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Old 06-06-2007, 05:31 PM   #1
stretchsje
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Default Sway bars and total spring rates (why sway bars sometimes do too much)

Someone asked me to repost an IWSTI thread of mine here for discussion. This is a few posts of mine combined into one, so hopefully it still reads well. Here goes:
================================================== ====

The Math

The formula for calculating the resistance of a solid sway bar, according to Fred Puhn, is:

Code:
                           500,000 D^4
K (lbs/in) =  -------------------------------------
               (0.4244 x A^2 x B) + (0.2264 x C^3)


               B
       _________________
A|    /                 \  C
 |   /                   \

A - Length of end perpendicular to B (torque arm - inches)
B - Length of center section (inches)
C - Length of end (inches)
D - Diameter bar (inches)
This formula does not take into account the flex of the bushings used to mount the sway bar, which can be significant. It also doesn't account for when the lever arms are physically longer than the actual lever arm they form (a bent bar, like the front sway), but that affect is pretty minor. I've measured the stock STI sway bars (roughly, not precisely) at:

Stock STI Front sway:
A: 5 in
B: 32 in
C: 7 in
D: 0.79 in
hence, K = 467lb/in

Stock STI Rear sway:
A: 7 in
B: 42 in
C: 7 in
D: 0.79 in
hence, K = 205lb/in

Now, what matters isn't the spring rate of the bar, but the spring rate at the wheels. The motion ratios front and rear in the STI are about 0.75 and 0.875, respectively. To get the wheel rate of the sway bar, we multiply by the spring rate (K from above) by the square of the motion ratio.

WHEEL RATE = K * Mr ^ 2

Thus, the final wheel rates from just your sway bars are:

Front: 267lb/in
Rear: 157lb/in

Add this to your coil spring rates to get your total wheel rate. The stock front springs are 224lb/in with a motion ratio of 0.97 (=210lb/in at the wheels), and the rear springs are 194lb/in with a motion ratio of 0.98 (=190lb/in at the wheels). A stock STI rides on its bump stops up front, which causes these spring rates to hike tremendously, but I'm going to ignore that for this conversation and assume a suspension with adequate suspension travel.

Final Stock STI Wheel Rates:

477lb/in front (267lb/in from sway bar, 210lb/in from coil spring)
347lb/in rear (157lb/in from sway bar, 190lb/in from coil spring)

The distribution of these total spring rates match the car's weight distribution almost exactly.

Anybody want to measure the Whiteline sway bars? If they're the same as stock, except for the diameter, you'd get spring rates (not wheel rates) of:

Whiteline Front:
24mm: 955lb/in
27mm: 1877lb/in *this is not accurate because this bar reduces to 24mm prior to the bushings

Whiteline Rear:
24mm: 419lb/in
27mm: 671lb/in *this is not accurate because this bar reduces to 24mm prior to the bushings

You can see that just minor bumps in sway diameter increase resistance quite a bit- it actually goes up by a power of four! So, the question I'm arriving at: is a 24mm sway bar too big? What about a 27mm sway bar?

Javid (of 6gun Racing) has said his car, which uses high spring rates and big Whiteline sway bars, is slower than the competition running without sway bars (but having more body roll). This actually makes a lot of theoretical sense. Quite simply, the car's spring frequency becomes too high for optimal use of the car's tires, which most racing literature suggests takes place around 2.0 to 2.5hz. (Further reading about how to determine your spring frequency based on your wheel rate.)


What is your spring frequency?

It's the number by which you should measure your car's spring rate.
http://www.smithees-racetech.com.au/...cefactors.html

Quote:
The most usefull measure of suspension stiffness is the spring frequency. It is directly comparable between all race cars. We can take our experience with one race car and use it to help choose spring stiffness for another. For instance, we find that small sedans and production sports cars around 1000kgs, without aero devices, will work best around 120 to 130 cycles per minute, running on Dot racing tyres. This is a lot stiffer than road car springs, where spring frequencies might be around 80 to 100 cpm. Other considerations might require us to run stiffer again. But 120 to 130 is what we'd like to run for maximum grip. If we can run quality racing shocks, we tend towards softer springs and more shock compression.
My guess is the weight of the car does not matter much so long as it is proportional to the load rating of the tire (heavier cars use tires with a higher load rating). The two variables seem to be amount of downforce and type of tires. Street tires would have a lower resonance frequency and thus I bet work better at lower spring frequencies.

Dennis Grant recommends a little higher spring frequency: http://www.wincom.net/trog/autocross_secrets5.html
Quote:
A spring change to a stiffer spring limits the amount of motion that the suspension undergoes in reaction to a particular acceleration (so does a change in CG height and track/wheelbase, but those are much harder to change than springs and for most practical purposes less effective too)

But there are upper limits on how stiff we can go with the springs, so we need a measure of "stiffness" to set the boundaries.

That number is the natural frequency of the suspension.... Rule of thumb is rear NF slightly higher than front (by a tenth of a Hz or two) Street car: 0.8 Hz. Occasional autocrosser: 1-1.5 Hz. Full-bore autocrosser: 2.2-2.5 Hz.

Yes, it really is that simple. Measure your corner weights, unsprung masses, and motion ratios, and then pick springs that put the front NF at 2.2 Hz and the rear at 2.5 Hz.

If you look at a completely stock STI with total wheel rates of 477lb/in and 347lb/in (as calculated above), it already has a spring frequency of about 2.25 front and rear. (Actually your bump stops increase this while your soft strut tops and sway bushings decrease this, so the actual spring frequency is quite dynamic.) So, you're already pretty high on a stock suspension. Again, that's already in the optimal range for use on racing compound tires.

I know a stock STI feels mushy and has a lot of body roll, but I think that is due to the car's low roll center (also debatably a good thing). Body roll isn't necessarily bad so long as you have enough negative camber, but for sure the STI has more body roll than most similar cars with a multilink rear suspension. Another thing to consider is that a stock car rides on its bump stops, creating horrible corner entry understeer and a jacking effect on turn-in. There are a host of problems on a stock car that get fixed by adding a large sway bar even if it's not technically ideal. Adding a large sway bar can be three steps forward even if it's one step back. In other words, your choice of sway bar will depend on what other problems you haven't yet fixed.

I think Prodrive might have the right idea with their RB320 suspension. They keep the stock front sway bar and bump up the spring rates what I assume is a mild to moderate amount. Once you've increased your stock spring rates, I'm not sure a larger sway is desirable anymore so long as you have enough camber. Prodrive uses a slightly larger rear sway bar to aid rotation, which is understandable given the car's weight distribution.

So, I think that big 27mm sway bars are useful on cars with soft springs to reduce body roll, but on cars with firm springs (400lb/in front, 350lb/in rear or higher), smaller (22mm or stock) sway bar sizes should be used for optimal grip. Again, this assumes the car has sufficient camber and enough suspension travel- in other words, no other pre-existing, more significant problems. Therein lies the dilemma- do you gain more grip than you lose when increasing body roll? You might be taking one step forward but two steps back.


Compromises and Design Decisions

Consider that if you go back to the stock sway bar (from a 27mm bar), you're going to have about twice as much roll due to body movement since your spring rate will have been reduced by about two thirds. While mathematically you're spring rate will be close to ideal, I'm not convinced this is the best solution. You'll have a lot of body roll and that in itself can cause problems. At minimum, you'll probably need to double up on your negative camber to compensate for this. This is probably the most important thing to consider. Do you want to run 3.5 degrees of static negative camber? A roll center adjuster (ball joint extension) would probably be helpful too, this will cut down on body roll (potentially significantly). But, in theory, your mechanical grip would increase with the softer wheel rate.

It's important when discussing this to remember that a significant amount of body roll comes from tire deflection and will exist regardless of how high your spring rates are. Put more weight on a tire and the rolling radius of the tire will shrink, just like a tire that's low on air. So, when discussing body roll, it's important to realize that on a very stiff car, body roll due to spring compression and extension may be less than half of your actual total body roll.

So, you may see a car on racing tires rolling three degrees and wonder how that happens on such stiff springs. With most track cars running over 1000lb/in wheel rates, the car could be on two wheels (100% weight transfer) and still have only compressed the outside wheel 3/4 of an inch. That's about a degree and a half of body roll. The rest of the roll you see is from tire deflection and would happen even if you welded your struts solid. Cutting your spring rate in half will double body roll due to your roll resistance (springs), but it will not affect roll from tire deflection. Tire deflection should happen less on wider, larger tires.

Said differently, doubling your spring rate will not cut body roll in half because your tire deflection remains the same. You may only be adding 50% more body roll (4.5 degrees instead of 3). But since you're using double the stroke in the suspension, you're also gaining more dynamic camber (assuming you're still in the correct part of the curve) in the turns, too. The point here is that having body roll is just a fact of life, and you just need to make sure your car is set up for it. You'll need lots of suspension stroke and lots of camber. Again, there's lots of variables to consider here- in the end, I think the best thing to do is bring a lot of tools to a test-and-tune autocross day and experiment. Driver feel comes into play too.

And now we get into that gray area I know little about. Is it possible to properly dampen a car with big sway bars? You're either underdamped in turns or overdamped on the straights.

I'm certain this is why race cars tend to use smaller sway bars: because sways make damper valving a compromise. However, on a street car, we make that sacrifice to reduce body roll while still being able to run soft, comfortable springs for a good highway ride.


Closing Thoughts:

I don't mean to say that such-and-such is best, only that it's worth trying. I haven't actually tested all this in the real world, and I'm not preaching from experience. Hell, I don't even have an opinion on what an optimal spring frequency is- I'm just regurgitating that information. My experience says larger sway bars can be 3 steps forward and only one step back. So, I absolutely am not saying big sway bars are bad- they're one of the best modifications for an otherwise stock car. On the other hand, my theory says that you should ditch them once you've prepped the rest of the car. I know opinions are like buttholes- everybody has one. However, at least Javid of 6gun racing has written some anecdotal evidence- from actual data- suggesting the theory is correct. It was actually one of his posts that got me started on this.

I hope this helps some of you make suspension decisions. Comments are appreciated (and inevitable)!


EDIT: I spoke with an engineer who assured me my numbers (from Puhn's book) were wrong in regards to body roll. Since you have twice as much bar flex in a body roll situation (inside and outside wheel move roughly equal amounts in opposite directions), the sway bar rates I calculated should be DOUBLE what I originally said.

In other words, take the number from the original equation and double it.

My original equation only works for a one wheel bump. I thought the doubled force was divided among the two wheels (thus you wouldn't double the rate), but it isn't. That's where I was wrong. The sway bar force is equally applied to both wheels.

So, again- as extreme as the sway bars sounded earlier, double that.[/i]
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Last edited by stretchsje; 08-16-2007 at 06:56 AM.
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Old 06-06-2007, 06:37 PM   #2
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Great post, thanks. It's something I've wondered about with all this talk about big swaybars.
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Old 06-06-2007, 06:54 PM   #3
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Very good and informative post. I have a few comments:

My, and a number of successful BSP/ESP STi owners problem with sway bars (or big sway bars) is that they will limit suspension travel on the inside wheels. This becomes an issue once you run wide slicks that have enough grip to cause full transfer of weight. This leads to a number of problems for either track or autoX. This (12k F/R, 24mm F/R, on 275 V710s) is not as fast as it could be (looks cool as hell though ):



Right now I have 12k springs front and rear and a 24mm front bar. I have no rear bar, on big slicks the rear was way too loose on turn in with the bar. I am going to tray the stock front bar. My guess is that if I wanted to ditch the front bar all together, I would need about 14 to 16k spring.

Of course the amount of roll is dependent on the geometry as much as the load. A high roll center and better camber curve mean that less of a bar is needed.

Above is an underlying point I would like to stress, dynamic alignment with geometry change. On the front of the impreza, camber is lost with compression at a very high rate compared to the rear or many other sports cars. So limiting roll is limiting compression on the outside which retains a flatter tire. On a DSM chassis the rear of the car has a lot of toe-in in the rear under compression. Fast DSMs limit rear movement with big bars.

Sway bars also effect the loading between the front and rear of a car which can be both good and bad and certainly complicates things. With out bars, loads are transferred diagonally, loading the outside front means unloading the inside rear. With a front bar, the outside front is now unloading the inside front and loading the inside rear. Unloading the wrong tires with big bars can be a bad thing and out weigh the benefit of not rolling the car over as much.

Like anything else, 'what is best' depends on 'what your goals are'.

In a stock class a 29mm bar will work best.

For a more modified car on street tires 24mm will work well for a higher car and 27/29 may work best for a car with a very low RC.
Regular sized r-comps may still work well so long as the spring rates aren't too high. For the double duty car setups, more adjustment in the parts, time in the seat, and hopping in other setups for reference point is likely the best advise any one can give.

For large r-comps and slicks stock or no bars will likely work best.

Javid
6Gun Racing

Last edited by javid; 08-15-2007 at 11:37 AM.
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Old 06-06-2007, 07:58 PM   #4
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^^^ I thought I was out of my mind when I thought I got more oversteer and looseness with 275 r-tires than with my re92s. brb going to go disconnect my rear bar.
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Old 06-07-2007, 06:14 PM   #5
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So, one thing I can't figure out, and I'm going to totally discredit my own spring frequency analysis by asking:

How the hell can a car with 4+ degrees of body roll possibly be so stiff that it overwhelms the tires?

I earnestly believe that there's such a thing as too high of a spring frequency and that a lot of members here exceed it. I do think it's much higher than I've calculated (which anything beyond a stock STI will do). So what's the rule? Speaking strictly in terms of ideal spring frequency, are larger sways an appropriate response to a lower roll center so long as you keep your total roll resistance relatively constant? And what do you use as a baseline? The whole spring frequency discussion is quite vague in regards to how we plan for sway bars. Again, if you have 4+ degrees of roll, how can your sway bars in any way be considered too big?
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Old 06-07-2007, 06:41 PM   #6
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I'm not entirely sure that the math works out here on adding up the spring rates. It's funny that this topic came up today, as I was working up the math on it yesterday. The big problem is that the sway bar is NOT just a torsion bar that is rigidly mounted and has a wheel rate of 267 lb/in. The other end of that sway bar is effectively mounted to the spring on the other side, so the total rate of the sway bar at the wheel has to take into account the rate of the spring on the other side.

Rates drop dramatically when you stack springs, which is basically what is happening here. The sway bar is like a spring stacked with the inside wheel, pushing it up- so I don't think the numbers are quite as crazy as this simple analysis makes them out to be.

Using a basic dual spring calculator with the wheel rates, it only comes out to 117 lb/in, and with the motion ratio taken into account that only brings it to 75 lb/in. I don't know if the math works out there, but that seems to make more sense for the total rates than adding the full rate of the bar.

(edit) the sway bar is also basically lifting up the unspring mass on the other side too... I guess that throws a wrench into the calculations too. Yikes!

Can anybody else give a definitive answer here?
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Old 06-07-2007, 06:58 PM   #7
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Sway bars do NOT contribute to ride rate or ride frequency.

Wheel mode frequencies are dominated by tire rate and therefore damper tuning for wheel hop is not based on ride spring stiffness.

Last edited by Blue5spdWRXWgn; 06-07-2007 at 07:06 PM.
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Old 06-07-2007, 08:30 PM   #8
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Quote:
Originally Posted by Blue5spdWRXWgn View Post
Sway bars do NOT contribute to ride rate or ride frequency.
I was wondering about that. The roll rate is for sure affected, but I think part of suspension frequency tuning probably also considers the roll AND pitch stiffness, considering both the lateral and longitudinal weight transfers.

Quote:
Originally Posted by remowgn View Post
I'm not entirely sure that the math works out here on adding up the spring rates. It's funny that this topic came up today, as I was working up the math on it yesterday. The big problem is that the sway bar is NOT just a torsion bar that is rigidly mounted and has a wheel rate of 267 lb/in. The other end of that sway bar is effectively mounted to the spring on the other side, so the total rate of the sway bar at the wheel has to take into account the rate of the spring on the other side.
I have this concern as well. The other end of the sway is definitely not rigidly mounted to the body, so it seems like the calculation should be different. Here's where I get confused... thinking of the swaybar as a mechanism that transfers some the compression resistance to the outside wheel, if the swaybar were 100% stiff (ie infinite spring rate), then the outside wheel would effectively experience 2x of the spring rate, because it would completely transfer the force from the inside spring. But, if the bar didn't twist, then the car wouldn't roll (ignoring tire effects for the moment)... so... on the one hand, we get a car with 2x rate on the outside wheel, that will still roll... on the other hand, we have a car that can't roll...

Quote:
Originally Posted by javid View Post
With a front bar, the outside front is now unloading the inside front and the inside rear.
With a bigger front bar, doesn't this unload the inside front but load the inside rear?

Last edited by Mind; 06-07-2007 at 08:42 PM.
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Old 06-08-2007, 12:05 AM   #9
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Quote:
Originally Posted by Blue5spdWRXWgn View Post
Sway bars do NOT contribute to ride rate or ride frequency.

Wheel mode frequencies are dominated by tire rate and therefore damper tuning for wheel hop is not based on ride spring stiffness.
Um, that makes no sense. The bar is atached to another spring. Can you point me to a reference?
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Old 06-08-2007, 12:08 AM   #10
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Quote:
Originally Posted by Mind View Post
With a bigger front bar, doesn't this unload the inside front but load the inside rear?
Yes, scarry how forgetting one would can mess up an entire sentance.
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Old 08-11-2007, 05:18 PM   #11
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Quote:
Originally Posted by javid View Post
Yes, scarry how forgetting one would can mess up an entire sentance.
So why not correct the above post?
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Old 08-15-2007, 11:38 AM   #12
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Quote:
Originally Posted by wobbletop View Post
So why not correct the above post?
Scary how much sense that makes

Fixed
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Old 08-15-2007, 04:16 PM   #13
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So either the rate of the spring should be brought down or the sways be reduced in size right? Where do you hit an equilibrium?
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Old 08-15-2007, 09:47 PM   #14
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I spoke with an engineer who assured me my numbers (from Puhn's book) were wrong in regards to body roll. Since you have twice as much bar flex in a body roll situation (inside and outside wheel move roughly equal amounts in opposite directions), the sway bar rates I calculated should be DOUBLE what I originally said.

In other words, take the number from the original equation and double it.

My original equation only works for a one wheel bump. I thought the doubled force was divided among the two wheels (thus you wouldn't double the rate), but it isn't. That's where I was wrong. The sway bar force is equally applied to both wheels.

So, again- as extreme as the sway bars sounded earlier, double that.
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Old 08-15-2007, 10:09 PM   #15
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Quote:
Originally Posted by javid View Post
Um, that makes no sense. The bar is atached to another spring. Can you point me to a reference?
Ride rate and frequency are calculated for heave mode (two wheel bump). Sway bars are assessed with roll rate and roll couple distribution.

Try Gillespie or Milliken.
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Old 08-15-2007, 10:10 PM   #16
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This is a great mathematical explanation, but the sway bar facts already told us this. A suspension is a system and therefore it is usually big bars and softer springs or stiff springs and smaller bars.

http://forums.nasioc.com/forums/show....php?t=1152714

buttdyno told us all of this months ago, but being an engineer I love seeing real numbers in the explanation. I recommend this be added to the sway bar facts sticky.
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Old 08-15-2007, 11:55 PM   #17
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Quote:
Originally Posted by Blue5spdWRXWgn View Post
Ride rate and frequency are calculated for heave mode (two wheel bump). Sway bars are assessed with roll rate and roll couple distribution.

Try Gillespie or Milliken.
Right, so in a corner, with roll, sway bars will contribute to wheel frequency and ultimately grip.
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Old 08-18-2007, 12:38 PM   #18
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So...considering I run a 25mm adj bar up front and a 22mm adj bar out back...what are some spring rates I should consider?
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Old 08-18-2007, 06:12 PM   #19
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What are you trying to do with the car?
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Old 08-20-2007, 09:13 AM   #20
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Daily driver/weekend track car. I don't mind "harshness" I've run 7/9 on the car previously, and I'm wondering if this is too much or too little with the sways I'm using in conjunction..

Last edited by Drift Monkey; 08-20-2007 at 11:03 AM.
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Old 01-16-2009, 06:47 PM   #21
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Quote:
Originally Posted by javid View Post
Very good and informative post. I have a few comments:

My, and a number of successful BSP/ESP STi owners problem with sway bars (or big sway bars) is that they will limit suspension travel on the inside wheels. This becomes an issue once you run wide slicks that have enough grip to cause full transfer of weight. This leads to a number of problems for either track or autoX. This (12k F/R, 24mm F/R, on 275 V710s) is not as fast as it could be (looks cool as hell though ):



Right now I have 12k springs front and rear and a 24mm front bar.
[bumping dead thread]
What does 12k translate to in lbs?
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Old 01-16-2009, 10:05 PM   #22
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Multiply by 57.
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Old 01-16-2009, 11:55 PM   #23
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Some very interesting theories being talked about recently. I've been thinking about trying some out this upcoming year. Run 400# springs in front 340# in the rear with 22mm sways all around. Total curb weight is right around 2700 lbs. Might try switching to a 18mm rear sway and see what it does.
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Old 01-17-2009, 04:24 PM   #24
BIGSKYWRX
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Quote:
Originally Posted by stretchsje View Post
Now, what matters isn't the spring rate of the bar, but the spring rate at the wheels. The motion ratios front and rear in the STI are about 0.75 and 0.875, respectively.
MR for the 04-07 STi (and WRX) is much closer to .97 front and rear (MacPherson struts are very, very, very close to 1.0, where are you getting .75 and .87?
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Old 04-30-2009, 04:28 PM   #25
speedkills1133
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good post i will do the conversion later to figure out what i need
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