Plotting Cn-Cy and Cn-Ay Graphs.

[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.Heavy-Service-Dual-Wheel-Swivel-Caster.jpg

[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!?

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,

... 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.