RedRevolver

Ok so for my independent study this quarter I decided to figure out optimum spring frequencies for a FWD autocross vehicle (gee i wonder what that applies to).

Anyways my first task was to create a spring frequency calculator, and unfortunately, everything I came across was at least slightly inaccurate, even eibach's calculator on their own website. So, I finally just finished the calculations and I believe everything is accurate, it is mostly based on eibachs calculator, but i've modified it so that it actually works. my front frequency on my del sol came out to be 1.32 Hz using 182lb/in springs, which seems about right for a stock del sol S. (I don't know what stock spring rates on a 93 sol S are, but i saw a post saying 92-95 civics were 182F/102R so i went with that)

Anyways, what I'm asking you guys to do is to read this over and see if you can find any discrepancies, or things that are outright wrong and let me know. Also, if nothings wrong with it, have fun calculating your spring frequencies!



Calculating Spring Frequencies:

Calculating spring frequencies requires a few different measurements and calculations. The first thing your going to need is the sprung weight of your car. This means to take the weight of the car minus all of the pieces that are being held up by the springs. Mostly this is the weight of the wheels and tires and brake components. There is some other stuff but for the sake of simplicity we'll just take into account these two. The stock weight of my Honda Del Sol is 2,270 pounds. Each wheel and tire of mine weighs 34 pounds so, 136 pounds for those, and the brake assemblies are about an estimated weight of say 15 pounds on each corner, so another 60 pounds off of the weight, putting my approximate sprung weight at 2,074 pounds.

Next up is the motion ratio of the spring. The leverage of the suspension arm acting on the spring has to be taken into account when doing these calculations. There are two distances that you need for this, and they are pretty easy to measure. The first is the distance between the spring centerline to the lower control arms inner pivot point (d1). The second is the distance from that same pivot point, out to the outer ball joint (d2).
The diagram below is for an A-Arm/Double wishbone suspension, but can be applied to a MacPhearson strut as well.






If you have a beam axle suspension then the motion ratio is calculated a little differently, by using the distance in between the spring centerlines (d3) and the distance between tire centerlines (d4).





For both of these suspension types you want to take your measurements and divide them. You want to take the smaller number (d1 & d3) and divide it by the larger (d2 & d4). For example, on my car, which utilizes a MacPhearson setup, d1=10" and d2=14", so my motion ratio is .714.

Formula: d1/d2

This is all so that you end up with the proper ratio for calculating the next thing we need, the wheel rate.

The wheel rate figure is the figure that tells you how much of the spring rate is actually acting at the wheel. For example, if your spring rate is 200 lb/in, then to compress the spring one inch, it takes 200 lbs of force. But, if you calculate the wheel rate and it comes out to be something like 160 lb/in, then your wheel will be moving one inch for every 160 lbs of force applied to it, thus giving you a much more useful number for calculating the acutal movement of the vehicle under loads.

To calculate the wheel rate though, we also need to take into account the angle correction factor, to account for the angle that the spring is mounted at. This is a pretty easy thing to figure out, just take the angle of the spring from vertical, and take the Cosine of it, making sure your calculator is in the degrees setting (as opposed to radians). A diagram of how to measure the angle (A) is shown below





Since my front springs are mounted at a 17 degree angle, my angle correction factor (ACF) comes out to be .956.

Formula: Cos(A)

This will be used in our wheel rate calculation now.

The wheel rate calculation, now that you have all of this other stuff, becomes quite easy. All you need is your spring rate (SR) divided by the motion ratio (MR) squared multiplied by the angle correction factor (ACF). The reason the MR is squared is because when calculating the wheel rate, it acts as a lever, multiplying the force applied to the spring.

Thus your formula becomes:

SR
--------------------
MR(squared) x ACF

Broken down, it is:

SR
-------------------
(d1/d2)(squared) x (Cos(A))

So, based on this, my car, with a front spring rate of 182 lbs/in, and distances 10" and 14", with an angle of 17, the formula becomes:

182
--------------------- =
(10/14)(squared) x (Cos(17)



182
------------------ =
(.714)(squared) x .956



182
------------------- =
.5102 x .956


182
-------------------
.487



= 373.7 lbs/in Wheel Rate

Finally, we get to total up all this information into the final calculation for the spring frequency. The spring frequency (SF) is the square root of the wheel rate that we just figured out, divided by the sprung weight, all multiplied by 187.8.

Formula: SF = 187.8 x (√(WR/Sprung Weight))

So, based upon my car, this would end up being:

187.8 x √ (373.7/2074) = 187.8 x √ 1.801 = 187.8 x .4244 =

79.7 Cycles per minute (CPM) suspension frequency. the problem with this is that most people tend to use spring frequencies in Hz not CPM. Luckily for us, this an easy conversion, just divide the CPM by 60. Therefore:

79.7 CPM / 60 = 1.32 Hz

This would be the suspension frequency for the front of my car. For the rear, all I have to do is go back and change the values to the correct ones for my rear suspension.

So, to review, calculating the suspension frequency requires: Sprung weight, spring rate, motion ratio, and angle correction factor.

And now, all the formulas again:

MR = d1/d2
ACF = Cos(A)
WR = SR/(MR(squared)xACF)
SF = 187.8 x √(WR/Sprung Weight)

ddd4114

You're way off - I get 187.6 in your last equation, not 187.8.

Everything looks good to me, nice write-up.

Premium Dude

The spring rate is multiplied not divided by the motion ratio in order to get the wheel rate.

beanbag

The geometry is slightly wrong. You need both the angle btw the shock and lca, and the angle of the lca to the ground. Consider the pathological case where the shock is parallel to the lca, and both are 45 deg relative to the ground. Your equation gives an ACF of sqrt(.5). The actual ACF would be zero. For LCA almost parallel to the ground, your eq is mostly correct.

I didn't check how you came up with 187.8.

ddd4114

That's never been clear to me. I've always seen it as the product of the spring rate and the square of the installation ratio. However, I've seen the installation ratio described both as being equivalent to the motion ratio and as the inverse of the motion ratio. I don't know which is right.

beanbag

I have seen it get defined both ways. Multiply or divide, whichever makes the wheel rate less than the spring rate

ddd4114

Yeah, it's a little unclear; I had to stare at it for a bit. In the text, he describes it as the angle between the shock and vertical, but in the diagram, it looks like it's between the shock and a line normal to the LCA. Technically, he should also account for the change in installation ratio and shock angle with displacement, but I'm assuming that he's using a stiffly sprung approximation. If that was the case, he should use what's in his text, using the angle relative to vertical. Either way, the diagram should be clarified.

RedRevolver

Well, like i said this is mostly based off of eibachs with a few tweaks ( otherwise i come up with a product of 8 cpm....). I'm gonna see if i can actually talk to someone at eibach and find out where the 187.8 came from.

as far as the dividing to get the wheel rate, again I followed eibachs way to do that, but I have seen the other method which if i remember correctly is ((motion ratio squared)*(spring rate))*(sinA), but then i get an answer of like 27lb/in for wheel rate, which is definitly wrong lol. and i thought wheel rate is usually higher than spring rate?

anyways, i'll look into that LCA angle and work on fixing that, thanks for pointing it out. I'll look into the wheel rate more, and talk to my professor about it as well if he has time.

ddd4114

I was joking around. They just rounded acceleration due to gravity to 32.2 and pi to 3.14. When I do that, I get 187.8 too. It's just rounding error and not a big deal at all.

One thought though - you said this is for determining optimal spring frequencies. How will you use these calculations for that?

beanbag

Archimedes is rolling over in his grave right now.

slammed_93_hatch

I understand you are doing this for academic reasons, which is great but something to keep in mind.

There is no optimum ANYTHING as far as suspension is concerned...

There are really fast/well placing national championship autoX cars that run EXTREMELY different setups...

One person might run 1000lbs front springs with a 26mm front bar, and 600lbs rear springs with 22mm rear bar.

and then another person will run 800lbs front springs 22mm front bar, 1350lbs rear springs and 22mm rear bar.

(shocks, chassis, and tires are the same between the cars. note there are cars that are VERY close to this and are in the top 3 nationally.)

Really what is more important then the optimal "suspension setup" is what the drive is comfortable with and what they prefer.

TunerN00b

If you follow the belief that there is a maximum suspension frequency for tire traction for a given tire type (higher frequency for race tires vs. street tires), then you work the spring rates backwards from a chosen frequency and fine tune from there.

For example, I've read that street tires don't like to be taken past 1.8Hz or so. However, many autocrossers have demonstrated that you can be fast with higher frequencies, especially in the rear of a FWD car.

RedRevolver

Yeah I suppose I should have clarified on that one. I'm doing this for theoretical optimum spring rates. Which is going off of the fact that Theoretically, on a perfect surface, you wouldn't need any sort of suspension to absorb bumps, so, theoretically, the stiffer your springs the better. So, more or less i'm finding out how stiff of springs you can have on the road, while still be able to safely drive it down the freeway over all those nasty bumps, meaning, for this project, that the wheel has to stay on the ground when hitting a bump on the freeway.

This of course all completely ignores driver feel, and I do realize that while it is a big factor for racing, this is more or less about safety rather than being the perfect setup for a particular driver.

Also about the wheel rate, realize that I really have just kind of jumped into this, I'm still a freshman in college and my advisor was willing to let me just explore this subject because I'm interested in it. He doesn't really know a whole lot in the suspension area, he's an engine guy, so if you guys have formulas and reasons why they work, please let me know, I'm kind of on my own through this and internet information seems to be sparse and hard to find. Any book recomendations are great too, I don't mind spending money on useful books.

string

Wheel rate stiffer than the spring itself? Something wrong :D

ddd4114

A good, cheap book is Carroll Smith's "Tune to Win". I'd recommend that to anybody.

For more in-depth material,
"Fundamentals of Vehicle Dynamics" by Thomas Gillespie
"Race Car Vehicle Dynamics" by William/Doug Milliken

Those are considerably more expensive and are more heavy in math, so keep that in mind before you dump money into them. Also, students can get SAE memberships for $10/yr, and you could get all of that money back in savings for these books.

There are others, but I'm drawing a blank right now.

RedRevolver

hmm, i did get an SAE membership a month or so ago, we're required to get one to go to competition for Formula SAE West. thats good to know. And yeah Carroll Smith books were the first I was gonna look into =P

beanbag

Back in my day, before Al Gore invented the Internet, we solved problems ourselves by using a piece of paper and pencil. Failing that, we walked through snow or blistering heat to the library.

RedRevolver

No need to be a dick dude....i'm just trying to come up with a useful tool for EVERYONE. think about it. spring frequencies are comparable across different cars. Instead of everyone asking what the hell spring rates they should get for their specific car, they can do a little bit of math and figure it out for themselves, and actually LEARN something about their car maybe.

Apparently nobody on the internet has come up with a decent way for calculating these where all the necessary measurements and equations are compiled into one place. I mean good god even Eibach's own website is WRONG. If you know something we don't please share. I'm trying to make this a useful thread thats about LEARNING. if you can't make a useful contribution, please do not post.

Anyways, back to our regularly scheduled thread, I am pretty swamped this week with classes and tests, so I'm not gonna be getting around to fixing stuff for a little while, but, if you've got a good way to calculate wheel rate, let me know, and i'll "reverse engineer" it to see why/if it works, unless of course you can provide an explanation yourself. (in which case i'll still be checking, but it'll help me move a little faster =P)

mustclime

May I sugest you read through this and the links there.....

http://farnorthracing.com/autocross_secrets5.html


I worked through my ep3's numbers a while ago.....

http://forums.clubep3.net/showthread.php?t=565676

different motion ratios and wts though from what you have to do......


BTW, I got my motion ratios with a ruler and my wights with a corner balancing and a scale for the unsprung wts....

RedRevolver

Thanks dude, definitly have those bookmarked now and I'll be reading through them soon. Thanks to everyone here helping me out