Understanding Relative Wind, Yaw Angles, and Aerodynamic Performance in Cycling

When you ride your bicycle, you’re not just moving through still air—far from it! The wind you actually feel as you pedal is the apparent or relative wind, which results from the combination of your ground speed and the prevailing wind. This phenomenon is very similar to what sailors experience. A sailboat sailing upwind (or across the wind) aligns its sails to capture the apparent wind rather than just the true wind blowing over the water.

In the context of cycling, understanding the concept of relative wind and the yaw angles it creates is essential for designing and riding on aerodynamic wheels. It helps us figure out how to minimize drag, increase efficiency, and appreciate why certain wheels perform better in crosswinds. This article breaks down these concepts with enough theoretical grounding to help you see the bigger picture and includes a dash of math to illustrate how they work in practice.

1. Relative (Apparent) Wind and Velocity Vectors

What is Relative or Apparent Wind?

When you’re riding your bicycle at a particular velocity, denoted Vbike​, and there’s wind blowing at a velocity Vwind​, the wind you actually experience on your body (and bike) is the vector difference:

Vapp = Vwind – Vbike

• Vbike​ is the velocity of the bicycle (and rider) relative to the ground.
• Vwind is the velocity of the wind relative to the ground.
• Vapp​ is the apparent (or relative) wind you feel.

The subtraction is set up so that if the wind is blowing in the same direction you’re riding, the apparent wind is smaller. Conversely, if the wind is blowing directly into your face, you’ll experience a larger apparent wind speed.

Example 1 Inline Wind:

• Suppose you’re riding at 10 m/s (about 36 km/h) due east, so Vbike = 10 m/s.
• If there’s a wind blowing 5 m/s from the east (blowing from the east), then Vwind = 5j m/s.

The relative wind is:

Vapp = 10 m/s + 5 m/s = 15 m/s

When you ride straight into a headwind you simply add the two together. If this were a tailwind you would subtract the wind ending up with a 5 m/s apparent wind.

Example 2 Angled Wind:

• Suppose you’re riding at 10 m/s (about 36 km/h) due east, so Vbike = 10î m/s, where î is the unit vector pointing east.
• If there’s a wind blowing 5 m/s from the north (pointing south to north), then Vwind = 5j​ m/s, where j​ is the unit vector pointing north.

The relative wind is:

Vapp = 5j – 10î = 10î + 5j

In plain language, the wind you feel comes from a direction that is part headwind (to the west, since you’re going east, so it becomes negative east or −î and part crosswind (to the south-to-north direction, j​).

2. Yaw Angle: The Key to Aerodynamic Wheel Design

Defining Yaw Angle

In cycling aerodynamics, yaw angle is the angle between the direction of travel of the bike and the apparent wind vector. A zero yaw angle would mean the apparent wind is coming straight at you from the front (or straight behind you). A non-zero yaw angle means you’re experiencing a crosswind component.

Mathematically, you can think of yaw angle, β, as:

tan(β)= (lateral component of Vapp / ​longitudinal component of Vapp) ​​= (Vapp,y / ​Vapp,​x)

Here:

• Vapp,x​ is the component of the apparent wind in the direction of the bike’s forward travel (longitudinal).
• Vapp,y​ is the component perpendicular to the bike’s forward travel (lateral).

Why Does Yaw Angle Matter?

From an aerodynamic wheel design standpoint, yaw angle is crucial because:

1. Drag and Lift Forces: At non-zero yaw angles, your wheels experience both drag and a side (or “lift”) force. Modern aerodynamic wheels are designed to leverage small to moderate yaw angles in a way that can even generate forward-driving forces from side winds—much like a sail.
2. Stability: Larger yaw angles can introduce more significant side forces, affecting bike handling. Deeper-section wheels may provide aerodynamic advantages but can be more susceptible to gusty crosswinds.
3. Real-World Cycling Conditions: You rarely ride in zero-yaw situations unless there’s absolutely no wind or you ride in a perfect headwind/tailwind scenario. Real-world cycling is often done at yaw angles ranging from a few degrees to 15 degrees or more, depending on the wind conditions and your speed. 80% of your time is spent between -10 degrees and +10 degrees. We learned this after performing on-road studies collecting real world wind condition data on a variety of cycling courses.

3. Relating to the Real Wind: Headwinds, Tailwinds, and Side Winds

Let’s break down common scenarios cyclists face:

3.1 Headwind

• Scenario: The wind is coming directly toward you while you ride forward.
• Vectors: If we treat forward (east) as î, and the wind is blowing due west (i.e., −î):

Vwind = -Vwind î

• Apparent Wind:

Vapp = (-Vwind – Vbike)î

This means the apparent wind is straight into your face, and the magnitude is simply Vwind + Vbike​. Yaw angle in this scenario is 0 degrees because it’s head-on (no crosswind component).

3.2 Tailwind

• Scenario: The wind is coming directly from behind you while you ride forward.
• Vectors: If you ride east and the wind also blows east:

Vwind = -Vwind î

• Apparent Wind:

Vapp = (Vwind – Vbike)î

If Vwind > Vbike ​you’ll feel a wind pushing you forward. If Vwind < Vbike​ you might still experience a slight headwind (just smaller). Yaw angle here is also 0 degrees.

3.2 Side Wind

• Scenario: The wind blows at 90° to your direction of travel (e.g., you’re riding east, wind blowing north). This is very uncommon.
• Vectors:

Vwind = -Vwind j

• Magnitude:

|Vapp| = sqrt((Vwind)^2 – (Vbike)^2)

• Yaw Angle:

β = tan^-1 (Vwind /Vbike)

This yaw angle can be significant, and for deep-section wheels, it can be both an aerodynamic advantage (the wheel can create a sail-like effect) and a handling challenge (it can cause the bike to feel “pushy” from the side). This is exactly why a disc wheel is illegal in Kona and Cozumel. Again this is shown as an example but in the real world is very rare. In most situations a disc wheel like our FLO DISC is the fastest rear wheel and helps stabilize the bike.

3.4 Oblique Winds

In reality, most winds you experience aren’t perfectly head-on, tail-on, or side-on but something in between. You can treat the wind vector Vwind​ in its components:

Vwind ​= (Vwind ​cos θw​)î + (Vwind​ sin θw​)j

where θw is the angle of the wind relative to the east (or your direction of travel). Then, combine this with Vbike​ to find the resultant Vapp​. From there, you calculate the yaw angle.

4. Why All of This Matters to Aerodynamic Cycling Wheels

Modern aerodynamic wheel designs are optimized around a range of yaw angles. Wind tunnel testing or computational fluid dynamics (CFD) simulations are typically run from yaw angles of 0° up to around 20° (and sometimes more).

• Low Yaw (0°–5°): When riding in a near headwind or tailwind situation, the wheel’s leading edge is fairly aligned with the wind. Deep-section wheels can still lower aerodynamic drag, but the effect of crosswind forces is minimal. However, our studies show that a cyclist spends about 50 % of their time in this yaw angle range.
• Moderate Yaw (5°–15°): The sweet spot for many aerodynamic wheels. Here, the rim’s shape can create a beneficial pressure distribution that can actually reduce net drag or, in rare cases, produce a small forward thrust component. Manufacturers carefully shape rims (using airfoil-like profiles) so that at these angles, the air stays attached to the rim surface as much as possible, reducing turbulence and improving performance. Just remember that a rim shaped to optimize performance over 10 degrees of yaw is not ideal for the real world since 80% of the cyclists time is spent between 0-10 degrees of yaw.
• High Yaw (15°+): In heavier crosswinds or faster riding speeds with slight crosswinds, stability becomes more critical. A deep rim can generate significant side force. This is where a wheel’s design must strike a balance between low drag and manageable steering torque.

At FLO we used our real world data collection to develop an algorithm that searches for rim shapes that perform well in the yaw angles seen on the road. It also considers a weighted balance of aerodynamics and stability. If a wheel is very aero but unstable we don’t consider it.

5. Putting It All Together: A Simple Example (Yaw ≈ 5°)

Scenario

You’re riding in a slight cross-tailwind. We’ll do a quick back-of-the-envelope calculation to illustrate how you can end up with a relatively small yaw angle of around 5°.

Rider Speed

• The rider travels due east at 10 m/s10 \text{ m/s}10 m/s (36 km/h).
• In vector form (using i^\hat{i}i^ for east and j^\hat{j}j^​ for north):

Vbike = 10î (m/s)

Wind Speed and Direction

• Let the wind blow at 12 m/s12 \text{ m/s}12 m/s (43.2 km/h) from nearly the same direction (west to east) but slightly “north” of the direct east axis—just 0.84° off to the north.
• Measured in the standard mathematical sense (0° = directly east, angles increasing counterclockwise):

θw​ ≈ 0.84∘

• Therefore, the wind’s components are:

Vwind,x​ = 12cos(0.84∘), Vwind,y ​= 12sin(0.84∘)

• Numerically:

Vwind,x​ ​≈ 12×0.9999 ≈ 11.998m/s

Vwind,y ≈ 12×0.0146 ≈ 0.175 m/s

• So:

Vwind​ ≈ 11.998î + 0.175j ​(m/s)

Apparent (relative) Wind

• The apparent wind is:

Vapp ​= Vwind​ − Vbike ​= (11.998î + 0.175j​) − (10î) = ( 11.998 − 10)î + 0.175j ​= 1.998î + 0.175i ​(m/s)

Magnitude

• This means you feel roughly a 2.0 m/s breeze (just over 7 km/h) from in front-left of your direction of travel.

|Vapp| ​= sqrt((1.998)^2 + (0.175)^2) = 2.01 m/s

Yaw Angle

• By definition, yaw angle β is the arctangent of the ratio of the lateral component to the longitudinal component of the apparent wind:

β = tan^−1 (Vapp,y/​Vapp,x​​) = tan^−1 (0.175/1.998​)

• Numerically:

0.175/1.998 ​≈ 0.0876, β ≈ tan^−1 (0.0876) ≈ 5.0∘

6. Practical Takeaways for Cyclists

1. Wheel Choice: In consistently windy or variable conditions, a shallower from wheel can offer more confident handling. In calmer conditions or for time trials with expected low wind, deeper rims can provide the best aero benefit.
2. Bike Handling: Understanding that you’re experiencing the relative wind, not just the ground wind, helps you anticipate the push or pull on your bike when winds change direction.
3. Positioning and Technique: In crosswinds, tucking elbows in and lowering your torso can reduce your frontal area. Staying relaxed in the upper body can help you manage gusts more effectively.
4. Speed and Direction Changes: As your riding speed fluctuates (like climbing slower or descending faster), the yaw angle changes. If you slow down, the wind vector dominates more, potentially increasing yaw angle and side force.
5. Training: Practicing in windier conditions on different wheel setups can make you a more confident rider, especially during races or long rides where conditions are rarely perfect.
6. Mental State: When considering crosswind you either don’t care, don’t mind it, or hate it. How you think of crosswind can impact your heart rate and mental state. We’ve had 230lbs men on a 30mm front wheel and 100lbs women on a 90mm front wheel. You have to know your feeling for a wheel and know you ability to handle it.

7. Conclusion

Cyclists, like sailors, operate under the influence of apparent wind—a resulting airflow that stems from both the motion of the bike and the atmospheric wind. This relative wind produces yaw angles that significantly influence aerodynamics, stability, and overall performance. By appreciating how ground wind speed and direction translate to the apparent wind you feel on the bike, you can make more informed decisions about wheel choice, riding style, and event strategy.

Deeper aerodynamic rims can offer huge gains in the right yaw angle window, but they can also become more challenging to handle at higher yaw angles. As a mechanical engineer with over a decade designing aero wheels, I’ve seen firsthand how critical it is to balance speed gains with predictable handling.

For everyday riders, simply being aware that real-world wind conditions rarely come at you head-on explains why wheel designs focus so heavily on performance at yaw angles around 0°–10°. So, the next time you’re out on a windy ride, remember: you’re not just fighting (or riding with) the ground wind—you’re negotiating with a relative wind that arises from your own forward motion. Understanding this concept is the key to better aerodynamic performance and safer, more confident riding.