moment diagram with weight transfer

[DougMilliken]

JT A. gave a good hint.

...1000 thanks to your father, Doug, for such a mind-blowing chapter on this in RCVD.

I'd pass it along, but you are a few years too late -- http://blog.hemmings.com/index.php/2...ken-1911-2012/

[jpusb]

I understand what you mean because that was my first thought and it is easy to understand/visualize when saturating just one end of the car. For instance, leaving beta = 0 and increasing steering, it is obvious that the diagram will fold up on itself due to front saturation (as shown at the very beginning of that chapter in RCVD).

However, what is intriguing me is how this fold occurs (to the right, or to the left, or over the same constant-beta line?) and why does it behave like that (the more Ay, the more it folds to the right for a constant beta). I think this is the product of some geometry and angles, but it also may be the combination of increasing scrub (longitudinal drag-force component of Fy) with increasing slip angles, which also produce a negative contribution to CN, I don't know. It may also be as simple as the Fy vs SA curves not peaking for high load (hence, high load transfer) cases. Even more curious is how/why is this effect amplified when the two saturated regions (front and rear) meet, at the untrimmed max-g end of the diagram (which is what actually forms this candy-wrapping paper shape).

To finally shed some light, I took some minutes to prepare the diagrams to be presentable for upload here, I removed the numbers because that is not the point anyway. I will only show the constant velocity diagram but the candy feature appears on all my diagrams (constant velocity and constant radius, including infinite which is the simplest case). Below I put links to the two figures, the first is the complete diagram (the axes on this diagram are symetrical so CN = 0 and Ay = 0 is right in the middle) and the second one is a detailed view of the max-g area. Blue lines represent constant steer situations and grayscale lines represent constant chassis slip. The darker the line, the larger its corresponding absolute value, so the brightest blue and gray lines are for zero steering delta and chassis slip respectively.

Complete diagram https://dl.dropboxusercontent.com/u/...%20-%20V11.png

Detailed view https://dl.dropboxusercontent.com/u/...%20-%20V11.png

What do you guys think?

JP

[Silente]

After the discussion has deviated a bit, i would like to redirect it a bit on the original topic, the yaw moment diagram and its use.

I would love to have the feedback of more expert people about the post i published on page 8:

http://www.fsae.com/forums/showthrea...transfer/page8

As i said, i revised the tool mainly about the sign conventions and, although the results don't change dramatically in comparison with the old one, it looks now more correct to me.

The study refers to a very high downforce car, about 1000 kg, cornering at high speed (so aero loads are here important).

I would love to have your feedback about the results i am showing there (both the plot and the numbers) and it would be great to have some hints at what you would actually look, to identify car behaviors and tendencies (max lat acceleration, max lat acceleration in trimmed conditions, stability, control, ...?). Could you eventually advice on "realistic numbers for these metrics"?

@ jpusb,

my study doesn't show the candy effect that you i can see in your pictures and i am not really sure what it could depend of. But could it simply be something related to plotting? The lines are going back on themselves at a certain points, maybe your plotting tool draw somehow simply a "bigger" curve.

[Flight909]

my study doesn't show the candy effect that you i can see in your pictures and i am not really sure what it could depend of. But could it simply be something related to plotting? The lines are going back on themselves at a certain points, maybe your plotting tool draw somehow simply a "bigger" curve.

I think we has to thinking about the tyres, because the limit of the diagram will deppend on the tyre limit. Which is the shape of your tire curve at the limit? If one axle has a big drop-of and the other not, you can for example maybe see this candy effect? I think the quality of the tire model will be very important for this diagrams, maybe not so much for central behaviour (were cornering stiffness will be a mayor factor), but absolutely for limit.

[DougMilliken]

... drop-of and the other not, you can for example maybe see this candy effect?...

I think Roy Rice (CAL/Calspan, RCVD Fig 13.11, p.464-67) started calling this "fold over" of the tire data, when plotted on one of the MMM-style force-moment plots. It does have sort-of a 3D appearance.

[BillCobb]

That's why we make 'carpet plots' of tire data, pressure effort curves for steering valves, and the value of money.

Add a third independent variable (maybe camber, pressure or figmosity for instance) to make it a real 3D curve. This just means you are missing something...

[jpusb]

@ Silente. I don't think it is a plotting feature at all. I can trace this points to actual calculated "car states", and you can see it clearly in the zoomed in figure, where the lines show the trend quite smoothly. What tire model are you using for making your diagram? The boundary in your diagram is so strongly defined! I know you said Pacejka but, could you post some of your Fy vs Sa curves for a sweep of Fz tire curves? (you could plot them without numbers just as I did, I would just like to see their shape). At the moment I am using the TTC round 2, Hoosier 20.5x7.0 front and rear. When I have time, maybe in months haha, I will migrate to TTC 3 which is the latest I have around. Like you, I am also ignoring kinematic curves (motion ratio and stuff are just constants), camber, and so on. I also read you are not considering MZs and FXs. I am considering both, but MZs are really really small compared to the torque the FYs put in. For FXs, in my model, the rear wheels just push the longitudinal component of the front FYs (I call this scrub, is this term correct?), with an open diff though, and no traction circle so they do not compromise their FY capacity for giving thrust. However, I did check this and the thrust they need to give just to react front scrub is so small that they would not loose FY at all.

@ Doug. I don't clearly understand what you say Roy Rice defined as "fold over". I would have guessed the "fold over" would be what is shown in the top-left area of the zoomed in figure I posted, where the diagram folds over on itself due to front tire saturation, as you know. However, the candy feature is produced in the zone combining the two limits and it is different. Is this area what Roy Rice called "fold over"?. If so, damn! I thought maybe someday someone would use the "candy feature" term in a legendary book such as RCVD, you heard it here first! Just in case

@ Bill. I took a quick look at the plot you posted and I can't work out the X axis. However, I am sleepy and just took a very quick look, I will look into it with patience and organize my thoughts before rushing to ask you silly questions! Thanks for the input though.

I think this forum has long needed a thread such as this one.

[DougMilliken]

It's been a long time, Roy Rice died before RCVD was written. I don't remember exactly how he defined things, but my best guess is that this was all called fold over, on the front, rear or both. Saturating the color for larger values seems to work well, a nice touch. One thing to try is to limit the delta-beta range which should reduce (or eliminate) the fold over. Then you can look for other effects at the Ay limit.

[Silente]

Jpusb,

here a picture showing the slip curve of a front tire i am using, with vetical loads varying between 2000 and 6000N.

What is the point exactly in simulating the longitudinal forces if you don't consider how they are influencing the lateral ones? Just to have the weight transfer effect and see what it brings?

Mz are a good point which i want to include as well, as soon as possible.

Again, i would be interested to share about the metrics to look at and their values. I guess there is no universal rule and the sign convention depends influence also the signs of the results, but it would be nonetheless interesting to discuss about how to "read" and use dN/dDelta or dN/dBeta (as suggested by Claude to measure stability and control) both close to the origin and to the maximum lateral acceleration.

What i see is that both this metrics are, in my case, positive and very big in magnitude close to the origin; they then become negative at max lateral acceleration, at least in the base case scenario with TLLTD = 50% at the front.
Moving the TLLTD more at the front (60%), makes the dN/dBeta to further reduce (bigger in magnitude, but always negative) at max Ay (although the max Ay is now smaller) while the dN/dDelta see an increase (still being negative, but now smaller in magnitude).
Moving the TLLTD more at the rear (40%), makes the dN/dBeta to become positive at max Ay (although the max Ay is now smaller) while the dN/dDelta see adecrease (still being negative, but now bigger in magnitude, so "more negative").

[jpusb]

@ Silente. Thank you for uploading the curves. Our tires differ quite a bit in how they respond to load. Your tires peak at smaller slip angles as the load is increased, mine are the opposite way. Maybe that is why we get so different shapes, I don't know. Important question, since both our diagrams are at constant velocity, do you correct the turn radius (thus, slip angles) for each Ay calculated?

Regarding FXs. The way I see it, there are various important aspects of including the FXs. The longitudinal component of the FY on the outside front tire is, of course, greater than the same force on the inside front, this introduces a counter-steering moment, which I think is important. Obviously, this effect increases with increasing slip angles are, which is the case near the boundaries we are discussing here. I did include the traction circle but I just turn it off to simplify things (runs faster too). Last, when I turn the aerodynamics switch on (which is off in the diagram posted above), drag becomes important and it must be pushed by the rear wheels, so maaaybe here the traction circle will be necessary, but I don't know, since drag comes with downforce of course. In a near or distant future, all this FX stuff will have a nice spice up once I include a model for the LSD diff and the FXs of the two rear wheels stop being equal, introducing an oversteering moment that could reshape the diagram quite a bit, I think.

Regarding MZs, although they are small they may alter the shape of the diagram if your car is very balanced (say, the max. untrimmed lat. g is at CN = 0), but I never checked their influence since I always included them (it is too easy to include them really). Furthermore, when say, front tires, are saturated, their contribution to CN is also saturated so MZs will also alter the shape of the boundary of the diagram I think.

Of course, if I had a lot of time I would answer many of my questions myself just by turning on/off things like weight transfer, MZs, FXs, considering or not FY-scrub, etc and analyzing more. I would also be considerably more motivated to continue the development of this model and all if I was in a FSAE team with moderate data acquisition capabilities so to validate, understand, and further develop the car. But I don't have either free time nor FSAE car with data at the moment, so I properly speculate away.

I would love to read the input of the rest of the known or unknown authorities on this subject, including Z's.