Red Bulls flexy wing explained

[Wats-on]

Now since someone has cracked the code, it remains to be seen how long it takes before others copy it...

The Fluid-Structure Interaction implemented by MSC is a so-called partitioned approach, in which the two separate domains are represented by separate software algorithms, and coupled together. The alternative is a so-called monolithic approach, in which both domains are represented in the same piece of software.

It's conceivable that the latter approach could also be used to represent front-wing elasticity. One could have an Arbitrary Lagrange Eulerian (ALE) simulation, in which some of the mesh corresponds to the interior of front wing, with its distinctive density and constitutive relation (between stress and strain), while the rest of the mesh corresponds to the surrounding air, with its distinctive density and viscosity. In those regions of airflow where turbulence develops, one would avoid mesh-tangling issues by allowing the mesh to become Eulerian.

All such approaches are non-reductionistic, in the sense that they are more effective than trying to solve the time-dependent Schrodinger equation for 10^23 particles. Clearly, however, the partitioned approach introduces an additional type of modularity to the representation of the macroworld.

I think, if RBR doesn´t use some exotic material sensitive at one given action, that inside of wing have "something" (maybe a fine work with carbon fiber, maybe other think) simply allowing a bigger deflection when applied a calculated horizontal load (the drag of the wing make that).
The FIA test only use a vertical load, if they add a horizontal load, with the value of the maximal drag of the wing, the "thing" is easely watchable.

So we can hypothesise that Red Bull are representing the solid interior of their front-wing with a Lagrangian simulation, and coupling it to a Eulerian hydrocode to represent the airflow around it. Some further explanation of these terms is perhaps in order.

Both Lagrangian and Eulerian computer simulations divide a continuous domain, occupied by a solid or fluid, into a discrete mesh of cells. The corners of the cells are called the nodes of the mesh. In a Lagrangian simulation, the mesh moves with the motion of the solid or fluid, whereas in a Eulerian simulation, the mesh is fixed in space, and the solid or fluid moves through the mesh. A computer simulation also divides the continuous flow of time into a sequence of discrete time-steps, using the final data from one time-step as the initial data for the next.

If Red Bull are using a Lagrangian simulation to represent the solid front-wing, then they are using a mesh which moves with the wing as it deforms. At the beginning of each time-step in such a simulation, one has the coordinates of each node, the velocity of each node, and the stress and strain associated with each cell. The strain represents the relative displacement, or stretch, which the points inside the solid body are subjected to under the influence of external loads. A solid body responds to strain by generating internal restoring forces, called stresses. The stress and the strain each have isotropic components, and when the isotropic components are subtracted, what remains are essentially the shear stresses and shear strains. These are dubbed the deviatoric stress and deviatoric strain.

The task of a Lagrangian simulation is to go from the nodal positions and velocities, and the stresses and strains inside each cell, at the beginning of each time-step, to the positions, velocities, stresses and strains at the end of the time-step. In the case of Red Bull's front-wing, the aerodynamic pressures at the beginning of each time-step will simply be part of the boundary data.

The basic method for solving this problem is as follows: Use the stresses to calculate the forces on the nodes, thence the acceleration of the nodes, and from this update the velocities of the nodes; use the velocities of the nodes to update the positions of the nodes; calculate the rate-of-strain from the velocities, infer the rate-of-stress from the rate-of-strain, and update the stress and the strain. (In reality there's a lot of shuttling back-and-forth with half time-steps and the like to minimise numerical errors, but these are the basic ideas).

The method of updating the stress is quite involved. Given the nodal velocities, one can simply take the gradient of the velocity field, (and symmetrise it), to obtain the rate-of-strain. (In the case of a racing-car front-wing, all the strain will be elastic, so there is no need to worry about plastic strain). The rate-of-strain can be divided into the deviatoric rate-of-strain and the isotropic rate-of-strain. The rate of deviatoric stress can then be calculated using the shear modulus of the material, and the rate of isotropic stress can be calculated using the elastic modulus. (In the case of Red Bull's front-wing, one can expect the elastic modulus and shear modulus to vary with position across the wing). The deviatoric and isotropic stresses can then be updated.

With the Lagrangian time-step for the solid front-wing deformation completed, the boundary of the deformed configuration can be fed as initial data to the next time-step in the Eulerian hydrocode representing the airflow over the front-wing. (Although, once again, one presumes there is a more sophisticated shuttling back-and-forth between the Lagrangian and Eulerian codes to minimise errors). The Eulerian code will calculate new pressure forces on the boundary of the front-wing, and the cycle will begin all over again.

Of course, realising the desired front-wing performance not only requires the development of this type of simulation technology, but also an understanding of how to implement the requisite elasticity via the orientation of the carbon-fibre plies. Nevertheless, it remains a surprise that so many F1 teams rely on off-the-shelf simulation software rather than developing their own.

Gordon McCabe

[John S]

Ouch!    Now my brain hurts even trying to get to grips with that very technical explanation Wats-on.     

Is that chap trying to say the Red Bull Wings are like under done waffles rather than plywood sections?      

[Wats-on]

Something like that.

In a nutshell: if you want to flex the wings, push them both down and backwards. Just down doesn't make them bend down.

How it's done exactly, I don't know because this kind of English is too much for me as Dutchman.

Any way, I suppose McLaren and Ferrari have three options: reading this article and copying it, asking the FIA to change the way they check the wings, or just protest.

[Scott]

If the theory is true (not that I have a clue what that guy was saying - sounded like they were getting down to the molecular level), and this explanation gets out, I guess the FIA will have a new test before the european season. 

It's a shame, because clever people is what is wonderful about F1 and it's ever evolving technology.  Why try to constantly stop it?  Oh yeah, money.  Well, if someone is this clever, Bernie should start sharing a bit more.   

[Andy B]

Well I am pleased I read that and it explains it all it was only a matter of time that the others caught up.
Erm! What are we talking about?

[Cam]

Wats-on is on the money, but in effect it is stating the obvious, RBR have designed a wing with one stiffness profile under the FIA test static vertical loading and a different stiffness profile under actual racing loading.

Without computer simulation it would be virtually impossible to design a wing that flexed in very precise ways under the two different loading conditions.  All this chap is describing is a computer program that combines structural analysis and fluid dynamics analysis to enable this to be done.  Believe it or not I understand what he is saying, it is all valid, and he is clearly very passionate about his subject!

I would bet my hat the other teams have figured out what they are doing, but not quite how.  They would all have the software but it still requires some smarts to be put in.