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How to choose springs for a street/track car

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Old 01-12-2011, 09:34 AM
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Default How to choose springs for a street/track car

I continued my investigation in search of the optimal spring rates for a primarily street-driven car that is also driven at the track.

I'm illiterate in the matter, so the experts are welcomed to chip in.

I learned a great deal from this search, so I wanted to share the information obtained. It may be a little complicated, so I tried to simplify things, to help people like me, understand things a little better.

So, here is what I learned, so far...

1. Spring rate is the actual force needed to compress a spring. It is usually measured in pounds per inch (lb/in) or kilograms per millimeter (Kg/mm).

2. A more meaningful value than the spring rate itself, is the wheel rate, which is the spring rate measured at the wheel.

3. The wheel rate is calculated using the motion ratio, which in any given axle, describes the amount of shock travel for a given amount of wheel travel.

4. In the case of the S2000, the motion ratios have been measured at:

Front: 0.70
Rear: 0.67

5. In vertically installed springs, the wheel rate is calculated using the following formula:

WR = SR x MR^2 x ACF

Where:

WR: Wheel rate
SR: Spring rate (lb/in)
MR: Motion ratio
ACF: Angle Correction Factor. This is the cosine of the angle (a) between the spring and the vertical plane.

6. Since in the S2000, the spring is mounted almost vertically, for practical purposes, you could asume this angle as zero, and ignore this value, since the
cos(0) is 1.

7. For the OCD's here, I went and measured this angle. It's about 20 degrees front and rear. At stock height. Therefore:

cos (20) = 0.94

ACF = 0.94

8. Before choosing a spring rate, you have to choose your desired spring frequencies, front and rear.

9. The spring frequency is the undamped natural frequency (up and down movement) of the spring in ride. This will determine how the car will react over bumps.

10. Lower spring frequencies provide softer ride with more mechanical grip but slower transient suspension response.

11. As a gross estimate, these are the spring frequencies usually used (in Hz, or cycles per second).

0.5-1.5 Hz : Passenger cars
1.5 - 2.0 Hz : Dual-purpose street/track cars
2.0 - 2.5 Hz : Dedicated track/race cars
2.5+ Hz : Downforce racecars

12. For street driven cars (with comfort as the primary objective), it is recommended to run higher spring frequencies in the rear. The reason for this is that the front will almost always hit a bump first. With equal frequencies, the timing of the front and rear spring oscillations will be off, making the chassis pitch fore and aft, creating an unpleasant rocking sensation. This is usually fixed by running a higher rear frequency which would allow the back to oscillate faster and "catch up" with the front. This explains why Honda used rear biased springs for the S2000 (except for the CR which is their track-oriented model, and comfort is less of an issue).

13. For comfort at the primary objective, it is recommended to have rear springs with 10-20% higher frequency compared to the front.

14. Once you choose your desired spring frequency, you can now calculate your effective wheel rate.

WR = (SF/187.8)^2 x SW

Where:

WR = Wheel rate
SF = Spring frequency in cycles per minute, or CPM (just multiply Hz x 60)
SW = Sprung weight for a given corner

15. From the previously given formula to calculate the wheel rate, we can now deduct this final formula to find the spring rate needed:

SR = SF^2 x SW / [ACF x (MR x 187.8)^2]

Where:

SR: Spring rate (lb/in)
SF: Spring frequency (in CPM)
SW: Sprung Weight (lb)
ACF: Angle correction Factor
MR: Motion ratio

16. You can estimate your corner's sprung weight (SW) by subtracting its unsprung weight (roughly 7.5% of the corner's weight) from the total corner's weight. In the case of the S2000, due to its 50/50 weight distribution, the sprung weight (SW) for each corner is grossly equal on all corners, aproximately 23.125% of the car's weight. Don't forget to add the driver's weight to the car's dry weight to get the actual car's weight.

Corner Sprung Weight = Total Car Weight (with driver) x 0.23125

17. These resulting initial spring rates are just an estimate. These calculations are just used as a starting point. Real world testing is the best way to find your optimal rates, based on your priorities. These numbers may mean nothing to you if you primarily track your car, as comfort is not an issue in that case.

18. This topic was made for people who want to improve the performance of their cars without disturbing too much the drivability of the vehicle during street-driving (which is primarily measured by straight line comfort).

19. The turning balance (behavior during a turn, i.e. oversteer/understeer) can be further tuned by means of sway bars (for example, you may need a stiffer bar in the front, or softer in the rear, or both if you need to correct oversteer).

20. Example: For a 2850 lb car, with a 150 lb driver, and goal spring frequencies of 2.0 Hz rear and 1.9 Hz front, the spring rates would be 574 lb/in rear and 475 lb/in front.

21. To convert your new found spring rates from lb/in to Kg/mm, just divide by 55.88.

SR (lb/in) = SR (kg/mm) / 55.88

22. Good reading:

OptimumG Tech Tips

Stretch's Notes


Happy Motoring!
Old 01-12-2011, 10:27 AM
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Old 01-12-2011, 10:51 AM
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Originally Posted by Naka,Jan 12 2011, 01:34 PM
I continued my investigation in search of the optimal spring rates for a primarily street-driven car that is also driven at the track.

I'm illiterate in the matter, so the experts are welcomed to chip in.

I learned a great deal from this search, so I wanted to share the information obtained. It may be a little complicated, so I tried to simplify things, to help people like me, understand things a little better.

So, here is what I learned, so far...

1. Spring rate is the actual force needed to compress a spring. It is usually measured in pounds per inch (lb/in) or kilograms per millimeter (Kg/mm).

2. A more meaningful value than the spring rate itself, is the wheel rate, which is the spring rate measured at the wheel.

3. The wheel rate is calculated using the motion ratio, which in any given axle, describes the amount of shock travel for a given amount of wheel travel.

4. In the case of the S2000, the motion ratios have been measured at:

Front: 0.70
Rear: 0.67

5. In vertically installed springs, the wheel rate is calculated using the following formula:

WR = SR x MR^2 x ACF

Where:

WR: Wheel rate
SR: Spring rate (lb/in)
MR: Motion ratio
ACF: Angle Correction Factor. This is the cosine of the angle (a) between the spring and the vertical plane.

6. Since in the S2000, the spring is mounted almost vertically, for practical purposes, you could asume this angle as zero, and ignore this value, since the
cos(0) is 1.

7. For the OCD's here, I went and measured this angle. It's about 20 degrees front and rear. At stock height. Therefore:

cos (20) = 0.94

ACF = 0.94

8. Before choosing a spring rate, you have to choose your desired spring frequencies, front and rear.

9. The spring frequency is the undamped natural frequency (up and down movement) of the spring in ride. This will determine how the car will react over bumps.

10. Lower spring frequencies provide softer ride with more mechanical grip but slower transient suspension response.

11. As a gross estimate, these are the spring frequencies usually used (in Hz, or cycles per second).

0.5-1.5 Hz : Passenger cars
1.5 - 2.0 Hz : Dual-purpose street/track cars
2.0 - 2.5 Hz : Dedicated track/race cars
2.5+ Hz : Downforce racecars

12. For street driven cars (with comfort as the primary objective), it is recommended to run higher spring frequencies in the rear. The reason for this is that the front will almost always hit a bump first. With equal frequencies, the timing of the front and rear spring oscillations will be off, making the chassis pitch fore and aft, creating an unpleasant rocking sensation. This is usually fixed by running a higher rear frequency which would allow the back to oscillate faster and "catch up" with the front. This explains why Honda used rear biased springs for the S2000 (except for the CR which is their track-oriented model, and comfort is less of an issue).

13. For comfort at the primary objective, it is recommended to have rear springs with 10-20% higher frequency compared to the front.

14. Once you choose your desired spring frequency, you can now calculate your effective wheel rate.

WR = (SF/187.8)^2 x SW

Where:

WR = Wheel rate
SF = Spring frequency in cycles per minute, or CPM (just multiply Hz x 60)
SW = Sprung weight for a given corner

15. From the previously given formula to calculate the wheel rate, we can now deduct this final formula to find the spring rate needed:

SR = SF^2 x SW / [ACF x (MR x 187.8)^2]

Where:

SR: Spring rate (lb/in)
SF: Spring frequency (in CPM)
SW: Sprung Weight (lb)
ACF: Angle correction Factor
MR: Motion ratio

16. You can estimate your corner's sprung weight (SW) by subtracting its unsprung weight (roughly 7.5% of the corner's weight) from the total corner's weight. In the case of the S2000, due to its 50/50 weight distribution, the sprung weight (SW) for each corner is grossly equal on all corners, aproximately 23.125% of the car's weight. Don't forget to add the driver's weight to the car's dry weight to get the actual car's weight.

Corner Sprung Weight = Total Car Weight (with driver) x 0.23125

17. These resulting initial spring rates are just an estimate. These calculations are just used as a starting point. Real world testing is the best way to find your optimal rates, based on your priorities. These numbers may mean nothing to you if you primarily track your car, as comfort is not an issue in that case.

18. This topic was made for people who want to improve the performance of their cars without disturbing too much the drivability of the vehicle during street-driving (which is primarily measured by straight line comfort).

19. The turning balance (behavior during a turn, i.e. oversteer/understeer) can be further tuned by means of sway bars (for example, you may need a stiffer bar in the front, or softer in the rear, or both if you need to correct oversteer).

20. Example: For a 2850 lb car, with a 150 lb driver, and goal spring frequencies of 2.0 Hz rear and 1.9 Hz front, the spring rates would be 574 lb/in rear and 475 lb/in front.

21. To convert your new found spring rates from lb/in to Kg/mm, just divide by 55.88.

SR (lb/in) = SR (kg/mm) / 55.88

22. Good reading:

OptimumG Tech Tips

Stretch's Notes


Happy Motoring!
Does all your math account for weight distribution? I don't see that being factored in...
Old 01-12-2011, 11:09 AM
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Originally Posted by RedCelica,Jan 12 2011, 02:51 PM
Does all your math account for weight distribution? I don't see that being factored in...
Actually I did.

In paragraph #16, I mention that you can grossly estimate your corner sprung weight by subtracting 7.5% from the total (measured) corner weight (or multiplying the corner weight x 0.925).

For the sake of simplicity, on my example, I assumed a stock car, with stock weight and stock 50:50 weight distribution (25% of the total weight in each corner).

My apologies for not being clear enough.
Old 01-12-2011, 04:09 PM
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Looks about right. In part 5, I use WR = SR x (MR x ACF)^2 (i.e. square both factors), but I've seen it both ways. I'll look into it some more tonight. In part 15, you can delete the factor of 187.8.

I got the same value as you did for ACF. For unsprung weight, note that on the S2000 it's more like 12% -- not because the unsprung bits are so heavy, but because the rest of the car is so light. I guesstimate 80-90 lbs per corner: wheel/tire (40+lbs), shock/spring and lower arm (20ish), brake rotor/caliper (20ish), and hub/axle (5-10ish).

Finally, keep in mind that the ride frequency ranges you gave are subjective, having evolved over the years along with the public's taste (Milliken & Milliken used to state that only racecars would use 1.5 Hz or higher). Also, they're only the starting point for spring design, since springs are key not just to ride but to roll. But that's a discussion for another day...
Old 01-12-2011, 05:54 PM
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Originally Posted by Naka,Jan 12 2011, 03:09 PM
Actually I did.

In paragraph #16, I mention that you can grossly estimate your corner sprung weight by subtracting 7.5% from the total (measured) corner weight (or multiplying the corner weight x 0.925).

For the sake of simplicity, on my example, I assumed a stock car, with stock weight and stock 50:50 weight distribution (25% of the total weight in each corner).

My apologies for not being clear enough.
Maybe I'm over-generalizing here...but what if the weight dis. is not 50/50...does the equation still work? Or do you have to change the 23.125% number? I've always assumed the best handling sus. setups were equal f/r sr's
Old 01-12-2011, 07:44 PM
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Originally Posted by twohoos,Jan 12 2011, 08:09 PM
Looks about right. In part 5, I use WR = SR x (MR x ACF)^2 (i.e. square both factors), but I've seen it both ways. I'll look into it some more tonight. In part 15, you can delete the factor of 187.8.
Thanks for your input! Greatly appreciated.

I obtained the formulas from the Eibach website:

Eibach Suspension Worksheet
Old 01-12-2011, 08:27 PM
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Originally Posted by RedCelica,Jan 12 2011, 09:54 PM
Maybe I'm over-generalizing here...but what if the weight dis. is not 50/50...does the equation still work? Or do you have to change the 23.125% number? I've always assumed the best handling sus. setups were equal f/r sr's
No, you are 100% correct. I was the one who was over-generalizing, for the purpose of making things easier for simple minds like mine.

Ideally, you want to corner weight your car, and then weight your unsprung mass, as Twohoos above did. Then use those numbers and deduct your sprung mass.

To measure the actual unsprung mass, you will need to weight your caliper/rotor/wheel/tire/knuckle and add this to 50% of the weight of the spring/shock/arms/axle.

Although a lot of people may do that, most people here, like me, won't. So I just gave a "guesstimate" of 7.5% of the actual corner weight, based on my readings.

Twohoos states that it is more like 12% for our car, or 90 lbs, so I stand corrected, until somebody confronts him. Obviously your mileage may vary depending on wheel and tire sizes, etc.

As I stated in the original post, my numbers were just a gross estimate.

Let's review my example. If a stock car weighs 3,000 with driver, and the unsprung weight is about 90lb per corner, the weight distribution is 50:50, and spring frequencies of 2.0 Hz rear and 1.9 Hz front are chosen; then the spring rates would be 640 lb/in rear and 528 lb/in front (compared to 574R/475F on my original calculation).

But at the end, if the biggest portion of the "guess" is when choosing your spring frequency, then there is not much difference. If you look at both examples, for a spring frequency of around 2 Hz, the needed spring rates would be 600R and 500F.

I honestly did not write this post for the suspension guru's. They already know all of this. They've probably tried different things already. I was just trying to give a starting point to enthusiast like me, that don't plan to dismantle their cars just to find out their "actual" unsprung mass.

But your input is greatly appreciated. It allows me to correct/clarify the inaccuracies.
Old 01-13-2011, 12:04 AM
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^Shouldn't the required spring rate decrease if the sprung weight decreased? Or did you also square the ACF?

Speaking of ACF, just checked M&M and Puhn and nothing conclusive about squaring or not... The basic question is whether the moment (force) experienced by the spring is affected by the shock's mounting angle to the chassis, or if it depends solely on the lower-arm mounting point. (We know that the amount the spring is compressed depends on both factors; just not sure about the force as seen by the canted spring.) Either way, as you noted -- it's only 6%, so well within the error of our calculations!
Old 01-13-2011, 06:04 AM
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Originally Posted by twohoos,Jan 13 2011, 04:04 AM
^Shouldn't the required spring rate decrease if the sprung weight decreased? Or did you also square the ACF?
You are right, Sir!

I went and looked back at my scrap notes. My last example was accurate. The first one looked "lower" because I somehow read my estimated 694 lbs of sprung corner weight as 594 lbs. Duh!

Anyhow, thanks to your input, that first example was already corrected for the more appropriate unsprung weight, so the second example is the most accurate.

Even with those miscalculations, and estimates, it seems to me that 600F and 500F would be a good place to start.

Thanks!


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