I finally got around to putting together some calculations for springs and swaybars, and how they affect overall wheel rates in ride and roll. I wanted to see, for the combination of springs/bars I was running, where that put me in terms of total roll resistance and wheel frequencies. A lot of this info/methods is already out there and known, but I haven't really seen it all put together for the GR so I thought I'd share.
The aftermarket Subaru community is pretty good with information regarding spring rates, and the OEM rates are known. For bars, the diameter information is almost always available. But even though we know the rates/diameters of the bars and springs themselves, there’s still some information missing about how the changes affect the system as a whole. Knowing this information might help understand what kind of impacts any given change makes on the overall handling characteristics and ride quality.
Knowing spring rate and swaybar stiffness is the first part of the equation. The next step is to translate those numbers to the wheel. Since suspensions are comprised of linkages where the springs, bars, and wheels connect at various locations, we need to do some math to figure out what the spring rate “at the wheel” is. The basic equation to translate spring rate to the wheel is
Kw = Ks*(MR)^2
Kw = spring rate at the wheel
Ks = spring rate of the actual spring
MR = Motion Ratio*
The Motion Ratio is defined as the amount of vertical motion present at the spring per a given vertical motion of the wheel.
*depending on where you’re looking, the MR can also be called the Installation Ratio (IR). Sometimes it’s expressed as MR = (IR)^2, but for the purposes here we’ll just consider MR to be the IR. Basically, the ratio of the spring/wheel motion needs to be squared, regardless of what you call it.
The Motion Ratio is affected by a couple of things. The first is the distance that the spring attaches to the control arm relative to where the wheel/hub attachmes (the distance is usually the same for a McStrut but very different for a wishbone/multilink). The other thing that affects the motion ratio is the angle of the spring – this effect can be minimal depending on the spring angle, but once the spring angle starts exceeding 10 degrees it starts to become significant enough to include in calculations (the GR has a nominal SAI value of ~15 deg and nominal caster values of ~6.2). There is a lot of information available on the internet to learn about calculating motion ratios.
If the springs and bars attach at different points on the suspension, then they will each have their own motion ratios. Here are the Motion Ratios I’m using for the following calcs:
0.96 = Front Spring MR (assuming SAI of 17 degrees since I’m running camber plates)
0.67 = Front Bar MR**
0.78 = Rear Spring MR (assuming spring angle of 4 degrees – dunno if this is true but I know it’s not perfectly vertical
0.59 = Rear Bar MR**
(**thanks to senna1a for the measurements seen here:http://www.iwsti.com/forums/3742979-post42.html)
And here are some base values for spring rates that I’ve run (http://www.iwsti.com/forums/2817712-post7.html):)
One thing to keep in mind with swaybar rates – since the bar is attached at both ends, and roll is symmetrical (the inside wheel droops as much as the outside wheel compresses), the linear “lb/in” of the swaybar needs to be doubled since the swaybar will be twisting twice as much.
So knowing the rates and applying the wheel rate equation, I plugged the values into the different OEM setups and the setups I’ve run. Here’s how the calculations turned out for the springs and bars:
You can see right away that the rollbars add a lot more wheel rate in roll than the springs do. The Front and Rear Dist % columns represent how much percentage of the total rate comes from the front and rear springs or bars. Weight distribution for the GR is about 58F/42R, and it’s interesting to note that the relative front/rear rate distribution of the springs and bars seem to hover around the weight split (not surprising). Also, note that my TIC SST setup is 8k/8k, when it usually comes with 7k front spring (~392 lb/in).
And adding the spring and bars together to determine total wheel rates in roll:
Again, the Front and Rear Dist % is the percentage of the total wheel rates in roll that are from the front and rear. “WRf” is Wheel Rate Front, “WRr” is Wheel Rate Rear, and “WRtot” is the total wheel rates in roll, WRf+WRr. The last 2 “Roll Share” columns are meant to express how much the springs contribute to the overall roll stiffness (I just made up that term btw). Also the “RCE Fs Rh” indicates RCE swaybars, front soft, rear hard settings.
So a few interesting things, not in any particular order.
The last thing here is to give some context to wheel rates. Since cars all don’t weigh the same, a useful way to determine and compare the stiffness of one car to another is to calculate the undamped natural frequency of the spring-mass system. We just calculated the wheel rates, and to figure out the frequencies we need the unsprung mass. For my purposes, I assumed 3373 as the OEM curb weight (this seems pretty accurate), subtracted out estimates for unsprung masses (based on old WRX threads that determined unsprung mass, I added some unsprung weight due to the STI having larger wheels/tires, brakes, etc). Since I’m mostly interested in autocross I also subtracted out weight for trunk junk, floor mats, my muffler delete, running on only ¼ of fuel, and also added in my weight. The equation to calculate NF is 3.13*sqrt(kw/m), where kw is the corner wheel rate in lb/in, and m is the corner weight in lbs. Here are the results (all values in Hz):
The first two columns are ride only, meaning it only takes into account the springs. The last two columns on the right includes the bars (so total roll rate) – I’m not really sure what value that has in and of itself, it’s more a point of context that says “if we were only to rely on springs for our roll control, and wanted to still achieve the roll stiffness that we can get with the corresponding spring/bar configuration, what would our ride frequencies need to be”. Answer: a lot.
In general it’s recommended to have a slightly higher rear frequency in the rear than in the front, but this isn’t really exact science so there are varying opinions. There’s a lot out there in suspension texts and the internet to recommend what frequencies you’d want to be at for what purposes.
So running equal spring rates in the front and rear (2010 SE, RCE, my TIC setup) will result in about equal ride frequencies front and in the rear, and for my setup, ever so slightly higher in the rear. If you run higher spring rates in the rear by 1kg/mm (or ~56 lbs/in), that results in a rear ride frequency about .1-.15 hz greater than the front.
Hopefully this adds some context to springs and bars. One thing to note - this is only looking at springs, bars, and ride/roll rates in a vacuum - there are still many other factors that will address roll and handling (ride heights, roll centers, alignment and alignment change through articulation, damping, etc etc etc).
Also, this is entirely analytical, and is relying on info mainly gathered on the internet
lol - to get more accurate numbers, you could actually measure your motion ratios through a range of travel centered around your ride heights (in fact motion ratios will change through articulation), spring rates are often progressive (especially on OEM shape springs), you could actually measure bar stiffness, etc etc etc...
Hope this helps.
The aftermarket Subaru community is pretty good with information regarding spring rates, and the OEM rates are known. For bars, the diameter information is almost always available. But even though we know the rates/diameters of the bars and springs themselves, there’s still some information missing about how the changes affect the system as a whole. Knowing this information might help understand what kind of impacts any given change makes on the overall handling characteristics and ride quality.
Knowing spring rate and swaybar stiffness is the first part of the equation. The next step is to translate those numbers to the wheel. Since suspensions are comprised of linkages where the springs, bars, and wheels connect at various locations, we need to do some math to figure out what the spring rate “at the wheel” is. The basic equation to translate spring rate to the wheel is
Kw = Ks*(MR)^2
Kw = spring rate at the wheel
Ks = spring rate of the actual spring
MR = Motion Ratio*
The Motion Ratio is defined as the amount of vertical motion present at the spring per a given vertical motion of the wheel.
*depending on where you’re looking, the MR can also be called the Installation Ratio (IR). Sometimes it’s expressed as MR = (IR)^2, but for the purposes here we’ll just consider MR to be the IR. Basically, the ratio of the spring/wheel motion needs to be squared, regardless of what you call it.
The Motion Ratio is affected by a couple of things. The first is the distance that the spring attaches to the control arm relative to where the wheel/hub attachmes (the distance is usually the same for a McStrut but very different for a wishbone/multilink). The other thing that affects the motion ratio is the angle of the spring – this effect can be minimal depending on the spring angle, but once the spring angle starts exceeding 10 degrees it starts to become significant enough to include in calculations (the GR has a nominal SAI value of ~15 deg and nominal caster values of ~6.2). There is a lot of information available on the internet to learn about calculating motion ratios.
If the springs and bars attach at different points on the suspension, then they will each have their own motion ratios. Here are the Motion Ratios I’m using for the following calcs:
0.96 = Front Spring MR (assuming SAI of 17 degrees since I’m running camber plates)
0.67 = Front Bar MR**
0.78 = Rear Spring MR (assuming spring angle of 4 degrees – dunno if this is true but I know it’s not perfectly vertical
0.59 = Rear Bar MR**
(**thanks to senna1a for the measurements seen here:http://www.iwsti.com/forums/3742979-post42.html)
And here are some base values for spring rates that I’ve run (http://www.iwsti.com/forums/2817712-post7.html):)
And thanks again to senna1a, here is the same info for swaybars***. Note that the rate provided is the force required to deflect the bar at the endlink attachment (http://www.iwsti.com/forums/3742979-post42.html).
***Swaybar rates can vary quite a bit due to material, shape, exact dimensions, but this is the best info available right now and should provide good ballparking info.
One thing to keep in mind with swaybar rates – since the bar is attached at both ends, and roll is symmetrical (the inside wheel droops as much as the outside wheel compresses), the linear “lb/in” of the swaybar needs to be doubled since the swaybar will be twisting twice as much.
So knowing the rates and applying the wheel rate equation, I plugged the values into the different OEM setups and the setups I’ve run. Here’s how the calculations turned out for the springs and bars:
Code:
Spring Spring Wheel Wheel
Rate Rate Rate Rate Front Rear
Front Rear Front Rear Dist Dist
Springs (lb/in) (lb/in) (lb/in) (lb/in) (%) (%)
-----------------------------------------------------------
2008 OEM 217 194 198 117 0.63 0.37
2010 SE 251 249 230 151 0.60 0.40
2011 OEM 251 297 230 180 0.56 0.44
RCE Black 320 320 293 194 0.60 0.40
TIC AST SST 448 448 410 271 0.60 0.40
Code:
Bar Bar Bar Bar Wheel Wheel
Dia Rate Dia Rate Rate Rate Front Rear
Front Front Rear Rear Front Rear Dist Dist
Bars (in) (lb/in)(in) (lb/in)(lb/in) (lb/in) (%) (%)
-------------------------------------------------------------
2008 OEM 20 400 18 285 359 198 0.64 0.36
2010 SE 20 400 19 360 359 251 0.59 0.41
2011 OEM 21 485 19 360 435 251 0.63 0.37
RCE Soft 22.7 665 22.7 725 597 505 0.54 0.46
RCE Hard 23.5 770 23.5 840 691 585 0.54 0.46And adding the spring and bars together to determine total wheel rates in roll:
Code:
Front Rear
Spring Spring
Front Rear Roll Roll
System WRf WRr WRtot Dist Dist Share Share
Config (lb/in)(lb/in) (lb/in) (%) (%) (%) (%)
---------------------------------------------------------
2008 OEM 558 316 873 0.64 0.36 0.36 0.37
2010 SE 589 401 990 0.59 0.41 0.39 0.38
2011 OEM 665 430 1095 0.61 0.39 0.35 0.42
RCE Springs
+RCE Fs Rh 890 779 1668 0.53 0.47 0.33 0.25
TIC Springs
+RCE Fs Rh 1007 856 1863 0.54 0.46 0.41 0.32So a few interesting things, not in any particular order.
- Swaybars contribute a lot more to roll control than springs (springs on average contribute upper-30’s % of roll resistance)
- The 2011 OEM setup should be about 25% stiffer in overall roll stiffness than the 2008
- The RCE bars, assuming the front and rear are set the same (soft or hard), bias roll resistance to the rear by quite a bit (and running front soft rear hard throws the bias way toward the rear). Actually, running the front hard and rear soft comes very close to matching the OEM weight bias (58/42).
- The 2010 SE suspension setup, while having a less total roll resistance than the 2011, is a little more rear-biased and is probably the most neutral of the OEM setups (the 1mm increase on front bar dia for the 2011 does more than offset the giant leap in rear spring rate)
- The 2008 setup leaves a lot to be desired
- My TIC setup is only about 12% stiffer in roll than my RCE spring setup.
- My TIC setup is 113% stiffer in roll than the 2008, and 70% stiffer than the 2011.
The last thing here is to give some context to wheel rates. Since cars all don’t weigh the same, a useful way to determine and compare the stiffness of one car to another is to calculate the undamped natural frequency of the spring-mass system. We just calculated the wheel rates, and to figure out the frequencies we need the unsprung mass. For my purposes, I assumed 3373 as the OEM curb weight (this seems pretty accurate), subtracted out estimates for unsprung masses (based on old WRX threads that determined unsprung mass, I added some unsprung weight due to the STI having larger wheels/tires, brakes, etc). Since I’m mostly interested in autocross I also subtracted out weight for trunk junk, floor mats, my muffler delete, running on only ¼ of fuel, and also added in my weight. The equation to calculate NF is 3.13*sqrt(kw/m), where kw is the corner wheel rate in lb/in, and m is the corner weight in lbs. Here are the results (all values in Hz):
Code:
System Front NF Rear NF Front NF Rear NF
Config Ride Ride Roll Roll
------------------------------------------------
2008 OEM 1.49 1.43 2.50 2.34
2010 SE 1.60 1.62 2.56 2.64
2011 OEM 1.60 1.77 2.73 2.74
RCE Springs
+RCE Fs Rh 1.81 1.84 3.15 3.68
TIC Springs
+RCE Fs Rh 2.14 2.17 3.35 3.86In general it’s recommended to have a slightly higher rear frequency in the rear than in the front, but this isn’t really exact science so there are varying opinions. There’s a lot out there in suspension texts and the internet to recommend what frequencies you’d want to be at for what purposes.
So running equal spring rates in the front and rear (2010 SE, RCE, my TIC setup) will result in about equal ride frequencies front and in the rear, and for my setup, ever so slightly higher in the rear. If you run higher spring rates in the rear by 1kg/mm (or ~56 lbs/in), that results in a rear ride frequency about .1-.15 hz greater than the front.
Hopefully this adds some context to springs and bars. One thing to note - this is only looking at springs, bars, and ride/roll rates in a vacuum - there are still many other factors that will address roll and handling (ride heights, roll centers, alignment and alignment change through articulation, damping, etc etc etc).
Also, this is entirely analytical, and is relying on info mainly gathered on the internet
lol - to get more accurate numbers, you could actually measure your motion ratios through a range of travel centered around your ride heights (in fact motion ratios will change through articulation), spring rates are often progressive (especially on OEM shape springs), you could actually measure bar stiffness, etc etc etc...Hope this helps.
