Nate Tempest

Definitely wasn't understeering on the way into that corner. Most of the time the front bites really well. Could be I'm trail braking in deeper than you and managing understeer that way? I've been paying a bit more attention to this, and the situation where I do get understeer is mid corner on slow corners, if I try to dial in more steering angle than it can handle. In those cases I'm off the brakes and just at maintenance level on the throttle, so the front/rear weights will be near static. I don't spend much time in that situation though; usually when I do lose grip it's somewhere during turn-in, when I'll still have a bit of trail braking. (Although usually it's more progressive than that clip above—fairly easy to catch without losing speed.) I don't usually break loose at exit (which is making me wonder now if I need to focus on getting on the throttle faster!) In the few cases I recall, it's usually oversteer, but I've seen both.

For what it's worth, if you check out the STR setups thread, everyone runs stiffer springs front than rear, and almost everyone moves to a stiffer front and softer rear bar (or no rear bar). To be sure, most of us are probably copying from the few guys who've done the testing, but it does seem to work well. Obviously some amount of front roll bias makes sense given trail braking and RWD, but it could just be that these cars can be fast with a wide range of setups, if the driver is used to how it behaves.

BTW I'm still hoping to update my calculations above to account for sprung vs unsprung weight and centers of gravity, and ideally to work through the damper's effects, but thus far real life has taken precedence..

Fokker

Speaking from personal experience, with similar balance of spring rates and stabilizer bar, I find the car to be understeer-prone at a track, especially more technical ones. I normally soften my bar to at least 842 lb/in (2/2).

Nate Tempest

Next time I'm at my local track I'll try going softer in the front just to see the difference. Will have to adjust my trail braking and try not to spin though, I suspect!

Would probably actually make sense to go softer with both bars on the track, compared to the autocross setup.

Nate Tempest

Edit: Updated the post below to fix the calculations based on motion ratios.

OK, so I had a chance to re-run some numbers, taking into account the estimated unsprung vs sprung weight, and inelastic (unsprung) center of gravity. Also took into account a few different scenarios. I'll mostly just go through the numbers in this post, then discuss in the next one.

So, to start with, I estimated unsprung weights to be 150lb per axle, based loosely off the guesses in this thread: https://www.s2ki.com/forums/s2000-ra...-weight-71916/.

Axle height is about 12.5", which is a good estimate for unsprung center of gravity.


Given our overall center of gravity of 18" and total weight of 2965lb, we can work out the elastic (sprung) center of gravity, which will be about 18.6":

300*12.5 + (2965-300)x = 2965*18
x = 18.6" = 0.472m

Subtracting the unsprung weight from the corner weights, the initial unsprung weights on the wheels in pounds are:

700 FL, 635 FR, 695 RL, 635 RR

This post gives the S2000 motion ratios, and defines them as spring displacement / wheel displacement (it’s sometimes also defined as the inverse), the motion ratios of the S2000 are: https://www.s2ki.com/forums/s2000-br...atios-1160445/

So dividing unsprung wheel weights by motion ratios of the dampers, we get static loads on the springs of:

1188 FL, 1078 FR, 1202 RL, 1098 RR (lb)

Spring rates are 750lb/in front, 550lb/in rear.

This means the springs are initially compressed by
1.58, 1.44, 2.18, and 2.00 (inches)

And equivalent wheel displacements you can get by dividing the spring displacements by motion ratios again, or equivalently by dividing the unsprung weights on the wheels by the wheel rates, which are the spring rates times motion ratio squared. (See that post I linked for a full explanation.)

Wheel displacements from full extension of springs:
2.68, 2.44, 3.77, 3.46 (inches)

So that’s how big a dip the wheels would have to fall into to completely unload the main springs. Of course, it’s possible the wheel would instead be suspended by the sway bar, which we’ll see later. Also, even if the main spring isn’t completely unloaded, as it gets closer it will transfer more weight off of that wheel, so it’s possible to get an undesirable amount of weight transfer in a dip that’s still too small to completely unload the spring.

Nate Tempest

Edit: updated to account for motion ratios
Edit 2: Still an approximation since doesn't account for the roll center, but with the car lowered that should be fairly close to the ground.

So, now looking at a steady state corner at 1.2G, we have this for unsprung weight transfer (converting to SI units for the calculations since they're better ):

Cornering force: 1.2*9.8*(300/2.2) = 1600N
COG ~= axle height = 12.5" = 0.317m
Torque about ground to COG = 1600*0.317 ~= 508Nm
Unsprung weight transfer = torque / track width = 508Nm / 1.47m = 78lb, or 39lb per wheel

For the elastic weight transfer, the calculations are the same, except we use the sprung weight and the sprung center of gravity:
Cornering force at 1.2G is 1.2*9.8*(2650/2.2) = 14165N
Torque is 14165*0.472m ~= 6700Nm
Elastic (sprung) weight transfer = (6700/1.47)N ~= 1020lb

Again, springs are 750lb/in front, 550lb/in rear
Sway bars are 1072lb/in front, 145lb/in rear
Damper motion ratios are: 0.589 Front and 0.578 Rear
ARB motion ratios are: 0.492 Front and 0.343 Rear

To determine the total roll in such a corner, we use the wheel rates including springs and sway bars. So our total roll (extension of springs on one side and compression on the other) is

1020lb / (750*0.589^2+1072*0.492^2+550*0.578^2+145*0.343^2) lb/in =
1020lb / (260 + 259 + 184 + 17) =
1.42"

Aside: and our roll bias: (260+259) / (260+259+184+17) = 72.1%

Which means ~735lb front weight transfer, and ~285lb rear, unsprung, at the wheels.

So, the force on a spring in a corner will be the initial load (unsprung corner weight divided by damper motion ratio) plus (minus) the wheel displacement due to roll, multiplied by the damper motion ratio and the spring rate. (Ignoring any slight wheel lift.)

Static spring forces are:
1188 FL, 1078 FR, 1202 RL, 1098 RR (lb)

So in a 1.2G left-hand corner, the weights on the springs in lb will be:

1188-1.42*0.589*750 FL, 1078+1.42*0.589*750 FR, 1202-1.42*0.578*550 RL, 1098+1.42*0.578*550 RR =
561 FL, 1705 FR, 751 RL, 1549 RR (lb on springs)

In a right-hander,
1815 FL, 450 FR, 1653 RL, 647 RR

Again in both cases adding the sprung and unsprung weight transfers show the front wheels just barely lifting in such a corner. Mine actually aren't, as far as I'm aware, which can be explained by 1) the chassis will flex somewhat, which will reduce the front roll bias somewhat from the theoretical 72.1%, and 2) the center of gravity may be lower than what I've estimated here. The numbers definitely appear to be close though.


What about pitch? The car accelerates at about 0.3G at steady state. (Will get into why I'm only looking at steady state in the next post.) Wheelbase is 94.5", 2.4m. Using the same elastic center of gravity and calculations as above, that gives 157lb of total weight transfer, or ~80lb per wheel, 135lb per front spring. (Except of course we won't be able to accelerate at 0.3G while cornering at 1.2. Perhaps more like 1G. So that situation isn't going to unload the front springs much more than max cornering.)

Looking at the rear wheels in a braking event, say we could brake in a straight line at 1.1G. (It's going to be less than cornering, and probably even 1.1G is optimistic.) Using the same calculation as for forward pitch, we get 576lb of weight transfer, 283lb per wheel. So dividing that by the motion ratios and adding to the static forces on the springs, under straight braking, spring forces would be:

1668 FL, 1558 FR, 712 RL, 608 RR

(So rear wheels get lighter under straight braking than cornering.) Sway bars of course have no effect here.


Worst case for unloading a rear wheel will be trail braking though. If we manage to pull 1.1G at a diagonal to the car, that's 0.94G longitudinally and 0.57G laterally. So 492lb (246lb / wheel) forward transfer, and 485lb lateral transfer, 351 in the front, and 134 in the rear.

Roll will be 485 lb / (260 + 259 + 184 + 17) lb/in = 0.68"

Adding the forward weight transfer (divided by motion ratios) to the static spring loads gives these loads on the springs:

1606 FL, 1496 FR, 776 RL, 672 RR (lb)

Then adding the roll effects (as per roll calcs above)

Left hand corner: 1306 FL, 1796 FR, 560 RL, 888 RR
Right hand corner 1906 FL, 1196 FR, 992 RL, 456 RR


So at the lowest we'll have about 450lb on a rear spring, at steady state. (Or around 50lb less if the gas tank is empty.) Will get into why I think that matters next post!

Nate Tempest

New post since I'm sure almost everyone skipped the previous one! So, stepping back for a moment, why do we care about body roll? As I understand it, body roll is bad for two reasons:

1. The more the chassis rolls, the longer it takes to overcome its inertia when you want the car to change directions. This is especially an issue for quick transitions in eg chicanes or slaloms.
2. As the body rolls (or pitches) the suspension articulates, which changes the the angles at which the tires contact the pavement. Cars are generally set up with camber gain to partially counteract the effect of roll on the contact patch, but it cannot be set up to counter it 100%, since camber gain will also take effect when the car pitches, which will end up reducing contact patch in braking. The more the chassis rolls, the more static camber will be required to keep a good contact patch in cornering, which again will make things worse when braking, so there's always a tradeoff. The less roll, the less the suspension geometry changes, and the more you can maximize contact patch in both cornering and braking (and acceleration).

To reduce roll, we can use stiffer springs and/or stiffer sway bars.

Stiff spring pros:

• Counter both roll and pitch

Stiff spring cons:

• Result in harsh ride, lack of compliance for rough pavement, bumps, dips—ie more weight transfer as a result of these surface imperfections.

Stiff sway bar pros:

• Counters body roll, like a stiff spring
• Less effect on 'ride': small surface variations do not engage sway bars, and so car will be more compliant on rough surfaces than with stiff springs.

Stiff sway bar cons:

• Can not prevent pitch
• Can transfer bumps felt by one wheel to the opposite side, potentially upsetting the car worse than an equivalently stiff spring, when a bump is encountered on only one side.

Another benefit of sway bars in general is that they can be tuned on the fly, unlike springs.
Because of these pros and cons, it generally makes sense to use a combination of spring and sway bar to get the desired roll (and pitch) resistance.

Now, in theory, tender springs can add some of the advantages of softer springs, without sacrificing roll resistance, or they can be used to make a tradeoff between the two. There are two main ways tenders (or other dual-rate spring setups are used):

1. At static ride height, the tender springs are not fully compressed. This gives the car a softer, more compliant ride normally. Under hard cornering or braking, the loaded tender springs compress fully (the becomes 'solid'), and so the effective spring rates at those wheels becomes that of the main springs, resisting further roll or pitch. So a car set up this way will have a good ride, will show significant initial roll or pitch when entering a corner or braking zone, but then less once the loaded tender springs are fully compressed. (Although still more from that point than a car with the same main springs and no tenders, since the unloaded spring rates also impact the degree of roll.)

2. At static ride height, the tender springs are fully compressed (solid). The car will ride as if it didn't have tender springs, based on the spring rate of the main springs. Under cornering it will initially roll little (again, based on the main springs and sway bars). If weight transfer is sufficiently large that one of the tender springs begins to expand, body roll will increase (again, because the spring rates on unloaded wheels play a roll in roll (pun intended) just as the more loaded 'outside' springs do). A car set up this way may handle dips on the inside wheels in a corner better than a car without tender springs, because the dip will un-load the wheel, allowing the tender spring to expand, and reducing the spring rate at that corner. This will cause the wheel to maintain better contact with the ground (regardless of the shock damping), and will result in less weight transfer away from that wheel due to the dip. (And so also less chassis movement and less sudden weight transfer back onto the wheel when coming out of the dip.)

For a track car, #2 is the setup that would generally make more sense. In my opinion, you would want to choose tender springs such that even in max cornering or trail braking at steady state, the tenders are still solid, so you're not increasing body roll or pitch in normal circumstances. However, if you hit a dip with an un-loaded wheel, the tender could then extend, giving the advantages described above.

Based on the numbers in the post above from my car, that means the front tenders would need to be fully compressed with about 400lb of force, and the rears with no more than 450lb. Ideally less for some margin for error, although if the weight on one of the springs ends up falling slightly below the threshold to keep it solid and it extends very slightly, that will only have a correspondingly slight effect on roll, so it's not a big deal.

Now, as mentioned before, in the front, such a tender wouldn't hurt, but it probably wouldn't help much either. That's because once the car is cornering hard enough for there to be close to 400lb on an inside front spring, there is almost no weight remaining on that wheel. So hitting a dip wouldn't do anything—the sway bar would just hold the wheel in the air, and the tender spring would remain solid.

In theory front tenders could be useful when hitting a large dip on the flat, when the sway bar would have less effect. My lighter front wheel has a corner weight of 710lb, so if it hits a dip, the force on that wheel is equal to that starting weight, minus the spring’s wheel rate times the distance dropped, and minus half the sway bar’s wheel rate times distance dropped (since only half the bar is moving):

w = 710 - d*0.589^2*750 - d*1072/2*0.492^2 = 0 when wheel lifts
d=1.82

So the wheel could dip 1.82” before it lifted completely, at which point the spring would be loaded with about 275 lb. So, if we sized the tender to be solid at 400lb, it could have a slight effect on large dips. (Or smaller ones if hit by both wheels.)


The rears are a bit more interesting. At a minimum we have ~450lb on the rear springs. To be safe, could look at a tender that's solid at around 400lb. It would only take a small dip to engage a tender of that weight when hit by a light rear wheel under cornering and/or braking, and in such a situation it would allow the car to follow the dip better, with less weight transfer. This should be possible without any real disadvantage, since the tender spring would be solid under normal circumstances (steady state cornering, braking, trail braking).

So! I'm going to play with the numbers some more (and would love it if another person like me* wanted to check my work!) Want to see what things look like if I tweak the sway bars and such, since I might end up doing that in reality. But if everything checks out, it looks like I may be shopping for rear tenders at least. Also need to take a look at how much space I have to fill at droop, as well as how much room I have to move the perch down, to make room for the compressed tender and the divider. Only company I've been able to find so far that makes tenders in 2.25" ID, which is what my JRZ RS Pros want, is Eibach. Theirs are all 150lb/in, but come in various lengths, so that might just work, in something with ~2 to 2.5” of travel. Of course, that might not be long enough to prevent the springs floating at full droop, but even if so it would make the re-seating much gentler. (And if necessary I think I can adjust the droop of the shocks to make up the difference.)

*ie an ex-engineer who apparently misses doing math and didn't realize it until now... :P

ncrx

swift makes helpers/tenders in various rates and sizes, but are metric i think the smallest being 60mm.
they're also well priced and include the couplers.

AlpineFD

WOW =)

I don't see motion ratio of the spring and sway bar taken into account in the calculation, shouldn't those be added?

Nate Tempest

Ahhh you're totally right. I didn't really think about it, but had sort of assumed they'd be close enough to 1 to discount. Definitely not the case.

Traveling right now, but will update the previous as soon as I have a chance. Thanks!

s2000Junky

Please don't