start-out with a clear understanding of what you are modelling, such as "points" or "rigid-bodies", and you then continue to be very clear with the DEFINITIONS of the noodles used to represent said modelled things.

But just picking up a bowl of thoroughly pre-stirred alphabet-soup, and expecting to make sense of it, is a recipe for misunderstanding.

Z

[DougMilliken]

It could be simplified to a straight bit wire, dragging behind the car from a simple hook.
You'll also need a counterbalance (in front of the hook), or the wire will swing out on turns. But now that it's balanced there isn't any contact force between the trailing wire and the road...back to the rubber band, oops, the rubber band also exerts a centering force when the wire trails off to one side. Moral--transducer design isn't that simple.


...some arbitrary decisions made by some Cottage-Industry workers many generations ago,
No need to wonder, we name names and give references in RCVD Chapter 4. While you may not like it, the SAE vehicle axis system came from aeronautical practice. Given the number of successful aircraft, it can't be all that bad as you make out.

[Z]

Doug,

Well, I just spent 5 minutes making a "L-shaped wire and elastic-(rubber)-band" slip-angle sensor, and it works a treat!

I fitted it to the back of my wheelbarrow, for easier visual checking of how it works, and to allow very large roll and slip-angles to be checked. In short, the frictional drag-force on the end of the wire dominates over any "KPI self-centring" effect.

Still lots of polishing, calibration, and validation that could be done. But IMO students will learn a lot more about instrumentation accuracy by taking this route, or the more upmarket castor-wheel version, than by buying an expensive, off-the-shelf, sensor, and then quoting all their slip-angles to 9 (12?, 15?) significant digits. As they tend to do these days.

As for "Cottage-Industry alphabet-soup", I have no real problem with this approach. My main annoyance is the very sloppy way this "cogitatio caeca" (= "blind thinking") is presented these days. Super-sized bowls of noodles served-up as deep and meaningful truths, but with no clear explanation of assumptions, derivation, limitations, and so on.

So, has no one else seen the massive errors in Claude's "yaw moment equation", that I referred to earlier?

The errors are most obvious in Figure 1 of RCE2.pdf. So much so that two of them stick out like the proverbial dog's bollocks!

Z

[mech5496]

There was a post in here somewhere, I believe by Bill, on using optical mouse sensors to build a relatively simple and cheap, vision-based slip angle sensor. Shame I cannot find it anymore.

[Tim.Wright]

Tim, I am going to look stupid but I have to ask: what is a caster wheel? Do you have picture or a simple sketch?
A caster wheel ('roulette pivotante' in french accoring to leo.org) in its simplest form is a shopping trolley wheel. The wheel will, in steady state, point along the velocity vector of the mounting location w.r.t. ground. The transient slip angle can be found using the angle and rate measured by the trailing arm and the vehicle velocity as measured by the rotating wheels.

I drew up a design for this while I was still in university but never had the time to make it. The concept can be found here:
https://1drv.ms/b/s!AioEiFs0jfZSgVc5hbwAOWexfqFI

The design was made to have the CG of the trailing arm assy along the vertical pivot axis but the counter balance the Doug mentioned were to be included in the green plate in front of the pivot if any corrections were required.

I've seen a similar concept used in the cottage industry too where its more accurate at low speeds than the GPS based systems which cost 50k+. I know my old uni trialled a similar concept last year. I will let them elaborate if they want.

You still need a gyro though to transform the slip angle from the measurement point to the CG and front and rear axles for cornering compliance analyses.

I doubt the idea can be any good though because my track record is nothing special. My FSAE team always came last and every shool I went to in my life was demolished shortly after I left.

In terms of definitions the slip angle is, in my opinion, unambiguously defined in Milliken, Guiggiani, Pacejka, ISO 8855 and SAE J670e. Clear as a dogs donger in my opinion - I don't get what all the fuss is about.

[DougMilliken]

Tim,

Quick question, what is the assembly with #11 pointing at it? Seems like the vertical (slip angle) pivot must be inside the blue cylinder?

Yours looks much more robust than the one I made ages ago, I had the extra constraint of very low vertical height, to fit under the CG of a production car without any big holes in the floor. Too bad that yours wasn't tried, looks like it should have worked OK to me.

[Owen Thomas]

There was a post in here somewhere, I believe by Bill, on using optical mouse sensors to build a relatively simple and cheap, vision-based slip angle sensor. Shame I cannot find it anymore.

I saved the paper that post was centered around, unfortunately it's above the 19.5 KB (!?) limit for PDF attachments. If anyone is interested google "Development of a Low Cost Slip-Angle Sensor" and it should come up for you in the first couple hits - published 2013 by Nathan Tarlinton of University of Wollongong.

Taking that approach is a nice middle ground between the low-tech castor wheel (and ultra low-tech wire) and a black box high end sensor package. It's arguably going to teach a lot more about modern instrumentation in the process too, as long as the right steps are taken for proper data acquisition.

[Tim.Wright]

Tim,

Quick question, what is the assembly with #11 pointing at it? Seems like the vertical (slip angle) pivot must be inside the blue cylinder?

Yours looks much more robust than the one I made ages ago, I had the extra constraint of very low vertical height, to fit under the CG of a production car without any big holes in the floor. Too bad that yours wasn't tried, looks like it should have worked OK to me.

That assembly is a steel tube which houses the potentiometer (blue cylinder) and 2 bearings for the vertical spindle. The tube is threaded on the outside surface for mounting to the vehicle.

I didn't worry about height as I assumed it would be mounted off the front or rear of the vehicle and then the measurement transformed to the CG using the yawrate.

The only thing missing that I feel is important is the velocity measurement using the wheel speeds. With such small wheels I don't know how accurate the velocity reading would be. Actually there isn't any real reason that the wheels have to be that small.

[rory.gover]

Harry,
I believe I linked to the article you are referring to: http://journals.sfu.ca/vte-j/index.php/vte-j/article/view/6.

Erik,
I think we're on much the same page here, though we come at the matter with different tacts. Perhaps I am too subtle and that is a failing of mine? I would say that in general, motorsport VD relies far too heavily on models utilising implicit (behavior generation through gradient extrapolation and iteration), Eulerian (fixed particle, flowing field) schemes without necessarily understanding the limitations of the strategies (or perhaps not understanding that the scheme is inherent in the calculations).

The way I read your critique of moment diagrams (save for critiques of both personalities and typographic renderings) leads me to surmise you are suggesting modelling - through time - the motion of a rigid body through space (using tyres for et al) and subsequently measuring the body path through space to determine parameters including yaw rates, slips etc. This could be described at an explicit (current behaviours integrated updated through time over small time steps), Lagrangian (moving particle, fixed frame ) model. This akin to the (bicycle?) model you presented in thread a while back, and is something that I advocate for relatively strongly. When people speak of 'transient' models, this is more often what they are discussing (n.b. transient, non-linear behaviours can be, in general modelled using implicit techniques and are often more efficiently modelled in an implicit time scheme).

Using a well-prescribed test to examine the performance limits allow for much greater insight into the vehicle behaviour; a chirp steer test (constant velocity with increasing steer frequency) is great for looking at normal and yaw acceleration limits. The below is a four-wheel, suspended chassis and suspended wheel model, with absolute bodge vehicle parameters.
https://i.imgur.com/8rBpUej.png

Once you have the explicit, Lagrangian vehicle model ready, you can feed in whatever test characteristics you want. This framework allows you to conduct other tests with relative ease (e.g. understeer, constant radius, etc.) to characterise a vehicle concept readily.

[Z]

Tim,

Sorry, just some small corrections. :)


A caster wheel ... will, in steady state, point along the velocity vector of the mounting location w.r.t. ground.

Actually, it points along the velocity-vector of the Car-Body-reference-frame, at the castor's WHEELPRINT-"POINT", wrt Ground.

So the "Slip-Angle" is measured at a point in the CB's reference-frame that moves around as the castor (or caster) swings left and right. So if the castor has a long "trail", and the corner radius is very tight, then there can be significant differences between the SAs at the castor's "mounting location pivot-point", and at its "wheelprint-point".

However, with a short "trail" of say a few centimetres, and even with the typically tight FS/FSAE corner radii, I doubt this "error" would be a problem. Anyway, it is an error that can easily be subtracted by some post-processing of the signal.
~o0o~


You still need a gyro though to transform the slip angle from the measurement point to the CG and front and rear axles for cornering compliance analyses.

Or you can fit TWO castor-wheels, one at front-of-car, and one at rear. The two measured velocity-vectors, of front and rear of Car-Body-frame, wrt Ground, then give a complete description of the motion of the Car-Body wrt Ground, at least in Flatland.

But, in fact, it is even easier. You just need the angle and rolling velocity of one castor, and then ONLY THE ANGLE of the second castor. Kinematic's "Axiom of Rigidity" then lets you find the velocity of all other points on the Car (ie. you assume the Car-body is rigid, so it stays the same shape, always...).
~o0o~

Nevertheless, I DO LIKE the idea of a castor-wheel. My L-shaped wire has left scratches all over my driveway! (Grrr ... hopefully should buff out...)

Z

[Z]

Rory,


The way I read your critique of moment diagrams ... leads me to surmise you are suggesting modelling - through time - the motion of a rigid body through space ... and subsequently measuring the body path through space to determine parameters including yaw rates, slips etc. This could be described as [being like the] explicit ... Lagrangian ... model you presented in [another] thread a while back...

Yes, that is the way I generally prefer to do things. Three points below to explain the "why":

1. These "mathematical models" are tools. And as with all tools, different people have their different preferences. One person will use a laser-guided, diamond-tipped, boring-tool, while another prefers his sledge-hammer. Ultimately, the only thing that matters is that the job gets done. That is, the job is finished properly, correctly, everthing works as it should, and so on.

But, of course, some tools will get the job done more quickly, or easily, or cheaply, or, most importantly, with less chance of cock-ups.
~o0o~

2. With these mathematical models, I see a great advantage in choosing a model, or a "map", that, to human eyes and mind, looks as close as possible to the "terrain" that you are trying to navigate, or investigate.

So the rather abstract graphs of a YMD/MMM, or the left two images in your last post, might be able to be read by a VD-specialist with long training in such things. But any anomolous car behaviour appearing in that map might NOT be so obvious to the less trained eye. Or, indeed, not even to the trained eye that only has time for a quick glance.

Your third, rightmost, graph (maybe with equal X, Y scales) gives a more obvious and compelling indication of anything that might be wrong VD-wise. Especially if it is animated (ie. moving pictures) and it includes tyre-screeching sounds, possibly followed by the car rolling over and bursting into flames!

That is, I find the model that is easy to understand, and hence with less chance of my missing something important (= less chance of cocking-up), as the preferable one.
~o0o~

3. This next point is a huge subject, and was much debated throughout the 1600s and 1700s ++, so only the briefest comments here.

The old-fashioned Geometric way of solving problems, epitomised in Euclid's "Elements", involved symbolically representing the "real world" with ink lines on flat sheets of paper. (In fact, originally by using a stick to draw lines in smooth sand.) This is a SYMBOLIC ABSTRACTION of the real world, albeit one that is NOT TOO FAR removed from reality. A Chinaman, Masai, or Eskimo will all be able to grasp the connections between "map" and "terrain" quite easily.

This all changed when Rene Descartes added the short appendix "La Geometrie" to a much longer book he was writing on philosophy (~1637?). Here Rene put forward a new method of solving, or proving, Euclidean problems/propositions. I recall he ended an example in that appendix with something like "See, I have solved it without drawing a single figure!". That method is now commonly known as "analytic geometry", and like Rene it still uses "a, b, c"s for the knowns, "x, y, z"s for the unknowns, "Cartesian" axes, and so on.

As noted, when Rene's book was published there was much controversy over this new "cogitatio caeca" way of doing things. Along with "blind thinking", it was also described as "mechanical" or "imaginationless" thinking. These names were given because there was virtually NO connection between the symbolism, namely the abc's and xyz's, and the actual physical problem. It was perhaps AN ABSTRACTION TOO FAR. And once the problem was cast into its alphabet-soup form (<- err, my term), it became nothing more than a mechanical process of stirring the soup (ie. manipulating the equations) until the desired result appeared. With never any hint of how far from reality you might be drifting.

To stress this again, throughout the process of stirring the soup, or manipulating the equations, there is NO VISUAL CONNECTION between the "map" (<- the algebra) and the "terrain" (<- the real problem). Hence the description of a "blind" or "imaginationless" approach. Contrast this with, say, a geometrical solution to Free-Body-Diagrams. Here, each step of the process involves "seeing" something that looks very like the "real forces" acting on the "real body", albeit with the forces combined or decomposed in many different ways.

Anyway, Newton was initially besotted by this "New Maths" as a young man. But when he got older, and wiser, he wrote his "Principia" in a style that was remarkably similar to Euclid's Elements. (One day I will have to rant about the "piece of string" that lies at the core of the Elements, and why the ancient Geometers were so highly regarded...)

More recently the Western Education system has settled for the Cartesian approach, unfortunately exclusively, with never a mention of Euclid! I speculate that this has been driven mostly by the ease of typesetting "equations", and the apparent difficulty of presenting "figures" or "sketches". This Forum is a good example, with NO sketching facility! Grrrrr...
~o0o~

End of rant. Will probably hit character limit soon.

But remember, just because everyone else is doing it, surely don't mean it's the best way!

So YMD/MMM? Or visual graphics of a car fish-tailing around a bend?

I prefer the second, with sound-effects!

Z

(PS. I'll give an example of "visual" versus "blind" thinking tomorrow.)

[rory.gover]

At 5x speed, a chirp steer test conducted at 50 km/h over 20 sec. Red-line connects vehicles CoM to CoM centre of curvature (obviously this tends to +- infinity as the normal acceleration tends to zero), blue-line indicates vehicle heading.

https://i.imgur.com/SqYdb0b.gif

[Z]

Rory,

Yes! The first step to understanding VD, IMO, is being able to watch a car, either real or modelled, do its thing. As such, your above type of "map" should be one of the first outputs of the modelling process.

(And it seems that .gifs delivered via "imgur" work much better than the google/picassa rubbish that I had to jump through so many hoops to get working, many years ago. More grrr...)

Also, as you said earlier, "Once you have the explicit, Lagrangian vehicle model ready, you can feed in whatever test characteristics you want [which] allows you to conduct other tests with relative ease (e.g. understeer, constant radius, etc.) to characterise a vehicle concept...

It also makes it very easy to pull any amount of performance data, or "DAQ", out of the model, because all the data is being generated by the computer as the tests are run (as you also noted). So all the Betas, Thetas, Yaw-rates ("r"s), Tyre-forces, Tyre-SAs, +++, are all already in the box, and you can plot them any which way you want.
~~~~~o0o~~~~~

Back to alphabet-soup, or "blind" versus "visual" thinking.

Here is a screen-shot (hopefully!) of Figure 1 of Claude's second article, RCE2.pdf. At the top of the image is a visual depiction of a car, that, while certainly being a "symbolic abstraction" of reality, is also something that most people can recognize as a top-view of a car, together with some superimposed arrows. At the bottom of the image is the "super"-symbolic, alphabet-soup representation of those "closer-to-reality"-symbolic arrows.

http://www.fsae.com/forums/attachment.php?attachmentid=1296&stc=1

Right at the start of the article Claude writes, "...there are 12 causes for the yaw moment: four tyre lateral forces Fy, four tyre longitudinal forces Fx; and four tyre self-alignment moments Mz.". So it is reasonable to interpret most of those arrows drawn on the visual image as the four tyres' Fx, Fy, and Mz forces.

Now, does anyone see something that looks not quite right, either in the image, or in the soup?

Can anyone see the dog's proverbials?

For me, it took just a quick glance around the visual depiction of the car and its arrows, before I was thinking "Why the hell does he have the front-wheel-yellow-arrows, presumably the "Fx"s, aligned with the chassis-frame, and not in the wheel-frame where they should be, namely perpendicular to the blue-axial-arrows, presumably the "Fy"s???". This ease of "seeing things" in such visual maps, is, of course, their huge advantage.

Anyway, I then trudged through the alphabet-soup version of the same thing, a slower and more painful process, and found many errors. Short list:
1. Both front-wheel-Fx COS- and SIN-delta components missing, given that the Fxs should be cranked around to be perpendicular to the Fys.
2. Both front-wheel-Fy SIN-delta components missing. (They do NOT cancel out, because Fyrf is much bigger than Fylf.)
3. A "+" near the right-side of the bowl of soup should be a "-".

And as a lesser note it would be helpful to have the arrows on the visual map suitably labelled. And to read in the text something like "... aero-forces ignored...".

Z

[BillCobb]

A Message to Garcia: a widely distributed essay written by Elbert Hubbard in 1899, expressing the value of individual initiative and conscientiousness in work. Hubbard, from my nearby hometown of East Aurora N.Y.

ATTN: I'm trying to promote a .pdf file format for relevant presentation material on this thread's topic, but it's too big to attach. Who can I send it to to load ?

[BillCobb]

OK boys and girls, somebody tell me if this link gets you connected with my trivial offerings.

https://drive.google.com/drive/folders/1Xusvpu_QOvjfZgCDzHut0yiCQq29SX3V?usp=sharing

[maxay1]

Bill, looks like the link works: I see some chirp test documents (thanks for those) and an image of a 'vette being tasked with hauling hay.

[rory.gover]

I tried out the pulse steer method to tease out the freq response from a vehicle (again, Lagrangian mechanical vehicle model). results below (gifs @ 120 km/h).

Pulse steer - 10 deg SW over 2.5 sec with 10 sec test length
https://i.imgur.com/p3QXKcs.pnghttps://i.imgur.com/FwbpjFw.gif

Chirp Steer - 10 deg SW with steer freqs from 1/10 through 2 Hz over 20 sec
https://i.imgur.com/nrHrd9c.pnghttps://i.imgur.com/rYoKsNc.gif

Seems that in this scenario (and with this vehicle model), the pulse steer methodology correlates reasonably at low freqs but can't sense the info at the mid speeds. Obviously, this depends on the details put into the pulse definition. On the plus side, the size of the testing domain is reduced bigly.

[BillCobb]

A Sim should easily produce results looking like this. Both time based and complex frequency based (as shown).1297130113021303

See if this works now.

https://drive.google.com/drive/folders/1Tcv5a8MaYmlDRjbru8UXlE1fnK2NaGND?usp=sharing