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Old 01-17-2013, 04:10 PM   #1
Shankenstein
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Developing a Proper Suspension Model

Although this effort may seem worthless to some 86ers, I'd like to start a thread that compiles known data about the stock vehicle and uses this to develop a virtual model of the car.

Available programs:
  • ADAMS - Powerful and complex. Full vehicle dynamics
  • Lotus - Simple and effective. Awkward interface.
  • WinGeo3 - Simple and effective. Akward interface.
  • SolidWorks + Cosmos - Powerful and complex. Takes alot of work to get meaningful results.
  • Optimum K - Never used it.
  • SuspensionAnalyzer - Never Used it.
  • DIY Excel - Hardcore Mode. Requires alot of brains and time.
Similar discussions have been done HERE. I'm comfortable with Lotus. WinGeo3 is standard for alot of FSAE guys. ADAMS is for ballers. Whatever people would be most comfortable with, we can use.

The goal would be to analyze the stock package and look at how various aftermarket options would perform. Since each person has a different goal (autocross, street, rally, drift, etc) their interest will push the project in that direction. I'll be pushing the limits of SCCA street tire.

The Facts (in 'Murika units and Sissy units):
Curb Weight (FR-S, no spare/tools/mats, minimal gas) = 2645 lbs or 1200 kg LINK
Corner Weights:
LF = 823 lbs (701 ideal) or 373.3 kg (318.0 ideal) or 3660.9 N (3118.2 ideal)
RF = 684 lbs (701 ideal) or 310.3 kg (318.0 ideal) or 3042.6 N (3118.2 ideal)
LR = 513 lbs (622 ideal) or 232.7 kg (282.1 ideal) or 2281.9 N (2766.8 ideal)
RR = 625 lbs (622 ideal) or 283.5 kg (282.1 ideal) or 2780.1 N (2766.8 ideal)
Unsprung Weight: (best guess - LINK )
83 lbs or 37.6 kg or 369.2 N per corner
Sprung Weight:
LF = 740 lbs (618 ideal) or 335.7 kg (280.4 ideal) or 3291.7 N (2749 ideal)
RF = 601 lbs (618 ideal) or 272.4 kg (280.4 ideal) or 2673.4 N (2749 ideal)
LR = 430 lbs (539 ideal) or 195.1 kg (244.5 ideal) or 1912.7 N (2397.6 ideal)
RR = 542 lbs (539 ideal) or 245.9 kg (244.5 ideal) or 2410.9 N (2397.6 ideal)

Dampers = SHOWA non-inverted, twin-tube, low-pressure Nitrogen, conventional strut

Shock Dyno:


Suspension Spring Rates: LINK
Front = 131 lbs/in or or 22970 N/m
Rear = 211 lbs/in or 36998 N/m


Spring Dimensions: Link to Bordom.is.me's post
FRONT:
  • External Diameter = 4.625"
  • Internal Coil Diameter = 3.625"
  • Wire Diameter = .5"
  • Free Length = 11.625"
  • Active Coils = 5 (excluding grinding of bottom coil)
REAR:
  • External Diameter = 4.125"
  • Internal Coil Diameter = 3.125"
  • Wire Diameter = .5"
  • Free Length = 10.5"
  • Active Coils = 4 (excluding grinding of bottom coil)
Tire Spring Rates: (FSAE guru states 350 N/mm for passenger tires at passenger pressures. I concur.)
30 psi = 6500 lbs/in or 114000 kg/m
45 psi = ~10000 lbs/in or 175000 kg/m
Sway Bar Spring Rate:
Front = 141 lbs/in or 2467 kg/m

Rear = 113 lbs/in or 1978 kg/m
Effective Wheel Rate (in roll, including sway bar):
Front (FR-S) = 373 lbs/in or 6528 kg/m (70% from sway bar)

Front (BRZ) = 410 lbs/in or 7175 kg/m (64% from sway bar)

Rear (FR-S) = 212 lbs/in or 3710 kg/m (37% from sway bar)
Rear (BRZ) = 200 lbs/in or 3500 kg/m (39% from sway bar)
Caster Angle: Link
Front = -5.937 deg
Roll Center Height: Link
Front = 3.140" (stock height) --> ground plane (1" of compression)
Spring Angle:
Front = 15.5 deg

Rear = 4 deg
Spring Motion Ratio:
Front = 1.050 (2.5" compression) --> 0.997 (1.5" compression) --> 0.95 (OEM height) Link

Rear = 0.768 (2" compression) --> 0.763 (OEM height) --> 0.758 (2" rebound) LINK
Sway Bar Motion Ratio:
Front = 0.92

Rear = 0.59
Natural Frequency (in ride):
Front (FR-S) = 1.24 Hz

Front (BRZ) = 1.43 Hz
Rear (FR-S) = 1.54 Hz

Rear (BRZ) = 1.47 Hz
Natural Frequency (in roll):
Front (FR-S) = 2.27 Hz

Front (BRZ) = 2.38 Hz
Rear (FR-S) = 1.95 Hz

Rear (BRZ) = 1.89 Hz
Tire Info:
215/45-17 Michelin Primacy HP LINK
Section Width = 8.46 in or 0.215 m
Contact Width = 7.5 in or 0.1905 m via TireRack measurement
Contact Length (at 60 mph and stock pressure) = ~5.71 in or 0.145 m
Overall Diameter = 24.7 in or 0.6274 m
Load Rating = 87W SL (168 mph or or 270 kph)
UTQG = 240 A A (hmm... A?)
Max Load (at rated pressure) = 1201 lbs or 545 kg
Max Rated Pressure = 51 psi
Tread Depth = 9.5/32 in
Material = Green X - Low Rolling Resistance
Wheel Info:
Wheel Diameter = 17 in or 0.432 m
Wheel Width = 7 in or 0.178 m
Wheel Offset = +48 mm or 1.89 in or 0.048 m
Track Width: LINK
Front = 59.8 in or 1.51m
Rear = 60.6 in or 1.54m
Roll Bar Diameter: LINK
Front = 0.71 in or 0.018m
Rear = 0.55 in or 0.014m
Center of Gravity Height = 18.1 in or 0.46 m LINK

Roll Center Height:
Front = 2.1 in
Rear = 3.8 in
Wheelbase = 101.2 in or 2.5705 m LINK

Suspension Travel:
Bump Travel = 2.5 in or 0.1 m
Rebound Travel = 3.5 in or 0.15 m
Max Roll Angle = +/- 2.3 deg
Max Pitch Angle = 0.9 deg (braking)
Roll Resistance on Front: 61%
Braking on Front = 60%
Anti-dive Under Braking: 5% (front)
Anti-lift Under Braking: 196% (rear)
Anti-squat Under Acceleration: 64% (rear)
Steering Ratio: 14.3 (on center) - 14.4 (at 90 deg)

Distance (axial) between lower strut bolts = 2.4" (or 60.5 mm)

Thickness of lower flange = 1 in (or 25.4 mm)

Distance (radial) from strut center to lower bolt = 2.4 in (or 60.7 mm)

Distance (axial) from AST's lower bolt to hat mount = 15.4 in (or 392 mm)

Upper strut thread:
- AST = M12x1.25-25, with 1 mm of thread relief, 5 mm long (for camber plate)
- KW = M14x1.5-30, with 0 mm of thread relief, 10 mm long (for camber plate)

Length of AST's spring = 7.1 in (or 181 mm)

Distance (axial) from lower bolt to sway bar mount = 4.5 in (or 115 mm)

Distance (radial) from strut axis to sway bar mount = 1.97 in (or 50 mm)

Diameter of sway bar mount hole = 0.4 in (or 10.2 mm)

Here's a cool MATLAB function that helps you simulate shock dyno graphs:
function y=critdamp(cwlbs,srppi,spmr,shmr,lsd,knee,hsd)
%cwlbs=corner weight, lbs minus unsprung for more accuracy
%srppi=spring rate, lbs per inch
%spmr=spring motion ratio
%shmr=shock motion ratio
%lsd=low speed damping, percentage of critical
%hsd=high speed damping, percentage of critical
%knee=location of knee, in inch per second

lbf2n=4.448; % 1 lbf = 4.448 newtons
m2i=39.37; % 1 meter = 39.37 inch
p2kg=0.4536; % 1 lb=0.453 kg
if (spmr>1)+(shmr>1)
disp('Motion ratios must be less than 1, but I''ll convert it for you')
spmr=1/spmr;shmr=1/shmr;
end
wheelratestandard=srppi*spmr^2
wheelratemetric=wheelratestandard*lbf2n*m2i
cd=2*sqrt(wheelratemetric*cwlbs*p2kg)/lbf2n/m2i/shmr^2
vel=(0:0.1:20);

damp=lsd*cd*(0:0.1:knee);
hispeed=damp(end)+(0:0.1:20-knee)*cd*hsd;
damp=[damp hispeed(2:end)];
plot(vel,damp,'r','linewidth',2,'displayname',['LS:' num2str(lsd*100) '% Knee:' num2str(knee) ' ips HS:' num2str(hsd*100) '%'])
legend('off');legend('show','location','east')


Still looking for accurate suspension geometry coordinates (X,Y,Z). The current "best guess" is housed in a Google Docs spreadsheet: LINK

Special Thanks to MLA163, Wepeel, and Boredom.is.me for contributing measurements and discussion.

Last edited by Shankenstein; 02-24-2016 at 02:20 PM.
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Old 01-17-2013, 04:11 PM   #2
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Saved for pretty pictures!
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Old 01-17-2013, 04:33 PM   #3
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Quote:
Originally Posted by Shankenstein View Post
Tire Info:
245/45-17 Michelin Primacy HP
Section Width = 9.646 in
Contact Width at 60 mph = ~9.05 in LINK
Contact Length = ~6.05 in
215/45/17 my friend. 8.4" Section width...
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Old 01-17-2013, 04:52 PM   #4
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Sorry aboot that. I grabbed my info from the Car & Driver tire swap article:
LINK


Fixed and Thanks!
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Old 01-17-2013, 10:39 PM   #5
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The stock front swaybar is 18mm, rear is 14mm.
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Old 01-18-2013, 12:10 AM   #6
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The info I found from a Subaru forum suggested 17 and 13. Probably just difference in calipers and paint. Will change anyways.

How about a teaser, you say? Got the geometry style in... but no points or parameters have been entered.

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Old 01-18-2013, 10:12 AM   #7
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Updates made to suspension parameters, but not specific coordinates. Can I get a second set of eyes on this?

Requires peer review:
Bump Travel = 4 in or 0.1 m
Rebound Travel = 6 in or 0.15 m
Max Roll Angle = 6 deg
Braking on Front = 60%
Tire Rolling Radius = 9 in or 0.225 m

Still looking for suspension geometry coordinates (X,Y,Z), if anyone has logged them
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Old 01-18-2013, 01:25 PM   #8
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Right on brother.

I got 18mm / 14mm sways from measuring. I don't want to scuff up the coating to find pure steel, but would 1mm of powder coat be normal?
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Old 01-18-2013, 03:26 PM   #9
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I misspoke. Powdercoating is generally a couple mils thick, which would only give you 0.1 mm or so, even considering both sides and caliper inaccuracy.

Turns out that 3" bump, 4" rebound, 5 deg roll is more appropriate (for now).

Front View


Driver's Side View


Top View (Passenger Side)



Values are all still "eyeballed" from the pictures and general information.

Next, the rear suspension~!

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Old 01-18-2013, 03:55 PM   #10
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ooohhhhh...
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Old 01-18-2013, 04:21 PM   #11
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Mac-Strut motion ratio STILL isn't 1.00... if you are going to bother being accurate, be accurate.
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Old 01-18-2013, 04:31 PM   #12
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I've got an excel sheet I made as part of my senior project for my undergrad... I'll dig it up and run some of these numbers through and see what I get... We need an actual front motion ration though hehe
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Old 01-18-2013, 04:39 PM   #13
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According to racecomp, the front motion ratio is pretty darn close to 1. I'm not sure which side of one it sides on though.

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Old 01-18-2013, 04:51 PM   #14
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Airline food, I mean come on...

You're correct SCCABRZ192, it will be slightly less than one. What value that is... I couldn't tell you without some coordinates or parts in front of me.

This is not a traditional calculation for a wishbone, but the closest that I can imagine is to consider the knuckle and it's connections to be rigid. So, something like this:
distance from lower wishbone pivot axis to strut mount
Motion Ratio = --------------------------------------------------
distance from lower wishbone pivot axis to spindle center
Maybe 0.9? The good news is that a kinematic solver doesn't care about the parameter of motion ratio, it just solves a bunch of free body diagrams and spits out positions.

If you have more precise coordinates, I'd gladly put them in.

Last edited by Shankenstein; 01-18-2013 at 05:14 PM.
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