V-Shape vs. Toroidal Carbon Wheels

We had a great question posted to the Tokyowheel Forum by @edward_de_cobourg.

I understand the benefits of a toroidal shaped rim and the disadvantage/advantages of a v-rim. Now I am wondering if the toroidal in the back is over-rated. Rather, you should have a toroidal in the front but stick with v-rim on the back?

It's a great question.

Let's further define the question, then look at the answer. First let's clarify our terminology. A torus is a donut shape, so actually the old-school V-Shaped rims were V-shaped tori. What we want to compare is a V-shaped torus to and elliptical, O-Shaped, torus (the basic shape of Tokyowheel EPIC rims). The elliptical torus is a better performing aerodynamic shape for wheels, and here is why.

The 'tear drop' is a low drag laminar shape that has a wider leading edge, and a narrower trailing edge. This is generally the ideal shape for reducing aerodynamic drag. It's the shape of the V-Shape rim.

I made a few quick sketches to help explain.

The big difference between the aerodynamics of a bicycle wheel and most other things is that the leading edge must also function as the trailing edge, and vice versa.

The reason why an ellipse works so well as the cross sectional shape for the rim, is that it has similarly low drag in both directions parallel to motion. It also has lower drag perpendicular to the direction of motion, compared to the flat sided V-Shaped rim (this means it has good crosswind performance)

If you take a look at the new EPIC 5.6 system optimized rims you'll notice that they aren't pure elliptic toroids. they are a more advanced shape, that we tune with computational fluid dynamics to perform in the specific front wheel, back wheel orientation.

They are much closer to an elliptic toroid, than a V-shaped toroid, because the elliptic toroid has less aerodynamic drag in both the leading and symmetric trailing edge orientation.

And to finally answer @edward_de_cobourg 's question. Because the rear wheel is directly behind the seat tube, there is less air pressure on the front half of the rear wheel, and more pressure on the back half of the wheel, that controls airflow off the back of the bike.

If we used the V-shaped shaped rim on the rear wheel, then we would be using the V-shape in it's least aerodynamic (backwards tear-drop), position. That would be a higher drag shape than the elliptic toroid. Especially for the rear wheel, the elliptic toroidal shape performs best.

Let me know what other aspects of engineering you'd like me to explain, and I'd be happy to share my knowledge.

-James