Bag over coils performance

[KyleAnderson]

You see, theoretically anyway, bag pressure should be a constant no matter the system height if two conditions are met: 1. the system is at rest, as in the corner is not being compressed or in rebound. 2. the system is not at either its maximum or minimum height, where pressure does indeed become a factor in the system's performance.

The physics of this are relatively straightforward since it takes a constant force (whatever the corner weight of the car is) to keep the corner at any given height off the ground. Whether the car is sitting 1" off the ground or 2' off the ground, the pressure inside the bag should be the same, assuming the conditions outlined above.

Agreed- in a simplified model (but not theory), pressure should be the same at any height between min and max. The volume of air would only increase, but this also assumes that the available air space would increase the same amount to accommodate it. In our case, we're adding more air to a container whose volume remains the same before a load is added. When a load is added, the volume changes due to bag deflection.

The other very big, and incorrect assumption in a simplified model is that air is incompressible. Air will compress by a certain ratio. The more air you add, the more there is to compress. This is the major reason why pressure increases exponentially as ride height increases linearly. If you want to make it even more complicated, this ratio is affected by temperature, humidity, and content of the air, but to much lesser effects.

I find it easiest to think about this problem in two steps: before and after loading.

Before, we have a container of nearly constant volume (and shape). A gas takes the shape of its container, so adding air will only increase pressure, and therefore force exerted on the end cap.

After a force is applied, the pressure must increase by reducing the available volume until the force exerted equals the force applied. It's in this step that the effects of changing bag shape (diameter especially) and compressibility of air need to be factored in.

...but also increases the area of the bag that can provide upward force proportional to the increase in diameter of the bag.

This is the one point I disagree on. The force is exerted by end cap of the bag, which is unchanging.

[Oh Damn, it's Sam]

Great information in this thread. Just some clarification, what your saying Sam is that at a lower ride height the effective spring rate is higher? my example here is I have a 2002 lexus gs300. I am running UAS aero sport bags and bilstein shocks and accuair elevel for management.

At ride height I would say I have an addition 1.5-2 inches to full lift, this is not at the bag but I'm roughly estimating from the tire/fender. when I ride at cruise height, .5-1 inch lower, I feel that the suspension is softer? I bottom out more, or generally more movement in the suspension not only because of the lower ride height but less "spring" to counter act bumps. When I ride at my #3 setting, it feels stiffer? less movement in the suspension,"more spring"

As of lately I have noticed that my rear shocks are wearing out, getting loose,semi bouncy, squeaky noise. yet when I ride at a lower ride height there is less bounce after a bump in the road. In my head I'm imagining that as the shocks have gotten weaker the effective spring rate at ride height was "over sprung" causing bounciness. with less air in the bag, a lower "spring rate", the shocks are still able to damper the motion? any thoughts?

sorry didnt mean to thread jack op, didnt think it was worth making a new thread since its sort of on topic.

Hey, sorry for the slow reply to your query - finals week and all that.

What I'm going to do at this point is just totally punt on your question, for one single reason: I don't think the effects of bag pressure are adequately attested to in my cheesy little model.

You see, theoretically anyway, bag pressure should be a constant no matter the system height if two conditions are met: 1. the system is at rest, as in the corner is not being compressed or in rebound. 2. the system is not at either its maximum or minimum height, where pressure does indeed become a factor in the system's performance.

The physics of this are relatively straightforward since it takes a constant force (whatever the corner weight of the car is) to keep the corner at any given height off the ground. Whether the car is sitting 1" off the ground or 2' off the ground, the pressure inside the bag should be the same, assuming the conditions outlined above.

Except I'm not 100% convinced this is the case in practice. The issue, as KyleAnderson above alluded to, is that the bag changes shape according to both pressure and compression, extending outward under both conditions, which both decreases the pressure inside the bag proportional to the corresponding increase in volume, but also increases the area of the bag that can provide upward force proportional to the increase in diameter of the bag. These are not factors that my simplified model takes into account at the moment, and I'm not convinced that these are as negligible of variables as I initially suspected.

What I would like to do at this point is to get my car back on air (coming soon, I swear to God Almighty) and take some precise measurements of pressure and bag dimension under a number of conditions similar to what Mr. Anderson has outlined above. From this, I should be able to perform an analysis that will isolate the pertinent variables. The result will still be an approximation obviously, since suspension geometry also comes into play here and I'll be damned if I'm going to create a mathematical model for all of that shit. Nevertheless, I think it will still be useful.

Stay tuned.

[i2ice]

Great information in this thread. Just some clarification, what your saying Sam is that at a lower ride height the effective spring rate is higher? my example here is I have a 2002 lexus gs300. I am running UAS aero sport bags and bilstein shocks and accuair elevel for management.

At ride height I would say I have an addition 1.5-2 inches to full lift, this is not at the bag but I'm roughly estimating from the tire/fender. when I ride at cruise height, .5-1 inch lower, I feel that the suspension is softer? I bottom out more, or generally more movement in the suspension not only because of the lower ride height but less "spring" to counter act bumps. When I ride at my #3 setting, it feels stiffer? less movement in the suspension,"more spring"

As of lately I have noticed that my rear shocks are wearing out, getting loose,semi bouncy, squeaky noise. yet when I ride at a lower ride height there is less bounce after a bump in the road. In my head I'm imagining that as the shocks have gotten weaker the effective spring rate at ride height was "over sprung" causing bounciness. with less air in the bag, a lower "spring rate", the shocks are still able to damper the motion? any thoughts?

sorry didnt mean to thread jack op, didnt think it was worth making a new thread since its sort of on topic.

[Will@BagRiders]

European Car recently published the results from their Tuner grand prix event.

AccuAir's B8 S4 with their Sport Kit (Universal bags over the factory dampers up front - separate bags and shocks in the rear) held it's own against all the other cars. The AccuAir car wasn't the fastest around the track, but it did really well. This says a lot for a properly setup air suspension kit.

The goal shouldn't be to maintain "some" performance. Why not maintain all of it? Of course if you're goal is to have the car aligned at a super low height (this was not AccuAir's goal for the Tuner Gran Prix) then you might have to sacrifice a little, but it is possible to essentially have the best of both worlds.

As for the comments above. I agree, it would be nice to know our 'spring rate' equivalents on the fly. I'm really not much help in that department.

[Wiggins3377]

Bump for updates on this thread. I drive a 370z and debating a "bag over" setup with stance coils and universal bags. I'd love to figure out a happy medium of a great looking drop and maintain "some" performance.

[KyleAnderson]

I would like very much if we can devise a relatively straightforward solution to describe instantaneous spring rate on air bags in real-world application, rather than the purely theoretical approach I've outlined above. Obviously the dynamics of each individual suspension system will affect the real-world precision of any mathematical solution somewhat, but it seems like we ought to be able to come up with something here.

Same here... the air ride community could really use something like this. It would be helpful in cases like the OP where they're unsure if the performance of air can meet their needs. Even if the calculation is complicated (which I think it has to be), I could make a simple Excel worksheet. Do you see additional variables, errors, or refinements in the way I worked through it?

[Oh Damn, it's Sam]

I'll get you those measurements as soon as possible. Right now, my Merc is back on coils until I can get my final bracket design finished (damn those Mercedes engineers for making the rear suspension on the W124 so damn claustrophobic!), so it might be a little bit of time.

I would like very much if we can devise a relatively straightforward solution to describe instantaneous spring rate on air bags in real-world application, rather than the purely theoretical approach I've outlined above. Obviously the dynamics of each individual suspension system will affect the real-world precision of any mathematical solution somewhat, but it seems like we ought to be able to come up with something here.

[KyleAnderson]

This was really bugging me, so I did some math based of 5 different starting pressures...

2.7" compressed
6.0" extended
4.3" stroke

(estimated, this should really be bag inside diameter) 4.5" diameter end cap = 15.896 in^2
15.896 in^2 x 4.3" = 68.35 in^3 = 1.12 L

PV = nRT

R = .08206
T = 295.372 K

psi to pascal:
10 psi = 68950 Pa
20 psi = 137900 Pa
30 psi = 206850 Pa
40 psi = 275800 Pa
50 psi = 344750 Pa

Moles of air:
(Pa x 1.12L)/(.08206 x 295.372) = number of moles
10 psi = 3186.042
20 psi = 6372.084
30 psi = 9558.126
40 psi = 12744.168
50 psi = 15930.210

corner weight 998 lbs over 4.5" diameter end cap = 62.783 psi
(not ideal, not applied over all area, doesn't account for bag flex or account for compressibility of air)

Add to...

10 psi + 72.783 psi = 501821 Pa
20 psi + 82.783 psi = 570769 Pa
30 psi + 92.783 psi = 639716 Pa
40 psi + 102.783 psi = 708664 Pa
50 psi + 112.783 psi = 777611 Pa

Volume of compressed air.
PV = nRT .... nRT/P = V
(3186.042 x .08206 x 295.372 K) / 501821 Pa = .154 L
(6372.084 x .08206 x 295.372 K) / 570769 Pa = .271 L
(9558.126 x .08206 x 295.372 K) / 639716 Pa = .362 L
(12744.168 x .08206 x 295.372 K) / 708664 Pa = .436 L
(15930.210 x .08206 x 295.372 K) / 777611 Pa = .497 L

Liters to cubic inches:
9.39 in^3
16.54 in^3
22.09 in^3
26.61 in^3
30.33 in^3

Divided by end cap area (15.896 in^2) = length
.591"
1.041"
1.390"
1.674"
1.908"

Subtract from bag stroke (4.3") for amount compressed:
3.709"
3.259"
2.910"
2.626"
2.392"

Instantaneous spring rate = corner weight (998 lbs) / amount compressed
10 psi = 269 in/lbs
20 psi = 306 in/lbs
30 psi = 343 in/lbs
40 psi = 380 in/lbs
50 psi = 417 in/lbs

-------------------------

Adding pressure will have a linear affect on instantaneous spring rate until the amount of force exerted exceeds the force applied. In this case it is 998lbs/15.896in^2 = 62.8 psi. Theoretically this would be maximum lift... force exerted equals force applied. This would be closer to the truth for an air cylinder, but the one huge issue is that the bag is flexible and changes shape/volume depending on height. It's impossible to accurately calculate the spring rate of a rubber air bag. My numbers are very, very rough estimates. The only way to do it right is with a spring dyno.

Sam, I assume your example numbers are based on your own setup. Would you be able to unload the bag which would have 998 lbs on it (jack the car up), air it up to 50 psi, measure the extended length, then lower the car and measure how much it compresses? I'm curious to see just how accurate my calculations are. It could also be done for 10, 20, 30, and 40 psi to check those too. If it's anywhere close, I would be glad to simplify the equation for others to use.

[Oh Damn, it's Sam]

Okay, that was extremely helpful thank you!

However, I dont think you realize the spring rates arent as crazy as they seem.
320 lb/in is approx 5.7k

So for me to achieve an IDEAL 10k front setup, Id need to run 560 lb/in.
I dont think I need that stiff either. The standard 8k 6k setup commonly seen on many coil type suspension is 450lb/in.

So from what I can gather from what you said, that kind of stiffness shouldnt be too hard to obtain, correct?
Obviously an air spring is completely progressive, while a coil spring is linear(or that alteast try to be) and fluctuation will occur, but as long as you got the properly sized bag, I think a stiffer setup would be very obtainable.

Am I correct in this thought or am I still not getting something?

Aha! No, those are not as crazy of numbers as I had suspected. I wasn't sure what units you were specifying, and knowing some people run insanely stiff setups for stuff like drag use, I simply assumed you were talking in lb/in. My mistake! Amerocentrism at its finest

Alright, since we're back in the realm of reality, I thought I might share with you the equation I developed for calculating approximate instantaneous spring rate for an air bag setup. It is as follows:



where:

wc = the weight of the corner of the vehicle, measured in whatever units you want your result to be in (kg, n, lbs, whatever)
x1 = the height of the bag at ride height, again measured in whatever units you want the result to be in (in, mm, etc.)
x0 = the height of the bag when fully compressed.
d = the amount of deflection from ride height you're interested in measuring the spring rate at. This will give you an idea of how progressive your setup will be. For the spring rate at rest, insert zero. For the spring rate when compressed, set this number positive. For extended, negative.

This will spit out a spring rate in whatever units you feed into it, and this is the exact equation I used in the calculations above. For example, at ride height, my front bags sit at about 6" tall, and can compress to 2.7". Since we're interested in ride height, deflection is zero. Thus:



If I want to see how progressive my air bags are, I can add in the amount of deflection I'm interested in. Here, I'm interested in seeing how stiff the bags are when compressed 1":



This is obviously a simplified equation and the dynamics of a suspension system have more going on than the four variables that can be fed in here. Nevertheless, this should get you in the ballpark. Some hasty calculation on my part indicates that you are likely not to have a whole lot of uptravel when at ride height, simply because your vehicle weighs considerably less than my heavy pig of a car and you're looking for a much stiffer rate. Still, play around with the equation and see if you can get anywhere close to what you're looking for.

[Legoctf]

As Sam initially thought, why not just do an air'd topmount?

Best of both worlds with that setup.

Air'd topmounts (like the muller air cup setup from Fortune Auto) isn't really good for driving around on, they are for temporary lifts, not for street driving.
My goal here is to have the ability of slammed parking status, but still be able to throw the car hard in corners like it was designed for. My evo currently I think is at a decent low for driving around. However its too low for hard driving.

On top of that when a properly setup bagged car drops to perfect fitment its just beautiful.

[Legoctf]

I think you might be misunderstanding slightly. It's not that air isn't tunable for excellent performance - it absolutely is. I spent hours performing calculations on the design of the air ride setup for my Mercedes, and I am thus far extremely pleased with its performance. My goals were 300 lb/in at ride height, 200 lb/in at 90% extension, and 550 lb/in at low cruise. In all three cases, I have been able to hit within 10% of my targeted spring rate at ride heights that I'm pleased with.

What air is not good at is being extremely stiff. As I've alluded to above, there are two ways to make an air ride setup stiff as the dickens:

1. Drive around with the bags at max extension and just put a shitload of pressure in them, which is not sweet, because at full extension you have zero downtravel.

2. Since instantaneous spring rate of an air bag is inversely proportional to the ratio between bag volume at ride height and minimum bag volume, just set this ratio as low as possible. Essentially, this means you're driving almost aired-out. The obvious limitation of this is uptravel, which will be nonexistent. The non-obvious limitation of this is repeatability and upper range, as 1badg35 indicated. Since the spring rate is proportional to the negative cube of the linear extension of the bag, minor fluctuations in actual ride height can cause wild fluctuations in actual spring rate at the extreme end of the bag's compression.

To give you an example from my own vehicle, at ride height my front bags sit at 6" extension and have a spring rate of 320 lb/in. A half inch lower produces 374 lb/in and a half inch higher, 280. Ergo, if my eLevel controller doesn't quite peg my desired ride height and is off even by a half inch, my spring rate is still relatively close to my desired specs. Not that my eLevel system is that inaccurate mind you - it consistently nails my desired ride height, but this is a thought experiment.

Alright, let's continue our thought experiment. Say I wanted a stiffer ride and were willing to pay the price of limited uptravel. I now set up my bags such that ride height is at 4" of bag extension. My instantaneous spring rate is now 785 lb/in. Yet, a half inch higher and my rate drops all the way to 571 lb/in. And if my eLevel misses and goes a half inch lower, my rate is a whopping 1264 lb/in!

So, you see what's going on here? If you push a bag to offer an extremely stiff spring rate, you either wind up with zero downtravel (lame), or zero uptravel AND fairly unpredictable behavior (super lame). None of this is to say that a bag setup cannot be highly tuned –it absolutely can– but merely that air ride setups excel at a range of spring rates from soft to medium-stiff, and simply cannot easily reproduce the extreme stiffness that a metal coil spring can.

Okay, that was extremely helpful thank you!

However, I dont think you realize the spring rates arent as crazy as they seem.
320 lb/in is approx 5.7k

So for me to achieve an IDEAL 10k front setup, Id need to run 560 lb/in.
I dont think I need that stiff either. The standard 8k 6k setup commonly seen on many coil type suspension is 450lb/in.

So from what I can gather from what you said, that kind of stiffness shouldnt be too hard to obtain, correct?
Obviously an air spring is completely progressive, while a coil spring is linear(or that alteast try to be) and fluctuation will occur, but as long as you got the properly sized bag, I think a stiffer setup would be very obtainable.

Am I correct in this thought or am I still not getting something?

[Oh Damn, it's Sam]

:/

Pretty depressing to hear that.

So with that methodology, the Airlift STI and Accuair S4 both run a setup they put A LOT into developing for proper feel and performance. To the point where it would be near impossible to emulate on another chassis?

Forgive me, but I really feel like its not quite that hard, as people have ideal psi's for driving around etc, I feel you could easily ascertain an ideal PSI for good handling. Obviously this all opinion and thought, as I dont have an air setup to test this with.

I think you might be misunderstanding slightly. It's not that air isn't tunable for excellent performance - it absolutely is. I spent hours performing calculations on the design of the air ride setup for my Mercedes, and I am thus far extremely pleased with its performance. My goals were 300 lb/in at ride height, 200 lb/in at 90% extension, and 550 lb/in at low cruise. In all three cases, I have been able to hit within 10% of my targeted spring rate at ride heights that I'm pleased with.

What air is not good at is being extremely stiff. As I've alluded to above, there are two ways to make an air ride setup stiff as the dickens:

1. Drive around with the bags at max extension and just put a shitload of pressure in them, which is not sweet, because at full extension you have zero downtravel.

2. Since instantaneous spring rate of an air bag is inversely proportional to the ratio between bag volume at ride height and minimum bag volume, just set this ratio as low as possible. Essentially, this means you're driving almost aired-out. The obvious limitation of this is uptravel, which will be nonexistent. The non-obvious limitation of this is repeatability and upper range, as 1badg35 indicated. Since the spring rate is proportional to the negative cube of the linear extension of the bag, minor fluctuations in actual ride height can cause wild fluctuations in actual spring rate at the extreme end of the bag's compression.

To give you an example from my own vehicle, at ride height my front bags sit at 6" extension and have a spring rate of 320 lb/in. A half inch lower produces 374 lb/in and a half inch higher, 280. Ergo, if my eLevel controller doesn't quite peg my desired ride height and is off even by a half inch, my spring rate is still relatively close to my desired specs. Not that my eLevel system is that inaccurate mind you - it consistently nails my desired ride height, but this is a thought experiment.

Alright, let's continue our thought experiment. Say I wanted a stiffer ride and were willing to pay the price of limited uptravel. I now set up my bags such that ride height is at 4" of bag extension. My instantaneous spring rate is now 785 lb/in. Yet, a half inch higher and my rate drops all the way to 571 lb/in. And if my eLevel misses and goes a half inch lower, my rate is a whopping 1264 lb/in!

So, you see what's going on here? If you push a bag to offer an extremely stiff spring rate, you either wind up with zero downtravel (lame), or zero uptravel AND fairly unpredictable behavior (super lame). None of this is to say that a bag setup cannot be highly tuned –it absolutely can– but merely that air ride setups excel at a range of spring rates from soft to medium-stiff, and simply cannot easily reproduce the extreme stiffness that a metal coil spring can.

[NeilP]

As Sam initially thought, why not just do an air'd topmount?

Best of both worlds with that setup.

[Legoctf]

We made an attempt at the studio to create a custom bag setup using coilovers dampened to 16k and our threaded billet bag sleeves we designed, and specifically sized bags in order to reach the desired spring rate at drive height, but we were never able to get anywhere near desired spec.. Wound up scrapping the project altogether

Its a fine line between not enough air in the bag, and too much air in the bag. As stated above, it will take a bunch of engineering to get it all perfect. And from our past experience from bagged setups, if its not perfectly set up, the car will not drive like you want it to.

:/

Pretty depressing to hear that.

So with that methodology, the Airlift STI and Accuair S4 both run a setup they put A LOT into developing for proper feel and performance. To the point where it would be near impossible to emulate on another chassis?

Forgive me, but I really feel like its not quite that hard, as people have ideal psi's for driving around etc, I feel you could easily ascertain an ideal PSI for good handling. Obviously this all opinion and thought, as I dont have an air setup to test this with.

[1badg35]

We made an attempt at the studio to create a custom bag setup using coilovers dampened to 16k and our threaded billet bag sleeves we designed, and specifically sized bags in order to reach the desired spring rate at drive height, but we were never able to get anywhere near desired spec.. Wound up scrapping the project altogether

Its a fine line between not enough air in the bag, and too much air in the bag. As stated above, it will take a bunch of engineering to get it all perfect. And from our past experience from bagged setups, if its not perfectly set up, the car will not drive like you want it to.