Restrainment and Boundaries? No, this is not Badger’s take on Fifty Variations between Black and White, but a look at the dark and mysterious world of Finite Element Analysis (FEA).

I suspect it’s not an area that is going to generate a vast amount of interest, so I’ll forgive you if you switch off (or just fall asleep) now. But it’s pretty fundamental to F1, so I thought I’d raise the topic and see what happens.

FEA (Finite Element Analysis) is the basis of the engineering that goes into making an F1 car. Every part is analyzed and designed using it, and FEA can be considered part of the holy trinity of design tools: FEA, CAD and CFD (for those not in the know, the other two are Computer Aided Design and Computational Fluid Dynamics)

I guess most people know that CAD is used by most F1 designers to design the parts of an F1 car. And from my days in an engineering  drawing office, I know that in the old days (let’s opt for the 70s/80s) the analysis of parts in most areas of engineering was left mainly to experience.

Take Colin Chapman for example. If a part didn’t break during a race he’d make it thinner and lighter, until it did break, and then he’d make it slightly thicker, knowing that he’s reached the limit. But if you look at the reliability of F1 cars now compared to any decade of the last century and you’ll see an amazing difference. Cars are now much less likely to fail to finish because of component failures: Michael Schumacher aside, the only reliability issues have been brakes in Canada (known to be the toughest circuit on brakes), electrics in Monaco (it was wet) and Petrov’s DNS at Silverstone. And of course the remote detonation of two Renault alternators to ensure a home win for Alonso in Valencia – surely that was the cause? Or maybe a faulty batch or inspection process.

I think you get the point I’m trying to make – in the 1992 Monaco GP (picked at random from 20 years ago) 10 cars had non accident-related failures; nowadays, two is typical.

It used to be said that it was better to build a fast F1 car rather than a reliable one, because you could make a quick car reliable, but the other way round didn’t work. In those days, teams could run thousands of kilometres in testing, now they can’t. A car has to be reliable out of the box. Especially when a missed finish in the points could make a potential difference of millions of dollars to a team.

FEA is used in engineering primarily to increase quality and decrease cost. In F1 the emphasis is more on quality and performance/weight – cost is less of an issue. So what is it exactly?

Traditionally put, FEA “provides the numerical solution of governing physical equations over complicated geometric domains”.

Er, OK, thanks. So what is it exactly?

In a nutshell, FEA will tell you what will happen to a part depending on various loads applied to it. If you’re remotely interested, I’d suggest you look at the Open University course on FEA, which follows the development of two key parts at Red Bull, a front wheel hub and the tub itself. You can find a series of videos in the iTunesU app on iPhones and via your desktop – probably be around for other media too.

Red Bull 2009 - Front Hub

The part being analysed (e.g. a wheel hub, as in the picture) is divided into many small simple-shaped regions called “finite elements” (FEs). The physical behavior within each element is understood in theoretical terms (for example it is known how much force can be applied to, say, a steel bar before it bends or shears) and so for any given material, it’s possible to make a theoretical “mesh” model of a part from a whole series of small FEs (in the same way that a large digital photo is made up of lots of tiny pixels) and apply theoretical loads to it and see what happens.

The FEs are commonly tetrahedral in shape, or a group of tetrahedrons “stuck” together. In the case of the wheel hub on the 2009 Red Bull, over 72,000 FEs were used to construct the model of just this one part.

The engineer can then apply restraints (the wheel hub mates up against the surface of the upright, and the wheel also press against the flange, held by the load of the wheel nut) and boundaries (what sort of forces are likely to be applied). For a wheel hub, which will be evaluated in all six degrees of freedom (lateral/sideways, vertically, longitudinally (forwards/backwards), yaw, pitch and roll) the key forces will be generated by cornering (lateral), kerbs (vertical) and braking (longitudinally). The largest of these forces will be lateral, and so this would be one of the key boundaries for the evaluation of the hub.

The engineer can then check out his design for a part and look at various options. In the case of the wheel hub, they would evaluate different materials (various steels, titanium etc) as well as the thickness of the metal. You’d also look at reducing the width of the flange (possibly) in order to reduce width, whilst still retaining the strength necessary to deal with the known loads – which will be measured during testing and practice with strain gauges mounted on the car.

In this way, engineers can be highly confident that parts are able to withstand the loads that will be applied. It also explains why (like the Toro Rosso front suspension failure in China 2010) in some very unusual circumstances parts will fail when unforeseen loads are experienced.

But remember, that’s just one part. And there are lots of parts in an F1 car…

The mesh is also used in CFD modelling but that’s a topic for another time. If you’re still awake that is.