Coilover spring rate calculations

[chevynut]

I posted previously about Ridetech's coilover spring rate calculator and have looked at several others recently, and very few of them actually help you pick a spring rate from scratch when you know your car's weight and suspension dimensions. Some require you to buy a "baseline" spring, take measurements, then calculate the actual spring rate you need by making corrections. Others require you to pick a wheel rate and get the spring rate from that, which I think is absurd. Here's some examples:

http://eibach.com/america/en/motorsport/products/suspension-worksheet
http://www.crawlpedia.com/spring_rate_calculator.htm
http://f-o-a.com/foa-suspension-calculator/
https://www.qa1.net/technical-support/street-performance-racing-spring-rate-tech
http://www.hypercoils.com/spring-calculator

I developed a spreadsheet long ago to do these calculations but have long wondered why you need to square the motion ratio of the suspension to calculate the required spring rate, and now I'm back to believing you don't have to. This recent investigation confirms that to me and I believe I have been over-specing spring rates somewhat. You only need to square the motion ratio to calculate the WHEEL RATE. I also read once where you have to square the shock angle factor, but I don't see why that is necessary and other calculators don't do that, not even for wheel rate calculations.

Here's a sample spring rate calculation for an IFS that I've used to calculate the required spring rate, once you know or estimate the car's sprung corner weight and suspension parameters.

Corner sprung weight: 950 pounds
Distance from lower a-arm pivot center to shock mount bolt center: 12"
Distance from lower a-arm pivot center to balljoint center: 15"
Shock angle: 22 degrees
Total shock stroke: 4"
Desired shock compression at ride height: 40% or 1.6"
Desired spring preload (for adjustment purposes up/down): 1"

The first thing to do is to calculate the axial load on the shock at ride height. To do this you need the total corner sprung weight (CW), motion ratio, and shock angle.

The motion ratio is the a-arm pivot to balljoint distance divided by the a-arm pivot to shock mount distance:

MR = 15/12 = 1.25

The angle correction factor is the cosine of the shock angle:

AF = cos 22* = .93

The total axial load on the shock is CW multiplied by MR, and divided by AF:

L = CW*MR/AF = 950*1.25/.93 = 1277 pounds

Now that we have the axial load we need the total spring compression desired to support that load. With a 1.6" shock compression and a 1" spring preload, we have a total spring compression (TSC) of 2.6" at ride height.

To calculate the spring rate needed to support the car at this ride height, you divide the total load (L) by the spring compression (TSC):

SR = L/TSC = 1277/2.6 = 491 lb/in

To calculate the wheel rate, which is what determines ride quality, you need to divide the spring rate by the motion ratio SQUARED and multiply by AF:

WR = SR/MR^2*AF = 491/1.25^2*.93 = 292 lb/in


I plugged these numbers into the Hyperco calculator which I just found today and got the same results :):

http://www.hypercoils.com/spring-calculator

Using their calculator, you have to remember to add the spring preload (how much the spring seat is compressing the spring from free height) to the shock compression length. Also, they measure their shock angle from horizontal and I measure it from vertical. So my 22 degree shock angle would be 68 degrees using their calculator.

[Rick_L]

I thought the "motion ratio" was about wheel rate and nothing else?

[NickP]

I thought the "motion ratio" was about wheel rate and nothing else?
I have ZERO idea but this Koni worksheet may assist for others.

6590

[chevynut]

I thought the "motion ratio" was about wheel rate and nothing else?

The "motion ratio" is the ratio between the two dimensions on the lower a-arm and it determines how much leverage the force at the wheel has on the shock/spring. The further inboard the shock mount is, the more leverage there is and the higher the force on the spring.

The question I always had, after doing a Force diagram, was why you would square the motion ratio for a static situation. That's what my calculator was for, to give the right spring rate to support the car at ride height given the weight, a-arm dimensions, shock angle, and desired preload. Of course there's more than one solution for a given shock and suspension, but different solutions require different preloads.

If you want a higher WHEEL rate than the calculations give, you need to LOWER the preload and the calculations will result in an increase the spring rate AND the wheel rate. You can only increase the preload so far, before you run out of threads. So that's the LOWEST spring rate and wheel rate you can get with those constraints. I like to run the lowest spring rate I can on the C4 suspensions to get the best ride, and the wheel rate is usually fairly high. You also have to watch out for spring bind at full shock compression as you preload the spring.

[chevynut]

I have ZERO idea but this Koni worksheet may assist for others.

Nick, notice again that Koni sheet doesn't help you to choose a spring rate (C) for the correct shock ride height or travel. They expect you to have a wheel rate in mind, then you select the spring rate from that....how the hell does that work? Who knows what wheel rate they want? How can you be sure you can even set the suspension at the correct ride height with that wheel rate? They completely ignore spring preload.

Also, there is a BIG error in that sheet. They show motion ratio as the square of the a-arm dimensions (which is wrong) and then they square it again to calculate wheel rate. Take a look at my other links and you'll see MR is just the ratio of the two dimensions, not squared. That's either a typo or a big blunder.

Also, there's another error in "tip 2". using simple algebra from the formula in "step 2" you can see that the two formulas are inconsistent. I don't trust anything on that sheet without going through the math myself.

One thing I hadn't considered is the situation with the beam axle and the motion ratio involved there. I always assumed the MR was 1 for a beam axle because there was no leverage, but it makes sense looking at their diagram that there is leverage around the tire contact patches. However, what they're showing doesn't seem right to me. Wouldn't the beam axle motion ratio be the ratio of the distance from one tire centerline to the opposite lower shock mount divided by the track (width of tire centerlines)? It doesn't seem right to use the distance between the lower shock mounts because that's not what the axle is pivoting around.

[Rick_L]

From a discussion that you and I had 12 years ago:


I found the answer to the motion ratio. I wasn't smart enough to figure it out myself, but I was smart enough to go to a resource that explained it. (Racecar Engineering and Mechainics by van Valkenburgh.) It's actually straightforward once all is thought through.

As we have discussed the force ratio at the wheel or ball joint is the ratio of the distances. BUT, the distance traveled at the wheel is doubled also. It's probably easiest to describe it with a simple example.

If you had a 18" lower control arm and the spring was mounted 12" from the pivot point, and we use a 100 lb/in spring, then if the spring is displaced 1", there is 100 lb of force at the spring. Now if we move out to the ball joint, the force required there to put 100 pounds load in the spring is 2/3 that, or 67 lb. BUT, the travel at the ball joint is more than what the travel at the spring is, in this case it's 1.5". So the spring rate at the ball joint (or wheel) is 67 pounds/1.5 inches = 44 lb/in. Note that the force ratio is 2/3 and the spring rate ratio is (2/3)squared - 4/9, or rounded off, 0.44.

van Valkenburgh keeps things in perpective by using the terms force ratio, displacement ratio, and spring rate ratio instead of the generic "motion ratio". For shocks the same math applies.

If you correct for the angle before applying the force ratio and displacement ratio, you'll come out OK. The angle correction will be a function of the cosine squared after you apply the force ratio and displacement ratio.


There is an edit needed here, in the second paragraph, it says "the wheel motion is doubled also". It should read "the wheel motion increases also". (This is due to switching examples in midstream in that old thread.)

Note that the case stated is for force and displacement at the ball joint. You need to use the instant center math in Nick's example to get wheel rate.

[55 Rescue Dog]

I'm going to try something different, the (KISS) method using only a digital level, a tape measure, and no calculations. I'm going to try and match the F/R weights of the stock C4 to the 55 conversion frame using the stock 96 springs I have to start. The C4 spec I read show F/R weight percentage at 51/49, with a front weight of 1695 and, 1630 rear. Total 3325lbs.
I'll check the stock suspension angles on my friend's stock 95 C4, and by simply adding engine/body parts the new chassis one piece at time until the front and rear suspension angles match the stock C4's design ride height. When I get to that point, it will be interesting to see how many parts, and which ones I have left over. Then I will make adjustments from that point, either by weight reduction, or springs. No AC on this car for sure, and to use a front bumper, I'll probably be stuck buying an aluminum block LS engine at some point. On a fair weather car without AC, who needs side widows anyway? Been driving my other car with only a windshield for 5 years, and the ventilation is fantastic. I wouldn't even have a windshield, but that is required by law, for good reason. I just want to build a different, quick 55 Chevy hotrod, that I rescued 100 yards from the crusher at a junk yard, and not a pretty cruiser.
I wish I knew how I even got pulled back into messing with a 1955 Chevy, other than that is my first memory of any car, that my Dad, and Grandpa bought new, when I was 2.

[chevynut]

From a discussion that you and I had 12 years ago

Wow, I remember having a discussion once about it but don't remember the outcome. I think we were talking about why the motion ratio was squared and you explained it that way, which makes sense when determining wheel rate. However, I also used it for the static case in my spreadsheet which is where my error came into play. When all you're doing is balancing loads, you don't square the motion ratio.

Nick's example is full of errors as I mentioned before. I don't know what "instant center" you're referring to. Note also that D2 is specified as the INTERSECTION of the two axes, the shock axis and the spindle axis, which I believe is wrong too. It's simply the horizontal distance from the pivot to the balljoint center.

[chevynut]

I'm going to try something different, the (KISS) method using only a digital level, a tape measure, and no calculations. I'm going to try and match the F/R weights of the stock C4 to the 55 conversion frame using the stock 96 springs I have to start. The C4 spec I read show F/R weight percentage at 51/49, with a front weight of 1695 and, 1630 rear. Total 3325lbs.
I'll check the stock suspension angles on my friend's stock 95 C4, and by simply adding engine/body parts the new chassis one piece at time until the front and rear suspension angles match the stock C4's design ride height. When I get to that point, it will be interesting to see how many parts, and which ones I have left over. Then I will make adjustments from that point, either by weight reduction, or springs.

I guess that's one way to get the ride height you want, just add or remove weight from the car. :D

[Rick_L]

don't remember the outcome.

It was correct then, and you agreed. The math hasn't changed despite both Obama's and Trump's election. :eek:

[Rick_L]

By the way, this IS a static calculation. Dynamic is when time is introduced - and along with it velocity, acceleration, frequency response, etc.

[chevynut]

Rick, I think you read about 10% of what I post. I said the static forces are determined by the motion ratio and the wheel rate is determined by the SQUARE of the motion ratio in my first post on this thread. Are you arguing otherwise?

There is no reason to square the motion ratio for a static calculation. Al you need to do is calculate the axial load on the coilover spring, which is determined by the angle factor and the leverage of the lower a-arm, which is nothing but the ratio of the two dimensions. There is no reason you have to square that ratio for the STATIC calculation. Once you have the load, you just divide that by the total spring compression at the desired settings (shock compression plus preload).

Take a look at the Hyperco site I linked and it shows the formulas correctly. The Koni website was put together by some idiot who doesn't understand engineering and it's full of BS crap. You don't extend the balljoint centers to intersect the shock axis and use that for D2...if you did then SAI would come into play which is DOES NOT. The spindle simply pulls upward on the balljoint regardless of SAI. I mentioned the other errors above...they should be ashamed to post that crap on the internet.

[chevynut]

By the way, this IS a static calculation. Dynamic is when time is introduced - and along with it velocity, acceleration, frequency response, etc.


No, dynamic is when motion is introduced. Time has nothing to do with spring rate or wheel rate calculations.