Spring rates

[Ulix]

Awesome discussion Steve.
I remembered the ride vs. handling spring rate bias discussion from last time you explained it.
Keeping the 1.5:1 ratio (for ride quality) in mind, I just looked at my spring rates.
The german street coilover setup I have uses H&R springs and comes with 40/60 N/mm spring rates. Exactly the roll ratio of 1.5 that you mentioned.
It does ride much better than other similar setups.
Years ago, I had a contact who worked at a place with a professional spring tester.
He tested some springs for us.
The stock springs were surprisingly linear in rate, much more so than the lowering springs that most people around here are using.
The rates of the stock springs were determined to be 23/37 N/mm. So their roll ratio is 1.6.

Installing the ADDCO swaybar made my car more stable in fast corners on the race track.
Confidence on turn-in was much improved.

 

[autox19]

I wanted to make a separate post to address the no swaybar ride issues of my racecars. My DSP X1/9 weighed about 1930 lbs, on grid, ready to run. Weight bias was in the 44/56 F/R range. The front springs were 750 lbs/in and the rears 500ish lbs/in. When I first tried the car with no swaybars I was in the 550/400 range. Before I understood the issues of favored speed and another characteristic called "center of suspension" (the point between the two axles where an applied vertical load compresses both ends of the car equally), I didn't understand why the rear end of the car was pitching up and down excessively.

That motion was caused by a moment arm that is the difference between the center of gravity and the center of suspension. Much like the moment arm that is the difference between the car's roll center and center of gravity, that causes the body to roll in a turn, the center of suspension moment arm levers that end of the car up and down. Effectively, the center of gravity of the rear weight bias car is closer to the rear axle than the front. The center of suspension (see above description) is closer to the front axle due to the stiffer front springs. So when the car passes over a bump, regardless of the ride frequencies the center of gravity acts at the end of the fairly long lever (moment arm) and pitches the rear end up and down in response to the motion. The rear mass literally over powers the rear springs and shocks.

Once I learned the cause, and understood the principles involved, I could adapt. I learned to adjust the rear shock valving to manage the mass and motion. This is key in making the no swaybar work effectively. Another key factor I learned with the MR2. I stared the MR2 off with very similar ride frequencies and roll ratios to the X1/9 because the X1/9 was so good. As I continued to develop the car, work with the newer generations of tires and increased levels of grip, I kept going higher on spring rates and ride frequencies. Now the MR2, which weights 300 lbs less than the X1/9 is on 800/500 F/R spring rates. The ride frequencies are much higher than the X's. In fact, my ride frequencies are in the same range as the IMSA Prototype class racecars. Yet with highly developed shock valving the car rides quite nicely. When I let other people drive the car, and tell them what the ride frequencies are, they expect a punishing ride. However, the comments I usually get after their first drives on course are "I never noticed the ride quality". The do notice the car's responsiveness and feedback.

Below are a couple of photos that, at first look may not seem that impressive, but once you understand what is happening the perspective changes:

First is a photo of my DSP X1/9. I am trail braking the car into a corner. One of the comments I get from skeptics is "That car is too stiff to work". In other words, the car can't move on its suspension and therefore can't generate weight transfer. Look closely at the amount of body roll and compression on the outside front corner. Its important to note that at static ride height this car was very close to sitting on what would have been the stock bump stops. The suspension system I had on the car added a great deal of compression travel. So note that the right front suspension is compressed well past where the stock car would have bottomed out yet still hasn't bottomed. And, most importantly, those are 750 lbs/in front springs. Now consider the amount of weight transfer to compress that spring that far.

View attachment 38287

Now look at this photo and note how little body roll the car has. It has no swaybars. The tires are Hoosier radials racing tires. The car is pulling about 1.5 lateral g in this photo. If you doubt the lateral g number, look at the tire deflection at the contact patch. View attachment 38288

I know it is a tight balancing act, but looking at the MR2's front divers tire, seems like there is still more to gain if you can do something to keep it fully in contact. Educate me if I am wrong.

odie

 

[Dr.Jeff]

<deeper into the rabbit hole...>

If we are looking purely at ride quality and ignore handling balance, ride frequency and favored speed are the only variable.

To understand "favored speed" consider our X1/9 approaching a speed bump. The characteristic of an ideal ride would be to pick the speed at which we are traveling and then, when the car hits the speed bump, the two ends of the car complete their cycles at the same time. The speed at which both ends complete their cycles at the same time is the 'favored speed'. Given that the front hits the bump first for it to finish at the same time as the rear (that is; to complete its up/down motion in response to the bump) it must have a significantly slower cycle time than the rear, given that the rear hits the bump well after the front.

With consideration of the above, the closer the two frequencies are the higher the speed at which the cycles synchronize their finish. The further apart the frequencies are the slower the speed at which the cycles synchronize their finish. We can set a favored speed by picking the speed at which we want the best ride quality and the computing the cycle times so that they synchronize their finish (for the given wheelbase).

So to directly address the question quoted; using the same rates at both ends would produce a negative favored speed. This is because the heavier rear end of the X1/9 would have a lower ride frequency than the front given both ends using the same spring rate. That is; the favored speed could only be achieved in reverse.

The frequency differential is what determines the favored speed. Typically, the rear frequency (base) is chosen first and the front computed to match. Using this method you can choose the base (rear) frequency to produce the ride comfort you want. If you want a luxury ride, you would choose a lower frequency at 1 Hz or less, then match the front to that. If you wanted a more sporting/firmer ride quality you might choose a higher base (rear) frequency of say 1.5 Hz, and again match the front to that. It is the higher ride frequency and higher favored speed of performance cars, and especially European sedans, that give the sensation that the car rides better at higher speeds. I first noticed this when driving a '70s era Mercedes sedan as a teenager. I noticed the car seemed to have a much better ride and feel at 70~80+ mph than it did at 55~60 mph. I would add that 8~9 degrees of steering caster also contributed to that effect.

I appreciate that you addressed this in a seperate post. It really doesn't apply to our primary discussion and I knew when I wrote the question that it could easily sidetrack things.

 

[MikeHynes]

I know it is a tight balancing act, but looking at the MR2's front divers tire, seems like there is still more to gain if you can do something to keep it fully in contact. Educate me if I am wrong.

odie

Thanks for sharing your knowledge of suspension tuning. I love hearing about this stuff, I've got a LOT to learn.
Along the lines of odie's remark. It seems to me that a sway bar would only HELP lift the inside front tire, keeping the inside tire from making contact with the road. But...I guess how much traction you lose by lifting the inside tire is tied to how much weight has transferred to the outside. If the inside tire doesn't have much weight on it, it's probably not going to help with the traction much anyway, even if it remained in contact with the road?
Also, when the weight is shifted to the outside front tire, isn't it also shifted to the inside rear tire? Doesn't that help to upset the balance in the rear? (Yes, I know, I have a lot to learn.)

 

[Dr.Jeff]

I wanted to make a separate post to address the no swaybar ride issues of my racecars.

I understand the theory and the concepts involved. However I sort of feel like we are talking about two different things; a purpose build race car that is only used on a smooth track surface vs a road only car that has to deal with potholes, bumps, road construction, speed bumps, driveway dips, decayed surfaces, and on and on. While using extremely heavy springs and matching dampeners makes for a great handling race car, it simply won't work for regular street use. I've had a 'track' type setup on a road car in the past and it was unbearably uncomfortable. But that's not to say the information isn't useful. And I'm attempting to apply that information to a non-track situation with completely different goals. But I'm just not clear that my initial question has been answered (I'm not intending to sound argumentative at all, simply looking for clarity).

So let me try and state it differently. Assume that no sway bars can be used. And assume a maximum spring rate of 250 pounds anywhere on the vehicle. Also assume that adjustable dampeners are used and can be set according to any spring rates chosen. Furthermore assume the goals are: 1) the vehicle will only be driven on the street, 2) a comfortable ride is desired, 3) decent handling shouldn't be omitted from the result. Given those limitations, and realizing compromises are needed, what end would you put those springs on, and what rates would you put on the other end? That's about as simple as I think I can say it.

Hope you follow my point and see it as me wanting to better understand the application of the theory.

 

[Steve Hoelscher]

I understand the theory and the concepts involved. However I sort of feel like we are talking about two different things; a purpose build race car that is only used on a smooth track surface vs a road only car that has to deal with potholes, bumps, road construction, speed bumps, driveway dips, decayed surfaces, and on and on. While using extremely heavy springs and matching dampeners makes for a great handling race car, it simply won't work for regular street use. I've had a 'track' type setup on a road car in the past and it was unbearably uncomfortable. But that's not to say the information isn't useful. And I'm attempting to apply that information to a non-track situation with completely different goals. But I'm just not clear that my initial question has been answered (I'm not intending to sound argumentative at all, simply looking for clarity).

So let me try and state it differently. Assume that no sway bars can be used. And assume a maximum spring rate of 250 pounds anywhere on the vehicle. Also assume that adjustable dampeners are used and can be set according to any spring rates chosen. Furthermore assume the goals are: 1) the vehicle will only be driven on the street, 2) a comfortable ride is desired, 3) decent handling shouldn't be omitted from the result. Given those limitations, and realizing compromises are needed, what end would you put those springs on, and what rates would you put on the other end? That's about as simple as I think I can say it.

Hope you follow my point and see it as me wanting to better understand the application of the theory.

OK. I get it.

If I assume this is an X1/9 (or any other mid/rear engine configuration), you have a problem. It was what I was trying to point out with the principles; To achieve a good ride quality, you must have a significantly softer front spring to lower the front ride frequency of the lighter front axle to below the heavier rear axle frequency. When you do that, you end up with a roll ratio biased to the rear of the car. Something in the range of 1 to 1.5 F/R.

The rear roll ratio bias will result in a pronounced oversteer handling balance. This is the reason for adding a front swaybar on street cars. It adds back front roll stiffness that is lost with the softer front springs. To achieve a good ride quality given the 250 lbs/in spring limit you would put 250s on the rear and something like 150~175s on the front, and without a front bar the car would oversteer excessively. This is why I use a front swaybar on my street X1/9s.

The problem is mostly negated if you swap the weight distribution. Using a front engine, rear drive, layout, the mismatch in ride frequencies goes away and the car has a better ride quality and still can maintain handling balance without the need for a front swaybar.

I hope this addresses your question more directly.

 

[Dr.Jeff]

OK. I get it.

If I assume this is an X1/9 (or any other mid/rear engine configuration), you have a problem. It was what I was trying to point out with the principles; To achieve a good ride quality, you must have a significantly softer front spring to lower the front ride frequency of the lighter front axle to below the heavier rear axle frequency. When you do that, you end up with a roll ratio biased to the rear of the car. Something in the range of 1 to 1.5 F/R.

The rear roll ratio bias will result in a pronounced oversteer handling balance. This is the reason for adding a front swaybar on street cars. It adds back front roll stiffness that is lost with the softer front springs. To achieve a good ride quality given the 250 lbs/in spring limit you would put 250s on the rear and something like 150~175s on the front, and without a front bar the car would oversteer excessively. This is why I use a front swaybar on my street X1/9s.

The problem is mostly negated if you swap the weight distribution. Using a front engine, rear drive, layout, the mismatch in ride frequencies goes away and the car has a better ride quality and still can maintain handling balance without the need for a front swaybar.

I hope this addresses your question more directly.

Excellent, thanks Steve. Honestly that is exactly what I believe you had already said, but when the much higher spring rates kept being mentioned it made me question my understanding of things. So I appreciate your patience with the added clarity.
Aside from the oversteer problem, it sounds like the spring rates desired for a decent roll ratio are achievable with "soft" springs for a 'comfort' ride quality. So that would be the trade off - oversteer for comfort.

 

[Steve Hoelscher]

Excellent, thanks Steve. Honestly that is exactly what I believe you had already said, but when the much higher spring rates kept being mentioned it made me question my understanding of things. So I appreciate your patience with the added clarity.
Aside from the oversteer problem, it sounds like the spring rates desired for a decent roll ratio are achievable with "soft" springs for a 'comfort' ride quality. So that would be the trade off - oversteer for comfort.

The principles don't change with rate or ride frequency.

We are talking about theory and IMSA Prototype rates but there are more 'real world' examples that we can see for ourselves. Take your typical sedan that has a typical ride quality for a modern car when you're driving alone. Then put three good sized people in the back seat and the effect it has on ride quality. The ride quality is typically tuned for a comfortable and controlled ride with only a light load in the back. Add 400 lbs to the rear axle weight and you change the ride characteristics entirely. The rear ride frequency, which was nicely matched with a slightly higher rate than the front now has a rate significantly lower than the front. And when driving over low frequency undulations in the road the rear feels as though it is pivoting on the front axle as it moves up/down excessively. This is exactly what was happening to my X1/9 before I figured out the cause and fixed the problem.

I grew up on a farm as a kid. We had an old F250 Ford pickup. The rear end of that truck rode extremely harshly on rough surfaces due to the high spring rates and lightly loaded axle when the bed was empty. But put 500~1000 lbs back there and the ride frequency slowed to a much friendlier 1 Hz and it was actually pretty nice despite the stiff spring rate. Basically, it had the reverse problem to my X1/9.

 

[Ulix]

it sounds like the spring rates desired for a decent roll ratio are achievable with "soft" springs for a 'comfort' ride quality. So that would be the trade off - oversteer for comfort.

Jeff, I think what you are describing is the stock springs!
An X with stock springs is really comfortable. For a while I ran stock springs with a front swaybar and other than looks, I really liked it for street driving.

 

[autox19]

just a quick note. I love this conversation. What i LOVE about the X is even in worn out stock form it out handles most of todays cars!!!

Odie

 

[Dr.Jeff]

Jeff, I think what you are describing is the stock springs!
An X with stock springs is really comfortable.

Yes and no. What I failed to add to that comment was having spring rates that are higher than stock, but not so high as to lose a lot of the ride quality. In other words, where is the trade off point before the ride gets significantly sacrificed for further handling improvements. Sort of the best of both worlds; a somewhat stockish ride but somewhat improved handling (hence the "yes and no" response). Which I guess is what most of the aftermarket "sport" springs are. Often they are about 20% stiffer than stock. So working from the stock rates and adding about 20% you get around 175 front and 225 rear (according to my stock springs and calculations). Therefore I wondered how those numbers faired with Steve's theoretical calculation of desired rates with those goals. And they pretty much match. The only real difference is he recommends a slightly higher rear rate than that (closer to 250) - which is why I pursued understanding his theory clearly.

Thanks again to everyone for this.

 

[Ulix]

As a compromise, I like the lowering springs that everyone is using on this side of the pond. Don‘t know if they are the same as the ones available in the US.
The have a progressive rate.
My buddy even runs them on track and is no slower than me with my coilovers.
His car is a good bit more comfortable on the street.

 

[dllubin]

I put some progressive rate Eibach lowering springs on my T5R and they actually improved the ride over the stock springs.

 

[Dr.Jeff]

As a compromise, I like the lowering springs that everyone is using on this side of the pond. Don‘t know if they are the same as the ones available in the US.

I'll bet they are the same as the "lowering" or "sport" springs offered here. As mentioned, they are typically around 20% stiffer than stock (as well as shorter). That's the rates I have for my coilovers, which was the whole reason I wanted to verify all this info about rates. Combined with the adjustable Koni damper inserts they should offer a good ride but some improved handling, plus adjustable ride height.

I put some progressive rate Eibach lowering springs on my T5R and they actually improved the ride over the stock springs.

Agreed, progressive springs have a nice ride quality.

 

[Steve Hoelscher]

When I was still daily driving a '77 1300 (while in college) and just beginning autocrossing, it was common practice to cut a coil off the rear springs and about 1.5 coils off the front springs. Reducing the active coils on the spring will raise its rate. So cutting the springs down, in addition to lowering the car, also stiffened the spring rate about 20%. It was enough to sharpen up the response noticeably and lower the car to a more sporting ride height.

I later learned that cutting down a pair of rear springs and using them on the front significantly improved the handling with the additional front spring rate. I really didn't notice a change in ride quality, but then I was in my early 20s.

Over the years I have had a range of rates on my various street X1/9s. I found the stock springs a little too soft for my taste. Slightly firmer and a modest front swaybar was the setup I preferred for street use.

 

[Rupunzell]

Spring rates on the LeMons exxe with the Mazda 12A peripheral port race rotary (about 200 bhp @ 9500 rpm).
Car all up about 1/2 full fuel cell weights about 1,700 pounds, no driver.

Front spring rates are 650lb/in, Rear spring rates are 475lb/in. Dampers are "sport adjustable" Konis from a Volvo which are similar to a Koni 8610 single adjustable damper. Damper setting was tweaked to work good with these spring rates by track testing. Suspension is adjusted as needed for what the drivers like (mixed agreement on this) with tire temps in consideration. Early on there was significant wheel spin on corner exit, fixed by adjusting the rear spring rates.

~Going up in spring rates does not work at all unless the dampers are properly matched to the increased spring rates.
One advantage of a strut suspension, the dampers get essentially direct wheel travel to work on. This is important as hydraulic fluid dampers are velocity sensitive devices that rely on change in motion to work. In comparison to the double A-arm suspension on a Miata NA-NB which is ratio_ed, it is more difficult to get a damper to work at its best due to the reduced damper motion relative to wheel motion. This is one of the reasons why dampers are such a BIG deal in the Miata NA-NB community. Stock miata use its bump stops to effectively increase spring rate as the suspension nears it's bump stops. There are a variety of progressive bump stops to alter the transition from spring to bump stop to effectively increase spring rates at the wheel. This can be done on most suspension, if properly set up, this is another chassis-suspension tuning-set up tool.

LeMons racing has a spec tire rating of DOT180 and no softer. This is the effective speed limiter at LeMons. When the chassis-suspension is properly set up, we do an entire race on one set of Dunlop Direzza with some tread sort of on the casing (long as the drivers don't abuse the tires or some "event" occurs).


Bernice

 

[Rupunzell]

On the 74' which is a street car, It retains essentially the stock suspension with cut down springs front & rear with stock dampers.
This is good enough for now.

 

[autox19]

Hey steve, with all this spring talk, i am suprised you havent brought up your granada spring set up

Odie

 

[Steve Hoelscher]

Thanks for sharing your knowledge of suspension tuning. I love hearing about this stuff, I've got a LOT to learn.
Along the lines of odie's remark. It seems to me that a sway bar would only HELP lift the inside front tire, keeping the inside tire from making contact with the road. But...I guess how much traction you lose by lifting the inside tire is tied to how much weight has transferred to the outside. If the inside tire doesn't have much weight on it, it's probably not going to help with the traction much anyway, even if it remained in contact with the road?
Also, when the weight is shifted to the outside front tire, isn't it also shifted to the inside rear tire? Doesn't that help to upset the balance in the rear? (Yes, I know, I have a lot to learn.)

You and Odie are both correct. Yes, if you can maximize the inside front (or rear for that matter) tire's contact patch, you would get more net grip.

The answer to this question is very complex. Its a combination of the limitations of strut suspension, roll center height, roll ratio and total weight transfer. First we'll address the strut issue. McPherson strut suspensions are used because they are more simple, easier to package and cheaper to manufacture, than a double (upper/lower) wishbone design. The double wishbone design permits a design that incorporates camber gain in compression. That is, as the suspension compresses, negative camber increases. This allows the tire's contact patch to remain square with the road surface as the car rolls in response to lateral g and weight transfer. And also why it is the preferred suspension design for most racing cars. McPherson strut suspension, in most applications, has a camber curve (the plot of a wheel's camber through its range of motion) that starts negative from static ride height but quickly goes positive. Thus the wheel/tire contact patch rolls onto the outside shoulder as the chassis rolls from lateral g and the outside suspension compresses. To address this problem most strut suspensions, in performance or racing applications, are set with a great deal of static negative camber to compensate for the loss of camber when the car rolls and the suspension compresses. If you look at the MR2 you will see that the outside tires are pretty much square with the road surface to maximize grip. For the inside tires -4 degrees of static camber means that only the inside edge of the tire contacts the surface. Its a big compromise to maximize the outside tire's grip.

The reason for the big compromise noted above is because of load transfer. Lateral g and the resulting body roll transfers weight across the axle from the inside tires to the outside. Ideally, you want as little load transfer as possible to keep all four tires as equally loaded as possible. But physics still applies so there will be load transfer. The car is at maximum grip when you achieve 100% load transfer. That is, all of an axle's weight is transferred to the outside tire and the inside tire is at zero load. When we add roll ratio it gets complicated. Remember the 1.5:1 roll ratio mentioned in a previous post. If the front axle has 1.5 times the roll stiffness of the rear it will transfer more load across the axle for a given amount of body roll. So it will achieve 100% load transfer before the rear does, for a given amount of body roll. When the front axle is at 100% load transfer (and also grip), the rear is, in theory, at .667 of its total load transfer and therefore available grip. Now remember the car's weight distribution. The rear is heavier than the front. So there is approximately 15% more lateral load applied to the rear tires from the rear weight bias. To maintain the handling balance (in steady state cornering) we need more mechanical rear grip. We achieve that by having more of the load transfer across the front axle which leaves the rears more evenly loaded and thus more mechanical grip to accommodate the additional rear lateral load.

Now consider this; if the front axle is at 100% lateral load, and therefore at maximum lateral grip, and the handling balance is perfectly tuned, then the rear is at .667 load transfer, and with the additional weight it is at 100% lateral grip. So both axles are achieving maximum grip. We're perfect right? Well, maybe not, because that inside front tire has only a contact patch the size of postage stamp right? So lets assume we can adjust camber to square that tire up in that turn and maximize the contact patch and gain grip. If that is possible, then we have additional front grip to use and we can go faster and generate more lateral g. The problem now is the rear was also at max lateral grip because of the weight it has to deal with. So if we go faster and generate more lateral g the car will go loose because the rear has no additional capacity. But wait.... we can adjust the inside rear camber as we did the front right? Assuming that then we gain max lateral grip and again reduce the inside front tire loading and we are back to the same condition but at a slightly higher lateral g (and therefore speed). That's good but we aren't racing on an oval, we have to turn right at some point. So we can't compromise out static camber to turn one direction only.

There is another factor at play here. Roll center axis. You are likely familiar with the term roll center, defined at the point about which the car's body rolls. It is determined by suspension geometry. Because both the front and rear suspension each have their own roll center locations the roll axle is the line drawn through both roll center locations and is the axis about which the entire body rolls. Roll axis is a key factor in the car's handling and stability when turning. Typically, you want the end of the car that weights more to have a roll center below the location of the lighter end. This helps promote mechanical grip on the heavier axle. It is also used to tune the car's corner entry and exit characteristics.

You can see in the picture below that the inside front tire is completely off the ground. This is not an uncommon situation for a car with a lot of front roll stiffness (often from a big front swaybar). In the case of my MR2 there is no bar but there is a roll ratio of 1.7:1 so it has a LOT of front roll stiffness.

The reason I made note of this is because of the comment about the big front bar lifting the inside front tire. Yes, a big front swaybar will do that causing the 100% lateral load transfer to happen at slightly lower lateral g than can be achieved without a front swaybar. So it can cause a net loss of grip. But that's not the only negative. When the inside front tire looses contact with the road surface the roll center location instantly moves to the contact patch of the outside front tire. Its important to note that its the roll center location BETWEEN the tires that prevents the car from rolling over at 100% lateral grip. When the roll center moves to the outside tire's contact patch the only thing preventing the car from rolling over is the outside rear tire. So when the inside tire lifts off the surface, the outside rear tire gets a significant increase in load transfer because its the only "out rigger) preventing the car from rolling. To the driver, when the inside tire lifts the car goes almost instantly loose. Think of the car now as a tricycle and what prevents a tricycle from rolling over in a turn.

Now we get back to complicated things again. Remember that the rear roll center is below the front. So the moment arm between the rear roll center and the center of gravity is longer than the front. So the rear has more leverage to roll the car than the front does. If that differential in roll center heights (which defines the roll axis angle compared to the ground level) is enough the additional leverage at the rear can actually force the car to pickup the inside front tire earlier than it should, than if the roll axis was closer to parallel to the ground. The reason this is undesirable is all because the mismatch in roll axis was enough to lift the inside front tire before the car achieved a natural 100% load transfer and thus cannot produce as much lateral g. The reason for noting this is that tuning the roll axis by adjusting the roll center height contributes greatly to the net lateral grip and why you see that tiny little amount of contact patch in the earlier photo. That little dime sized contact patch is extremely valuable in the greater scheme of the car's handling. In the photo immediately above with the inside front off, the camera is level, the track surface has a pronounced slope which makes the turn significantly off camber and right at the point of hard acceleration, both of which forced the tire to lift right when the photographer snapped the photo.

 

[Steve Hoelscher]

Hey steve, with all this spring talk, i am suprised you havent brought up your granada spring set up

Odie

That came up recently in another thread.

Spring rate is spring rate, doesn't matter if you buy H&R Coil Overs or Granada take-offs.