The Official Spring Rate Calculator Thread Part I

[BGKYK5]

So was thinking it would be cool to crunch some numbers and be able to approximate different leaf spring rates. There's only one problem, which spring rate calculation to use? - I have found about six of them. So here is the deal (get ready for audience participation). If you have a favorite leaf spring rate calculator or equation, post it up in this thread. Also, if you think a specific calculator or equation is way off, post that up too. Here are the ones I have come up with so far (in no particular order).

1. SAE HS-788 (SAE Manual on Design and Application of Leak Springs)

2. Chassis Engineering by Herb Adams

3. Ranger Station

4. Dirt Forum

5. A couple Excel Spreadsheets on Pirate

6. Race Dezert


2-6 all seem pretty similar, I haven't take the time yet to see if they are identical or what the differences may be. The SAE leaf spring model is more complex than the others, but should be the most accurate. There are also some FEA approaches, but they are impractical for the average off-roader.

My plan is this: we can settle on a few we think are the best (Phase I), and then we (and by we, I mean you) get all sciencey and take some measurements of common leaf springs with published rates (like on this little website) and I'll compare how accurately each method predicts the spring rate (Phase II).

Just to be clear, we are only looking at the raw spring rate, not the wheel rate, not the rate with the shackle (we all know shackle angle changes the effective rate). When you post up, please include a link or reference to the original source.

The CK5er who posts up the most useful information will win a cool prize!*








*not really

 

[rjpastor]

Math makes my head hurt.

 

[pvfjr]

I did a spring rate test once....

Told me what I needed to know

 

[Masiony]

I did a spring rate test once....

Told me what I needed to know

you would do that wouldnt you...

 

[Greg72]

You will need to publish the formulas from each of those sources.... I own a few of those books, but I'm not buying anything else just to play this game!!!

Sounds like fun to me, but I'm not normal.

 

[BGKYK5]

Greg, I'll publish the formulas when possible. There are no formula's on the sites of some of the web calculators so it is difficult to know what formula they are using. Also SAE HS-788 doesn't have a simple formula. It is a series of equations and lookup tables so you can't really post how it is done without reproducing a bunch of pages in their entirety.

pvfjr, that works reasonably well as long as you already have the spring you want to test. It doesn't work so well if you are trying to decide between several springs unless you buy them all first. The idea is to find the "best" method for approximating spring rates so you can play what-if games when deciding what suspension components to choose. The "winner" will of course get posted up for other nerds like me to play with when we can't get our hands dirty.

 

[pvfjr]

Yeah, I got you. Just posting as a joke, no one else had really added much. We had some ZR2 springs, some 52's, some waggy springs, and a couple others. We were playing a different kind of what if game. What if we use this junk laying around the yard and stick it under an S10 front end?

 

[BGKYK5]

 

[BGKYK5]

Hey can somebody else try using the calculators at Ranger Station and Dirt Forum (3 and 4 in the first post). I don't know if the calculators only work for members of those boards, but I can't get them to work with my Firefox browser.

You can use the following if you don't have any measurements handy:

Length: 52"
Number of Leaves: 4
Width of Leaves: 2.5"
Thickness of Main Leaf: 0.332"


Those are the measurements of the stock (as far as I know) rear springs from my '91 Blazer. SAE HS-788 gives a spring rate of about 263lb/in.

 

[UPS]

I am not a member of them and they both say 216.88lb/in.

Mike

 

[BGKYK5]

Thanks, I just tried Dirt Forum and got the same result here at work (running IE). It looks like the Ranger Station site is down at the moment. I wonder why the calculators didn't work with Firefox?

 

[Masiony]

Thanks, I just tried Dirt Forum and got the same result here at work (running IE). It looks like the Ranger Station site is down at the moment. I wonder why the calculators didn't work with Firefox?

i find this sometimes with certain sites. i just check it with IE, and it usually works so i just go with it.

 

[BGKYK5]

The Ranger Station site is back up and I get the same result (216.88 lbs-in.) without factoring the leaf taper, 202.79 lbs-in with factoring it in. I think it is fair so say that they use the same formula. Ranger Station does add the ability to take into account the taper effect. I guess I'll just have to use those sites from work, cause I won't use IE at home.

 

[BGKYK5]

There are two equations posted on Race Dezert. Here is the first:

Load (P) = (4 * E * b * t^3 * F) / (L^3)

That is for a flat spring of uniform thickness without fixed end conditions.

Parameters are as follows:

P = Load (pounds)
E = Modulus of Elasticity in Tension (psi)
b = widest width of rectangular wire (inches)
t = thickness (inches)
F = Deflection (inches)
L = Active length (inches)

A little algebra leads to:

Rate (R) = (4 * E * b * t^3 ) / (L^3)

R = Rate (lbs/in)
E = Modulus of Elasticity in Tension (about 30,000,000psi for most steels)
b = widest width of rectangular wire (inches)
t = thickness (inches)
L = Active length (inches)*

*The key here is active length. The area between the u-bolt centerlines is not active (it is firmly clamped between the spring plate and perch and doesn't flex......much) According to my measurements the active length of a 52" spring is about 48.5" (with my 14BFF).

Plug in the numbers and get.....

Rate = (4 * 30,000,000 * 2.5 * 0.332^3)/(48.5^3) = 96.2 lb/in (but that is only for the main leaf)

Without all the hoopla, here is Herb Adams' equation

Leaf spring rate = ((W X N) / 12) X ((1000 X T) / L)^3

W = Width
N = Number of Leaves
T = Thickness of one leaf
L = Length of the main leaf

For the 52" spring I get 216.88.....Hmm sound familiar? That must be the equation both Ranger Station and Dirt Forum are using.

Stay tuned.... there are a couple more things to check out tomorrow.

 

[BGKYK5]

Some more math..........

From one of the Excel spreadsheets on Pirate (by Triaged):

R = ((2+(N'/N))*(E)*N*W*(T^3))/(6*(L/2)^3)

R = Rate (lbs/in)
N = number of leaves
N' = number of full length leaves (usually 1)
E = Modulus of Elasticity in Tension (about 30,000,000psi for most steels)
T = Thickness of one leaf
L = Length of the main leaf

Using that equation and my 52" spring gives a rate of 234.2 lbs/in

It looks like the other equation on Pirate boils down to the same thing.

 

[BGKYK5]

So here is a summary of the estimates I get for my 52" spring:

1. SAE HS-788 - 263lb/in (The "gold standard" ???)

2. Chassis Engineering by Herb Adams - 217lb/in (much easier to calculate than HS-788)

3. Ranger Station - 217lb/in )uses the same equation as #2? Also has an (undetermined) method for factoring in leaf spring taper. That results in a rate of 203lb/in)

4. Dirt Forum - 217lb/in (uses the same equation as #2?)

5. A couple Excel Spreadsheets on Pirate - 234lb/in (both equations are basically the same, they are similar to #2 with the addition of compensation for how many leaves are full length)

6. Race Dezert - I'm not sure these equations are workable for our application. They are intended for single leaf setups.

That is a wider range of rates than I was hoping to see. However when I go and re-calculate them all using the active length (48.5"), as opposed to the entire main leaf length, I get the following:

1. SAE HSS-788 - 263lb/in
2. Chassis Engineering - 267lb/in
3. Ranger Station w/ taper - 253lb/in
5. Excel from Pirate - 289lb/in

Not too bad, they are all within 15%. Now which one is "best"? Does anybody know the "actual" rate of that spring?

 

[BGKYK5]

For more fun and games, visit Part II