e46 M3 suspension setup, or how to not downgrade your car with suspension mods

[cobra]

Pretty much what I thought – i.e. the gas force "has to be overcome" in the same sense as a spring's force has to be overcome. So we could say the gas pressure functions like adding a bit of both rate and preload to the spring, all of which could be fully compensated by taking some of those out of the spring itself. Accurate?

Correct. The gas force would be like a really soft spring with a lot of preload. So likely your spring rate wouldnt need to change but it would affect your ride height.
The only time the gas spring will contribute more would be towards the end of travel as the gas volume gets small and the pressure ramps up. Depends on the shock

[IamFODI]

Nice. Thanks, cobra.

[duracellttu]

Regarding Duracell's experience, my immediate thought was that the damper is not controlling (rebound) the stiff 700lb spring well enough, which makes it feel bouncy.

Try a stout damper like MCS! My 628lbs feel so perfect. No bounciness, just firm. I only needed to slow the rebound by a few clicks on the mcs. Even on full soft it had almost slow enough rebound. Dampers make a huge difference! Feels better than my B6s with 550lb springs.

I originally thought my dampers were the issue as well. That's why I moved from TCK SA to FCM Stage 3. Even after I upgraded the damper to FCM is was still getting the oscillations. The oscillations were the back end bouncing up and down uncontrollably. It was the weirdest thing.

I've since moved to 400/600 setup and the oscillating isn't there anymore. The 700 rear springs were linear 5” springs which might have been the issue. All other setups are beehive shape.

[elbert]

Pretty much what I thought – i.e. the gas force "has to be overcome" in the same sense as a spring's force has to be overcome. So we could say the gas pressure functions like adding a bit of both rate and preload to the spring, all of which could be fully compensated by taking some of those out of the spring itself. Accurate?

On certain dampers, you can also adjust the gas pressure.

[Bry5on]

Copy/pasting another post from my build thread that folks here might find useful. This has been a super interesting and cool project for me:

New feature, because everyone needs more math in their life!

It occurred to me that since I've got suspension geometry and center of mass information, I could now add jacking force calculations to get a true representation of suspension travel (jacking is basically the geometry forcing the body upwards during lateral cornering). This led me to a cool realization! The reason BMW uses an inboard spring is probably all about minimizing jacking travel! Jacking is a force internal to the car, so it acts at the spring rate & suspension lever ratio, where your suspension normally acts on the tires, a force external to the car, so it acts at the spring rate and motion ratio (lever ratio squared). BMW chose to have a high rear roll center for suspension dynamics, and this means that there's a lot of jacking force. To minimize the effects of jacking, you need a stiff spring rate. If BMW had put the spring over the shock with a similar ride frequency (probably the easiest thing to do honestly) then the car would rise about 50% more in the rear during cornering, totally jacking up (pun intended) your rear camber! With the spring in the location the factory chose, it turns out the math shows how little rear compression travel is used in corners. Most of the rear roll comes from the inner side of the rear lifting in a corner! The front is different, jacking forces are low due to the roll center being just above the ground.

So, PSA: Don't run rear coilovers unless you 1) really know what you're doing and 2) are running super stiff springs (because you have aero is the only real excuse)
Also, PSA: Don't lower the front of your car unless you 1) really know what you're doing and 2) are running super stiff springs and/or sways

In any case, my fancy suspension spreadsheet will calculate jacking forces and suspension travel for various G-loads in corners. Take a peek at the travel numbers for front vs rear and inner vs outer below:


CG location change_332it.xlsx

[cobra]

Very interesting stuff.

What else can we learn from these calculations in terms of externals we can modify? Spring rates? Sways? Bump stops?

During one of my iterations just playing with springs, I had the rear swaybar removed. I was surprised by the insane amount of rear end grip the car had, but the position data showed that it was bottoming out pretty frequently. Even a small turn and it would use up most of its travel. I think I was running 500lb springs. The temporary fix was to add more bump stop to hold it up until I got stiffer springs in there and eventually added back the swaybar too.

I'm not sure I really understand how the spring position affects the jacking. Can you explain more or point to a reference? What about an extreme case, such as an imaginary torsion spring concentric with the pivot?

[heinzboehmer]

I'm not sure I really understand how the spring position affects the jacking. Can you explain more or point to a reference? What about an extreme case, such as an imaginary torsion spring concentric with the pivot?

I'll let Bryson actually explain, but I think it's mostly just torque about the front-rear axis of the vehicle. Closer to the origin means less torque on the chassis and thus less upwards force on it too.

Edit: yeah no, read the posts below for the actual explanation

[Bry5on]

Very interesting stuff.

What else can we learn from these calculations in terms of externals we can modify? Spring rates? Sways? Bump stops?

During one of my iterations just playing with springs, I had the rear swaybar removed. I was surprised by the insane amount of rear end grip the car had, but the position data showed that it was bottoming out pretty frequently. Even a small turn and it would use up most of its travel. I think I was running 500lb springs. The temporary fix was to add more bump stop to hold it up until I got stiffer springs in there and eventually added back the swaybar too.

I'm not sure I really understand how the spring position affects the jacking. Can you explain more or point to a reference? What about an extreme case, such as an imaginary torsion spring concentric with the pivot?

The force of jacking is applied at the subframe/body and does not have the lever arm of the motion ratio multiplied through a second time (MR^2 for wheel rate) because the force is not applied through the upper control arm lever. I'm probably explaining this poorly, but some quick googling for jacking force calculations should give some more detailed/thorough responses, better than I can summarize.

Dropping your spring rates & corner weights into this calculator can help you set your static camber (for dynamic targets), choose spring & roll (sway) rates, and yes definitely help with selecting bump stop height as you can estimate free travel. In theory, you can also start adding tire vertical/lateral load info to actually get to accurate numbers for some more of these calculations (I ballparked for the jacking calcs). Since the calculator also allows you to add/remove weight from wherever you want in the car, you can simulate changes from things like carbon roofs and other weight savings, along with optimizing your geometry.

If I didn't think the stock spring rates were already a perfect street/canyon spring rate, I'd be going down this rabbit hole with springs The Dinan stuff probably isn't far off with a bigger front bar and another .5-.75" of front travel, and folks are on the right track with the ~300/700 springs and not lowering the car too much. These things are sometimes difficult to tune by feel, so the math can be super helpful to get your baseline set. My rear end was absolutely sticky as hell with the hotchkis front bar on soft and the stock rear bar with square tires and stock springs, but I could still get the rear loose under certain conditions. The math gave me the confidence to try a bigger CSL rear bar, and the car is much more balanced now, even though I thought it was pretty good before. Still hooks up great under power, but the wavetrac is probably helping there too, hard to say.

[IamFODI]

The force of jacking is applied at the subframe/body and does not have the lever arm of the motion ratio multiplied through a second time (MR^2 for wheel rate) because the force is not applied through the upper control arm lever. I'm probably explaining this poorly, but some quick googling for jacking force calculations should give some more detailed/thorough responses, better than I can summarize.

Trying to understand this and not finding much success. My amateur brain would have thought springs would exacerbate jacking given that they operate in the same direction.

Does the right-side spring resist jacking on the left side, and vice-versa?

[Bry5on]

Trying to understand this and not finding much success. My amateur brain would have thought springs would exacerbate jacking given that they operate in the same direction.

Does the right-side spring resist jacking on the left side, and vice-versa?

Think of jacking just like placing a jack under your rear subframe and lifting. That’s essentially where the force is acting, pretty near the middle of the car, so the whole suspension is lifted roughly equally Left-Right (why the inside lifts so much).

This will be a little over simplified, but not by too much: Because the lower control arm can only take force along its axis, and the control arm points up and in, when you corner, there’s a cornering force along the ground, and an upward force. Add the size of those two forces to make a triangle where the hypotenuse angle is the lower control arm angle. The inner wheel does a little bit to help reduce jacking, because the inner lower control arm is in tension (opposite direction forces), but it doesn’t generate as much grip, so you end up with a net jacking force.

I’m approximating it for the sake of simplicity and tried to simplify it in my model to only the net contribution by doing the math on the outside tire and knocking the number down to account for the contribution of the inner tire. It’s enough to be close and simplifies the calculations.

edit: the real math uses roll or instant centers and tire contact patch, but thinking about the control arm angle is probably way easier to get the concept right.

[IamFODI]

Think of jacking just like placing a jack under your rear subframe and lifting. That’s essentially where the force is acting, pretty near the middle of the car, so the whole suspension is lifted roughly equally Left-Right (why the inside lifts so much).

This will be a little over simplified, but not by too much: Because the lower control arm can only take force along its axis, and the control arm points up and in, when you corner, there’s a cornering force along the ground, and an upward force. Add the size of those two forces to make a triangle where the hypotenuse angle is the lower control arm angle. The inner wheel does a little bit to help reduce jacking, because the inner lower control arm is in tension (opposite direction forces), but it doesn’t generate as much grip, so you end up with a net jacking force.

I’m approximating it for the sake of simplicity and tried to simplify it in my model to only the net contribution by doing the math on the outside tire and knocking the number down to account for the contribution of the inner tire. It’s enough to be close and simplifies the calculations.

Thanks for this, and for your patience.

Here's where I think I'm confused. The idea that stiff springs mitigate jacking implies that, at some point, the spring force opposes the jacking force, right? But if I put a jack under my subframe and lift, the suspension goes into extension, which is exactly what the springs are trying to do. IOW, the spring force and the jacking force are acting in the same direction, not opposing each other – which would mean adding spring rate would make jacking worse, not better. Does that make sense? What am I missing/misunderstanding?

[Bry5on]

Thanks for this, and for your patience.

Here's where I think I'm confused. The idea that stiff springs mitigate jacking implies that, at some point, the spring force opposes the jacking force, right? But if I put a jack under my subframe and lift, the suspension goes into extension, which is exactly what the springs are trying to do. IOW, the spring force and the jacking force are acting in the same direction, not opposing each other – which would mean adding spring rate would make jacking worse, not better. Does that make sense? What am I missing/misunderstanding?

Yeah, you’re on the right track, just got the spring force and reaction a little backwards. Simplifying for the concept (the math isn’t exactly this simple). So the springs put out a linear force, let’s say 400lb/in, so if you have 200lb of jacking force, the springs will be pushing with the commensurate 200lb less force (since your car’s weight hasn’t changed and the tires are still supporting the full car’s weight, but some of it is going to jacking). If the springs are pushing with 200lb less force, they’ll be compressed by 1/2” less. This is where the jacking height (due to the force) increases relative to spring rate.

Now let’s say you have an 800lb/in spring and you still have the same 200lb jacking force. You’ll now be decompressing the spring half as much, just 1/4”. Since the force is the same, based on CG, roll center and cornering force, it doesn’t change (much) based on spring rate choice. If your springs are stiffer, the suspension will change height less due to jacking, in a similar way that the body will roll, dive and squat less with a stiffer spring. Hope that makes sense, I’m shooting from the hip a bit here.

[IamFODI]

Yeah, you’re on the right track, just got the spring force and reaction a little backwards. Simplifying for the concept (the math isn’t exactly this simple). So the springs put out a linear force, let’s say 400lb/in, so if you have 200lb of jacking force, the springs will be pushing with the commensurate 200lb less force (since your car’s weight hasn’t changed and the tires are still supporting the full car’s weight, but some of it is going to jacking). If the springs are pushing with 200lb less force, they’ll be compressed by 1/2” less. This is where the jacking height (due to the force) increases relative to spring rate.

Now let’s say you have an 800lb/in spring and you still have the same 200lb jacking force. You’ll now be decompressing the spring half as much, just 1/4”. Since the force is the same, based on CG, roll center and cornering force, it doesn’t change (much) based on spring rate choice. If your springs are stiffer, the suspension will change height less due to jacking, in a similar way that the body will roll, dive and squat less with a stiffer spring. Hope that makes sense, I’m shooting from the hip a bit here.

Okay, I think I'm starting to get it.

So, it's not that the springs act against the jacking force per se; it's that, if the suspension is set up around very stiff springs, the relative contribution of any jacking force will be less? Is that about right?

Still not sure how spring position plays into this. If the function of a spring is to manage the position of the wheel WRT the body or vice-versa, wouldn't all forces on the spring be affected by the motion ratio?

[Bry5on]

Okay, I think I'm starting to get it.

So, it's not that the springs act against the jacking force per se; it's that, if the suspension is set up around very stiff springs, the relative contribution of any jacking force will be less? Is that about right?

Still not sure how spring position plays into this. If the function of a spring is to manage the position of the wheel WRT the body or vice-versa, wouldn't all forces on the spring be affected by the motion ratio?

A little hard to explain briefly (I maybe over simplified this too much originally, in retrospect) but the motion ratio is the square of the upper control arm spring lever ratio. The wheel acts at the motion ratio because the lever arm reacts in a squared way (derivation here: https://enderw88.wordpress.com/autom...g-rate-theory/ ). When you apply a force to the frame of the car, it only reacts with the lever arm (d1/d2) and not the square of the lever arm as there is no additional ratio of displacement to multiply it through a second time.

This would be much easier to explain with a whiteboard and some free body diagrams (and more time), but hopefully the link plus description above helps. I’ll bet there are some good YouTube videos that show the derivation of wheel spring rate with motion ratio out there.

[Obioban]

I increasingly feel like the more I know about suspension, the less I know about suspension.

... and that deviating from stock as little as possible (but as much as necessary) is the best strategy-- especially in ride height and geometry.