apparent wind angles

APPARENT WIND ANGLES [goto yaw angle calculator]

A lot of articles about this topic can be found in the internet. Many of them are quite difficult to be understood, some are even not completely correct. To give a better understanding about the relationships between bike speed, wind speed, wind angle and the apparent wind angle (yaw angle) we generated some sketches and graphs, which you will find together with some explanations below.	Sketch 1 shows the respective velocity vectors acting on a wheel. The wheel moves forward with the velocity V_bike and is hit by side wind with the velocity V_wind under an angle of α_wind. By adding both vectors, you will get the effective air speed V_effective. The angle between the effective air speed and the riding direction is called yaw angle. The air speed, acting from straight ahead of you, is the effective head wind V_head.
Sketch 1: velocity vectors	Sketch 2: wheel rotation and wind direction
When you are riding your bike with 40 km/h and the wind is coming from straight ahead of you (α_wind = 0°) with a speed of 9 km/h, the effective air speed would be 49 km/h with a yaw angle of 0°. As you turn away from this wind, keeping your speed, the wind angle and so the yaw angle increases (Graph 1). For our example, the max. yaw angle would be 13° with a wind angle α_wind = 103° (already tail wind!) and an effective head wind of 38 km/h.	Graph 1: yaw angle vs wind angle for const. bike speed of 40 km/h
But the real world of biking works different. Instead of keeping a const. bike speed under varying wind conditions, you rather would experience const. effective head wind speed, i.e. if you turn into the wind (0° < α_wind < 90°), your bike speed would decrease, whereas if you turn away from the wind (90° < α_wind < 180°), your bike speed would increase.	This leads to totally different yaw angles than for the first example in Graph 1. Graph 2a shows the yaw angle for a const. head wind speed of 50 km/h for a range of wind speed between 3 and 30 km/h. Now the highest yaw angles will be experienced with cross winds of 90° to the bike. Graph 2b shows the respective bike speeds for the same cases. Graphs 3a,b to 5a,b are variations in head wind speed of 45, 40 and 35 km/h.
Graph 2a: yaw angle vs wind angle for const. head wind speed of 50 km/h	Graph 2b: bike speed vs wind angle for const. head wind speed of 50 km/h
Graph 3a: yaw angle vs wind angle for const. head wind speed of 45 km/h	Graph 3b: bike speed vs wind angle for const. head wind speed of 45 km/h
Graph 4a: yaw angle vs wind angle for const. head wind speed of 40 km/h	Graph 4b: bike speed vs wind angle for const. head wind speed of 40 km/h
Graph 5a: yaw angle vs wind angle for const. head wind speed of 35 km/h	Graph 5b: bike speed vs wind angle for const. head wind speed of 35 km/h
In other words: the faster the rider, the lower the yaw angle the more the rider changes his direction, the lower the average yaw angle the slower the wind speed, the lower the yaw angle But what does that mean when it comes to developing a wheel, or when you are thinking about buying a new set of wheels for your competitions? Graph 6 shows the occurrence of yaw angles for 4 different head wind speeds and wind speeds between 0 and 18 km/h, which is an average value which you will experience in real life. In more than 55% of all cases (wind angles) the yaw angle is less than 10°, even for a hobby cyclist with an average head wind speed of 35 km/h.	A professional TT rider, who is able to race with avg. head wind between 45 and 50 km/h, will experience avg. yaw angles below 10° in more than 63%! Yaw angles above 20° occur in only 14% of the mentioned wind cases (for slower riders) and in only less than 5% for professional riders. Even if we take into account wind speeds up to very strong 30 km/h, yaw angles above 20° are very rare (Graph 7). This leads to the fact, that in terms of aerodynamic performance a wheel manufacturer should try to develop their wheels for wind conditions below 20° yaw angle. And if you are a bicyclist, who likes to compete in bike races, time trials or triathlons, and want to buy a competitive set of wheels, you should look especially for wheels which are optimised for yaw angles between 0° and 20°.
Graph 6: distribution of yaw angles for wind speeds between 0 and 18 km/h	Graph 7: distribution of yaw angles for wind speeds between 0 and 30 km/h

Yaw Angle Calculator