S2K Al

edit: FULL DISCLOSURE
I'm not a vendor on here, but I do have a business interest in coilovers and potentially in coilovers for the S2000. The data I've taken down and calculated were out of my own curiosity but feedback and other data I can glean from this thread I may put towards S2000 coilovers down the road. I figured I should put that out there in case it changes anyone's attitude towards sharing.

I hope others may find this useful at some point. What I'd like to do is gather numbers for a stock S2000's suspension components, for the purposes of helping folks calculate sprung/unsprung mass, corner weights, weight savings (when considering aftermarket parts) and performing calculations necessary to choose spring rates. More generally, just to promote knowledge of this aspect of the S2000.

I can see this thread getting very math-heavy and I absolutely hope that it will. Up front, I will admit that my math skills are horrendous and I 100% welcome corrections. The numbers I will start this thread out with were validated on corner-balance scales, and were from a stock AP2. The only things that were not stock were the tires, and I made an average assumption for driver weight, so those weights may vary.

My data:
S2000
Driver = 190lbs

Front - per corner
Tire/wheel 35
Shock/Spring 11
Swaybar 22
Upper a-arm 4
Rotor 15
Caliper 11 (inc. pads)
Lower a-arm 6
Hub 10
93 lbs total unsprung weight
Left Front: 622lbs sprung weight
Right Front: 571lbs sprung weight

Rear - per corner
Tire/wheel 40
Shock/Spring 12
Swaybar 11
Driveshaft 20
Upper a-arm 5
Lower a-arm 11
Caliper 8 (inc. pads)
Hub/rotor 23
111lbs total unsprung weight
Left Rear: 607lbs sprung weight
Right Rear: 546lbs sprung weight

Crossweight 1372/1379
F/R %: 50/50

Motion ratios:
front lower control arm
a: 9"
b: 12 1/2"
Motion Ratio: 1.39

rear lower control arm
a: 10 1/2"
b: 15 1/8"
Motion Ratio: 1.44

Left Front: 715
Wheel Travel: 6"
Wheel Rate: 259.17
Spring Rate: 508LBS/IN
Shock Angle: 9*
Angle Correction Factor = .98

Right Front: 664
Wheel Travel: 6"
Wheel Rate: 237.92
Spring Rate: 467LBS/IN
Shock Angle: 9*
Angle Correction Factor: .98

Left Rear: 718
Wheel Travel: 6"
Wheel Rate: 252.19
Spring Rate: 536LBS/IN
Shock Angle: 9*
Angle Correction Factor: .98

Right Rear: 657
Wheel Travel: 6"
Wheel Rate: 259.17
Spring Rate: 580LBS/IN
Shock Angle: 9*
Angle Correction Factor: .98

My Notes:
1. Units are standard.
2. Weights for split sprung/unsprung components were halved when calculating final sprung weight (eg. swaybars, control arms)
3. I estimated Wheel Travel and the Shock Angle as best I could. I think any difference in the Angle/ACF would be negligible for most purposes.
4. Based on the below data, and targeting Ride Frequency of 2.0Hz in the front and 2.2Hz in the rear, I came up with spring rates of 995lbs/in in the front and 1271lbs/in in the rear. Something tells me that I've made a miscalculation somewhere as these rates seem too high compared to what we see the fastest S2000's in the country running.
5. No consideration was made for square or staggered tire setups, aero, or aftermarket swaybars.
6. I found motion ratios to be 1.429 in the front and 1.493 in the rear.

User Freetors had some helpful comments in another post and I hope he/she will chime in with feedback on the above numbers. Personally, I'd like some insight from the knowledgeable folks on here on how/why the spring rates I've ended up at seem so high, when the rest of my measurements and methods seem reasonable.

User 121020

My recommendation is to define your abbreviations and variables (ACF, MR, a, b, A, C, etc.) so that people can better understand the nomenclature you are using. Some of the parameters, such as MR and WR, are more obvious - motion ratio and wheel rate. Others, such as C, WT, AFC, and A, are not as obvious.

The common motion ratios thrown around S2ki are ~.72 for front and ~.70 for rear suspension. How did you measure your MR values?

freetors

nmrado, the motion ratio he has derived is wheel travel/shock travel (I actually prefer this notation because it's more granular and real to me), simply take the reciprocal and you should get similar numbers. Whenever you quote motion ratios you need to clearly define which one you're using as some formulas use one form and some use the other.

That said, I measured my motion ratio (geometrically, not with a dial indicator) and I came up with 1.5 and 1.63 f/r or 0.67 and 0.61 f/r if you prefer that notation.

I don't have corner weight scales and I'm not serious enough to go somewhere that does, but my weight estimates put me at about 2.1Hz on the front and 1.8 Hz at the rear. I use optimumG's ride frequency formula but you have to be very careful with the units. Once you figure out how to use the formula correctly you should probably just put it into an excel spreadsheet. You said your target ride frequency was higher in the rear. I would advise against this. That follows flat ride theory which is more comfortable at street speeds but doesn't really work at racing speeds. Flat ride would also promote oversteer in a car like ours. The earlier model years would have had a higher ride frequency in the rear, among other things like the swaybars, that contributed to the oversteer nature of them. By my calculations and your weight data it would take about 950/1100# springs f/r to get a 205Hz ride frequency.

It's really awesome that you collected unsprung weight data though! Regarding that, remember that a decent approximation is that about half the shocks weight contributes to unsprung weight, BUT the spring only contributes one-third!

S2K Al

nmrado: Recommendation noted, I'll make those additions to the original post, thanks!

freetors: Appreciate the insight regarding the ride frequencies, that does explain the trend I've seen among the faster drivers in the country to run spring rates that result in a lower rear frequency. I'll be re-measuring the S2000 (my own, stock) during the down season to double check my numbers, and I'll take that opportunity to measure the shocks and springs separately to more accurately account for the weight of the springs.

I went so far as to work out some base damping curves but that is where things started to get very wonky. I lost track of my units somewhere along the line, and I've got Newtons along the Y axis but measuring only as high as 4, not 400 but just 4. So something is definitely wrong but I think its just the units. Here are the baseline curves, with the only adjustment made being that called out by the method detailed in OptimumG, to make compression 2/3 of the initial and rebound 1.5 initial.

freetors

Do you think you could post up your calculations so we could try to catch your errors? What did you get for your critical damping at 1"/sec? I find it easier to work in english units for this stuff. For my spring rates, the "ideal" damping force at 1"/sec is about 25-30 lbs.

S2K Al

Sure can. Its all in Excel so I'll take some time to translate it into forum-friendly format.

Dr (Damping Ratio): Chose .7, which I think was based on OptimumG
Rf (Ride Frequency): As noted, chose 2.0Hz front and 2.2Hz rear but that needs to change
MR (Motion Ratio): As noted above, 1.39 front and 1.44 rear but not clearly not definitive

Ccr (Critical Damping Coefficient): 2sqrt(Kw*msm)
-Kw = Wheel Rate in newton/meter
-msm = Sprung Mass in Kgs
-Front Ccr: 13.58
-Rear Ccr: 14.44

Kw (Wheel Rate): Ks / MRsquared
-Ks = Spring Rate
-MR = Motion Ratio
-Front Kw: 85.27
-Rear Kw: 99.73

Ks (Spring Rate): Ks (n/m) = 4Pisquared * Rfsquared * msm * MRsquared
Here is where I suspect things got crazy. I believe I'm calculating spring rate here, but my notes say that the resulting end units should be in Newton/Meter, which I've then divided by 1000 and then multiplied by 5.72 to get to my final lbs/in number for spring rate....
-Front Spring Rate: 995.30 lbs/in
-Rear Spring Rate: 1270.84 lbs/in

Df (Damping Force): Ccr * Dr
-Front Df: 9.51 (? units)
-Rear Df: 10.11 (? units)

Df was then used to plot 22 baseline damping points each for compression and rebound, with each point being Df * speed using .025 m/sec intervals starting at 0 m/sec and up to .525 m/sec (roughly 20 in/sec) which was higher than I felt any damper would operate.

Then to make the 2/3 compression and 3/2 rebound adjustments I just multiplied the initial damping points (Cinitial and Rinitial) by .67 and 1.5 respectively. The plots posted above are the result.

Beyond that, I intend to end the nose/start the knee at .15m/sec, and taper off high speed at .4m/sec but the shape of those curves would be controlled more by the piston used I feel, less by math.

Edit2: As you can fee freetors I didn't end up calculating critical damping specifically for any speeds as all my damping points take into account the .7 Damping Ratio to soften things up. I could back it out but still my units are all messed up so I couldn't even begin to translate them into lbf.

tcjensen

I've never understood the concept of 65-70% critical damping to generate an entire damper curve. Don't you have to pick a damping ratio at each shock piston velocity?

S2K Al

The damping ratio is applied to each individually defined point on the plot, which itself is just c-crit * piston speed. So I *think* it is technically correct to say that the damping ratio is applied to the entire damping curve insomuch as the curve is comprised of these individual points.

User 121020

The damping coefficient is the slope of the Force vs. Piston Speed plot (also referred to as the dyno plot). The units for "C" are force per unit velocity, lb/in/sec or newtons/m/sec.

The two most common implementations of damping for automotive shocks are linear and digressive curves.

Linear plots are what S2K AI is showing above. The damping coefficient is constant for the entire plot. Though there is an error in the math somewhere. The force values are off by about two orders of magnitude.

Digressive damping is where you'd have a more aggressive slope up to the "knee". Above that, the damping coefficient is much lower. This allows for a large amount of low-speed damping to support chassis roll and pitch while not generating huge amounts of damping at higher piston speeds, such as those generated by bumps. Low speed is typically defined as 0-3 in/sec (0-.075 m/sec). High speed is anything beyond those piston speeds. Again, those are just typical parameters. Damper manufacturers might have their own preferences regarding where the knee occurs.

S2K Al

Yes exactly right. I've given up on trying to track down the math error, it kept me up for most of the evening and I made no progress so I just have to apologize for the shoddy math. Hopefully someone more mathematically inclined can find the error.