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Discussion Starter #1
So with all of this talk about LSS vs the standard suspension, I thought I'd try to take an engineering approach to the problem.

Generally speaking the "stiffness" of the suspension is best measured by its natural frequency. While the damper setups for the LSS might be different, lets just assume for now that Lotus chose to critically damp both setups in the same manner.

The best info I could find for how to calculate the frequency was from eibach.

Based on the info attached, I get the following numbers:

Stock:
F: 1.93Hz
R: 2.22Hz

LSS:
F: 2.16Hz
R: 2.42Hz

If anyone has some updated facts, or can find fault with my worksheet, please contribute. I'd also be interested in a table of the suspension frequencies of production cars. I know I have a book at home with a few in it, but I don't have it here at the office. (Speaking of office, maybe I should get back to work now:) )
 

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How sure are you that they would critically damp the suspension? My guess would be that it would be overdamped...but by how much I have no idea. I know that when I swapped Koni dampers into my Spyder it got stiffer and that before the Koni swap the car was definately not underdamped.

Perhaps someone with real suspension engineering experience could comment on whether performance suspensions are typically overdamped and by how much. I guess in the end knowing this stuff properly really comes down to getting the actual damping values on the standard and LSS dampers.
 

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Discussion Starter #4
Nochmal said:
How sure are you that they would critically damp the suspension? My guess would be that it would be overdamped...but by how much I have no idea. I know that when I swapped Koni dampers into my Spyder it got stiffer and that before the Koni swap the car was definately not underdamped.
As an experiment, sit on your fender and jump off. If the car bounces up, then settles down, it is criticly damped. If it bounces up down up (or more), it is underdamped. If it Justs eases up it is overdamped. Bounce and rebounds are different which makes this whole thing a bit more complicated, but anyway, my point was to examine the stuff we know and can measure. For the rest of the stuff we should just assume they are the same. As we get more information, we can refine the model.
 

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Evl said:
As an experiment, sit on your fender and jump off. If the car bounces up, then settles down, it is criticly damped. If it bounces up down up (or more), it is underdamped. If it Justs eases up it is overdamped. Bounce and rebounds are different which makes this whole thing a bit more complicated, but anyway, my point was to examine the stuff we know and can measure. For the rest of the stuff we should just assume they are the same. As we get more information, we can refine the model.
Agreed, more info = more refinement.

As you say, you can easily tell if your car is over/critically/underdamped. A nice visual explaination can be found at places like http://hyperphysics.phy-astr.gsu.edu/hbase/oscda2.html .

My stock Spyder was either critically damped or overdamped (you can't really tell the difference by eye very well). The Konis offer higher damping (must be overdamped since less stiff was at least critically damped) and the car handles better with the higher damping.

So, my hunch is that the Elise is probably overdamped for both the standard and LSS suspensions.
 

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Evl said:
As an experiment, sit on your fender and jump off. If the car bounces up, [..]
There are a couple more options: ;)
  • If the car never moved when you sat down, you have really stiff springs.
  • If you end up with a dent in your fender, your car has thin sheet metal. :(

Evl: I think you need real numbers for MR and A in the spreadsheet to get valid values for the suspension frequency. Especially the motion ratio will be critical. I wouldn't know where to find those for an Elise, maybe one of our Euopean friends knows them?
 

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The sitting on the car test, like the jumping on the car test have gotten pretty much to the point of useless for today's dampers.

Dampers have become a "black" art... consider that today's racing damper is anywhere from 6 to 10 way adjustable. There's bump & rebound for all the various piston speeds.

Slow speed is for roll conditions, like cornering. High speed is for going over bumps and potholes.

This means you can valve a damper to be soft on high speed = softer ride, but stiff on low speed = more weight transfer and slower roll.

Like so much of what goes into a car, it is all about the compromises and priorities.

If any company understands the dynamics of dampers & springs it's Lotus. Afterall they invented and were the 1st to race a fully active suspension F1 car in the early 90's with Senna driving. They won the US GP on the streets of Detroit because they could handle the bumps of the track and have the car lower for aero downforce.
 

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Discussion Starter #8
ConeFusion said:

Evl: I think you need real numbers for MR and A in the spreadsheet to get valid values for the suspension frequency. Especially the motion ratio will be critical. I wouldn't know where to find those for an Elise, maybe one of our Euopean friends knows them?
I agree. Re MR, the next time someone gets to see the car in person, maybe they can whip out the tape measure again. I re-ran the number with an MR of .77 which I get assuming the spring mount is 2 inches inboard, and that the arm is roughly 16". That gives us:

Stock:
F: 1.69Hz
R: 1.95Hz

LSS:
F: 1.89Hz
R: 2.11Hz

These are starting to approach "normal" numbers, so thats probably headed in the right direction, but measurements are king.

For the spring angle, does anyone who's seen it have a ballpark estimate from memory??
 

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khamai said:
The sitting on the car test, like the jumping on the car test have gotten pretty much to the point of useless for today's dampers.

Dampers have become a "black" art... consider that today's racing damper is anywhere from 6 to 10 way adjustable. There's bump & rebound for all the various piston speeds.

Slow speed is for roll conditions, like cornering. High speed is for going over bumps and potholes.

This means you can valve a damper to be soft on high speed = softer ride, but stiff on low speed = more weight transfer and slower roll.

Taking all that into account certainly makes things more difficult to do completely correctly but I kind of hope we could gloss over some of the details and still be able to answer the question of how much stiffer the LSS might feel. :)

Here is a plot from Koni for the damping force of their shocks as a function of the velocity of your compression/damping:



Some other examples that supposedly apply to Koni and Bilstein shocks from http://www.whiteline.com.au/default.asp?page=/faqshocks01.htm :





In all cases it seems that the high speed characteristics of the damper are linear with velocity. Our discussions of overdamped vs. underdamped etc. and Evl's calculations essentially assume that the damping force is linearly proportional to the velocity. So, it looks like we probably aren't way off here.

Additionally, the percieved stiffness of the ride is going to be dominated by how high the damping forces are for high speed wheel compression/rebound. As said above, the plots I've included seem to show that that is where the damper response is particularly linear. So, again, it looks like we are on the right track...

As long as we assume the correct slope of the damping force as a function of velocity we're going to get a pretty good feel for the relative stiffness of the suspension. The tricky bit is figuring out what the correct slope is. What Evl as done so far is assume that the damping force is a "critical damping".

Some details...cause I can't help it...I'm a physicist and this is the kind of stuff I love think about...bear with me. :)

Let's say that C is the slope of the damping vs. speed line at high velocity

(i.e. F_damping = C * velocity).

Given that, the damping coefficient for a simple harmonic oscillator (gamma) is defined as

gamma = C / (2*mass of oscillator).

In the case of a car wheel you have to take the lever-arm effect of the suspension arms (which Evl has done if I understand correctly). So, instead of the mass of the oscillator you essentially have an effective mass I think.

Anyway, a system is said to be critically damped when the damping coefficient is equal to the undamped resonant frequency of the oscillator. It is overdamped if the coefficient is greater than the resonant frequency and is underdamped if it is less than the resonant frequency.

So, what I think all this means is that Evl is doing the right stuff (although I'm too lazy to check the details of his calculation, he seems like a trustworthy guy :) )...we just have to have the right inputs for his calculation and we'll have a pretty good idea of the suspension's stiffness. The only thing I think Evl is maybe doing wrong is underestimating the stiffness of the shocks by assuming critical damping...my WAG is that it is overdamped and therefore probably stiffer.

Anyone have details for another car to cross check this stuff with?

I'll go sit quietly now...
 

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the other issue is that if you want to compare the ride stiffness with another car you would have to factor in chassis stiffness as well.

-Steve
 

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So we are talking ride stiffness (high piston damper speed) then, not roll stiffness (low piston damper speed). So, focus on high speed bump stiffness.
 

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ConeFusion said:
There are a couple more options: ;)
  • If the car never moved when you sat down, you have really stiff springs.
  • If you end up with a dent in your fender, your car has thin sheet metal. :(

Evl: I think you need real numbers for MR and A in the spreadsheet to get valid values for the suspension frequency. Especially the motion ratio will be critical. I wouldn't know where to find those for an Elise, maybe one of our Euopean friends knows them?
Last option:

If the car never comes back up, your ass is way to fat!





I know this isn't constructive; however, I couldn't help myself.

:p
 

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Not sure how you'd factor in the softer bushing. Lotus seem to feel that was the bigger change in improving ride quality. The sport packages gets the stiffer Euro version.
 

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LarryB said:
Not sure how you'd factor in the softer bushing. Lotus seem to feel that was the bigger change in improving ride quality. The sport packages gets the stiffer Euro version.
Is this true? I heard just the opposite elsewhere.
 

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khamai said:
So we are talking ride stiffness (high piston damper speed) then, not roll stiffness (low piston damper speed). So, focus on high speed bump stiffness.
Khamai says in two sentences what my entire last post says with lots of plots and words...perhaps I should take lessons. :)
 

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PS. Those eiboch springs are 50.00 each from Ground Control in CA. I already have a few sets from my old e30 m3 racecar. I measured the springs on the non LSS car and I think it is going to be pretty easy to change the springs, and shocks if needed..


Adam P
 

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Nochmal,
The plots are quite interesting... You righfully pointed out that the dampening rate is linear, which makes sense since it is proportional to the spring rate. The fact that the dampening rate is greater at low speeds (roll) illustrates that the dampers (in bump) are retarding the spring's ability to deflect due to added load. Thus the resultant roll stiffness.

Beyond these basics I pretty ignorant about dampers. If you like to have a deeper discussion I would suggest you contact a friend and Lotus enthusiast, Paul Haney. Paul has written a couple of books on racing technology. His most recent is about Racing tires. Anyway, Paul was working on a book about dampers and might be able to give you more insight. You can reach Paul at:
http://www.insideracingtechnology.com

Tell Paul you know Kiyoshi!
 
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