Black & Tan 332iT

[Bry5on]

If I understand you correctly, you are saying previously you thought the hub pivoted off of the inner control arm joints and the trailing arms just set toe. But in actuality the hub pivots off the front trailing arm location and the control arms just set camber?

Not exactly, but something close to that yes. Previously I assumed that the rear control arms inboard termination point was close to the axis of the hubs. If that were true, you could calculate the instant center and roll center pretty accurately without factoring in the location of the trailing arm bushing.

The e46 hub is always pivoting around an axis that includes the trailing arm bushing on that axis. The second point that defines that axis is a virtual location where the upper and lower control arms meet (I’ll get to this in a second). If you extend that axis in three dimensions, the instant center is the point where that axis crosses an imaginary vertical plane that intersects both rear wheel/hub centers. Then the roll center is the intersection point of the left and right instant centers.

Ok, so that virtual point where the control arms meet (above). It’s always moving with suspension travel, it’s not technically fixed in space like a true semi trailing arm. However! Because the two inner mounting locations are SO close together, that point baaarely moves as we sweep through suspension travel, which effectively approximates a static point, like a semi trailing arm.

So in conclusion, the e46 is not technically the same as a semi-trailing arm rear suspension, but practically speaking it behaves the same with a very small deviation. That amount of small deviation is related to providing the degrees of freedom necessary to easily adjust camber and toe without changing the suspension geometry much at all.

So, for all intents and purposes, a semi-trailing arm suspension that has adjustable camber and toe. Hopefully that was followable.

[Bry5on]

What would it take to get / make a Mullet tune for those of us w/ CSL airbox + CSL software and different cams (288/280s)? Been doing a LOT of reading about datalogging, tuning, etc.

Mike

Realistically pretty unlikely. Either an engine dyno and a lot of time, or I’d need to daily that setup and iterate for several months. Sorry!

[Bry5on]

Modeled the e46 for fun, now I can do a real analysis of camber, toe and track changes at some point

[Bry5on]

Well. I'll. Be. Damned.

All this time I've been calculating the roll center height of the rear as something astronomical and offensive at ~12" versus a nicer 4-6". After re-running the analysis, I'm calculating a rear roll center height of about 130mm or just over 5" - just about where it should be.

Turns out I'm the fool and I've got egg on my face for making a bad assumption. The roll center height is *just fine*. The front seems to be about 40mm high, so you might argue that a rear roll center closer to 100mm might be better, but you'd be splitting hairs.

Now, the toe control and ride comfort balance still sucks, and the suspension is still heavy and high inertia so there are still gains to be had from the e39 suspension, but the geometry isn't likely to be one of them...

[YoitsTmac]

Is there a book you'd recommend to those who are not engineers who want to learn more about vehicle dynamics and how all these factors (roll axis, CG, multi link vs trailing, frequency response etc) that affect how a car feels and handles?

[Bry5on]

Is there a book you'd recommend to those who are not engineers who want to learn more about vehicle dynamics and how all these factors (roll axis, CG, multi link vs trailing, frequency response etc) that affect how a car feels and handles?

Race Car Vehicle Dynamics by Milliken and Milliken is my favorite: https://www.amazon.com/Vehicle-Dynam.../dp/1560915269

These days there are also lots of great YouTube videos. More recently, the Suspensions Explained Channel has put out a few great videos.

Ultimately the best way for me to understand is to experiment on my own cars by isolating and changing one variable at a time (you see lots of that in this thread, despite the effort of doing jobs twice or even more times). I had an e31 850i manual that I turned into a corner carving monster that used to clean up e46 M3s at autocross after reading the book above and incrementally experimenting until it was great.

[heinzboehmer]

What changed in the way you were calculating roll center?

[YoitsTmac]

Race Car Vehicle Dynamics by Milliken and Milliken is my favorite: https://www.amazon.com/Vehicle-Dynam.../dp/1560915269

These days there are also lots of great YouTube videos. More recently, the Suspensions Explained Channel has put out a few great videos.

Ultimately the best way for me to understand is to experiment on my own cars by isolating and changing one variable at a time (you see lots of that in this thread, despite the effort of doing jobs twice or even more times). I had an e31 850i manual that I turned into a corner carving monster that used to clean up e46 M3s at autocross after reading the book above and incrementally experimenting until it was great.

Thank you! Instant buy. There's also a guy building a cybertruck vehicle of sorts (channel Project66). He did a phenomenal video talking about building optimal suspension setups, but I feel what's optimal depends on your weight distribution and where your CG is. Another great guy talks about building suspension but leaves the details out - still a great watch (channel XF Motorsports). He's absolutely unhinged and lets his dreams steer his engineering. Very cool stuff

[Bry5on]

What changed in the way you were calculating roll center?

Pulling what I wrote in from the sister e46f thread:

The instant center is basically an imaginary point that defines the roll center when combined with the tire location and track width. It is an important part of handling characteristics. In previous posts I’d estimated the instant center location as the virtual point that the upper and lower control arms make, this was an error as I hadn’t considered the true angle of the upper and lower control arms when looking up/down on the car. As a result, the instant center is significantly farther outboard, which means the roll center is much lower and more reasonably placed than I had originally thought. I’ll have to redo the roll center calculation and update my suspension geometry/roll calculator. I’m disappointed in myself for missing this!

So instead of just projecting the upper and lower control arms to a point and assuming that’s roughly where the IC is, I’m projecting those arms to a point, and using that point to define a line that extends outward to define the IC (and in turn, roll center). Very hard to describe in words, I can show you with a model open some time.

Worth noting that jacking is still an issue with the suspension design due to that lower control arm angle, and with the added fore/aft angle I’d been ignoring, jacking looks like it’s even worse. So the butt isn’t lying but it’s not from the roll center itself, just the placement of the members.

[Bry5on]

Thank you! Instant buy. There's also a guy building a cybertruck vehicle of sorts (channel Project66). He did a phenomenal video talking about building optimal suspension setups, but I feel what's optimal depends on your weight distribution and where your CG is. Another great guy talks about building suspension but leaves the details out - still a great watch (channel XF Motorsports). He's absolutely unhinged and lets his dreams steer his engineering. Very cool stuff

Definitely will be pulling up some of those channels, thanks!

[heinzboehmer]

Pulling what I wrote in from the sister e46f thread:


So instead of just projecting the upper and lower control arms to a point and assuming that’s roughly where the IC is, I’m projecting those arms to a point, and using that point to define a line that extends outward to define the IC (and in turn, roll center). Very hard to describe in words, I can show you with a model open some time.

Worth noting that jacking is still an issue with the suspension design due to that lower control arm angle, and with the added fore/aft angle I’d been ignoring, jacking looks like it’s even worse. So the butt isn’t lying but it’s not from the roll center itself, just the placement of the members.

Aah I see. Think I got it, but down to peek at your models sometime.

[nuc1]

Realistically pretty unlikely. Either an engine dyno and a lot of time, or I’d need to daily that setup and iterate for several months. Sorry!

No worries. The same general concept applies, correct? Datalog and make iterative changes to the appropriate maps. I purchased a HTE tune so should be able to adjust part throttle response from there if i’m on the right track.

Mike

[Bry5on]

No worries. The same general concept applies, correct? Datalog and make iterative changes to the appropriate maps. I purchased a HTE tune so should be able to adjust part throttle response from there if i’m on the right track.

Mike

Kinda - you really need an engine dyno to get the cam angles correct with custom cams unfortunately. There’s really no replacement for that. More thorough than what I’ve been doing for sure.

[Bry5on]

Okay, jacking. Let's do some quick math.

Let's assume that the car weighs 3400lb with 50/50 weight distribution and for the sake of simplicity, it's cornering with 1G and 100% of the load on the outside tires. So 1700lb load on each of the two tires. We'll also assume bushings behave like ball joints, which is close enough for this analysis. Also for this analysis, we're going to assume that the suspension isn't moving, which isn't accurate but again, close enough for a first order approximation.

For axes, x will be left-right, y will be forward-aft and z will be up-down.
The lower control arm is 11.2 degrees from horizon
The upper control arm is 6.4 degrees from horizon
Both control arms are ~25 degrees looking down
Lower outer ball joint is 162mm high
Upper outer ball joint is 404mm high

Given that the angle of the rear control arms are in 3 dimensions, and each link can only take force along its axis we need to break this into a couple trigonometry calculations.

First, sum moments about lower link:

(404-162)*upper reaction_x = 162*Load
Upper reaction_x = 162/242*1700lb
Upper reaction_x  = 1,138.0165 lb tension

Sum moments about upper link:

Lower reaction_x =404/242*1700lb
Lower reaction_x  = 2,838.0165 lb compression

Check your math with som of forces in x:

2838 - 1138 = 1700 - check

Now we convert the loads from x to loads in xy. These are all increasing because math.

cos(25) = 2838/Lower_reaction_xy
Lower_reaction_xy = 3131lb
Upper_reaction_xy = 1256lb

Then we add the vertical component of the loads:

Lower reaction_xyz = 3131/cos(11.2)
Lower reaction_xyz = 3192lb
Upper reaction_xyz = 1256/cos(6.4)
Upper reaction_xyz = 1264lb

Now let’s make it easier to understand and normalize the forces for every 100lb of cornering force on the tire:

Lower/100lb = 188lb compression
Upper/100lb = 74lb tension

Now, finally, let’s perform jacking calculations. Both numbers add to jacking because of the angle from horizontal of each arm. Nice.

Jacking_lower/100lb = 188*sin(11.2)
Jacking_lower/100lb = 36.5lb
Jacking_upper/100lb = 74*sin(6.4)
Jacking_upper/100lb = 8.2lb

And sum them together:

Jacking/100lb = 44.7lb

So for every 100lb of cornering load on the outside tire, the e46 suspension is applying 45lb of jacking force to the chassis. That’s kinda nuts.

And now let’s turn this into displacement. Stock springs are 380lb/in (there are two of them)

Displacement/100lb = Jacking/100lb / Spring Rate = .06in

So finally, for every 100lb of cornering load on the tire (this is not much), the outside tire will increase rear ride height by 1/16”

We’ve ignored the opposing force from the inside tire, which counteracts some of the jacking, but its effect is much smaller because the load on that tire is much lower.

If you do some other hand wavy math that I’ll skip, a first order approximation of rear suspension lift due to jacking in the rear is .5-.75” at about 1G, which is about what you can expect from your tires. Yep, you’ll feel that. Twinkle toes rear suspension.

[Bry5on]

Ok screw it, let’s just cover the hand wavy math:

Maximum G of 21.5” (546mm) CG before 100% load on outside tire. Sum moments about the tire:
0 = 1G * track width/2 - xG * CG height
xG = (1G*1525mm/2)/(546mm)
= 1.4G

Outside tire load is then, let’s assume it’s linear for simplicity:
50% @ 0G, 100% @ 1.4G

Let’s now assume that the tire cornering force relationship is linear with its vertical force, which is close enough for a first order approximation. Let’s now calculate the lift for 1G of cornering load using all the numbers:

1G = 86% load on outside tire, 24% on inside tire (total is 1700)
Outside cornering load = 1462lb
Inside cornering load = 408lb
Outside jacking = .855"
Inside jacking = -0.24"
Total jacking = 0.62"

And contrast this with the front, where at 1G we’ll see almost no jacking given the same load. If you’re lowered, you’re actually likely to be jacking DOWN! The worst of all.