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Motion Ratios, Natural frequencies, Wheel Rates, etc.

8.1K views 32 replies 13 participants last post by  G-forces  
#1 ·
I'm trying to find more info about Motion Ratios, Natural frequencies, Wheel Rates, etc., for my STF ZX3 build.

I've searched these topics a lot, but haven't found much. Mostly just people asking for more info on these subjects, with seemingly few answers or guesstimates. Does anyone recall a thread that discusses these things in depth?
 
#3 · (Edited)
At this point, I'm mostly just looking for a point of reference when choosing spring rates, sway bars, etc.

I've been thinking of going with a somewhat more mild version of your FSP set up. I've seen a lot of people complain of inside wheel-spin issues while running a front bar. So my plan has been to increase front spring rates and remove the front bar, and run a big rear bar to assist in lateral weight transfer/rotation. As for spring rates, it's kind of guesswork without knowing actual numbers. Based on various builds I've researched, something like 650-700# front and 450-500# rear seems like it would be a good starting point for STF. I'm not sure I would need to go with much higher rates than that on street tires. I'm open to ideas, though.

Edit: I've also considered using the 18mm SPI front bar.
 
#4 ·
Nothing really useful to contribute to this thread other than to say if I ever get around to it I've got a SPI front bar, H&R race springs, H&R 24mm rear bar, and some revalved Konis (fronts shortened too, bought here on FJ a year or two ago) to install. Open to suggestions on how to tweak that plan before install if anything seems too flawed. I know I may need to up the rear bar (would probably go straight to the Steeda 28.6mm bar) even further to get it to do what I want and/or mess with spring rates.
 
#5 ·
All these terms confuse me. I really know nothing of suspension. but I have a feeble grasp on Physics and the end goal of racing/suspension/geometry.

In racing, I don't think natural frequencies would play any part. That pertains to a constant mass. In racing mass is being transferred about the car through corners, acceleration and braking. Each time the natural frequency would change.
But I guess you could develop a model of ranges per corner. You'd have to know static corner weights and compression and extension limits of each corner. From that you could find min and max. So your natural frequencies would fall somewhere in between at all times.

If I understand wheels correctly, they are mass-less, or mass constant. The Centripetal force causes the mass to always be constant. Or a heavier wheel/tire can be included in the corner weights and no other calculation is needed. But I guess that does/should only apply to a rigid body. The tire being pliable might change it some. I'll have to think/read on that one.


If you feed me some data I can probably put together a spreadsheet for it.
 
#7 ·
All these terms confuse me.
This has been referenced many times on various car forums, but there is a lot of good info here: http://farnorthracing.com/autocross_secrets5.html

You'll have to figure out your corner weights and unsprung weights first. Then you'll need to measure spring angle and the distance from the control arm pivot to the spring mounting point and the distance from the control arm pivot to ball joint.....or the center of the wheel barrel if it's offset. You'll also need to know the damper's sag length. From that you can figure out an effective spring rate and motion ratio which in turn will give you a wheel rate.
Right. Swaybar rate is another. I'm just surprised that I can't kind find these measurements or the resulting numbers for a chassis that's been around for 15 years.
 
#6 ·
You'll have to figure out your corner weights and unsprung weights first. Then you'll need to measure spring angle and the distance from the control arm pivot to the spring mounting point and the distance from the control arm pivot to ball joint.....or the center of the wheel barrel if it's offset. You'll also need to know the damper's sag length. From that you can figure out an effective spring rate and motion ratio which in turn will give you a wheel rate.
 
#8 ·
Probably because the vast majority of us are using components that have been proven through trial and error rather than straightforward math. There might be a few guys from the Spec Focus series that know. Unfortunately, part of being in a niche enthusiast group means doing things the hard way. If this was a Corvette club, I'm sure there would be a doctorate level thesis stickied at the top of the suspension forum.
 
#9 ·
Testing is absolutely the best way, but having some baseline numbers to work with can only help. I don't think anyone here is trying to build a car with just math. The Focus has very high production numbers and a lot of people have built them for autox, road-race, rally, etc. That's why I'm surprised that I can't find the numbers. I'm guessing someone HAS done the math, but may or may not have posted results.
 
#10 ·
From Mazda3forums.com (2006 Mazda3):

Spring rate=(2*pi*F)^2 *SM *(MR)^2
F=frequency: rate at which the wheel hub oscillates up and down
SM=sprung mass: only the weight supported on top of the springs
MR=motion ratio: vertical distance wheel hub travels compared to spring's travel distance

Guestimated numbers for our cars:
SM= 2750+/- (sprung mass of car + driver)
Weight distribution= 60% front
SM front= 825 lbm
SM rear= 550 lbm
MR front= 0.95-0.97
MR rear= 0.70-0.725

Desired frequencies:
F/R= 20%
F front= 2
F rear= 2.4

Pound mass (lbm) to pound force (lbf) factor= 1/386

Equation:
Front= (2*pi*2)^2 *825/386 *(1/(0.95^2))
Rear= (2*pi*2.4)^2 *550/386 *(1/(0.71^2))

Theoretical spring rates:
Spring rate front= 374 lbf/in
Spring rate rear= 643 lbf/in
I realize the 3 chassis isn't identical to the Focus, but they are really close. So these numbers are somewhat useful.
 
#14 ·
From Mazda3forums.com (2006 Mazda3):

Originally Posted by clemsonmz3 View Post
Spring rate=(2*pi*F)^2 *SM *(MR)^2
F=frequency: rate at which the wheel hub oscillates up and down
SM=sprung mass: only the weight supported on top of the springs
MR=motion ratio: vertical distance wheel hub travels compared to spring's travel distance

Guestimated numbers for our cars:
SM= 2750+/- (sprung mass of car + driver)
Weight distribution= 60% front
SM front= 825 lbm
SM rear= 550 lbm
MR front= 0.95-0.97
MR rear= 0.70-0.725

Desired frequencies:
F/R= 20%
F front= 2
F rear= 2.4

Pound mass (lbm) to pound force (lbf) factor= 1/386

Equation:
Front= (2*pi*2)^2 *825/386 *(1/(0.95^2))
Rear= (2*pi*2.4)^2 *550/386 *(1/(0.71^2))

Theoretical spring rates:
Spring rate front= 374 lbf/in
Spring rate rear= 643 lbf/in
I realize the 3 chassis isn't identical to the Focus, but they are really close. So these numbers are somewhat useful.

The problem I am finding with this is, that only reflects the frequency the car moves up or down (spring rate).
A natural frequency depends on the weight of the spring itself, from what I understand.
So basically, the math is not applied correctly for what you're asking.

See this for more --> https://www.efunda.com/designstandards/springs/calc_comp_designer.cfm
 
#11 ·
Don't forget the inherent secrecy of racing teams... they don't hold meetings to announce what their set-up numbers or tune parameters are, only the ruling body gets to know what they need to know and that's it. I wouldn't hold too much hope for finding what you're after on-line. Best to try a couple well suggest kits and see which matches your driving style.

What kind of application is the above spring rate for?
 
#17 · (Edited)
"512 front 400 rear. Stock 21mm front bar, progress 25mm rear sway. On a focus with square size tires, id try a smaller spi 18mm front bar and maybe also another 50lbs in rate for the rear"

^I just copied and pasted Clint's answer to this very question that he texted me for his optimum tarmac setup.
Your results may vary.
I believe Steeda's Spec car ran no rear bar but if I remember correctly from a conversation with one of their techs they ran 800# rears.
 
#21 ·
I run a road race tire, not a slick but a little greater stick than a street tire, kumho z710 treadware of 20, no front bar quaife box and camber plates with spring rates of 700. H & R coilovers with revalved bilstien inserts. Except for all but the slow speed corners we have been able to dial out most of the push, and I believe it's more my style of driving in the slow speed areas causing my trouble.
 
#24 ·
Here's an interesting post I found while digging around in the archives like Gandalf:
Ron, thanks so much for giving FJ muti quote!!! :lol:



yeah that 700lbs spring up front is way to hard, the koni you have may not be in the damping range of that hard of a spring, AND its just too hard in general consider the suspensions motion ratio and front end weight. Honda guys run such hard springs because their motion ratio from their double wishbone suspension configeration is different then our strut type suspension. Take into account the example im about to use is just estimations for the sake of explination, i could look up the motion ratios and do some math but its not all that important. When a civic runs lets say a 800lbs front spring, because of how the suspension configeration is, that 800 lbs is actaully only really like a 500lb spring, on our strut type front suspension, the motion ratio is near 1 to 1, so a 400 spring is actaully a 400 spring. Our rear mutil link is somewhat different since the spring is located somewhat in board, making for a slightly different motion ratio then the front, so a 400 lb spring in the rear of our cars is slightly softer, maybe like a 360lb spring, im sure someone will chime in with the proper motion ratios that im talking about, or ill look them up later:lol:



yes, that is a important part of spring rate selection, I run a 512 front spring and a 400 rear spring, BUT i run no front sway, so having a spring as hard as i do is cirtical since i dont have a sway up their to help it out with body roll. the reason i run no front sway is to keep maximum inside wheel grip under load so my diff doesnt open up under power. This is not much a issue for NA foci, mostly a issue with turbo guys, so with your super charged setup, you may or may not have to do what i did, experiment for your self and see whats best, disconnecting one end link on your front sway is easy to do at track.
As for the rear, i only run a 22mm progress sway, since i run a staggared wheel/tire combo, i dont need a big rear sway for proper rotation characteristics, but if you plan to run symetrical tire sizes, a bigger rear sway then what i run maybe in order.




brads setup is prolly has the best handling per dollar ratio for a focus, and plenty of people have used this setup with sucess.

yeah man, i want that grand am's JRZ's SO BAD!!!! :lol:



i think your going to like it, i do:thumbup: the dampers on the H&R coils are great



x2
Wanna read the thread? Go here: http://forums.focaljet.com/focus-road-racing/610130-typical-spring-rates-road-raced-focus.html
 
#27 ·
I try. And it was your posts and one in the stupid stance section that caused me to start writing this. One size fits all just didn't make sense and had too many assumptions to appease me. Springs and Camber should be covered. Now to move on to Toe, and that one I'll have to measure things again. Good thing I'll be swapping my Summer suspension in today.
 
#29 ·
This is sorta on topic.

dealing with fitment with PSS9s. They have helper springs. which looks like they do a bit to help center the strut in their range of motion. Which you mentioned is important to keeping all 4 on the ground.

Do you have more information on this or can you point me to somewhere that does? I am in need of more reading.
 
#30 ·
Your PM box is full,


Devanmc said:
You mentioned in the big FF write up you linked on here about. You briefly mention strut motion range for keeping all 4 on the ground, in racing.

How important is this? I am dealing with the figment issues of pss9s. What affects will removing the helper spring from this setup have? I will be running stock height. So I shouldn't have issues with the spring coming unseated.


Thanks and I hope this makes sense.

Sent from my One using Tapatalk

So long and static ride height is in the center of the strut/shock travel, then a tire should not come off the ground. If that requires removing a helper spring, so be it.
The other thing you can consider is the bump stop. It can make up the difference, although you really don't want to bottom out suspension. It would keep all 4 on the ground though.

The shock is easy to measure. Just extended length minus compressed length, divided by 2. And that is where you want static ride height to be.
The strut is a bit more difficult. Take the assembly as extended height. Compressed height will be the spring wire diameter times the number of coils, that assumes the strut can bottom out where the spring is fully compressed. Minus the 2 and divide again. That should get you close to where static ride height should be.
The front isn't as big of a deal as the rear though, you rarely have a front tire come off the ground.

On the helper spring, I would imagine that under most conditions it's fully compressed. So that means when fully extended it's just there to make sure the main spring doesn't jump around. For the most part I think helpers are worthless. The main spring should have been longer of there's an unseating issue.


-John
 
#31 ·
I'd love to revive this thread if anyone who participated in it earlier is still around :lol:
Was watching the latest Speed Academy vid (love these guys, I'll link the video below) and the topic of motion ratio/spring rates has come up again.
I basically run Clint's old set up on the street albeit with a H&R front bar on soft and a Quaife. Was wondering if anyone has anything more to offer here especially regarding spring rates both on track and on the street, and how you've set up the car to be neutral, or even a bit tail happy.
Btw, my cars are extremely sensitive to tire changes on their current set up. My '04 handles way way better than my '06, the only difference between them being tires. The '04 has a mildly staggered Pirelli PZero GT set up with a bit softer compound and more sidewall than the '06 which has an old crappy staggered Goodyear F1 Asymmetrico setup that is leftover from my performstance days <----functional but tends to understeer quite badly at or even before the limit. I will be switching to Michelin Pilot Super Sports here this year on the '04 and see how they perform.
Here's the link to the Speed Academy vid:
 
#32 ·
Having put some feedback towards this thread after rereading all the info I don't know if my input is as based in fact other than the butt o meter. Ok I run a four door 05 st. The static ride height is 5.75" front to the rocker panel and 6" to the rear on 15" wheel. This car is strictly a track racecar. Gutted with 1/4 tank of fuel and driver we cross the scales at 2720. I run in Scca IT class so I have a rules set I must meet. Ride height is no lower than 5.5" I have to run the ford designed rear, spring and shock. Starting from the rear trying to lower the height has had us go the 5" spring with adjustable perches and kyb adjustable shocks. Instead of a spring tender we have a rear suspension limiting strap to insure the spring stays put. Spring rates I followed the traditional fwd theory as I have had good success. After reading all attached who knows. So we started with a stock bar, moved to a steeda 28mm bar, now on a 32mm adjustable unit. Spring rate is 950, 5" spring. I run zero toe, 2.5 neg camber. As of late we are running Hoosier 205/50-15 r comp tires. Front H&R coilovers custom valved bilstien inserts, 750 rate springs 6" length. Front no bar. 3 degrees neg up front zero toe. Front we have moved to 225/45-15 in the front. Hoosier. Current transmission is equipped with a Kaaz unit where we were running a quiafe. Corner weight of the car is dependent on track but the most stable is when we have a equal split left to right, but it's not the fastest. Normally we have the car sitting on the scales with 60% up front, 40 rear. The car is running 2.3 Duratec motor. The reason we have gone to staggered tire setup is the 205 series tire and weight of the vehicle tied to my driving style we were running out of tire mid race, the 225 has shown much greater durability and better ability to last the race.
 
#33 ·
I think you'll love the Michelin Pilots. As long as your front-to-rear spring and sway bar ratio is close to SVT (or a bit stiffer rear), then try running a little toe-out up front, that should let the rear come around without too much driver effort, especially with your LSD.