“I’m wondering about wind in an out-and-back situation on a bike. The ideal situation in a straight out-and-back would be zero wind, while having a headwind then tailwind or vice versa would not be desirable?” – Mike

This question required a two-part answer. In the first part, #AskTriNerd: Headwinds & Tailwinds, we saw that any headwind and tailwind on an out-and-back course does in fact produce slower average speeds than no wind at all. However, contrary to popular belief, windless conditions are not always fastest. In this post, we’ll see how crosswinds can be surprisingly advantageous in some cases, at least in theory.

Sections in italics contain supplementary info. Skip, skim or scrutinize these dorktastic details at your discretion.

Your first thought may be that crosswinds can’t possibly be helpful. Gusting crosswinds can buffet you and make handling a nightmare. They can also wear you down psychologically and disrupt your focus. These factors are important, but difficult to quantify, so we aren’t going to consider them in this analysis.

First, we need to go over some background info. Because a cyclist in motion effectively generates their own wind in addition to any actual wind (from weather conditions), the wind that a cyclist actually feels is called the apparent wind. It depends on 1) the cyclist’s speed, 2) the wind speed, and 3) the wind angle relative to the cyclist.

Apparent wind & yaw angle

The apparent wind v is given by the vector subtraction of the velocity of the wind minus the velocity of the cyclist. The angle between the apparent wind and the direction of motion is called the yaw angle. Check out this article by Mavic for more info on yaw angles.

Aerodynamic drag is the largest force resisting motion while cycling at speeds above about 15-20 km/h. Drag varies not only with the apparent wind speed, but also with the direction of the apparent wind relative to the cyclist, called the yaw angle. Drag can be measured in the wind tunnel, producing graphs over a range of yaw angles like the one below. Notice how drag is greatest at zero yaw and tends to decrease at higher yaw angles, at least until about ±20°, which is around the highest yaw angle you would commonly encounter. This inverted-v shape is typical.

Axial & lateral forces

If you’re paying attention, drag graphs like the one above may seem strange. It’s reasonable that a cyclist’s drag coefficient and area should vary a bit with yaw angle, but why does drag decrease so sharply with yaw angle? These graphs are a little misleading. The so-called “drag force” commonly reported in wind tunnel test results is really just the axial component of the total drag force, i.e. the force parallel to the bike, not to the wind along the tunnel axis.

When the yaw angle is nonzero, there is also a lateral component to the total drag force that is perpendicular to the cyclist. Outside of the wind tunnel, this lateral force has at least two effects that influence speed: tire scrub (dragging the tires sideways across the road) and induced lean (titling the bike into the wind). Neither of these effects has been well described, but that doesn’t mean that they aren’t significant. More on this at the end…

There’s more funny business going on. In the wind tunnel, wind speed is held constant while the bike is rotated to simulate crosswinds. The velocity component in the axis of the bike decreases as the angle β between the tunnel axis and the bike axis increases. (Note that β is not the same as the yaw angle.) We are more interested in testing a constant bike speed than a constant wind speed. Therefore, to account for this effect, a correction factor (1/cos²β) is typically applied to the measured axial force.

Now that we have the necessary background knowledge, let’s see how crosswinds can be advantageous under specific circumstances. Let’s consider a cyclist riding at a speed of 40 km/h with a steady, perpendicular crosswind. The graphs below show how yaw angle and apparent wind speed both increase with crosswind speed. As we saw previously, increasing the yaw angle tends to reduce drag in the direction of motion. On the other hand, higher apparent wind speed increases drag. In some cases, the former effect can outweigh the latter yielding a net reduction in the drag force and potentially higher speeds compared to no wind at all!

To examine this phenomenon, we could do calculations similar to the last post. Instead, I think it’s more interesting to model a real scenario with Best Bike Split. BBS uses an optimization algorithm to predict speed based on cyclist, equipment, course and weather inputs.

We’ll look at the Texas 70.3 bike course, which is essentially a straight out-and-back course along the exposed coastline. Let’s compare two cases: 1) no wind, and 2) constant 20 km/h southeast wind, which is perpendicular to nearly the entire course.

Let’s consider a cyclist with a average power of about 250 watts with the default drag profile for a high end triathlon bike and an aggressive position. The values for other inputs aren’t too important since they won’t affect the general conclusion.

Comparing the two cases, Best Bike Split predicts that the cyclist would be significantly faster with a crosswind than with no wind, all else equal.

The reason for this extra speed becomes apparent when we look at the predicted yaw angle distribution. With a crosswind, almost the entire ride falls into the ±20-25° yaw angle range. With no wind, the yaw angle is always right around zero. Remember that drag opposing forward motion tends to be lower at higher yaw angles.

We looked at an idealized case of a crosswind perpendicular to almost the entire course. What if you had a quartering wind or some sections with a headwind or tailwind? The answer lies somewhere in between the potential benefit of the perfect crosswind case and the definite penalty of the perfect headwind/tailwind case. In general, the closer the average yaw angle is to zero, the more you would lose the modest benefit of a crosswind.

Too good to be true?

If the theoretical benefit from crosswinds sounds too good to be true, you may be right. In addition to the potential handling and psychological drawbacks mentioned before, a recent discussion on Slowtwitch brought some other confounding factors to my attention. The effects of lateral forces, including tire scrub and lean induced by crosswinds or other factors which were not accounted for in this analysis, could entirely outweigh any reductions in drag. Suffice it to say that crosswinds can be faster under specific circumstances—in theory—and that many cyclists have anecdotal evidence to support this phenomenon.

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