Cycling and Yaw Angle

I've been contemplating aerodynamics recently, and decided to try and graph air resistance (speed and yaw angle). Below is a chart of the result.

The analysis works thus:
- the bicycle is considered to travel in a straight line at 40kph.
- wind is plotted from a headwind (0 degrees) to tailwind (180 degrees).
- wind is at a constant speed (30kph)

The chart
Y axis is both yaw angle and air resistance.
X axis is yaw angle relative to a bike heading of 0 degrees.

The black solid line is effective air resistance.
Black arrows indicate yaw angle, derived from dotted grey line.

Method (in Microsoft Excel)

Bike speed and Wind speed have to be resolved into X and Y vectors.

Bike speed doesn't vary, therefore
Xbike = 0
Ybike = 40kph.

Wind vectors vary as wind swings from 0 to 180 degrees.
Xwind = wind speed * SIN(wind angle *PI()/180)
Ywind = wind speed * COS(wind angle*PI()/180)

Vectors are then summed to derive effective air resistance
=SQRT((Xbike+Xwind)^2+(Ybike+Ywind)^2)

Yaw Angle is determined thus:
= (ATAN (Xsummed speeds/Ysummed speeds)*(180/PI()))


Note that a 30kph wind (16knots), is typical of Brisbane afternoons.
A bike speed of 40kph is typical of Masters criterium racing on a reasonably flat course.

The plot reveals yaw angle does not exceed 50 degrees.
However, as the wind swings, effective wind resistance decreases.
Note that for the rider to maintain 40kph, he would reduce power output as the wind swung to a tailwind.