Coilover spring rates/wheel frequency

[document]

A couple books I have read about building a car/suspension from scratch (Staniforth's suspension book, for one) make heavy reference to wheel frequency in choosing at least ballpark spring rates, where wheel frequency is the number of cycles per minute that the car will naturally tend to bounce at with no dampers, just spring. It's related to the wheel rate and the sprung weight at that wheel (wf = 187.8 * (wr/sw)^1/2), and roughly corresponds to how firm the ride is -- a 4000 pound M5 should have a similar ride to a 2400 pound miata if they have similar wheel frequencies, as I understand it.

It is said that you generally want a wheel frequency of ~120-140 for a sports car on a road course, and you also will typically want a WF of ~10% more in the rear than the front, to avoid resonant pogoing of the car (Carroll Smith doesn't seem concerned about that, though).

So, here's what I find interesting. If you look at a typical coilover set up for the e36 M3, it will have, say, 375 pound springs in the front, and 450-500 in the rear. That gives a front WF of around 135. The rear is trickier, because the spring is located in the middle of the trailing arm, dropping the wheel rate. I read recently that for the e36 m3, wr = .46 * spring rate. If that's right, a 500 lb/in spring in the rear equates to a WF of around 105. To get a rear WF of 110% the front WF, you'd need nearly 1000 lb/in springs (to give a ~450 lb/in wheel rate, interestingly).

Anyway, three questions:

1) Is .46 the right factor for determining rear wheel rate from spring rate for an e36?

2) Anyone ever tried a crazy 950 pound spring in the rear (or whatever would give a WF of ~145cpm, if the 0.46 factor is wrong) with a ~400 pound front spring? I get the impression this would yield a super harsh ride, judging from what people say about running 600+ pound springs in the rear.

3) Anyone know of a good technical forum where people talk about this kind of stuff?

[B.Watts]

Originally posted by document
A couple books I have read about building a car/suspension from scratch

Key phrase more than likely. Building a race car suspension from scratch is much different than taking a street suspension and trying to adapt it to racing with springs/shocks and very, very limited changes in the actual mounting points and geometry.

1) Is .46 the right factor for determining rear wheel rate from spring rate for an e36?

Good question. It should be close to .5 just eyeballing it. We use a real rear coilover now on my dad's car, so, I haven't really thought about it or bothered to find out.

3) Anyone know of a good technical forum where people talk about this kind of stuff?

Hmm...I don't. And, when you are talking folks who are really serious about it, they are likely either racers or team engineers and don't really want to give away their secrets or theories anyway. If you find something, let me know, as I'd like to lurk!

BTW, what corner weights did you use for your calculations?

[document]

I'm not sure it matters much whether you're talking about building a car from scratch or just picking and choosing the right rates for a production car. I say that because these books tend to cover the whole range of possible suspensions, from a live axle rear to double a-arms. Basically, very different set ups and mounting points and leverages and couplings, and yet this rule of thumb of 120-140 CPM wheel frequency seems to hold.

From a table in Staniforth's book (Competition Car Suspension, if anyone is curious), it looks like there isn't much relationship between WF and f/r weight distribution, either. From mid-engined single seaters to a crappy 1600 Sunbeam rally car with pretty much the opposite weight distribution, the numbers are very similar.

I used 725 lbs. for my corner weights, guessing about 75 lbs. per corner of unsprung weight. Pure guess for me, though. I was mostly just trying to see if the discrepancy between the prevailing wisdom of e36 m3 set up and this more general rule of thumb was as bad as it looked like it would be, given the spring rates in question. I do find it a little curious that the non-adjusted spring rate for the rear is what the wheel rate should be if you buy the rule of thumb, but at the same time I don't really think this is the kind of thing shops like ground control would overlook. So, I'm wondering what the rationale is, if it's anything other than just empirical.

[Geo31]

I've only run into one other person before who really spent any time figuring out the wheel frequency. Now, I don't know if that's because people are too lazy to figure it out, or if it's just not important (mainly academic). I suspect a bit of both.

Add to that the ease of changing springs with coilovers and I think the exercize probably becomes a waste of time for a racing team.

Lastly, as you pointed out, the late Carroll Smith (more or less the US dean of race car engineering) thought it was pretty much a red herring. That has probably influenced many a person specing modified suspension.

I'd love to know how this turns out though.

[melmyers12]

Originally posted by document
you also will typically want a WF of ~10% more in the rear than the front, to avoid resonant pogoing of the car (Carroll Smith doesn't seem concerned about that, though).

Probably because that 10% rule was developed for cars with underdamped suspension systems (street cars) is my guess. Race cars have very near critically damped systems, so by the time the rear wheel sees the bump (which is mostly small on a race track), the front end has already attenuated the vibration.

Of course wheel freqency (undamped natural frequency) is important with spring selection, that is the most basic component of any spring-mass vibration system. If you really want to get technical, you need to figure in the spring constant (probably non-linear) and damping coefficients for a tire, and all the bushings in a suspension, along with the elastic give that the components have. It can become quite a non-trivial problem ;-).

We did some of these tire-wheel-spring-mass-damper problems in Vibrations I in school. Doesn't really get difficult until you start dealing with non-linear stuff, which is what happens in the real world. Sometimes lots of math and thinking take longer than just going out and testing, granted some of the back-of-the-envelope calcs are good to get you into the ballpark so you at least know what range of springs to start with. Either that, or just asking the supplier usually works too ;-).

[B.Watts]

Originally posted by document
I'm not sure it matters much whether you're talking about building a car from scratch or just picking and choosing the right rates for a production car.

I was more trying to get to what Mel was referring to, but didn't explain it all that well. When dealing with a production based race car, particularly at the club level, you are dealing with a chassis that flexes quite a bit, along with bushings and suspension parts that contribute to the spring rate as well. In a purpose built race car, these parts are ALL solidly mounted, usually stronger, and mounted to a chassis that is usually stiffer (tube frame or carbon). My point was that there are a lot of "factors" that can't be taken into consideration simply using the rate of the actual spring. Calculating the true wheel weight would be a task better left for engineering students, and impractical in the real world where you can simply pop in a new spring and go drive a few laps.

Further, it seems that just eyeballing the sprung weights would tend to throw off your calculations as well, though I haven't really run the numbers to see what small changes in sprung weight would mean to the final #'s.

[melmyers12]

Bryan,

You are correct, the total system is very very complex, there are many pieces to the puzzle to try to model. Auto manufacturers are just now getting to the point where they can somewhat accurately model the whole system in the computer at one time. This is what some people and divisions of companies spend their whole careers doing.

But what you need to understand Bryan, is what engineers do is isolate 'independant' systems as best they can, and start the problem with good engineering assumsions. You can still model outside influences to your system as part of the assumsions.

Engineering assumsions are the only way that you can actually start a problem and solve it in a reasonable amount of time. You can always make a problem more complex, and thus more accurate; here is an example of a problem.

Take a simple projectile, in this case a bullet fired from a gun. You are wanting to hit the bullseye of the target by aiming it at an exact inclination. In algebra class we learned that you can solve projectile problems with simple parabolic flight paths (y=ax^2+bx+c, and derived variations) for example. But in order to do that look what assumsions you are making.

1) You have the ability to precicely aim the gun.
2) There is no drag on the projectile
a) the drag on the projectile would be a linear relationship with velocity, which it is not for travel near the speed of sound.
3) The effect of the rotation of the bullet.
4) Any wind or breeze
5) Differences in the weight of the bullet from manufacturing variation.
6) Differences in the amount or powder charge used due to manufacturing variation.
7) Any dirt that may exist in the barrel, and it's effect on muzzle velocity or direction.
8) Density and humidity of the air (are you at sea level, and what day is it?)
9) The gun is itself inheretly accurate.
10) Wear on the gun barrel.
11) General differences in the projectile due to it's manufacture, ie. surface finish, shape, etc.
12) Slight difference in the Earth's gravity, altitude, near any large objects such as mountains, etc.
13) Lunar phase, gravity due to the moon.
14) And my favorite: reference frame effects: Coreolis effect. Since we are assuming this would be fired somewhere other than the equator, it is subject to our percieved course variance. (simply, the earth moves below the bullet during flight.)


I am sure there could be more, but there is always going to be more, that is what you begin to understand as an engineering student.

There is also the method of superposition, where you can model each system independantly, and then put the results of each into a larger system, and then solve the large scale problem.

For the most part, these highly complex non-linear problems can only be solved on a computer with highly advanced software. Even then, you are relying on how well the software engineer is at programming.

I don't remember what my point is anymore, but basicaly the only thing engineers can do is the best they can given the conditions and their ability to solve the problem. Give more time and money, one increases the accurace of the calculation.

[B.Watts]

I don't care what the hell you engineers do as long as it makes me car go faster.

As a driver with no formal engineering training, but a quick enough mind to understand most things that are explained to me, the most depth I really care to get into involves "Engineer to Win." Past that, I'd rather be driving and letting someone else do the engineering of the car.

I know just enough to be really, really dangerous with my assumptions.

[B.Watts]

Originally posted by melmyers12

14) And my favorite: reference frame effects: Coreolis effect. Since we are assuming this would be fired somewhere other than the equator, it is subject to our percieved course variance. (simply, the earth moves below the bullet during flight.)

When those WRC guys hit the really big jumps, I wonder if they worry about the earth not being where they thought it would be when they land?

[document]

It's a good point some of you guys are making about other contributors to suspension than just the dampers/springs/levers from the idealized world. However, it's my impression that these extras don't make an enormous difference, for a couple reasons. One, in anything but a ground effects car, these other sources of compliance are going to be operating at some combination of a MUCH higher spring rate, a MUCH lower damping rate, over a MUCH smaller travel. Two, it's my gut feeling that they're going to be pretty much the same between the front and the rear on any given car, especially if the tires are the same f and r.

Not sure if Mel is actually saying this in his longer post, but you should be capturing much of the gist of the problem with the idealized WF calculations. Get in the ballpark and then do some testing. Also, Geo31, Carroll Smith isn't throwing the baby out with the bathwater and saying you should just blow off WF. For example, he states in Tune or Engineer or Something to Win that you shouldn't bother changing springs in increments of much less than ~10% of WF.

Bryan, as long as the unsprung corner weight is consistent front and rear, it doesn't seem to matter too much what numbers you pick. For example, in the front with a 375 lb/in spring, a weight of 700 gives WF = 139, while 800 gives 128. Not an insignificant difference, but again, as long as f and r sprung weights are within 50 pounds or so of each other, my estimates should be close to within a few CPM between f and r.

My original inclination was to trust the suppliers, but the numbers are so far off it's making me suspicious. I think I need a copy of Race Car Vehicle Dynamics. Or maybe I should just buy myself some 900+ pound rear springs.

[document]

Originally posted by melmyers12
Probably because that 10% rule was developed for cars with underdamped suspension systems (street cars) is my guess. Race cars have very near critically damped systems, so by the time the rear wheel sees the bump (which is mostly small on a race track), the front end has already attenuated the vibration.

Yeah, that makes sense. Small bumps and lots of damping probably keep pitch problems to a minimum. I think he also says that you're really unlikely to have a car with identical WF f and r, but I'm not sure how close they would have to be before a problem could arise.

[B.Watts]

I say buy the springs and test them! It's only a few $$. I think Mel's comment concerning modern race damper technology is very relevant though:

Probably because that 10% rule was developed for cars with underdamped suspension systems (street cars) is my guess. Race cars have very near critically damped systems, so by the time the rear wheel sees the bump (which is mostly small on a race track), the front end has already attenuated the vibration.

Further, there's no doubt in my mind that the car is going to become an oversteering nightmare by nearly doubling the rear spring rate. What's more important, achieving an ideal F/R Wheel Frequency or an ideal F/R handling balance?

Be wary of "overengineering" the situation. Some of the better solutions we've come up with at the track include compromises between myself (the driver, w/ limited engineering knowledge) and my engineer (Masters in ME). If you focused too specifically on solving one "problem", you can often cause many more. Designing a race car suspension is all about making the correct compromises.

[document]

Originally posted by BMWRacerITS
I say buy the springs and test them! It's only a few $$.

Further, there's no doubt in my mind that the car is going to become an oversteering nightmare by nearly doubling the rear spring rate. What's more important, achieving an ideal F/R Wheel Frequency or an ideal F/R handling balance?

Yeah, obviously the ultimate goal is to get the car handling as well as it can. The idea behind setting the WF in this range is that it should lead to a car that handles pretty well. If you're serious, you then try springs on either side of the baseline, in different combinations front and rear. When you feel like you're really close, you should be able to tweak the handling as necessary with the anti-roll bars.

A possible correction on the calculations, btw: According to
http://e30m3performance.com/tech_art.../eff_rate2.htm

the e30 M3, which has the same front control arms as the e36 m3 afaik, has a measured spring rate to wheel rate factor of 0.88. So, a 375 lb/in spring actually gives a WF of 129. Not a very big difference, actually. You'd need a 750 lb/in rear coil to approximately equal that frequency.

I would tend to agree that this sounds like a recipe for oversteer, just based on the springs people are generally using, but that's just a guess from me. I haven't gotten to actually play around with this stuff yet.

Be wary of "overengineering" the situation. Some of the better solutions we've come up with at the track include compromises between myself (the driver, w/ limited engineering knowledge) and my engineer (Masters in ME). If you focused too specifically on solving one "problem", you can often cause many more. Designing a race car suspension is all about making the correct compromises.

I hear you. With the minimal calculations involved so far, I'm not worried about overengineering. I would love to see at least SOME actual engineering or empirical analysis of this stuff, though. Like you say, people don't necessarily want to give that stuff away for free, though.

I know some tuners try and sell a set up that runs no rear anti-roll bar, but stiffer than usual rear springs. Anyone know what kind of spring rates they're selling their kits with?

[sunir]

dude just slap a suspension on that eggplant M3 of yours and just get out there and drive...quit thinkin' so damn much ....

My car is down right now due to another blown head gasket incident..happened a week ago at VIR when I was intructing for Car Guys in their Summer VIR school. Hopefully I'll have it back late September so I'll be able to get some track time with it before next season....

Hey Bryan and Mel, I'm looking to do like 3 - 4 races (or more based on budgetary constraints....want to do the races at VIR, Summit Point, Watkins Glen, and Mid-Ohio) next season in BMW CCA CR...I already went to the website and studied the rulebook (looks like my LTW will be in H-prepared). I also spoke with Fran in applications...I'll be sending mine in next week and get my introduction/rookie packet soon after. I'll spend time in the winter getting the cage completed and getting the car preped for next season but I am looking forward to it! Hey, you guys got any info or advice for a newbie ?

[B.Watts]

Originally posted by document
I know some tuners try and sell a set up that runs no rear anti-roll bar, but stiffer than usual rear springs. Anyone know what kind of spring rates they're selling their kits with?

I could tell ya what we are running, but then I'd have to kill ya.

I'd be willing to bet it's closer to the 10% variance you're looking for though. And yes, I had forgotten that the front is not a perfect 1:1 of wheel rate to spring rate either, which should have a definite effect.

[B.Watts]

Originally posted by sunir
Hey, you guys got any info or advice for a newbie ?

Yeah, stay the hell out of my way.

Just kidding, I should be saying take it easy on me judging by some of the lap times you've been posting. :

If you have any rules questions, let me know or post them here. Most of the rules are pretty easy to understand. Adhere strictly to the principle of "If it doesn't explicitly say you CAN, you CAN'T!" and you'll be fine.

[Erik@EDGE]

.46 is the motion ratio for the rear of the e36 according to Jay at GC, there was a thread on this a while ago, you should be able to find it on a search

[melmyers12]

Originally posted by sunir
Hey, you guys got any info or advice for a newbie ?

My advice is simple HAVE FUN! There are way too many people out ther in CR that take this stuff way too seriously. It is a lot more fun to just go out and blow them all away, and not even care.

Also, get to know a good shop in your area very well, and get a good parts supplier programmed in your speed-dial on your cell phone .

As far as the suspension stuff, I think this falls into the same category as the thread about lightenening the car. Basically, don't try and overthink the subject, get out and drive, and try what others have found that works (that means FAST!) already as a starting point. Then work from there on tweaking to your tastes (with a stopwatch, not by feel).

On the no-rear bar setup thing. You can find out what the rates and setup is, but it costs about $2500 to start. ;-) They don't give out the info for free.

[B.Watts]

Sunir...email me. I might have some parts (i.e. already gutted alumninum doors, etc.) that you could use so you don't have to tear up your OEM stuff. That way, you might be able to turn your OEM aluminum doors around and sell them to an auto-x guy that still needs the window and door panel, etc.

[kitwetzler]

I've run a 400/700 lb/in combo with an eibch front bar and no rear bar with some success. steady state balance was ok, but my shocks weren't able to control the rear springs, not enough rebound damping. And, the front wasn't stiff enough. I just bit the bullet and welded up the rear sway bar mounts and haven't had a problem since.

If you have fully independently adjustable shocks, i think it won't be hard to get a good setup for the track with no rear bar, but with most street shocks (SA konis, Bilsteins, etc) you'd have to get them custom valved to deal with the rear spring.

If you think calculating the wheel rate of the springs was a headache, you gotta realize that you forgot to take into account the sway bars. They have a pronounced effect on handling, and the add to the natural frequency of the suspension. You gotta calculate the effective wheel rate that the sway bar adds, just use the standard modulus of steel. Remember that you gotta take into account the length of the arms, the cross section and twisting moment of the straight part, as well as the bending of the arms. The Freqs you described above are fine except that they are assuming you aren't running a bar.

sway bars are a pain to calculate. Plus, don't forget to include them in your unsprung weight calculations, too.

[Geo31]

Originally posted by document
It's a good point some of you guys are making about other contributors to suspension than just the dampers/springs/levers from the idealized world. However, it's my impression that these extras don't make an enormous difference, for a couple reasons. One, in anything but a ground effects car, these other sources of compliance are going to be operating at some combination of a MUCH higher spring rate, a MUCH lower damping rate, over a MUCH smaller travel.

Nicht so (or in Texan "Whoa big fella").

While BMWs are a fair bit more rigid that most cars, there are cars where this is a real problem. Kit can attest to this as he used to have a Nissan NX2000 and last I knew was involved in building one for SE-R Cup. Anyway, these cars and the Sentra SE-R are so flexible in the rear that above about 275 lb springs, the springs are stiffer than the chassis.

I race a Sentra SE-R currently in SCCA ITS and unless you have a very well designed welded cage in the car, you have to be careful with your rear spring rates.

I know this is a BMW forum and this probably doesn't apply to most Bimmers people here will build, I wish to point out that such an assumption can get you into trouble.

[B.Watts]

Originally posted by kitwetzler
If you think calculating the wheel rate of the springs was a headache, you gotta realize that you forgot to take into account the sway bars. They have a pronounced effect on handling, and the add to the natural frequency of the suspension.

If we are simply comparing front to rear WF, the anti-roll bars shouldn't have any real effect. The assumption when comparing Front to Rear is that both wheels on each end are experiencing the same movement at the same time. In that case, the anti-roll bar has very minimal effect on spring rate save for the friction created by the bar moving within the mounting bushings.

[Geo31]

Originally posted by document
Also, Geo31, Carroll Smith isn't throwing the baby out with the bathwater and saying you should just blow off WF. For example, he states in Tune or Engineer or Something to Win that you shouldn't bother changing springs in increments of much less than ~10% of WF.

Also nicht so.

From Tune to Win:

"Most of the books on vehicle dynamics tell us that we should be vitally interested in the natural frequency of our springs. I have never figured out why. I will admit that if the natural frequency of the front suspension were equal to that of the rear, the car could get into a pogo stick mode, but with the natural harmonic frequency of the unsprung massesmodified by the tire hop frequency and the whole messdampened [sic] by the adjustable shocks, it becomes a real mess to calculate, and the odds against the front and rear ending up at the same harmonic frequency are negligible. I ignore spring frequency."

[B.Watts]

Originally posted by Geo31
Anyway, these cars and the Sentra SE-R are so flexible in the rear that above about 275 lb springs, the springs are stiffer than the chassis.

Cool, so the chassis becomes a "tender" spring, and you now have a variable rate race suspension.

HAHA!

[B.Watts]

Originally posted by kitwetzler
If you think calculating the wheel rate of the springs was a headache, you gotta realize that you forgot to take into account the sway bars.

BTW, if we are getting technical here, then what the hell is a SWAY bar? I've never seen a car sway.

I have seen a car ROLL around it's roll center.