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Wepeel · 09-04-2013, 04:46 PM

I put together some calculations to give some context to spring rates, swaybar rates, wheel rates, and undamped frequencies.

Here are some assumptions I used for to calculate wheel rates due to springs and bars:

Front Spring Motion Ratio
1.0
Front Spring Angle (based on nominal SAI)
15.5 degrees
Front Bar Motion Ratio (same as Front Spring combined MR due to attachment to the strut):
0.964
Rear Spring Motion Ratio (measured)
0.78
Rear Bar Motion Ratio (measured)
0.59
Rear Spring Angle (still needs to be verified – I know it’s not perfectly vertical but it doesn’t look that large either; as long as it remains smallish it shouldn’t affect calcs much)
4 degrees

BRZ Spring Rates (measured by Vorshlag http://www.vorshlag.com/forums/showp...16&postcount=5)
160 Front / 200 Rear lb/in
FRS Spring Rates (measured by Vorshlag http://www.vorshlag.com/forums/showp...16&postcount=5)
125 Front / 220 Rear lb/in

Front Swaybar Diameter
18 mm
Rear Swaybar Diameter
14 mm

Front Swaybar Spring rate (measured by Eibach http://www.phastekperformance.com/20...-sway-bars.htm)
141 lb/in
Rear Swaybar Spring Rate (measured by Eibach http://www.phastekperformance.com/20...-sway-bars.htm)
113 lb/in

To get wheel rates, I multiplied the rated spring rate by the square of the product of the Motion Ratio and Cosine of the Spring Angle. The calcs:

Code:

             Spring  Spring  Wheel   Wheel
             Rate    Rate    Rate    Rate    Front    Rear
             Front   Rear    Front   Rear    Dist     Dist
Springs      (lb/in) (lb/in) (lb/in) (lb/in) (%)      (%)
-----------------------------------------------------------
OEM BRZ      160     200     149     121     0.55     0.45
OEM FRS      125     220     111     133     0.46     0.54

Code:

          Bar   Bar    Bar  Bar    Wheel   Wheel
          Dia   Rate   Dia  Rate   Rate    Rate    Front Rear
          Front Front  Rear Rear   Front   Rear    Dist  Dist
Bars      (in)  (lb/in)(in) (lb/in)(lb/in) (lb/in) (%)   (%)
-------------------------------------------------------------
OEM FRZ      18   141    14   113    262    79     0.77  0.23

The wheel rate for the bars is the wheel rate in roll. For one-wheel bump, those bar wheel rates would be halved. The reason they're doubled in the roll calculation is because in roll, as the loaded side (outside) travels in bump, the unloaded side (inside) droops the same amount, so it's actually double the "twist".

The "Front Dist" and "Rear Dist" columns indicate how biased the total wheel rates (front + rear) are front to rear. This isn't that relevant without weights (and hence frequencies which I'll touch on below), but it's interesting to compare it to the 55/45 weight distribution of the car. I've seen with other cars how wheel rate front/rear bias closely matches the weight distribution of the car, which makes sense.

Notice how much work the front bar is doing – it provides a lot more wheel rate than the springs do. So looking at the springs and bars combined in roll:

Code:

                                            Front  Rear
                                            Spring Spring
                                 Front Rear Roll   Roll
System    WRf    WRr     WRtot   Dist  Dist Share  Share
Config    (lb/in)(lb/in) (lb/in) (%)   (%)  (%)    (%)
---------------------------------------------------------
OEM BRZ     410   200    610   0.67   0.33  0.36  0.61
OEM FRS     373   212    585   0.64   0.36  0.30  0.63

WRf = Wheel Rate Front
WRr = Wheel Rate Rear
WRtot = WRf + WRr

The BRZ is overall about 4% stiffer than the FRS, but it is also more front biased. What the “Roll Share” columns are calculating is how much of the wheel rates in roll are due to the springs and bars (i.e. for the BRZ, in the front, the springs are providing 36% of the roll resistance, while the bar is providing the remaining 64% of the roll resistance – so ~2/3 of the roll resistance is coming from the bar). For the rears the springs are doing more work than the bar. If you run the calculations for front and rear combined, the bars are providing 56% of the total roll resistance for the BRZ and 58% for the FRS.

Adding a little more context, it's useful to calculate the undamped natural frequency of the suspension as a normalization to determine "how stiff" a car actually is. Calculating the NF takes into account spring rates and weights and results in a metric that can be compared across different cars. And in general, there are ranges of frequencies that are desirable based on what you want to do with the car (smooth ride, sporty street, low speed track, high speed track, etc).

Assumptions: I started with the published curb weight of the BRZ Limited (2776 lbs), assumed a 55/45 weight distribution, 90 lbs front unsprung mass, 83 lbs rear unsprung mass, 60 lbs less over the rear axle due to lower fuel, and added 145 lbs to both axles for driver weight. Also assumed symmetrical left/right weights. This comes to corner weights of 707 lbs per front and 548 lbs per rear. Obviously more accurate numbers could be attained from corner weighting. The equation to calculate NF is 3.13*sqrt(kw/m), where kw is the corner wheel rate in lb/in, and m is the corner weight in lbs. Using these corner weights and the wheel rates above:

Code:

System      Front NF  Rear NF  Front NF  Rear NF
Config      Ride      Ride     Roll      Roll
------------------------------------------------
OEM BRZ     1.43     1.47     2.38     1.89
OEM FRS     1.24     1.54     2.27     1.95

The “Ride” NFs (Hz) are based on the spring only, the “Roll” NFs are for the springs and bars in roll. I actually have never seen that “Roll Frequency” metric anywhere before, but thought it would be useful to see the overall roll stiffness normalized.

The information isn’t that surprising – Ride NFs are right in line with sporty cars (similar to a stock 2008 STI), Roll NFs are also similar, although for the twins there is a lot less rear roll stiffness (mainly due to the disproportionately small bar).

So knowing all the equations and motion ratios, it should be straightforward to calculate individual setups. E.g., adding only a Strano front bar to the mix (advertised as 85% stiffer than the stock front and common for stock class autocrossers) increases overall roll stiffness by 36% and biases the overall roll rate to 76% front (up from 67%). Another setup – the RCE T2s that come in 400/400 result in NFs of 2.27 Hz Front and 2.16 Hz rear.

Check my numbers?

09-04-2013, 04:46 PM	#107
Wepeel Senior Member Join Date: May 2012 Drives: '13 BRZ Ltd Location: PA Posts: 458 Thanks: 265 Thanked 230 Times in 117 Posts Mentioned: 8 Post(s) Tagged: 0 Thread(s)	Springs, Swaybars, Wheel Rates and Frequency I put together some calculations to give some context to spring rates, swaybar rates, wheel rates, and undamped frequencies. Here are some assumptions I used for to calculate wheel rates due to springs and bars: Front Spring Motion Ratio 1.0 Front Spring Angle (based on nominal SAI) 15.5 degrees Front Bar Motion Ratio (same as Front Spring combined MR due to attachment to the strut): 0.964 Rear Spring Motion Ratio (measured) 0.78 Rear Bar Motion Ratio (measured) 0.59 Rear Spring Angle (still needs to be verified – I know it’s not perfectly vertical but it doesn’t look that large either; as long as it remains smallish it shouldn’t affect calcs much) 4 degrees BRZ Spring Rates (measured by Vorshlag http://www.vorshlag.com/forums/showp...16&postcount=5) 160 Front / 200 Rear lb/in FRS Spring Rates (measured by Vorshlag http://www.vorshlag.com/forums/showp...16&postcount=5) 125 Front / 220 Rear lb/in Front Swaybar Diameter 18 mm Rear Swaybar Diameter 14 mm Front Swaybar Spring rate (measured by Eibach http://www.phastekperformance.com/20...-sway-bars.htm) 141 lb/in Rear Swaybar Spring Rate (measured by Eibach http://www.phastekperformance.com/20...-sway-bars.htm) 113 lb/in To get wheel rates, I multiplied the rated spring rate by the square of the product of the Motion Ratio and Cosine of the Spring Angle. The calcs: Code: Spring Spring Wheel Wheel Rate Rate Rate Rate Front Rear Front Rear Front Rear Dist Dist Springs (lb/in) (lb/in) (lb/in) (lb/in) (%) (%) ----------------------------------------------------------- OEM BRZ 160 200 149 121 0.55 0.45 OEM FRS 125 220 111 133 0.46 0.54 Code: Bar Bar Bar Bar Wheel Wheel Dia Rate Dia Rate Rate Rate Front Rear Front Front Rear Rear Front Rear Dist Dist Bars (in) (lb/in)(in) (lb/in)(lb/in) (lb/in) (%) (%) ------------------------------------------------------------- OEM FRZ 18 141 14 113 262 79 0.77 0.23 The wheel rate for the bars is the wheel rate in roll. For one-wheel bump, those bar wheel rates would be halved. The reason they're doubled in the roll calculation is because in roll, as the loaded side (outside) travels in bump, the unloaded side (inside) droops the same amount, so it's actually double the "twist". The "Front Dist" and "Rear Dist" columns indicate how biased the total wheel rates (front + rear) are front to rear. This isn't that relevant without weights (and hence frequencies which I'll touch on below), but it's interesting to compare it to the 55/45 weight distribution of the car. I've seen with other cars how wheel rate front/rear bias closely matches the weight distribution of the car, which makes sense. Notice how much work the front bar is doing – it provides a lot more wheel rate than the springs do. So looking at the springs and bars combined in roll: Code: Front Rear Spring Spring Front Rear Roll Roll System WRf WRr WRtot Dist Dist Share Share Config (lb/in)(lb/in) (lb/in) (%) (%) (%) (%) --------------------------------------------------------- OEM BRZ 410 200 610 0.67 0.33 0.36 0.61 OEM FRS 373 212 585 0.64 0.36 0.30 0.63 WRf = Wheel Rate Front WRr = Wheel Rate Rear WRtot = WRf + WRr The BRZ is overall about 4% stiffer than the FRS, but it is also more front biased. What the “Roll Share” columns are calculating is how much of the wheel rates in roll are due to the springs and bars (i.e. for the BRZ, in the front, the springs are providing 36% of the roll resistance, while the bar is providing the remaining 64% of the roll resistance – so ~2/3 of the roll resistance is coming from the bar). For the rears the springs are doing more work than the bar. If you run the calculations for front and rear combined, the bars are providing 56% of the total roll resistance for the BRZ and 58% for the FRS. Adding a little more context, it's useful to calculate the undamped natural frequency of the suspension as a normalization to determine "how stiff" a car actually is. Calculating the NF takes into account spring rates and weights and results in a metric that can be compared across different cars. And in general, there are ranges of frequencies that are desirable based on what you want to do with the car (smooth ride, sporty street, low speed track, high speed track, etc). Assumptions: I started with the published curb weight of the BRZ Limited (2776 lbs), assumed a 55/45 weight distribution, 90 lbs front unsprung mass, 83 lbs rear unsprung mass, 60 lbs less over the rear axle due to lower fuel, and added 145 lbs to both axles for driver weight. Also assumed symmetrical left/right weights. This comes to corner weights of 707 lbs per front and 548 lbs per rear. Obviously more accurate numbers could be attained from corner weighting. The equation to calculate NF is 3.13*sqrt(kw/m), where kw is the corner wheel rate in lb/in, and m is the corner weight in lbs. Using these corner weights and the wheel rates above: Code: System Front NF Rear NF Front NF Rear NF Config Ride Ride Roll Roll ------------------------------------------------ OEM BRZ 1.43 1.47 2.38 1.89 OEM FRS 1.24 1.54 2.27 1.95 The “Ride” NFs (Hz) are based on the spring only, the “Roll” NFs are for the springs and bars in roll. I actually have never seen that “Roll Frequency” metric anywhere before, but thought it would be useful to see the overall roll stiffness normalized. The information isn’t that surprising – Ride NFs are right in line with sporty cars (similar to a stock 2008 STI), Roll NFs are also similar, although for the twins there is a lot less rear roll stiffness (mainly due to the disproportionately small bar). So knowing all the equations and motion ratios, it should be straightforward to calculate individual setups. E.g., adding only a Strano front bar to the mix (advertised as 85% stiffer than the stock front and common for stock class autocrossers) increases overall roll stiffness by 36% and biases the overall roll rate to 76% front (up from 67%). Another setup – the RCE T2s that come in 400/400 result in NFs of 2.27 Hz Front and 2.16 Hz rear. Check my numbers?