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 