Spring rate balance questions...

[kcbrown]

Well, I worked out the formula for determining the proper rear spring rate for maintaining the "flat ride" that the stock suspension has, if given a desired new front spring rate. The formula is this:

Knr = (1/(1/sqrt(Knf) - 1/sqrt(Kf) + 1/sqrt(Kr)))^2
​

where Kf is the current front spring rate, Kr is the current rear spring rate, Knf is the new front spring rate, and Knr is the new rear spring rate.


The Brembo cars have 131 lbs/in front springs and 167 lbs/in rear springs. If I decided (for whatever reason, which can include experimentation) to go with the Boss 302 front springs, at 148 lbs/in, the above gets me a desired rear spring rate of 192 lbs/in. That just happens to be just 1 lb/in more than the rear spring rate of the Laguna Seca, and just 2 lbs/in shy of the rear spring rate on the 2012 GT500 SVT Performance Package.


But armed with the above, I should now be able to select spring rates for one end of the car that will maintain the front:rear ride quality characteristics of the stock suspension (or at least come close) while I vary the spring rate on the other end to suit my needs. So, for instance, if I wanted the front to be 250 lbs/in, I'd need to use 350 lbs/in springs in the rear to maintain the "flat ride".

The higher the front spring rate, the greater the rear:front spring proportion necessary to maintain the "flat ride". There probably comes a point at which the front:rear balance is so far off that it can't reasonably be compensated for with stabilizer bars for the purpose of maintaining a given understeer/oversteer characteristic. I haven't a clue where that point is.


Given my (limited, but useful) experience with coilovers thus far, it seems obvious that really good dampers can give me a very good ride even with relatively high spring rates, and with the above, I'll be able to maintain the ride characteristics I want as I ratchet up the spring rates.

This is going to be interesting! But first, I have to get some experience with the car in stock trim under my belt, to see how I like the car's current balance.

 

[Norm Peterson]

That formula may work well enough for smallish increases in spring rate (front spring rate at least in the examples), but it doesn't work generally because flat ride behavior also involves the time it takes for the car to travel a distance equal to its wheelbase. Equating flat ride behavior presumes that you wish to retain the same flat ride speed, which means that part of an equation for flat ride remains constant while the other two parts vary.

"Flat ride" behavior isn't just about the one theoretically perfect flat ride speed - it's generally pretty good over a range of mph either side of theory. Note too that flat ride speed is influenced by the amount of damping that's present, as damping reduces vibration frequencies. Slowly at first with small damping (i.e. dead shocks), but the as the effect becomes greater the frequencies also drop faster. Even the [lack of good] flat ride behavior from poorly chosen spring rates can be tamed with enough damping, if perhaps at some cost in bump harshness. The attached plots are my original work. "Pitch jerk" is a measure of how fast pitch acceleration varies, which translates to the difficulty in keeping your head from bobbing back and forth because the inertia force from it that you're trying to balance with voluntary muscle effort is not remaining constant.


Norm

 

[kcbrown]

That formula may work well enough for smallish increases in spring rate (front spring rate at least in the examples), but it doesn't work generally because flat ride behavior also involves the time it takes for the car to travel a distance equal to its wheelbase. Equating flat ride behavior presumes that you wish to retain the same flat ride speed, which means that part of an equation for flat ride remains constant while the other two parts vary.

Yes, exactly.

I presumed that the flat ride speed chosen by Ford was the proper one for this car. I can easily imagine all sorts of factors going into it, including characteristics of the platform itself (e.g., harmonic characteristics of the chassis).

"Flat ride" behavior isn't just about the one theoretically perfect flat ride speed - it's generally pretty good over a range of mph either side of theory. Note too that flat ride speed is influenced by the amount of damping that's present, as damping reduces vibration frequencies. Slowly at first with small damping (i.e. dead shocks), but the as the effect becomes greater the frequencies also drop faster. Even the [lack of good] flat ride behavior from poorly chosen spring rates can be tamed with enough damping, if perhaps at some cost in bump harshness. The attached plots are my original work. "Pitch jerk" is a measure of how fast pitch acceleration varies, which translates to the difficulty in keeping your head from bobbing back and forth because the inertia force from it that you're trying to balance with voluntary muscle effort is not remaining constant.

Yeah, I figured there was some acceptable variation from the chosen speed that would work (with variations in speed, the waveforms will still converge, just not in such a way as to zero out at exactly the same point. But though the result may be some pitch change, the amount of pitch change will not be noticeable within a range of speeds, if my understanding of this is correct). In this case, I presumed firstly that the ride speed needed to be the same, and secondly that what was desired was convergence at 3/4 wavelength (it happens that the 3/4 term drops out). The reference I was using when reading about "flat ride" theory used 70% critical damping. That reference is: http://www.optimumg.com/docs/Springs&Dampers_Tech_Tip_1.pdf.

It is, of course, important to get the damping right regardless. I'm not suggesting in my previous that I can get away with simply changing the springs out without also doing something about the dampers! Quite the opposite: greater spring rates are going to require greater rebound damping, and probably retuned compression damping as well.

It raises the question of just what kind of dampers I would really need in order to be able to accomplish the goal properly. Would rebound-only control be enough? Getting the dampers revalved every time I change spring rates seems a bit excessive, so that raises the question of, assuming I have dampers with adjustable rebound, how much spring rate variation can be tolerated while allowing me to maintain the ride quality goals I have before I have to get the compression damping retuned through revalving. It also raises the question of whether I would have to deal with revalving the dampers if the dampers are double-adjustable.

 

[Norm Peterson]

Ford is very likely to end up with a flat ride speed on the low side, as there is a wider range of speed with the same "acceptability" above than below and Ford doesn't need to sacrifice control of head toss at 30 mph for gains at 100+.

FWIW, I'm seeing flat ride speeds a bit above 50 mph for the earlier cars (at 136/142 springing) and under 35 mph for the newer ones with 131/167-ish springing. If you were picking dual purpose street / track day springs with this in mind, you'd probably want to use a theoretical flat ride speed higher than either of those.

Rebound damping controls spring extension by opposing it, which works to minimize the sprung mass "overshooting" its new equilibrium position. If you only choose one adjustability that should be it. Bump damping adjustability mainly works with the unsprung mass moving upward, but adds damping force to the increase in spring loading.

Ideally and with no restrictions on cost, modification points, or class-legality, you'd choose 4-way adjustability, with separate control over high and low (shock piston) speed damping. That can be used to take the sting out of firm bump control at the speeds that body motion occurs at, once you start hitting bumps (which is high shock piston speed stuff). If you can keep from getting lost.


Norm

 

[kcbrown]

Ford is very likely to end up with a flat ride speed on the low side, as there is a wider range of speed with the same "acceptability" above than below and Ford doesn't need to sacrifice control of head toss at 30 mph for gains at 100+.

FWIW, I'm seeing flat ride speeds a bit above 50 mph for the earlier cars (at 136/142 springing) and under 35 mph for the newer ones with 131/167-ish springing. If you were picking dual purpose street / track day springs with this in mind, you'd probably want to use a theoretical flat ride speed higher than either of those.

What values should I be using for the sprung mass and the motion ratios (obviously separate values for front and rear)? I was able to avoid needing those values in what I did because those terms in the equation magically drop out when you're preserving the speed, but that's no longer the case once that presumption goes away.

Rebound damping controls spring extension by opposing it, which works to minimize the sprung mass "overshooting" its new equilibrium position. If you only choose one adjustability that should be it. Bump damping adjustability mainly works with the unsprung mass moving upward, but adds damping force to the increase in spring loading.

Ideally and with no restrictions on cost, modification points, or class-legality, you'd choose 4-way adjustability, with separate control over high and low (shock piston) speed damping. That can be used to take the sting out of firm bump control at the speeds that body motion occurs at, once you start hitting bumps (which is high shock piston speed stuff). If you can keep from getting lost.

I imagine that 4-way adjustability gets you into the many thousands of dollars range. But the problem as I see it is that adjustability of any type is still something of a coarse control. You're not really finely controlling the shape of the damping curves involved, right?

But I dunno. Maybe the amount of control you get with 4-way adjustability is sufficient for these purposes.

 

[kcbrown]

Ford is very likely to end up with a flat ride speed on the low side, as there is a wider range of speed with the same "acceptability" above than below and Ford doesn't need to sacrifice control of head toss at 30 mph for gains at 100+.

FWIW, I'm seeing flat ride speeds a bit above 50 mph for the earlier cars (at 136/142 springing) and under 35 mph for the newer ones with 131/167-ish springing. If you were picking dual purpose street / track day springs with this in mind, you'd probably want to use a theoretical flat ride speed higher than either of those.

That's possible, but it occurs to me that pitching motions at lower speeds are likely to be of greater magnitude and, regardless, probably more noticeable to the passengers than those that occur at higher speeds. So not only is the range of acceptability wider above the target speed than below, the sensitivity is probably lower above the target speed as well.

As such, I actually don't know that I'd gain a lot by going with a higher "flat ride" base speed than that selected by Ford, especially since my car is going to be spending the vast bulk of its time as a daily-driven street car, with (I anticipate) no more than perhaps 12 track events per year.


This does raise the very relevant question: is it possible to adjust the "flat ride" speed through changes to the damper settings? If so, how?

 

[Norm Peterson]

Most strut suspensions can use a motion ratio of about 0.95 for the spring and damper with pretty good accuracy. For pitch, use a motion ratio of 1.0 for a rear axle with the springs seated on top of the axle tubes (it's a little more complicated if they're mounted elsewhere).

It's easier to deduct the front and rear unsprung weights from the front and rear weights you calculate from the total car weight and its front:rear weight distribution. Ideally, you'd have weighed weights for everything, but 100 lbs plus the weight of both front wheel & tire assemblies is probably reasonable for the total front unsprung weight, and 200 or so lbs plus the weight of both rear wheels & tires out back is probably good enough there. It really doesn't matter if your theoretically calculated flat ride speed is off a little because you don't truly know all the weights, as this whole business is something of an approximation anyway.


Norm