An Iterative Approach to Rear Wing Design.

Updated: May 14, 2021

The Question

I had another one of those inspiring ‘I wonder’ moments not so long ago when I was asked by a client to consider what the most efficient wing would look like in the context of a project we were discussing.

I’m familiar with aerodynamics and the flow considerations of aerofoils - things to look out for and which characteristics might be useful for lift generation with considerations of efficiency, but at the time didn’t have any data to support my judgement.

The project started to take shape as with previous projects (a few of which I’ve written up also) - I discover a question i can’t immediately answer, and and put together a list of activities I’d need to undertake to reach an answer. Primarily a learning tool for me in that aspect.

The question was quite simple - what does an ‘effective’ wing look like in the context of a saloon/GT style race car such as a LM GTE car? 

The objective was really to generate some quantitative data to allow an intelligent decision to be made, but also to help me to visualise flow and give me a better understanding as to what features are conducive to what kind of flow structures; be it the formation of vortices or flow separation etc.

So, the following article will take you step by step through the process I followed, somewhat informally. This isn’t a technical report but an article for more casual reading in the hopes that I can pass on my findings to those interested.

The first task on the list was to create a design of experiments (DoE) to identify the optimal aerofoil configuration for our application. ‘Optimal’ in this context is defined as the profile enabling the generation of high lift, with an acceptable efficiency at the kind of speeds we can expect in our chosen arena (GT cars).

The next step was to identify a series of aerofoils for the test. There are three major design variables concerned with aerofoil function: camber, position of maximum camber, and thickness, as illustrated below.

Figure 1: Aerofoil Terminology - Credit: Oliver Cleynen

The NACA (National Advisory Committee for Aeronautics), who have performed extensive research into aerofoil performance have developed a 4-digit designation system to classify basic aerofoil parameters. For the purpose of this study that is what I adopted.

I’ll explain this designation system with an example - an aerofoil classified as a NACA 6412 series has the following characteristics:

  • Maximum camber of 0.06c, or 6% of the chord length.

  • Position of maximum camber at 0.4c, or 40% of the chord length.

  • Maximum thickness of 0.12c, or 12% of the chord length.

I know from experience that asymmetric aerofoils generate a reasonable amount of lift at low speeds with a gentle camber, so considered a NACA 6412 series aerofoil as a good point to serve as a baseline to start exploring.

Creating the Test

With the above outlined, I generated a group of aerofoils as follows. 

Table 1: Test wing profiles (shown at 0° AoA)

(12) and (18) were placed in brackets for clarity - the NACA 4-digit series designations only use single digit camber values, so I improvised.

With this completed, the CFD could begin. For an initial sensitivity study, I chose to run the simulation in 2D to save computational time. the simulation of 3D flow characteristics wasn’t necessary to model at this point, so we could simply look at the performance of the test aerofoils and compare to to each other.

The test setup was as follows:

Table 2: Specification of simulation inputs.

The speed chosen was 100mph as this is around the average speed of a LM GTE car around a circuit (LM GTE PRO fastest lap of Shanghai during the race was with an average speed of 100.86mph). 

Figure 2: Porsche 911 in LM GTE Spec.

I wanted to gain confidence that the performance of a particular aerofoil was quantifiable over a range of wing adjustment angles. This would represent a scenario of adjusting a wing trackside to play with downforce levels and balance whilst also highlighting any range of AoA (angle of attack) that a particular profile performed strongly in relation to others. I ran the test aerofoils at 5°, 10°, 15° and 20°. 

I also wanted to be sure that performance of each of the three test variables of camber, position of max. camber and thickness were evaluated separately so that there were no interactions. I proceeded one variable at a time.

We won’t be concerned with absolute numbers for now as this 2D simulation is not a representative test however they will do just fine for comparison. I have also kept away from using lift and drag coefficients to describe performance in this study; mainly as we are using a constant aerofoil area throughout, but also as I feel the raw numbers are more insightful to the reader.

The DoE

Camber Sensitivity

Results quickly showed (as most would expect) the relationship between camber and lift was strongly proportional. Interestingly, the high camber wings followed an almost linear pattern, while the lower camber wings - 0012 and 6412 showed a decrease in lift at AoA of 15° and up. 

Chart 1: Relationship between AoA and lift for variation in aerofoil camber.

This indicates the onset of stall and that flow separation was occurring. This was also confirmed by drag values, which increased at the same AoA.

Separation is a flow phenomenon which presents itself when the boundary layer on the LP (low pressure) side of the aerofoil, travelling towards an adverse pressure gradient (low -> high, rather than the usual high -> low) does not have enough energy to remain laminar, flow detaches from the surface of the aerofoil and creates a region of low pressure, circulating and turbulent flow. Reducing lift and increasing pressure drag. This is usually observed in higher AoA - the aerospace industry identify this as ‘stall’.

Efficiency (-Lift/Drag) of the cambered wings was an interesting one. From 6412 to (18)412 it followed a trend of falling from 5° to 10° as you might expect as the air is worked harder, only to counter intuitively increase from 10° to 15° AoA, before falling again at 20°. 

It seems that there was separation occurring at high AoA even with the highly cambered wings at some point between 10° to 15°. 

Chart 2: Relationship between AoA and efficiency for variation in aerofoil camber.

Max. Camber Position Sensitivity

Results from variation of position of maximum camber position showed similar effects of separation, but with different mechanisms.

The low AoA results (5° to 10°) show that the rearmost max camber position generated the highest lift (6512), maximising the Bernoulli effect, but as the AoA increased, the relatively high camber gradient on this profile at the point of max. camber lead to flow separation which saw lift decrease, drag increase and the efficiency nosedive (no pun!). 

The benchmark wing, 6412 also showed the same pattern, although with greater efficiency.

Chart 3: Relationship between AoA and lift for variation in max. camber position.

6312, the wing with frontward position of max camber showed no signs of separation across the range of AoA, and at 20° was the best performing with the most efficient profile.


Lastly, let’s see what’s happening when we alter the variable of max thickness.

Chart 4: Relationship between AoA and lift for variation in thickness.

With regards to lift; the profiles mainly fell in order, increasing from the low to high thickness profiles. I’d attribute this simply to a more significant Bernoulli effect leading to a larger pressure gradient between the surfaces. The larger leading edge radius provides a more gentle gradient for the flow which serves to condition it more efficiently at higher AoA.

Chart 5: Relationship between AoA and drag for variation in thickness.

Drag on the other hand followed a different trend. The lowest drag section was the middle thickness aerofoil - 6412. Out of the remaining two, a higher thickness appeared to just slightly generate the largest drag. This would leave me to think that there are two separate flow mechanisms at work here. 

What this does mean is that at AoA of 5° and (you might extrapolate) lower, the thin profile; 6407 is very efficient, with a gradual pressure gradient and high energy, laminar flow over both high pressure and low pressure surfaces.

Chart 6: Relationship between AoA and efficiency for variation in thickness.

I have summarised the results with the table below, adding some clarification.

Table 3: Matrix of +ve and -ve for each profile, profiles judged as optimal are marked with green.

Selecting the optimal characteristic from each variable leads me to find the (12)512 section as the most suitable for this application.

A Question of Dimensions

With the previous experiments performed using only a 2D analysis, now that we have our optimum section it was time to add another dimension to the simulations and upgrade to a 3D run. I used 15° AoA as it would capture some separated flow and allow us to get deeper into the analysis, hopefully learning a little more. 

Figure 3: (12)512 - the optimal profile from the DoE

Main observations; vortices forming on the surfaces of the wing - in particular at the edge of the span (wingtip vortices), span wise flow and recirculating volumes of air where separation has occurred.

Let’s compare the data from a 2D and 3D run of the same aerofoil to understand how these 3D flow structures have impacted performance.

Table 4: Comparison of results from 2D and 3D analyses of the same profile.