Self-aligning torque (SAT) relationship vs slip angle and camber

@kunos

Hi all, I open this thread to discuss about the effects of self-aligning torque in AC tyres. For those who don’t know what it is:

Self-aligning torque, also known as aligning torque, SAT, or Mz, is the torque that a tire creates as it rolls along, which tends to steer it, i.e. rotate it around its vertical axis. In the presence of a non-zero slip angle, this torque tends to steer the tire toward the direction in which it is traveling, hence its name.


So, I made a test with the McLaren 650S GT3 and default setup, and recorded telemetry from it. The process was very simple; accelerate until 4th gear, hit the max speed, and start turning slowly. This is the result:

c5433d3d24b38ba7ffe64411ec907034.png


So, few things to talk about. First and more obvious, the SAT curve (top left chart) goes below zero very early, even before reaching the slip angle peak where the lateral force is at maximum (top right chart, peak happens about 6 deg of slip angle). In this case, it reaches zero at just ~3.6 degrees.

Next, here I compare two runs. One is with cambers at -1 degrees (white), and the other one with -3.5 deg (green). The difference in the buildup part of the curve is quite important, as it already produces significant torque even at 0ish slip angle, and peaks very soon, around 1.5 deg (and the FR tyre is already quite loaded, about 7 kN). Also, the run with lowest camber seems to produce higher total torque, which seems strange. Basically, compared to the low camber run, running higher cambers seem to shift the curve left and down. It could make sense to shift left as higher camber should increase lateral forces in the buildup area of the curve (although it's not very noticeable in this test...). But producing lower torque is weird I think.

1904faae2053940d8dd81cc7db434cf8.png




Here are SAT curves gathered from Internet, sadly there are no comparisons at different camber angles.


Figure-3-Best-and-worst-case-fits-for-a-18570R14-tyre-self-aligning-torque-data.png


eUFmOmc.jpg



T3249Qu.jpg


sa1.jpg



sa2.jpg


b26f85b727f936314b90c8c6f898fd35.png



One might argue that tires are different, and they might not be racing slicks like in the McLaren GT3, but the effect happens as well in the street tyres of the 458 Italia for example (same two options again, low camber vs default camber)

928345f54fc988c133bedfc039bed21a.png


So, in conclusion. I can’t say for sure that “this is wrong”, but to me it looks like the shape of the curve drops too fast. Most of the data shows an aggressive dropoff past the peak, as expected, however in most cases it approaches 0 way later, and in some cases it doesn’t even go below 0, depending on the load, etc. I think this explains a bit (personal opinion) the springy feel of AC FFB, making it go full force as soon as you start steering (though this also depends on the suspension geometry), and already drops an important amount of force when you are cornering at grip peak.

I don’t know if Stefano reads RD anymore, so please feel free to open a thread in AC physics bugs and issues sub forum and copy paste this post, as I am banned from their forum. He confirmed when I asked him in the last streaming that the SAT curve shouldn’t go below 0 earlier than the lateral force slip angle peak, so he might want to check this.

Sorry if you are totally confused with this thread, I am a bit as well, and I sometimes struggle to put order in my explanations :D
 
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