Measuring torsional stiffness of the MR2

Ever wonder just how stiff (or not stiff?) the MR2 chassis is?  Or how much difference various braces make to chassis stiffness?  Me too!

The Test Rig

Measuring torsional chassis stiffness is actually easier than one might think.  Support the chassis on 3 points, apply a torque to the end with the single support, and measure the deflection.  I will admit, I copied the basic method from a YouTube video. I supported the rear of the car with two jack stands under the rear mounting bolts of the rear cross member. 

Rear support for chassis stiffness testing on the MR2

 

For the front, I built a bar that attaches to the front strut rod pivot bolts.  The single front support goes under one end of this bar, and a dial indicator is positioned under the other attachment point (24" from the pivot).  Because the support and dial indicator are directly below the attachment points to the chassis, flex in the bar can be ignored and we can measure only the deflection of the chassis itself.  At the end of the bar (8ft from the single jack stand), a bucket of sand with a 25lb weight on top gives me a 90 lb weight that can easily be hung from the end of the bar in a repeatable manner.  This gives me 720ft-lb of torque on the chassis.

Front support and torque bar for chassis stiffness testing on the MR2


The Test

For each change that I made to the car, I tested three times.  Apply the weight, record the dial indicator.  Remove the weight, record the dial indicator.  Repeat 3x.  Usually there was not more than about .001" variation between these three tests.  I then lifted the car straight up using the 2-post lift, set it back down, and recorded the dial indicator.  I repeated that a second time.  This reading does not factor into the final results, it was more of a check for consistency, and a bit of a curiosity (I eventually stopped taking these measurements to save time, as they weren't really providing any useful data that I could see).

Each change to the car was made with the car on the lift.  It was then set back on the three jack stands, and an initial reading of the dial indicator taken.  As with the post test lift & reset readings, this does not factor into the final results.  It can be an interesting gauge of changing stiffness however, as it gives an idea of how much the chassis flexes under it's own weight. Changes in this reading from one test to another are at least interesting in this regard.  However since I am not applying a known torque when these readings are taken I cannot include this flex in any calculation of actual stiffness.


The Results

The results here are broken down into two sections.  First the individual contributions of a few of the bigger items such as strut bars and testing of my prototype tunnel braces (for sale soon!).  Each line on the table below represents a unique test configuration, with only the listed part added, removed, or changed.  That part was then reinstalled before the next change.  The tunnel braces and baseline configurations were tested at least a half dozen times each with the results averaged below.

  Average Deflection (in) Stiffness
 (ft-lb / deg)
Stiffness
(nm / deg)
% Change vs Baseline
Baseline 0.0480 6283 8520  
Remove Custom Rear Strut Bar 0.0488 6185 8387 -1.6%
Remove Custom Front Strut Bar 0.0520 5796 7859 -7.8%
Install STOCK Front Strut Bar 0.0494 6103 8276 -2.9%
Add Steel Tunnel Brace, 8 bolts 0.0467 6459 8759 2.8%
Add Steel Tunnel Brace, 10 bolts 0.0465 6486 8795 3.2%
Add Aluminum Tunnel Brace, 8 bolts 0.0467 6453 8750 2.7%
Add Aluminum Tunnel Brace, 10 bolts 0.0462 6523 8845 3.8%

One thing to note here is that the stock front strut bar is actually quite effective, providing about a 5% improvement in chassis stiffness on it's own.  Adding a cross bar to the front strut bar as my custom bar does gives you another couple percent improvement.  The rear bar alone only provides about a 1.6% improvement, although I found the driving feel (on the track) to be significantly improved by this particular rear brace (compared to a different, less effective rear brace).

The custom front and rear strut bars used in this testing were ones I made a few years ago.  Pictures from other blog posts for reference:

Custom front strut bar

Custom rear strut bar

The 8 bolt tunnel brace attaches at the 6 OEM locations, plus the two new ones at the front.  The 10 bolt adds two additional points rearward of the 6 stock points.  Interestingly the aluminum brace proved to be slightly more effective than the steel one (assuming all 10 bolts), probably as a result of it's increased thickness (3/16" vs 1/8").  It's also about half the weight. 

3.8% improvement may not sound like a lot, but it's more than 2x the benefit that I measured from the rear strut bar, and 1.3x the benefit of an aftermarket front strut bar (vs stock) so it should be quite significant.

Prototype Wilhelm Raceworks tunnel brace on SW20 MR2


In the following tests, each change builds on the previous.  I started with all braces installed, then removed things one at a time, starting with the strut bars and followed by the under body "cancer bars", the bracket under the fuel tank that supports the parking brake bell crank, then removed the T-tops, and even opened the doors.  I then reversed the process, installing each piece in the reverse order (I did skip a couple of steps here, installing all of the under body braces in a single step).  Where applicable, the results are averaged to create the table below (the raw data can be found at the end of this article).

  Average Deflection (in) Stiffness
 (ft-lb / deg)
Stiffness
(nm / deg)
% Change vs  Previous % Change vs Baseline
Baseline 0.0480 6283 8520    
Remove Front and Rear Strut Bars 0.0522 5781 7840 -8.0% -8.0%
Remove Front "Cancer Bars" 0.0530 5690 7716 -1.6% -9.4%
Remove Parking Brake Bracket 0.0530 5690 7716 0.0% -9.4%
Remove Rear "Cancer Bars" 0.0533 5655 7668 -0.6% -10.0%
Remove T-Tops 0.0538 5602 7597 -0.9% -10.8%
Open Doors 0.0557 5418 7347 -3.3% -13.8%

 

The "cancer bars" (so called because they are so often rusted out!), seem to make more of a difference than you might expect.  Not much of an effect, but some. 

I tested the removal of the parking brake bracket for a couple of reasons.  One, I had removed it along with the parking brake system earlier this year for weight reduction reasons.  Two, the center tunnel of the car is where a lot of the cars strength comes from, and tying the bottom of the tunnel together can have a significant effect (a square tube being much stronger than a C section).  In this case it didn't seem to change much, but I'm not ruling out a brace there as an area for future improvement.

Interestingly the T-tops, even being held in place only by sliding pins, have a small effect on stiffness.  Not much, but something.  I was inspired to test this after noticing how much movement there was in the t-top joint when picking the car up and setting it back down on the jack stands. I would be interesting to do this same test with a hardtop, but T-tops are what I have.  I have been considering replacing the T-top latch with some sort of bolt in bar that would tie the front A and B pillars together, but I haven't figured out yet how I want to implement that.  Ideally, in a not-irreversible manner.

Testing with the doors open was also inspired by watching the door gap change as I lifted the car.  It's almost as dramatic as the T-tops.  Not that I think people are driving around with their doors open!  But, the amount of difference due to opening the doors makes me wonder if those TRD "Door Stabilizers" that everyone seems so skeptical of might actually make a worth while difference.  I might just have to get a set.  If I do, I will of course test them in this manner!

SORRY, I tested the TRD door stabilizers and saw no measurable improvement.  Clever design... but not very effective.

Overall, ~8500 nm/deg isn't fantastic, but it could be worse.  Compared to other cars, we have a long ways to go to get to Porsche Cayman levels of stiffness (31,000-41,000 nm/deg, depending on generation).  But compared to other cars of the same era it's not too bad.  It's 75% stiffer than a Miata of the same year (4880 nm/deg), and not too much lower than an E36 M3 (10,900 nm/deg) or a C5 Corvette (9,100 nm/deg).


The Raw Data

For those looking to really nerd out, here's the raw data for the incremental tests.  Note the difference in average deflection between the first row and the last is only .0006".  There is a bit more variation between some of the install / remove tests in the middle, but the consistency in returning to the fully braced configuration is, in my opinion, impressive.  The stiffness columns are based 720ft-lb of torque and the average deflection with a 24" distance between the pivot and measure points.  The average deflection column is the average of Test 1, Test 2, and Test 3 ("apply" measurement minus "remove" measurement for each test, giving only the elastic deflection due to the application of the torque).

  Start Test 1 Test 2 Test 3 Lift & Reset 1 Lift & Reset 2   Average Deflection Stiffness ft-lb / deg Stiffness nm / deg
Apply Remove Apply Remove Apply Remove
All Braces Installed 0.000 0.055 0.007 0.055 0.007 0.056 0.007 0.002 0.002   0.0483 6240 8461
Remove Front Strut Bar 0.006 0.065 0.013 0.066 0.014 0.066 0.014 0.007 0.006   0.0520 5800 7865
Remove Rear Strut Bar 0.006 0.067 0.014 0.067 0.014 0.068 0.015 0.008 0.007   0.0530 5690 7716
Remove Front "Cancer Bars" 0.007 0.068 0.015 0.068 0.015 0.068 0.015 0.008 0.008   0.0530 5690 7716
Remove Parking Brake Bracket 0.008 0.068 0.015 0.068 0.015 0.068 0.015 0.009 0.009   0.0530 5690 7716
Remove Rear "Cancer Bars" 0.008 0.069 0.015 0.069 0.016 0.069 0.016 0.010 0.010   0.0533 5655 7668
Remove T-Tops 0.010 0.071 0.017 0.071 0.018 0.072 0.018 0.014 0.014   0.0537 5620 7620
Open Doors 0.015 0.071 0.015 0.071 0.015 0.071 0.016 0.012 0.012   0.0557 5418 7347
Close Doors 0.014 0.070 0.016 0.071 0.017 0.071 0.017 0.014 0.014   0.0540 5585 7573
Install T-Tops 0.013 0.072 0.021 0.073 0.021 0.073 0.021 0.014 0.014   0.0517 5837 7915
Install Underbody Braces 0.017 0.076 0.024 0.076 0.025 0.076 0.025 0.018 0.018   0.0513 5875 7967
Install Rear Strut Bar 0.010 0.070 0.018 0.070 0.018 0.070 0.018 0.012 0.012   0.0520 5800 7865
Install Front Strut Bar 0.004 0.058 0.010 0.058 0.011 0.059 0.011 0.005 0.005   0.0477 6327 8580

2 comments

  1. Wednesday, 07 December 2022 12:11

    Former owner of 2 2nd gen N/A mr2s and 1 3rd gen.  Currently on a GR86, though of course I miss the mid-engine layout.  At least the weight is similar to the N/A 2nd gen.  Question.  If you had a choice between steel, aluminum, or titanium for a front brace (in this case for a GR86), which would you pick?  Steel is obviously the heaviest, Titanium is roughly 5lbs, Aluminum is half the mass or weight of steel, but also the most likely to deflect.  These are what I'm looking at:

     

    https://www.blackhawkjapan.com/products/okuyama-621-065-2?_pos=4&_sid=9149d639a&_ss=r

     

    https://www.blackhawkjapan.com/en-us/products/okuyama-611-065-2?_pos=6&_sid=9149d639a&_ss=r

     

    https://www.blackhawkjapan.com/products/okuyama-618-065-2?_pos=12&_sid=9149d639a&_ss=r

     

    Keep up the great work!

  2. Wednesday, 07 December 2022 14:00

    Aluminum isn't a great material for bracing, as it has much lower stiffness than steel.  And on something like this, stiffness is the key.  Aluminum and steel have very similar stiffness to weight ratios, so to get equal stiffness out of aluminum, you tend to have to use more of it, likely leading to similar weight.  If I remember right, Titanium is the same situation.  Personally I would probably go with steel and spend the money elsewhere.

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