Thread: Plotting Cn-Cy and Cn-Ay Graphs.

1. 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)

***

2. Originally Posted by Claude Rouelle

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.

3. 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!

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...

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!)

5. 'constrained forces and moments' vs 'cornering sequence' diagrams

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?

6. Originally Posted by Goost
... 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.

7. 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.

8. 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".

9. 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

10. Race Car engineering articles about the yaw moment Vs lateral acceleration method

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/