How To Calculate Spring Rate–and How to Understand Cutting Coils | Handling Basics

[Editor's Note: This article originally ran in the May/June 1997 issue of Grassroots Motorsports]

Story by John Hagerman

For the last four decades, serious race cars have sported fully independent suspensions. Street cars, including some of the most notorious sports models, have tradition-ally used independent suspension at the front end only; at the rear, designers usually opted for the simplicity and …

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Fascinating.

I will have to read this several more times to get it.  lol

noddaz said:

Fascinating.

I will have to read this several more times to get it.  lol

 

Cool. We recently posted a few other suspension fundamental articles from the same series:

Understanding anti-roll bars

Understanding alignments

Love it Good stuff from GRM.... back from the historical times when I was young, dumb and did not know about GRM.

Thanks for (re)sharing!

Greg

Back in '88 I put all this in Excel. I added fields for current and desired ride heights, length of control arm, where the shock/ strut mount intersected that arm (so it could calculate the lever arm length), and spring compressed and free heights. From these plus the items in the article, the current spring's stiffness and the weight on that corner are calculated.

Then I use Excel's "goal seek" Tool for a "number of coils to cut" field, which calculates to 1/10th of a coil to get to the desired ride height. As it iteratively cuts 1/10th of a coil at a time, it recalculates the increase in spring rate (due to fewer free coils/ reduced free height) and the resulting drop in ride height. When the difference between the desired and calculated ride heights goes negative, it stops and reports the most recent iteration.

The "incremental steps for reference" are just there as a sanity check that the calculated number of coils to cut are reasonable. 

I've used it successfully on several Mustangs (street and track), a Toyota AE86, a Mitsubishi Mighty Max (Dodge D-50) oval track truck, and a Formula Ford. 

Interesting "spring steel" and regular steel act the same way.  Had no idea.

"...an increase of as little as 0.200 of an inch in spring wire diameter can stiffen a spring by over 20 percent (based on a 0.333-inch wire diameter spring)."

Does not compute! *smoke from ears* 

Also steal vs steel is peeving my pet off.

"Therefore, an increase of as little as 0.200 of an inch in spring wire diameter can stiffen a spring by over 20 percent (based on a 0.333-inch wire diameter spring)."

Can't be right

0.333e4 is  .01229

.533e4 is  0.0807,  or 6 1/2 times the spring rate. Now if you were to say

"Therefore, an increase of as little as 0.0200 of an inch in spring wire diameter can stiffen a spring by over 20 percent (based on a 0.333-inch wire diameter spring).",

0.353e4 is 0.01552, now you're talking 20%

Or am I missing something?

I miss John Hagerman, he really nails the engineering.  Is he still around, David Wallens?

I do think he left out an important consideration in cutting springs, however.  Most stock spring have a lot of preload, and that raises the effective spring rate.  Like the adjustable lower spring perch on some motorcycle shocks, especially vintage Japanese.  
 

Thus, when we cut coils from a stock spring, we do stiffen the spring as in article, but we reduce preload, so the change is not as much as it might be.

RP

Preload doesn't necessarily have the same stiffening effect on a typical car suspension.  Unless you're running so much preload that the weight of the car is less than the preload force (and therefore the suspension is fully extended at rest), reducing preload won't have any effect on the effective spring rate except for when the suspension is fully drooped.  

A warning on calculating spring rates from spring dimensions: This is rocket science and it's very easy to get it extremely wrong, it should only be attempted as a last resort. Better ways to find a spring rate include searching parts catalogs for information and doing practical experiments. Put a spring on a bathroom scale, apply as much downward pressure as you're comfortable with and have an assistant measure its length under pressure and write down the scale reading, this can give you a ballpark figure with much less potential for error than an equation where you take a bunch of measurements that are very easy to get slightly wrong (do your springs have a paint or epoxy coating, and if coated just how thick is it? Where exactly to you measure mean spring diameter and how do you average it for an oval or conical spring? Are you really sure about the number of active coils and the spring's metallurgy?) and then raise them to a power of 3 or 4.

I have been down the path of cutting springs before on two different cars. All subesequent projects I replaced the factory springs with performance springs that were designed to lower the car a specific amount and provide a specific spring rate, or I used a coilover setup with a fixed spring rate that allowed adjusting ride height and preload to the desired amount. Both of the latter two choices were by far the better choices with the coilover choice being the absolute best choice. Your mileage may vary of course, and if cutting your springs works for you and you get the desired result, its obviously a much less expensive approach. But everytime I think about doing it I am reminded of previous results and the old adage "you get what you pay for, if you're lucky"