Wheels, brakes, and coilovers - Pt. 3 Status Update

A lot has been going on and documenting it hasn't been the highest priority.  I wish I had the time in to make a great engineering focused youtube channel but it takes a lot to do it well.  For now this blog will have to do and I want to deep dive into something I expect may attract some attention.  The focus for today from my overall goals are in bold.

  • Objective 1 - Develop the perfect wheel design (IMO) for my personal car, an Estoril Blue BMW F30
    • KR2 - Achieve SAE J2530 certification (USA version of JWL VIA)
    • KR3 - Create an FEA model that accurately represents tire loads and replicates SAE tests


Personally, this is what I've been most excited to get into.  I started this process the same as many before it, scholarly article research.  These papers can be fountains of priceless information, never underestimate what you can learn from a grad student.  Also, never trust a grad student.

tire load distribution

There are two clear benefits and one gaping hole to the research done so far.  First, many papers I've found have fatigue related data and analyses that will greatly inform and improve my designs.  Second, occasionally you can find research that had real funding behind it for physical testing verification and some commercial partnerships to better inform the research.  I was lucky enough to find exactly that after a lot of searching/reading.  Finally the gaping hole.  What if everything I'm reading from these grad students does not align with what industry professionals do?  Does real experience developing expensive products blow up certain assumptions?

I'll tackle that last bit first.  I hired a contractor with experience as the simulation engineer and engineering manager at a wheel company you have heard of.  I'm not fucking around, it was worth it and the work is ongoing as I write this.  So problem solved!  Now as far as what to do with the research data?  I believe it will refine and improve what I'm learning from my contract engineer.  Full disclosure, I'm a little surprised at the low sophistication inputs and boundary conditions required in FEA to pass physical SAE/TUV testing often on the first attempt.  That tells me the wheels are over-designed due to the way they're simulated which is fine by me for my first design.

Now onto the real content I want to share.  SAE J2530 is the guiding document for aftermarket wheel certification in the USA and is very similar to the VIA specification.  What I've come to find out is there is a lot of room for interpretation on the variables involved to achieve a specific wheel load rating.  I'm going to explain my process in detail.

In order to certify a wheel to a specific load rating the manufacturer needs to pass three tests based on the stated load rating for the specific wheel design.  These are the dynamic cornering fatigue, dynamic radial fatigue, and impact tests.  So what goes into choosing a wheel load rating?

Cornering Fatigue Calcs

The bare minimum cornering test torque for a vehicle per SAE is based on two main factors.  1) GAWR or gross axle weight rating divide by 2.  That is the maximum weight allowed per axle divided in half to provide a number per wheel.  2) Maximum tire radius for the wheel being tested.  Another important factor is the coefficient of friction for the tire which SAE sets as 0.7.  As an example, the bare minimum for an F30 BMW with a GAWR of 1161kg should have a wheel load rating of at least 580kg (1279lbs).

580kg is reasonable for a daily driven car with all season tires.  But what should I design to if I wanted to allow for any tire including racing slicks on a track?  Well then I could assume (and then validate with testing) a higher coefficient of friction.  Lets say our customer's racing tires are upwards of 1.3.

SAE friction comparison
Not surprising, the moment "Mrace" required to pass the test is nearly twice the "Msae" standard.  There is a problem here though.  The variable "Wsae" is the wheel load rating I will be certified to which doesn't change and this is a marketing nightmare.  My testing requirement and wheel strength isn't even close to what another company could claim for the same wheel load rating.  If you saw Brand X wheel with Y load rating fail on a similar car to yours at an SCCA event you'd probably think, "I need a higher wheel load rating!"  Or Brand X has the same wheel load rating but weighs Y pounds less.  Lets come back to this later, there are more calcs to consider.

Radial Fatigue Calcs

This is more straightforward. It is a rolling fatigue test with no camber so friction isn't a factor.  It's purely wheel load times a load factor which is there to accelerate the test.  However, lets assume I'm designing for an SCCA track car and maybe my customer has a big ole wing that generates 600lbs of downforce.  This would be a conservative approach and I'm going to add that force to the radial force for the test AND THEN correct the wheel load rating based on the aero assumption.

Faero load correction

"F_aero" shows a small increase in the radial force and I can then correct the wheel load rating "Wsae" to capture that increase in the wheel load rating.

Corrected Wsae

So aero bumped my wheel load rating from 580kg to 634kg.  Not a crazy jump up but worthwhile added safety margin. Now I can go back to the cornering load calc using this new "Wsae_final" force and solve for the coefficient of friction required to achieve the same cornering force as the "Mrace" equation with the assumed coefficient of friction equal to 1.3.  I know it gets a little confusing here.

 Corrected cornering moment

So, "Msae_final" uses the new higher wheel load "Wsae_final" and is the same result as the earlier "Mrace" with the race tires.  The actual coefficient of friction required to make all this magic work is 1.17.

If we compare the same 634kg wheel load rating based on the SAE standard 0.7 coefficient of friction:

  • Cornering test torque = 3,622 N-m compared to my 5,671 N-m This is a big difference in wheel strength required.
  • Radial test forces are equal
  • Impact test forces are equal

Whoa, Let's Summarize

What I've just walked through is an argument I'm making that the cornering fatigue test, which factors in the vehicle weight, aero, wheel size, and now reasonably high friction is representative of the customer I'm targeting.  I can also say the same for the radial fatigue test.  What the hell does this mean?  Well, it now comes full circle to that marketing nightmare I mentioned.  I've outlined a reasonable way to design a seriously strong wheel with a load rating barely over the minimum required.

The next question for me is, what would my equivalent wheel load rating be if I solved for that using the very high cornering load and the SAE standard 0.7 coefficient of friction?

equivalent wheel load

992kg or 2,188lbs!  That's a wheel that sounds like it'll stand up to the 12hrs of Sebring!  What's the problem?  Throw that wheel rating back into the radial fatigue test calc and you would have to design a wheel to withstand over 1 million cycles with 24,320 Newtons (5,467lbs) acting on it.  That doesn't make any sense.


Kudos if you made it this far.  Someone tell me I did something wrong before I start spending money and have to hop on the marketing strugglebus using my "equivalent wheel load rating".

If you're interested in the wheel designs I'm working on, keep an eye on this page.  https://www.pdvmotorsports.com/pages/pdv-forged-wheels

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