# Shapely Curves, Girdle Free

The convention of mapping a wheel's aerodynamic drag against a range of Angles of Attack (AOA) produces a graph with curves that let you quickly compare the aero performance of multiple wheelsets. Less drag is better, so the curve that sits on the bottom is usually considered the aerodynamically fastest wheel. Usually however, it's not quite that simple. Different wheels produce curves of different shapes. Some wheels' curves dip down lowest at AOAs of 15 or 20 degrees, some hit their troughs at narrower AOAs. But the frequency of AOAs varies at different speeds (be thankful I'm the one writing this blog and not Dave - you'll have another 3000 words ahead of you when he takes it on). Narrow AOAs (0 - 5 degrees) are more common at higher speeds, which is also where aerodynamic impact is amplified. Wider AOAs (15 degrees and above) are more common at lower speeds, where the benefits of aerodynamics are mitigated.

What this means is that the wheel with the curve that dips down the lowest is not necessarily the fastest in the real world. When we calculate relative times for a 40K TT at 30mph, we use AOA frequencies that are appropriate to that speed. If we were to calculate a 40K TT at 20 or 25mph we would need to plug in different AOA distributions for each. When trying to interpret AOA curves, it's important to realize that the faster you go, the more important the left side of the charts become.

Here are the AOA sweet spots at different speeds:

20mph: 10 degrees and up (64% of AOAs occur here)
25mph: 5 - 15 degrees (66%)
30mph: 0 - 7.5 degrees (69%)

If you're looking for a wheel for holding a steady speed in a TT or triathlon, you'll want to pay more attention to the curve shapes in the middle and right side of the charts depending on how fast you ride. If you compete in road races or crits where the periods at higher speeds have a greater bearing on the results (sprints, attacks, breakaways, premes), a wheel's performance at narrower AOAs on the left side of the curve is more relevant to you.

When we sent the Rail down to the A2 wind tunnel in NC for testing, we sent a Zipp 404 Firecrest clincher along as a benchmark. Actually we sent the 404 as two benchmarks. Not only did we want to see how the Rail measured up against the Zipp under the exact same conditions (same tire, same protocol, same test session); we also wanted to see how our test of the Zipp compared to other public tests of the Zipp. What we found is that the conditions can have a profound impact on how a wheel tests in the tunnel, affecting both the shape and the placement against the Y-axis of the resulting AOA curves.

First, here is the shape of the 404 curve in the tests by Zipp, Bontrager and November. I've normalized them at the same point at a 0 degree AOA to allow you to see more accurately how the curves change at different angles.

Zipp claims that the 404 FC is optimized around a 15 degree AOA, which is borne out by the curve resulting from the tests in the conditions they selected, suggesting that the 404 performs better at slower speeds than it does at higher speeds. The curve produced by Bontrager's test of the Zipp 404 FC shows the trough shifted to the left with narrower AOAs. Based on Bontrager's test conditions, the 404 looks to be at its best in the middle AOAs that compromise the 25mph sweet spot. Finally, our own test of the Zipp moves the trough further still to the left, suggesting that the Zipp may actually be at its best at medium to high speeds.

Now of course what you are seeing here are not tests of different wheels, but tests of the same wheel under different conditions. There is no way to know all of the conditions present that may impact aerodynamic performance in each of these tests. Everything from humidity to temperature to spoke tension to valve stem length and decal placement can all have an impact. And even if all of that is the same, two different wheels of the same exact model and specs tested during the same session can also produce different results. So we cannot know all of what drives the curves above to look differently.

However, we do know the big changes present in each of these conditions, which fortunately for consumers is something they have choice over themselves - tire make and model, width and style. Bontrager selected the exact same 23mm Bontrager Race XXX Lite tubular tire for all of their tests, switching it from wheel to wheel. We did the same thing with a 23mm Vittoria Evo Corsa CX tire. Zipp says that the 404 is optimized for a 21mm tire and since they make an aerodynamics-forward 21mm tire of their own called the Tangente, it is a reasonable assumption the testing results they publish are with that tire. I'm sure they have disclosed their testing protocol somewhere but I can't find it. If anyone has seen, please share in the comments.

One assumption then from the curves above and what we know about the test conditions for each is that the tire make, model, width and style can alter the shape of the curves and therefore the wheel's performance at different AOAs (and by extension, different speeds). We don't know this for sure until we test a single wheel against a range of different tires, which was beyond the scope of this trip to the tunnel. So the impact of the tire on aerodynamic performance remains a hypothesis, though in our opinion a credible one.

Is it possible then that in addition to having an impact on the shape of the AOA curves, the choice of tire - particularly tire width - can affect the drag so that the AOA curves sit higher or lower on the Y-axis? Bontrager in their testing did find this to be true. They tested a set of their wheels against Zipps using the same 23mm tire and then the same 27mm tire and found that the wider tire created 20 to 100 more grams of drag depending on the AOA (have a look at their excellent white paper (PDF), page 29).

Here is the same data from the chart above showing the AOA curves of the Zipp 404 FC tests conducted by Zipp, Bontrager and November, only without the normalization at 0 degrees:

The Zipp 404 FC created more drag in our test conditions than it did in Zipp's. (Let's throw out Bontrager's for now since it's a tubular and not a clincher - you can't take your FC clinchers and run a Bontrager Race XXX Lite tubular tire on them to make them faster.) If Zipp did in fact test with a 21mm tire, it is somewhere between possible and likely that the disparity in drag of 30g - 100g you see in this chart is a result of the different tire width. Again, we do not know for certain because we did not test different tire widths ourselves at this session. The Rail's inside width is optimized for the 23mm tires the vast majority of riders and racers use. Testing it with a 21mm tire would be an exercise in curiosity but not practicality.

Next time I'll show how the Rail's AOA curves plot against the 404, and also against our current RFSC wheelsets.